Mechanisms Governing the Growth, Reactivity and

Stability of Iron Sulfides

by

Francis William Herbert

M.Eng, Materials Science, University of Oxford, UK

Submitted to the Department of Materials Science and Engineeringin partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Materials Science and Engineering

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

February 2015

c© Massachusetts Institute of Technology 2015. All rights reserved.

Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Department of Materials Science and Engineering

November 20, 2014

Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Bilge Yildiz

Associate Professor of Nuclear Science and EngineeringThesis Supervisor

Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Krystyn J. Van Vliet

Associate Professor of Materials Science and EngineeringThesis Supervisor

Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Donald Sadoway

John F. Elliott Professor of Materials ChemistryChair, Departmental Committee on Graduate Students

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Mechanisms Governing the Growth, Reactivity and Stability of IronSulfides

byFrancis William Herbert

Submitted to the Department of Materials Science and Engineeringon November 20, 2014, in partial fulfillment of the

requirements for the degree ofDoctor of Philosophy in Materials Science and Engineering

Abstract

The kinetics of electrochemical processes in ionic materials are fundamentally governedby dynamic events at the atomic scale, including point defect formation and migration,and molecular interactions at the surface. A corrosion system comprising an iron sulfidefilm (passive layer) formed on iron or steel in contact with an hydrogen sulfide (H2S)-rich fluid can thus, in principle, be modeled by a series of unit reaction steps that controlthe rate of degradation under given thermodynamic conditions. This overarching thesisgoal necessitates a concerted experimental and computational approach to determinethe relevant kinetic parameters such as activation barriers Ea and rate constants νofor the homogeneous and heterogeneous reactions of interest. These fundamental val-ues can be obtained experimentally via temperature-dependent measurements on pure,model iron sulfide samples. This thesis therefore consists of three case studies on thestable Fe-S phases pyrrhotite (Fe1-xS) and pyrite (FeS2) to identify the elementary cor-rosion mechanisms and their kinetic parameters. Pyrrhotite is of interest because theoff-stoichiometry of this phase leads to relatively rapid bulk processes such as diffusion;pyrite has a comparitively inert bulk but this work showed that it has a chemically labilesurface.

The first study focuses on two basic, rate-controlling steps in the growth of pyrrhotite:cation diffusion and sulfur exchange at the surface. First, iron self-diffusivity *DFe is de-termined across the temperature range 170-400 oC through magnetokinetic studies ofthe diffusion-driven "λ" magnetic transformation, as well as direct tracer diffusion mea-surements in Fe1-xS crystals using secondary ion mass spectrometry (SIMS). This rangeencompasses the sponteneous magnetic and structural order-disorder temperature TN= 315 oC in pyrrhotite. The effect of spontaneous magnetization below TN is to increasethe Fe vacancy migration energy by a combined 40% increasing Ea for diffusion from0.83 eV in paramagnetic Fe1-xS to ∼1.20 eV in the fully magnetized state. An extrapola-tion of the Arrhenius law from the paramagnetic regime would therefore overestimateactual diffusivities by up to 102 times at 150 oC. Second, the surface exchange of sulfurfrom H2S into the solid state in Fe1-xS is measured using electrical conductivity relax-ation, yielding Ea = 1.1 eV for sulfur incorporation into pyrrhotite. With their similarthermal dependence, there is no clear temperature crossover from cation diffusion- tosurface exchange-limiting regimes, or vice versa. Instead, surface exchange is expectedto constrain pyrrhotite growth for films under ∼ 100 µm thickness, beyond which dif-fusion becomes the rate limiting mechanism, independent of external driving factorssuch as temperature.

The second study explores the role of surface electronic states on the electrochemi-cal reactivity of pyrite. Charge transfer between a solid surface and an adsorbate suchas H2S requires the mutual availability of filled/empty electronic states at the same en-ergy level. The semiconducting FeS2(100) surface is predicted to have intrinsic surfacestates (SS’s) from Fe and S dangling bonds, as well as extrinsic SS’s related to delo-calized defects at the surface, both of which would affect charge transfer character-istics. A novel, broadly-applicable methodology is developed in this thesis to quantify

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the energy and density of these SS’s, based on experimental scanning tunneling mi-croscopy/spectroscopy (STM/STS) in conjunction with first principles tunneling cur-rent modeling. As a result, a decreased surface band gap Eg of 0.4 eV, compared to 0.95eV in bulk pyrite, is measured. The findings highlight the need to differentiate betweenbulk and surface electronic structure when assessing heterogeneous reactivity, and haveimplications for the use of FeS2 in potential technological applications, for example asa photovoltaic adsorber.

Finally, the dynamics of point defect formation and clustering on FeS2(100) underhigh-temperature, reducing conditions are investigated to understand the stability ofthe surface under extreme conditions. Synchrotron x-ray photoelectron spectroscopy(XPS) is used to measure a formation energy ∆H f for sulfur vacancies in the topmostatomic layer of 0.1 eV up to approximately 240 oC. Above this temperature, however,point defects are shown to condense into surface pits as measured by scnaning tunnelingmicroscopy (STM). The combined, experimental XPS and STM results are replicatedwith high precision by a kinetic Monte Carlo (kMC) simulation, developed by AravindKrishnamoorthy towards his doctoral thesis, of surface degradation on realistic length-and timescales of 10−10 − 10−7 m and up to several hours, respectively. The findingshave implications for the initiation of surface breakdown via pitting in ionic passivefilms, as well as providing a broader understanding of the non-stoichiometry of thepyrite surface.

The common thread is a focus on events at the atomic and electronic scale, with anemphasis on point defects. The results thereby facilitate a bottom-up approach to mod-eling electrochemical processes such as corrosion in Fe-S phases, in which the unit stepsare cast into probabilistic simulation tools. While the three studies here comprise onlya partial examination of the atomic-scale events regulating the behavior of Fe-S passivelayers, this approach makes inroads towards more accurate component lifetime pre-diction and the design of robust materials for aggressive environments. Moreover, thefundamental surface and bulk physical chemistry of iron sulfides explored in this workhas implications beyond corrosion to other uses of these materials, including potentialmagnetic devices (Fe1-xS) and earth-abundant photovoltaic and photoelectrochemicaladsorbers (FeS2).

Thesis Supervisor: Bilge YildizTitle: Associate Professor of Nuclear Science and Engineering

Thesis Supervisor: Krystyn J. Van VlietTitle: Associate Professor of Materials Science and Engineering

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Acknowledgments

I am deeply grateful to my co-advisors, Professor Bilge Yildiz and Professor Krystyn vanVliet, for their encouragement, guidance and support. It has been an immense pleasureto witness both Bilge and Krystyn establish themselves with tenure at MIT during mytime here and be part of two flourishing laboratories. Meanwhile, Bilge’s passion forsolid state chemistry and keen eye for important details, and Krystyn’s diligent andorganized approach to high-quality scientific inquiry have greatly inspired me. I alsothank Krystyn for teaching me how to spell "properly": the word sulphide seems as aliento me now as sulfide did five years ago.

This work would not have been possible without my ever-dependable collaborator andfriend Aravind Krishnamoorthy. He is gifted not only with a brilliant scientific intellect,but an immensely humble and generous personality that has made working together onthis project a richer experience. His efforts truly allowed our combined computationaland experimental approach to become more than the sum of its parts.

I am also thankful to my collaborators on this project and others, including: Wen Ma,Yan Chen and Qiyang Lu from the Laboratory for Electrochemical Interfaces at MIT; Pe-ter Albrecht at Brookhaven National Laboratory; Predrag Lasic and Rickard Armiento(Ceder group, MIT); Rupak Chakraborty and Katy Hartman (Buonassissi group, MIT).Thank you to Prof. Randall Feenstra at Carnegie Mellon University for his help deci-phering the SEMITIP code for tunneling spectroscopy simulations.

I would like to thank all members, past and present, from my two fantastic reasearchgroups: the Laboratory for Electrochemical Interfaces (LEI) and the Laboratory for Ma-terial Chemomechanics who have taught me so much, from defect chemistry in ionicsolids to the mechanics of living cells. In particular, I am very grateful to Roza Mah-moodian for her support and for putting up with my incessant complaining over failedexperiments. Also to Bal Mukund Dhar for his infectious enthusiasm and help with CVD,and to Lucy Rands for her help and eagerness as a summer intern.

I am indebted to my thesis committee - Prof. Carl Thompson and Prof. Harry Tuller - fortheir useful comments and constructive criticism. In addition, I greatly thank Prof. ChrisSchuh for providing invaluable feedback, despite not sitting on my final committee.

BP Plc. had already supported my education for over 20 years when they arrived at MITto propose this project, so I am delighted they extended their commitment to my grad-uate studies. In particular, I would like to thank Sai Venkatesweran, Richard Woolam,Steve Shademan and their colleagues for their help and advice.

My parents, Richard and Kate, have inspired and guided me my whole life; I would notbe here without the opportunities and unwavering support they have provided. And Icannot omit the other four fifths of my band of brothers who are my frame of referencefor everything and never stop injecting humour and happiness into my life.

Finally, thank you to all those who have made my time at MIT so special outside of thelab. My family away from home; the eclectic and dynamic community at "Martha" (216Norfolk St): Sam, Katy, Georgie, Jake, Benji, Ines, Chris, Nina, Alex, Federico, Elison,Andre, James, Andre, Stephanie, Rob, Balthazar, Simon, Sebastian, Nico, Melissa, Ser-jumbi, Aron, all of our other guests, and last but not least Teresa for not losing faith inme after all these years.

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Contents

1 Introduction 13

1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2 Passivity: a brief introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Iron sulfide phases and corrosion products . . . . . . . . . . . . . . . . . . 14

1.3.1 Sour corrosion mechanism: lab and field experience . . . . . . . . 17

1.3.2 Model phases: Pyrrhotite (Fe1-xS) and Pyrite (FeS2) . . . . . . . . 19

1.4 Towards a predictive, multiscale corrosion model . . . . . . . . . . . . . . 20

1.4.1 Existing passive film models . . . . . . . . . . . . . . . . . . . . . . . 20

1.4.2 Unit processes controlling Fe-S passive layer behavior . . . . . . . 23

1.4.3 The need for experimentally-derived parameters . . . . . . . . . . 24

1.5 Thesis goals and organization . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 Growth: cation diffusion and surface exchange as rate-limiting mechanismsin pyrrhotite, Fe1-xS 27

2.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2 Pyrrhotite: polytypes and transitions . . . . . . . . . . . . . . . . . . . . . . 29

2.2.1 Structural and magnetic properties . . . . . . . . . . . . . . . . . . . 30

2.2.2 The λ-transition in NC pyrrhotites . . . . . . . . . . . . . . . . . . . 34

2.3 Diffusion-limited λ transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.3.3 Continuous re-ordering of ferrimagnetic superlattice . . . . . . . 40

2.3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.4 Isotope tracer diffusion measurements . . . . . . . . . . . . . . . . . . . . . 45

2.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.4.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.5 Sulfur exchange kinetics at the Fe1-xS surface . . . . . . . . . . . . . . . . . 54

2.5.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.5.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.6 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

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3 Reactivity: quantification of electronic band gap and surface states on FeS2(100) 693.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.1.1 Electrochemical charge transfer in semiconductor-absorbate sys-tems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.1.2 Surface states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.1.3 Scanning tunneling spectroscopy and TIBB . . . . . . . . . . . . . . 743.1.4 The FeS2(100) surface . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.2.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.2.2 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.3.1 Current-separation and current-voltage tunneling spectroscopy . 803.3.2 Simulated tunneling spectra based on DFT-calculated DOS . . . . 82

3.4 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.4.2 Implications for other applications of FeS2, e.g. PV . . . . . . . . . 893.4.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4 Stability: dynamics of point defect formation, clustering and pit initiationon the pyrite surface 914.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.1.1 Chapter goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.1.2 Passivity breakdown by pitting . . . . . . . . . . . . . . . . . . . . . 924.1.3 FeS2 surface chemistry and non-stoichiometry . . . . . . . . . . . . 94

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.2.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.2.2 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.3.1 Evolution of pyrite surface structure and chemistry . . . . . . . . . 974.3.2 Mechanism of vacancy formation and coalescence . . . . . . . . . 103

4.4 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.4.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5 Conclusions 1095.1 Summary of activation barriers . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.3 Outlook and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

A Pourbaix diagrams for the Fe-H2S-H2O system 113

B Chemical Vapor Deposition of Fe-S 119B.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119B.2 Methods: CVD setup and apparatus . . . . . . . . . . . . . . . . . . . . . . . 119B.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

C Diffusivity measurements using thin film samples 129

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List of Figures

1-1 Potential E vs. current i (polarization) curve for a generic metal. . . . . . 141-2 Global sour oil and gas statistics. . . . . . . . . . . . . . . . . . . . . . . . . . 151-3 Thermodynamic predictions of corrosion products. . . . . . . . . . . . . . 171-4 Mechanism of iron sulfide formation on steels in H2S-bearing electrolytes. 181-5 Iron sulfide stability phase diagram. . . . . . . . . . . . . . . . . . . . . . . . 201-6 Sulfide corrosion of 4130 carbon steel at 220 oC. . . . . . . . . . . . . . . . 221-7 Schematic of unit processes in Fe-S passive layers. . . . . . . . . . . . . . . 241-8 Overview of strategy to construct a non-empirical passive film model. . . 25

2-1 Collected literature values of Fe self-diffusivity. . . . . . . . . . . . . . . . . 282-2 Structural unit cells of pyrrhotite. . . . . . . . . . . . . . . . . . . . . . . . . 302-3 Pyrrhotite structural and magnetic phase diagrams. . . . . . . . . . . . . . 322-4 Idealized Fe1-xS superstructures. . . . . . . . . . . . . . . . . . . . . . . . . . 332-5 Distributions of vacancies in 4C and NC pyrrhotites. . . . . . . . . . . . . . 332-6 The peak-like λ-transition in NC Fe1-xS. . . . . . . . . . . . . . . . . . . . . 342-7 X-ray diffraction of synthetic pyrrhotites. . . . . . . . . . . . . . . . . . . . . 352-8 Setup of cubic kinetic Monte Carlo (kMC) grid. . . . . . . . . . . . . . . . . 362-9 Temperature-dependent magnetization σ(T ). . . . . . . . . . . . . . . . . . 382-10 Magnetization vs. applied field (σ-H). . . . . . . . . . . . . . . . . . . . . . 382-11 Reversible magnetic transformation at short timescales. . . . . . . . . . . 402-12 Best fits to exponential equation. . . . . . . . . . . . . . . . . . . . . . . . . 412-13 Long-timescale isothermal magnetization. . . . . . . . . . . . . . . . . . . . 422-14 Differential scanning calorimetry (DSC) results. . . . . . . . . . . . . . . . 432-15 Continuous re-ordering towards ferrimagnetic state. . . . . . . . . . . . . 442-16 Cross section of sulfide scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . 452-17 Cu-kα powder XRD pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . 462-18 Energy-dispersive X-ray spectroscopy (EDS) . . . . . . . . . . . . . . . . . . 472-19 Sources of error considered in statistical analysis of diffusion data. . . . 492-20 Secondary ion mass spectrometry (SIMS) profiles. . . . . . . . . . . . . . . 492-21 Error function solution to diffusion profiles. . . . . . . . . . . . . . . . . . . 502-22 Values for iron self-diffusion coefficient *DFe. . . . . . . . . . . . . . . . . . 522-23 Sputter deposited thin films for ECR experiments. . . . . . . . . . . . . . . 552-24 Electrical conductivity relaxation apparatus setup. . . . . . . . . . . . . . . 562-25 Temperature-pressure equilibrium phase diagram for Fe-S. . . . . . . . . . 572-26 X-ray photoelectron spectroscopy (XPS) from a Fe1-xS thin film sample. . 592-27 Electrical resistance relaxation at 565 oC. . . . . . . . . . . . . . . . . . . . 622-28 Electrical conductivity relaxation results. . . . . . . . . . . . . . . . . . . . . 632-29 Drift, stability and repeatability of ECR experiments. . . . . . . . . . . . . 652-30 Temperature- and film thickness dependence of rate limiting steps. . . . 66

3-1 Charge transfer in electrochemical (corrosion) systems. . . . . . . . . . . 723-2 Band bending effects in STS measurement. . . . . . . . . . . . . . . . . . . 753-3 FeS2 single crystal samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

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3-4 Distributions of surface states as defined in the SEMITIP program. . . . . 803-5 Scanning tunneling spectroscopy (STM) images of the as-grown FeS2(100)

surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813-6 Current-separation spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . 823-7 Current-voltage spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 833-8 Pyrite valence band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833-9 Modeling tunneling spectroscopy with surface states . . . . . . . . . . . . 853-10 Density functional theory (DFT)-computed band structures. . . . . . . . . 863-11 Fitting to experimental surface Eg. . . . . . . . . . . . . . . . . . . . . . . . . 873-12 Visualization of FeS2(100) surface charge q . . . . . . . . . . . . . . . . . . 883-13 Low surface bandgap implications for PV. . . . . . . . . . . . . . . . . . . . 893-14 Preliminary investigations on bulk and 2-dimensional MoS2. . . . . . . . 90

4-1 Proposed mechanisms of passivity breakdown and pitting. . . . . . . . . . 934-2 Nanopits formed by vacancy agglomeration. . . . . . . . . . . . . . . . . . 944-3 XPS sample clamp for FeS2 crystals. . . . . . . . . . . . . . . . . . . . . . . . 964-4 S 2p photoelectron spectra of FeS2(100). . . . . . . . . . . . . . . . . . . . 984-5 Atomic model of the FeS2(100) surface as viewed side-on. . . . . . . . . . 994-6 Sulfur monomer vacancy concentration. . . . . . . . . . . . . . . . . . . . . 1014-7 Proportion of the M and S components of the S 2p photoelectron spectra. 1014-8 Scanning tunneling microscopy (STM) images of single crystal FeS2(100)

surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024-9 Pits are one half- or one lattice parameter deep. . . . . . . . . . . . . . . . 1044-10 Illustration of atomic processes involved in the proposed mechanism of

pit formation and growth on pyrite (100). . . . . . . . . . . . . . . . . . . . 1054-11 kinetic Monte Carlo simulation results. . . . . . . . . . . . . . . . . . . . . . 105

B-1 Home-made Chemical Vapor Deposition (CVD) system. . . . . . . . . . . . 121B-2 Description and safety information for Fe and S precursors. . . . . . . . . 122B-3 Iron sulfide films deposited from Fe(acac)3 and TBDS. . . . . . . . . . . . 124B-4 Carbon contamination in Fe-S films from Fe(acac)3. . . . . . . . . . . . . . 125B-5 Iron sulfide films deposited from Fe(CO)5 and TBMS. . . . . . . . . . . . . 125B-6 Iron sulfide films deposited from Fe(CO)5 and H2S. . . . . . . . . . . . . . 126B-7 Template stripping for ultrasmooth sulfide surfaces. . . . . . . . . . . . . . 127

C-1 Iron self-diffusivity *DFe measurements. . . . . . . . . . . . . . . . . . . . . 130C-2 X-ray diffraction of thiin films for ECR experiments. . . . . . . . . . . . . . 131C-3 Representative diffusion profiles. . . . . . . . . . . . . . . . . . . . . . . . . 132C-4 Oxidation of samples annealed in quartz vials. . . . . . . . . . . . . . . . . 133

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List of Tables

1.1 Stable and metastable iron sulfide phases. . . . . . . . . . . . . . . . . . . . 161.2 Reactions describing the basic unit processes. . . . . . . . . . . . . . . . . . 23

2.1 Fe1-xS polytypes: composition and structure. . . . . . . . . . . . . . . . . . 312.2 Thermodynamic values for pyrrhotite compounds. . . . . . . . . . . . . . . 372.3 Best fit parameters n and τ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.4 Isotopic composition of naturally-occurring iron. . . . . . . . . . . . . . . . 472.5 Iron self-diffusion *DFe measurement results for Fe1-xS crystals. . . . . . . 512.6 Kp (T) values used to calculate sulfur partial pressure. . . . . . . . . . . . 572.7 Deconvolution of Fe 2p and S 2p x-ray photoelectron spectroscopy (XPS)

peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.8 Electrical conductivity relaxation results for oxidation experiments. . . . 612.9 Electrical conductivity relaxation results for reduction experiments. . . . 612.10 Key activation energies for pyrrhotite growth. . . . . . . . . . . . . . . . . . 68

3.1 Calculated bulk band gap Eg, and surface Eg. . . . . . . . . . . . . . . . . . 773.2 Experimental surface Eg measurements by scanning tunneling spectroscopy

(STS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.3 Input parameters for tunneling spectroscopy simulations using the SEMI-

TIP program. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.1 XPS core level shift (CLS) for S 2p peak. . . . . . . . . . . . . . . . . . . . . 97

5.1 Summary of experimentally determined activation barriers Ea. . . . . . . 109

A.1 Thermodynamic data for species in H2S-H2O-Fe system. . . . . . . . . . . 114A.2 Input parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114A.3 Fe-H2O Reactions and reversible potentials. . . . . . . . . . . . . . . . . . . 115A.4 Mackinawite-Fe-H2O system equilibrium reactions. . . . . . . . . . . . . . 116A.5 Pyrrhotite-Fe-H2O system equilibrium reactions. . . . . . . . . . . . . . . . 116A.6 Pyrite-Fe-H2O system equilibrium reactions. . . . . . . . . . . . . . . . . . . 117

B.1 CVD of Fe-S phases by other authors. . . . . . . . . . . . . . . . . . . . . . . 122B.2 Chemical Vapor Deposition conditions for Fe-S phases: literature. . . . . 123

11

12

Chapter 1

Introduction

1.1 Context

Vast amounts of energy are consumed in distilling ferrous and non-ferrous metals fromtheir ground states, married to reactive atoms such as oxygen and sulfur in ores. Oncefashioned into the components that undergird our energy, transportation and construc-tion infrastructures, the thermodynamic tendency of these metals to regress to theirprimitive compounds locks us in a Sysyphean struggle against materials degradationand corrosion. But while thermodynamics dictates this ultimatly pessimistic outcome,the slow kinetics of the required reactions ensures that metals and alloys can remainuncompromised for many years, even under the most aggressive chemical, thermal andmechanical conditions. Passivity - the ability of metals to self-protect by forming a thin,inert skin of an ionic compound through a partial reaction at the environment interface- thus constitutes one of our most useful tools in combating degradation. The growth,reactivity and stability of these passive layers all contribute to their overall protective-ness. In this thesis we ask: is it possible to understand and subsequently simulate thesecharacteristics a priori, starting from the atomic scale? We can begin by defining a se-ries of kinetically rate-limiting processes, including mass transport (i.e., diffusion) andsurface reactions such as oxidation, reduction and dissolution. By investigating the fun-damental unit steps involved, and modeling these steps across multiple length- andtimescales, we can aspire not only to predict accurately how metals will behave whenplaced in harsh environments, but also to design more robust materials that will betterself-protect and last longer.

1.2 Passivity: a brief introduction

The study of passivity as a scientific discipline perhaps originated with James Keir in1790, who documented that although iron readily dissolves in dilute nitric acid, it coun-terintuitively remains inert in concentrated HNO3. Michael Faraday, as early as 1830,before the invention of the necessary characterization tools, correctly predicted the exis-tence of an ultrathin, electronically conducting surface film that protects the underlyingmetal. [1] We now have a better understanding of the passive state, as defined by Uh-lig [2]:

A metal is passive if it substantially resists corrosion in a given environmentdespite a marked thermodynamic tendency to react.

This definition gives us an insight into the essence of passivity; it is a metastable state,one in constant flux. The formation of a passive film does not provide an infinite bar-rier to metal dissolution in a given aggressive environment, but it does reduce corro-

13

-610

1

-2L

og i (

A c

m)

Active Passive Transpassive

Pitting

Eo Ep Epit E1

E (V)

(a)(b) (c)

(a) Cr, Ni

(b) Fe

(c) Valve metals

Al, Ti, Ta, Zr, Hf

Schematic polarization curve for passive system

Figure 1-1: Potential E vs. current i (polarization) curve for a generic metal, showing the active, passiveand transpassive regions, as discussed in the text. The valve metals form extremely stable oxide passive filmsand display a very large transpassive region. After Marcus et al. [3]

sion currents by several orders of magnitude (as much as 106 times for certain alloyssuch as stainless steels, and metals such as Al, Si, Ti, Ta and Nb, that form very sta-ble passive films). Figure 1-1 shows a schematic of a typical polarization curve for ageneric, passive-film forming metal. [3] At a critical passivation potential Ep the corro-sion current drops dramatically, coincident with the formation of a passive layer. Thethermodynamic conditions for this can be predicted from fundamental electrochemi-cal principles, the basis of the Pourbaix diagram. [4] However, at higher potentials Epitthe passive layer can be prone to localized breakdown or pitting. Eventually, localizedfailure avalanches into a full breakdown of the passive film and the corrosion currentshoots up in the transpassive region. The structure of passive films is typically bi- ormulti-layered. In the case of an oxide this typically means a thin (<100 nm), adherent,dense inner barrier layer that forms rapidly under the correct anodizing conditions.An outer layer can form by precipitation or solid-state reaction of cations transmittedthrough the barrier layer with anionic species in the aqueous media, e.g. H2S, CO3

2-,HS-. Depending on the exact conditions of temperature, pH, concentration of reactivespecies, pressure etc., the outer layer - which can grow up to 100-1000x the thicknessof the inner barrier layer - may contain multiple compounds and different phases. Inoilfield brines with dissolved CO2 and H2S, both FeCO3 and a variety of FeS phases maybe present in the outer layer, possibly along with oxides.

1.3 Iron sulfide phases and corrosion products

Early oil prospectors had a rudimentary test for the quality of their discoveries: a smudgedfingertip to the tongue, hence the terminology still used today: "sweet" or "sour" crude,depending on whether the sulfur content is above or below 0.5 vol

The solution- and solid-state chemistry of iron sulfides has been studied by geo-chemists, microbiologists and thermodynamicists for many decades. A comprehensivereview by Rickard and Luther covers much of the accumulated knowledge in this field.[9] The iron sulfide family of phases and their interrelations are complex: up to ninediscrete phases have been characterized, as listed in Table 1.1. Several of these aremetastable and will convert over time to either stable iron monosulfide (pyrrhotite,Fe1-xS, 0 ≤ x ≤ 0.125 ) or iron disulfide (pyrite, FeS2). We limit the discussion hereto the three phases which came up most often while reviewing the literature on sour

14

Canada- oil sands 3.4%

US Mid-continent 0.4%

West Texas1.9%

Thunderhorse0.9%

Venezuela1.5-2.3%

North Sea Brent 0.4%

Siberian Basin0.8-1.8%

Saudi2-3%

Nigeria 0.2%

Indonesia (Arjuna)0.1%

Iran 1-2%

0 30 110 270Proven oil reserves, bbl

Urals 1.3-2.5%

Crude OilSulfur Content

(a)

0.9

1

1.1

1.2

1.3

1.4

1.5

Avera

ge %

S

Year

Non-OPEC

World

OPEC

(b)

World petroleum reserves with selected crude sulfur content (2013)

600

400

200

0

o260 C

o205 Co150 C

10 20 40 600

69

MP

a

13

8 M

Pa

24

1 M

Pa

Static Reservoir Pressure (kpsi)

oR

ese

rvoir T

em

pera

ture

F

2015 2025 2035

(c)Souring of world oil production High pressure/high temperature

HPHT-hc

Ultra HPHT

HPHT

Figure 1-2: Global sour oil and gas statistics. (a) Proven world crude oil reserves [5], with the averagesulfur content highlighted for several representative countries. [6, 7]. (b) The average sulfur content of oilfor Organization of the Petroleum Exporting Countries (OPEC) and worldwide. [5] (c) Definitions of highpressure-high temperature well conditions by Schlumberger, Ltd. [8]

corrosion: mackinawite, pyrrhotite and pyrite. Mackinwawite, FeS1-x is a 2-dimensional(2D) layered chalcogenide, generally considered to be the initial corrosion product toform under most conditions in H2S-bearing solutions. [10]

Figures 1-3a and b show potential vs. pH (Pourbaix) diagrams for the Fe-H2S-H2Osystem under standard conditions of 1 atm pressure and 25 oC. Full details of the ther-modynamic diagrams are provided in Appendix A and Refs. [11–14]. The stable phasespyrrhotite and pyrite are excluded in Figure 1-3a, given that mackinawite manifests it-self as the predominant metastable corrosion product for neutral to alkaline solutions.This would correspond to "slightly" sour conditions of T < oC and hydrogen sulfidepartial pressures PH2S < 0.01 MPa [15], or for relatively short exposures up to hun-dreds of hours. Naturally, the thermodynamic data would predict the stable phases topredominate eventually (Fig. 1-3b), which in reality means after long steady-state expo-sure or higher temperatures. Evidently the kinetics of iron sulfide formation, dissolutionand transformation preclude the prediction of corrosion product phases from thermody-namic principles alone. In particular, the effect of H2S partial pressure is omitted. Figure1-3c is a summary of available phase identification from laboratory tests across a rangeof sour conditions. Mackinawite prevails under slightly sour conditions, but pyrrhotiteor a mixture of pyrrhotite and pyrite is more often observed at moderately-highly sourconditions as indicated on the diagram.

15

Tabl

e1.

1:St

able

and

met

asta

ble

iron

sulfi

deph

ases

.Ada

pted

from

Ref

s.[9

,10]

.

Phas

eC

ompo

siti

onSt

ruct

ure

Met

a-(M

)/St

able

(S)

Com

men

ts

Am

orph

ous

Iron

Sulfi

deFe

S m,F

eS1-

xA

mor

phou

s/na

nocr

ysta

lline

MB

elie

ved

byso

me

auth

ors

tobe

sim

ply

nano

crys

talli

nefo

rmof

mac

kina

w-

ite.

Mac

kina

wit

eFe

S m,F

eS1-

xTe

trag

onal

,2D

laye

rP4/n

mm

MC

omm

only

obse

rved

first

corr

osio

npr

oduc

tin

sour

solu

tion

s.

Cub

icFe

SFe

S cC

ubic

F43m

MTr

ansf

orm

sto

mac

kina

wit

e,py

rrho

tite

orpy

rite

.Not

obse

rved

inna

ture

.

Troi

lite

FeS

Hex

agon

alP6

2cS

Fully

stoi

chio

met

ric

end

mem

ber

ofth

eFe

1-xS

fam

ily.

Pyrr

hoti

teFe

1-xS(0≤

x≤

0.17)

Mon

oclin

icA2/a

orH

exag

onal

P6/m

mc

SIr

on-d

efici

ent

mon

osul

fide.

Off

-sto

ichi

omet

ryac

com

odat

edby

iron

va-

canc

ysu

pers

truc

ture

sbe

low

315

oC

.

Smyt

hite

Fe3+

xS4(0≤

x≤

0.3)

Trig

onal

-hex

agon

alR3

mM

Sub-

phas

efr

ompy

rrho

tite

grou

p.

Gre

igit

eFe

3S 4

Cub

icFd

3mM

Con

tain

sm

ixtu

reof

Fe2+

and

Fe3+

ions

.mor

e

Pyri

teFe

S 2C

ubic

Pa3

S”F

ools

gold

”:st

oich

iom

etri

cir

ondi

sulfi

de.

Mar

casi

teFe

S 2O

rtho

rhom

bic

Pnnm

MC

omm

only

obse

rved

inhy

drot

herm

alsy

stem

s;tr

ansf

orm

sto

pyri

te.

16

0 50 100 150 200 250

10-4

10-2

100

Temperature (oC)

H2S

Pa

rtia

l Pre

ssu

re (

MP

a)

Mackinawite

Pyrrhotite

Pyrrh. & Pyrite“Slightly Sour”

“Moderately Sour” “Highly Sour”

Fe2O3Fe3+

Fe2+

Fe

Mackinawite

(a) Pourbaix diagram: metastable Fe-S

+-

2H +2e =H2

+-

O +4H +4e =2H O

2

2

Pyrrhotite

Fe2+

Fe

Pyrite

-1.5

-1

-0.5

1

1.5

0

0.5

0 2 4 6 8 10 12 14pH

(b) Pourbaix diagram: stable Fe-S

E (

V)

rev

0 2 4 6 8 10 12 14pH

-1.5

-1

-0.5

1

1.5

0

0.5

(c) Fe-S scales observed in lab/field tests

E (

V)

rev

Figure 1-3: Thermodynamic predictions of corrosion products are only of limited usefulness. (a) pH-electrode potential (Pourbaix) diagram constructed for the Fe-H2S-H2O system, excluding the stable phasesfrom reactions. (b) Once the stable products pyrrhotite Fe1-xS and pyrite FeS2 are added, the mackinawitefield disappears entirely. These diagrams cannot predict the existence of a given corrosion product a priori.In (c), we show a temperature-H2S partial pressure PH2S diagram, overlaid with experimentally-observedphase identifications from several sources. [15–18] Mackinawite is widely observed at lower temperaturesand PH2S ("slightly sour" conditions; at elevated temperatures and partial pressures the product mix shifts tothe more stable pyrrhotite and pyrite phases. Exposure time is another factor not considered in these purelythermodynamic diagrams; mackinwaite commonly forms first, but is more likely to transform over longertimes up to 100s of hours due to its metastability.

1.3.1 Sour corrosion mechanism: lab and field experience

Despite more than seventy years’ worth of investigations into iron sulfide corrosionproducts, there is still no solid consensus surrounding the mechanism of sour corrosionand the extent of protectiveness conferred by the passive state. The presence of an ironsulfide scale is generally thought to reduce corrosion rates by up to several orders ofmagnitude, at least upon initial formation on bare steel. However, there is uncertaintyregarding the long term stability of otherwise protective films comprising Fe-S. [19]Here we briefly review the observations from laboratory and field experience that al-low us to form an empirical picture of the sour corrosion process from a mechanisticperspective. We refererence to Figure 1-4, we broadly describe a multi-stage growthmechanism whereby mackinawite nucleates first, grows to a critical thickness and then

17

Inner layer~ 100 nm

30µm

Fe-C

Porous outer layer10’s of μm

2+ +Fe +H S = FeS +2H(aq) 2 (aq) m (s) (aq)

+ -Fe +H S = FeS +2H +2e(s) 2 (aq) m (s) (aq)

Dissolution: 0 +

FeS , FeHS

(a) Initial formation of bi-layered mackinawite film

(b) Pitting at delamination sites

Fe-C

Fe-C

-Cl

(c) Nucleation & growth of stable iron sulfides

20 μm

Figure 1-4: Mechanism of iron sulfide formation on steels in H2S-bearing electrolytes. (a) A thin, adher-ent mackinawite film (∼ 100 nm thick) forms via solid state reaction or local precipitation at the bare steelsurface. The mackinawite continually dissolves and re-precipitates out of the supersaturated solution in theadjacent boundary layer, building up a much thicker, outer porous layer of mackinawite. [16] (b) because ofvolumetric stresees, the film may delaminate locally, leading to the formation of pits with bubble-like sulfidedeposits. [18] (c) At the repassivated pit sites, a high local concentration of cations in solution may lead tothe nucleation of more stable phases: needle-like crystals of hexagonal Fe1-xS or cubic grains of FeS2. [17]

ruptures. Following film rupture, a second stage of FeS film growth occurs during whichit is possible that other, more stable Fe-S phases may form.

Mackinawite formation: Bare carbon steel - even with a pre-existing oxide pasive film -is thought to undergo a solid state reaction (SSR) with H2S in solution, in other wordsa direct heterogeneous chemical reaction, to form nanocrystalline mackinawite FeSm(occasionally referred to as "amorphous" mackinawite). The evidence for a SSR revolvesaround the extremely rapid formation of iron sulfide on the surface over a timescale ofseveral seconds. By contrast, carbonate scale precipitation in CO2 solutions requiresminutes to hours for a semi-protective barrier film to form. [16, 19, 20] The formationof a compact mackinawite layer with thickness << 1 mm confers a degree of passivityto the steel, with a corresponding drop in measured corrosion rate on the order of 5-10 times. The film serves primarily as a diffusion barrier to ionic transport. Above the

18

compact, solid-state reacted mackinawite layer, a thicker - up to hundreds of mm - outermackinawite layer is typically observed (Figure 1-4b). This outer film is more porousand less protective than the inner one. According to Nesic et al., mechanical instabilityof the inner film caused by epitaxial stresses as it grows lead to a cyclic process ofmicrocracking, delamination and re-passivation that over time build up a thicker, porousouter layer. [21] Either way, outer film growth rate and eventual thickness depend onthe temperature, pH and flow conditions of the solution. Its development leads to asteady further reduction in corrosion rate over periods up to hundreds of hours. [18]The corrosion rate is controlled by rate of mackinawite dissolution, the transfer of ionsthrough the compact inner film and porous outer film as well as mass transport throughthe liquid boundary layer at the electrolyte-film interface.

Re-passivation: At a certain thickness, the mackinawite film can delaminate entirely fromthe steel surface (Figure 1-4a). The solution in contact with the microcracks, or newlyexposed steel surface, becomes supersaturated with Fe(HS)+ or Fe2+. At this point, thereare several developments that can occur, depending on the exact conditions at the dam-aged film locations. The first possibility is that the steel re-passivates with mackinawitethrough either SSR, or by precipitation. This is most likely when the solution is lessacidic - above pH 6, atypical for oilfield brines - and at low temperatures since ferrousion and H2S levels are close to saturation limits for other phases such as troilite andpyrrhotite. Under these conditions the continuous spallation and repassivation of themackinawite film confers a semi-passive state with general corrosion rates on the orderof 1 mm/year.

Pitting: Another possibility is that the freshly exposed area of bare alloy becomes sus-ceptible to increased local attack by species in the environment. Particularly where chlo-ride ions are involved in the disruption of the passive state, such a situation has beenobserved to lead to surface pitting of carbon steels and other alloys. [18,22] Ex situ ex-aminations of pitted regions have revealed large deposits of iron sulfide directly abovethe pit (Figure 1-4b); this provides further evidence of increased, localized attack andalso suggests that pits may become re-passivated by precipitation from the electrolyte.

Pyrrhotite and pyrite nucleation: Finally, certain environments are conducive to theformation of other iron sulfide phases. Mackinawite may undergo direct, solid statetransformation to pyrrhotite under reducing conditions, or supersaturated conditions inbreaks at the mackinawite layer may lead to the direct nucleation of elcongated troiliteneedles or hexagonal pyrrhotite plates. [17, 23] Eventually, such a process would leadto the build up of a thick scale (10s-100s of µm’s) of the more stable sour corrosionproducts pyrrhotite and pyrite. These phases are more than an order of magnitude lesssoluble than mackinawite. Once they have formed a continuous film, the further forma-tion of mackinawite or other metastable phases is essentially inhibited by the greatlyreduced local ferrous ion activity in solution. [15]

1.3.2 Model phases: Pyrrhotite (Fe1-xS) and Pyrite (FeS2)

Despite the fact that mackinawite is an important phase in the early stages of aque-ous iron sulfide formation on steels, this thesis concentrates on pyrrhotite and pyrite.This was motivated in large part by the relative ease with which high-quality and well-defined samples of the stable iron sulfides could be made. Mackinawite is a flaky brownprecipitate that can only be formed from solution and oxidises rapidly upon exposureto air, therefore requiring careful handling under inert atmospheres and presenting ad-ditional technical challenges. Instead, pyrrhotite and pyrite served as model systemsto investigate the physical chemistry of processes involving point defects in iron sul-fides. The equilibrium phase diagram and crystal structures of the stable Fe-S phases

19

Pyrite FeS2NiAs-type Fe S1-xTroilite FeS

bc

abc

abc

a

(a)

(b)

S

Fe

Fe-S Equilibrium Phase Diagram

(c) (d)

Figure 1-5: Iron sulfide stability phase diagram. (a) Equilibrium Fe-S phase diagram. Pyrrhotite refers toa set of iron monosulfide polytypes, described in more detail in Chapter 2. Pyrite is a line compound at thefixed composition Fe:S = 1:2. (b) The crystal structure of the hexagonal pyrrhotite end-member, known asTroilite; (c) other pyrrhotites can be described by a hexagonal, NiAs-like subcell. (d) Cubic pyrite unit cell,described in Chapter 3.

is shown in Figure 1-5a. Pyrrhotite Fe1-xS forms a complicated series of polytypes atlow temperatures, from stoichiometric troilite (hexagonal FeS, Fig. 1-5b) to a rangeof vacancy-ordered superstructures based on the NiAs structure (Fig. 1-5c). Pyrite, bycontrast, is a line compound that is nominally stoichiometric in the bulk. [24]

1.4 Towards a predictive, multiscale corrosion model

1.4.1 Existing passive film models

The broader aim of this thesis is to investigate a set of elementary processes at the atomicscale which govern the protectiveness of passive sulfide layers. As we have seen above,real passive layers are complex materials systems: often multi-phase, highly defectiveand sensitive to changes in electrolyte chemistry as well as global variables such astemperature and stress state. For the purposes of building a passive film model, we mustnecessarily reduce the system to a series of elementary unit processes that occur on theatmoic scale. Hence, in addition to thermodynamics we need to consider the kinetics

20

of the corrosion process also. The interest in analytical and computational modeling ofpassive layers dates back at least 70 years. We do not attempt an exhaustive review ofall the available models here; instead, let us briefly examine some of the more relevantexamples to understand their advantages and shortcomings:

High Field Models account for the incipient oxidation of metals. [25–27] In the limitof small passive layer thickness L (on the order of nanometers) the field strength thatdrops across the film is extremely high, and the oxidation rate is inversely proportionalto time t, yielding a logarithmic law:

L(t) = ke log(αt + 1) (1.1)

where ke and α are temperature- and field- dependent constants and L is film thickness.However, this only holds for very thin passive layers, applicable to the very early stagesof oxidation or at low temperatures.

Wagner theory describes the growth of passive films in anhydrous environments, i.e. inthe absence of scale dissolution. [28] Assuming migration of ions through the film israte-controlling, a parabolic law is obtained of the form:

L(t) =q

kp t (1.2)

where kp is the parabolic rate constant, a function of the ionic diffusivity D of the mobilespecies. Dry sulfidation of iron at elevated temperatures > 500 oC is well described byWagner theory [29–31]; however, it cannot account for scale dissolution in aqueousenvironments or the case when surface reactions, such as molecular dissociation, arekinetically limiting.

The Point Defect Model (PDM) of Macdonald et al. is perhaps the most complete, deter-ministic analytical framework for describing the growth and protectiveness of genericpassive layers. [32,33]Originally inspired by Wagner’s theory of diffusion-limited growth,it further incorporates interfacial reactions and scale dissolution. Interfacial reactionssuch as cation injection from the metal and redox exchange at the surface typicallyfollow linear kinetics:

L(t) = ki t (1.3)

where ki is a surface exchange coefficient. The passive layer is treated as a bi-layer of in-ner, compact and highly defective oxide plus outer scale up to 100x thicker. Besides L(t)and corrosion currents i(t), the PDM can make quantitative predictions about passivitybreakdown.

Mackinawite formation models that describe iron sulfide scale formation have been pro-posed by Sun, Nesic et al.. [10, 16] The model assumes a bi-layered mackinawite filmcomprised of a thin (10 nm), compact inner layer and porous outer scale, 100s of µmthick. The corrosion rate is limited by mass transport (diffusion) through the mass trans-fer boundary layer at the scale-electrolyte interface, through the liquid in the porousouter scale and finally thorugh the compact inner sulfide. In addition, scale damageby hydrodynamic stresses is considered. However, the model is inherently empirical,requiring several unknown parameters to be fitted using experimental data. Moreover,the evolution of the scale to form stable sulfides at longer times is not considered.

Stochastic pitting models have been developed to simulate pit growth kinetics in stain-less steels. [34, 35] Based on Monte Carlo simulations of stochastic pitting, they canreplicate pitting potentials observed using potentiodynamic experiements. However, the

21

o(a) Gaseous Ar-10% H S (220 C)2

o(b) Aqueous 10% H S, 1% NaCl (220 C)2

Figure 1-6: Sulfide corrosion of 4130 carbon steel at 220 oC. (a) Amount of sulfur reacted (mass gain ofsample) with time in a dry, gaseous environment of 10% H2S. An initial logarithmic transient due to sufidefilm formation gives way to a linear regime where the rate of sulfidation is limited by surface exchange ofsulfur, described by the overall reaction: H2S(g) + 2e− ⇔ S2−

FeS + H2(g). At approx. 225 hours, the linearregime transitions to a "mixed" region in which diffusion of cations begins to limit the overall reaction rate.(b) Corrosion rate as a function of time in aqueous solution containing H2S. The scale grows under mixeddiffusion and interfacial (surface reaction) control. After 60 hours, the rate of scale growth is balanced byscale dissolution to produce a steady state in the corrosion rate. [17]

models do not predict pitting initiation through passivity breakdown at the nanoscale,instead the starting point is a just-nucleated pit.

To illustrate some of the rate limiting steps identified by the growth models above,Figures 1-6a and b show experimental results for steel sulfidation by H2S at elevatedtemperatures of 220 oC, under dry gaseous and aqueous conditions, respectively. Inthe dry case (Fig. 1-6a), from the amount of reacted sulfur we see a transition fromlogarithmic sulfide scale growth (High Field Model) at short times, to linear growth(surface reaction, as described by PDM) and finally after a certain thickness to a "mixed"interfacial and diffusion-limiited regime (Wagner theory). By contrast, under aqueousconditions (Fig. 1-6a; the y-axis is now corrosion rate CR), the CR initially falls rapidlyas the scale forms. After approximately 60 hours, a steady state CR is reached wherethe scale growth rate matches that of scale dissolution.

22

Table 1.2: Reactions describing the basic unit processes used to model the kinetics of iron sulfide layerformation, growth and breakdown. After the Point Defect Model. [32]

Partial process Reaction Parameters

Metal injection Fe+ V′′

Fe ⇔ FeFe + 2e− ν, φ

Fe⇔ FeFe + V ••S + 2e− ν, φ

Cation diffusion Fe(1)Fe ⇔ Fe(2)Fe∗DFe(T,φ)

Anion diffusion S(1)S ⇔ S(2)S∗DS(T,φ)

Dissolution FeFe + SS + 2H+⇔ H2S + Fe2+(aq) Kp

Surface vacancy formation FeFe ⇔ V′′

Fe + Fe2+(aq)

S2 + 2H+⇔ V ••S +H2 ∆HSf

1.4.2 Unit processes controlling Fe-S passive layer behavior

None of the models described above can successfully predict the transient and steadystate passive layer behavior in Figure 1-6 a priori. Moreover, localized breakdown phe-nomena such as pitting remain largely unaccounted for. The overarching motivationfor this project is to work towards a deterministic model. A robust model for such acomplicated electrochemical system must be able to predict a priori degradation ratesand trends under realistic pipeline corrosion conditions, using parameters that can bemeasured and compared through experiment. Moreover, the model’s predictive capa-bilities should serve as a platform for designing more protective materials and chemicalinhibitors. Its characteristics should be:

1. Non-empirical: able to calculate passive layer growth rates L(t), transient andsteady state corrosion currents i(t) and passivity breakdown (e.g. pitting proba-bility P(t) and stable pit growth rate dx/dt) using a "bottom-up" approach, i.e. bysimulating unit steps such as atomic diffusion and charge transfer reactions. Themodel should have as few empirical (fitted) parameters as possible.

2. Predictive: able to make accurate predictions that can be related to corrosion testsand cover a range of environmental conditions such as temperature, pressure,sulfur concentration and applied potential.

3. Modular: complexity can be added or removed by considering unit processes asseparate elements of the model.

4. Bridges length- and timescales: can make predictions from the atomic- andnanometer scale in fractions of a second, to the macroscopic level over timescalesof hours and years that can be compared to laboratory experiments and industrytests.

As of writing in November 2014, a global Fe-S passive film model is under continueddevelopment by Aravind Krishnamoorthy and others in the Yildiz and Van Vliet groupsat MIT, and will be presented in more detail in Aravind Krishnamoorthy’s PhD the-sis, expected 2015. In Figure 1-7, the processes considered in the model are outlinedschematically. In Figure 1-7a, some of the key atomic steps investigated in these two the-ses thesis are shown; these include ionic diffusion, surface exchange (interfacial chargetransfer reactions) and vacancy formation at surfaces under reducing conditions. Figure1-7b, on the other hand, depicts other important phenomena affecting the stability ofpassive films. Although beyond the the scope of this thesis and a rudimentary versionof the proposed model, they are included for completeness. Finally, the basic chemicalreactions that define sulfide passive layer behavior are listed in Table 1.2.

23

STEEL

Fe-SLAYER

ELECTROLYTE

0

L

φ = - dV/dx

x

φ

2+Fe

Hads

+H

Hads

H2

-HS

-2e(cathodic)

(anodic)

-2e

2-SVFe

(a) Elementary rate-limiting processes in iron sulfide films

Ionicdiffusion

Potential dropacross film

Interfacial charge transfer

Vacancy formation & pitting

STEEL

Fe-SLAYER

ELECTROLYTE

(a) Other considerations for generalized passive layer model

Voids/poresPhase stability, transformations

Pit chemistry

Interfacial stresses,film delamination

+ -H S ↔ H + HS2

Solution chemistry& thermodynamics

Chemicalinhibitors

Flow/erosion

Alloy microstructure& chemistry

- 2+X + Fe +

↔ FeX

Dissolution

g.b

pearlite

2-S

Figure 1-7: Schematic of unit processes in Fe-S passive layers: (a) basic kinetic rate-limiting corrosion pro-cesses for a homogeneous iron sulfide passive film on steel. (b) additional considerations for multiphase films,substrates, and different electrolyte chemistries. In addition, mechanical effects such as flow can influencecorrosion rate.

1.4.3 The need for experimentally-derived parameters

The high-level, proposed approach to formulate a non-empirical iron sulfide passivelayer model from fundamental atomic processes is outlined in Figure 1-8. Activationbarriers Ea and rate constants νo can be obtained by performing both ex situ and insitu experiments, combined with predictions from first principles by Density FunctionalTheory (DFT). In situ refers to corrosion tests using sulfidic electrolyte solutions; nonewere completed in the course of this thesis, but we will come back to potential experi-ments in Chapter 5. In their simplest incarnation, experiments are designed to measurea given kinetic process as a function of temperature, yielding the desired parametersthrough fitting to a universal Arrhenius law of the form:

P = νo exp[−Ea

kB T] (1.4)

where P is the probability (yielding average macroscopic rate) of the given process, andkB is Boltzmann’s constant. A kinetic Monte Carlo simulation calculates the dynamicsof local unit steps at the metal-passive layer and passive layer-electrolyte interfaces.

24

Experiments

“ex situ” “in situ”

GrowthChapter 2

Density Functional Theory

ReactivityChapter 3

StabilityChapter 4

Activation barriers Ea

Rate constants ν o

P = ν exp[- E / k T]o a B

kinetic Monte CarloPhase Field model

Laboratory testsField experience

Thermodynamics(literature)

Passive layer model: global strategy and thesis contributions

Figure 1-8: Overview of strategy to construct a non-empirical passive film model. Contributions of thisthesis are shown in red font. Experiments and first-principles Density Functional Theory (DFT) are employedto calculate activation barriers Ea and rate constants νo for the unit processes outlined in Figure 1-7. These arefed into a probabilistic model on the atomic scale, which updates a kinetic Monte Carlo (kMC) simulation.The microscopic fluctuations tend towards certain macroscopic states under an input thermodynamic biascalculated from temperature, chemical potentials, etc. This macroscopic behavior is calculated through aPhase Field model at greater lengthscales than kMC. Finally, the model should allow comparison to lab- andfield tests for re-optimization and iteration.

The kMC is coupled to a macroscopic Phase Field model which is able to update thestructure on greater length- and timescales. Finally, the proposed model will be merelyan academic exercise unless it can be usefully compared and contrasted to real resultson sour corrosion from laboratory tests and the field. In future studies, these shouldbe fed back into experimental design to improve the collection of useful, non-empiricalmodel inputs.

25

1.5 Thesis goals and organization

Having introduced the background and general strategy, the following three chaptersdig deeper into some of the phenomena depicted in Figure 1-7a, using the model ironsulfide phases Fe1-xS and FeS2. No in situ corrosion tests are conducted, nor do we con-sider the formation of sulfides on steel or iron substrates. Instead, this thesis comprisesthree individual case studies that test the hypothesis that we can construct a globalmodel by considering local, atomic processes in isolation. The physical chemistry ofpure iron sulfide surfaces and bulk processes are investigated and, where appropriate,the implications of the findings beyond passive film behavior are discussed.

• Chapter 2 ("Growth") addresses the unit processes of cation diffusion and sur-face exchange as rate limiting mechanisms in Fe1-xS (pyrrhotite). This phaseis interesting due to a magneto-structural transition at 315 oC, below which Fediffusion had previously not been studied. Is there an effect from magnetic andstructural ordering on Fe diffusion in Fe1-xS? Under what conditions does diffu-sion in pyrrhotite limit the rate of scaling or corrosion with respect to surfacereactions, and vice versa? Both phenomena are studied as a function of temper-ature to extract average activation energies which are cast into a rudimentarypyrrhotite scale growth model.

• Chapter 3 ("Reactivity") explores the effect of surface electronic structure on re-dox charge transfer, by quantifiying the electronic band gap and surface stateson FeS2(100) as a model sulfide phase. For semiconducting passive layers, elec-tron exchange with redox species in the environment occurs by horizontal transferfrom (to) occupied (unoccupied) states. How does the surface electronic structurediffer from that of the bulk? To probe locally at the surface, the scanning tunnel-ing microscope (STM) is used in spectroscopy mode (STS). However, there is nowell-defined protocol for interpreting STS results. A systematic methodology isdeveloped to identify tunneling current contributions from surface states whichmediate charge transfer during reactions, extendible to other similar materials.Finally, the implications of these findings beyond passive layer electrochemistryare discussed; for example, regarding earth-abundant, FeS2 photovoltaics for en-ergy production.

• Chapter 4 ("Stability") describes the dynamics of point defect formation, clus-tering and pit initiation on the FeS2 surface. The inherent protectiveness of apassive layer relies on the physicochemical barrier remaining intact against chem-ical, electrochemical or mechanical stimuli. A key postulate of the PDM is that pas-sivity breakdown originates from vacancy condensation on the cation sublattice ofthe barrier layer. Can we form a mechanistic picture of this process, informed byexperiment? The formation of sulfur defects at elevated temperatures and in UHVon FeS2 is obsered and quantified using x-ray photoelectron spectroscopy (XPS)and in situ STM. The experimental results are used to inform a kinetic MonteCarlo (kMC) simulation for vacancy condensation that predicts the formation ofnanocavities at passive film interfaces that can serve as pitting initiation sites.

• Chapter 5 "Conclusions" summarises the findings and key contributions fromthese three case studies above. The insights are contextualized under the scopeof the ambitious, global passive film model proposed in Chapter 1. The contri-bution of such precise physico-chemical studies on atomic processes in modelpassive layers is revisited and appraised. Finally, the steps required for the futuredevelopment of a more practical, deterministic passive layer model are discussed,including suggestions for in situ experiments under realistic aqueous conditions.

26

Chapter 2

Growth: cation diffusion andsurface exchange asrate-limiting mechanisms inpyrrhotite, Fe1-xS

Synopsis Cation diffusion and the surface exchange of sulfur, constituting the pre-dominant kinetically-limiting processes in the growth of pyrrhotite (Fe1-xS) in sour en-vironments, are investigated on model thin film and bulk samples. Diffusion is studiedvia two methods to understand the influence of the spontaneous magnetic and struc-tural order-disorder transition at the Néel temperature TN of 315 oC in Fe1-xS. Theself-diffusivity of iron *DFe in pyrrhotite above TN follows an Arrhenius law with an ac-tivation energy Ea = 0.83 eV. First, magnetokinetic measurements of the antiferromag-netic to ferrimagnetic "λ-transition" between 180-210 oC yield Ea = 1.1 eV for cationdiffusion. Second, we confirm this higher Ea in magnetic pyrrhotite using 57Fe tracer dif-fusion measurements below TN, obtained via secondary ion mass spectrometry (SIMS).These demonstate a downwards deviation from the extrapolated, paramagnetic Arrhe-nius trend by up to two orders of magnitude at 150 oC. The results are described by amagnetic diffusion anomaly, whereby vacancy formation and migration energies for thecation sublattice are increased by approximately 40% over the paramagnetic state, dueto spontaneous magnetization. Finally, we study sulfur exchange kinetics using the elec-trical conductivity relaxation (ECR) technique on Fe1-xS thin films, in which diffusion isvery rapid. The chemical exchange coefficient for sulfur incorporation, kox is found tohave an activation energy 1.0 eV. Our experimental activation barrier values for theseunit processes can be fed into a multiscale corrosion model to predict growth rates forpyrrhotite scales. The similarity in surface exchange and diffusive barriers suggests thatthe crossover from the former to latter rate-limiting steps should occur at approximatelythe same film thickness of 100-1000 µm, independent of temperature. The computa-tional work in this chapter, including the development of kinetic Monte Carlo codes,was discussed and carried out in collaboration with Aravind Krishnamoorthy.

2.1 Background and Motivation

Pyrrhotite is a stable iron sulfide phase that forms under higher temperature, moresour conditions (Chapter 1). It was selected for this study because iron diffusion isknown to be a relatively rapid process in Fe1-xS, due to its high degree of cation off-stoichiometry. In fact, the surface exchange of sulfur can constitute a relatively slower

27

1.0 1.5 2.0 2.5-11000/T (K )

Fe

2-1

log

[*D

] (c

ms

)

-6

-8

-10

-12

-14

-16

-18

900 700 500 400 300 200 150

0.8 1.0 1.2

oTemperature ( C)

0.0040.0070.0130.030.070.14

x in Fe S1-x

-6

-7

-8

-9

Fe

2-1

log[*

D] (c

ms

)

1.0 1.5 2.0

X

Y

(x ≈ 0)II c-axis

c-axisFe

2-1

log[*

D] (c

ms

)

-8

-9

-10

-11

-12

-11000/T (K )

†Fryt†

Worrell†

Sterten‡Hobbins

‡Condit§Marusak Z

Y

X

(a) (b)

(c)

-11000/T (K )

Non-stoichiometry

Anisotropy

?

?

Figure 2-1: Collected literature values of Fe self-diffusivity. (a) experimental ∗DFe values obtained usingdifferent techniques as listed. The aim of the work in this thesis was to measure a reliable set of data below 300oC. (b) magnified Fryt data from region “X” on the main graph. Variations in stoichiometry x account for up toone order of magnitude variation in ∗DFe . (c) magnification of Hobbins data (region “Y”): crystal anisotropycan account for half an order of magnitude variation. Data from: Fryt [31] †, Worrell [37] †, Sterten [38]†, Hobbins [39] ‡, Condit [40] ‡, Marusak [41] §. († = sulfurization; ‡ = radiotracer; § = magnetokineticmeasurements).

kinetic process for pyrrhotite growth under certain conditions. [17,36] Solid-state masstransport (diffusion) produces a parabolic time-dependence of film growth of the form:

X ∼p

4Dt (2.1)

where X is film thickness and D is a diffusion coefficient. Surface exchange (the reactionbetween Fe1-xS and H2S) on the other hand should produce linear kinetics of the form:

X ∼ t/kchem (2.2)

where kchem is a surface exchage coefficient. The primary aim of this work was to eval-uate and compare the fundamental energy activation barriers for these two processesby considering their Arrhenius-like temperature dependence:

D ∼ Do exp

−Em

kB T

(2.3)

kchem ∼ ko exp

−Eex

kB T

(2.4)

where Do and ko are rate constants, Em is the activation energy barrier for migration,Eex is the barrier to surface exchange reactions and kB is Boltzmann’s constant. Thedevelopment of a multiscale, non-empirical passive layer model as the ultimate moti-vation for this project requires experimentally-determined values for these unit processparameters.

28

Diffusivity: effect of order-disorder transition?

Fe1-xS undergoes spontaneous magnetic and structural disordering above the criticalNéel temperature TN of 315 oC. [42] Previous measurements of Fe self-diffusion *DFe inparamagnetic Fe1-xS above TN have been carried out by several authors using thermo-gravimetric [31, 37, 38] and radiotracer [39, 40] methods, as compiled in Figure 2-1a.An isothermal spread in *DFe of less than one order of magnitude is observed, stem-ming from variations in stoichiometry (Fig. 2-1a) or crystalline anisotropy (Fig. 2-1b).Despite this, the results above ∼ 300 oC follow a standard Arrhenius law as a functionof temperature, given by D = Do exp[−QP/kB T], where Do is a prefactor, QP is the acti-vation energy for diffusion in the paramagnetic lattice, and kB is Boltzmann’s constant.However, already in 1974 Condit et al. predicted that vacancy ordering below TN wouldlead to an increase in activation barrier for Fe self-diffusion. [40] Indeed, the only avail-able *DFe measurements at temperatures lower than ∼ 300 oC, obtained via a uniquemagnetokinetic method (Figure 2-1a, data labelled "Z"), may substantiate this claim ifit weren’t for a lack of auxiliary data. A secondary goal of this chapter is to clarify therole of ordering at TN on Fe self-diffusion in Fe1-xS.

Chapter goals and layout

The primary aim of this chapter is to to compare the rates of the kinetically-limitingprocesses of diffusion (bulk) and sulfur exchange (surface) by studying these processeson controlled samples as a function of temperature. A secondary goal is to resolve theuncertainty over the effect of magneto-structural ordering below 315 oC on cation dif-fusivity. This chapter is split into five main sections, which are summarized below:

• Section 2.2 "Introduction to pyrrhotite polytypes and transitions" describesthe closely-coupled structural and magnetic properties of Fe1-xS.

• Section 2.3 "Diffusion-limited λ transition" explores cation diffusion via mag-netokinetic measurements of a single-phase reordering transformation in non-stoichiometric Fe1-xS, reviewing the experiments that gave rise to the data in re-gion "Z" of Figure 2-1.

• Section 2.4 "Isotope tracer diffusion measurements" fills in the missing Fe self-diffusivity data in the temperature range 170-400 oC through direct diffusivitymeasurements using secondary ion mass spectrometry (SIMS) on Fe1-xS crystals.

• Section 2.5 "Sulfur exchange kinetics at the Fe1-xS surface" describes kineticmeasurements of the transfer of sulfur from gaseous H2S to Fe1-xS thin films,under conditions where diffusion is not rate-limiting.

• Finally, in Section 2.6 "Outcomes", the experimentally-determined rates of dif-fusion and surface reaction are compared to predict from first principles the con-trolling processes in the sulfidation of iron under a range of scenarios.

2.2 Pyrrhotite: polytypes and transitions

In this section, the crystallography and basic physical properties of Fe1-xS are reviewed.This phase characterized by a complicated series of vacancy-ordered structures whichform below a common ordering temperature of 315 oC.

29

a

c

Fe

S

(a) NiAs unit cell (b) Superstructure AB-plane

C

B = 2√3aA = 2a

Figure 2-2: Structural unit cells of pyrrhotite.(a) NiAs-like unit cell, common for all pyrrhotites. (b) AB-plane of superstructure, showing only Fe atoms. Dashed rectangle indicates the unit area A = 2a, B = 23a.

2.2.1 Structural and magnetic properties

The term ‘pyrrhotite’ encompasses a set of cation-deficient iron sulfides across the nar-row composition range 0 ≤ x ≤ 0.125 in Fe1-xS, where the stoichiometric end-member(0 ≤ x < 0.05) is more specifically referred to as ‘troilite’. A comprehensive reviewof the known structural and physical properties of pyrrhotites was previously writtenby Wang and Salveson. [43] All pyrrhotites undergo a spontaneous magnetic orderingtransition at a Néel temperature TN = 315 oC which is known to be strongly coupledto the ’β-transition’ or order-disorder transition for Fe vacancies, VFe. [42] For the re-mainder of this chapter, we therefore use TN to describe the critical, magneto-structuralorder-disorder transition temperature in pyrrhotite.

Below TN the accommodation of relatively large concentrations of VFe up to 12.5%produces a series of complex, structurally ordered Fe1-xS superstructures, a principalfeature of which is the formation of Kagome nets: tetrahedra sharing apexes in allthree dimensions which arise to minimize total vacancy-vacancy interaction energyin magnetically-frustrated systems. [44] Such VFe ordering in turn bestows a remark-ably diverse range of low-temperature physical properties, such as magnetism and elec-tronic conduction, which remain ambiguous despite many years of investigation. Thebasic unit cell for all Fe1-xS compositions is NiAs-type hexagonal with lattice parame-ters a and c, and space group P62c (Fig. 2-2). However, x-ray diffraction refinement[45–48] and high-resolution electron microscopy [49] studies have identified severallow-temperature superstructures based on a supercell of dimensions A = 2a, B = 23aand C = c which can take either hexagonal or monoclinic symmetry. The supercell canbe described as a layering of iron AB-planes where vacancy segregation to certain planescreates structures requiring different C-axis repeats to complete unit cell symmetry. Thegeneric superstructure is thus described as NC, where N is an integral or non-integralrepeat distance in the C-axis. The polytypes of Fe1-xS described below can be understoodwith the help of Table 2.1 and the phase diagrams in Fig. 2-3.

The fundamental magnetic properties of non-stoichiometric pyrrhotites are knownto arise from ferromagnetic (↑↑↑↑) alignment of cations within metal AB-layers andantiferromagnetic (↑↓↑↓) coupling between adjacent layers. [52] The inoccupation ofan AB-plane by iron vacancies reduces its overall ferromagnetic moment; net magnetismis hence determined by the periodicity of full and partially-unoccupied layers. Thesephenomena are discussed together in more detail for each phase below.

2C (Troilite. Fe1-xS: 0 ≤ x ≤ 0.05):

Troilite adopts a 2C structure with dimensions A = B = 3a and C = 2c. Magnetic mo-ments on Fe atoms lying in AB-planes are anti-ferromagnetically ordered at room tem-perature but undergo a spin-flip transition (α-transition, see Fig. 2-3) at the 2C/1Csolvus - starting at 140 oC for FeS - to an in-plane ferromagnetic order with antifer-romagnetic coupling between adjacent AB-planes, imparting net zero magnetization.

30

Table 2.1: Fe1-xS polytypes: composition and structure. [50,51].

Type Formula Compositionrange

Symm. Supercell unitcell

Comments

1C Fe1-xS Full range Hex. A, 2C Elevated temperature dis-ordered form

2C FeS 0 ≤ x ≤ 0.05 Hex. 3A, 2C Troilite

NC Fe1-xS 0.8 ≤ x ≤ 0.11 Hex. 2A, NC 5 ≤ N ≤ 11

4C Fe7S8 x = 0.125 ±0.05

Mono. 23A, 2A, 4C “Magnetic” pyrrhotite

NA Fe1-xS Unknown Hex. NA, 3C High temp. metastable; 40≤ N ≤ 90

MC Fe1-xS Unknown Hex. 2A, MC High temp. metastable; 3≤ M ≤ 4

Beyond this, magnetic spins fully disorder to paramagnetic at TN= 320 ± 5 oC.

1C (high temperature, disordered form):

1C describes the disordered form of pyrrhotite where vacancies are randomly dispersedand hence no long-range order exists. 1C is the established structure for all compositionsat temperatures higher than TN at which magnetic order is lost. 1C is antiferromagneticbelow TN, and paramagnetic above TN.

4C (Fe1-xS: x = 0.125 ± 0.05):

At the iron-deficient extreme of x = 0.125 ± 0.005, pyrrhotite adopts a monoclinicstructure in which the stacking sequence of cation layers alternates between fully occu-pied and -defective in the sequence (. . . FAFBFCFD. . . ), where F denotes a full layer andA-D are defective layers with different in-plane vacancy arrangements. [43] The qua-drupling of the c-axis stacking periodicity leads to the designation of this phase as 4C(Fig. 2-4a). In the 4C superstructure, an uncompensated moment between alternatingfull and vacant sublattices results in net ferrimagnetism which persists up to TN. Thetemperature-dependent magnetization up to this point is described by standard Weiss-type behavior. Powell et al. demonstrated using neutron diffraction that at TN, coinci-dent with magnetic disordering, a structural disordering towards randomly-distributedvacancies with hexagonal, 1C periodicity also occurs. [42]

NA and MC (210 oC < T < 320 oC, unknown composition range):

There has been some evidence to suggest that intermediate, metastable pyrrhotites existabove ∼210 oC that can be refined with superstructure cell dimensions A= NA with 40≤ N ≤ 90 and C = 3C. [45, 48] and subsequently at around 260-300 oC as ‘MC’ (A= 2A and C = MC with 3 ≤ M ≤ 4). [45, 53] Due to the large A-axis repeat units andnon-integral C-axis repeat units proposed for NA and MC pyrrhotites, respectively, thesephases are at best ill-defined and likely comprise a mixture of metastable, ordered solidsolutions that on average resemble the supercell structures described above.

NC (Fe1-xS: 0.08 ≤ x ≤ 0.11):

In the composition range 0.08≤ x≤ 0.11, Fe1-xS forms a more complex set of hexagonalpyrrhotite superstructures known collectively as ‘NC’, where the repeat distance N of

31

50 49 48 47 33.3

4C

4C + FeS2

1C + FeS2

Liquid

Liquid1C +

1C + S(l)

1C

2C + 1C

2C + NC

325

275

225

175

125

75

at% Fe

oTem

pera

ture

(C

)

949985

TN

Tα

TC

NC+

4C

NA

NC

MCMC + 4C

NA + 4C

6C 11C 5C

50 49 48 47 33.3

325

275

225

175

125

75

at% Fe

oTem

pera

ture

(C

)

949985

TN

Tα

Antiferro-

↑↓↑↓↑↓c-axis

Antiferro-

→←→←c-axis

Antiferro-

→←→←c-axis

Antiferro-

↑↓↑↓↑↓c-axis

Ferri-

↑↓↑↓↑↓↑c-axis

Para-

↑↑ ↑↑↑ ↑

Ferri-

↑↓↑↓↑↓↑c-axis

(a) FeS-Fe S phase diagram7 8

(b) FeS-Fe S magnetism7 8

Figure 2-3: Pyrrhotite structural and magnetic phase diagrams.(a) showing existence ranges of 1C, NC,4C, NA and MC pyrrhotite superstructures, as described in the main text. Experimentally determined temper-atures for the α-, β− and λ−transition onsets Tα, TN and TC, respectively) are also shown. (b) Approximatemagnetic structures superimposed on phase fields; arrows refer to plane-by-plane magnetic moment alongthe c-axis. After: [45,53,54]

the NiAs subcell may be either integral or non-integral between 5 and 11. [43] Figure 2-4b shows an idealized 5C structure with a series of full and vacancy-bearing AB-layers,similar to 4C. However, the periodicity for 5C (...-AFFBFCFFDFA-...) has an antiferro-magnetic symmetry due to compensation between sublattices. Although several idealcrystal structure solutions such as this have been proposed for integral N values such asFe9S10 (5C), Fe10S11 (11C) and Fe11S12 (6C), no exact vacancy distributions have beenconclusively determined. [46–48] NC pyrrhotites are better characterized by a distri-bution of probability of vacancy occupancy (Fig. 2-5). The observation of incommensu-rate c-axis stacking [56] in some pyrrhotite samples makes it likely that intermediates

32

0.75 1

8

6

4

2

0

10

8

6

4

2

0

Ferrimagnetic 4C

Laye

r #

Occupancy

Laye

r #

0.75 1

Occupancy

2+Fe VFe Magnetic moment (size represents magnitude)

Antiferromagnetic 5C(a) (b)

A

F

B

F

C

F

D

F

A

.

..

.

..

A

F

F

B

FC

FFD

.

..

.

..

FA

Figure 2-4: Idealized Fe1-xS superstructures: (a) 4C with alternating full and partially vacant occupancyof AB-layers. An uncompensated magnetic moment results in net ferrimagnetism. (b) 5C with net magneticcompenstation between full and vacancy-bearing layers; this idealized structure is antiferromagnetic. Thelabels “F” refer to full Fe layers; A-D are vacancy-bearing layers with different in-plane vacancy arrangements.After Vaughan et al. [55]

2+Fe Probability of V occupancyFe

Fe S vacancy-bearing superstructures1-x

4C 5C 11C 6C

Figure 2-5: Distributions of vacancies in 4C and NC pyrrhotites.Vacancy distributions are represented bythe probability of site occupation for 4C, 5C, 11C and 6C pyrrhotites. [57]

(non-integral values of N) are simply mixtures of the well-structured 5C, 11C and 6Cpolytypes. Irrespective, fully-ordered NC pyrrhotites are consistently antiferromagneticat room temperature due to a net compensation of magnetic moments between vacantand full cation layers.

33

(a) Single crystal Fe S9 10 (b) FeS nanowires (c) Natural FeS

c-axis

II c-axisHeating

Cooling

6

3

0300 400 500 600

T (K)

χ (

me

mu

/g)

400 500300 100 300 500o

T ( C)

2

4

6

8

σ (

me

mu

/g)

1

σ (

me

mu

/g)

2

0

3

T (K)

Figure 2-6: The peak-like λ-transition in NC Fe1-xS (a) single crystals [64], (b) nanowires [61] and (c)natural, geological samples [51].

2.2.2 The λ-transition in NC pyrrhotites

The unusual magnetic properties of pyrrhotite have long been studied for their funda-mental interest. [58] The temperature-dependent magnetization of ordered NC pyrrhotitesis characterized by the appearance of a peak during heating, centered around 210 ± 10oC (Fig. 2-6) that is thought to arise from a structural rearrangement towards a ferri-magnetic superlattice. [59]More recently, Fe1-xS nanowires [60,61] and nanodisks [62]that display the so-called λmagnetic transition have been fabricated by different meansand the phenomenon has even been proposed for technological purposes such as phase-change magnetic memory. [63] The kinetics of the λ-transition has been studied beforeusing magnetic techniques, notably by Townsend et al. [64] and Marusak et al. [41].However, despite confirming the λ-transition to be a diffusion-controlled process, acoherent mechanistic description is still lacking. For example, both authors assumedsimplified exponential time-dependence for isothermal magnetization kinetics.

2.3 Diffusion-limited λ transition

The λ-transition in NC (specifically, 11C and 6C) pyrrhotites was investigated usingtemperature-dependent and time-dependent magnetization experiments (σ(T ) andσ(t),respectively). During the first heating ramp from 30-350 oC, σ(T ) for the 11C and 6Cpolytypes undergoes a peak, similar to that observed for 5C by other authors (Fig. 2-6), attributed to a rearrangement of the vacancy-bearing sublattice via diffusion. Ourwork described here constitutes the first systematic investigation into the AF-FI tran-sition in Fe1-xS since 1980. An initial attempt to replicate the earlier experiments ofMarusak et al. [41] revealed a more complex time-evolution of the ferrimagnetic su-perlattice. Instead of a simple exponential fit, we demonstrate the magnetokinetics arebetter modeled by a phenomenological, stretched exponential function of the form:

α(t) = 1− ex p [−(t/τ)n] (2.5)

where τ descrbes a temperature-dependent relaxation time, and n= 0.45± 0.05. More-over, we describe a kinetic Monte Carlo (kMC) simulation of the λ-transition that re-produces the structural evolution on the experimental timescale from an AF to FI latticeunder cation vacancy diffusion alone. The kMC results similarly give a stretched expo-nential time dependence and help understand the transition as a continuous-orderingtransformation. A physical basis for the stretched exponential form of the kinetics isdiscussed. Finally, we show the temperature dependence of τ in Eq.(2.5) yields an acti-vation energy of 1.1 ± 0.1 eV for the λ-transition, which can be taken as the migrationenergy for cation diffusion in ordered pyrrhotite.

34

42 43 44 452Θ

48 5046

48

50

52

at%Fe, Arnold et al.

Me

asu

red

at%

Fe

30 40 50 60 702Θ

Inte

nsi

ty (

arb

. u

nits

)

(10

0)

(10

1)

(10

2)

(11

0)

(10

3)

(00

4)

4C

5C

11C

6C

2C

4C

5C

11C

6C

2C

4C5C

11C6C

2C

(a) X-ray diffraction (b) (102) peak

(d)

(c) Composition

Figure 2-7: X-ray diffraction of synthetic pyrrhotites. (a) Comparison of as-synthesized 2C (FeS), 6C(Fe11S12), 11C (Fe10S11), 5C (Fe9S10) and 4C (Fe7S8) samples with labelled pyrrhotite peaks . (b) (102)peak, (c) the (102) peak position is used to estimate composition with reference to the calibration of Arnoldet al. [66]. (d) black pyrrhotites were stored in glass vials and were stable without a change in propertiesover several months.

2.3.1 Methods

Preparation of well-ordered 2C, NC and 4C type pyrrhotites Synthetic pyrrhotitesamples of different stoichiometry were prepared by reacting the requisite amounts ofiron powder (99.999% purity, 200 mesh, Alfa Aesar, Haverhill, MA) and sulfur granules(99.998% purity, also Alfa Aesar) in quartz tubes, sealed under vacuum to 10-3 mTorr.The target stoichiometries were: Fe7S8 (4C), Fe9S10 (5C), Fe10S11 (11C) and Fe11S12(6C). The sealed powders were subjected to an initial heat treatment to allow the el-ements to fully react [42]: 500 oC for 24 hours, then 800 oC for 48 hours, followedby cooling at 0.5 oC/minute to 250 oC and held for 24 hours before removal from thefurnace. The products were removed from the quartz tubes, re-ground with a porce-lain pestle and mortar, and re-sealed in fresh quartz tubes under vacuum. A secondheat treatment was subsequently applied to ensure each sample relaxed into its low-temperature, equilibrium ordered structure: 800 oC for 72 hours, followed by coolingat 0.1 oC/min to 250 oC, holding at 250 oC for 24 hours and finally cooled to 125 oC ata rate of 0.1 oC/min, at which point the samples were removed from the furnace andallowed to cool to room temperature.

Characterization of synthetic pyrrhotites: X-ray diffraction The structure and phasepurity of the as-synthesized powders was determined by x-ray diffraction (XRD) using aPANalytical X’Pert PRO XRPD instrument with Cu-kα radiation (Fig. 2-7). All peaks canbe attributed to the hexagonal and monoclinic pyrrhotite structures (ICSD references53528 and 151766, respectively). The position of the (102) peak was used to confirmthe iron content of the samples, using the peak position calibration described outlinedby Arnold et al. [65,66]. Only the as-synthesized 2C pyrrhotite did not follow the trendin composition; however this phase was not of primary interest to this work and wasnot used further.

Magnetic measurements Magnetic measurements were obtained using a variable-temperature Vibrating Sample Magnetometer (VSM), with an applied field of 10 kOe.Powders of synthetic pyrrhotite weighing approximately 0.02 g were attached to quartzrods using silver paste adhesive. The sample was purged with N2 during the measure-ment at a flow rate of 15 standard cubic feet per hour (scfh). For time-dependent mag-

35

B

A

C

P2

P1

P1

P1

P1

Jump probabilities on kMC grid

Figure 2-8: Setup of cubic kinetic Monte Carlo (kMC) grid. One superstructure unit cell is shown; hexagonalsymmetry was applied by biasing diffusion probabilities. There are four equivalent jumps, labelled P1 and onenon-equivalent jump, P2 > P1.

netization measurements, the sample temperature was first raised to the setpoint, fol-lowed by turning on the applied field. The lag between reaching the set temperatureand recording the first data point was approximately one minute. The instrument wascalibrated using a nickel disk of known magnetization.

Differential scanning calorimetry Differential scanning calorimetry (DSC) was per-formed using a a Q2000 DSC (TA Instruments, New Castle, DE) under a dynamicallypurged N2 environment.

Kinetic Monte Carlo simulations Kinetic Monte Carlo (kMC) simulations were per-formed on a model block of cation-deficient pyrrhotite to test the mechanistic hypothesisthat mass transport of vacancies between AB-planes at elevated temperatures can grad-ually convert an antiferromagnetic lattice to a ferrimagnetic one. The model aimed tosimulate the time-dependent magnetization of a superstructure containing randomly-dispersed vacancies as it evolves towards a more 4C-like, layer-by-layer alternating oc-cupancy structure. We defined an order parameter based on the ideal 4C pyrrhotitevacancy distribution shown in Figure 2-4a. to continually assess the magnetism of thestructure as it evolved in time through diffusive jumps of VFe alone. The setup of thekMC model and the execution of unit processes are described step-by-step below.

1. A three-dimensional, cubic Ising model block consisting of 20 x 20 x 20 unit cellswas set up. Only iron sites were considered, under the assumption that the sulfursub-lattice is saturated and therefore does not contribute to mass transport. Indi-vidual lattice points can be full (1) or vacant (0) only. The hexagonal symmetryof the NC-type pyrrhotite lattice was imposed by biasing the diffusion paths suchthat a hop in one of the diagonals was 3 times as unlikely (Fig. 2-8).

2. One in every eleven sites was selected to be “0” at random to simulate an anti-ferromagnetic, 11C lattice. The start point for the lattice is not ordered; however,there is no unique 11C structure established in the literature. Moreover, we foundthat imposing a rigid initial structure only added to computation time without af-fecting the time-evolution results.

3. A vacant site in the structure was selected at random and its nearest neighbor(NN) sites are evaluated as potential jump destinations. The only atomic processmodeled by the kMC code was the diffusion of VFe in the a-, b- and c- direc-tions. Occupied NN’s populated a list of diffusive jump locations; specifically, fivenon-equivalent diffusion paths with different jump probabilities were considered(Fig. 2-8). The probability P for a jump to any of these sites is calculated in a

36

Table 2.2: Thermodynamic values for pyrrhotite compounds. Enthalpy of formation ∆Hf, 298 K relative tothe elements in their standard states at 298 K, absolute third-law entropies S298 K at 298 K, and heat capacityfunctions Cp. Data from: [67]

Compound ∆Hf, 298 K

(kJ/mol)S298 K

(J/mol.K)Cp (J/(mol.K))

FeS (2C) -100.1 60.3 2437.1− 9.9T + 0.01T2 − (41.1× 106)T2

Fe11S12 (6C) -1148.1 755.2 -

Fe10S11 (11C) -1048.5 693.0 -

Fe9S10 (5C) -950.8 623.5 170.6− 0.5T + 0.0005T2 − (3.0× 106)T2

Fe7S8 (4C) -755.4 486.3 140.5− 0.7T + (3.1× 10−7)T2 − (3.9× 106)T2

sub-routine, based on: (a) the self-diffusivity or intrinsic activation barrier to mi-gration Em, in the absence of an imposed driving force; (b) an energy bias dueto a thermodynamic driving force towards ordering, Etherm, as described belowin step (4); (c) a bias due to the magnetic energy in the applied field of 10 kOe,Emag:

P = ν. exp

−Em

kB T

exp

−Etherm

kB T

exp

−Emag

kB T

(2.6)

4. Subsequent to each diffusive jump, the occupancy of the seven adjacent supercellAB-planes above and seven below the elected vacant site was assessed (Fig. 2-8). The closeness of the layer-by-layer occupancy of this volume was comparedto the idealized ferrimagnetic 4C-type lattice occupancy (. . . full, vacant, full,vacant. . . ) and was quantified by taking the root mean square (RMS) differencefrom the ideal 4C structure occupancy.

5. The energy landscape of the simulation was biased such that the structure is ther-modynamically driven to evolve towards a more 4C-like structure. A linear biasof the form Etherm = AΘ+B was used, where the parameters A and B provide thedifference in Gibbs free energy ∆G between a disordered vacancy structure andthe 4C structure at a given temperature of interest, and Θ is the order parameterwe assign to the system, with 0 assigned to a randomly-ordered antiferromagneticlattice and 1 representing the full 4C structure. The free energy G of each phaseat a given temperature was approximated via the relation:

G =∆H f ,298K +

T∫

298K

CpdT − T

S298K −

T∫

298K

Cp

TdT

(2.7)

where ∆H f , 298 K is the formation enthalpy at 298 K, S298 K is the entropy at298 K and Cp the heat capacity. Values for these thermodynamic parameters, aslisted in 2.2, were obtained from Walder and Pelton. [67]

2.3.2 Results and discussion

Temperature-dependent magnetization

Temperature-dependent magnetization σ(T ) results for the 4C, 11C and 6C Fe1-xS sam-ples are shown in Figure 2-9. The 4C sample followed typical FI, Weiss-type behavior

37

12

3

1

234

0 100 200 300oTemperature ( C)

1

23

45

150 200 250 3000.5

1

1.5

2

oT ( C)

-1M

(e

mu

.g)

0.5

1

1.5

2

-1M

(em

u.g

)

150 200 250 300o

T ( C)

0 100 200 300o

Temperature ( C)

0 100 200 300

oTemperature ( C)

0

5

10

15

20

-1M

ag

ne

tiza

tion

(e

mu

.g)

(a) 4C (Fe S ) 7 8 (b) 11C (Fe S ) 10 11 (c) 6C (Fe S ) 11 12

350350

Figure 2-9: Temperature-dependent magnetization σ(T ). (a) 4C, (b) 11C and (c) 6C pyrrhotite samples.Multiple consecutive forward and reverse sweeps between 30-330 oC, as labelled 1-5 on each of the graphs,were performed until no change from the previous sweep was observed. On (b) and (c) the inset graphs showa magnified region around the peak observed on the first sweep. The heating and cooling rates were both 0.2oC/min; the applied field was 10 kOe.

-10 -5 0 5 10-3

-2

-1

0

1

2

3

H (kOe)

σ (

me

mu

/g)

H (kOe) H (kOe) H (kOe)

o150 C o220 C o280 C o325 C

-10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10

11C (Fe S ) Hysteresis Curves10 11

Figure 2-10: Magnetization vs. applied field (σ-H). Obtained from 11C pyrrhotite samples held at differenttemperatures, as indicated. Magnetization reaches a maximum at 220 oC in this series. Inset on each curveis the region around zero applied field; the absence of hysteresis at 325 oC demonstrates paramagnetism.

as expected up to TN = 315 oC. This behavior is reversed upon cooling and can be re-peated without hysteresis (three heating-cooling cycles are shown in Fig. 2-9a). Theas-synthesized 5C sample produced similar results to 4C, indicating that the desired,equilibrium antiferromagnetic (AF) superstructure had not been formed. The 5C pow-ders were not used further of this work.

However, the other NC samples, 11C and 6C, displayed markedly different σ(T)behavior (Figs. 2-9(b) and (c)). On the first heating cycle, labelled (1) in the figures,σ started close to 0 emu/g, consistent with AF ordering. The λ-transition peak firstappeared at ∼ 180 oC, with a maximum at 210 oC. This is also observed in Figure 2-10 which shows a series of magnetization vs. applied field (σ-H) curves at differenttemperatures along the peak. The magnitude of σ for a given H first rose then fell be-tween 150 and 280 oC. At 325 oC the magnetic behavior is paramagnetic, evidencedby a lack of hysteresis. However, during cooling back from 350 oC, the λ peak wasnot reproduced and σ increased with Weiss behavior back to room temperature. Mul-tiple, repeated heating/cooling cycles (2-5) as indicated on the curves only served toincrease overall magnitization further. The maximum room temperature magnetizationσRT reached by 11C after several experimental cycles (∼ 13 emu/g) was greater thanthat of the 6C sample (∼ 10 emu/g); neither reached the maximum of the 4C sample(σRT ∼ 22 emu/g). Thus the final σ for a given structure is limited by the availabilityof iron vacancy VFe to maximize the magnetic asymmetry between vacancy-bearing andfull layers.

38

Time-dependent magnetization

The fact that several heating cycles were required to fully convert the 11C and 6C Fe1-xSto a metastable, FI superstructure (Figs. 2-9b and c) suggests that the kinetics of theλ-transformation are not instantaneous. To understand the transformation kinetics inmore detail, we performed isothermal, time-dependent magnetization σ(t) measure-ments on samples of 11C at various temperatures between 140-220 oC. Short-timescalekinetics (< 10 minutes) and longer-timescale behavior (up to several hours) are dis-cussed separately. Figure 2-11a shows the results of heating one sample consecutivelyin steps of 10 oC, holding at each temperature for 10 minutes (solid line series). It canbe seen that σ in this series was history-dependent: each time the sample was heated,the transformation proceeded from the end-point reached at the previous temperature.Conversely, the dashed curves in Fig. 2-11a were obtained on fresh samples heated di-rectly from 30 oC to the set temperature of 180-220 oC as indicated. The peak shapewas also reproduced, but a lack of transformation history means that σ did not reachthe same level as the sample subjected to consecutive heating steps.

We also observe from Fig. 2-11a that a large proportion of the rise in σ at a giventemperature occured very rapidly, within the first 5 minutes and is evidently at least par-tially reversible, since the curves overlap. The initial reversibility is more clearly seen inFigure 2-11b where the σ(t) of an 11C sample held at 210 oC for 4000 s continuously iscompared against that of another sample which was cooled to room temperature threetimes sequentially at 20 minute intervals between heating to 210 oC. We can infer fromthis that much of the rapid, initial increase in σt at a given temperature arose from asmall motion of VFe between adjacent planes, easily reversed upon cooling. Howeverafter a few minutes the gradient (dσ/d t) became less steep, i.e. the maximization of σrequires a more coordinated re-shuffling of the vacancy sublattice that remains macro-scopically irreversible, or metastable, once cooled back to room temperature.

To understand the transformation kinetics in more detail, we performed isother-mal, σ(t) measurements on samples of 11C at various temperatures between 140-220oC for longer times up to 10,000 s. The kinetics of the λ-transition in 5C Fe1-xS, studiedvia thermomagnetic techniques, has previously been shown to be limited by VFe diffu-sion. [64] Assuming exponential growth in σ during the λ-transition, iron self-diffusioncoefficients on the order of 10-17 cm2s-1 have been found by magnetokinetic methodswithin this transition temperature range [41] that are inconsistently low compared toextrapolated diffusivities obtained from high-temperature sulfidation [30, 31] and ra-diotracer diffusion studies [O(10-14 cm2s-1)]. [40] However, during an initial attempt toreplicate these experiments we found that our magnetokinetic data were not describedor fit by simple exponential functions. Instead, the stretched exponential in Eq. (2.5)provided a more accurate description (Figure 2-12).

Isothermalσt data were also collected at several temperatures along theλ-transitionfor longer times up to 10,000 s. Magnetization was converted to ‘phase fraction’ of FIordering, αF I , according to:

αF I =σt −σi

σ f −σi(2.8)

where σt is the measured magnetization at time t, σi is initial magnetization at t = 0and σ f is final magnetization assuming the transition were allowed to proceed to com-pletion. σ f values for the different temperatures were therefore obtained from curvenumber (4) in Figure 2-9b, i.e. the maximum FI magnetization at a given temperatureT.

39

0 10 20 30 40 50 60 70 80 901

1.5

2

2.5

3

3.5

Time from start of experiment (min)

Magnetiza

tion (

em

u/g

)o140 C

o150 C

o160 C

o170 C

o180 C

o190 C

o210 C

o200 C o220 C

Same sample

Fresh sampleseach run

(a) Short time-dependent magnetization

0 1000 2000 3000 40001

2

3

4

5

Time (s)

Sequential

Continuous

o210 C

1

2

3

(b) Reversible initial magnetization

Ma

gn

etiz

atio

n (

em

u/g

)

Figure 2-11: Reversible magnetic transformation at short timescales. (a) Isothermal, time-dependent mag-netization σ(t) of 11C pyrrhotite at different temperatures around the λ transition. The grey, solid curveswere obtained on the same sample, consecutively heated to the indicated set temperature, held for 10 minutesand cooled to room temperature (“add-on” magnetization). The dashed lines correspond to a series whereeach temperature measurement was performed with a fresh sample. (b) σ(t) of two 11C samples: one heldcontinuously at 210 oC for 4000 s (dashed line). The other is sequentially heated to 210 oC three times, withcooling to room temperature between each step.

2.3.3 Continuous re-ordering of ferrimagnetic superlattice

Figures 2-13a and 2-13b display the results for the experimental and simulated λ-transition magnetokinetics, respectively. For the experimental data, a common valueof n = 0.45 ± 0.05 was found to fit all curves reliably. For the kMC results, n = 0.67 ±0.05; a sensitivity analysis and details of fitting procedures are provided in Table 2-21.Nevertheless, the kMC model, based solely on cation diffusion, accurately replicatedthe stretched exponential form of the experimental result. The parameters τ and n inEq. (2.5) are not indicative of any specific atomic mechanism. Generally, τ representsa temperature-dependent relaxation time and n determines the lengthening of τ as thetransition progresses (i.e. a deceleration in transition kinetics). Stretched exponentialmagnetokinetics of this form have been observed for Li2(Li1-xFex)N (n= 0.4-0.8) at lowtemperatures < 20 K, related to finite magnetic moment relaxation. [68] However, thisis an unlikely explanation for the kinetics observed in this work at elevated tempera-tures, where magnetic relaxation should be instantaneous. Alternatively, we can think

40

0 10000 20000 0

0.2

0.4

0.6

0.8

1

5000 150000

0.2

0.4

0.6

0.8

1

0 10000 20000 5000 15000

Data

Exponential fit

Stretched exp. fit

Time (s) Time (s)Time (s)

α α

o(a) Experiment (210 C) o(b) kinetic Monte Carlo (210 C)

Exponential fit

Figure 2-12: Best fits to exponential equation α(t) = 1−exp [− (t/τ)] and stretched exponential equationα(t) = 1− exp [− (t/τ)n] for (a) experimental magnetization data obtained at 210 oC and (b) kinetic MonteCarlo simulated data at the same temperature.

Table 2.3: Best fit parameters n and τ in the fitting expression α(t) = αo[1− exp [− (t/τ)n]]+ (1−αo) forthe experimental and kinetic Monte Carlo results.

Temp. (oC) n t αo

Experimental: free parameters

180 0.48 548 ± 9 1.00

190 0.42 134 ± 2 0.99

200 0.40 78 ± 2 0.89

210 0.44 66 ± 3 0.90

Experimental: fixed n

180 0.45 ± 0.05 410 ± 211 1.00

190 0.45 ± 0.05 186 ± 95 0.98

200 0.45 ± 0.05 127 ± 65 0.86

210 0.45 ± 0.05 76 ± 39 0.89

kinetic Monte Carlo: free parameters

180 0.70 737 ± 38 N/A

190 0.73 651 ± 40 N/A

200 0.66 275 ± 19 N/A

210 0.62 150 ± 8 N/A

of the λ-transition as a classical nucleation and growth process, described by the semi-empirical Johnson-Mehl-Avrami-Kolmogorov (JMAK) relation that takes the same formas Eq. (2.5). For example, the first-order antiferromagnetic-ferromagnetic transition inFeRh has been described by a JMAK equation with n = 0.86. [69] The Avrami expo-nent n is typically temperature independent and may provide information about thenucleation and growth mechanisms. [70] A value of n = 0.5 to describe the formationof FI phase out of a homogeneous AF lattice would suggest one-dimensional growthwith zero nucleation rate, implying small nuclei of FI phase were pre-dispersed in the

41

(a) Experimental ferrimagnetic fraction

Data

Fit

0 5000 10000

0

0.2

0.4

0.6

0.8

1

Time (s)

α

o180 C

o210 C

o200 C

o190 C

α

0 5000 10000

0

0.2

0.4

0.6

0.8

1

Time (s)

o180 C

o210 C o200 C

o190 C

210

-7

-6

-5

-4

-3

ln(

-1 τ)

-3 -11/T x 10 (K )

1.1 ± 0.1 eV

(b) kinetic Monte Carlo results

200 190 180oT C

-7

-6

-5

ln(

-1 τ)

-3 -11/T x 10 (K )

210 200 190 180

1.1 eV

oT C

Data

Fit

Figure 2-13: Long-timescale isothermal magnetization. (a) Transformed ferrimagnetic volume fraction αmeasured over 10,000 s at four temperatures as indicated. We show every 20th point of the raw data aswell as a best fit line to the phenomenological, stretched exponential relation α(t) = 1 − exp [− (t/τ)n],with standard deviation error. Inset: Arrhenius fit of the temperature-dependent fitting parameter τ−1, witha slope corresponding to a transformation activation energy of 1.1 ± 0.1 eV. (b) kinetic Monte Carlo (kMC)reullts for magnetization transformation at the same temperatures, and fit to a similar stretched exponentialfit. Inset: corresponding activation energy of 1.1 eV calculated from computational τ−1.

equilibrium 11C lattice prior to transformation, and that the observed "growth" in αarises from the change in the magnetization order parameter along one axis alone (forexample, the c-axis). However, we believe the microscopic transition mechanism can bebetter described as a diffusion-limited, continuous re-ordering process akin to spinodaldecomposition. As such, the FI phase grows out of the AF lattice via an augmentationin small, layer-by-layer vacancy occupancy fluctuations. A second-order transition ofthis type is consistent with a continuity in enthalpy H but discontinuous heat capac-ity ∂ H/∂ T during the λ-transition, as measured by differential scanning calorimetry(Figure 2-14). The absence of a pronounced discontinuity in heat Q confirms that thediffusive rearrangement of the λ-transition is second order; that is, the new state ofincreased symmetry develops continuously from the highly-ordered, lower symmetry11C or 6C phases. The subsequent, spontaneous disordering at TN is then 1st-order,similarly to the 4C case, but since an already higher degree of disorder exists in the6C and 11C lattices which have not had time to form into a perfect alternating-layerFI structure, much less diffusion (and therefore latent heat) is required to undergo the

42

-500

0

500

Heat F

low

(m

W/g

)

-200

-100

0

100

200

Heat F

low

(m

W/g

)

50 100 150 200 250 300 350

-200

-100

0

100

200

Temperature (oC)

Heat F

low

(m

W/g

)

30.1 J/g o316 C

Endo.Heating

Cooling

4C

11C

6C

o314 C30.5 J/g

1.4 J/g

o210 C

o210 C o316 C

4.7 J/g

Heating

Cooling

Cooling

Heating

2.2 J/g 4.9 J/g

o316 C

2.5 J/g

o210 C

5.0 J/g

2.2 J/g 5.0 J/g

o316 C

(a)

(b)

(c)

Exo.

Differential Scanning Calorimetry

Figure 2-14: Differential scanning calorimetry (DSC) results from (a) 4C, (b) 11C, (c) 6C syntheticpyrrhotite samples. The heating rate was 10 oC/min; endothermic heat flow is negative on the y-axes. Theintegrated peak areas for heat uptake or evolution events, in units of J/g and demarcated with dashed lines,are shown on each figure next to the event.

full disordering transition.Figures 2-15a-e shows a series of magneto-structural order parameter Θ distribu-

tions on kMC lattice points, obtained at various times along the λ-transition at 200 oC.Rather than observing the formation of discrete FI nuclei (red dots in the figure) whichgrow along one axis and would thus be consistent with the JMAK interpretation, we in-stead visualize the emergence of regions of intermediate Θ that gradually spread acrossother lattice points diffusely. This simulated phenomenon is also clearly seen in Figure2-15f, where we see small fluctuations in layer-by-layer vacancy occupancy augmentwith time into an alternating-plane, FI structure. The stretched exponential fits in Eq.(2.5) to our σ(t) data take the same form as the Kohlrausch function [71], commonlyused to describe non-equilibrium dynamics in disordered condensed matter such as di-electric relaxation [72], relaxation in soft matter [73] and diffusion in complex systems,incluiding glassy materials and H migration in amorphous Si. [74] Although genericallysemi-empirical, a number of mathematical derivations for the Kohlrausch function havebeen put forward which provide a more physical basis for the ubiquitously observedstretched exponential behavior. [75] Kohlrausch behavior can arise in the presence asmall energy distribution of traps in systems with long-range correlations; this wouldlead to deviations from "random walk" Brownian motion diffusion in amorphous struc-tures. Alternatively, there may be a time-dependence in populating different energytraps, such that relaxation occurs in stages. [76] Although we do not wish to comparedirectly the stretched exponential magnetization observed in the λ-transition here toKohlrausch descriptions of decay in disordered materials, perhaps some parallels may

43

1

0

Ord

er

pa

ram

ete

r Θ

(a) 0 s (b) 7,000 s (c) 12,000 s (d) 45,000 s (e) 100,000 sFI

AF

0 2 4 6 8 10 12 14 16 18 20

0.85

0.9

0.95

Layer # along z-axis

Occu

pancy

0 s 12,000 s 100,000 s

(f)

Layer # along c-axis

c

a

average occupancy = 0.909

Figure 2-15: Continuous re-ordering towards ferrimagnetic state. Local order parameter Θ calculatedfor individual lattice points in the kinetic Monte Carlo (kMC) simulation at 200 oC, where 0 refers to fullyantiferromagnetic (AF) and 1 is ferrimagnetic (FI), corresponding to: (a) 0 s, (b) 7000 s, (c) 12000 s, (d)45000 s and (e) 100000 s along the λ-transition. (f) layer-by-layer occupancy for 20 planes along the c-axisfrom the kMC results obtained at different times. As the transition progresses, the difference in occupationbetween adjacent layers becomes more pronounced.

be drawn which give an intuitive physical insight into the phenomenon observed bothexperimentally and in the kMC results of this work. We can dismiss the possibility of adistribution in traps since Brownian motion was inherently assumed in our kMC model.On the other hand, a time-decay in the rate of magnetization evolution may be morecoherently explained by a combination of rapid and subordiante, slower processes. Inother words, given sufficient thermal energy, cation vacancies may migrate rapidly toadjacent planes under a large thermodynamic driving force and break the compensatingAF lattice symmetry. This leads to small regions with localized FI ordering that nonethe-less contribute a large increase in σ on the scale of 10-100s of seconds. At longer times,however, the formation of the optimal FI lattice structure for the available vacancy con-centration requires a more labored rearrangement of vacancies into long-range order,decelerating the growth in σ. Only inter-layer VFe hops contribute to a rise in magne-tization. We compared the ratio of inter- to intra-layer hops during the λ-transition inthe kMC model and found that it decreased over time. This is consistent with a relax-ation in the exponential kinetics for σ; the further the transition progresses, the lowerthe driving force for vacancy segragation and the smaller the probability of inter-layerjumps.

Finally, we turn to the significance of the activation energy of 1.1 ± 0.1 eV measuredby fitting the experimental σ(t). A migration barrier for diffusion of 1.2 eV was orig-inally cast into the kMC model. An analysis of the resulting kMC data using the samefitting procedure as for the experiment returned an apparent barrier value of 1.1 eV,confirming that the major rate-limiting step is cation diffusion. We therefore take 1.1eV to represent a slight underestimate to the activation barrier Em to Fe self-diffusionin magnetically-ordered Fe1-xS superstructures. The overall measured activation energyincludes a thermodynamic bias for the transformation on the order of 0.1 eV at 200oC (calculated from the data in Table 2.2), which serves to lower the diffusion barrier

44

Iron

Marker

Fe S1-x

Iron

Marker

Fe S1-x

Sulfidation of iron

Figure 2-16: Cross section of sulfide scale formed during the sulfidation of Fe for 20 mins at 800 oC. Aninert (Pt) marker indicates the position of the original iron-vapour interface. (100x) [30]

slightly.

2.3.4 Conclusions

In conclusion, we have investigated the antiferromagnetic to ferrimagnetic λ-transitionin NC-type pyrrhotites via magnetokinetic experiments and kinetic Monte Carlo simula-tions. In contrast to previous reports, the transformation is found to follow a stretchedexponential time-dependence. These experimental and computational results togethersupport a description of the λ-transition as a nucleation-free, continuous reorderingvia diffusion on the cation sublattice. Magnetization initially rises rapidly due to small,localized displacements, but a full optimization of the ferrimagnetic superstructure isa more complex process that emerges only at longer timescales. The migration energybarrier for Fe in magnetic pyrrhotite is shown to be approximately 1.1 eV. The resultsare helpful in predicting the barrier properties of pyrrhotite scales on ferrous alloysthat are exposed to sulfur environments, for example in oil and gas systems. Further,the eludication of the kinetics of the λ-transition encourages continued studies to iden-tify practical applications for this interesting magnetic phenomenon in synthetic Fe1-xS,for example magnetic switching or data recording devices based on earth abundantchemical elements.

2.4 Isotope tracer diffusion measurements

Consistent with the metal-deficient nature of Fe1-xS, the diffusion of cations is knownto be the primary solid state mass transport mechanism in pyrrhotite scales in bothaqueous [36] and dry [29–31] sulfide corrosion conditions. The self-diffusion coefficientfor sulfur in Fe1-xS is known to be several orders of magnitude lower than for Fe2+:*DS = O(10-11) cm2s-1 at 1000 oC compared to O(10-11) cm2s-1 for *DFe. [40]. Hencean inert marker placed at a steel-pyrrhotite interface will remain at the interface asthe Fe1-xS scale grows by the outward migration of cations (Fig. 2-16). In the previousstudy, an activation energy of 1.1± 0.1 eV was measured for a diffusion-limited vacancysuperstructure rearrangement process in ordered pyrrhotites. This should represent thebarrier for Fe migration through a Fe1-xS lattice in which a thermodynamic driving forceexists for ordering. In this section, iron self-diffusion *DFe is measured directly in bulkcrystals of Fe1-xS by means of iron-57 isotope tracer measurements using secondary ionmass spectrometry (SIMS).

45

42 43 44 452Θ

30 40 50 60 702Θ

Inte

nsi

ty (

arb

. un

its)

o43.65

(a) Natural Fe S XRD1-x (b) (102) peak

(100)

(100

)

(102)

(101

)

(110)

(103

)

(00

4)

(101)

Figure 2-17: Cu-kα powder XRD pattern from a representative sample of research grade natural pyrrhotite.(a) Hexagonal Fe1-xS peaks are labelled on the diagram. Inset: picture of crystals; approximately 5 x 5 x 1mm3 polished to < 50 nm roughness. (b) the hexagonal Fe1-xS (102) peak’s position of 43.65o indicates anaverage composition of 48.0 at% Fe.

2.4.1 Methods

Sample preparation

Natural pyrrhotite crystals were used for diffusion studies.1 Research-grade naturalcrystals of pyrrhotite were obtained from Ward’s Science (Rochester, NY). Individualspecimens were approximately 5x5x5 mm3 and were sourced from North Bend, WA. Arepresentative sample of several individual crystals from the package was ground to-gether into a powder in a porcelain mortar for XRD phase identification (Fig. 2-17a).Hexagonal pyrrhotite was found to be the only phase present. The position of the (102)peak (Fig. 2-17b) was used to estimate an average composition of 48.0 at% Fe, corre-sponding approximately to Fe11S12 (6C). [66]

The chemical composition of the natural crystals was investigated using energy-dispersive x-ray spectroscopy (EDS) in a JEOL 6610LV scanning electron microscope(SEM), to check for any large inclusions that may have affected the reliability of thediffusion studies. Figure 2-18 shows a series of chemical maps of a randomly-selectedbut representative surface, indicating that the majority elements were sulfur and iron.Some minor inclusions of oxide were present in thin seams. An search for potentialmetallic impurities such as Si and Al came up negative within the detection limit of theinstrument (approx. 0.1 wt% [77], implying that the inclusions are likely iron oxides.These were deemed sparse enough to not greatly affect the accuracy of the subsequentdiffusion studies. The self-diffusion coefficient of iron in Fe2O3 is very small below 500o C (< 10-28 cm2s-1. [78]

As-received crystals were polished using 1200, 2000 and 4000 grit sandpaper toachieve a flat surfaces followed by an extended polish of 5-10 minutes using 50 nmAl2O3 suspension. The resulting average surface root mean square (RMS) roughness,as measured by Atomic Force Microscopy (AFM) was< 50 nm; in some 50x50 µm areasRMS roughness was as low as 17 nm.

Temperature-dependent magnetization studies as described in Section 2.3.1 con-firmed the natural pyrrhotite samples to be antiferromagnetic at room temperature and

1In fact, diffusion studies were attempted using three different types of pyrrhotite samples: Chemical vapordeposited (CVD) thin films (∼ 200-500 nm thickness, Appendix B), Sputter deposited thin films (∼ 1000 nmthickness, Section 2.5.1) and polished natural single crystals (100’s of µm thick). In this chapter, only thedata collected from the natural single crystals is included, since they are considered the most reliable fromthis study.

46

25 µm

250 µm

SEM S Fe

O Si Al

(a) (c) (e) (g)

(b) (d) (f) (h)

Chemical composition of natural pyrrhotite samples

Figure 2-18: Energy-dispersive X-ray spectroscopy (EDS) maps of an unpolished surface from a naturalcrystal used in this study. The scanning electron microscope (SEM) picture is reproduced and overlaid withchemical analysis maps of sulfur, iron, oxygen, silicon and aluminium.

Table 2.4: Isotopic composition of naturally-occurring iron. [79]

Isotope 54Fe 56Fe 57Fe 59Fe

Nat. abundance (at%) 5.85 91.75 2.12 0.28

Half-life > 3.1× 1022 years Stable Stable Stable

to undergo a peak-like λ-transition starting at 160 oC as described for synthetic 11Cand 6C pyrrhotite in Section 2, followed by a full magnetic disordering at TN = 316 oC.

57Fe deposition and diffusion annealing

To study iron self-diffusion, the stable isotope 57Fe was used as a tracer. 57Fe is a stableisotope with abundance in natural iron of around 2% (Table 2.4). Solid chips of 57Fe(96.06% enriched, Nakima Ltd., Israel) comprising a total mass of 200 mg were evap-orated onto the surface of ∼ 40 polished Fe1-xS crystals simultaneously using a SharonTE-1 thermal evaporator. The resulting deposit thickness, measured in situ with a quartzcrystal microbalance and confirmed ex situ by measuring a deposit shadow profile on aglass substrate, was 130 nm.

Once coated in 130 nm of 57Fe, pyrrhotite crystals were subjected to diffusion an-nealings at a range of temperatures between 170-400 oC for different lengths of time.Annealing was performed in a horizontal quartz tube furnace under a dynamic H2S:H2atmosphere in a molar ratio of 1:3500 (i.e. 0.03% H2S) which was within the sulfurpartial pressure stability window for Fe1-xS for the relevant range of temperatures (seeFig. 2-25 in Section 2.5.1). Maintaining this dynamic, reducing atmosphere prohibitedthe formation of oxide on the deposit or oxidatoin of the crystals themselves. Crystalswere mounted on a custom stage and inserted into the hot part of the furnace for apredetermined period of time before being removed outside the tube furnace for cool-ing under the H2S/H2 atmosphere. A thermocouple allowed in situ temperature profilerecording for each annealing run (e.g. Fig. 2-19a). Specimens that were left for periodslonger than 15 days to anneal were sealed under vacuum in quartz tubes and placed inheated silicone oil baths, rather than in the dynamic atmosphere quartz tube furnace. 2

2Only the 170 oC sample was annealed in a quartz tube. Thin film samples made by CVD and sputterdeposition were also annealed in quartz tubes. The surfaces of these specimens turned bright blue indicatingthe formation of a surface oxide on the 57Fe deposit of 10 nm thickness; for the thin film samples this affectedthe diffusion results, lowering them by approximately three orders of magnitude. For more details, please

47

Secondary Ion Mass Spectrometry (SIMS)

Depth profiling of as-annealed specimens was performed in a CAMECA IMS-5f dy-namic SIMS at the Materials Research Laboratory of the University of Illinois, Urbana-Champaign. Up to 12 specimens could be mounted in a spring-loaded holder simulta-neously to expose a flat face to the primary ion beam. 57Fe and 56Fe depth profiles wereestablished by using a 10keV O- primary beam. In addition to these two species, theinstrument was calibrated to detect any metallic impurity elements (mainly Si, Al, Ca,Mg) during each measurement. Only areas of the samples where the signal from theseimpurities was below the detection limit of 10 ppm were used for diffusion analysis.Anions such as sulfur and oxygen could not be simultaneously measured along withcations using the O- primary beam and we do not include an analysis of these speciesin this work. The 57Fe concentration [57Fe ] as a function of sputtering time was de-termined from the intensities I of the secondary positive ions 56Fe + and 57Fe + using2.4.1

[57Fe] =I(57Fe)

I(57Fe) + I(56Fe)(2.9)

Conversion of sputtering time to profile depth was achieved by measuring the depthof the SIMS craters using a Dektak profilometer and assuming a constant sputtering rate(Figs. 2-19b and c). The main factors contributing to error in depth profiling are surfaceroughness and sample tilt. Tilt can be seen clearly in Figure 2-19b with a distortion ofthe square SIMS profile. However, the sputter rate was found to be correlated withprimary beam current, which could only be controlled accurately to within ± 25 nAbut was displayed on the instrument for every run (Fig. 2-19d). An ordinary linearregression of the measured sputter rate on primary beam current was used to estimatea standard deviation for diffusion profiles that are subjected to such systematic errors.Diffusion profiles were fit to the error function solution in Eq. (2.12) using the CurveFitting application in MATLAB R2012b.

2.4.2 Results and Discussion

Fitting of diffusion profiles

Figure 2-20 compares the [57Fe ] diffusion profile of an un-annealed sample with theoriginal 57Fe deposit versus a typical profile of an annealed sample (275 oC, 5 minutes).The original SIMS spectra as a function of time for the annealed sample are inset in thefigure. The un-annealed profile contains a sharp interface between the original 57Fedeposit and the Fe1-xS crystal, located at 130 nm depth. After annealing, a [57Fe] tailfrom diffusion extends approximately 800 nm into the crystal. Nevertheless, even afterdiffusion annealing at 275 oC, a substantial proportion of the initial, pure 57Fe remainedon the Fe1-xS surface. This essentially acted as a semi-infinite source of isotopic ironin the limit of the relatively short annealing times used in this work. We can thereforeassume the concentration at the diffusion couple interface (i.e. at 130 nm depth) is fixedat c = co for the duration of the annealing run. The initial and boundary conditions arehence:

c(x , t = 0) = 0 (2.10)

and:

c(x = 0, t) = co (2.11)

refer to Appendix C. For the bulk, natural sample the thickness of the surface 57Fe deposit was too thick forthe formation of a surface tarnish oxide to affect the diffusion result.

48

150 200 250 3001

1.5

2

2.5

Sputter current (nA)

Sp

utt

er

rate

(n

m.s

-1)

0 100 200 300 400 500-7

-6

-5

-4

-3

-2

-1

0

1

x (µm)

z (µ

m)

100 µm

(a) Typical annealing cycle (b) SIMS crater for diffusion profile

(c) Depth profile of crater in (b) (d) Sputter rate linear regression

0 100 200 300 400 500100

150

200

250

300

350

400

Time (s)

Tem

pera

ture

(o C)

Heating transient

Cooling transient

Time at 95% of Tset

Figure 2-19: Sources of error considered in statistical analysis of diffusion data. (a) representative an-nealing profile. The time used for each measurement was total time within 5% of the setpoint. (b) opticalmicrograph of a tilted SIMS crater, indicating the position of the depth profile line scan in (c). (d) One wayto quantify the effects of sputtering error is to take the entire sample set and measure sputtering rate (=crater depth/sputter time). This should be linearly correlated with primary ion sputter power; the standarddeviation is used to estimate error in the depth of the diffusion profiles.

oAnnealed 275 C 5 min.

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Depth (nm)

[57 F

e]

0 500 100010

4

106

108

Time (s)

Inte

nsi

ty (

arb

. units

)

Original deposit 130 nm

56Fe

57Fe

SIMS depth profiles

Figure 2-20: Secondary ion mass spectrometry (SIMS) profiles. The interdiffusion of a 130 nm-thick 57Fedeposit on Fe1-xS crystals was measured by SIMS. The black curve shows the SIMS profile from an un-annealedsample, indicating the depth of the original deposit. Inset: raw SIMS data for a sample annealed for 5 minutesat 275 oC; converted in the main plot to 57Fe concentration vs. depth into the crystal (grey curve).

49

0 1000 2000 3000

0

0.2

0.4

0.6

0.8

1

Depth (nm)

[57F

e]

-0.020

0.02

-0.020

0.02R

esid

ua

ls

Measurementn

Error f fit

o225 C

13000 s

1800 s

Error function fits

Figure 2-21: Error function solution to diffusion profiles. The tail of each profile was fit to Eq. (2.12).Example fits for two samples annealed at 225 oC for approx. 1800 and 13000 s are shown.

Then it can be shown there exists an error function solution to Fick’s second law in theform [70]:

c(x , t) = co

1− er f

x4Dt)

(2.12)

The diffusion tails beyond the 130 nm original deposit were normalized to an initial,interfacial concentration co = 1 and fit using Eq. (2.12). Figure 2-21 shows an exampleof fitting two profiles from samples annealed at the same temperature of 225 oC butfor different times of 1.8 x 103 and 1.3 x 104 s. The sample annealed longer has a 57Feprofile that extends further into the sample, as expected. However, the measured *DFevalues from fitting were close: 4.6 and 3.4×10−13, respectively. Wherever possible, morethan one measurement at a single temperature was obtained to check for consistency.The best-fit error function solutions are overlaid on top of experimental data with arange of uncertainty in Figure 2-21.

Increased diffusion activation energy from spontaneous magnetization

Values of *DFe obtained from error function fitting are listed in Table 2.5 and plotted inArrhenius form on Figure 2-22, alongside representatitive literature data from Fryt etal. [31] and Condit et al. [40] (also shown in Figure 2-1). We include for comparisononly those data corresponding to the stoichiometry range of 0.03 ≤ x ≤ 0.1 in Fe1-xS,which is close to the composition of our samples analyzed via SIMS. Above∼ 300 oC, ourmeasurements are consistent with the previous results, corresponding to an activationenergy QP = 0.83 ± 0.03 eV, which represents the mean and standard deviation slopesobtained by regression fitting. From Figure 2-22, we also observe that below TN our*DFe values are considerably lower than the extrapolated Arrhenius trend with a slopeof −QP/kB. A deviation of this type beginning around 300 oC was previously observedby Condit et al., who postulated that vacancy ordering reduced the number of mobilevacancies by fixing Fe vacancies in equlibrium superlattice positions where they havelong residence times. Despite this observation, their experiments were not pursued tolow enough temperatures to confirm this hypothesis or to quantify the activation energyin the new regime. In this study, we also considered the possilibity that vacancy orderingmay produce the observed, anomalous behavior at T ≤ TN. By comparison, however,

50

Table 2.5: Iron self-diffusion *DFe measurement results for Fe1-xS crystals.

Temperature(oC)

Annealingtime (s)

*DFe (cm2s-1) Error in *DFe

(cm2s-1)

170 1976400 5.14 x 10-16 6.12 x 10-17

186 54000 9.24 x 10-15 3.25 x 10-15

202 72000 3.02 x 10-14 7.75 x 10-15

202 72000 4.99 x 10-14 7.43 x 10-15

205 5762 1.27 x 10-13 1.78 x 10-14

209 145800 3.33 x 10-14 3.96 x 10-15

225 1794 4.63 x 10-13 7.47 x 10-14

225 12900 3.40 x 10-13 4.37 x 10-14

249 3348 1.08 x 10-12 1.36 x 10-13

249 19830 2.22 x 10-12 2.71 x 10-13

251 573 8.39 x 10-13 4.00 x 10-16

288 116 7.56 x 10-12 6.06 x 10-13

298 449 8.77 x 10-12 1.52 x 10-12

326 596 1.89 x 10-11 2.98 x 10-12

350 86 1.53 x 10-10 6.56 x 10-11

352 410 1.76 x 10-10 3.29 x 10-11

376 94 2.87 x 10-10 4.57 x 10-11

377 276 1.54 x 10-10 3.16 x 10-11

403 98 5.19 x 10-10 8.60 x 10-11

oxides that undergo structural order-disorder transitions display large, discontinuousdrops in diffusivity, by up to several orders of magnitude, at the critical ordering tem-perature. [80] Conversely, the change in Arrhenius behavior of *DFe in Figure 2-22 iscontinuous and does not seem to be consistent with the expected effect of a first-orderstructural reorganization, and is more reminiscent of the so-called "magnetic diffusionanomaly" observed at the paramagnetic-ferromagnetic critical point or Curie tempera-ture TC in ferromagnetic materials. Self-diffusion [81–83] and solute diffusion [84,85]in Fe, interdiffusion in Fe-Ni alloys [86] and, to a lesser extent, diffusion in Co [83] alldisplay a deviation from the Arrhenius law extrapolated from the paramagnetic regionat TC, characterized by a sharp spike or disontinuity in the effective activation energyQeff given by:

Qe f f = −kBd(ln D(T ))

d(1/T )(2.13)

In other words, the magnetic transition has a second-order effect on D, manifested inan abrupt change in Arrhenius slope. Ruch et al. derived a theoretical model for themagnetic diffusion anomaly, based on a constant diffusivity prefactor Do and a mag-netic contribution to the activation energy for diffusion that varies with temperature asS(T )2, where S is the reduced magnetization relative to magnetization at zero Kelvin:S(T ) = M(T )/M(T = 0K). [87] Beginning with a generic formula for the temperaturedependence of the diffusion coefficient:

51

1.0 1.5 2.0 2.5

-11000/T (K )

Fe

2-1

log[*

D]

(cm

s)

700 500 400 300 200 150

ParamagneticQ = 0.83 eVP

Magnetic2Q = Q + αSM P

Fryt *

Condit **

This work

Literature

Model fit

Data

900-6

-8

-10

-12

-14

-16

oTemperature ( C)

Fe self-diffusion in Fe S below ordering temperature1-x

oT = 316 CN

(outlier)

Figure 2-22: Values for iron self-diffusion coefficient *DFe obtained in this work are compared to literaturedata from Fryt et al. [31] and Condit et al. [40]. The known magneto-structural ordering (Néel) temperatureTN of 316 oC is indicated with a dashed line. Above TN the activation energy slope in the paramagnetic stateis QP = 0.83±0.03 eV. However, our results below TN deviate below the extrapolated Arrhenius relationship.The data are fit using an activation energy QM for the spontaneously magnetized state that depends onreduced magnetization S as: QM =QP +αS(T )2. The outlying data point at 170 oC marked with an arrow isexcluded from the trendline fit. Literature data correspond to pyrrhotite stoichiometries close to the samplesused in tihs work (x in Fe1-xS ∼ 0.04) : * Fryt, x =0.04 [31]; ** Condit, average of data from 0.03≤ x ≤ 0.1.[40]

D = f gd2ΓvCv (2.14)

where f is a correlation function, g a geometrical factor depending on crystallography,and d the characteristic jump distance, Γv is defined as the frequency of diffusive hopsand Cv as the average vacancy concentration. Γv depends on S according to:

Γv = νe f f exp

−Eo

m + CS2

kB T

(2.15)

where νe f f is an effective attempt frequency, Eom is the migration energy in the para-

magnetic state, i.e. the difference in energy between an atom in an activated positionfor a diffusive hop and that of a adjacent atom in an equilibrium position, and C is aconstant. Cv is likewise given by:

Cv = exp

−Eo

f + (zJ/2)S2

kB T

(2.16)

where Eof is the formation energy of a vacancy in a paramagnetic crystal, z is the coor-

dination number and J the exchange coupling constant for magnetic spins. Defining:

α=C + 1

2 zJ

Qp(2.17)

then the generic diffusion coefficient in a magnetically ordered system can be written:

52

D(T ) = Do exp

−Qp(1+αS(T )2)

kB T

(2.18)

The *DFe data in Figure 2-22 are fit to Eq. (2.18) using the temperature variation ofthe (001)NiAs magnetic reflection in synthetic Fe7S8 obtained by Powell et al. [42] Thefactor α thus quantifies the magnetic ordering effect on the vacancy formation andmigration energies, leading to an effective ferromagnetic activation energy for diffusionQM = QP + αS(T )2. From our results we obtained a best fit of α = 0.41 ± 0.06. Inother words, the activation energy for diffusion at maximum magnetization (0 K) isapproximately 1.18-1.30 eV, as opposed to 0.83 eV in the paramagnetic crystal at hightemperatures. We assume here that the vacancy concentration remained fixed at theoriginal bulk value of CV = 0.04 during the annealing experiments. In other words,the effectively semi-infinite sample into which the Fe-57 exchanged remained at fixedstoichiometry. In this case, the increase in overall diffusion activation energy can beattributed solely to the magnetic influence on migration barrier, i.e. the constant C inEq. 2.17.

Nevertheless, it is worth adding a small comment regarding the reliability of ourresults as pure self-diffusivity measurments. Since pure Fe-57 was used as the tracerexchange material on top of the sulfide specimens, a small extent of chemical diffu-sion undoubtedly would have affected the measured diffusion profiles. The chemicalcontribution to diffusion arises from a small concentration gradient developing duringannealing, altering the stoichiometry in the topmost, interdiffused volume towards aFe:S ratio of 1:1. Such a chemical diffusion component would thus be expected to in-crease the diffusion rate and hence lead to a slight overestimate in self-diffusion values*DFe. We did not quantify the extent of chemical diffusion contribution directly in ouranalysis, but, judging by the overlap of our data with the literature values in Figure 2-22,it is likely to be small. Moreover, an unintended overestimate in *DFe does not changethe key observation of a magnetic diffusion anomaly, which leads to values considerablylower than the extrapolated, paramagnetic trend with temperature.

The implications of the magnetic diffusion anomaly in pyrrhotite are twofold. First,the growth conditions for Fe1-xS in solution both as a by-product of H2S corrosion oniron and steels in energy infrastructure, as well as intentionally via solvothermal or elec-trodeposition methods, are typically below 300 oC. Therefore any a priori prediction ofgrowth rates from a consideration of cation diffusion must account for the effect of spon-taneous magnetization, which reduces *DFe by up to 100x at 150 oC when comparedto a linear extrapolation of the Arrhenius slope from above the spontaneous orderingtemperature. The accuracy of predictive tools for H2S corrosion as well as more carefulcontrol of Fe1-xS nanocrystal synthesis both stand to benefit from these findings. Sec-ond, although Fe1-xS has long been studied for its interesting magnetic properties, to theauthors’ knowledge there is no example of a successful technological implementation ofthis material. Since the magnetic switching phenomena of interest in Fe1-xS involve thelocal, diffusive rearragement of vacancies, knowing the activation energy for Fe vacancymigration and formation in the magnetized state permits the development of simulationtools to design useful devices from this material, such as temperature- and/or electricfield-driven magnetic switching and memory applications.

2.4.3 Conclusions

In conclusion, 57Fe tracer diffusion measurements were performed to determine ironself-diffusivity *DFe in Fe1-xS as a function of temperature in the range 170-400 oC,which extends across the known magnetostructural order-disorder transition temper-ature TN= 315 oC. Our results for *DFe above TN agree well with measurements fromprevious studies in paramagnetic and structurally-disordered pyrrhotite, with an activa-

53

tion energy QP = 0.83 eV. However, below TN, iron self-diffusivity deviates downwardsfrom the extrapolated paramagnetic Arrhenius trend by approximately a factor of 10at 200 oC and 100 times at 150 oC. This can be rationalized by considering a magneticordering effect on Fe vacancy migration energy, which increases the overall diffusionactivation energy by up to 41% or to approximately 1.18-1.30 eV in the fully magneti-cally ordered state. To our best knowledge, this work constitutes the first description ofa magnetic diffusion anomaly in an ionic compound or a ferrimagnetic material. Morepracticallly, the knowledge of a magnetic contribution to diffusivity allows more ac-curate crystal growth rate predictions of ferrous sulfide barrier layers encountered inenergy systems containing H2S and other aggressive sulfidizing agents, as well as in thesolution-based synthesis of Fe1-xS where temperatures are below 315 oC.

2.5 Sulfur exchange kinetics at the Fe1-xS surface

The final section of this chapter addresses the kinetics of sulfur transfer from the gasphase into solid pyrrhotite. Aside from ionic diffusion through the sulfide corrosionproduct barrier, this reaction is known to be the other major rate-limiting mechanismfor sulfide corrosion on steels. [17, 36] For example, with H2S as the primary sulfur-bearing molecule, the net rate of sulfur transfer reaction can be represented by:

H2S(g)⇐⇒ H2(g) + S(in Fe1−x S) (2.19)

where the dissociation of adsorbed H2S(ad) or HS−(ad) at the sulfide surface is thoughtto be the rate limiting step. [37] The kinetics of this process at 600 oC have been in-vestigated using a resistance relaxation technique in sulfidized iron foils by Pareek etal. [88], who similarly looked at sulfur transfer in the other non-stoichiometric sulfidesCu2-xS [89] and Ag2+xS [90]. In this section, the results of an electrical conductivity re-laxation (ECR) study on Fe1-xS thin films inspired by those studies are described. How-ever, rather than focus on identifying rate-limiting steps and mechanisms, the primarymotivation here was to obtain a series of kinetic rates for sulfur transfer as a function oftemperature. Consistent with the theme of this chapter, the aim was to establish an ex-perimental value for the activation barrier of this process such that it can be comparedto the kinetics of diffusion.

2.5.1 Methods

Preparation and characterization of Fe1-xS thin films

Pyrrhotite thin films were sputter deposited in an AJA International ATC-1800 sputterdeposition system in the Microsystems Technology Laboratory (MTL) at MIT. The tar-get was 99.9% iron monosulfide (FeS) (Semiconductor Wafer, Inc., Taiwan). 1 x 1 cm2

soda lime glass pieces served as the substrates and 350 nm FeS was deposited at a rateof approximately 1 Å/s using an Ar plasma at 250 W power. Figure 2-23a shows thesurface and through-thickness morphology of a typical, as-sputtered film. Grain sizeswere on the order of 50-100 nm in plan view; however, the tilted view reveals grainsare columnar with lengths on the order of several hundreds of nm. To test the ther-mal stability of the film morphology, the same sample was imaged after annealing for4 hours under a dynamic, 0.001% H2S-H2 environment at 450 oC. All samples used inthis work were subjected to a four-hour post-anneal treatment under these conditionsafter sputtering to equilibrate the microstructure prior to ECR experiements. Althoughgrain boundaries became more clearly defined, there was no major coarsening or mor-phological change of the grain structure after four hours of post-anealing, and it can beassumed that under subsequent ECR conditions no further structural change occurredthat could have affected the measurements. Figure 2-23c shows a Cu-kα radiation XRD

54

300 nm

As sputtered film H S annealed 450 C2

20 30 40 50 602Θ

Inte

nsity

(arb

. units

)

(100)3

3

(110)

(102)(100) (102) (110)

(a) (b)

(c) (d)

6x10

2x10

XRD: texture in annealed film Pole figure scans

Figure 2-23: Sputter deposited thin films for ECR experiments. (a) scanning electron microscope (SEM)of as-sputtered film (inset: 60 o tilted view). (b) the microstructure coarsened slightly after annealing for 4hours under a dynamic H2S atmosphere; no additional changes were observed for further annealing up to12 hours. (c) conventional Cu-kα x-ray diffraction (XRD) scan revealed only two hexagonal Fe1-xS reflexes,as labelled. (d) pole figure XRD scans confirm the high (100) texture of the samples.

scan for such a post-annealed film. Only two peaks are visible that can be attributedto (100) and (110) in hexagonal pyrrhotite (ICSD reference 53528). Interestingly, the

102

peak, the predominant reflex from polycrystalline pyrrhotite was not observedin 2Θ XRD scans. Pole figure scans at fixed 2Θ corresponding to the three peaks (100),

102

and (110) are shown in Figure 2-23d, suggesting a high (100) texture. Similaroriented crystallite growth of pyrrhotite was observed by Birkholtz et al. during Fe-Ssputtering under reducing conditions. [91]

X-ray photoelectron spectroscopy (XPS) was performed on pre- and post-annealedFe1-xS films using Al-kα radiation at 1487 eV. Samples were cleaned by Ar+ sputteringat 500 eV in the ultra-high vacuum (UHV) chamber. The base pressure during XPSmeasurement was < 10-9 Torr. XPS spectra were obtained using a pass energy of 20eV at steps of 0.1 eV. Fitting of the Fe 2p32 spectra was performed according to theprocedure outlined by Pratt et al. [92], for pyrrhotite and based on calculations byGupta and Sen of theoretical core p levels multiplet structures to distinguish betweenFe2+and Fe3+in Fe2O3. [93, 94] The S 2p spectra were fitted by assuming monosulfide(S2−), disulfide (S2−

2 ) and polysulfide (S2−n ). [92]

Electrical Conductivity Relaxation (ECR)

A custom-built ECR setup was made using a Thermo Scientific TF55030A-1 tube fur-nace. A schematic of the experimental apparatus is shown in Figure 2-24. A bufferedH2/H2S gas mixture was flown through a 40 cm-long quartz furnace at predeteriminedflow rates up to 500 sccm, controlled by Omega FVL-Series mass flow controllers. Thepure gases used were of 5% H2-balance N2 and either 100 ppm H2S-balance He or 4%

55

Pt contact wires

Schematic of ECR apparatus

Al O stage2 3

Fe S sample1-x

Figure 2-24: Electrical conductivity relaxation apparatus setup. Schematic of experimental setup for elec-trical conductivity relaxation (ECR) experiements. The inset picture of the sample stage shows platinum wirescrew contacts on a 1 x 1 cm2, sputtered Fe1-xS thin film sample.

H2S-balance N2, depending on the desired partial pressure. A four-way valve at the gasinlet for the furnace tube allowed the atmosphere in the hot zone of the furnace to beswitched rapidly between two different gas mixtures and hence partial pressures of sul-fur. The flush time of the reactor (i.e. time to fully replace the atmosphere with a newmixture) was on the order of 30 s. In the following sections, conductivity relaxation re-sults are presented where the experimental timescale is 102-103 s. We therefore deemthe reactor flush time negligible in the analysis of our results. The Fe1-xS samples sup-ported on glass were contacted directly with spring-like platinum wires in a four-probeformat (Fig. 2-24, inset). Each Pt contact was maintaned on the sample by compressingit with stainless steel screws. 3

The contacts were connected via Pt wires to four stainless steel gas/electrical feedthroughswhich in turn were connected to a Keithley 2400 source meter for automated 4-probeelectrical conductivity measurement. The source meter was controlled by a custom-designed LabView program written by Qiyang Lu (MIT) and run from a standard lap-top PC. The program initiated and recorded in situ conductivity measurements of theFe1-xS samples at intervals of 1-20 s. We do not provide conductivity measurements inthis work since we did not perform average four-probe (van der Pauw) electrical mea-surements between all the electrodes. Instead we kept the current-sourcing wires fixed;even though the conductance was thus sensitive to the placing of electrodes, measuringthe relative change in conductance was adequate for these kinetic experiments.

Control of sulfur partial pressure

Atmospheres of fixed sulfur partial pressure were established in the apparatus by mixingH2/H2S gases, as described above. The equilibrium relation H2S(g) ⇐⇒ H2(g) +

12 S2(g)

was assumed, for which the equilibrium constant can be written:

Kp(T ) =pH2

pS122

pH2S(2.20)

The experimental values of Kp(T) as determined by Yuan and Kröger [95], Pitzer[96] and Fryt et al. [31]were compared and found to be consistent within a few percent

3Additional, e-beam deposited contact pads of 200 nm Au or Pt with an adhesion layer of 10 nm Cr on thesamples were also tried; these facilitated the establishment of good electrical contact initially, but were foundto be unstable at elevated temperatures of > 350 oC and delaminated. The high conductivity of pyrrhotiteitself allowed the formation of decent electrical contacts simply by touching the compressed Pt springs to thesample surface.

56

Table 2.6: Kp (T) values used to calculate sulfur partial pressure.

Author Expression Ref.

Yuan and Kröger log Kp(T ) = −4570

T + 2.35[95]

Pitzer ln Kp(T ) = −10806

T − 5.87[96]

Fryt et al. ln Kp(T ) = −

90249−50.08×TRT

[31]

Liquid

FeS2

bccFe

fccFe

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1-1000/T (K )

Fe S7 8

-12

-8

-4

0

4

log

(f

/ba

r)S

2

1000 800 600 500 400 300

oTemperature ( C)

Fe S1-x 10% H S21% H S2

0.1% H S20.01% H S20.001% H S2

Thermodynamic stability range of pyrrhotite

Figure 2-25: Temperature-pressure equilibrium phase diagram for Fe-S. Isomolar H2S lines are superim-posed to show the range of gas mixtures that could be used while maintaining Fe1-xS stability.

in the temperature range of interest 300-600 oC (Table 2.6). The mean value given bythese three literature sources was used to set the sulfur partial pressures used in ECRexperiments.

The stability range of pyrrhotite limited the range of sulfur partial pressures thatcould be used in ECR experiments and had to be carefully controlled to not reduce thesamples to pure Fe, or conversely oxidize them to FeS2. The T-pS2

phase diagram in Fig.2-25 shows the stability range of Fe1-xS along with the predicted pS2

trends for differentH2/H2S gas mixtures containing between 0.001-10% H2S.

2.5.2 Results and Discussion

In this section, we review the defect chemistry that allows electrical conductivity relax-ation measurements to be made in Fe1-xS, by rapidly changing the partial pressure ofsulfur in the atmosphere and allowing the sample to equilibrate over time to a new sul-fur activity. Experimental, kinetic measurements for oxidation and reduction of Fe1-xSby sulfur as a function of temperature are presented. Although the influence of sul-fur chemical potential difference ∆µS remained unclear, the temperature activation ofboth oxidation and reduction was evident from the results. Finally, some of the incon-

57

sistencies and inaccuracies in the current ECR experiments on thin films are discussed-including surface contamination, thermal history and lack of precise control over gascomposition.

Mechanism of electrical conductivity relaxation in Fe1-xS

Besides the work already mentioned on dignetite Cu2-xS [89] and silver sulfide Ag2+xS,the vast majority of ECR studies investigated mixed ionic-electronic conduction in ox-ides. [97–103] Briefly, the technique can be described as follows: the electrical con-ductivity of the sample to be studied must have a dependence on the degree of off-stoichiometry. Moreover, the intended sample must be appropriately thin such thatdiffusional processes are very rapid in the temperature range of interest compared tomolecular dissociation and incorporation of the active species at the surface. When theseconditions are met, a sudden change in partial pressure of the reactive anion-bearingmolecule in the atmosphere (H2S in this case) will cause the sample to equilibrate overtime with the gas, and the change in conductivity during this process can be measuredcontinuously in situ to determine the kinetics of the anion transfer process.

We can assume linear surface exchange kinetics to give the mass conversion law[98,99]:

∂ cS(t)∂ t

= −AV

.k [cS(t)− cS(∞)] (2.21)

where A and V are the surface area and volume of the film, respectively; k is the surfaceexchange coefficient; cS(t) is the sulfur concentration at time t and cS(∞) the sulfurconcentration at the new equilibrium. Eq. (2.21) can be integrated to yield:

cS(t)− cS(0)cS(∞)− cS(0)

= 1− exp

−tτ

(2.22)

with:

τ=lk

(2.23)

where l is the thickness of the sample.For Fe1-xS we assume the only ionic defects to be iron vacancies VFe . For different

sulfur valence states m = 2-8, the charge transfer process of interest can be written:

H2S(g) +me−⇔ Sm−(ad) +H2(g) (2.24)

Sm−(ad)⇔ S(ad) +me− (2.25)

Adopting Kröger-Vink notation for defect equilibria, the adsorbed sulfur atom isincorporated into a lattice site by the formation of a charged Fe vacancy.

S(ad)⇔ SS + VFe (2.26)

VFe + 2e′⇔ V

′′

Fe (2.27)

The conduction mechanism in iron sulfides has been proposed to involve hole hop-ping in a band of predominantly d character, requiring holes to be generated by the pres-ence of Fe3+ ions. [52] Figure 2-26a shows the Fe 2p3/2 XPS spectrum of a pyrrhotitesample in the H2S post-annealed condition which reveals a substantial proportion (upto 40%) of ferric ions in the near-surface. The S 2p peak for the same sample is il-lustrated in Table 2-26b, revealing a majority of monosulfide S2−. Figure 2-26c and d

58

2+Fe

3+Fe

2-S

2- 2-S , S2 n

Inte

nsity

(arb

. units)

Binding Energy (eV)716 712 708 704

Binding Energy (eV)170 166 162 158

725 715 705B.E. (eV)

Data

Fit

275285295

526530534538Binding Energy (eV)

Fe 2p photoemission S 2p C 1s

O 1s

As sputtered

Annealed

As sputtered

Annealed

(a) (b) (c)

(d)

Figure 2-26: X-ray photoelectron spectroscopy (XPS) from a Fe1-xS thin film sample. (a) Fe 2p spectrum,deconvoluted into Fe2+ and Fe3+ according to [92]. (b) S 2p spectrum indicating an almost entirely S2−

binding environment. (c) and (d) show the reduction in carbon and oxygen contamination, respectively,after annealing the films under an H2S atmosphere prior to ECR experimentation.

Table 2.7: Deconvolution of Fe 2p and S 2p x-ray photoelectron spectroscopy (XPS) peaks.

Peak Chemical State Binding Energy(eV)

FWHM(eV)

Area (%)

Fe 2p3/2 Fe(II)-S 706.5 1.4 10.9

Fe(II)-S* 707.4 1.8 31.6

Fe(II)-S 708.3 1.4 12.7

Fe(II)-S sattelite 713.3 2.7 4.9

Fe(III)-S 709.2 1.5 18.8

Fe(III)-S* 710.3 1.5 11.4

Fe(III)-S 711.3 1.5 5.6

Fe(III)-S 712.3 1.5 4.2

S 2p Monosulfide 2p3/2 161.2 1.2 85.2

Monosulfide 2p1/2 162.3 1.2 -

Disulfide 2p3/2 162.4 1.6 6.0

Disulfide 2p1/2 163.6 1.6 -

Polysulfide 2p3/2 162.9 2.0 8.8

Polysulfide 2p1/2 164.1 2.0 -

confirm that the carbon and oxygen content of the films, respectively, is reduced sub-stantially by annealing in an H2S atmosphere and that these likely do not contribute tothe existence of ferric ions in the lattice (e.g. as Fe2O3 ). The fitting parameters for theFe 2p3/2 and S 2p1/2 peak deconvolution are shown in Figure 2.7. The photoemissionspectra taken together therefore indicate the presence of Fe3+ and substantiate a con-duction mechanism that would involve hole hopping on ferric ion sites. A conductionmechanism of this kind is also observed at high temperatures in metallic conductingoxides such as Nd2NiO4, with itinerant electrons in the conduction band. [104]

Assuming a conduction mechanism of this type, where semi-mobile holes hop fromFe3+ to Fe3+ ion sites, a net charge neutrality condition can be written:

59

2

V′′

Fe

≈ p∝ n−1∝ a−1e (2.28)

where p and n are the positive and negative charge carrier concentrations, respectively,and ae is the chemical potential of electrons. The concentration of Fe ions cFe in a molarvolume Vm of Fe1-xS is:

cFe(t) = 1− cS(t) =1− x(t)

Vm(2.29)

Therefore:

p =1

Vm− cFe(t) (2.30)

Electrical conductivity se in a p-type dominated conductor is given by:

se = pµhF (2.31)

where µh is hole mobility, which we assume to be constant during isothermal ECR ex-periments. From Eqs. (2.29), (2.30) and (2.31) therefore, we can write the normalizedconductivity g(t) during the measurements in terms of he concentration of sulfur in thefilm:

g(t) =se(t)− se(0)

se(∞)− se(0)=

cS(t)− cS(0)cS(∞)− cS(0)

(2.32)

With reference to Eq. (2.22), the normalized conductivity of a sample undergoing achange in sulfur activity to a new equilibrium is expected to follow a single exponentialdecay of the form:

g(t) = 1− exp

−tτ

(2.33)

Figure 2-27 illustrates the change of resistance of a Fe1-xS sample subjected to threeconsecutive changes in gas concentration from 5-10% H2S (balance H2), followed by10-15% H2S and finally 15-20% H2S at 565 oC. The resistance fell in an exponential-like manner each time the atmosphere is enriched in sulfur and the sample incorporatesmore S atoms, accommodated by an increased

V′′

Fe

and hence mobile hole concen-tration. In the following section, as-recorded resistance was converted to normalizedconductivity g(t) and fitted to an exponential function following Eq. (2.33).

Temperature-dependence of sulfur exchange kinetics

The full results of the ECR experiments are listed in Tables 2.8 (oxidation) and 2.9 (re-duction). For each experiment, the sulfur partial pressure was changed from an initialvalue pS2,i to a final value pS2, f as indicated. pS2

values were calculated from the equi-librium constants in Table 2.6. The normalized conductivity data for each were fit to asingle exponential function (Eq. (2.33)) and the chemical exchange coefficient kox foroxidation relaxation curves and kred for corresponding reduction were derived from thebest fit values of τ. Representative conductivity relaxation curves at a range of temper-atures are given in Figures 2-28a and b. The decent exponential fits to the data (Figs.2-28a and c) confirm that a single activation process is limiting the relaxation of conduc-tivity. For a film thickness d = 350 nm and the *DFe results in Figure 2-1 of this chapter,typical diffusion timescales tdiff can be estimated using tdi f f ∼ d2/(4DFe). For the low-est temperature used in the ECR experiments of 390 oC (*DFe ≈ 10-10cm2s-1), tdiff ∼ 3s. Diffusion should therefore be on the order of 1000x faster than the observed relax-ation process, implying that the observed exponential decay should arise from surfaceexchange processes alone.

60

Table 2.8: Electrical conductivity relaxation results for oxidation experiments: initial (pS2 ,i) and final(pS2 ,i) sulfur partial pressure values; surface exchange coefficient kox from exponential fits. These data areplotted for clearer comparison in Figure 2-28.

T (oC) log pS2 ,i (atm) log pS2 , f (atm) kox (x 10-9 cm/s)

390 -14.6 -13.2 16.5

390 -14.6 -12.6 23.9

390 -14.6 -12.6 7.34

390 -13.2 -11.8 5.75

400 -18.0 -17.0 14.4

400 -18.0 -17.0 19.6

400 -19.0 -17.0 24.9

430 -17.0 -16.0 9.86

450 -16.0 -14.0 14.6

450 -17.0 -16.0 62.2

480 -16.7 -14.7 55.1

490 -11.4 -10.2 164

510 -11.4 -10.2 194

513 -11.0 -10.1 94.7

520 -10.9 -9.8 120

520 -16.0 -14.0 314

520 -16.0 -14.0 124

520 -16.0 -14.0 300

565 -8.7 -8.1 670

567 -10.3 -9.1 832

Table 2.9: Electrical conductivity relaxation results for reduction experiments: initial (pS2 ,i) and final(pS2 ,i) sulfur partial pressure values; surface exchange coefficient kred from exponential fits. These data areplotted for clearer comparison in Figure 2-28.

T (oC) log pS2 ,i (atm) log pS2 , f (atm) kred(x 10-9 cm/s)

400 -17.0 -18.0 23.2

400 -17.0 -18.0 22.0

400 -17.0 -18.0 28.6

513 -10.1 -11.0 63.3

520 -14.0 -16.0 76.8

520 -14.0 -16.0 118

520 -14.0 -16.0 115

565 -8.6 -9.1 418

565 -9.1 -10.3 350

61

Time (s)

Re

sist

an

ce (Ω

)

0 500 1000 1500 200010

10.5

11

11.5

5

10

15

20

5-10% H S2

10-15% H S2

15-20% H S2

% H

S in

mix

2

oElectrical resistance relaxation at 565 C

Figure 2-27: Electrical resistance relaxation at 565 oC upon three successive changes in H2S-H2 gas mixturein the furnace atmosphere, as indicated.

The clearest observation from the tabulated results is an overall trend of increas-ing k towards higher temperatures, seen more clearly when the data are presentedgraphically in Figures 2-28a and b. Ignoring for now the dependence on sulfur partialpressure, we use this trend to determine an average activation energy for the surfacechemical exchange process Echem of 1.05 ± 0.20 eV for oxidation and 0.79 ± 0.23 eVfor reduction.

The relaxation time should also, in theory, be affected by a chemical driving force, ashas been shown in studies of bulk oxides. [98,99] This can be defined as the differencein the equilibrium chemical potentials of sulfur∆µS in the sample in the inital and finalstates. Assuming the ideal gas law and zero activity constant:

∆µS =RT2

ln

pS2,i

pS2, f

(2.34)

Tables 2.8 and 2.9 also list the initial and final sulfur partial pressures used in eachexperiment. There is no definitive correlation between relaxation time and partial pres-sures in our data. The uncertainty in each reading is evident by comparing experimentsperformed at constant temperature. For example, in Table 2.8 the 390 oC measurementsinclude two results obtained with log

pS2,i

= −14.6 and log

pS2, f

= −12.6, yieldingtwo disparate values of kox = 23.9×10−9 and 7.34×10−9 cm/s. The other two resultsfor oxidation at 390 oC were taken using different values of pS2,i and pS2, f ; however,the resulting values of kox fall between 23.9×10−9 and 7.34×10−9cm/s. No conclusiveverdict can be reached on the influence of ∆µS from these data. The same is true forother readings obtained at constant temperature.

In the following section, some of the inaccuracies that may contribute to this un-certainty are discussed in more detail. The ECR technique for pyrrhotite thin films asdescribed here is judged to be reasonable for obtaining the broad temperature depen-dence of the oxidation and reduction processes. However, in their present form thekinetic measurements are too variable and ambiguous to reveal more intricate informa-

62

1.1 1.2 1.3 1.4 1.5 1.6-1

1000/T (K )

-1ln

(k)

(cm

.s)

-14

-15

-16

-17

-18

-19

375400450500550600

oTemperature ( C)

Linear regression95 % C.I.

0

0.2

0.4

0.6

0.8

1

No

rma

lize

d c

on

du

ctiv

ity

0 2000 4000 60000

0.2

0.4

0.6

0.8

1

Time (s)

No

rma

lize

d c

on

du

ctiv

ity

0 2000 4000 6000

Time (s)

1.1 1.2 1.3 1.4 1.5 1.6-11000/T (K )

-1ln

(k)

(cm

.s)

-14

-15

-16

-17

-18

-19

375400450500550600

oTemperature ( C)

Linear regression95 % C.I.

o390 C

o400 C o

480 C o520 C o565 C

Fit:σ = 1 - exp[-t/τ ]ox.

o400 C o

520 C o

565 C

Fit:σ = 1 - exp[-t/τ ]red.

E = 1.05 ± 0.20 eVa, ox

E = 0.79 ± 0.23 eVa, red

(a) Normalized conductivity: oxidation (c) Exchange coefficient: oxidation

(b) Normalized conductivity: reduction (d) Exchange coefficient: reduction

2 ΔP = 10 atmS 2

1 ΔP = 10 atmS 2

2 ΔP = 10 atmS 2

1 ΔP = 10 atmS 2

Figure 2-28: Electrical conductivity relaxation results: (a) representative oxidation relaxation curves (datapoints) obtained at different temperatures with best fit exponentials (solid lines). (b) representative reductionrelaxation curves. Chemical exchange coefficients for (c) oxidative sulfur transfer from H2S to Fe1-xS and (d)the reverse reductive transfer into the gas phase: individual data and best-fit Arrhenius line with 95 "%"confidence interval. k values corresponding to the individual curves shown in (a) and (b) are demarcatedwith arrows.

tion over secondary effects such as that of the chemical driving force.

Measurement consistency and surface degradation

The inconsistencies in our ECR results, even among results obtained under identicalconditions as discussed above, underscore the high sensitivity of sulfur exchange re-action to the condition of the sample surface. In Figures 2-29a and b, two sets of insitu resistance measurements are shown that were obtained at 520 oC and 400 oC overthe course of several hours each. Several oxidation/reduction cycles were performedby switching the sulfur partial pressures between two consistent values as shown andallowing the sample to equilibrate each time. At first glance, the redox cycling looksfairly repeatable with little hysteresis, despite a constant upwards drift on the order of

63

50-60 S/hour.

However, in Figure 2-29c we plot some other results obtained at 400 oC on anothersample. This time the conductivity is normalized to the equilibrium conductivity at thestart of each cycle. revealing a consistent attenuation with successive cycles that is sug-gestive of a history-dependent surface degradation process. For example, the percentagechange in conductance during the first oxidation step "O1" is approximately 1.7%, butis reduced to only 0.6% for the subsequent reduction step "R1" performed after "O1".By the fifth cycle "O5", the conductance relaxation has reduced to only 0.4%.

The gradual degradation in the results after repeated cycling on a single samplerules out sample-to-sample differences to be responsible for the variation in measuredk values; all samples were fabricated and pre-annealed identically. The reason is morelikely to be related to a degradation in the condition of the sample surfaces with time.Scanning electron microscopy investigations of the Fe1-xS samples after different stagesof experiment revealed the columnar film morphology and grain size to be stable athigh temperature over the course of 12 hours. Moreover, an XPS investigation of a sam-ple subjected to a typical ECR experiment did not expose any atypical surface chem-istry, such as increased carbon, oxygen, or other foreign elements. On the contrary, thecarbon and oxygen content of the films was decreased by post-annealing in an H2S at-mosphere after deposition (Fig. 2-26) and subsequently remained stable during furtherECR experiments. Surface contamination can thus be ruled out as an explanation forthe degradation. The as-deposited Fe1-xS films used in this work had a roughness on theorder of 10-20 nm; prolonged annelealing did not measurably change the roughness.

The instability and lack of repeatability observed in these sulfide ECR experimentsare common also in similar work with oxide samples, particularly where thin filmsand/or carefully engineered surface chemistry or nanostructuring is involved. [101] Forexample, Wang et al. observed the oxygen exchange surface kinetics on La0.6Sr0.4Fe0.8Co0.2O3(LSFCO) to degrade after annealing at 900 oC. Here also, no changes in surface chem-istry were detected by XPS that could provide an explanation for the degradation in oxy-gen transfer properties. Conversely, Chen et al. found in another study using epitaxiallanthanum strontium cobalt oxide (LSCO) that the oxygen exchange activity increasedsubstantially after annealing. They attributed this to a roughening of the surface, whichintroduced surface steps and edges. [105] The surface exchange process for Fe1-xS in-volves a sulfur atom taking a vacant anion site on the surface; grain boundaries andsurface steps/edges are known to be catalytically active sites for dissociative adsorp-tion. More work is needed to undersand the high sensitivity of ECR experiments to thesurface condition, leading to inconsistent results.

2.5.3 Conclusions

ECR was used to monitor the sulfur surface exchange kinetics for Fe1-xS thin film sam-ples subjected to changes in sulfur partial pressure in buffered H2S/H2gas mixtures.Results can be fit to a single exponential curve, confirming that surface exchange is thesole rate-limiting process. A clear temperature dependence of the exchange coefficientk allowed us to determine the activation barrier Echem to sulfur exchange of 1.05 ± 0.20eV for oxidation and 0.79 ± 0.23 eV for reduction. However, the technique is not sen-sitive enough to determine the secondary effect of chemical driving force on exchangekinetics. Moreover, the measurements are history-dependent: multiple redox cyclingleads to an attenuation in the relative resistance change upon subsequent oxidationor reduction steps. There is no clear explanation for this based on changes in surfacemorphology or chemistry, and more work must be done to understand the influence ofsurface state on kinetics in more detail.

64

13.2

13.8

16.2

16.3

16.4

16.5

Conduct

ance

(x

100 S

)

0 0.5 1 1.5 2 2.5 3 3.5

Time (104s)

< 1% change

~ 4%change

Ox.

Red.

o400 C

(b)

(a)

0 2000 4000 6000 80000.98

0.99

1

1.01

1.02

Time (s)

Norm

aliz

ed c

onductivity σ

t/σo

O1

O2O3O4

R1

R2R3

Ox.

Red.

1 hour

60 S

o520 C

0 0.5 1 1.5 2 2.5 3 3.5

Time (104s)

Inconsistencies in ECR measurements

Conduct

ance

(x

100 S

)

13.4

13.6

13.0

14.0

Figure 2-29: Drift, stability and repeatability of ECR experiments. (a) conductance measurement for day-long repeated oxidation and reduction cycles at 520 oC. The global drift is on the order of 60 S/hour. Thereare also points at which conductance is unstable and jumps suddenly. (b) repeated redox cycling at 400 oC.The timescale for individual relaxations is longer than for measurements at 520 oC. (c) repeated oxidation(O1-O4) and reduction (R1-R3) cycles on a different sample at 400 oC. Relative conductivity is obtainedby normalizing results by the equilibrium conductance at the beginning of each cycle; we see a gradualdegradation in the magnitude of the overall change after the first oxidation cycle O1.

2.6 Outcomes

2.6.1 Conclusions

The primary aim of the work described in this chapter was to compare activation bar-riers Ea and kinetic rates of the unit processes of cation diffusion (bulk) and exchangeof sulfur (surface) in Fe1-xS. The experimentally-determined values of Ea are listed inTable 2.10. Since the two processes have a similar temperature dependence, there is

65

1

10

100

1000 -2.5-2

-1.5-1

-0.5

10-10

10-5

100

1000/T (K- 1)

Film Thickness(μm)

-1E

qu

ilib

ratio

n c

on

st.

(s

)

Faster

Slower

Surface limited

Surface limited

Mixed

Diffusionlimited

Surface exchange slower at all temperatures until film is 1000 μm thick

Fe diffusionS exchange

Figure 2-30: Temperature- and film thickness dependence of rate limiting steps. The "equilibration con-stant" τeq for both processes, as a measure of the kinetic rate, is plotted as a function of both temperature andalso film thickness x. As the film gets thicker from 1 to 1000 µm, the overall rate of both processes becomesslower. However, since the diffusion rate decreases parabolically with x, a crossover from surface exchangelimited growth to diffusion limited growth would be expected at around x = 100-1000 µm.

no clear transition temperature above which one would be expected to dominate overthe other in controlling the rate of sulfidation of iron. However, we can take an ana-lytical approach to understanding rate-limiiting regimes by considering the "equilibra-tion constant" τeq for each process. This can be thought of as the characteristic timeconstant for the given process to occur, assuming an exponential rate R of the formR(t) = Ro exp [−t/τeq]. For diffusion, we can write τeq = 4D/x2, whereas for surfaceexchange, τeq = kex/x . In Figure 2-30 we plot the equlibration constant for differentfilm thicknesses of 1, 10, 100 and 1000 µm. It can be seen that for 1- and 10 µm-thickfilms, surface exchange as determined experiementally using ECR is a slower kineticprocess (smaller τeq), irrespective of the temperature. However, due to the parabolicdependence of diffusion on film thickness, above 100 µm, the rates become approxi-mately similar, and a crossover would be expected from surface control to bulk diffusioncontrol in the rate of pyrrhotite growth on iron. Moreover, these basic kinetic rate pa-rameters can be fed into the global kMC and phase field model as described in Chapter1.

The secondary aim was to understand the influence of the critical magneto-structuralorder-disorder transition temperature TN = 315 oC on Fe diffusion in pyrrhotite. Thiswas studied by two different techniques: first through in situ magnetization measure-ments of the diffusion-driven, λmagnetic transition and second through tracer diffusionstudies using SIMS. Both studies converged on approximately the same Ea in magneticpyrrhotite below TN, which is up to 40% higher than that for non-magnetic pyrrhotite(Table 2.10). Besides clarifying the effect of TN on diffusion, the results are more prac-tically important in estimating rates of degradation where pyrrhotite forms a passivelayer. For example, assuming a simple extrapolation of the paramagnetic Arrhenius law

66

down to 150 oC would overestimate real diffusivities by up to two orders of magnitude.

2.6.2 Future work

The self-diffusivity of iron was measured here under dry, gaseous conditions in solid(non-porous) samples. However, real corrosion scales in aqueous conditions could be-have markedly differently from this idealized case. It would be of interest to confirm*DFe values at temperatures below 300 oC, but under in situ, aqueous conditions. High-temperature sulfidation and/or corrosion experiments in the range 100-300 oC are re-quired to confirm empirically the rates of both diffusion and surface reaction found hereon pure, dense samples. Such studies are also crucial to validating and improving thebottom-up passive film mode that serves as the overarching goal of this work.

More work must be done to explain the sensitivity of the ECR technique to surface con-ditions, and to determine whether fundamentally accurate kinetic rates are measurablevia this method. This would involve repeated oxidation/reduction, with careful surfaceanalysis using XPS and AFM/STM imaging to understand any surface changes that mayalter the kinetics.

67

Table 2.10: Key activation energies for pyrrhotite growth.

Process T range (oC) Technique Ea (eV)

Fe diffusion 315-700 Literature 0.83 ± 0.03

Fe diffusion 185-315 SIMS 0.83 + αS(T )2 1

Fe diffusion 180-210 Magnetokinetics 1.10 ± 0.10

Surf. Exch. (ox.) 350-600 ECR 1.05 ± 0.20

Surf. Exch. (red.) 350-600 ECR 0.79 ± 0.231 α = 0.41 ±0.06 and S(T ) is the reduced magnetization (= 0 at 0 K).

68

Chapter 3

Reactivity: quantification ofelectronic band gap and surfacestates on FeS2(100)

Synopsis The scanning tunneling microscope (STM) is used to investigate the surfaceelectronic structure of pyrite, FeS2, as a model, semiconducting passive layer phase.The STM allows us to probe controllably the energy levels of FeS2and quantitativelyevaluate the surface electronic features which affect its charge transfer characteristics,with respect to a redox species in the environment such as H2S. The interfacial elec-tronic properties of pyrite are greatly influenced by the presence of electronic states atthe crystal free surface. Scanning tunneling spectroscopy (STS) results are interpretedusing tunneling current simulations informed by density functional theory (DFT). In-trinsic, dangling bond surface states located at the band edges reduce the fundamentalband gap Eg from 0.95 eV in bulk FeS2 to 0.4 ± 0.1 eV at the surface. Extrinsic sur-face states from sulfur and iron defects contribute to Fermi level pinning but, due totheir relatively low density of states, no detectable tunneling current was measured atenergies within the intrinsic surface Eg. These findings help elucidate the nature of en-ergy alignment for electron transfer processes at pyrite surfaces, which are relevant toevaluation of electrochemical processes including corrosion. Finally, the broader util-ity of the methodology developed in this work for reliably interpreting STS results isdiscussed. This includes determining the fundamental surface energy band gap for lesscommonly-studied semiconductors for use in earth-abundant photovoltaics and otherapplications. Portions of this chapter were published in Surface Science. [106] All DFTcalculations in this work were performed by Aravind Krishnamoorthy.

3.1 Background and motivation

At the end of Chapter 3 of this thesis, the kinetics of charge transfer between gaseousH2S and pyrrhotite (Fe1-xS) were investigated experimentally by measuring the electri-cal response of a sample to changes in sulfur chemical potential. This electrochemicalprocess, a necessary step for the incorporation of sulfur from the environment into agrowing iron sulfide passive layer, can be summarized by the cathodic half-reactions:H2S(g)⇔ S2−+2H+ and 2H++e−⇔ H2(g) where the electrons are transferred from theiron sulfide barrier layer to reduce hydrogen sulfide. The electrical conductivity relax-ation experiments in Chapter 3 give a practical, macroscopic measure of reaction ratesthat can be used to predict average rates of sulfur transfer. However, they do not pro-vide any mechanistic insight into the physics of interfacial electron exchange between

69

the solid film and molecular redox species.

Chapter goals

In this chapter, we aim to investigate surface reaction in more detail by asking thequestion: how do the electronic properties at the surface of an ionic solid affect thepropensity for charge transfer in an electrochemical system? Instead of pyrrhotite, weinvestigate the surface of pyrite (FeS2) as a model, semiconducting passive film material.FeS2 was chosen because of its broader interest to the electrochemical community:other applications including photovoltaics and battery anodes are discussed briefly inSections 3.1.4 and 3.4.2. Open questions over the surface electronic structure of pyritefrom the literature partly motivated this work, and the existing amount of data helpedbenchmark our experimental and computational results.

The key questions addressed in this chaper are summarized as: (1) can the sur-face band gap of FeS2 (and by extension, other similar semiconducting materials) bequantified a priori using STS? (2) how do both intrinsic and extrinsic surface states onFeS2(100), as a model passive layer material, affect charge transfer in electrochemicalsystems?

3.1.1 Electrochemical charge transfer in semiconductor-absorbatesystems

The theory of charge transfer during surface reactions between solid, semiconductingmaterials and molecular adsorbates in corrosion systems is covered in the book Cor-rosion mechanisms in theory & practice by Marcus et al.. [3] The key points are sum-marized here to contextualize the remaining work in this chapter. Complex, coupledelectrochemical systems such as a metal-passive layer-electrolyte structure can be re-duced to a connected set of energy levels. Under an applied bias (electrode potential),it is the transfer of electrons across these energy levels which determines the overallreaction current and therefore rate of metal oxidation during corrosion. Let us imaginea basic system comprising the three interconnected components of a metal, a passivelayer, and an electrolyte containing a molecular species which can assume a reduced oroxidized state:

Metal: (e.g. Fe in steel) has a high concentration of mobile charge carriers, typicallyO(1023cm-3).

Passive layer: typically semiconducting or insulating, we represent the passive layerwith a conduction band, valence band and Fermi level dependent on level of dop-ing. The volume fraction of defects is typically very high for in situ formed passivelayers, with high concentrations of intrinsic (point) defects and extrinsic defects(substitutional elements). [32] Charge carrier concentrations are commonly inthe range 1015-1019 cm-3.

Redox couple: a molecule in the electrolyte that reacts with the passive layer can berepresented electronically by occupied and unoccupied levels, corresponding tothe reduced and oxidized components of the redox system, respectively. Each levelis depicted as a Gaussian distribution of states, accounting for the uncertainty inrearrangement energy for the solvation shell around the molecule during a reac-tion. L represents the energy required to reorganize the shell of H2O moleculessurrounding a redox species after charge exchange (see Fig. 3-1). The charge con-centration of the redox couple is related to the concentration of ions in solution.For example, a 1 M solution contains 2NA× 10−3 ≈ 1021 ions.cm-3.

70

We assume that the Fermi levels of each component in the system align at equi-librium. An additional, applied electrochemical potential biases the energy levels de-pending on the activity of reduced and oxidized species in the electrolyte, aRed and aOx,respectively:

Ered = EΘred −RTzF

lnaRed

aOx(3.1)

where Ered is the half-cell reduction potential at a temperature T, EΘred is the standardreduction potential, R is the universal gas constant, z is the charge transferred per re-action and F is Faraday’s constant. [3]

Due to the high availability of charge carriers in the metal and electrolyte, andrelative dearth in the passive layer, the potential difference is accommodated acrossthe passive layer. This leads to potential drops at the metal/passive layer and passivelayer/electrolyte interfaces; the passive layer’s semiconducting band structure is offsetat these interfaces to maintain a constant EF. In other words, charge accumulates or de-pletes at the passive layer surfaces, resulting in a space-charge layer and band bending(see detailed introduction to band bending below).

At the metal-passive film interface, we usually assume very rapid charge transfer.At the passive layer-electrolyte interface, the potential drop can be divided into thepotential dropped within the electrical double layer (Helmholtz layer) of ions in theelectrolyte ∆ϕH and the potential dropped within the semiconducting passive layeritself ∆ϕSC (Fig. 3-1a). For a constant thickness Helmholtz layer, ∆ϕH is determinedby the pH of the electrolyte.∆ϕSC similarly depends on the charge carrier concentrationof the passive layer, which determines the Debye length β . For example, considering ann-type semiconductor with donor concentration ND:

β =

√

√

√εεokB Te2

o ND(3.2)

where ε and εo are the relative and vacuum permittivities, respectively; eois the ele-mentary charge and kB is Boltzmann’s constant. The depth of the resulting space-chargelayer in the passive layer dSC (Fig. 3-1b) can then be written:

dSC = β

√

√2eo(E − EFB)kB T

(3.3)

where E is the applied potential and EFB the flat-band potential (no bias). We can there-fore see that the width of the space-charge region is potential dependent; in other words,the passive layer surface compensates for any changes in applied electrode potential.

Band bending For a negative electrode potential η applied to an n-type semiconduc-tor, the EF of the redox couple is lowered relative to that of the passive layer, and freeelectrons accumulate at the semiconductor surface until the Fermi levels equilibrate.This can be represented as a downwards bending of the conduction and valence bandsat the surface (Fig. 3-1a). Conversely, a positive η gives rise to a depletion of electonsat the surface and upwards band bending (Fig. 3-1b). Semiconductor surfaces whosebands are free to shift up/down in this manner are said to have an "unpinned’" EF.

3.1.2 Surface states

The reactivity of semiconducting materials can be significantly altered by surface statesthat are either intrinsic to the crystal termination or arise from the presence of crys-talline defects at the surface.

71

Meta

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72

Intrinsic surface states: The abrupt discontinuation of periodic potential at semicon-ductor surfaces can impose severe perturbations to the crystal’s electronic structure.Unless a surface reconstructs to remove dangling bonds and autopassivate, the topmostatoms’ crystalline orbitals destabilize in the direction of their free atom orbital characterand energy. Binary semiconductors like FeS2, whose (100) surface does not reconstruct,are predicted from ligand field models [107] and DFT calculations [108–110] to havetwo associated intrinsic surface states: one for the anion dangling bonds and one forcations. However, the intrinsic surface states have never been experimentally charac-terized up to this point.

Extrinsic surface states: in reality these states are localized at defects such as anionor cation vacancies on the surface steps, kinks, dislocations or impurities [111, 112].However there is evidence to suggest that these types of defects (as well as step edgesor intersecting dislocations) can affect the surface electronic structure over nanometerdistances.

Horizontal charge transfer Adiabatic charge transfer between a redox couple and asemiconducting passive layer must be horizontal, that is- must occur at the same energylevel. Electrons may be exchanged in either direction: anodic transfer refers to electronstransferred from the electrolyte, and cathodic transfer in the opposite direction. If weignore for the moment the role of surface states, and other potential transfer pathwayssuch as hopping mechanisms and via bulk, intra-band states, charge exchange with thebulk bands of the passive layer may occur by two mechanisms: direct exchange andtunneling. [3]

Direct transfer (see Fig. 3-1a) from the semiconductor requires filled states in theCB to be higher in energy, i.e. overlap, than the empty states (oxidized species) of theredox couple. The more negative η is in this scenario, the greater the overlap of elec-tronic states and charge transfer can increase exponentially. This is the fundamentalexplanation behind the well known linear Tafel slope on a plot of log(cur rent) vs. ηfor corrosion systems.

Tunneling transfer (see Fig. 3-1b) refers to quantum tunneling of electrons throughthe space-charge layer. Thus, the larger the band bending, the smaller the tunnelingdistance dT and the greater the probability of tunneling T:

T =16E(Vo − E)

V 2o

exp

−2κdT

h

(3.4)

where the coefficient κ describes the dependence on barrier height: κ=p

2m∗(Vo − E),where Vo is the total energy barrier, E is the energy level of the tunneling electron andm* is the reduced electron mass. Charge transfer at the passive layer surface is thereforeproportional to the density of occupied states of the redox system D(Red) and that ofthe empty states within the passive layer CB, D(Ox). By integrating over all energiesabove EF where overlapping occupied and empty states may interfere, the tunnelingexchange current i+is therefore:

i+ = −F

∫

T.D(Ox).D(Red).dE (3.5)

The size of the band gap and density of electronic states at the surface is thereforecrucial to understanding the propensity for electron exchange. Some oxides that havea large band gap, e.g. Ta2O5 (Eg > 3 eV), such levels are not available and they do notshow redox processes even at very positive applied potentials, i.e. would require highband bending to meet the condition of electron tunneling through the space chargelayer.

73

3.1.3 Scanning tunneling spectroscopy and TIBB

In the work presented in this chapter, the aim was to understand the role of surfacestates in determining the surface Eg through quantitative analysis of tunneling spec-troscopy (STS) measurements. We adopt the approaches developed in modeling STSdata from semiconductor surfaces that was advanced from the late 1980s by R.M. Feen-stra and others. Early work began with the traditional cubic tetrahedrally bonded [113]and III-V [114] semiconductors, on which band edges and surface-related features couldbe determined to within an accuracy of ± 0.03 eV. The concurrent development of tun-neling spectrum models based on computations of potential distributions and tunnelingcurrent has helped identify the role of other physical phenomena in experimental STSspectra, such as tip-induced band bending (TIBB) [115] and surface states [116]. TIBBgreatly affects the STS measurement of unpinned semiconductor surfaces, in whichchanges in the tip-induced electric field lead to an unrestricted accumulation or deple-tion of charge carriers at the surface which act to screen the tip potential. In this case,the electron chemical potential µe in the sample shifts freely with applied bias, distort-ing the CB and VB near the surface. However, if surface states are present on the sample,charges from the bulk bands can fall into them and EF becomes pinned at the level towhich the surface states are occupied. STS spectra of EF-pinned surfaces typically yieldmore consistent band onsets and are less affected by localized quantum effects such asinversion or accumulation currents arising from TIBB.

The large, localized electric field from the proximate tip extends through the vac-uum region and into the surface of the pyrite sample. Consequently, a fraction of theapplied potential can be dropped within the sample itself, causing the valence and con-duction bands to bend and obscuring the energy scale of the measured STS spectra. Acomprehensive description of TIBB can be found in previous reports [115–118], but themain points are outlined here for completeness. The contact potential ∆ϕ is defined asthe difference in work function between the metal tip and the semiconductor:

∆ϕ = ϕm −χ − (EC − EF ) (3.6)

whereϕm is the metal work function, χ is the electron affinity of the semiconductor, andEC and EF are the conduction band minimum and Fermi level of the sample, respectively(Fig. 3-2a). Even in the absence of applied bias, a non-zero ∆ϕ leads to band bendingand the formation of a depletion region in the sample. For example, a positive ∆ϕproduces upwards band bending in the semiconductor as the Fermi level aligns withthat of the tip; negative charge correspondingly accumulates at the surface to screenthe potential (Fig. 3-2b). The effect is to shift the energy E of any given state at thesurface by an amount ϕo:

E − EF = eV −ϕo (3.7)

When EF at the surface is unpinned in this manner, the resulting experimental i(V)measurement can yield a very wide apparent surface Eg, as the band edges shift with thesweeping voltage and the onset of tunneling is delayed to more positive (for the CB) ornegative (for VB) voltages (Fig. 3-2c). Such a situation arises on defect-free ZnO(110)surfaces [119], where the apparent band gap from STS can be larger than the acceptedbulk gap of the material (Fig. 3-2e) , or on GaN(1100) where quantitative Eg determi-nation was not possible [121]. Severe band bending can also introduce large tunnelingcurrents from local states when the semiconductor EF is pushed into the VB (inversion)or CB (accumulation) [115, 122]. The presence of intrinsic (dangling bond) surfacestates on semiconductors typically limits TIBB by pinning EF (Fig. 3-2d) [116, 123].These states accumulate charge as they become occupied and effectively screen theelectrostatic potential from the tip, reducing the distortion of STS spectra arising fromTIBB. By analogy, on metallic materials with freely-available conduction band electrons

74

TIP FeS2

Evac

EF,tip

E0

EC

EV

EF

EC

EV

EF

EC

EV

EF

Δφ

φtip

Wtip

χEvac

EF,tip

E0

Δφ

φo

(a) No tunnel contact (b) E alignmentF

(c) No surface states (d) Surface states

Δφ+eV Δφ+eV

(c) ZnO(110) E > E app g, bulk (d) InN(100) E < E app g, bulk

EF,tip

Evac

Figure 3-2: Band bending effects in STS measurement. Schematic energy band diagrams for a n-type pyritesample where (a) tip and sample are not in tunneling contact; (b) there is an open circuit tunneling junction.With a positive contact potential ∆ϕ, an upwards band bending of magnitude ϕo occurs. In addition to theparameters described in the text: Evac is the vacuum energy level, Eo the ground level, and EV is the valenceband maximum of the semiconductor. Wtip is the energy difference between the metal’s Fermi level and thebottom of the metal valence band, typically ∼8 eV for PtIr tips. EF,tip is the tip Fermi level. All filled states areshaded in grey. (c) upon applying a positive sample bias V, further upwards tip-induced band bending (TIBB)occurs if EF is unpinned. However, surface states, e.g. shaded in black in (d), can accommodate enough surfacecharge to pin EF and minimize TIBB (after Feenstra et al. [115]). (e) no surface states exist on ZnO(110);EF remains unpinned and STS measurement gives an overestimate of Eg due to band bending. [119]. (f)Conversely, extrinsic surface states on InN(110) pin EF and reduce the apparent Eg. [120]

at the surface, the tip potential drops entirely at the surface and does not extend intothe sample. Similarly, extrinsic states (arising from disorder, defects or unintentionalcontamination), even at low densities of 0.01 monolayers (3x1014 cm-2) or less, canhold enough charge to significantly affect the magnitude of TIBB and pin EF, e.g. onInN(110) (Fig. 3-2f) [120]. Below, we rationalize these two competing effects in ourexperimental STS spectra by simulating the effect of different surface state features, thecharacteristics of which are known from DFT simulations.

75

3.1.4 The FeS2(100) surface

Applications of FeS2 beyond sulfide corrosion studies Pyrite or FeS2 is a semicon-ducting mineral for which the electronic structure has been intensively studied in rela-tion to reactivity in geochemical [124–129] and bio-catalytic [130–132] processes, aswell as for photovoltaic (PV) and photoelectrochemical properties [24,133–136]. Het-erostructures of FeS2 and perovskite oxides such as LaAlO3 have recently been proposedas promising devices for spintronics applications [137]. In the context of PV, low opencircuit voltages (VOC) of < 200 mV (or ∼21% of the widely accepted bulk band gap of0.95 eV) have been attributed to poor interfacial electronic properties of synthetic FeS2systems [24].

(100) surface crystallography and electronic properties The crystal structure ofFeS2 (space group Pa3) comprises two interpenetrating cation (Fe2+) and anion (S2

2-)face centered cubic (fcc) sublattices, the latter of which is made up of S2 persulfidedimers aligned along the cube diagonal direction <111>. Pyrite is a compound, d-band semiconductor with an electronic structure that can be qualitatively understoodwith the aid of a simple ligand field model [107]. Each Fe2+ ion in the bulk is octa-hedrally coordinated by S2

2- ions (symmetry group Oh), creating a strong ligand fieldthat splits the metal d states into non-bonding, triply degenerate Fe 3d t2g states (dxy,dyz and dx2−y2) at the top of the valence band (VB). The conduction band (CB) min-imum consists of doubly degenerate Fe 3d eg states (dz2 and dx2−y2) hybridized withS ppσ* orbitals. An indirect, bulk band gap Eg of 0.83-1.01 eV has been measured insynthetic FeS2 using various optical [138,139], photoconductivity [140,141] and x-rayabsorption/emission spectroscopy studies [142]. At the unreconstructed (100) surfacetermination of pyrite, the predominant growth and cleavage face, the symmetry of theFe2+ site is reduced from Oh to square pyramidal C4v, leading to a loss of degeneracyamong the Fe 3d t2g and eg states. These further split into two discrete, intrinsic surfacestates associated with the Fe dangling bond. Recent density functional theory (DFT) cal-culations are consistent in identifying these two pronounced surface states to be locatedaround the VB maximum (Fe-dx2 character) and at the CB minimum (Fe-dx2−y2). Themagnitude of the surface states decays almost entirely to zero beyond approximatelythree atomic layers into the bulk [109]. As a result it is theoretically estimated that Egat the FeS2 free surface is reduced by up to 0.3-0.4 eV, as compared to the bulk value(Table 3.1). We define surface Eg as the energy difference between the extrema of thesurface bands that extend into the bulk gap, rather than the gap between empty andfilled surface bands which may exist as discrete states within Eg; this distinction wasused by Feenstra et al. for investigating states on Ge(111)c(2x8) surfaces [117]. If thesurface states are fully degenerate with the bulk bands (i.e., lie within the fundamentalbulk Eg) they are not considered in the quantification of the surface Eg. In addition tothe intrinsic surface states on FeS2(100), computational studies have identified a seriesof further surface states that appear within the fundamental surface Eg local to interfa-cial point defects [108,109,132]. We refer to such states as "defect" or "extrinsic" statesto differentiate them from intrinsic surface states. Significant concentrations of neutralsulfur monomer vacancies VS have been measured by x-ray photoelectron spectroscopy(XPS) on fractured FeS2(100) [143–147] as well as in situ ion-bombarded [148] andannealed [106] growth faces. Indeed, the formation energy ∆Hf for VS is estimated tobe as low as 0.1 eV experimentally [106] and 0.4-0.42 eV computationally [109,110],suggesting that up to 20% of surface sulfur sites on FeS2(100) may be vacant at ambienttemperatures of 298 K, and therefore VS electronic states are prevalent. Moreover, neu-tral Fe vacancies VFe on the surface have been imaged at the atomic scale by STM andshown to comprise a comparably high fraction of the surface [149]. Via DFT, Zhang et al.predicted a maximum surface Eg of 0.72 eV for stoichiometric (Fe:S = 1/2) FeS2(100),but only 0.56-0.71 eV and 0-0.3 eV for sulfur-deficient and sulfur-rich surfaces, respec-

76

Table 3.1: Calculated bulk band gap Eg, and surface Eg for pristine and defective FeS2(100). Defectivesurface here refers to the presence of a single sulfur vacancy VS in a single 1 x 1 unit surface supercell.

Eg(eV)

Bulk Pristine Surface Defective Surface Ref.0.87 0.40 0.27 [132]1.02 0.56-0.71 N/A [110]0.86 0.55 0-0.2 [108]0.90 0.60 0.0 [109]

Table 3.2: Experimental surface Eg measurements by scanning tunneling spectroscopy (STS).

Sample/Surface Type Surface Eg (eV) Ref.Natural, fractured in UHV 0.04 [151]Natural, fractured in air 0.20 [152]Synthetic, as-grown surface 0.95 [50]Synthetic, fractured in air 0.00 [153]

tively. Other authors have theoretically calculated that VS at the surface can reduce thesurface Eg by more than this, even making the surface metallic [109]. Such argumentshave been used, for example, to explain the low resistivity (O(10-1) Ω.cm) of manufac-tured pyrite thin films for PV applications [150]. Despite this recognition that FeS2(100)interfaces are non-stoichiometric, there remains a need to demonstrate experimentallythe effect of defects on the electronic structure.

The scanning tunneling microscope (STM) operating in ultra high vacuum (UHV)provides a controllable metal-vacuum-semiconductor tunnel junction to probe theseelectronic states at the surface. A limited number of STS studies on natural [151,152]andsynthetic [50,153] FeS2 single crystals have produced inconsistent results, with appar-ent band gaps ranging from ∼ 0 eV to the accepted bulk value of 0.95 eV (Table 3.2),and a lack of detailed insight into the nature of the pyrite surface states.

3.2 Methods

3.2.1 Experimental

FeS2 single crystal synthesis High purity single crystals of FeS2 were synthesized bychemical vapor transport (CVT) in closed quartz ampoules, based on techniques de-scribed in Refs. [139, 154]. Raw materials were procured from Alfa Aesar (Haverhill,MA). A 1:2 stoichiometric mixture of 99.999% pure Fe powder and 99.995% S granulestotaling 4 g – along with ∼0.3 g of 98% pure anhydrous FeBr3 - was sealed in an evac-uated, 20 cm long quartz tube and heated to 700oC for 15 days to form polycrystallinepyrite aggregates. This precursor pyrite was removed, cleaned in acetone and methanoland resealed in a similar quartz tube with 0.3 g of fresh FeBr3 and a small amount ofsolid sulfur to provide a sulfur-rich environment for single crystal growth. The quartztube was placed in a temperature gradient from 700 to 550oC, with the polycrystallinepyrite charge placed at the hot end, and left for up to 30 days. The mechanism of pyritegrowth by CVT is described in Ref. [24]. The resulting crystals were typically cuboidalin shape with 5-10 mm edge lengths (Fig. 3-3a) and predominant 100 growth faces asdetermined by electron backscatter diffraction (EBSD) and single crystal x-ray diffrac-tion (XRD) (Fig. 3-3a). As-grown crystals were checked for phase purity using Ramanspectroscopy (Fig. 3-3b) and were found to be n-type semiconducting, with a donorconcentration ND in the range 1-5 x 1016 cm-3 by Hall measurement at 21oC. In addi-tion, an indirect Eg of 0.9-0.95 eV was detected by optical absorption on FeS2 single

77

0.7 0.8 0.9 1

200

400

600

800

1000

Energy (eV)

α-1

(cm

)

30 40 50 60 70 80 90 1002θ

(200)

Inte

nsity

(a

rb.)

(a) Single crystal XRD

300 350 400 450-1Raman Shift (cm )

Inte

nsi

ty (

arb

.)

344

380

418

(b) Raman spectroscopy

(c) Absorption spectrum: optical E > 0.9 eVg

Figure 3-3: FeS2 single crystal samples. (a) Co-Kα X-ray diffraction (XRD) pattern. (b) Raman spectrum.(c) Absorption coefficient α measured as a function of photon energy, showing an optical (bulk) band gap Eg= 0.9-0.95 eV. Inset: photograph of FeS2 single crystals prepared by chemical vapor transport (CVT). Eachsquare on the background corresponds to 10 x 10 mm2.

crystals polished down into 200 µm-thick plates (Fig. 3-3c). Absorption measurementswere performed with a Perkins Ellmer LAMBDA 1050 Uv/Vis spectrophotometer.

Scanning tunneling microscopy and spectroscopy Scanning tunneling microscopy(STM) was carried out using an Omicron VT-AFM system (Omicron Nanotechnology,GmbH, Germany) under UHV at pressures in the 10-10 Torr range. We used electro-chemically etched Pt-Ir tips that were annealed at 150oC for 2 hours under UHV toremove absorbed H2O and hydrocarbons prior to taking measurements. Single crystal,100 growth faces of FeS2 were investigated by STM subsequent to ex situ cleaningby the following procedure: sealed quartz tubes containing freshly-grown crystals wereopened in a glove box under a high purity, 95% N2 – 5% H2 environment to controlsurface oxidation and were ultrasonically cleaned in acetone and methanol to removeresidual Br2, which was proposed to be a source of contamination in previous STMstudies of synthetic pyrite [153]. Samples were clamped in a custom made aluminumstage and transferred to vacuum within< 1 min to minimize exposure to laboratory air.STM and STS results from samples prepared in this way were compared with similardata obtained using in situ fractured, synthetic FeS2 single crystals which are known tohave stepped, (100)-oriented faces [155, 156]. The STS results from as-grown and insitu fractured surfaces were quantitatively indistinguishable.

X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy-valence band(XPS-VB) spectra were obtained at the U12A beam line of the National SynchrotronLight Source (Brookhaven National Laboratory, Upton, NY), using a photon excitationenergy of 210 eV. Single crystal growth faces of FeS2 were prepared in a similar fashionas described above and were cooled in situ under UHV to approximately -170oC beforeperforming XPS-VB measurements.

78

Table 3.3: Input parameters for tunneling spectroscopy simulations using the SEMITIP program. (a) bulkHall measurement on FeS2 single crystals in this work, (b) effective masses optimized from DFT-computedband structure; (c) contact potential estimated from DFT calculation of work function, supported by experi-mental evidence in Ref. [24].

Property Symbol Value Used UnitDonor concentration (a) ND 1x1016 cm-3

CB effective mass (b) mc 0.09-0.15 me N/AHeavy hole effective mass (b) mhh 0.6-2.0 me N/AContact potential (c) ∆ϕ 1.0-1.2 eVTip-sample separation s 0.8-1.0 nmTip radius r 50 nm

3.2.2 Computational

Density functional theory (DFT) Density functional theory (DFT) calculations forthis study were carried out by Aravind Krishnamoorthy. The full details on DFT compu-tational methods on the FeS2 system can be found in Refs. [106,108].

Tunneling current simulation (SEMITIP)

Computations of tunneling current for simulating STS data were carried out using thefull three-dimensional (MultInt3) version of the open-source program SEMITIP v.6,courtesy of R.M. Feenstra [157]. The program is a Poisson solver that treats the case of ahyperbolic-shaped tip in tunneling contact with a semiconductor sample. A complete de-scription of the physics involved in the calculations is given in Refs. [115,116,158–160].

Table 3.3 summarizes the key input parameters for tunneling current calculationsthat are related to the electronic properties of the tip and sample, and the geometryof the tunneling simulation. Given the large number of input variables, we found anefficient approach to modeling proceeded along the following routine: first, all knownvariables are assigned their experimentally or computationally measured values. Sec-ond, the tip-sample separation distance s and tip radius R were estimated based onprevious literature [115, 122]. Finally, we allocated to the remaining free variables aphysically realistic range of values and performed a sensitivity analysis to optimize thefits (see Appendix 5). In practice, it was found that only the major semiconductor prop-erties such as donor concentration ND, conduction band effective mass mc and heavyhole effective mass mhh, along with the contact potential ∆ϕ, had a significant quanti-tative influence on the model output of tunneling current.

In the tunneling spectrum model, we accounted for the existence of charge accu-mulating surface states on FeS2 by introducing them explicitly into SEMITIP, either asa pair of Gaussian-distributed functions (Figure 3-4a), or as a uniform band across apredefined energy range (Figure 3-4b). For each of these surface state distributions, wefixed the charge neutrality level EN. Here, EN connotes the energy level below whichstates are neutral when filled and positively charged when empty, or, conversely, abovewhich they are negatively charged when filled and neutral when empty. In the case ofthe double Gaussian distribution, the additional variables of centroid energy (the dis-placements of the states in Energy either side of EN) and the full width half maximum(FWHM) of the peaks were assigned optimized values for fitting (see Appendix 5). It isimportant to note that surface states in the tunneling model are treated as completelylocalized at the surface, i.e., their magnitude does not decay exponentially into the bulk.Surface states thus affect only the electrostatic potential part of the calculation and arenot included in the computation of tunneling current.

79

EC

EV

EF

Centroid EEN

FWHMEC

EV

EF

EN

CB CB

VB VB

(a) (b)

Possible surface state distributions in SEMITIP

Figure 3-4: Distributions of surface states as defined in the SEMITIP program: (a) uniform distribution,with charge neutrality level EN and (b) double Gaussian distribution, where FWHM is the full width halfmaximum of the peaks, and the centroid energy defines their separation either side of EN. Filled states areshaded in grey. VB and CB refer to the bulk valence and conduction bands respectively.

3.3 Results and Discussion

3.3.1 Current-separation and current-voltage tunneling spectroscopy

STS results were obtained experimentally on single crystal FeS2(100), measured at var-ious tip-sample separation distances s. Due to the well-known exponential dependenceof tunneling current itunn on s, the onset of detectable tunneling current either side of0 V bias (nominally the VB and CB edges), which give rise to an apparent surface Egin the data, depends on the initial set point tunneling conditions for STS acquisition.Therefore we normalize the data to the constant tip-sample separation so at which aconsistent "gap"’ of approximately 0.5 eV is visible. However, we explain why the quan-tification of Eg directly from STS spectra in this manner can be misleading, since it doesnot account for the phenomenon of TIBB, as described in Section 3.1.3. Stable STMimages were initially taken at relatively low magnification (500 x 500 nm2) to locatesizeable flat terraces for consistent STS data acquisition (Figure 3-5a). The tip was sub-sequently scanned over 20 x 20 nm2, or smaller, atomically-flat areas (Figure 3-5b) toobtain tunneling spectroscopic information at various set point currents (iset) and biases(Vset). The tip was then briefly paused over randomly selected points during which thefeedback loop was turned off for 1 ms to acquire current-separation i(s) or current-biasi(V) spectra.

The magnitude of the measured tunneling current im as a function of bias voltageV is affected by the vertical tip displacement at the instant of STS acquisition. Thisseparation distance s can be related to the setpoint conditions isetand Vsetthrough thesimple exponential decay relation i(s) = ioex p(−2κs), where io is a constant and κ is thevacuum tunnel coefficient, otherwise known as the decay constant. κ is approximatedfor one-dimensional tunneling and reasonable Vset by [123,161]:

κ=

√

√2me

B −|eVset |

2

+

kq

2(3.8)

where me is electron mass, B the effective tunneling barrier and kq the parallel wave vec-tor of the tunneling electrons. The decay constant κ for pyrite was determined via i(s)spectroscopy at a range of different setpoint biases. Figure 3-6a shows the i(s) responseat Vset = -1.4 V (main image) and Vset = 0.4, 1.2 and 2.0 V (inset), each averaged overapproximately 20 measurements at different points on the FeS2 sample surface. Themagnitude of κ over the range -2V ≤ V ≤ 2V varied linearly from approximately 0.3Å-1 at large bias to 0.5 Å-1 near 0 V, and was symmetric for negative and positive bias

80

+4

0

-4

-8

+25

0

-25

-50

z (nm) z (pm)

100 nm 0.5 nm

Fe S

(a) (b)

Square pyramidal FeS (100) surface imaged by STM2

Figure 3-5: Scanning tunneling spectroscopy (STM) images of the as-grown FeS2(100) surface: (a) show-ing large atomic terraces with step edges oriented along the <100> direction. Tunneling conditions: Vset =- 1.5 V, iset = 0.5 nA. Scanning tunneling spectroscopy (STS) was performed on selected 20 x 20 nm2 flatareas, (b). Fe atoms are resolved on the FeS2(100) surface. The inset figure displays an atomic model forcomparison, with one unit cell of Fe atoms outlined by the dashed square. Tunneling conditions: Vset = 0.2V, iset = 4 nA.

(Figure 3-6b). The average effective tunneling barrier B, calculated using Eq. (3.8) andassuming k=0, was 1.2 eV. This corresponds to the average work function between themetallic tip and the pyrite sample at the tunnel junction.

Figure 3-7a displays a series of individual i(V) spectra taken at four different val-ues of s, where the set point Vset = 1.5 V and iset = 200 pA was arbitrarily chosenas the reference separation so. The other values of s were calculated relative to so us-ing the exponential decay relation for tunneling with the experimentally-determinedκ from i(s) spectroscopy. At more positive s (larger tip-sample separation), the mea-sured current around 0 V becomes very small and the Eg appears larger, up to approx-imately 1.7 eV for s = so + 1.8 Å. To correct for the exponential decay in transmissioncoefficient for tunneling, the i(V) data are normalized in Figure 3-7b to a constanttip-sample separation distance by converting the measured current im to “distance cor-rected current” is = imex p [2κ(V ) s], where s = 0 at the reference separation distanceso. Separation distance-normalized data are displayed with a logarithmic current scaleto enable discrimination among spectra. The four curves overlap consistently, indicatingthat throughout the tunneling set point range used in this work the tunneling spectragive a true representation of the tunneling response without metallic behavior due topoint contact at very small s, or anomalously insulating behavior at large s. Further, wenormalize the data to normalized conductance (di/dV )/(i/V ) (Figure 3-7c) which isknown to approximate the DOS in semiconducting or metallic samples [113]. We cal-culated (di/dV )by numerical differentiation from the i(V) response. To correct for thewell-known divergence of the direct conductance (i/V) at small values of i, i/V wasbroadened to i/V using a Gaussian distribution described previously [114].

A first approximation of surface Eg from the i(V) response is 0.5 eV, obtained bytaking the average voltage separation between the CB and VB current onsets at 1 pAcurrent, which is approximately the instrument resolution or "noise floor" below whichcurrent is not reliably measured in the STM used for this study (Figure 3-7b). Never-theless, the direct quantification of surface Ebg in this manner does not account for thepossible occurrence of TIBB, as described in Section 3.1.3.

81

0 2 4 6 8-1

-0.8

-0.6

-0.4

-0.2

0

s (Å)i (

nA

)

i = io

exp(-2κs)

Experimental i(s)

2.0V1.2V0.4V

2 4 6Δs (Å)

-6

-4

-2

ln(i)

(nA

)

0 1 2-2 -1Sample Bias (V)

2κ

-1

(Å)

0.4

0.6

0.8

1

1.2(b)

(a)

Determine decay constant κ:

Figure 3-6: Current-separation spectroscopy: (a) Tunneling current i as a function of tip-sample separations at a set point bias of -1.4 V (solid line). A fitted exponential function i = ioex p (−2κs) with decay constantκ = 0.80 Å-1 is overlaid on the experimental data (open circles). Inset: experimental data for 0.4, 1.2 and2.0 V biases, plotted on a log scale. (b) κ variation across the bias range used in this work. The dashed linesare to guide the eye, and do not represent a fit to the data.

3.3.2 Simulated tunneling spectra based on DFT-calculated DOS

We interpret the underlying electronic structure in our measured STS results on FeS2by simulating the tunneling spectra using an explicit calculation of the electrostatic po-tential across the tip-vacuum-pyrite system, followed by a full numerical integration ofthe resulting tunneling current. Using DFT as a guide for the position and distributionof intrinsic and defect-related surface states, we explored several different configura-tions of surface electronic structure as the input for the tunneling spectra computationsand optimized the fit to the experimental STS data in each case. We first compare theDFT-calculated DOS for pyrite with the valence band spectrum of a synthetic sample,measured using synchrotron x-ray photoelectron spectroscopy (Figure 3-8). A promi-nent, Fe 3d-related band and the broad, hybridized Fe 3d and S 2p states between 1-7eV below EV [107,162] are clearly visible in both the experimental and theoretical data,indicating a general correlation which justifies the use of this DFT data in guiding ouranalysis.

To investigate the origin of the apparent 0.5 eV surface Eg in the STS results we con-sidered the calculated DOS in energy region surrounding the bulk band gap (approxi-mately EV - 0.5 eV ≤ E ≤ EV + 1.5 eV) and present here the results for four differentsimulated electronic structures, which could conceivably give rise to the experimentaltunneling spectra. These four models are based on DFT calculations for the bulk crys-tal (Figure 3-9a), a pristine (stoichiometric) surface (Figure 3-9d,g), and a defectivesurface containing both charge neutral VFe and VS (Figure 3-9j). For the purposes ofsimulating the tunneling current as a function of bias, each of these characteristic DOSdistributions was converted to a simplified representation with inputs for the bulk va-lence and conduction bands and the requisite surface states. The computed tunneling

82

1 pA noise floor

-800

-400

0

400

800

010

110

210

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

s +0.9Åo

s +1.8Åo

so

s -1.2Åo

0.5 eV

1.7 eV

curr

ent (p

A)

|curr

ent| (

pA

)(d

i/dV

)/(i/V

)(a

rb u

nits

)

(b) Distance corrected i(V)/exp[-2κ.s]

(a)Raw i(V) data

(c) Normalized conductance

Sample Bias (V)

Precise E not quantifiable straight from i(V) curvesg

Figure 3-7: Current-voltage spectroscopy: (a) Tunneling current-voltage i(V) curves measured on FeS2(100)with varying tip-sample separations s. so corresponds to a tunneling set point of Vset = 1.5 V and iset = 200 pA.(b) the same i-V data normalized to constant tip-sample separation, plotted on a logarithmic i axis to facilitatecomparison. (c) normalized conductance (di/dV )/(i/V )as a measure of local density of states (DOS). Anestimate of surface band gap Eg width using the instrument resolution of 1 pA is ∼0.5 eV.

-10 -5 0 5

E-EV (eV)

DO

S (

arb

. units

)

XPS hν = 210 eV

DFT calculatedIronSulfurTotal

Fe-3d states at valence band edge

Figure 3-8: Pyrite valence band: Experimental valence band spectrum obtained using synchrotron x-rayphotoelectron spectroscopy (XPS) at photon energy hυ = 210 eV (top) compared against DFT-computeddensity of states for FeS2(100) (bottom), also showing partial DOS contributions from iron and sulfur. Thedashed line marks the valence band edge.

current that resulted from the different simulated DOS representations was comparedto the experimental STS results from Figure 3-7.

The four theoretical electronic structures that were matched to the experimentaldata can be described in more detail as:

1. FeS2 bulk-like density of states as calculated by DFT (Figure 3-9a). In the simpli-

83

fied STS model, the VB and CB extrema are separated by an assumed bulk bandgap of 0.95 eV and no surface states exist (Figure 3-9b).

2. Pristine FeS2(100) surface density of states, including intrinsic surface states aris-ing from Fe dangling bonds (Figure 3-9d). In the theoretical tunneling spectrainput (Figure 3-9e), a double Gaussian distribution of surface states is included,straddling the VB and CB edges. The density of surface states is set to 6.8 x 1014

cm-2.eV-1, consistent with the density of Fe dangling bonds at the unreconstructed(100) surface. The charge neutrality level EN is fixed exactly halfway between theVB maximum and CB minimum, while the FWHM and centroid energies of thesurface states were optimized within a reasonable range to provide the closestmatch to experiment. In this model, the intrinsic surface states can accumulate ordeplete in charge depending on the applied bias, and thus serve to screen the tippotential, but do not produce itunn. Eg is still 0.95 eV at the surface.

3. Pristine FeS2(100) surface density of states, similar to that described in Model(2), but we now postulate that intrinsic surface states are homogeneously con-nected to the bulk VB and CB. Therefore, surface states are not explicitly definedin this model, but rather the bulk Eg in the input is decreased from 0.95 to 0.5eV, to approximate the tunneling contribution of intrinsic surface states (Figure3-9h). It is important to note that no surface states were explicitly defined in thecomputations employing this model so no EF pinning would be expected. We in-clude the gray, double Gaussian states in Figure 3-9vh merely to draw the eye tohow they effectively reduce the surface Eg.

4. Defective FeS2(100) surface density of states. The surface Eg is reduced to 0.5 eVby the intrinsic surface states, as in Model (3), but we also include defect statesfrom VFe and VS with 12.5% surface coverage each, i.e. density of 8.5 x 1013

cm-2.eV-1 (Figure 3-9j). In this theoretical tunneling spectrum model, the defectstates form a broad band across the width of the reduced Eg and only contributefree charge to screen the tip potential, without contributing further tunnelingcurrent (Figure 3-9k).

The results for the four different tunneling spectra simulations are presented ad-jacent to their corresponding DOS graphs in Figure 3-9. Together with each simulatedcurve we also show the same, repeated experimental STS result obtained using set pointtunneling conditions of Vset = 1.5 V and iset = 200 pA, equivalent to the reference tip-sample separation of so in Figure 3-7. As expected, the first model of bulk-like densityof states (Figure 3-9c), which excludes any surface states, gives a poor fit to the ex-perimental results. In the absence of available free charge at the surface to pin EF, thesemiconductor bands are free to shift with the applied bias, and the CB (VB) edge isdragged to higher (lower) energies with increasing positive (negative) bias. The ap-parent surface Eg width is therefore > 0.95 eV. The second model (Figure 3-9f) withsurface-localized, non-tunneling intrinsic states seems to approximate the experimentalresult better, but still does not reliably capture the small size of the zero tunnel currentregion, nominally corresponding to Eg, which is 0.3-0.5 eV larger than the experimen-tal STS results would suggest. A parametric sensitivity study was conducted, and noadjustment of the relative surface state positions or widths produced a fit better thanthat shown in Figure 3-9f, as quantified by minimizing the root mean squared (RMS)difference between the simulated and experimental results (see Appendix 5). We con-clude that the effect of these intrinsic surface states extends beyond a simple screeningof the tip potential distribution, as they are defined in the tunneling spectrum model.Consequently, close replication of the experimental spectra can instead be achieved bydefining a narrower forbidden energy region Eg in the model input, simulating the casewhere significant tunneling current originates from the surface states when the biasis swept across biases in the range of approximately 0.4 V and below. In Figure 3-9i

84

-0.5

00.5

11.5

E -

E (

eV

)V

Density of States (arb. units)

-2-1

01

2

Current (pA)0

500

-500 0

500

-500

-0.5

00.5

11.5

EC

EV

E=

0.9

5 e

Vg

E=

0.5

eV

g

ST

S M

odel

Exp

erim

ent

VB

CB

(b)

(c)

(e)

(f)

(h)

(i)

(k)

(l)

(a)

(d)

(g)

(j)

Tunnelin

gS

creen p

ote

ntia

l

E -

E (

eV

)V

Sam

ple

Bia

s (

V)

Bulk

-lik

e s

tate

s

Intr

insi

c S

S s

creen tip

Tunnelin

g fro

m in

trin

sic

SS

Intr

insi

c &

defe

ct S

S

Pro

gre

ssiv

ely

ad

d c

om

pu

ted

su

rface s

tate

s in

to S

TS

mo

del to

matc

h e

xp

eri

men

tal re

su

lt

Figu

re3-

9:M

odel

ing

tun

nel

ing

spec

tros

copy

wit

hsu

rfac

est

ates

:(Le

ftco

lum

n)de

nsit

yof

stat

es(D

OS)

calc

ulat

edby

dens

ity

func

tion

alth

eory

(DFT

)w

ith

(mid

dle

colu

mn)

thei

rco

rres

pond

ing,

sim

plifi

edan

alog

sus

edin

tunn

elin

gsp

ectr

osco

pym

odel

ing.

The

shad

edre

gion

sco

rres

pond

tosu

rfac

est

ates

(SS’

s)th

atei

ther

just

scre

enti

ppo

tent

ial

(bla

ck)

or,

alte

rnat

ivel

y,co

ntri

bute

toth

etu

nnel

ing

curr

ent

(gre

y)in

the

tunn

elin

gsp

ectr

am

odel

inpu

t.(R

ight

mos

tco

lum

n)th

eou

tput

from

each

tunn

elin

gsp

ectr

umm

odel

(sol

idlin

e)is

disp

laye

dal

ongs

ide

the

sam

e,re

peat

edex

peri

men

tal

scan

ning

tunn

elin

gsp

ectr

osco

py(S

TS)

resu

lt(o

pen

circ

les)

,co

rres

pond

ing

toa

tip-

sam

ple

sepa

rati

onof

soas

desc

ribe

din

the

mai

nte

xt.

(a),

(b)

and

(c):

bulk

-lik

eel

ectr

onic

stru

ctur

ew

ith

band

gap

E g=

0.95

eVan

dno

SS’s

.(d)

,(e)

and

(f)

incl

ude

intr

insi

cSS

’sat

the

FeS 2

(100

)su

rfac

e,bo

rder

ing

the

band

edge

sbu

tno

tco

ntri

buti

ngto

tunn

elin

gcu

rren

t(i

tunn

)w

ithi

nth

efu

ndam

enta

l,bu

lkE g

.(g)

,(h)

and

(i):

the

intr

insi

cSS

’sno

wm

edia

tetu

nnel

ing

and

the

band

gap

isre

duce

dto

0.5

eV.(

j),(

k),a

nd(l

)co

rres

pond

toa

FeS 2

(100

)su

rfac

ew

ith

redu

ced

E gof

0.5

eVco

ntai

ning

12.5

%ir

onpo

int

defe

cts

(VFe

)an

dsu

lfur

mon

ovac

anci

es(V

S).

85

L

k pointX K

-0.5

0

0.5

1

1.5

En

erg

y (e

V)

L Γ LX KL Γ LX KL Γ

Defect State

(a) (b) (c)

Intrinsic surface states connected; extrinsic form discrete band

Figure 3-10: Density functional theory (DFT)-computed band structures for (a) bulk FeS2, (b) a 4-layersurface slab with (100) termination, where we show in the red region the additional bands arising fromintrinsic surface states, and (c) the same surface slab but containing a single sulfur vacancy VS in the topmostlayer. The single band coming from the defect is highlighted with a bold, blue line.

the intrinsic surface states are included continuously with the VB and CB in this man-ner, i.e., the Eg for the simulation is reduced now to only 0.5 eV. This input producessimulated tunneling currents that match the experiment much better around the zerocurrent region. However, the best fit to the experimental data was achieved when wefurther include a broad, distributed band of defect states that simulate a 12.5% con-centration of both VFe and VS, at the surface (Figure 3-9l). In the model these defectstates do not mediate electron tunneling but their effect on the simulated spectrum isto reduce the effect of TIBB by screening the tip potential. Physically, we interpret thisto mean that the defect surface states that exist within Eg are too dilute and sparselydistributed to contribute significantly to tunneling and thus further reduce Eg. Never-theless, their presence sufficiently affects the tunneling spectra through EF pinning. Tohelp understand the lack of measured tunneling current from inter-band defect states,in Figure 3-10 we compare the band structure of bulk FeS2 alongside that of a pristine(100) surface and a defective (100) surface containing a 12.5% concentration of VS,as calculated by DFT. The additional, intrinsic surface state bands - highlighted in redin Figures 3-10b,c - form a dense network of states that overlap continuously with thebulk VB and CB. By comparison, the VS defect state is manifested in a single, isolatedband 0.2-0.3 eV below EC. Moreover, we see the minimum energy point on this defectband clearly dips down at the L point of the Brillouin zone. During the tunneling pro-cess, the perpendicular wave vector for the electron k⊥ is relatively small compared tothose from intrinsic surface bands, where the empty-state minimum is very flat acrossthe entire k point range shown. Together, these facts suggest the tunneling from intrin-sic surface states would be much stronger than for the defect states, explaining why weobserve the intrinsic surface states directly in the experimental tunneling spectra, butthe defect states have a more subtle effect.

In order to quantify the width of the surface Eg from the experimental data, a sensi-tivity analysis of Model (4) was performed with the range 0.3 ≤ Eg ≤ 0.6 as the input.The results plotted with logarithmically displayed current in Figure 3-11 indicate a bestfit to experimental tunneling current can conceivably be achieved with Eg= 0.4 ± 0.1eV. The close match between the experimental and the simulated tunneling spectrumresults suggest that the presence of dangling bond surface states on the FeS2(100) freesurface leads to a reduction in Eg by∼0.5 eV over the accepted bulk Eg of 0.95 eV. These

86

-2 -1 0 1 2

100

102

104

106

108

Sample Bias (V)

Tun

ne

ling c

urr

ent (p

A)

0.3 eV

0.4 eV

0.5 eV

0.6 eV

Expt.Model

Surface E = 0.4 ± 0.1 eVg

Figure 3-11: Fitting to experimental surface Eg. Comparison of experimentally measured tunneling current-voltage i(V) spectrum (open circles, Vset = 1.5 V and iset = 200 pA) , with defective FeS2(100) surface Model(4) and four different magnitudes of Eg as listed beside each curve: 0.3, 0.4, 0.5 and 0.6 eV. The absolute valueson the tunneling current scale are arbitrary and the curves have been separated by a uniform multiplicationof the current data for ease of comparison. We have omitted showing the experimental and modeled databelow a current of 1 pA which is the instrument resolution for experimental data acquisition.

intrinsic surface states form continuous bands connected to the bulk electronic statesand therefore offer available energy levels into which and from which electron tunnel-ing can occur in the presence of the biased probe tip. In contrast, surface states arisingfrom distributed point defects do not contribute to electron tunneling during STS, butinstead provide states across a broad range of energies within the fundamental surfaceEg that can accrue additional charge from the bulk. This acts to pin the Fermi leveland moderate the amount of TIBB during STS. By accounting for both of these surfacecontributions in tandem, the theoretical model most accurately replicates the experi-mental STS data. The requirement for such a seemingly high surface defect concentra-tion of 12.5% in the model raises the question of whether this is realistic for a pristineFeS2(100) surface. The existence of a vacant site at one in every eight surface-boundsulfur sites, with a correspondingly similar density of vacant iron sites, would implyone cation and one anion vacancy per four surface unit cells. As we have already dis-cussed, there is a large body of XPS evidence suggesting that up to 20% of pristine pyritesurfaces can comprise VS, even at ambient temperatures of 298 K, including our workin parallel to this study [106]. Likewise, high concentrations of surface VFe have beenimaged on pyrite by STM [149]. It is probable that the synthetic samples used in thecurrent work contain a significant concentration of VFe, given the sulfur-rich conditionsof single crystal synthesis. Therefore the assumption of 12.5% as an average for bothtypes of ionic point defect seems plausible. In addition, the effect of extrinsic (S-Br)2-

defects - a known source of impurity in CVT-grown pyrite [163] - has not been consid-ered in our analysis. Although the surface states associated with these defects would belocalized at the defects themselves, there is evidence to suggest that vacancies (as wellas other defects such as step edges, substitutional dopants and intersecting dislocations)can affect the electronic structure at nanometer distances through the redistribution of

87

Delocalized defect state

Figure 3-12: Visualization of FeS2(100) surface charge q surrounding a single sulfur point defect (VS)located at the arrow. We show only the difference in q between the defective and defect-free surfaces, i.e.∆q (VS − S). Positive and negative 0.014 e/Å3 isosurfaces are colored in red and blue, respectively. Unit celledges are shown as dashed lines; one defect in this area corresponds to a VS concentration of 12.5%.

surface charge [164–166]. Figure 3-12 displays the charge density difference between asupercell of four unit cells of FeS2(100) containing a charge-neutral VS defect and thatof the perfect host, with an isosurface of 0.014 e/Å3. The delocalized positive and neg-ative charge resulting from the VS defect is distributed over almost the entire 2 x 2 unitcell area of the simulation, equivalent to approximately 10.8 x 10.8 Å2 on the surface.This extent of delocalization would suggest that the charge from a density of only 12.5%VS on the surface could affect the experimental tunneling spectroscopy measurement,regardless of the exact location that the probe tip is placed during the data acquisition.

3.4 Outcomes

3.4.1 Conclusions

An accurate, quantitative assessment of the surface electronic structure of semiconduct-ing pyrite, FeS2(100), is necessary for understanding the behavior of pyrite in a widerange of applications, including geochemical, bio-catalytic, and corrosion processes, aswell as pyrite’s photovoltaic and photoelectrochemical properties. While scanning tun-neling spectroscopy is an ideal tool for this purpose, the analysis is complicated by thewell-known effect of tip-induced band bending, the presence of intrinsic surface states,and the additional effects of defect states associated with native ionic vacancies andother defects. We performed systematic STS measurements on synthetic FeS2 singlecrystals at different tip-sample separations and demonstrated that the apparent surfaceband gap is consistently 0.4 ± 0.1 eV, or ∼0.55 eV smaller than the widely-acceptedbulk band gap of 0.95 eV for pyrite. By basing our tunneling current simulations onmethodically varied, simplified DFT-calculated electronic structures, we link the originof this reduction in Eg to the presence of intrinsic surface states from Fe dangling bondsat the free surface termination. The electronic bands arising from the intrinsic surfacestates overlap continuously with the bulk bands. In addition, the experimental tunnel-ing spectra results can be modeled most accurately if a second distribution of surfacestates arising from cation and anion vacancies is incorporated into the tunneling cur-rent simulations. These defect states do not contribute significantly to overall tunnelingcurrent but have an influence on the tunneling spectra by accumulating charge at thepyrite surface, which screens the tip potential during measurement and pins the Fermi

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Into

crystal

(100) Free

surface

Surface states affect photovoltaic performance

Figure 3-13: Low surface bandgap implications for PV. A smaller surface band gap may lower overall pyritesolar cell open circuit voltage and therefore performance by supplying a connected set of energy levels intowhich excited states can thermalize before being usefully extracted. Image from Ref. [167].

level. Our findings confirm the influence of both intrinsic and defect surface states onthe electronic structure of pyrite. The presence of a reduced band gap on the surface, aswell as the existence of defect states within the band gap, has implications for electronicprocesses such as charge transfer during electrochemical redox reactions.

3.4.2 Implications for other applications of FeS2, e.g. PV

One of the several motivations for this work, outside the central scope of this thesis,was the applicability of FeS2 to photovoltaic (PV) solar cells. In a paper written by La-sic, Armiento et al., to which the author of this thesis contributed, an attempt was madeto explain the low open circuit voltage (OCV) of pyrite devices, which have not exceeded0.2 V (out of a potential 0.95 V maximum as dictated by the bulk Eg). [167] One argu-ment was that the surface states responsible for the lowered surface Eg are connecteddirectly to bulk bands in pyrite. Any photoexcited carriers could then thermalize intolower energy levels at interfaces, before being usfully extracted (Figure 3-13).

Since this work was published, another group advanced a theory for a conductiveinversion layer at the FeS2(100) surface, essentially comprising positively-charged sur-face states. [168] The authors suggested this would be consistent with our STS mea-surements in this work, and provided evidence that surface states can be passivated,offering hope that pyrite devices with OCV > 0.5 V may one day be feasible.

3.4.3 Future work

The next step in improving the methodology for quantifying surface band gaps and sur-face states directly from scanning tunneling spectroscopy is to modify the SEMITIP codefor a direct input of DFT data. Such a collaboration was discussed with Prof. Feenstra,the author of SEMITIP, but this was not pursued further during this thesis. However,the next generation of code should allow direct input of first-principles calculated sur-face density of states, rather than the relatively coarse, parabolic band inputs currentlyallowed by the program. Moreover, the code as it stands at the time of writing cannotcompute tunneling current from surface states. The next version should be able to dealwith tunneling from predicted, charged states that also pin the Fermi level.

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20 Å

3.2 Å

50

0

-50

z (pm)

(b) MoS basal plane2

210-1-2Sample Bias (V)

[di/dV

] /

[i/V

](a

rb.

un

its)

-2.5V, 1nAMoS Bulk Crystal2

MoS Single Layer2

(a) MoS : facile STM over large areas2

(c) Preliminary STS inconclusive

Figure 3-14: Preliminary investigations on bulk and 2-dimensional MoS2. (a) stripped MoS2 offers high-quality surfaces for scanning tunneling microscopy. (b) higher-magnification image, showing Mo atoms inhexagonal arrangement. (c) an initial study to compare the surface band gap of multilayered ("bulk") vs.single layer MoS2 was inconclusive; however the methodology for STS quantification outlined in this chapteroffers a systematic way to further investigate this and other, similar open questions.

Experimentally, we hope that the methodology outlined in this chapter will be used andimproved by other researchers to test other interesting materials with poorly-characterizedsurface electronic properties. For example, as part of a collaboration with the Palaciosgroup of the Department of Electrical Engineering at MIT, the author made some pre-liminary measurements of the MoS2 surface to compare the surface band gap of single-layered versus multi-layered samples. Figure 3-14 presents some initial findings; thesurface is very conducive to imaging by STM. However, the collected STS data was in-conclusive without further analysis using a similar technique to that described in thischapter. The surface Eg of both multi- and single-layered MoS2 was found to be close tothe known bulk value of 1.2 eV. Many other chalcogenide and other rare semiconduct-ing surfaces should be convenient for such coupled experimental and computationalanalysis of their surface electronic structure.

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Chapter 4

Stability: dynamics of pointdefect formation, clustering andpit initiation on the pyritesurface

Synopsis The collective behavior of point defects formed on the free surfaces of ioniccrystals under redox conditions can lead to initiation of local breakdown by pitting.Here, we controllably generated sulfur vacancies on single crystal FeS2(100) throughin vacuo annealing, and investigated the resulting evolution of surface chemistry usingsynchrotron x-ray photoelectron spectroscopy (XPS). By measuring the S 2p photoe-mission signal intensity arising from sulfur defects as a function of temperature, theenthalpy of formation of sulfur vacancies was found to be 0.1 ± 0.03 eV, significantlylower than the reduction enthalpy of bulk FeS2. Above 200 oC, the created sulfur vacan-cies together with preexisting iron vacancies condensed into nm-scale defect clusters,or pits, on the surface, as evidenced by scanning tunneling microscopy (STM). We pro-vide a mechanistic description for the initiation of pits that requires concerted behaviorof both the sulfur and iron vacancies, and validate this model with kinetic Monte Carlo(kMC) simulations. The model probes realistic length and time scales, providing goodagreement with the experimental results from XPS and STM measurements. Our re-sults mechanistically and quantitatively describe the atomic scale processes occurringat pyrite surfaces under chemically reducing environments, important in many natu-ral and technological settings, ranging from its role as a passivating film in corrosionto its potential use as a photovoltaic absorber in solar energy conversion. Portions ofthis chapter were published in Electrochimica Acta [169]. The kMC simulations weredeveloped by Aravind Krishnamoorthy.

4.1 Background and motivation

As we have seen in Chapters 2 and 3, a stable passive layer can hinder ion or electrontransport to/from the metal, and suppress charge transfer at the surface. However, theinherent protectiveness of a passive layer relies on this physicochemical barrier remain-ing intact. Passive films can break down due to chemical, electrochemical or mechanicalstimuli, resulting in more rapid, localized corrosion that accelerates equipment failure.Localized degradation of the barrier layer can expose bare metal to the corrosive envi-ronment. In many cases, the metal will quickly re-passivate. However, in some instancesa failure to re-passivate will result in the formation of a stable pit, which can rapidly

91

expand due to localized galvanic corrosion (the exposed, small area becomes anodicrelative to the surrounding passivated metal). In the extreme case, a pipe wall may becompromised well before the expected service life of the structure. On stressed compo-nents, a pit may serve as the nucleation site for a critical crack. Aggressive anions inthe environment such as chloride Cl-are known to promote pitting, as will be discussedin Section 4.1.2 below. Certain theoretical approaches have been developed to predictpassivity breakdown, such as the point defect model (PDM) of Macdonald et al. whichasserts that pitting is a deterministic process that can be modeled by individual, atom-istic processes such as point defect formation and condensation. [32] Despite this, localcorrosion rates are often non-linear and highly unpredictable.

4.1.1 Chapter goals

In this chapter, we aim to understand: (1) the dynamic process of pit nucleation inionic passive films at the atomic scale, by studying the surface of pyrite as a modelsystem and (2) whether the reported off-stoichiometry in polycrystalline pyrite can beattributed to easily-reducible surfaces. Both these aspects are introduced in more detailin the following Sections 4.1.2 and 4.1.3:

4.1.2 Passivity breakdown by pitting

The first and foremost motivation for this study was to uncover the atomic-scale mecha-nism behind vacancy condensation into nanometer-scale imperfections that could serveas nuclei for the localized breakdown of ionic passive layers, i.e. pitting. There is exper-imental evidence that vacancy condensation both at the metal-passive layer interface(Figure 4-2a and b) and the passive layer-electrolyte interface (Figure 4-2c) can leadto the localized breakdown of passivity. Various mechanistic theories and models havebeen proposed to describe this process [170], the most comprehensive of which is thePoint Defect Model (PDM) which serves as the key, non-empirical framework guidingthe development of a multiscale model in this project. The PDM has been developed tosuccessfully account for the critical breakdown parameters (critical breakdown voltage,Vc, and induction time, tind) for single breakdown sites on the surface, for the distri-butions in these quantities, and for their pH- and chloride concentration-dependencies.The PDM also provides the first, mechanistically-based explanation of the role of al-loying elements in the inhibition of passivity breakdown and hence localized corrosion.Despite a long-standing correlation of global environmental variables to corrosion rates,microscopic mechanisms of passivity and breakdown are not quantitatively understood.Consequently, localized corrosion and the associated macroscopic failure are typically,but incorrectly, identified as being stochastic in nature. However, passivity breakdownis not a matter of chance, but occurs for a well-defined, mechanistic reason, i.e. a de-terministic process. A schematic illustrating some of the proposed causes of pitting isshown in Figure 4-1, with a brief description of each provided in the caption. Belowwe briefly review some of the motivations for the study of surface point defects in thischapter:

Aggressive anions and point defects. Chloride is the most commonly observed andwell-known pitting agent, although other halides and SO42− can also have an accel-erating effect on localized corrosion. [3] While the presence of chloride ion is knownto lead to localized attack, preferentially at structural and chemical discontinutities inthe barrier layer such as grain boundaries and inclusions [171], the key mechanismresponsible for the X− induced pitting is still debated. Two broad, descriptive modelsaccount for the action of X− on locally degrading the oxide film: the PDM suggests thatanions absorb into oxygen vacancy sites at the oxide surface, leading to the creation ofcation vacancies in the oxide (Figure 4-1a). [170] This increase in cation point defect

92

(b)

(c)

(a)

Proposed pitting mechanisms

Figure 4-1: Proposed mechanisms of passivity breakdown and pitting. (a) Halide ions X− preferentiallyadsorb at inhomogeneites in the barrier layer such as nanopits and vacant lattice sites, leading to the creationof cation vacancies. The Point Defect Model (PDM) postulates that the resulting, enhanced metal vacancyflux to the alloy interface cause voiding. (b) enhanced dissolution at surface defects can lead to blistering andrupture due to film growth stresses σ, to expose bare metal. (c) If the metal does not repassivate, a stablepit may grow. Hydrolysis of cations enhances local acidity, attracting more negatively-charged X− ions andpropagating further pitting. Large pits may serve as nucleation sites for more catastrophic failure modes, e.g.stress corrosion cracking (SCC).

concentration in turn leads to enhanced vacancy flux in localized channels in the oxidebarrier layer; if the rate of metal vacancy accumulation at the metal interface cannotbe matched by absorption into the metal, macroscopic voids may form at the interface.These cavities can subsequently chemically or mechanically destabilize the overlayingfilm, creating a pit on the nanometer scale.

Surface imperfections as initiation sites. Open questions remain over halide-defectassociation as described above. However what is clear is that surface imperfectionsserve as initiation sites for localized corrosion. Microstructural or micro-chemical inho-mogeneities in the passive film itself are known to play an important role in pitting, andeven in the absence of aggressive anions these can lead to differential rates of dissolu-tion which nucleate metastable pits. [172]

Modeling pitting: realistic length- and timescales. Both on metals and on ionicpassive films, clustering of point defects (vacancies) is thought to be necessary for pitinitiation, the rate-controlling step in overall pitting corrosion [110]. This process hasbeen observed on pure metals [173] and alloys. [174] On the other hand, understand-ing the surface pitting mechanism on ionic passive films has been a challenge, exper-imentally limited to only few successfully studied systems such as Ni-O, Ni-OH andCr2O3, [175,176] and without a concerted modeling and experimental demonstrationat the atomic scale. Even insimpler systems such as pure metals and semiconductors,where surface pitting is relatively better understood, modeling of surface degradationis generally limited to the use of empirical kinetic parameters. Matching simulated timescales to experimental ones has remained challenging and has lacked experimental val-

93

(b)

(c)(a)

Metal-barrier interface Barrier-electrolyte interface

Figure 4-2: Nanopits formed by vacancy agglomeration. (a) Scanning tunneling microscopy (STM) imagesof vacancy condensation to form nanocavities at intermetallic-oxide interfaces, leading to spallation of thepassive layer. [179] (b) nanopits formed by localized dissolution (vacancy formation) at NiO surfaces, asrecorded by electrochemical STM [175].

idation of model results. [177,178]

4.1.3 FeS2 surface chemistry and non-stoichiometry

The second motivation for this investigation, which is complementary to the first, re-gards the unresolved non-stoichiometry of pyrite surfaces, which cannot be explainedbased on defect chemistry of the bulk material. Native point defect concentrations inbulk FeS2 are generally low (O(106) cm3) at room temperature. [135] On the otherhand, anionic vacancies, specifically sulfur vacancies denoted as VS, are expected tobe far more prevalent at free surfaces, with calculated formation enthalpies as low as0.4 eV. [109, 134] This has led to difficulties in obtaining surfaces with low intrinsicdefect concentrations in nanocrystalline pyrite precursors and films. [133, 150] Sulfurdeficiency is typically put forward as a source of non-ideal electronic and optical prop-erties in synthetic FeS2. However, there remains a need to experimentally quantify theformation energy of VS on the surface to understand whether these defects are indeed asignificant source of off-stoichiometry in pyrite surfaces. As described in Chapter 4, thecrystal structure of pyrite is NaCl-type cubic, with Fe2+ at the cation site and S2−

2 dimersat the anion site, aligned along the cube diagonal <111>. The (100) surface of FeS2 isunreconstructed and is the most stable surface, as shown by low energy electron diffrac-tion (LEED) [151,156] and scanning tunneling microscopy (STM). [149,181] The sulfurS 2p x-ray photoemission peak of pyrite, when accessedusing soft x-ray synchrotron ra-diation, reveals highly detailed information about the different binding environmentsof sulfur inthe near-surface region. In addition to the dimer S2−

2 signal from the crys-tal bulk, pyrite’s S 2p photoelectron spectrum distinguishes two additional, surface-localized and coordinately reduced sulfur environments at more negative binding ener-gies. [143,145,146,148] Quantification of these surface-localized defect environmentsenables further understanding of the two open areas summarized above.

94

4.2 Methods

4.2.1 Experimental

Samples Single crystal pyrite samples were synthesized by chemical vapour trans-port (CVT) in the presence of Br as a transport agent, described in Chapter 4. Growthfaces were identified to be primarily (100) by electron back-scattered diffraction (EBSD;ZeissSupra-55 scanning electron microscope). Phase purity of the single-crystalline syn-thesized pyrite was confirmed using Raman spectroscopy and X-ray diffraction. We notethat the synthesis of FeS2 single crystals was performed under a high partial pressure ofsulfur. Although the pyrite phase has a stoichiometric ratio of Fe/S = 0.5 in the bulk inambient conditions, such sulfur-rich growth conditions are expected to favor the incor-poration of iron vacancies in the bulk, consistent with previous calculations of defectformation energies as a function of sulfur chemical potential. [108, 135] After coolingthe as-synthesized crystals at ∼ 5 oC/min under sulfur-rich conditions inside quartztubes, a non-equilibrium high concentration of VFe remainedquenched within the bulkFeS2. We propose this quenched-in iron deficiency to be the source of mobile iron va-cancies near/on the surface under the reducing environment (i.e., under a low chemicalpotential of sulfur) during our subsequent experiments. Elevated temperatures assist inthe migration of VFe to the surface from the bulk that has become supersaturated, asthe bulk evolves toward thermal equilibrium with a lower vacancy concentration. Therole of such iron vacancies on the surface is discussed in more detail in Section 4.3.2.

Soft x-ray photoelectron spectroscopy (s-XPS)

Synchrotron x-ray photoelectron spectroscopy (XPS) was performed at Brookhaven Na-tional Lab (Upton, NY) at the U12A beamline of the National Synchrotron Light Source(NSLS), in order to deduce the temperature dependence and the formation enthalpyof surface defects. The radiation source was tuneable, monochromatized soft x-rays inthe energy range 100-600 eV with a resolution ∆E/E of 2 x 102–103 and spot size of 1mm2 on the sample surface. The base pressure in the vacuum chamber remained below1010 Torr for the duration of the experiment. Clean single crystal FeS2 samples with(100)-oriented growth faces larger than 5 x 5 mm2 were prepared by ultrasonicationin acetone then methanol in an inert atmosphere glove box, before being mounted in amechanical sample clamp (Figure 4-3). During transfer into the UHV environment, thesamples were limited to <5 min air exposure to minimize surface oxidation and othercontamination. We did not observe any secondary peaks from sulfates or other oxidationproducts. [144] Controllable, in situ heating between 120-330 oC at steps of 30 oC wasachieved using a resistively-heated coil placed behind the sample. The heating appara-tus and sample stage were cooled collectively by flowing liquid N2 through the manipu-lator, which was attached to the sample via a large copper block. Each in situ annealingcycle lasted 150 min, which was adequate for the pyrite surface to reach equilibriumwith the UHV base pressure; subsequently, the sample was allowed to cool to approxi-mately -170 oC for XPS measurements in order to quench in the surface chemistry andalso minimize phonon broadening of the XPS signal. S 2p photoemission spectra wereobtained at excitation energies of 210, 350 and 500 eV with an energy resolution of 100meV and pass energy of 10 eV. Peak fitting of the S 2p XPS spectra was carried out usingCasaXPS Version 2.3.16. Shirley background subtraction was applied to all spectra andindividual components were fit with 95% Gaussian-5% Lorentzian peak distributions,unless otherwise specified

Scanning tunneling microscopy (STM)

Scanning tunneling microscopy (STM) images were collected in order to visualize theevolution of surface defects at elevated temperatures. An STM system (Omicron VT-

95

25 mm

3.2 mm

3.5 mm

20 mm

12 mm

4 mm

Screw for T.C.

(b) FeS₂ sample in vice

(a) XPS sample holder

(d) Side view

(c) Sample clamp dimensions

Figure 4-3: XPS sample clamp for FeS2 crystals.(a) circular holder for synchrotron x-ray photoelectronspectroscopy (s-XPS) equipment. (b) custom-built aluminium sample clamp, showing FeS2 single crystal with(100) face exposed. (c and d) sample holder design schematics with approximate dimensions.

STM; Omicron Nanotechnology, GmbH, Germany) was used under UHV conditions be-low 109 Torr. Electrochemically etched PtIr tips were annealed in the chamber at 150oC to clean them prior to taking measurements. FeS2 samples used for STM/STS weresynthesized and prepared in a manner similar to that described above for the XPS ex-periments. STM images were subjected to a global flattening procedure and horizontalnoise removal using SPIP 4.8.4 software from Image Metrology (Denmark).

4.2.2 Computational

Density functional theory (DFT)

DFT calculations of the FeS2(100) surface for this work were made by Aravind Krish-namoorthy. Details can be found in Refs. [108,182]

kinetic Monte Carlo (kMC)

Kinetic Monte Carlo (kMC) simulations were performed on a model of the pyrite (100)surface to understand the processes responsible for the experimentally observed time-evolution of the surface defect structure under non-equilibrium conditions. The kMCwas formulated by FWH and Aravind Krishnamoorthy, and coded by Aravind Krish-namoorthy. A full description is available in Ref. [182]. Briefly, we modeled a small setof elementary processes that were able to reproduce the experimentally-observed de-fect phenomena, including sulfur and iron vacancy formation. and vacancy diffusiondiffusion processes.

The probability of each process occuring, J, was given by the Arrhenius equation:J = νexp (−Ea/kB T ), where ν is the attempt frequency and Ea the activation barrier.The two processes described above were subjected to geometrical constraints based onthe FeS2(100) surface. It is worth mentioning briefly that the activation energy for sur-face VS formation was based on the value of 0.1 eV obtained from the XPS experimentsin this work.

96

Table 4.1: XPS core level shift (CLS) for S 2p peak, relative to the bulk pyrite dimer signal B, and full widthhalf maximum (FWHM) of fitted S 2p peaks (B, S, M and HE) used for quantification.

Excitation En-ergy

CLS (eV) / FWHM of fitted S 2p components

B S M HE

210 eV 0.00 / 0.77 ±0.03

-0.64 ± 0.03 /0.65 ± 0.02

-1.23 ± 0.04 /0.55 ± 0.02

+1.75 ± 0.02 /1.7 ± 0.30

350 eV 0.00 / 0.63 ±0.01

-0.65 ± 0.05 /0.53 ± 0.01

-1.25 ± 0.05 /0.57 ± 0.02

+1.80 ± 0.10 /2.2 ± 0.20

500 eV 0.00 / 0.78 ±0.02

-0.67 ± 0.02 /0.77 ± 0.02

-1.26 ± 0.02 /0.60 ± 0.03

+1.80 ± 0.20 /2.3 ± 0.30

4.3 Results and Discussion

We first demonstrate how the surface of FeS2 evolves under the reducing conditionsof the ultra-high vacuum environment and increasingly high temperature, through theinitial formation of sulfur monovacancies and the migration to the surface of iron va-cancies that were supersaturated in the bulk crystal. At a sufficiently high temperatureof ∼ 240 oC, vacant cation and anion siteswere observed to coalesce into pits of < 100nm in lateral dimension and of either exactly one-half or one lattice parameter depth.We employed the kMC model to substantiate our propoesed atomistic mechanism forthis phenomenon at realistic time and length scales.

4.3.1 Evolution of pyrite surface structure and chemistry

We examined the formation of individual and clustered point defects on the (100) sur-face of pyrite under successive reduction at increasing temperatures in the UHV environ-ment. The approach to gather element-specific signatures around an x-ray absorptionsite included analysis of core holes that result from core-level ionization and x-ray ab-sorption. Figure 4-4 shows a series of four S 2p spectra taken on single crystal FeS2(100)to illustrate the effects of varying the annealing temperature (210 oC and 330 oC, as la-beled), as well as the source excitation energy (350 eV in Fig. 4-4a and b; 210 eV in Fig.4-4c and d. The experimental data were deconvoluted by peak fitting into three doubletcomponents, consistent with the well-established S 2p features of pyrite. [128,145–148]Here, we adopt the nomenclature introduced by Andersson et al. [148] for the featuresB, S and M, as described below. The spin-orbit splitting 2p3/2 peak was fixed for eachcomponent at 1.18 eV above the corresponding 2p1/2 peak, with an intensity ratio of1:2 for the doublet pairs. Further constraints used in peak fitting are listed explicitly inTable 4.1. Feature B (“Bulk”), distinguished by a 2p3/2 peak centered at 162.8 eV bind-ing energy (BE), is ascribed to the signal from bulk sulfur S2−

2 dimers (see Fig. 4-5b).Feature S (“Surface”) has a core level shift (CLS) of -0.65 ± 0.05 eV BE relative to B andrepresents surface S2−

2 dimers (Fig.4-5c). Finally, feature M (“Monomer”) is at a CLS of-1.25± 0.05 eV BE relative to B and is related to the monomer defect (or monovacancy)species S2− at the surface (Fig. 4-5d) which is of primary interest for this work.

Quantifying the temperature dependence of proportion of the M contribution inthe S 2p spectrum enabled us to identify the sulfur vacancy formation enthalpy onthe pyrite surface, as described below. An additional singlet peak, which we refer toas the ‘high energy’ (HE) peak was fit to each spectrum at 1.8 ± 0.2 eV above themain B peak, with a 70% Gaussian-30% Lorenztian distribution. Previous reports of theFeS2(100) S 2p photoemission have either explicitly or implicitly dealt with a similarfeature. For example, Nesbitt et al. fit a single peak in their work and attributed it to

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98

(a) (b) (d)(c)

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001

010

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Three types of surface sulfur binding environment: B, S, M

Figure 4-5: Atomic model of the FeS2(100) surface as viewed side-on. (a) with highlighted sulfur atomscorresponding to x-ray photoelectron spectroscopy features denoted as: (b) Bulk ‘B’ sulfur binding environ-ment with 3 Fe-S bonds and 1 S-S bond, (c) surface ‘S’ environment with one fewer Fe-S bond, and (d)monomer ‘M’ with an adjacent sulfur vacancy and hence no S-S bond.

polysulfides (S2−n ) [143], Mattila et al. stipulated the additional signal in this region

to arise from the effect of the core hole [146], and Andersson et al. fitted their pyriteS 2p peaks with asymmetric tails towards higher binding energies to account for thiscontribution. [148] In our work, we did not observe the high-energy tail of the S 2pspectra to change significantly during the course of the annealing experiments from120-350 oC. As the experiments were conducted under reducing UHV conditions wedismiss the possibility of surface S2−

n contributing to the signal. We therefore postulatethat the fitted HE component is generated by the core hole effect in pyrite, and we usedsystematic fitting parameters to remove the influence of this peak on the quantificationof the other components B, S and M. The total intensity (area) of the HE peak wasconstrained to be 10% of the total S 2p signal and variation of this constraint by ± 5%had no quantitative effect on the relative proportions of the B, S and M features fitted oneach spectrum. The surface sensitivity of XPS is related to the inelastic mean free pathλ of the emitted photoelectrons. To minimize λ, the incident photon energy is chosensuch that the kinetic energy of the excited photoelectron is of the order 40-50 eV [46].For the S 2p peak at a BE of ∼ 160 eV this corresponds to an x-ray excitation energyhν of 200-210 eV. Hence the spectra in Fig.4-4c and d obtained using hν = 210 eVoriginate from the top 4.5 ± 1 Å (2-3 sulfur layers) while those in Fig. 4-4a and b at hν= 350 eV are attributable to the top 11± 1 Å (4-5 sulfur layers). For the other excitationenergy used in this work, hν = 500 eV, the estimated is 14 ± 1 Å (5-6 sulfur layers).At the 500 eV photon energy, the surface sulfur species of interest to this work haverelatively weak signal as compared to the bulk species B; therefore we do not includethe 500 eV XPS results in further discussion. Features S and M are most prominent inFig. 4-4c and d which were obtained using 210 eV excitation energy, indicating thatthese signals arise from the 1-2 atomic layers of pyrite closest to the (100) free surfaceof the crystal.The proportion of M as a fraction of the total S 2p signal, denoted as [M],increases with increasing annealing temperature up to 330 oC. This trend is consistentwith the formation of surface monomer defects as the sample surface is increasinglychemically reduced. In the intermediate temperature region between 120-240 oC, [M]increased consistently with temperature (Fig. 4-6).

To estimate the formation enthalpy of sulfur monomer vacancies, [M] in the mostsurface-sensitive measurement (hν = 210 eV) was quantified as a function of temper-ature. We assume the following simple defect reaction to form electronically neutralvacancies under UHV annealing:

99

FeS2⇔ Fe×Fe + S×Si+ V×Sii

+12

S2,(g) (4.1)

where the conventional Kröger-Vink notation [183] is used andthe subscripts Si andSii refer, in no particular order, to the two adjacent sulfur sites on any given anion dimer.Although the formal oxidation state of the newly formed sulfur monomer site (Sii here)should be S1-, it is understood this configuration relaxes to the more stable S2 by electrontransfer from an adjacent cation, leaving the vacant site electronically neutral. [110,143]We write the Gibbs free energy change of the defect formation reaction in Eq. (4.1)as ∆G f =∆H f − T∆S f , where ∆H f and∆S f are the enthalpy and entropy of vacancyformation, respectively. The sulfur vacancy concentration at a given temperature T canthen be written:

|VS |= p12S2

. exp§

−∆G f

kB T

ª

(4.2)

where kB is Boltzmann’s constant, pS2is the equilibrium partial pressure of sulfur gas,

and we assume the activities of the solid to be unity. Finally, we note that a given changein [M] can be used as anestimate for change in [Vs], if we apply the reasonable assump-tion that the only defect species contributing to the increase in [M] is the monomervacancy, Vs.

Figure 4-6 shows the results for the increase in relative contribution attributed toM, as ln[M] vs. 1/T, in the annealing temperature range of 120-240 oC. We presentonly the data obtained with 210 eV XPS excitation energy, which gives the most sur-face sensitive results. From the slope of the straight-line fit and Eq. (4.2) we infer theformation enthalpy ∆H f to be 0.1 ± 0.03 eV. Our estimated error in ∆H f is the differ-ence between maximum and minimum slope fits obtained from systematic variations insoftware-generated quantification of S 2p peak fits (including sensitivity to the selectionof the HE fitted component, giving rise to the error bars), and does not reflect experi-mental error associated with the sample, equipment or measurement. The optimal peakfit for each component was first chosen so as to minimize the total root mean squarederror between fitted data and experimental data. Error bars were then generated by me-thodically varying the peak positions of the M and S components relative to the positionof B, across the ranges listed in Table 4.1; we believe this gives a reasonable quantita-tive estimate of fitting error. However, in this quantification we neglect any clusteringof defects at lower temperatures that would effectively suppress the value of [M], asdiscussed in more detail below. This is reasonable given the high resolution achieved inour STM images, which suggest that these surfaces are not likely to have many smallclusters at the lower temperatures. As a result, the calculated ∆H f may only slightlyunderestimate thetrue activation enthalpy for vacancy formation.

Upon annealing to higher temperatures (240 oC - 330 oC) we observed a notice-able deviation from the Arrhenius behavior of [M] that is seen in Figure 4-6. Figure4-7a shows that the percentage of M reached a maximum at around 240 oC and thendropped by ∼ 3-4% of the total S 2p signal, before leveling off to a roughly constantvalue for temperatures above 270 oC. Furthermore, the total signal arising from the Scomponent increased in this temperature range up to 270 oC, by a roughly equivalentamount (∼10%) to M, then leveled to a consistent value of around 43% of the totalS 2p signal between 270 - 330 oC (Fig. 4-7b). Such non-Arrhenius behavior of [M]and [S] imply a more complicated phenomenon than the otherwise logical hypothesisthat surface-localized sulfur dimers (S) are converted directly to monomers (M) by thethermally-assisted breaking of the sulfur-sulfur bonds; in such a case we would expectany increase in M signal to be matched by a corresponding drop in S. We will revisit themechanisms that could explain such a non-monotonic change in sulfur monovacanciesvia later description of kMC simulations. However, the model underlying such compu-tational simulations is informed by direct observation of the surface reconstruction of

100

2 2.2 2.4 2.6

x 10-3

2.6

2.8

3

3.2

3.4

3.6

1/T (K- 1)

ln [M

]

240 200 160 120

T (oC)

fΔH = 0.1 ± 0.03 eV

Arrhenius growth in [M] at low temperatures

Figure 4-6: Sulfur monomer vacancy concentration [M] as a percentage of total S 2p photoelectron spec-trum signal vs. inverse temperature. The dashed line is the best linear fit to the data, and error bar generationis discussed in the text. ∆H f is calculated from the slope of this line, assuming the Arrhenius relationship inEq. (4.2).

210 eV300 eV500 eV

200 250 300 350

10

15

20

25

30

Annealing T (o

C)

%M

25

30

35

40

45

%S

(a)

(b)

200 250 300 350Annealing T (

oC)

Non-monotonic defect formation at higher T’s

Figure 4-7: Proportion of the M and S components of the S 2p photoelectron spectra on FeS2(100) at200-330 oC, measured using three different excitation energies: 210, 350 and 500 eV. (a) The fraction of thetotal signal represented by M increased upto 270 oC then dropped and stayed approximately constant, (b)The fraction of total signal represented by S also increased up to 270 oC but then remained unchanged to330oC . The dashed lines connecting the data points are shown as a guide for the eye.

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o25 C o220 C o300 Cz (nm) z (nm) z (nm)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

30 nm 50 nm 50 nm

10 nm 10 nm 10 nm

10 nm 10 nm 10 nm

EX

PE

RIM

EN

TA

LS

IMU

LA

TE

D

Nucleation and growth of surface vacancy pits by scanning tunneling microscopy

Figure 4-8: Scanning tunneling microscopy (STM) images of single crystal FeS2(100) surfaces (a, b) priorto any in situ annealing in ultra high vacuum, (d, e) after three hours of in situ annealing at 220 oC, and (g, h)after three hours at 300 oC. The surface morphology of atomically-flat terraces at room temperature changesunderannealing due to the formation of vacancy clusters. In addition, originally straight terrace edges, visiblein the bottom left corner of (a), develop into wavy lines, e.g. as indicated by the white arrow in (d). All STMdata were collected at room temperature using tunneling conditions in the range ± (1-2) V and 200-1000 nA.The bottom row of images (c, f, i) display the results of kinetic Monte Carlo (kMC) simulations performed atthe same temperatures of (c) 25 oC, (f) 220 oC and (i) 300 oC for comparison with the experimental images.The activation barrier values used in these kMC simulations are from Ref. [182].

pyrite, which we address next.Scanning tunneling microscopy (STM) images of single crystal pyrite (100) surfaces

both at room temperature and after in situ annealing to 220 oC and to 300 oC for> 150min (Fig. 4-8) provided further details on the behavior of defects underlying the resultsin Figure 4-7. For comparison, we include predictions from our temperature-dependentkMC simulations of point defect formation and clustering. These simulated results arediscussed in more detail in the following section. The initial surface condition of the FeS2single crystals consisted of multiple atomically-flat, featureless (100) terraces (Fig. 4-8aand b).

After annealing at 220oC in UHV, we observed two notable changes in surface mor-phology: first, the straight ledges separating atomic terraces became wavy, with small in-cursions into the terrace (Fig. 4-8d). Second, there appeared multiple small, irregularly-shaped depressions on the surface of flat terraces that arose from the agglomeration ofsurface anion and cation vacancies (Fig. 4-8e), henceforth referred to as vacancy clus-ters or ‘pits’. At 220 oC we observed a dispersion of cluster sizes (widths) from smallerthan 1 nm to ∼ 10 nm (Fig. 4-8e). Following annealing at 300 oC, these grew to forma more homogeneous spread of clusters with lateral dimensions consistently between5-10 nm (Fig. 4-8g, h and i). As described in Section 4.2.1,we believe the source ofthe observed iron vacancies (VFe) to be supersaturated VFe remaining in the bulk af-ter crystal synthesis under high sulfur chemical potential S. During annealing in thelow S experimental conditions in UHV, iron vacancies migrate to the surface to equi-

102

librate a stoichiometric bulk rid from VFe. This process effectively ‘provides’ cation va-cancies to the surface, leading to a situation similar to the dissolution of metal cationsinto liquid electrolytes in contact with a passive film. [184, 185] Similar surface va-cancy clusters have been observed on metals containing supersaturated vacancies fromquenching [173,186,187], non-stoichiometric oxides such as CeO2 [188,189] and alsonatural pyrrhotite Fe1-xS that have been subjected to heating under vacuum. The pitsexhibited a curved, non-faceted morphology that can be rationalized by comparisonto the curved terrace steps observed by Rosso et al. on conchoidal fracture surfaces ofFeS2. [151] Normal to the free surface of the crystal, the depth of the defect clustersalso changed between 220-300oC , as seen in the image height histograms of Figure4-9. After in situ annealing treatment at 220 oC, there existed a bimodal distribution ofpit depths, with the majority of pixels at the nominal surface level (normalized to 0 nmon the scale shown) and a subset located at a depth of approximately 0.25 nm. After insitu annealing at 300 oC, the pit depth distribution broadened and the mean depth ofthe minor peak in the histogram is shifted to approximately 0.55 nm. The line traces inFigures 4-9a, b and c provide more detail on the depth of pits: at 220 oC the surface pitswere consistently 2.7 ± 0.1 Å deep whereas at 300oC the majority of pits have a depthof 5.4 ± 0.1 Å. Given the lattice parameter of pyrite of 5.41 Å [162], these pit depthscorrespond to one half and one full lattice parameter, respectively.

4.3.2 Mechanism of vacancy formation and coalescence

The growth of defect clusters as evidenced by our STM results, along with the XPSresults presented in Figures 4-6 and 4-7, lead us to propose a mechanism involving threedistinct phenomena occurring in tandem during the in situ reduction of the FeS2(100)surface, as visualized in Fig. 4-10.

1. Formation of isolated S monovacancies (VS) and surface-ward migration of VFefrom the bulk, giving rise to increasing signals of sulfur species M and S, respec-tively;

2. surface diffusion of VS and VFe, followed by the stochastic clustering of smallnumbers of vacancies;

3. growth of vacancy clusters, which are more stable geometric features for the re-duced surface compared to dispersed point defects, due to a reduced formationenergy for sulfur vacancies at step edges.

The proposed mechanism was cast into our kMC model. The last row of images inFigure 4-8 shows the successive formation and growth of surface pits after simulatedannealing for 4 h. The model reproduces the flat, nearly featureless surface at ambienttemperatures (Fig. 4-8c), while a series of pits with average lateral dimension of 1 x 1nm2 becomes visible at 220o C (Fig. 4-8f) and larger pits on the order of 2 x 2 nm2 at300o C (Fig. 4-8i). For a complete discussion of the kMC results, the reader is referredto Ref. [182].

Below, we discuss in more detail the three phenomena that account for this pitinitiation mechanism:

1. Formation of sulfur and iron vacancies at and near the surface: Elemental sul-fur is highly volatile in comparison to iron, with a melting temperature of 115 oCat 1 atm pressure. We therefore assume sulfur sublimes from pyrite and is dynami-cally removed from the sample surface under vacuum until the pyrite equilibrateswith the ambient sulfur chemical potential, dictated by the chamber pressure of109-1010 mbar. We also noted the importance of iron vacancies in our model. Thecorresponding appearance of VFe near the surface is indicated by the growth ofthe S feature of the XPS S 2p spectra while the surface is increasingly reduced.

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5 10 15 20x (nm)

z (

nm

)

0

0 10 20

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z (

nm

)

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% o

f pix

els

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220oC

“M”

“S”4 8 12

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nm

)

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010

Fe S VS VFe

o200 C

o240 C

o300 C

Evolution of vacancy pit depth with temperature

(a)

(b)

(c)

(d)

Figure 4-9: Pits are one half- or one lattice parameter deep. (a-c) line traces taken across representativesurface features observed in scanning tunneling microscopy (STM) scans at 200, 240 and 300 oC. Inset ineach graph are STM images of the nanopits, with grey arrows indicating each line trace. The ball-and-stickatomic diagram next to each graph depics a side-on view of the surface at the pit edges. In (a), we observedsingle monomers or very small nanopits that could not be resolved on the atomic scale. By 240 oC in (b) themeasured pit depth is exactly one-half of a pyrite lattice parameter, or 2.7 Å. Finally, in (c) the step heighthas grown to a full lattice parameter of 5.4 Å. (d) shows height (z-axis) histograms of STM images obtainedafter annealing at 220o C (and at 300o C bimodal distributions of pit depths are observed at both annealingtemperatures; however the average pit gdepth is ∼0.25 nm in the former case and ∼ 0.55 nm in the latter.

Figure 4-5 illustrates how six new S binding environments would accompany theintroduction of a single VFe in the second atomic layer from the (100) surface(NB: only 4 S sites are shown in the plane of the graphic). Since Fe loss throughevaporation into vacuum is unlikely at the relatively low annealing temperaturescompared to the melting point Tm of iron (300o C < 0.2 Tm), the increaseof VFerequires an alternative explanation. It is known that the formation enthalpy ofthe VFe in pyrite increases by up to 1.42 eV as the environment changes fromsulfur-rich to one deficient in sulfur. [108] This large change implies that the siz-able number of VFe defects originally present in the pyrite crystal during synthesis

104

2+Fe

2-S2VS

VFe Formation

Diffusion

S2 (g)

(a) (b)

(c)

(d)

010

001

Atomic processes in pitting mechanism

Figure 4-10: Illustration of atomic processes involved in the proposed mechanism of pit formation andgrowth on pyrite (100). (a) Formation of surface sulfur monovacanciesVSthrough evaporation into vacuum.(b) Diffusion of VS to a pit site. (c) Agglomeration of vacancies on the iron and sulfur sublattices by diffusion,leading to theinitiation and growth of the pit. Presence of an initiated pit (as depicted in this fig-ure) is nota necessary precursor to the process in (c). (d) Iron vacancies, denotedas VFe, that are already present in thebulk migrate to the surface during annealing.(e) VS formation at under-coordinated sites surrounding pitshas lower formation enthalpy as compared to isolated vacancy formation process in (a).

0

0.1

0.2

0.3

0.4

200 240 280 320

[M]

Temperature (°C)

KMC

XPS (210 eV)

kMC result replicates M defect formation

Figure 4-11: kinetic Monte Carlo simulation results. Simulated values of the sulfur monomer vacancy con-centration [M] on the pyrite surface as a function of annealing temperature, obtained by kinetic MonteCarlosimulations (kMC) and indicated by the blue zone. The width of predicted [M] indicated by this blue bandis given by variation in kMC energy barrier values over the range described in Ref. [182]. Values of [M]experimentally determined from our XPS measurements (Fig. 4-7) are shown for comparison.

in sulfur-rich conditions are not stable in the sulfur-deficient conditions encoun-tered during the annealing process. In order to equilibrate the bulk under theseexperimental conditions, the oversaturated VFe point defects migrate from bulktowards the free surface at high temperatures to annihilate. In providing iron va-cancies to the surface, coincidentally in this work, the situation is analogous tothe dissolution of metal cations from the passive film in liquid electrolytes. [184]

2. Diffusion of sulfur and iron vacancies on the surface: the generation of in-cursions into pre-existing atomic terrace edges (Fig. 4-8d) and the nucleation of

105

small vacancy clusters on top ofterraces (e.g., as seen in Fig.4-8e), requires thediffusion of both VFe and VS across the surface. When two or more vacancies en-counter each other stochastically, a small cluster is formed which is more stablerelative to the dispersed individual vacancies. STM imaging by Rosso et al. hasrecorded surface diffusion of iron vacancies on natural single crystals of FeS2 atroom temperature over time scales of minutes, so diffusive processes are expectedto occur with low energy barriers. [149] In the kMC model in this work, a higherbarrier was taken for diffusion of vacant surface sites away from the pits comparedto diffusion of vacancies towards the pits, simulating the trapping of vacant sitesby the initiated pits.

3. Growth of pits: Once a stable pit nucleates, the reduced coordination of sulfuratoms at the newly-created step edges of pits reduces the formation energy forvacancies at these sites, and accelerates the growth of pits. Indeed, our DFT cal-culations showed that ∆H f for individual VS at a step edge of a pit could be upto ∼ 40% lower than that on an atomically-flat surface. This type of dependenceof defect formation on the local atomic configuration has also been observed insulfide inclusions in pitting corrosion. [190]

The formation and expansion of surface vacancy clusters in this manner providesan explanation for the surprisingly low ∆H f for sulfur vacancies of around 0.1 eV thatwe measured using XPS below 240 oC (Fig. 4-6), as compared to recent theoreticalpredictions in the range of 0.4-1.44 eV. [108,109,134] Upon raising the temperature togreater than 240 oC, the effect of growing the vacancy clusters is to maintain the XPSsignal intensity from M at a roughly constant value. This is because the removal of asulfur atom from the step edge of a vacancy cluster, while growing the cluster, does notresult in the creation of an adjacent monomer M site on the surface structure; thereforethe M signal intensity does not increase in the S 2p spectrum.

4.4 Outcomes

4.4.1 Conclusions

We have investigated the evolution of surface chemistry and morphology on syntheticpyrite single crystals as a function of annealing temperature in reducing conditions, inorder to visualize and quantify the mechanisms leading to pit initiation on the surface.The formation enthalpy for sulfur vacancies was found to be tobe 0.1± 0.03 eV from theexponential temperature dependence of the sulfur monomer vacancy (VS) binding en-vironment detected in the S 2p photoelectron spectra. However, at higher temperaturesabove 200 oC, the sulfur vacancy concentration decreased and deviated from Arrheniusbehavior, concurrent with the initiation of nanometer-scale surface pits. The depths ofthese pits were exactly one-half or one FeS2 lattice parameter, as imaged by STM. To ex-plain this behavior, we propose a mechanism involving the simultaneous formation andmigration of vacancies at the surface, with facilitated vacancy formation and agglomer-ation at step edge sites surrounding pits. A simple kinetic Monte Carlo simulation withthermally activated reactions was used to validate the proposed mechanism. We notetwo important implications of these findings. First, the observed, concerted agglomera-tion of point defects from both cation and anion sublattices to initiate nanoscale pits hasbroad consequences for ionic solids in reducing environments. The dynamics of surfacepoint defects observed under controlled reducing environments offer an atomistic leveldescription of the incipient stages of pit formation in passive films, as postulated in mod-els of surface degradation such as the Point Defect Model. Second, the relatively lowdefect formation energy that we measure for sulfur vacancies confirms the high chemi-cal reducibility of the FeS2 surface, often linked to poor electronic and electrochemicalproperties in synthetically grown pyrite.

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4.4.2 Future work

Having observed the formation of surface nanopits by reducing FeS2 in UHV at hightemperatures, it would be of interest to study in situ pitting nucleation at lower temper-atures (< 100 oC) but under electrochemical conditions, for example in model corrosivesolutions and/or under an applied electrode bias. The ideal instrument would be anelectrochemical STM, to investigate whether the same atomic processes as described inthis chapter apply when a high temperature gradient combined with chemical drivingforce is replaced by an electrochemical one.

Separately, it would be interesting to study the reactivity of surface defects and defectclusters towards molecules such as H2S and H2O, building on the work by Guevremontet al. [126] and others. [127] Since the publication of the work described in this chap-ter, Andersson et al. have reported the formation of monomers on the FeS2(100) surfaceunder energetic ion bombardment, suggesting that the surface chemical activity can bealtered greatly by sputtering. [191] However, their assessment of surface reactivity as-sumes that many monomer defects form individually, dispersed across the surface. Aswe have shown here, vacancies at elevated temperatures can cluster and reduce thenumber of dangling bonds available to catalyze heterogeneous reactions. A concertedexperimental and computational approach could help understand the reactivity of realpyrite surfaces in aggressive, electrochemical environments. Experimentally, tempera-ture programmed desorption (TPD) would be a good tool to study the adsorption andreactive properties of surface defects on pyrite.

Acknowledgements

We gratefully acknowledge support provided by BP Plc. through the BP-MIT Center forMaterials and Corrosion Research. We thank S. Yip (MIT), R. Woollam, Steven Shade-man and Sai P. Venkateswaran (BP) for discussions on pitting mechanisms in H2S, P.Lazic, R. Armiento and G. Ceder (MIT) for discussions on relevance of these resultsto PV performance of pyrite, Klas Andersson (formerly of Stockholm University, Swe-den) for discussions on pyrite surface chemistry and XPS, and R. Sun (MIT) and M.Kabir (IISER-Pune) for verification of some of the point defect formation energycalcu-lations. We thank D. Mullins and P. Albrecht at Oak Ridge National Laboratory for theuse of the U12A beamline (BrookhavenNational Laboratory) for XPS measurements.The U12a beamline is supported by the Division of Chemical Sciences, Geosciences,andBiosciences, Office of Basic Energy Sciences, U.S. Departmentof Energy, under contractDE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated byUT-Battelle, LLC. Use of the National Synchrotron Light Source, Brookhaven NationalLaboratory, was supported by the U.S. Department of Energy, Office of Science, Officeof Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. We thank the Na-tional Science Foundation for providing the computational resources for this projectthrough the Texas Advanced Computing Center under Grant No.TG-DMR120025.

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108

Chapter 5

Conclusions

5.1 Summary of activation barriers

This thesis explored the bulk and surface defect chemistry of the two stable Fe-S phasespyrrhotite and pyrite, to understand the governing mechanisms behind their protec-tiveness as passive layers formed on steels under sulfidizing conditions. A key goal wasto measure activation barriers Ea, the fundamental descriptor of kinetic rates, for theprocesses depicted in Figure 1-7a. To that end, a summary of the activation barriers ofinterest is given in Table 5.1.

Table 5.1: Summary of experimentally determined activation barriers Ea in eV for key unit processesinvestigated in the course of this work. Bold entries are contributed from the experiments described in thisthesis; those marked "N/A" were either not measured, or could not be found in the literature.

Process Temp. (oC) Pyrrhotite Fe1-xS Pyrite FeS2

Chapter 2: Growth

Bulk Fe diffusion *DFe 170-700 0.83 +αS(T )2 (a)

N/A

Bulk S diffusion *DS > 500 7.9 (b) 2.1 (c)

Surface S exchange (ox.) 350-600 1.05 ± 0.20 N/A

Surface S exchange (red.) 350-600 0.79 ± 0.23 N/A

Chapter 3: Reactivity

Bulk band gap Eg, bulk 25 0.30-0.80 (d) 0.95

Bulk band gap Eg, surf 25 N/A 0.40 ± 0.10Chapter 4: Stability

Surface Fe diffusion *DFe, surf 25 0.10-0.20 (e)

Fe surface vacancy ∆Hv,Fe 100-300 N/A N/A

S surface vacancy ∆Hv,S 100-300 N/A 0.10 ± 0.03(a) α = 0.41± 0.06 and S(T ) is the reduced magnetization (= 0 at 0 K), (b) Ref. [40], (c) Ref. [192], (d)Refs. [52,193], (e) Ref. [149]

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5.2 Contributions

With reference to Table 5.1 and to supplement the "Outcomes" from each of Chapters2, 3 and 4, the key scientific questions and corresponding contributions of this thesisare summarized below:

What are the rate limiting mechanisms in the growth of Fe1-xS on iron? Pyrrhotitescale growth occurs by Fe diffusion from the metal to the surface of the passive layer,where Fe combines with S transferred from molecular form such as in H2S in the en-vironement. Both Fe diffusion and heterogeneous surface exchange of S have a similaractivation energy of ∼1 eV. Hence, regardless of temperature (or electrochemical po-tential), the sulfidation of iron should always commence with linear kinetics, controlledby the surface reaction. However, since the diffusive transport depends on the squareof film thickness, eventually diffusion will become the limiting process in scale growth,marked by a transition to parabolic time dependence. From our studies on phase-purepyrrhotite thin film and bulk samples, this transition should occur when the film hasgrown to approximately 100-1000 µm thickness.

Does the order-disorder transition in Fe1-xS have an effect of iron diffusivity? Ironself diffusivity *DFe in pyrrhotite had not been systematically studied below the knownorder-disorder transition at TN = 315 oC. Above TN, iron atoms are paramagnetic andcation vacancies are consequently randomly arranged in the lattice. *DFe in the para-magnetic regime follows an Arrhenius trend with an average activation energy Ep =0.83 eV. However, below TN iron atoms spontaneously magnetize, imposing a drivingforce for Fe vacancy ordering that results in a series of complex ordered superstruc-tures at low temperature. The effect of spontaneous magnetization is to increase theFe vacancy migration barrier. Hence the activation enregy Em for self-diffusion belowTN has a magnetic dependence of the form: Em = Ep +αS(T )2, where S is the reducedmagnetization of pyrrhotite and α is a constant ∼0.4. Therfore, extrapolation of theparamagnetic trend to lower temperatures would overestimate real diffusivitites in thismaterial, by up to 100 times at 150 oC.

How can we quantitatively assess surface electronic structure via scanning tun-neling spectroscopy (STS)? The probability of charge transfer between a solid andadsorbate is ultimately dictated by the availability of electronic states at the correctenergy levels. FeS2 is a good example of a semiconducting material in which unsatu-rated "dangling" bonds at the surface introduce additional states to those present in thebulk. A seemingly ideal tool to confirm the existence of surface states experimentally isSTM; however, the inherent electronic properties of the surface are easily distorted bythe very high proximate electric field of the tip, frequently leading to misinterpretationof values such as surface band gap Eg. This thesis contributes a systematic methodol-ogy for quantifying the surface electronic strucutre by matching simulated tunnelingcurrent predictions to experimental results from the STM. This approach is extendibleto other semiconducting materials with similar characteristics, such as other transitionmetal chalcogenides.

What role do surface states play in charge transfer on FeS2(100)? Using the tech-nique outlined above, the (100) surface of FeS2 is confirmed to contain intrinsic surfacestates (SS’s) arising from Fe and S dangling bonds. These sit on the edges of the valenceand conduction band, respectively, and have the effect of reducing the surface band gapfrom 0.95 to 0.4 eV. Since the surface states form continuous bands with the bulk states,charge cannot localize at intrinsic SS’s and they do not pin the Fermi level EF. However,extrinsic surface states from surface point defects and adsorbates sit discretely within

110

the surface Eg and do pin EF. The implications for electrochemical reactions such as oxi-dation during corrosion are that horizontal charge transfer can occur at smaller overpo-tentials η via surface states than would be predicted if the bulk electronic structure wereevaluated alone. In considering a generalized passive film model, this finding highlightsthe need to differentiate carefully between bulk and surface electronic structure.

What are the atomic-scale dynamics of point defects on destabilized ionic passivefilm surfaces? According to the Point Defect Model of Macdonald et al. (see Chapter 1),pitting is a deterministic process in which the breakdown of passivity is controlled onthe microscopic scale by the interactions of point defects at the metal-passive layer andpassive layer-electrolyte interfaces. The formation of cavities at these interfaces requiresvacancies on both the anion and cation sublattice to coalesce, via vacancy formationand diffusion processes. We show on a model FeS2(100) surface that under reducingconditions at elevated temperatures, vacancies can condense into pit-like features whicheffectively comprise single atomic steps into the surface. While not necessarily potentialpit initiation sites per se, their characterization allow us to formulate a real-time andpredictive model of the dynamics and interactions of point defects at the surface as itdestabilizes under reducing conditions.

Can surface vacancies account for reported polycrystalline FeS2 off-stoichiometry?The formation of vacancies in bulk pyrite is calculated to be energetically costly; how-ever, the surface of pyrite is found to readily forgo sulfur, and this has been proposed asone reason for the observed off-stoichiometry in polycrystalline FeS2 prepared by hightemperature methods such as sulfurization. The distinct binding energies of surface Satoms that are either bound to another S or adjacent to a vacancy, thereby allowing usto quantify the formation of vacancies with increasing temperature. A very low forma-tion enthalpy ∆H f = 0.1 eV for sulfur vacancies implies that the surface is indeed verysusceptible to losing sulfur to the atmosphere at even mild temperatures> 100 oC. Suchfacile vacancy formation suggests that the pyrite surface in situ is constantly in flux -vacancies easily form but are also reactive sites for further sulfidation. More generally,these findings are critical to the fabrication of synthetic pyrite for photovoltaic or otherapplications where homogeneity and/or full stoichiometry are important.

5.3 Outlook and perspectives

This thesis began with the hypothesis that a multiscale model for passive layers canbe constructed via a "bottom-up" approach, that is, by studying the elementary phys-ical chemistry at the surface and in the bulk of the ionic materials that comprise thepassive film, and determining the key unit processes governing film growth, reactivityand stability. None of the experimental contributions outlined above were realized un-der authentic sour corrosion conditions or even laboratory simulated ones. Instead, themajority of the work was carried out under either ultra high vacuum (UHV), i.e. wheresensitive ion- and electron- detection equipment can operate, or high-temperature, gasenvironments. Therefore, we must ask to what extent these fundamental studies ad-vance the overarching goal of constructing the universal passive film model introducedin Chapter 1. The problem of the vacuum gap, which asks how practical it is to extenddiscoveries made under highly-controlled, low pressure conditions to the "real-world"environment, is not unique to the investigations described in this thesis. However, it isstill greatly important to understand these microscopic events on surfaces free of con-taminants in order to gain insight into behavior on the fundamental level. To accom-plish a fully non-empirical, predictive tool for electrochemical systems we must startby studying ionic point defects on clean surfaces and in pure materials before adding

111

further complexity in the form of microstructure, liquid interfaces, applied stresses andso on.

Nevertheless, the further advancement of these ideas necessitates bridging this gap to amore realistic environment, for example with in situ aqueous studies on the iron sulfidephases of interest. The structure and bonding of water at surfaces is central to all elec-trochemical reactions in water-based electrolytes. Therefore some of the further studiessuggested in the individual experimental Chapters 2-4 involve the introduction of wa-ter: is diffusion and therefore film growth more rapid in porous iron sulfide films formedin solution? In what way does an electrical double layer affect the inherent reactivity ofthe surface? Can this be modeled accurately from first principles by density functionaltheory? Would a pyrite surface imaged by electrochemical STM in a corrosive solution,and under an applied bias, undergo surface destabilization that can still be describedby the basic vacancy dynamics described here? These constitute a small set of the ques-tions that must be answered if we are to achieve a comprehensive passive film modelthat has real-world applicability.

Let us end with a perspective on the two practical drivers of this project: the simulationof microscopic events as a predictive tool, and as a platform to design more robustmaterials for service in aggressive conditions. As outlined in Chapter 1, the study ofpassive films on metals has an almost 300-year old history, and it would be a haughtyoverstatement to suggest this work is anything but a minor contribution to our overallunderstanding of the field. However, we have outlined a basic methodology by whichthe study of local phenomena at the basic level of materials - atoms and electrons -can be fashioned into a larger-scale, descriptive model that can serve both these endgoals. Through novel insights into the rate-limiting mechanisms of surface reactions anddiffusion, and continued advances in computing power, we can forsee the ability oneday to predict the integrity of the materials in our vast network of energy infrastructuredown to the sub-nanometer scale. While humbled by this lofty goal, it is exciting toconsider what is possible through our knowledge of these materials on the fundamentallevel.

112

Appendix A

Pourbaix diagrams for theFe-H2S-H2O system

The calculations in this Appendix give rise to the two Pourbaix diagrams shown in Figure1-3 in Chapter 1. The standard Gibbs free energies (∆Go

f ) and enthalpies (∆Hof ) of

the species involved in constructing the thermodynamic stability diagrams are listed inTable A.1, referring to reference conditions of 25 oC and 1 atm pressure.

H2S dissociation

The H2S activity input to the thermodynamic stability diagrams must account for thedissolution of H2S gas in the local aqueous environment:

H2S(g)KH2S/H2S

⇔ H2S(aq) (A.1)

with a corresponding solubility constant:

KH2S(aq)/H2S(g) =aH2S(aq)

γH2S.pH2S

(A.2)

where:

• γH2S is the fugacity coefficient of H2S which can vary between 0.4-1.0. [20]

• pH2S is the partial pressure of H2S in the system.

Aqueous H2S can proceed to dissociate in two partial steps (Equations A1.3 and A1.4followed by Equations A1.5 and A1.6):

H2S(aq)

Kd,1

⇔ H+ +HS− (A.3)

Kd,1 =aH+aHS−

aH2S(aq)

(A.4)

HS−Kd,2

⇔ H+ + S2− (A.5)

Kd,2 =aH+aS2−

aHS−(A.6)

In the diagrams here, the value of γH2S = 1 is used. The H2S gas-aqueous solubilityconstant expression determined experimentally by Suleimenov et al. [197], Equation

113

Table A.1: Thermodynamic data for species in H2S-H2O-Fe system.

Species ∆Gof (kJ/mol) ∆Ho

f (kJ/mol) Reference

H+(aq)G 0.00 0.00[194]

H2S(g) -33.3 -20.6[194]

H2S(aq) -27.9 -39.7[194]

H2O(l) -237.1 -241.80[194]

H2(aq) 17.7[194]

O2(aq) 16.5[194]

Fe (s) 0[194]

Fe2+(aq) -91.5 -92.3

[194]

Fe3+(aq) -17.2

[194]

Fe2O3 (s) -743.5[194]

Fe3O4 (s) -1017.4[194]

Fe(OH)2 (s) -492.0[194]

Fe(OH)3 (s) -705.5[194]

FeSm (s) Mackinawite -93.3 -92.0 *[195]

FeSp (s) Pyrrhotite -114.5 -101.7[194]

FeS2 (s) Pyrite -160.1 -171.5[194]

FeHS+ -104.3 -152.7 *[196]

Table A.2: Input parameters.

Temperature (oC) 25

ptotal (atm) 1

pH2S (atm) 0.01

aFe2+ (mol.dm-3) 1.8x10-4 (10 ppm)

aFe3+ (mol.dm-3) 1.0x10-6

pH2(atm) 1.0

pO2(atm) 1.0

114

Table A.3: Fe-H2O Reactions and reversible potentials.

No. Reaction Erevor pH

O O2 + 4H+ + 4e−⇔ 2H2O Erev(O) = Eorev(O) −

2.3RT4F log 1

(aH+ )4

H 2H+ + 2e−⇔ H2 Erev(H) = Eorev(H) −

2.3RT2F log

(pH2 )

(aH+ )2

1 Fe2+ + 2e−⇔ Fe Erev(1) = Eorev(1) −

2.3RT2F log 1

(aFe2+ )

2 Fe3+ + 2e−⇔ Fe Erev(2) = Eorev(2) −

2.3RT2F log 1

(aFe3+ )

3 Fe(OH)2 + 2H+ + 2e−⇔ Fe+ 2H2O Erev(3) = Eorev(3) −

2.3RT2F log 1

(aH+ )2

4 Fe3O4 + 2H2O+ 2H+ + 2e−⇔ 3Fe(OH)2 Erev(4) = Eorev(4) −

2.3RT2F log 1

(aH+ )2

5 6Fe2O3 + 4H+ + 4e−⇔ 4Fe3O4 + 2H2O Erev(5) = Eorev(5) −

2.3RT4F log 1

(aH+ )4

6 Fe3O4 + 8H+ + 2e−⇔ 3Fe2+ + 4H2O Erev(6) = Eorev(6) −

2.3RT2F log

(aFe2+ )3

(aH+ )8

7 2Fe2O3 + 12H+ + 4e−⇔ 4Fe2+ + 6H2O Erev(6) = Eorev(6) −

2.3RT4F log

(aFe2+ )4

(aH+ )12

8 2Fe3+ + 3H2O⇔ Fe2O3 + 6H+ pH = − 12 .log(K8.a2

Fe3+)

9 Fe2+ + 2H2O⇔ Fe(OH)2 + 2H+ pH = − 12 .log(K8.aFe2+)

(A.7). yields the aqueous H2S activity for a given partial pressure input for the referencetemperature T = 298 K.

log(KH2S(aq)/H2S(g)) = −634.27+ 0.2709T − 0.11132× 10−3T 2 −16719

T− 261.9logT

(A.7)

Fe-H2O equilibrium reactions

The reactions demarcating the equilibrium between different species in the Fe-H2O-H2O system are taken from Ref. [14]. Table A.3 lists the expected water-iron reactionsalong with the reversible oxygen and hydrogen evolution reactions. The column onthe far right explicitly shows the reversible electrode potential, or constant pH line, foreach reaction. The standard reversible electrode potential Eo

rev(n) for a given reaction nis calculated here by evaluation of the Gibbs free energy of the reaction ∆Gr(n) understandard conditions of 25 oC, 1 atm pressure and unit activities, in turn estimated by thesum of the Gibbs free energies of formation of product species minus reactant species:

Eorev(n) = −

∆Gr(n)

zF= −

1zF

i∑

m=0

∆Gprod.f −∆G react.

f

(A.8)

Mackinawite, FeSm

Mackinawite has been proposed to form on bare iron or steel via the sequential chemisorp-tion of SH- ions and the following anodic discharge reactions. [20]

Fe(s) +H2S +H2O⇔ FeSH−ads +H3O+

FeSH−ads ⇔ FeSH+ads + 2e−

The species FeSH+ can be incorporated directly into the growing layer of mackinaw-ite via:

115

Table A.4: Mackinawite-Fe-H2O system equilibrium reactions.

No. Reaction Erev , pH or K

10 FeSm+2H++2e−⇔ Fe+H2S(aq) Erev(10) = Eorev(10) −

2.3RT2F log

aH2S

(aH+ )2

11 Fe2O3 + 2H2S(aq) + 2H+ + 2e−⇔2FeSm + 3H2O

Erev(11) = Eorev(11) −

2.3RT2F log 1

(aH2S )2(aH+ )2

12 Fe3O4 + 3H2S(aq) + 2H+ + 2e−⇔3FeSm + 4H2O

Erev(12) = Eorev(12) −

2.3RT2F log 1

(aH2S )3(aH+ )2

13 FeSm + 2H+⇔ Fe2+ +H2S(aq) pH = − 12 log

aFe2+ aH2S

K13

14 Fe(OH)2 + H2S(aq) ⇔ FeSm +2H2O

K14 =1

aH2S

Table A.5: Pyrrhotite-Fe-H2O system equilibrium reactions.

No. Reaction Erev or pH

20 FeSp +2H++2e−⇔ Fe+H2S(aq) Erev(20) = Eorev(20) −

2.3RT2F log

aH2S

(a+H )2

21 Fe2O3 + 2H2S(aq) + 2H+ + 2e−⇔2FeSp + 3H2O

Erev(21) = Eorev(21) −

2.3RT2F log 1

(a+H )2(aH2S )2

22 Fe3S4 + 2H+ + 2e− ⇔ 3FeSp +H2S(aq)

Erev(22) = Eorev(22) −

2.3RT2F log

aH2S

(a+H )2

23 FeSp + 2H+⇔ Fe2+ +H2S(aq) pH = − 12 .log

aFe2+ aH2S

K23

Assume mackinawite→ pyrrhotite in solid state reaction

FeSH+ads ⇔ FeS1−x(aq) + xSH−(aq) + (1− x)H+

However, for the purposes of a simplified stability diagram, we can assume a se-ries of overall equilibrium mackinawite formation reactions such as a direct, solid statereaction (i.e. electrochemical reaction, No. 10 in Table A.4) or solution-phase precipi-tation (i.e pure chemical reaction, No. 13 in A.4). Other possible formation reactions ofmackinawite are also listed in Table A.4.

Pyrrhotite, FeSp

It is assumed that pyrrhotite forms by direct, solid-state transformation from macki-nawite. Since FeSp is the more thermodynamically stable phase, this reaction will oc-cur spontaneously under all conditions in which mackinawite initially forms and greig-ite/pyrite are unstable. Therfore addition of FeSp to the consideration of a Fe-H2S-H2Osystem Pourbaix diagram will necessarily displace macknawite. In reality, sluggish kinet-ics of the solid state transformation can "stabilise" mackinawite to long times observedin experiment and in the field, especially at low temperatures and H2S partial pressures,illustrating the major shortcoming of overreliance on thermodynamic stability diagramsfor corrosion product prediction. The other equilibrium reactions involving pyrrhotiteare listed in Table A.5.

Pyrite, FeS2

The reactions involving pyrite used for construction of the final stability diagram (in-corporating all the considered Fe-S phases) are listed in Table A.6.

116

Table A.6: Pyrite-Fe-H2O system equilibrium reactions.

No. Reaction Erev

24 FeS2 + 4H+ + 2e− ⇔ Fe2+ +2H2S(aq)

Erev(24) = Eorev(24) −

2.3RT2F log

(aH2S )2(aFe2+ )

(a+H )4

25 FeS2+4H++4e−⇔ Fe+2H2S(aq) Erev(25) = Eorev(25) −

2.3RT4F log

(aH2S )2

(a+H )4

26 2FeS2 + 3H2O + 2H+ + 2e− ⇔Fe2O3 + 4H2S(aq)

Erev(26) = Eorev(26) −

2.3RT2F log

(aH2S )4

(a+H )2

27 FeS2 + 2H+ + 2e− ⇔ FeSm +H2S(aq)

Erev(27) = Eorev(27) −

2.3RT2F log

aH2S

(a+H )2

28 FeS2 + 2H+ + 2e− ⇔ FeSp +H2S(aq)

Erev(28) = Eorev(28) −

2.3RT2F log

aH2S

(a+H )2

29 FeS2+4H++e−⇔ Fe3++2H2S(aq) Erev(29) = Eorev(29) −

2.3RTF log

(aH2S )2(aFe3+ )

(a+H )4

30 3FeS2 + 4H+ + 4e− ⇔ Fe3S4 +2H2S(aq)

Erev(30) = Eorev(30) −

2.3RT4F log

(aH2S )2

(a+H )4

117

118

Appendix B

Chemical Vapor Deposition ofFe-S

B.1 Motivation

A chemical vapor deposition (CVD) system was set up to fabricate thin films of pyrrhotite(Fe1-xS), with the primary objective of using them for tracer diffusion studies. To thisend, we aimed to make high-purity films supported on non-ferrous substrates thatwould simulate a thin pyrrhotite corrosion scale on the order of several hundreds ofnanometers thick. Besides pyrrhotite phase purity, it was desirable to investigate a filmgrowth technique that could allow control over stoichiometry and that produced sam-ples with low surface roughness. A set of samples fabricated via CVD were used ininitial diffusion studies for this thesis, the results of which are presented in Appendix3. The work described here constitutes an initial, empirical investigation into the ef-fects of deposition parameters (substrate temperature, precursors, flow conditions) onfilm chemistry and morphology. In this appendix, we describe the setup of a homemadeCVD system and the fabrication of different iron sulfide films through the use of com-binations of various substrates and organic Fe and S precursors, and as a function ofsubstrate temperature. Finally, we introduce the "template stripping" technique thatwas used to make Fe-S samples with atomically-flat smoothness. Several potential appli-cations of combined CVD/template stripping approach facilitated by this work include:

• deposition of ultrathin Fe-S (or other similar sulfides e.g. Ni-S, Co-S, etc.);

• atomically-flat, polycrystalline samples for STM studies;

• surface patterning: surface plasmonics with chalcogenides.

B.2 Methods: CVD setup and apparatus

A schematic of the CVD apparatus is shown in Figure B-1a, along with a photographof the equipment in Figure B-1b. The entire system was constructed in a fume hood toavoid any exposure to toxic precursors. The flow of inert gas (Ar or N2-5% H2) throughthe system was controlled electronically by Omega FMA-series mass flow controllers(MFCs). The various iron and sulfur precursors used in this work are described in FigureB-2: iron (III) acetylacetonate (Fe(acac)3), iron pentacarbonyl (Fe(CO)5), di-tert butyldisulfide (TBDS), tert butyl methyl-sulfide (TBMS) and hydrogen sulfide (H2S). Liquidprecursors were kept in glass vials. Stainless steel tubes, connected to the gas linesvia 1

4 -inch Swagelok fittings, passed through a rubber bung in the vial to carry theprecursor vapor into the furnace. The inlet gas tube was not submerged beneath the

119

liquid; due to the relatively high vapor pressures it was sufficient to simply have the gaspassing through the vial containing the liquid precursors. When the solid iron precursorFe(acac)3 was used, approximately 20 g of powder was placed in a stainless steel tube,which was wrapped in heating coils powered by an automatic temperature controllerto achieve the desired setpoint. The substrate was placed on an 10 o inclined Al2O3holder in a quartz tube placed inside a Thermo Scientific Lindberg Blue M Mini-mitetube furnace. Homemade stainess steel compression fittings served as gas inlet/outletseals to the quartz tube. The temperature variation from the front to back ends of thetube inside the furnace was up to 200 oC. The actual temperatures measured uisnga thermocouple at various positions along the furnace are shown in Figure B-1c, forfurnace setpoint temperatures of 300-600 oC. The deposition temperatures reportedhenceforth refer to this calibration. Finally, the exhaust was scrubbed by bubbling atthe surface of a bleach solution before being sent up the stack of the fume hood.

Various substrates were used, including polished, 5 x 5 mm2 SiO2 (y-cut) and MgO(100)(both from MTI Corp., Richmond CA), cleaved Muscovite Mica sheets and NaCl crystals(both from SPI supplies, West Chester PA) and cut, soda-lime glass slides (VWR Int.,Radnor PA). In a typical deposition run, the substrate was placed in the furnace in thedesired position and heated under flowing inert gas. Five minutes prior to the start ofthe deposition, the vessels containing the Fe and S precursors were flushed with inertgas at the desired flow rate to remove any residual oxygen. The liquid precursor flowduring flushing was diverted directly to the exhaust. To begin deposition, a three wayvalve was switched to redirect the liquid precursor into the furnace.

B.3 Results

Table B.1 lists a range of conditions used in several prior CVD syntheses of iron sul-fides by other authors. Generally, the target composition was FeS2 for applications inphotovoltaic adsorbers. In the following, we describe the phase composition, purityand morphology of sample deposited using different precursors and under the range ofconditions outlined in Table B.2. First, a combination of Fe(acac)3 and TBDS was used,producing iron disulfide (FeS2) films with substantial carbon contamination. To miti-gate this, we switched to Fe(CO)5 as an iron source. Finally, to produce monosulfide(Fe1-xS) films, we switched TBDS for TBMS and finally H2S, both of which contain asingle sulfur atom as opposed to a S-S dimer.

Fe(acac)3 and TBDS: mostly FeS2

The initial setup we used was similar to that described by Berry et al., using Fe(acac)3and TBDS sources. [198] Figure B-3 shows the phase identification and SEM micro-graphs of as-deposited films using this setup, as evidenced by Raman spectroscopy (Fig.B-3a) and x-ray diffraction (Fig. B-3b)a. Pyrite has Raman peaks at 337 and 370 cm-1

while marcasite is characterized by resonances at 321 and 384 cm-1. Pyrrhotite (Fe1-xS)has no Raman resonance. At a substrate temperature of 280 oC, the predominant phasespresent were pyrite and marcasite (both FeS2. Increasing the substrate temperature to400 oC increased the volume fraction of marcasite relative to pyrite. At lower temper-atures, the deposition of the disulfide phases is facilitated by the pre-existence of asulfur-sulfur bond in the TBDS. To obtain pure pyrite films, the as-deposited sampleswere post annealed in sealed and evacuated quartz tubes containing a small amount ofsulfur powder, removing any trace of metastable marcasite phase. Finally, at higher tem-peratures beyond 400 oC, the stability limit for FeS2 is reached and increasing amountsof pyrrhotite were deposited. At 600 oC, pyrrhotite was the only iron sulfide phase ob-served.

120

Ar

Fe(acac)o150 C

Mesh to mix gases

Substrate holderoinclined 10

d-TBDSo50 C

ExhaustScrubber

oFurnace 300-600 C

MFC 1

MFC 2MFC 3 Vent

O-ring sealsMFC’s

MFC’s Precursors Furnace Exhaust

(c) Temperature variation across furnace

(b) CVD apparatus without heating coils for precursors

(a) Schematic of original CVD apparatus

0 2 4 6 8 10 12 14100

200

300

400

500

600

700

Sample position (inches from gas inlet)

oM

ea

sure

d t

em

pe

ratu

re (

C)

oT = 600 Cset

oT = 500 Cset

oT = 400 Cset

oT = 300 Cset

Figure B-1: Home-made Chemical Vapor Deposition (CVD) system: (a) schematic drawing of setup forsolid iron (III) acetylacetonate (Fe(acac)3) and liquid di-tert-butyl disulfide (d-TBDS) sources. (b) photographof setup in fume hood, indicating the position of the components drawn in the schematic. (c) the furnacetemperature was not uniform; the graphs shows the variation as a function of position from the gas inlet ofthe furnace tube, for furnace set temperatures of 300, 400, 500 and 600 oC.

Carbon contamination from Fe(acac)3

However, the use of Fe(acac)3 and TBDS as precursors led to the contamination of thesamples with carbon. Figure B-4 indicates the amount of carbon measured in the films asa function of substrate temperature, as measured by electron dispersive spectrometry(EDS) in a JEOL Supra 55 SEM. The amount of carbon deposited increases approxi-mately linearly with increasing temperature up to ∼ 30 at% at a substrate temperatureof 550 oC. We believe the source of the carbon to be Fe(acac)3, since it is a large, com-plex molecule containing fifteen carbon atoms and only six oxygens; hence the removal

121

(a) Iron(III) acetylacetonate

[Fe(acac) ]3

(b) Iron pentacarbonyl [Fe(CO) ]5

(c) (Di)tert-butyl disulfide [TBDS]

(e) Hydrogen sulfide [H S]2

(d) Tert-butyl methylsulfide

[TBMS]

S

H C3

H C3

H C3

SH C3

H C3

H C3

CH3

S CH3

CH3

CH3

31 1

44 0

S

HH

IRON PRECURSORS SULFUR PRECURSORS

Red, air stable solid.

Harmful if swallowed.

Straw-colored liquid.

Very toxic, highly flammable.

Pungent gas.

Highly toxic, highly flammable.

Straw-colored liquid.

Flammable, low toxicity.

Straw-colored liquid.

Harmful to aquatic life.

Figure B-2: Description and safety information for Fe and S precursors: (a) and (b) iron precursors.Fe(CO)5 is toxic and requires special handling precautions; however, it is easier to control vapor flow in CVD.(c-e) sulfur precursors. TBDS is useful for making FeS2 because it already contains a sulfur-sulfur dimer bond.TBMS dissociates at elevated temperatures to leave an HS- reactive radical. H2S is the cleanest S source ofall (no carbon).

Table B.1: CVD of Fe-S phases by other authors.

Fe source S source Substrate T (oC) P (Torr) Phase Ref.

Fe(acac)3 TBDS Glass, Si 300 + A a) 760 Py. [198]

Fe(CO)5 TBDS Various 580 38 Py. [199]

Fe(CO)5 TBDS FeS2 475 38 Py. d) [200]

Fe(CO)5 TBDS Glass 475 38 Py., Po. [201]

Cp2Fe b) C3H6 Pyrex 410 c) 38/760 Po. [202]

Fe(CO)5 H2S/S Glass 140 760 Py. [203]Py = pyrite; Po = pyrrhotite; a) A = post anneal in S2 at 500 oC; b) Cp = η-C2H5; c) cold-walled reactor; d)epitaxial pyrite.

122

Tabl

eB

.2:C

hem

ical

Vapo

rD

epos

itio

nco

ndi

tion

sfo

rFe

-Sph

ases

:li

tera

ture

.

Iron

sou

rce

Sulf

ur

sou

rce

Car

rier

gas

(scc

m)

Subs

trat

eT

(oC

)Ph

ases

Dep

osit

ion

rate

(nm/h

r)R

emar

ks

Type

Tem

p.(o

C)

Flow

(scc

m)

Type

Tem

p.(o

C)

Flow

(scc

m)

Fe(a

cac)

316

030

0T

BD

S50

-60

200

Ar

(500

)30

0-60

0Fe

S 2,

Fe1-

xS10

0-50

0C

cont

amin

atio

n>

300

oC

Fe(C

O) 5

030

TB

MS

2550

-180

Ar

(400

)40

0-50

0Fe

1-xS

,Fe

20-1

00Fe

depo

sits<

450

oC

Fe(C

O) 5

05-

30H

2S

2535

0N

2-5

%H

237

5-55

0Fe

1-xS

20-1

00B

est

qual

ity

and

puri

ty

123

250 300 350 400 450Raman Shift (cm

- 1)

Inte

nsity

(arb

. u

nits

)

321

337432

384

370

Pyrrhotiteo

600 C

1 μm

20 30 40 50 60 70

Cu-kα 2Θ

Inte

nsity

(a

rb.

un

its)

*

*

**††

*

**

* *

oAnnealed in S 500 C2

As-grown CVDo

280 C

*†

PyriteMarcasite

(a) Fe(acac) and TBDS precursors Raman spectroscopy3 :

Marcasite + Pyriteo400 C

Pyriteo

Annealed S 500 C2

(b) X-ray diffracion of as-deposited and S -annealed samples 2

†

Pyrite + Marcasiteo

280 C

Figure B-3: Iron sulfide films deposited from Fe(acac)3 and TBDS: (a) Raman spectroscopy and corre-sponding scanning electron microscope (SEM) images for samples deposited at 600, 400, 280 oC and apyrite film post-annealed in sulfur vapor at 500 oC. (b) Cu-kα x-ray diffraction patterns for as-grown marca-site/pyrite and post-annealed pure pyrite films.

of carbon through reaction to carbon monoxide or dioxide is not 100% efficient.

Pyrrhotite (Fe1-xS) films with monosulfide precursors

With Fe(CO)5 serving as the iron precursor, the sulfur precursor was changed to TBMS(Fig. B-2d) to avoid the pre-existing S-S bond such as in TBDS, which would encouragethe formation of the disulfide phases. TBMS is a volatile but low-toxic liquid that couldbe kept at room temperature during deposition. Fe(CO)5, on the other hand is toxic andpyrophoric liquid that requires special handling (see Appendix 4 for MSDS). Fe(CO)5 isvery volatile and dissociates readily at temperatures as low as 150 oC, and therefore hadto be maintained in an ice bucket at 0 oC to avoid excessive metallic iron deposition.Nevertheless, as evidenced by the XRD results in Figure B-5, some pure iron phasewas deposited in films at temperatures below 450 oC. Finally, to increase the sulfidepartial pressure and ensure full reaction of the precursors, the TBMS was exchangedfor N2 - 4% H2S gas. All films deposited in the range 300-500 oC with Fe(CO)5/ H2S

124

200 300 400 500 6000

10

20

30

40

Substrate temperature (oC)

Carb

on c

onte

nt (a

t%)

Carbon contaminaton from Fe(acac)3

Figure B-4: Carbon contamination in Fe-S films from Fe(acac)3: as measured by electron dispersive spec-troscopy (EDS), as a function of substrate temperature during deposition.

30 40 50 60 70 80 90Cu-k α 2Θ

Inte

nsi

ty (

arb

. units

)

†

*

* **

** *

* **

**

†

†

† †

†

* ***

o400 C

o450 C

o300 C

** *

*†Hex. Fe S1-x

Metallic Fe

200 nm

Fe(CO) and TBMS precursors: pyrrhotite/iron films5

Figure B-5: Iron sulfide films deposited from Fe(CO)5 and TBMS: Cu-kα x-ray diffraction patterns forfilms deposited at 300, 400 and 450 oC with decreasing metallic Fe content; corresponding scanning electronmicroscopy (SEM) images of the as-deposited film surfaces.

were pure pyrrhotite. Moreover, this combination of precursors also offers the "cleanest"way to deposit FeS: i.e. without any source of carbon or other likely contamination.The downside is the toxicity of the precursors; beyond Fe(CO)5, hydrogen sulfide is anextremely toxic gas that requires special precautions and handling.

In Figure B-6 we show SEM micrographs of the top surface from samples depositedusing Fe(CO)5/ H2S on glass (Fig. B-6a), muscovite mica (Fig. B-6b and c) and NaCl(Fig. B-6d). The choice of substrate had little obvious effect on the morphology of theas-deposited Fe1-xS; in all cases the grains were roughly equiaxed with sizes betweenseveral hundreds of nm and one µm. Finally, the exact stoichiometry of the films couldnot be measured due to their thickness being on the order of 100-1000 nm. The signalfrom conventional chemical composition techniques, e.g. EDS, was not strong enoughto give adequate counting statistics and distinguish the Fe:S ratio within the Fe1-xS com-position of 0≤ x ≤ 0.125.

125

1 μm 3 μm

1 μm200 μm

Fe(CO) and H S precursors:5 2

(a) Glass substrate (b) Mica substrate

(d) NaCl substrate (b) Mica substrate

Figure B-6: Iron sulfide films deposited from Fe(CO)5 and H2S: scanning electron microscopy (SEM)images of films deposited on (a) glass slide, (b and c) mica, (d) NaCl(100) substrate.

Template stripping for atomically-smooth surfaces

The root-mean squared (RMS) roughness of as-deposited films using Fe(CO)5/H2S pre-cursors (Fig. B-7a) was on the order of 50+ nm, as measured by atomic force microscopy(AFM). Given the original motivation of the CVD project to produce thin film samplesfor tracer diffusion studies, a surface roughness of this order (i.e. greater than the targettracer deposit thickness of 10 nm) was not conducive to obtaining accurate diffusionprofiles. Therefore we explored ways to make the films smoother. By vastly reducing theFe precursor flow such that the overall deposition rate was just a few nm per hour, thefilms could be fabricated with RMS roughness < 10 nm. However, this approach wasimpractical for making samples with total thickness of 100 nm or more. Therefore weemployed the template stripping technique, which has been used to make "ultrasmooth",patterned metal films for surface plasmonics [204] or flexible electrodes [205] or TiO2for various applications. [206] The procedure is outlined in Figure B-7c: the as-grownfilm is coated with an epoxy resin, onto which a glass piece is pressed to remove airbubbles. The epoxy is left to set for the requisite time, before removing the originalsubstrate using the edge of a razor blade. Due to the low surface energy and chemicalincompatibility of the substrates (oxide substrates to sulfide films), the CVD film pref-erentially adheres to the epoxy, exposing the side grown directly onto the polished oratomically-flat, cleaved substrate surface (Fig. B-7b). This technique worked well on avariety of substrates. An alternative that was also attempted was to deposit on NaClcrystals, and wash away the NaCl using distilled water after supporting the FeS film ona glass slide with epoxy. Although also successful, this technique was not as clean as theoxide substrate version.

126

Grow film on flat substrate

Coat with hightemperature epoxy

Strip from substrate with razor blade

2 μm

(a) As-deposited surface (b) Smooth side

(c) Template stripping process

Figure B-7: Template stripping for ultrasmooth sulfide surfaces. Scanning electron microscopy (SEM)images of (a) as-deposited surface (Fe(CO)5 / H2S) and (b) template stripped (inverted) surface, as grownon polished SiO2. (c) schematic of the template stripping process.

127

128

Appendix C

Diffusivity measurements usingthin film samples

Before turning to bulk, natural samples to obtain the diffusivity measurements in thiswork, we carried out preliminary tests using synthetic thin film Fe1-xS samples, fabri-cated by either chemical vapor deposition (CVD) or sputter deposition. Shown in FigureC-1, iron self-diffusivity values measured from thin film samples were inconsistently lowas compared to data from literature or from our bulk samples measured in this work,and hence were not reported in the main text of this paper. Below, we briefly reporthow the films were fabricated, describe the diffusion measurement results, and discussthe likely sources of the disparate results.

Chemical Vapor Deposition of Fe1-xS films

CVD films were grown on soda lime glass pieces according to the procedure outlined inAppendix 2, using Fe(CO)5 and H2S as precursors. As-deposited films were on the orderof 300-700 nm thick. In order to obtain flat surfaces for SIMS analysis, we employedthe template stripping technique. [204, 206] The as-grown film was coated in a high-temperature epoxy (stable up to 350 oC), and covered with another glass piece, slightlylarger than the substrate size. After curing, the glass piece was removed with a razorblade, and the film preferentially adhered to the cured epoxy, stripping cleanly off theoriginal growth substrate and revealing a surface conforming to the substrate’s originaltopography. Various polished substrates such as MgO(100), SiO2, Si and soda lime glasswere experimented with; soda lime glass was found to give satisfactory results at thelowest cost. The x-ray diffraction (XRD) pattern of a typical CVD template stripped filmis shown in Figure

Sputter deposition of Fe1-xS films

Sputter deposited films were made according to the procedure outlined in Chapter 2.The XRD pattern is shown in Figure

Thin film diffusion measurements: results and discussion

Both CVD and sputtered film samples were coated in 10 nm of 57Fe using thermal evap-oration. Annealing runs to produce diffusion profiles were performed by holding thesamples in heated nitrate salt baths held at the desired temperature. Samples werevacuum-sealed in quartz tubes during immersion in salt baths. SIMS analysis to obtaindiffusion profiles of the annealed samples was as described in the main text. To fit thedata, we used the thin film diffusion solution to Fick’s second law [70]:

129

0.5 1 1.5 2 2.510

-20

10-15

10-10

10-5

1000/T (K- 1)

log

[*D

Fe]

(cm

2s

- 1)

900 700 500 400 300 200 150

Fryt *

Condit **

This work

Literature

Linear reg.

Bulk crystal

Model fit

CVD

Sputtered

oTemperature ( C)

0.94 eV

Full Fe self-diffusion results from Ch. 2 and for thin films

Figure C-1: Iron self-diffusivity *DFe measurements obtained from thin film, chemical vapor(CVD) and sputter deposited samples (triangles), alongside the literature data and bulk sam-ple measurements discussed in the main text. Our thin film measurements fall up to 3-4 orders ofmagnitude lower than the bulk sample results. We attribute the discrepancy to oxide formationfrom residual oxygen during annealing runs, which binds the 57Fe deposit as iron oxide and hencereduces the extent of interdiffusivity (discussed in the text below).

C(x , t) =Co

2

er fa− x

2p

Dt+ er f

a+ x

2p

Dt

(C.1)

where Co is the concentration at the surface, a is the original deposit thickness, and Dis diffusivity. In the limit of a very thin film, a Gaussian approximation to Eq. (C.1) canbe given:

C(x , t) =N

p4πDt

exp

−x2

4Dt

(C.2)

Figure C-3 shows selected results from thin film profile measurements. For CVD samples(Figures C-3a), we used Eq. (C.2) to fit the results. In Figure C-3b we re-plot the dataas C vs. x2, obtaining a straight line from which diffusivity D was calculated. For thesputter deposited samples, we fit the results using Eq. (C.1).

The results of our thin film diffusion experiments are presented in Figure C-1, along-side the literature values and the bulk sample results, as discussed in the main text.Although the slope, i.e. activation energy Q, is consistent with the bulk sample result inthe ordered regime below TN, the thin film diffusion coefficients are shifted down by 3-4orders of magnitude. This difference cannot be explained on the basis of difference instoichiometry alone (which would only account for approx 10x difference: see Figure 1b

130

XRD of thin film samples

30 40 50 60 70

Cu-k α 2Θ

Inte

nsity

(arb

. u

nits)

(100)

(101)(102)

(110)

(200)

(004)

CVD

Sputtered

Figure C-2: X-ray diffraction of thiin films for ECR experiments. (a) Cu-kα x-ray diffraction(XRD) scans for chemical vapor (CVD) and sputter deposited films, with hexagonal pyrrhotitereflections indicated. (b) scanning electron microscope (SEM) of sputtered film top surface, afterpost-annealing treatment (inset: 60 o tilted view). (c) pole figure XRD scans confirm the high(100) texture of the sputtered samples.

in the main text). Still, a very low iron vacancy concentration would be expected afterannealing due to the high volume of pure 57Fe deposit relative to Fe1-xS in the interdif-fused region, that would put *DFe values on the lower limit of the stoichiometric effect.We postulate a further reason for the vastly reduced diffusion coeffieicents: oxidation ofthe 57Fe deposit from residual oxygen during annealing. The quartz tubes used to sealthe samples during diffusion runs in salt baths were evacuated to ∼ 10-3 Torr, and thesample surface after annealing typically turned from metallic silver to a blue tinge. Weperformed a control test using a sample annealed under a dynamic flowing atmosphereof 1% H2S-N2, where the amount of available oxygen was practically nil. The resultsare presented in Figure C-4, for two samples (original 57Fe deposit thickness = 30 nm)annealed at 185 oC. Despite being held for a much shorter time of 5 days compared to25 days, the sample annealed in the H2S furnace had a completely flat [57Fe] profile,indicating that all the deposit had fully diffused through the specimen. Upon removingthe sample from the furnace after 5 days, the surface was found to still be metallic sil-very in color. Conversely, even after 25 days in the quartz vial, the other sample showeda much lesser extent of diffusion. Moreover, the surface coloration evolved into a bluelustre, indicative of iron oxide formation at the surface.

In conclusion, we believe two compounding factors lead to an underestimate of *DFefrom our measurements on thin film samples annealed in evacuated quartz vials. First,the residual oxygen in the vials reacted with the 57Fe deposit surface and tied it up asoxide, preventing rapid interdiffusion with the pyrrhotite substrate. Second, the lack ofavailable sulfur in the atmosphere to react with the deposit meant that vacancies in thesamples were "flooded" with Fe, making the samples highly iron-rich. Since Fe diffusionin Fe1-xS occurs via a vacancy-exchange mechanism, removing vacancies would have anadditional effect on reducing measured diffusion coefficients. After these initial trialswith thin film samples, we decided to utilize bulk natural crystals (giving the resultsoutlined in the main text) rather thanto further pursue thin films annealed under dy-namic, H2S-containing environments. The reason was that for thin tracer deposits of10’s of nm, the required annealing times to achieve measureable diffusion profiles be-came impractically short (on the order of seconds). For bulk samples, a much thicker

131

-4

-3.5

-3

-2.5

-2

-1.5

-1

0 40 80 120 160 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

00 0.4 0.8 1

x 104

x2 (nm2 )

0.60.2

Depth (nm)

ln[5

7 Fe]

[5

7 Fe]

oAnnealed at 250 C

36000s (10 hrs)

3600s

511440s (>5 days)

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Depth (nm)

% F

e57

oAnnealed at 300 C

3600 s

-15Fit D = 1.6 x 10-15Fit D = 1.1 x 10 -15Fit D = 1.4 x 10

1200 s360 s

36000 s

0 50 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Depth (nm)

% F

e57

Annealed 1 hour

o315 C

-16Fit D = 3.5 x 10-15Fit D = 1.1 x 10 -15Fit D = 1.4 x 10

o300 C

o275 C

(a) (b)

(c) (d)

SPUTTER DEPOSITED FILMS SPUTTER DEPOSITED FILMS

CVD FILMS CVD FILMS

oAnnealed at 250 C

Diffusion profiles for CVD films Fit to Gaussian diffusion solution

Diffusion profiles: constant temperature Diffusion profiles: constant anneal time

Figure C-3: Representative diffusion profiles of 57Fe in thin film Fe1-xS, measured by secondaryion mass spectrometry (SIMS) for: (a, b) chemical vapor deposited (CVD) samples annealed at250 oC for different lengths of time as indicated, fit to the Gaussian solution in Eq. (C.2); (c) sput-ter deposited samples annealed at 300 oC for different times, fit with the thin film error functionsolution in Eq. (C.1); (d) sputter deposited films annealed for 1 hour at different temperatures,as displayed.

depost of tracer can be made, allowing more reasonble annealing experiments on theorder of minutes-hours.

132

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

x (nm)

[57F

e] o185 C 5 days

H S furnace2

o185 C 25 daysQuartz vial

Surface oxidation of thin films reduces diffusion

Figure C-4: Oxidation of samples annealed in quartz vials. 57Fe diffusion profiles measured fortwo identically-produced Fe1-xS samples annealed at 185 oC inside an evacuated quartz vial, orunder a dynamic H2S-bearing envionment, as indicated. The quartz vial sample turned a bluelustre, whereas the furnace annealed sample retained its original silvery metallic surface.

133

134

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