Master thesis

Interactions between Nanoparticlesof Antiferromagnetic Materials

An investigation of interactions between ferrihydrite and CoO.

Master Thesisby

Britt Rosendahl Hansen

Niels Bohr Institute for Astronomy,Physics and Geophysics, University ofCopenhagen

Department of Physics, Technical Univer-sity of Denmark

Abstract

It is shown that CoO nanoparticles can be prepared from Co3O4 byball milling and subsequent reduction by heating in H2. From refinementof XRD spectra the size of the CoO nanoparticles is found to be ∼ 10nm.

The CoO nanoparticles were mixed with 6-line ferrihydrite and theeffect on the superparamagnetic relaxation of ferrihydrite was studied us-ing Mossbauer spectroscopy. The measurements showed that interactionwith CoO nanoparticles lead to a suppression of the superparamagneticrelaxation of ferrihydrite.

Interaction between the nanoparticles was also seen in magnetizationmeasurements, when comparing the data for the two nanoparticles witha mixed sample. A modified Langevin function and modified Curie lawwere fit to the magnetization data for ferrihydrite to obtain the particlemagnetic moment and the Neel temperature. The validity of the modifiedfunctions is questioned.

i

Preface andAcknowledgements

This thesis is submitted in partial fulfillment of the requirements for obtainingthe degree of Master of Science at the University of Copenhagen (KU). Thework detailed in the thesis was carried out at the Technical University ofDenmark (DTU) and in collaboration with Risø National Laboratory in theperiod from September 2003 to November 2004. Supervisors were ProfessorSteen Mørup of the Nanostructured Materials group at the Department ofPhysics, DTU, Senior Scientist Kim Lefmann from the Materials ResearchDepartment, Risø, and Associate Professor Morten Bo Madsen at the Centerfor Planetary Science, KU.

Special thanks are given to Professor Steen Mørup for his guidance andinitial suggestion that I do my thesis work in his group - it has been a wonderfuland educational time. Many thanks are given to Christian Robert HaffendenBahl for his help with experiments, for discussions, for transmission electronmicroscopy images and for creating a pleasant atmosphere in the office.

I would like to acknowledge Bente Lebech who provided valuable advice re-garding Rietveld refinement of XRD spectra. Also, Associate Professor MikkelFougt Hansen at the Department of Micro and Nanotechnology (MIC), DTU,was kind enough to help me with the LakeShore vibrating sample magnetome-ter and gave me valuable input on the interpretation of the data. Likewise,Associate Professor Leif Gerward from the Nanostructured Materials group,DTU, is acknowledged for instructing me in the operation of the x-ray diffrac-tometer at the Department of Physics. I am grateful for the opportunity to usethe above-mentioned instruments. I would also like to acknowledge CathrineFrandsen, who has been helpful with information and also contributed to theatmosphere in the group. Many thanks are given to Thomas Pedersen andPeter Gath Hansen for proofreading the thesis.

Also many thanks to Lis Lilleballe and Helge Rasmussen for their help inthe preparation of the studied nanoparticles and for their help with miscella-neous tasks in the chemistry and Mossbauer laboratories.

Britt Rosendahl HansenNovember 2004

iii

Contents

i

Contents iv

List of Figures vi

List of Tables ix

1 Introduction and Motivation 1

2 Theory of Magnetic Nanoparticles 72.1 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Magnetic Ordering . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . 112.5 Antiferromagnetic Nanoparticles . . . . . . . . . . . . . . . . . 132.6 The CGS Gaussian System versus the SI . . . . . . . . . . . . . 15

3 Experimental Methods 193.1 X-ray Powder Diffraction . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 X-ray Diffraction Setup . . . . . . . . . . . . . . . . . . 203.1.2 Crystallite Size Determination . . . . . . . . . . . . . . 213.1.3 Rietveld Refinement and Quantitative Phase Analysis . 23

3.2 Transmission Electron Microscopy (TEM) . . . . . . . . . . . . 243.2.1 Microscope Design . . . . . . . . . . . . . . . . . . . . . 24

3.3 Mossbauer Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 263.3.1 Mossbauer Spectroscopy Setup . . . . . . . . . . . . . . 283.3.2 Hyperfine Interactions Affecting the Mossbauer Spectrum 293.3.3 Intensities of Lines in Magnetically Split Spectra . . . . 343.3.4 Interpretation of 57Fe Mossbauer Spectra . . . . . . . . 35

3.4 Vibrating Sample Magnetometer (VSM) . . . . . . . . . . . . . 403.4.1 Vibrating Sample Magnetometer Setup . . . . . . . . . 413.4.2 Interpretation of VSM Data Obtained . . . . . . . . . . 43

4 Ferrihydrite and CoO 454.1 Ferrihydrite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Ferrihydrite in Living Organisms . . . . . . . . . . . . . 484.2 CoO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 Production of Ferrihydrite and CoO Nanoparticles 535.1 CoO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.1.1 Fritsch Pulverisette Ball Mill . . . . . . . . . . . . . . . 535.1.2 Step One: Ball-Milling of Co3O4 . . . . . . . . . . . . . 555.1.3 Step Two: Heating in H2 . . . . . . . . . . . . . . . . . 565.1.4 Production Details for Samples CoO1 and CoO6 . . . . 585.1.5 Samples CoO2, CoO3, CoO4 and CoO5 . . . . . . . . . 59

5.2 Ferrihydrite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6 Mossbauer study 636.1 Overview of Samples . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Ferrihydrite and Sample CoO6 . . . . . . . . . . . . . . . . . . 656.3 Effects of Grinding and Heating on Ferrihydrite. . . . . . . . . 676.4 Study of Ferrihydrite Mixed with CoO . . . . . . . . . . . . . . 73

6.4.1 Samples Mixed in Aqueous Solutions . . . . . . . . . . . 736.4.2 Reflux Water-Condenser Samples . . . . . . . . . . . . . 776.4.3 Sample Mixed with Ultrasound . . . . . . . . . . . . . . 796.4.4 Samples Mixed by Grinding and Heating . . . . . . . . 80

6.5 Room Temperature Mossbauer Spectra . . . . . . . . . . . . . . 86

7 VSM Measurements 897.1 Interactions between Nanoparticles . . . . . . . . . . . . . . . . 91

7.1.1 Comparison of the Three Samples . . . . . . . . . . . . 947.2 Langevin Fit of Ferrihydrite Field Curves . . . . . . . . . . . . 1027.3 Initial Susceptibility of Ferrihydrite . . . . . . . . . . . . . . . . 105

8 Conclusions 1098.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Appendices 111

A Units and Constants 113

B Conversion Table between CGS Gaussian and SI 115

C Element Analysis of Fritsch Pulverisette WC Grinding Bowl 117

D Ball Milling Timetable for Sample CoO1 119

Bibliography 121

v

List of Figures

List of Figures

1.1 Areal density trend of IBM hard disk drives . . . . . . . . . . . . . 1

2.1 The Langevin function and Curie-Weiss law. . . . . . . . . . . . . 92.2 Ferromagnetic domain structure. . . . . . . . . . . . . . . . . . . . 92.3 Ordered magnetic moments in an antiferromagnet. . . . . . . . . . 102.4 Temperature dependence of antiferromagnetic susceptibility. . . . . 112.5 Magnetic anisotropy energy in a crystal with uniaxial symmetry. . 122.6 Magnetic anisotropy constants K1 and K2 of Fe. . . . . . . . . . . 132.7 Antiferromagnetic nanoparticle. . . . . . . . . . . . . . . . . . . . . 142.8 Reversal of the magnetic moment in a nanoparticle. . . . . . . . . 142.9 Dipole and exchange interaction. . . . . . . . . . . . . . . . . . . . 15

3.1 Geometric derivation of Bragg’s equation. . . . . . . . . . . . . . . 203.2 Scattering planes given by their Miller indices (hkl). . . . . . . . . 203.3 Transitions and x-ray spectrum for Cu. . . . . . . . . . . . . . . . 213.4 In-house x-ray powder diffraction setup. . . . . . . . . . . . . . . . 223.5 Effects of isotropic and anisotropic strain on a scattering peak. . . 223.6 Refinement of XRD pattern of Si standard. . . . . . . . . . . . . . 243.7 The Jeol JEM-3000F TEM. . . . . . . . . . . . . . . . . . . . . . . 253.8 Resonant absorption of a γ-quantum. . . . . . . . . . . . . . . . . 273.9 The Mossbauer spectroscopy setup. . . . . . . . . . . . . . . . . . . 283.10 The decay scheme of 57Co. . . . . . . . . . . . . . . . . . . . . . . 293.11 The isomer shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.12 Quadrupole splitting. . . . . . . . . . . . . . . . . . . . . . . . . . 323.13 Magnetic hyperfine splitting. . . . . . . . . . . . . . . . . . . . . . 333.14 Octahedral and tetrahedral coordination. . . . . . . . . . . . . . . 363.15 Angular part of 3d orbitals. . . . . . . . . . . . . . . . . . . . . . . 373.16 eg and t2g orbitals in octahedral coordination. . . . . . . . . . . . . 383.17 Relative energies of the e and t2 orbitals. . . . . . . . . . . . . . . 383.18 High-spin and low-spin states. . . . . . . . . . . . . . . . . . . . . . 393.19 The basic setup of a VSM. . . . . . . . . . . . . . . . . . . . . . . 413.20 Output of demodulator in a lock-in amplifier. . . . . . . . . . . . . 423.21 Hysteresis loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1 Ferrihydrite in a ferriferous spring in Iceland. . . . . . . . . . . . . 45

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4.2 XRD spectra of ferrihydrite. . . . . . . . . . . . . . . . . . . . . . . 464.3 Idealized models of hematite and goethite. . . . . . . . . . . . . . . 474.4 Molecular model of ferritin . . . . . . . . . . . . . . . . . . . . . . 494.5 The cubic, trigonal and monoclinic Bravais lattices. . . . . . . . . . 494.6 Crystal and magnetic structure of CoO . . . . . . . . . . . . . . . 50

5.1 Refined XRD spectrum of as prepared Co3O4. . . . . . . . . . . . 545.2 Fritsch pulverisette 5 planetary mill. . . . . . . . . . . . . . . . . . 555.3 Broadening of Co3O4 XRD peak. . . . . . . . . . . . . . . . . . . 565.4 XRD spectra of as prepared Co3O4 reduced in H2. . . . . . . . . . 575.5 Refinement of XRD spectrum of sample CoO1. . . . . . . . . . . . 585.6 Refinement of XRD spectrum of sample CoO6. . . . . . . . . . . . 595.7 XRD spectrum of ferrihydrite sample. . . . . . . . . . . . . . . . . 605.8 TEM image of ferrihydrite showing agglomeration of the particles. 61

6.1 Mossbauer spectra and hyperfine field distributions of ferrihydrite. 666.2 Mossbauer spectrum of sample CoO6. . . . . . . . . . . . . . . . . 676.3 TEM image of ground ferrihydrite. . . . . . . . . . . . . . . . . . . 686.4 XRD spectra comparing untreated and ground ferrihydrite. . . . . 696.5 Mossbauer spectra of treated ferrihydrite. . . . . . . . . . . . . . . 706.6 Hyperfine field distributions of treated ferrihydrite. . . . . . . . . . 716.7 XRD spectra comparing untreated and heated ferrihydrite. . . . . 726.8 Mossbauer spectra of samples mixed in aqueous solutions . . . . . 746.9 Hyperfine field distributions of samples mixed in aqueous solutions. 756.10 Mossbauer spectrum of mixed sample FHCoO 2250 RTD . . . . 766.11 Mossbauer spectra of samples heated in a reflux water-condenser. . 786.12 Mossbauer spectrum of sample mixed with ultrasound. . . . . . . . 796.13 Mossbauer spectrum of mixed sample FHCoO6 Mix. . . . . . . . 806.14 Mossbauer spectrum of mixed sample FHCoO6 GH. . . . . . . . 816.15 Mossbauer spectra of samples mixed and heated in H2. . . . . . . 826.16 Mossbauer spectra of mixed samples heated in H2. . . . . . . . . . 846.17 Hyperfine field distributions of samples heated in H2. . . . . . . . 856.18 Mossbauer spectrum of ferrihydrite at room temperature. . . . . . 866.19 Room temperature spectra of ferrihydrite and two mixed samples. 87

7.1 Field sweep of empty sample cup. . . . . . . . . . . . . . . . . . . . 907.2 Low-field part of ZFC and FC hysteresis loops for ferrihydrite. . . 917.3 Field sweeps showing the progression in transformation. . . . . . . 927.4 Mossbauer spectra of transformed ferrihydrite. . . . . . . . . . . . 937.5 Comparison of FC hysteresis curves. . . . . . . . . . . . . . . . . . 947.6 Comparison of ZFC hysteresis curves. . . . . . . . . . . . . . . . . 957.7 Magnetic moment at maximum field (±16 kOe). . . . . . . . . . . 967.8 FC and ZFC hysteresis loops of mixed sample. . . . . . . . . . . . 967.9 The moment shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.10 Exchange bias of sample CoO1. . . . . . . . . . . . . . . . . . . . 987.11 Exchange bias of mixed sample FHCoO RTD. . . . . . . . . . . . 99

vii

List of Figures

7.12 Diagram showing the calculation of the coercivity. . . . . . . . . . 1007.13 Coercivity of FC and ZFC ferrihydrite. . . . . . . . . . . . . . . . . 1007.14 Coercivity of CoO1 showing a dip at 40 K. A line is drawn at 40

K to show this clearly. . . . . . . . . . . . . . . . . . . . . . . . . . 1017.15 Superposition of two curves and the effect on coercivity. . . . . . . 1017.16 Coercivity of mixed sample FHCoO RTD. . . . . . . . . . . . . . 1027.17 Temperature dependence of M0, µp and χa. . . . . . . . . . . . . . 1037.18 Thermoinduced magnetization. . . . . . . . . . . . . . . . . . . . . 1047.19 Field sweeps at 300 K with cryostat and oven mounted. . . . . . . 1067.20 Initial susceptibility and inverse initial susceptibility of ferrihydrite. 1067.21 Extrapolation of M0 to T = 0 K. . . . . . . . . . . . . . . . . . . . 1077.22 Plot of the susceptibility and result of TN estimate. . . . . . . . . . 108

viii

List of Tables

2.1 SI and CGS Gaussian units. . . . . . . . . . . . . . . . . . . . . . . 16

3.1 Transition probabilities for 57Fe. . . . . . . . . . . . . . . . . . . . 353.2 Typical values of isomer shift and electric quadrupole splitting. . . 39

6.1 Overview of samples. . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2 Parameters of room temperature spectra of ferrihydrite. . . . . . . 86

7.1 Temperature ranges of fields sweeps made on three samples. . . . . 90

D.1 Ball milling timetable for the sample CoO1. . . . . . . . . . . . . . 120

ix

One

Introduction and Motivation

Magnetic nanoparticles have received much attention during the last twodecades. One reason for this is that the computer hardware industry utilizesmagnetic nanoparticles in magnetic storage devices. These particles must beable to retain a magnetic field direction as this is how information is stored.If the magnetic properties are not stable, the information coupled to the par-ticles is lost. As the demand for storage space is high the industry seeks toincrease the areal density of stored information and one way to do this is tomake the particles smaller. This has been a trend for many years and, inaddition to improvements to the read and write heads, is the reason for thefar greater storage capacity of hard disk drives today compared to the 1950s,when hard disk drives were invented, see Fig. 1.1. When magnetic particles

Figure 1.1: Areal density trend of IBM hard disk drives [1].

1

1. Introduction and Motivation

become very small an effect known as superparamagnetism may be significantand can cause the magnetic moment direction of the nanoparticles to fluctu-ate or even flip, which constitutes a loss of data in magnetic storage media.The computer hardware industry has reached the so-called superparamagneticlimit and will in the future require innovative ideas if the current growth ratein areal densities is to continue. As magnetic storage such as a hard diskdrive is still the most important storage device in computers, the research inmagnetic nanoparticles is of great economic interest.

Another interesting application of magnetic nanoparticles is in biomedicine[2]. Here, magnetic nanoparticles are used for separation of specific biologicalentities. By coating the magnetic nanoparticles with biocompatible moleculestagging of the biological entities becomes possible and they may be separatedfrom their native environment by application of a magnetic field gradient.Other uses of magnetic nanoparticles in biomedicine being studied are drugdelivery and hyperthermia. By attaching a cytotoxic1 drug to a magneticnanoparticle carrier it is possible to target the therapy, which requires a lowerdosage and reduces side effects. Hyperthermia refers to the treatment of cancerby dispersion of magnetic particles throughout the target tissue and causingthem to heat up by applying an AC magnetic field. Again, the force lies inthe targeting possible with the magnetic particles.

For the scientist, magnetic nanoparticles offer a way to study small-scaleeffects. The magnetic properties of nanoparticles often differ markedly fromthose of bulk materials allowing new properties and thereby possibly newdevices and applications to be explored.

Thus, besides the obvious economic interests for the computer hardwareindustry, magnetic nanoparticles represents an area of basic science withpromises of technological spinoffs.

Interactions between magnetic nanoparticles affect their magnetic behaviorand makes it possible to manipulate their magnetic properties. For instance, ithas been shown that nanoparticle mixtures of the mineral hematite (α-Fe2O3)and the transition metal oxides CoO and NiO affect the superparamagneticrelaxation of hematite [3].

This thesis examines the effect on the superparamagnetic relaxation of themineral ferrihydrite by interactions with CoO nanoparticles. Ferrihydrite is anaturally occurring antiferromagnetic ferriferous2 mineral. The particles arealways of nanometer size, i.e. bulk ferrihydrite does not exist. The super-paramagnetic relaxation time, which is the time between flips of the magneticmoment, is exponentially dependent on the factor V

T , where V is the volumeof the particle and T is the temperature. When studying the magnetic prop-erties of nanoparticles the results obtained are conditional upon the time scaleof the measurement compared to the relaxation time. On the time scale ofMossbauer spectroscopy measurements ferrihydrite shows superparamagnetic

1Of, relating to, or producing a toxic effect on cells.2iron containing

2

relaxation at room temperature and some samples are superparamagnetic attemperatures as low as 23 K [4]. The fast superparamagnetic relaxation offerrihydrite makes it difficult to study its magnetic properties. If it is possibleto suppress the superparamagnetic relaxation, this would allow one to studythe magnetic properties of ferrihydrite at higher temperatures.

The suppression of the superparamagnetic relaxation is due to a stabilizingeffect via so-called magnetic exchange interaction by the CoO nanoparticleson the otherwise relaxing magnetic moments. In this study various recipesfor mixing the ferrihydrite and CoO nanoparticles are used in order to ex-amine what can be done to enhance the interaction leading to suppression ofthe superparamagnetic relaxation. Part of the thesis will also deal with theproduction of the CoO nanoparticles as this was no trivial task.

This study is part of the continued research on magnetic nanoparticles inthe Mossbauer Group at the Department of Physics at the Technical Univer-sity of Denmark (DTU). The research focuses on the magnetic behavior ofnanoparticles and inter-particle interactions.

Outline of thesis

The chapter headings should be self-explanatory and the thesis hopefully eas-ily navigated. The thesis is essentially in two parts: theory and experiment.The theoretical part, chapters 2, 3 and 4, describes magnetism and magneticnanoparticles, experimental methods used and gives a short description of fer-rihydrite and CoO. In the experimental part, chapters 5, 6 and 7, describesthe production of the nanoparticles, the Mossbauer spectroscopy study and vi-brating sample magnetometry study of the nanoparticles. Finally, conclusionsand thoughts on further studies are summarized in chapter 8.

A few common abbreviations used in the text are defined on first usageand listed below.

Abbreviations used in the text

FC Field CooledTEM Transmission Electron Microscope, Transmission Electron MicroscopyVSM Vibrating Sample Magnetometer, Vibrating Sample MagnetometryZFC Zero Field CooledXRD X-Ray Diffraction

3

Though this be madness, yetthere is method in’t.

William Shakespeare- Hamlet(II, ii, 206)

Theory and CharacterizationMethods

5

Two

Theory of Magnetic Nanoparticles

This chapter describes the theory of magnetic nanoparticles needed in orderto understand terminology and experimental findings of later chapters.

2.1 Magnetism

All materials display an extremely weak form of magnetism called diamag-netism when a magnetic field is applied. Diamagnetism arises from the effectof the applied magnetic field on the atomic orbits of the electrons and isusually a negligible effect if the atoms have a magnetic moment, which willcause a stronger response to the applied field. Atoms with unfilled electronshells possess a magnetic moment arising from the total orbital angular mo-mentum and total spin angular momentum of its electrons. In a materialcontaining magnetic atoms the magnetic moments may be correlated or un-correlated. If uncorrelated, the magnetic moments will be randomly orientedand the material is said to be paramagnetic. If correlated, long-range orderingof the moments exists and the orientation of a single moment is dependenton the orientation of its neighbors. Such ordered moments are the basis ofthe permanent magnets. All magnetically ordered materials have a transitiontemperature above which the ordering disappears and the material becomesparamagnetic. Materials with long-range ordering may be ferromagnetic, an-tiferromagnetic or ferrimagnetic. When a material is magnetically orderedpreferred directions of magnetization exist, which are given by the magneticanisotropy described in section 2.4.

Magnetization and susceptibility

Magnetization and susceptibility are two important quantities, when studyingthe magnetic properties of a compound. The terms are used extensively inlater chapters and the definitions and symbols given are here.

7

2. Theory of Magnetic Nanoparticles

The magnitude of the magnetic moment, ~µ, per unit volume is the mag-netization, ~M . Thus,

~M =~µ

V(2.1)

This quantity may also be characterized by the mass magnetization, ~σ, givenby

~σ =~µ

M(2.2)

where M is the mass. Susceptibility is a measure of how easily a materialresponds to an applied magnetic field, ~H, i.e. how magnetizable the materialis. The mass susceptibility, χ, is given by

χ =∂~σ

∂ ~H(2.3)

For small applied fields this reduces to

χ =~σ

~H(2.4)

2.2 Paramagnetism

In the paramagnetic state the magnetic moments are independent. A smallapplied magnetic field will cause some of the magnetic moments to align withthe field, but when the field is removed the moments will again orientatethemselves randomly. The amount of alignment in applied field depends onthe strength of the field, the size of the magnetic moment and the temperature.Classically, the average magnetization, 〈M〉, of a paramagnet is given by

〈M〉 = M0L(µB

kBT

)(2.5)

where M0 is the magnetization at saturation, i.e. when all the moments arealigned with the field, B is the magnetic flux density and L(y) is the Langevinfunction, see Fig. 2.1,

L(y) = coth(y)− 1y

(2.6)

For a paramagnet and for small applied fields, the susceptibility follows theCurie-Weiss law

χ =C

T − θ(2.7)

where θ is a constant. If θ > 0 the material is a ferromagnet above itstransition temperature, whereas θ < 0 indicates an antiferro- or ferrimagnet.

8

Magnetic Ordering

Figure 2.1: Left: The Langevin function used to describe the magnetization of anideal paramagnet when a magnetic field is applied. Right: Plot of the Curie-Weisslaw of susceptibility shown for the three cases θ < 0, θ = 0 and θ > 0.

2.3 Magnetic Ordering

Ferromagnetism

A ferromagnet has a magnetization even at zero applied field and is said tohave a spontaneous magnetization. The moments tend to align in parallel, butthe magnetization is dependent on the history of the ferromagnet. When aferromagnet is produced the moments are arranged in ferromagnetic domains,see Fig. 2.2, inside which all the magnetic moments are aligned in the samedirection. When a weak magnetic field is applied, the domains with moments

Figure 2.2: Ferromagnetic domain structure of a single crystal platelet [5].

9


pointing in the same direction as the field will grow at the expense of otherdomains. If a strong field is applied all the magnetic moments will alignwith the field. Between domains are domain walls, which are several hundredlattice constants thick, where the moments gradually turn. Having domainsis energetically favorable for bulk ferromagnets. In particles, however, thereis a critical size below which they have but a single domain.

The transition temperature above which a ferromagnet becomes paramag-netic is known as the Curie temperature.

Antiferromagnetism

In antiferromagnetic materials the magnetic moments are of equal magnitudeand antiparallel, see Fig. 2.3. Thus, a perfectly structured bulk antiferromag-net has no net magnetization below its ordering temperature, which is knownas the Neel temperature, TN . The antiferromagnetic lattice may be thought

Figure 2.3: Arrangement of magnetic moments in the antiferromagnet MnO belowits ordering temperature [6].

of as two interpenetrating lattices each of which consists of spins that are ori-ented in parallel to the rest of the spins on the same lattice. Thus, one way tovisualize antiferromagnet ordering is as two ferromagnetic lattices cancelingeach other out, but one should remember that this is just for visualization.The moments on the two sublattices are not independent but interacting.

As seen in Fig. 2.4 the antiferromagnetic susceptibility in a single crys-tal below the ordering temperature is dependent on whether the applied fieldis parallel or perpendicular to the spin axes. In a polycrystalline antiferro-magnet the susceptibility is a combination of the parallel and perpendicularsusceptibility. The decrease in inverse susceptibility with temperature is adistinguishing feature of bulk antiferromagnets. Antiferromagnetic materials

10

Magnetic Anisotropy

Figure 2.4: The temperature dependence of antiferromagnetic susceptibility [7].

may have a net magnetization due to lattice defects or, in nanoscale particles,uncompensated spins.

Ferrimagnetism

A ferrimagnet has magnetic moments arranged antiparallel or at an anglewith each other. If the moments are arranged antiparallel, what distinguishesit from an antiferromagnet is that the magnetizations of the sublattices areunequal. This can occur if there are more moments in one sublattice than inthe other or if the moments are of unequal magnitude. Thus, a ferrimagnethas a net magnetization.

2.4 Magnetic Anisotropy

Magnetic anisotropy means that the magnetic energy of the system is notinvariant with respect to the direction of the magnetization. In all magneticmaterials preferred directions of magnetization exist, so-called easy directionsof magnetization, which are defined by among other factors the crystal latticeand the shape of the sample. This is known as magnetocrystalline anisotropyand shape anisotropy, respectively. In the absence of an external magneticfield the direction of spontaneous magnetization will arrange itself accordingto the magnetic anisotropy so as to obtain a state with the lowest energy.

The directional effect of the magnetocrystalline anisotropy arises from thespin-orbit coupling. The orbital wavefunctions are affected by the symmetryof the crystal lattice and the spins are affected through the coupling. Shapeanisotropy is caused by dipole interaction between the stray field of the sample

11


and the individual magnetic moments inside the sample. In elongated particlesor thin films shape anisotropy is significant.

An increase in anisotropy energy occurs when the magnetization is rotatedout of a preferred direction by an applied magnetic field. Thus, the anisotropyenergy is a function of the angle, θ, by which the magnetization deviates froma preferred direction. In a crystal with uniaxial symmetry1 the magnetocrys-talline anisotropy energy is conventionally represented by a power series insin θ with only even terms as a reversal of the direction of magnetization doesnot change the anisotropy energy [7]. For a ferromagnet the anisotropy energyE(θ) is given by

E(θ) = K1V sin2 θ +K2V sin4 θ + . . . (2.8)

where Kn are magnetocrystalline anisotropy constants. For practical purposesit is often sufficient to use the first term in Eq. 2.8, so that E(θ) = KV sin2 θ.KV represents the energy barrier between the two easy directions of magne-tization, see Fig. 2.5.

Figure 2.5: The magnetic anisotropy energy as a function of the angle θ by whichthe magnetization deviates from a preferred direction in a crystal with uniaxialsymmetry.

In analogy with the ferromagnetic case the magnetocrystalline anisotropyenergy for an antiferromagnet with uniaxial symmetry is given by [8]

E(θ) =12KV (sin2 θA + sin2 θB) (2.9)

where θA (θB) is the angle between the sublattice magnetization MA (MB)and the easy direction.

1Symmetry about a single axis.

12

Antiferromagnetic Nanoparticles

The magnetocrystalline anisotropy constants are temperature- dependentand they must clearly be zero at the transition temperature where the mag-netic ordering disappears. In Fig. 2.6 is shown how the anisotropy constantsof a ferromagnet fall off with temperature much more rapidly than does themagnetization.

Figure 2.6: The magnetic anisotropy constants K1 and K2 of Fe as a function oftemperature [7].

In magnetic nanoparticles, V is small and thermal excitation can causethe magnetization to cross the energy barrier KV . This leads to superpara-magnetic relaxation, where the magnetization of the nanoparticles is no longerfixed in direction but fluctuates as described in subsection 2.5.

2.5 Antiferromagnetic Nanoparticles

As described in section 2.3 there is a minimum size below which magneticparticles have but a single domain. This critical size is, for typical materialparameters, 10− 100 nm in diameter. The moment distribution may be morecomplex as studies of nanoparticles below the critical size show that they oftenhave disordered surface moments. These surface moments interact with thecore moments and give rise to a variety of moment distributions even thoughthe size of the nanoparticles is within the single domain regime [9]. This is notexplored further in this thesis and the assumption is that the nanoparticlesdescribed here are single domain particles.

Bulk antiferromagnets have a net magnetization of zero as the magneticmoments cancel each other out. Due to the finite number of spins in an-tiferromagnetic nanoparticles, however, this cancelation may not be perfectleading to a net magnetization. A significant ratio of spins are located at the

13


surface and a simple picture is one where the net magnetization arises fromuncompensated surface spins as illustrated in Fig. 2.7.

Figure 2.7: Rough sketch of an antiferromagnetic nanoparticle with an imperfectcancelation of surface spins leading to a net magnetization.

Studies have shown that the Neel temperature of antiferromagnetic nanopar-ticles is sometimes less than that of a bulk sample, e.g. disc-shaped NiOnanoparticles [10] and goethite nanoparticles (α−FeOOH) [11].

Superparamagnetic relaxation

In two articles in 1949 [12, 13] Louis Neel theorized that if a single-domain par-ticle is small enough, thermal fluctuations may cause a reversal of its magneticmoment.

Figure 2.8: Reversal of themagnetic moment in ananoparticle with uni-axial symmetry.

This effect in nanoparticles is different from the sta-ble magnetic behavior of bulk magnetic materials.The articles are referenced often, but are in French.In his Nobel Lecture [14], however, Neel himselfmakes reference to having shown this effect knownas superparamagnetism as early as 1942.

The reversals take place between easy directionsof magnetization, see Fig. 2.8. The time betweentwo reversals in a particle in the superparamagneticstate is known as the relaxation time, i.e. a shortrelaxation time means rapid fluctuations. For non-interacting nanoparticles the relaxation time, τ , isusually described by the Arrhenius relation

τ = τ0 exp(KV

kBT

)(2.10)

where τ0 is of the order of 10−10 − 10−12 s [15], Kis the magnetic anisotropy constant and V is thevolume of the particle. When V becomes small, thefluctuations of the spin direction may be so fast thatthe nucleus senses a zero net magnetic field. Thiswill affect the Mossbauer spectrum as described in section 3.3.4. From Eq.

14

The CGS Gaussian System versus the SI

2.10 it should be clear that the spin reorientation can be slowed down by de-creasing the temperature. As described in section 2.4 on magnetic anisotropyKV represents the energy barrier between two easy directions of magnetiza-tion in a crystal with uniaxial symmetry.

In the superparamagnetic regime the magnetization of the particles willbehave as a super-spin. When a magnetic field is applied the response ofa super-spin not interacting with other particles will be super-paramagnetic.Thus, the average magnetization of a sample of superparamagnetic nanopar-ticles is described using a Langevin function

〈M〉 = M0L(µpB

kBT

)(2.11)

where µp is the magnetic moment per particle.

Interactions between antiferromagnetic nanoparticles

Magnetic particles may interact via dipole interaction, whereby the dipole fieldof the particles interact, or exchange interaction, whereby surface spins couple,see Fig. 2.9. Antiferromagnetic nanoparticles have very small dipole fields

Figure 2.9: Left: Dipole interaction between magnetic nanoparticles. Right: Ex-change interaction between magnetic nanoparticles.

and will interact via exchange coupling. Studies have shown that exchangeinteraction between antiferromagnetic nanoparticles may lead to suppressionof the superparamagnetic relaxation [3, 16].

2.6 The CGS Gaussian System versus the SI

For historical and practical reasons two metric systems are used in literatureon magnetism. These are the CGS Gaussian system and the SI (Systeme In-ternationale). The two metric systems use a different base unit for length andmass, but the same base unit for time. CGS stands for centimeter, gram andsecond. The SI (sometimes called the MKS system) has the meter, kilogram

15


and second as base units. With two different metric systems in use one mustbe careful when comparing obtained results with those found in literature es-pecially since what is sometimes used are so-called practical units which area mixture of the two.

The historical reason for the widespread use of the CGS system in earlyliterature is simply that it came first. In 1874 the British Association for theAdvancement of Science2 (BA) formally introduced the CGS system and itwas accepted by many scientists as the metric system of choice for decades tocome. A problem with the CGS system is that in time it was not one systembut several systems, because electricity and magnetism could be described inmany ways in terms of the three base units. The MKS system was introducedby the International Bureau of Weights and Measures3 (BIPM) in 1889. Formany years the MKS system was no better than the CGS system as theyboth had three base units, which differed only in size. In 1954 the TenthGeneral Conference on Weights and Measures (CGPM) adopted the MKSsystem and added ampere, degree Kelvin and candela as base units. Thename International System of Units (SI) was chosen in 1960 and today theSI has the seven base units: meter, kilogram, second, ampere, kelvin, candelaand mole. Even though the SI base and derived units are recommended foruse in all instances, practicality plays a role as well in the choice of metricsystem used.

SI CGS Gaussian

Magnetic field, H A/m Oersted (Oe)Magnetic flux density, B Tesla (T) Gauss (G)Magnetization, M A/m emu/cm3

Mass magnetization, σ A·m2/kg emu/gMass susceptibility, χ m3/kg emu/(Oe· g)

Table 2.1: SI and CGS Gaussian units for quantities, which are often given in CGSGaussian units.

In magnetic measurements the magnetic field, H, the magnetic induction(or magnetic flux density), B, the magnetization, M , the mass magnetization,σ and the mass susceptibility, χ, are often given in CGS Gaussian units. Itshould be noted that the magnetic induction, B, is often called the magneticfield, but as the units of B and H are different they can be distinguished inthis way. Table 2.1 shows the units used in the two metric systems. Onemay wonder that the CGS Gaussian system is still in use in literature onmagnetism, when the SI is far more consistent. One reason is that magneticflux densities and magnetizations measured in T and A/m sometimes givenumbers which are difficult to handle. Another reason is that in the CGS

2http://www.the-ba.net3http://www.bipm.fr

16

http://www.the-ba.net

http://www.bipm.fr

The CGS Gaussian System versus the SI

Gaussian system B and H are similar in that 1 G = 1 Oe in free space, whichis practical.

In this thesis magnetization measurements are given in a unit appropriatefor comparison with literature. A conversion table between the CGS Gaussiansystem and the SI is given in appendix B.

17

Three

Experimental Methods

Various experimental methods were employed to characterize and study themagnetic nanoparticles. The theory of x-ray powder diffraction, transmissionelectron microscopy, Mossbauer spectroscopy and vibrating sample magne-tometry is outlined in sufficient detail for the reader to understand the exper-iments performed in this study.

3.1 X-ray Powder Diffraction

X-ray diffraction is based on the constructive interference of x-ray waves scat-tered by a periodic distribution of electron densities. One form of a periodicdistribution of electron densities is a crystal lattice and x-rays are well suitedfor scattering by crystal lattices as the wavelength of x-rays (∼ 1A) is of thesame order as crystal spacings. The condition for constructive interference bywaves scattered in a crystal lattice is given by Bragg’s equation

mλ = 2d sin θ (3.1)

where m is the order of the reflection and an integer, d is the distance betweenscattering planes and θ is the angle between the scattering plane and the inci-dent beam. The formula is easily deduced using geometry and the conditionthat the difference in path lengths of the waves must be an integral numberof wavelengths, see Fig. 3.1. When performing x-ray diffraction (XRD) ona single crystal several different directions and angles of the incoming beamwill lead to constructive interference, see Fig. 3.2. In x-ray powder diffractionthe sample is a large number of small crystals oriented randomly. Thus, allpossible orientations of the crystals are irradiated by a single beam and onlythe angle need be altered. An x-ray powder diffraction spectrum is thereforea plot of reflected intensity versus angle, see Fig. 3.6 on page 24. All mate-rials have a characteristic x-ray powder spectrum as the peak positions andintensities depend on the structure of the material. Thus, XRD is an essentialtool for identification and purity control of samples. In addition information

19

3. Experimental Methods

Figure 3.1: Geometric derivation of Bragg’s equation. The difference in path lengthsof waves scattered by different planes is marked in blue.

Figure 3.2: Scattering planes given by their Miller indices (hkl).

on crystallite size and other structure parameters may be obtained from anXRD pattern.

3.1.1 X-ray Diffraction Setup

In-house x-ray sources can be produced in an evacuated x-ray tube, wherethe principal parts are a W (tungsten) filament and an anode. A current isrun through the filament causing it to heat up and thermionic emission ofelectrons takes place. The electrons are accelerated towards the anode by ahigh potential and interacts with the atoms in the anode. This interactionproduces mostly heat, but a small percentage (< 1%) of the electron energy isconverted to x-rays producing the spectrum seen in Fig. 3.3. Several materialsare suited for use as an anode, but Cu is the most commonly used. Twodistinct features are visible in this spectrum, the continuous bremsstrahlung,produced by deceleration of electrons impinging on the anode, and discretelines. The discrete lines are produced when an inner electron is removedcompletely by ionization followed by the transition of an electron from the Lor M shell to the vacancy in the K shell, see Fig. 3.3. The discrete lines areby far the most intense and for a Cu anode the ratio Kα1 :Kα2 :Kβ is 10:5:2.A Ni foil filter is used to attenuate the Cu Kβ radiation, so that only theKα1 and Kα2 radiations are used in the x-ray diffraction scattering. With two

20

X-ray Powder Diffraction

Figure 3.3: Left: The spectrum produced in an x-ray tube with a Cu anode showingthe continuous bremsstrahlung radiation and the discrete lines termed Kα and Kβ

originating from electron transitions between inner shells. Right: Schematic ofthe most common transitions for the K spectrum in Cu. Adapted from [17].

wavelengths impinging on the sample, two scattering peaks are seen in thespectrum with a spacing that increases as the angle increases. The two peakscan be distinguished when 2θ & 50◦ as seen in the diffraction pattern of a Sistandard in Fig. 3.6.

Instrumentation used

All x-ray powder spectra described in this thesis were recorded on a PhilipsPW 1050/25 goniometer with a PW 1965/60 proportional detector, see Fig.3.4, using Ni-filtered Cu K radiation.

3.1.2 Crystallite Size Determination

The width of an XRD peak is inversely proportional to the size of the effectivelength of coherent diffraction in the particles studied. It is not correct to thinkof this length as the particle size as the particles may contain several domains,termed crystallites, having different orientations.

The size of the crystallites is given by a formula known as the Scherrerformula, which states that the mean size of the crystallites, D, is given by [19]

D =kλ

β cos θ(3.2)

where k is the Scherrer constant, λ is the wavelength of the radiation,

21


Figure 3.4: Left: In-house x-ray powder diffraction setup. A) X-ray tube housing.B) X-ray radiation protection shield assembly containing the specimen holder. C)Proportional detector. Right: Scattering geometry [18].

Figure 3.5: Simplified view ofthe effects of isotropic andanisotropic strain on a scat-tering peak [17].

β is the full width at half maximum (FWHM)of the peak in radians corrected for instrumentbroadening and θ is the scattering angle.

In the original article the Scherrer constantwas found to be 0.93. Since then a myriad ofvalues for this constant have been calculatedfor different crystallite shapes, lattice indicesand size distributions. With D defined as theeffective length in the direction perpendicu-lar to the scattering plane it has been shownthat a value of k in the neighborhood of 0.9 isfound [20]. When using the Scherrer formulaone should be aware of factors other than thesize of the crystallites which may cause broad-ening of peaks. Isotropic strain will cause thepeaks to be shifted, whereas anisotropic strainwill lead to a broadening of peaks as seen inFig. 3.5. However, strain leads to a broad-ening with a different dependence on θ thancrystallite size broadening, which makes it pos-sible to differentiate between the two when aspectrum with several peaks is available. Thebroadening of a peak caused by stress is given

22

X-ray Powder Diffraction

by [17]

βε = 4ε tan θ (3.3)

where βε is the broadening in radians (again corrected for instrumental broad-ening) and ε is the residual strain.

It should also be remembered that the radiation produced by an x-raytube is not monochromatic. In an x-ray tube setup using Cu Kα radiation,scattering of both Kα1 and Kα2 will occur. As the energies of Kα1 and Kα2

are nearly the same, the scattering peaks of the two will be very close to eachother in a spectrum. If the spectrum shows broad lines, the two peaks willnot be discernible as such, and one may mistakenly fit as a single peak whatshould instead be fitted as two peaks.

3.1.3 Rietveld Refinement and Quantitative Phase Analysis

Using Rietveld refinement one may extract quantitative information about thedifferent phases in a diffraction pattern. Rietveld refinement is based on theminimization of a sum of weighted, squared differences between an observedand a calculated intensity for each step in a powder pattern. The functionminimized is [17, 21]

R =∑

j

wj |Ij(o) − Ij(c)|2 (3.4)

where Ij(o) and Ij(c) is the observed and calculated intensity at the jth step,respectively, and wj is the weight. For Rietveld refinement of an XRD pat-tern an approximate crystal structure, i.e. space group, lattice constants andatomic positions, must be known for each phase. The program used in thisstudy for Rietveld refinement of obtained XRD patterns is Fullprof 2000[22]. The program is used to determine crystallite size and the weight per-centages of different phases in produced samples.

Instrument resolution function

A spectrum of a Si standard was obtained and fitted to determine an instru-ment resolution function, see Fig. 3.6. The individual peaks in the Si patternwere fitted with a pseudo-Voigt function, which is an approximation to a con-volution of a Gaussian and a Lorentzian function. Both Kα1 and Kα2 peakswere fitted with λKα1 = 1.54056 and λKα2 = 1.54439. Half-width constantscharacterizing the instrument resolution function were determined and savedin a separate file for use in later refinements. When an instrument resolutionfile is provided, Fullprof 2000 can give an estimate of the mean crystallitesize using the Scherrer formula [21]. Strain and size broadening are discernedin the refinement.

23


Figure 3.6: Refinement of XRD pattern of Si standard used to determine the instru-ment resolution function.

3.2 Transmission Electron Microscopy (TEM)

In an x-ray tube an electron gun is used to produce x-ray radiation by ioniza-tion of inner electrons in a target anode as described in the previous section.In TEM the electrons themselves are used as probes. There are many waysin which electrons may interact with a sample; in TEM the electrons pass-ing through the sample are used for imaging. Thus, the samples used mustbe thin and special preparation of the sample is necessary. TEM has a veryhigh resolution and can provide morphological information such as the size,shape and arrangement of particles on nanometer scale. It may also yieldcrystallographic information such as lattice planes and atomic scale defects.

3.2.1 Microscope Design

A transmission electron microscope (TEM) is shown in Fig. 3.7. Basically,an electron source produces a stream of electrons, which is focused onto thesample by the use of condenser lenses. The image of the sample is magnifiedby the objective lens before hitting a CCD camera, which generates the image.

24

Transmission Electron Microscopy (TEM)

The entire column is evacuated to a high vacuum to increase the mean freepath of the electrons.

Figure 3.7: Schematic and picture of the Jeol JEM-3000F TEM. Images adapted from[23] and [24].

The wavelength, λ, of the electrons is given by the de Broglie relationship

λ =h

p(3.5)

Thus, the higher the energy of the electrons, the smaller the wavelength. Tofind the momentum of the electrons in the potential, V , one must use therelativistic formula,

p = m0c

√qV

m0c2

(2 +

qV

m0c2

)(3.6)

25


where m0 is the rest mass and q the charge of the electron. For a potential of300 kV as used for the TEM images in this study, we find that the electronshave a wavelength of 1.97 pm. The resolution of a TEM is very high, but stilllimited by aberrations in the objective lens.


All TEM images presented in this thesis were made by Christian R. H. Bahlon a Jeol JEM-3000F (UHR) TEM at the Materials Research Department,Risø National Laboratory. The specifications for this instrument [25] statesa point resolution of 0.17 nm, accelerating voltages of 100 − 300 kV and amagnification range of ×60 to ×1, 500, 000. Images are captured by a 16Megapixel CCD camera, which gives images with 4096 × 4096 pixels. TEMimages are shown in Fig. 5.8 on page 61 and Fig. 6.3 on page 68.

Preparation of samples

The powder sample is dispersed in distilled water and/or ethanol and givenultrasound to break up aggregates. The dilution and ultrasonic treatment isnecessary as the best results are obtained when the particles do not crowd orgather in aggregates. A drop of the dilute suspension is then placed on a laceycarbon grid and left to dry. The drying may be facilitated by a piece of filterpaper against the back of the grid. A lacey carbon grid is a finely meshedmetal grid coated with an amorphous carbon film, which forms a pattern ofholes of varying sizes.

Analysis of TEM images

Besides the morphological information immediately available from a TEM im-age, lattice planes may also be seen when Bragg scattering of the electrons oc-curs in crystalline samples. Using a program such as Gatan DigitalMicrographone can make a Fourier transform of the lattice planes seen in a TEM imageand obtain the lattice spacing. If more than one lattice plane is visible in aparticle it may be possible to identify the orientation of the sample from theMiller indices (hkl) of the planes.

3.3 Mossbauer Spectroscopy

Mossbauer spectroscopy is well suited for studying magnetic interactions as itis a nuclear spectroscopy with an energy resolution high enough to resolve thehyperfine structure of nuclear levels. Mossbauer spectra were obtained of allsamples in this study and the section describes the information that can begained from such spectra. Part of this section is taken from a report handedin during the three-weeks course 10322 Experimental Mossbauer Spectroscopyand based on the notes used in this course [15].

26

Mossbauer Spectroscopy

The Mossbauer effect is the recoil-free resonant absorption of γ-quanta insolids as described in the following. A transition in a source nucleus from anexcited state to the ground state results in the emission of a γ photon, seeFig. 3.8. This photon can then be absorbed by another nucleus in the groundstate if the energy of the photon is near the resonance energy of the nucleus.

Figure 3.8: Resonant absorption of a γ-quantum.

During the emission of such radiation a free nucleus recoils. This reducesthe energy, Eγ , of the photon by the recoil energy, ER, which is given by

ER =E2

γ

2Mc2(3.7)

where M is the mass of the nucleus. A free nucleus will also be in thermalmotion at a finite temperature, so that the emitted photon is Doppler-shifted.These phenomena make it impossible to have resonant absorption in free nucleias ER is much greater than the natural line width of the transition. If, however,the nuclei are bound in a crystal lattice a certain fraction, f , of the resonantabsorption events occur without recoil as the mass in Eq. (3.7) is the massof the entire crystal. The thermal Doppler-broadening is also very small foratoms in a solid and resonant absorption becomes possible.

The f-factor

The finite probability that no lattice vibration will occur when a γ-quantumis emitted is expressed by the so-called f -factor. The f -factor of the source(absorber) gives the probability that a γ-quantum will be emitted (absorbed)without phonon interaction. Thus, for resonant absorption we want the f -factor to be high in both source and absorber. The f -factor is given by

f = exp

(−E2

γ

~2c2〈x2〉

)(3.8)

where 〈x2〉 is the mean square amplitude of the thermal motion of the atomin the direction of emission. We see that f decreases as the temperatureincreases, because thermal vibrations increase. Using the Debye model for thephonon spectrum one finds the following approximation for high temperatures,

f ' exp(−6ERT

kBθ2D

)(T ≥ θD

2) (3.9)

The Debye temperature, θD, is typically of the order 200 − 400 K. WithθD = 300 K, f = 0.64 at room temperature.

27


3.3.1 Mossbauer Spectroscopy Setup

The experimental setup for producing a Mossbauer spectrum consists basicallyof a source, an absorber and a detector. The radioactive source is oscillatedback and forth, while the absorber is kept in a fixed position, see Fig. 3.9.The movement of the source Doppler shifts the energy of the emitted pho-

Figure 3.9: The Mossbauer spectroscopy setup.

tons and a sweep of energy around the emission line is created. A Mossbauerspectrum is then recorded in the detector as transmission of the radiationthrough the absorber as a function of velocity. Only one isotope in the ab-sorber contributes to the spectrum as the absorbing atoms must have the sameγ−transition as the source and the spectrum reveals information about thisparticular isotope. Several effects influence the nuclear energy levels of theisotope and the Mossbauer spectrum can tell us much about the surroundingsof the absorbing nuclei.

57Fe Mossbauer spectroscopy

Only a handful of isotopes are useful for Mossbauer spectroscopy and themost commonly used is 57Fe, which is also the one used in this study. For57Fe Mossbauer spectroscopy the source consists of the radioactive isotope57Co embedded in a Rh matrix. 57Co decays to an excited state of 57Fe viaelectron capture. This excited state then decays to the ground state of 57Femostly via an intermediate state. The transition of interest for Mossbauerspectroscopy is the 14.4 keV transition from the intermediate state as seen inthe decay scheme of 57Co in Fig. 3.10.

Preparation of samples

The powder samples studied were placed in round perspex containers eachmarked with the sample name. Such an absorber is characterized by thethickness factor, t,

t = fanaσ0 (3.10)

where σ0 is the absorption cross-section at full resonance, fa is the f -factorof the absorber and na is the surface density of the Mossbauer isotope in theabsorber. For a thin absorber (t � 1) the absorption, and thus the quality

28


Figure 3.10: The decay scheme of 57Co.

of the spectrum, increases proportionally to t, whereas for t & 1 saturationphenomena occur, so that thin absorbers with t ≈ 1 are preferable. Thick ab-sorbers result in changes in the relative absorption line intensities as describedin subsection 3.3.3.

3.3.2 Hyperfine Interactions Affecting the MossbauerSpectrum

The surroundings of the absorbing nuclei perturb and/or split the nuclear en-ergy levels, which affects the shape of the Mossbauer spectrum. Three interac-tions have a particularly large effect and are important for the understandingof the Mossbauer spectra obtained in this study. They are:

• The isomer shift.

• The electric quadrupole interaction.

• The magnetic hyperfine interaction.

The isomer shift

The s-electrons in an atom have a finite probability of being at the nucleus.This results in an interaction between the charge distribution of the nucleusand the density of the s-electrons inside the nucleus. As the density of thes-electrons is affected by chemical bonding through the outer electrons, theinteraction reflects the valence state and bond formation of the atom. Theinfluence of the s-electrons on the nucleus results in a shift of energy levels,

29


δE, which is different for the ground state and excited state because of thedifference in their radii. The shift in transition energy is then given by

∆E = δEE − δEG =1

10ε0Ze2(R2

E −R2G)|ψ(0)|2 (3.11)

where RE and RG are the radii of the nucleus in the excited state and groundstate, respectively, and ψ(0) is the density of s-electrons at the nucleus. If theatoms in the source and absorber have different chemical environments, ψ(0)will be different for the two and the difference in transition energy results inthe isomer shift, see Fig. 3.11. In measurements, the isomer shift is not given

Figure 3.11: The energy of the nuclear levels are shifted due to the interaction betweenthe charge distribution of the nucleus and the density of s-electrons at the nucleus.A Mossbauer spectrum shows a shifted singlet.

relative to the source, but rather relative to a reference material. Thus, theisomer shift, δ, is given by

δ =1

10ε0Ze2(R2

E −R2G)(|ψA(0)|2 − |ψR(0)|2) (3.12)

where |ψA(0)|2 and |ψR(0)|2 are the densities of s-electrons at the nuclei ofthe absorber and reference material, respectively.

30


Electric quadrupole interaction

If a nucleus has a non-spherical charge distribution, which is true for stateswith nuclear spin I > 1

2 , the electric quadrupole moment, eQ, of the nucleuswill be non-zero. This quadrupole moment will interact with the electrostaticfield at the nucleus, which is described by the electrostatic field gradient (EFG)tensor, Vxx Vxy Vxz

Vyx Vyy Vyz

Vzx Vzy Vzz

By choosing a suitable set of basis vectors, the off-diagonal terms in the matrixwill be zero and only Vxx, Vyy and Vzz will be non-zero. The EFG can bethought of as made up by two contributions:

1. A lattice contribution from the charges of the surrounding atoms.

2. A valence electron contribution from the Mossbauer atom itself.

The quadrupole interaction energy is given by

EQ =eQ

4I(2I − 1)Vzz[3m2 − I(I + 1)]

√1 +

η2

3(3.13)

where m is the nuclear magnetic spin quantum number and η is an asymmetryparameter defined as η = Vxx−Vyy

Vzz. We see that EQ is proportional to m2 and

thus causes a splitting of levels with the same value of the nuclear spin I butdifferent absolute values of the magnetic quantum number m, see Fig. 3.12.The observed quadrupole splitting, ∆, is then given by

∆ = EQ

(±3

2

)− EQ

(±1

2

)=eQVzz

2

√1 +

η2

3(3.14)

If the nuclear environment has cubic or spherical symmetry, Vxx = Vyy =Vzz = 0 and the quadrupole splitting is zero.

Magnetic hyperfine interaction

If the spin quantum number, I, of the nucleus is non-zero it will have a mag-netic dipole moment, ~µ, given by

~µ = gnβn ~mI (3.15)

where gn is the Lande g-factor and βn the nuclear magneton. This magneticmoment will interact with any effective magnetic induction, B, at the nucleusand the magnetic interaction energy is given by

E = −~µ · ~B = −gnβn(~mI · ~B) (3.16)

We see from this equation, that the magnetic interaction lifts the degeneracyof the 2I+1 states, see Fig. 3.13. Even though 8 transitions seem possible, only

31


Figure 3.12: Illustration of the effect of electric quadrupole interaction on the energylevels of 57Fe. Also shown is the isomer shift. A doublet is seen in the Mossbauerspectrum of FePO4 at room temperature due to quadrupole splitting.

6 are allowed as a selection rule for magnetic dipole radiation is ∆m = 0,±1.The total effective magnetic induction acting on the nucleus is given by

~B = ~Ba + ~Borb + ~BD + ~BC (3.17)

Here, Ba is an applied magnetic induction, Borb is the contribution from theorbital motion of the electrons, BD is the contribution from the spins of theelectrons outside the nucleus and BC is the contribution of the electron spin-density at the nucleus arising from s-electrons. BC is known as the Fermicontact field and is by far the largest contribution to ~B. For numbers, see thesubsection on crystal field splitting in section 3.3.4.

If the magnetic induction at the nucleus fluctuates as is the case with su-perparamagnetic relaxation complex spectra may arise as described in section3.3.4.

32


Figure 3.13: The magnetic hyperfine splitting shown in combination with quadrupoleinteraction. Also shown is a Mossbauer spectrum of the iron oxide hematite(α−Fe2O3) at 295 K showing a sextet.

33


Summary of hyperfine interactions

Interaction Influence on spectrum Physical backgroundIsomer shift, δ Center of spectrum is shifted

away from 0 mm/sDifference in s-electron den-sity compared to referencematerial. Gives informationon the valency and bond for-mation, i.e. on the chemicalbonding.

Quadrupole shift, ∆EQ If no magnetic splitting, twolines appear. Causes asymme-try of line positions in mag-netically split spectrum.

Reflects the symmetry of thenuclear environment.

Magnetic splitting Six lines appear as all degen-eracies are lifted.

Proportional to the magneticflux density acting on the nu-cleus.

Calibration

A reference material is used for calibration of a Mossbauer spectrometer. Theisomer shift of the known standard absorber used as reference is defined aszero such that the isomer shifts of other materials are given relative to this.Further, the known absorption lines of the reference material are used to cal-culate the number of mm/s per channel. In this way the relationship betweenchannel number and velocity is calibrated. In 57Fe Mossbauer spectroscopy,the reference material is α-Fe and one mm/s, which is a convenient unit inMossbauer spectroscopy, equals 4.8 × 10−8 eV. This unit is such that it ispossible to detect the changes in the energy of the excited state caused by thehyperfine interactions.

Instrumentation used in this report

All Mossbauer spectra in this study were obtained at the Mossbauer laboratoryat the Department of Physics, DTU. The spectrometers consist of a 57Co/Rhsource and a proportional counter in transmission geometry. The spectra arestored in multi channel analyzers. Lorentzian line fits of the spectra weremade using the program mfit [26] with doublets and sextets constrained tohave equal widths and intensities. Distributions of hyperfine fields are fittedusing the program distfit developed by C. Wivel and C. A. Oxborrow andmade available at DTU.

3.3.3 Intensities of Lines in Magnetically Split Spectra

The relative intensities in magnetically split spectra are dependent on theangle between the incoming photons and the magnetic field at the absorbingnucleus. If the sample is a powder with no preferred orientation and no appliedmagnetic field, the relative intensities of the magnetically split lines in an 57Fe

34


Mossbauer spectrum is 3:2:1 as seen for hematite in Fig. 3.13. This naturallycomes from the probabilities of transition between ground state and excitedstate as given in Table 3.1. The relative intensities are, however, a function of

Transition ∆m Angular dependence Random orientations

+32 → +1

2 −1 94(1 + cos2 θ) 3

−32 → −1

2 +1 94(1 + cos2 θ) 3

+12 → +1

2 0 3 sin2 θ 2

−12 → −1

2 0 3 sin2 θ 2

−12 → +1

2 +1 34(1 + cos2θ) 1

+12 → −1

2 −1 34(1 + cos2θ) 1

Table 3.1: Probabilities of transition for the magnetic dipole interaction of 57Fe, wherethe ground state has nuclear spin Ig = 1

2 and the excited state Ie = 32 .

absorber thickness. For thick absorbers the line intensities and areas saturate.As this happens earlier for the lines with the higher transition probabilitytheir relative line intensities are decreased. Thus, one might obtain lines withrelative intensities (3− x) : (2− y) : 1, where x and y are positive.

3.3.4 Interpretation of 57Fe Mossbauer Spectra

The most commonly used isotope for Mossbauer spectroscopy is 57Fe, whichhas Fe(II) and Fe(III) as its most common valence states. In Fe the electronconfiguration is [Ar]4s23d6. Ferrous iron, Fe(II), and ferric iron, Fe(III), havesix 3d and five 3d electrons, respectively, in the valence shell. The differingnumber of 3d electrons affects the density of the 3s electrons. The electrondensity of 3s electrons at the nucleus of Fe(II) is smaller than that of Fe(III)as it has more 3d electrons. Thus, |ψA(0)|2 − |ψR(0)|2 in the equation for theisomer shift,

δ =1

10ε0Ze2(R2

E −R2G)(|ψA(0)|2 − |ψR(0)|2) (3.18)

will be a larger (negative) quantity for Fe(II) than for Fe(III). However, thefactor (R2

E − R2G) from Eq. 3.18 is negative, as the nuclear radius of 57Fe in

the excited state is smaller than that of the ground state. Thus, the isomershift of Fe(II) is generally larger than that of Fe(III).

Crystal field splitting

From Mossbauer spectra one may also determine whether the absorbing ionsare in a so-called high-spin or low-spin state. In an ion the valence electrons

35


will arrange themselves in the orbitals according to the Pauli exclusion princi-ple and if the ion is free also according to Hund’s rules. The latter states thatthe electrons will occupy the orbitals in such a way that the ground state ischaracterized by:

1. The largest total spin angular momentum S. This rule is a result of theCoulomb repulsion between electrons.

2. The largest total orbital angular momentum L consistent with the firstrule.

3. The value of the total angular momentum, ~J = ~L+ ~S, is equal to |L−S|when the shell is less than half full and to |L+S| when the shell is morethan half full.

The rare earth ions follow Hund’s Rules very well even in complexes as their4f valence shell lies deep inside the ion and is shielded by the 5s and 5p shells.The valence shell in Fe, however, is the outermost shell. Thus, the electronsin the partially filled 3d shell are influenced by the electric field produced bythe neighboring ions. This electric field is known as the crystal field. Theeffect of the crystal field on the energy of an orbital depends on the symmetryof the local environment and the orientation of the orbital.

Fe is commonly octahedrally or tetrahedrally coordinated and the twosymmetries have different effects on the energy of the orbitals. An ion is octa-hedrally coordinated when the ligands1 are placed at the faces of a cube andtetrahedrally coordinated when the ligands are placed on alternate corners ofa cube, see Fig. 3.14. By looking at the angular part of the 3d electron wave-

Figure 3.14: Left: Octahedral coordination. Right: Tetrahedral coordination. [27]

functions in Fig. 3.15, we see that they are not spherically symmetric; onlys orbitals have this property. The radial part of the wavefunctions is ignoredas it is independent of direction. As stated above, the effect of the crystal

1An ion, a molecule, or a molecular group that binds to another chemical entity to forma larger complex.

36


Figure 3.15: Angular part of 3d orbitals [27]. The notations eg and t2g refer to the twosets of orbitals into which the five orbitals are split by an octahedral or tetrahedralenvironment as described in the text.

field depends on the symmetry of the point charges surrounding the orbitals.In crystal field theory this is described by group theory, where the symmetryoperations and elements of the local environment are given mathematically.In this context, the octahedron belongs to the group Oh and the tetrahedronto the group Td [28]. The splitting of the orbitals caused by the symmetryof the environment is then found by applying the symmetry operations of thegroup to the orbitals. Unless the symmetry is spherical this will cause theotherwise degenerate orbitals to be split into sets depending on the effect ofthe symmetry operations on the individual orbitals. In this way, one findsthat the five d orbitals are split into two irreducible sets by the Oh symmetry.These sets are the triply degenerate set T2g and the doubly degenerate setEg. The effect of the Td symmetry on the splitting of the orbitals is the same,but the irreducible sets are called T2 and E. The subscript g refers to thed orbitals being symmetric to inversion, but this has no meaning in an en-vironment that is not centrosymmetric such as the tetrahedral coordination.Now we know that the octahedral and tetrahedral environments cause thesame splitting of the orbitals, but what of the relative energies? We see inFig. 3.15 that the e orbitals extend along the axes, while the t2 orbitals lie inbetween the axes. Thus, in the octahedral environment the eg orbitals have ahigher energy than the t2g orbitals as they get closer to and are repelled more

37


by the charge density of the ligands located on the axes, see Fig. 3.16. The

Figure 3.16: eg and t2g orbitals in octahedral coordination. [29].

reverse is true for a tetrahedral environment and the energy splitting of theorbitals in the two symmetries is illustrated in Fig. 3.17. The energy splitting

Figure 3.17: The relative energies of the e and t2 orbitals due to the splitting of thed orbitals by octahedral and tetrahedral environments [28].

between the eg orbitals and the t2g orbitals is called the crystal field splittingenergy and is denoted ∆o or ∆t for octahedral and tetrahedral coordination,respectively. The splitting energy depends on the identity of the metal ion,the charge on this ion, and the nature of the ligands coordinated to the metalion. If ∆o is large compared to the pairing energy of the electrons Hund’s rulesneed to be modified as the t2g orbitals are filled before the eg orbitals and wehave a low-spin state. The high-spin state occurs when the splitting energy

38


is smaller that the pairing energy, see Fig. 3.18. Tetrahedral complexes are

Figure 3.18: High-spin and low-spin states of Fe(II) and Fe(III).

almost always high-spin as ∆t is small.The spin state of the Fe ion effects all the hyperfine interactions. Typical

values of the isomer shift and quadrupole splitting are given in Table 3.2.The quadrupole splitting of Fe(II) high-spin and Fe(III) low-spin states are

S δ[

mms

]∆[

mms

]Temp. dep. of ∆

Fe(II)low-spin 0 −0.1− 0.4 0.0− 2.0 noFe(III)low-spin 1

2 −0.1− 0.4 0.0− 3.0 yesFe(II)high-spin 2 0.9− 1.4 0.0− 4.5 yesFe(III)high-spin 5

2 0.2− 0.6 0.0− 2.0 no

Table 3.2: Typical values of the isomer shift (δ) and electric quadrupole splitting (∆)of Fe(II) and Fe(III) in the high-spin and low-spin states.

temperature-dependent as a spin transition may occur if the electron(s) arethermally excited. Further, the magnetic hyperfine field will depend on thevalence and spin state of the Fe ions. The Fermi contact field, see Eq. 3.17 isroughly proportional to the total spin of the ions and it is not surprising thatFe(III) in the high-spin state has the largest magnetic hyperfine field of theorder 50 − 60 T. The magnetic hyperfine field of Fe(II) is generally smallerthan that of Fe(III) because of the contribution from the orbital field Borb,which is opposite in direction to the Fermi contact field. The typical value ofthe magnetic hyperfine field for Fe(II) is 10−40 T. In Fe(III) the orbital fieldis zero due to quenching of the orbital angular moment.

Superparamagnetic relaxation

Thermal fluctuations of the magnetic moment of a single-domain particleis known as superparamagnetic relaxation and is described in section 2.5.Whether the relaxation of the magnetic moment influences the Mossbauerspectrum depends on the relaxation time, τ , compared to the time scale of

39


Mossbauer spectroscopy, which is the Larmor nuclear precession time, τL. Themagnetic moment of a nucleus precesses in the magnetic hyperfine field actingon it and τL is the time it takes for one precession. We have that

τL =2π~

2µnB(3.19)

where µn is the magnetic moment of the nucleus and B is the magnetic induc-tion acting on it. For a fully split sextet to appear in the Mossbauer spectrumthe hyperfine field must remain constant for at least one precession. For asample of nanoparticles there are three cases to consider:

• τ � τL means that the nuclei ’see’ a constant magnetic hyperfine fieldand a discrete sextet is seen in the Mossbauer spectrum.

• τ � τL results in a lack of magnetic splitting as the hyperfine fieldchanges so rapidly that it averages to zero.

• τ ≈ τL leads to a complex Mossbauer spectrum where a singlet or adoublet is superimposed on a distribution of sextets. This is due to thespread in particle sizes so that the particles have different relaxationtimes.

The time scale of 57Fe Mossbauer spectroscopy is about 10−8 − 10−9 s. Asτ is a function of temperature, a temperature series of Mossbauer spectrawill show a magnetically split spectrum at a low temperature and a gradualcollapse of the splitting with increasing temperature as seen, for instance, inFig. 6.1 on page 66. The temperature below which the superparamagneticrelaxation is slow compared to the time scale of the experimental technique isknown as the blocking temperature, TB.

3.4 Vibrating Sample Magnetometer (VSM)

The VSM is a versatile instrument widely used for the characterization ofmagnetic materials. It is based on Faraday’s law of induction, which statesthat a change in magnetic flux density induces an electric field,

∇×E = −∂B

∂t(3.20)

In an inductor coil with cross-sectional area, A, and N number of turns Eq.3.20 becomes

V = −NAdBdt

(3.21)

where V is the induced voltage. The sign in Eqs. 3.20 and 3.21 is given by arule known as Lenz’ law, which can be stated as: Nature abhors a change influx, i.e. when an electric field is induced by a time-varying magnetic field itwill be in such a direction that the flux it produces will oppose the change inmagnetic flux [30].

40

Vibrating Sample Magnetometer (VSM)

3.4.1 Vibrating Sample Magnetometer Setup

The principle of the VSM is illustrated in Fig. 3.19. The sample to be investi-

Figure 3.19: Left: Sketch of the first VSM built in 1955 illustrating the basicsetup. (1) loud-speaker transducer, (2) conical paper cup support, (3) drinkingstraw/sample tail, (4) reference sample, (5) sample, (6) reference coils, (7) samplecoils, (8) magnet poles, (9) metal container [31, 32]. Right: The LakeShore 7407VSM used in this work.

gated is placed in a sample holder, which is then mounted on a fiber glass rodknown as the sample tail (3). The sample tail is attached to the VSM drive(1) and vibrated sinusoidally and perpendicularly to a uniform magnetizingfield. Between the sample and the magnet poles (8) are placed pick-up coils(7). The oscillating magnetic field of the vibrating sample induces a voltagein the pick-up coils. This induced current is proportional to the magneticmoment of the sample. A second voltage is induced in the reference coils (6)by a reference sample (4) and used by the lock-in amplifier as described in thefollowing subsection. The voltage V across the pick-up coils is given by

V = GAωµ cos(ωt) (3.22)

where G is a constant depending on the geometry of the pick-up coils, Ais the amplitude of the sinusoidal vibration, µ is the magnetic moment ofthe sample and ω is the angular frequency with which the sample is moved.

41


For measurements where an applied magnetic field is needed an electromagnetsupplies a uniform magnetic field within the small region containing the sampleand pick-up coils.

Lock-in amplifier

The AC signal is measured using a lock-in amplifier, which provides a DCoutput proportional to the AC signal. The term lock-in refers to the fact thatthe amplifier is ’locked’ to a reference voltage, which has the same frequencyas the signal. In the VSM setup this reference signal for the lock-in amplifieris supplied by a reference sample (4) and a reference pick-up coil (6).

In the amplifier a demodulator multiplies the reference signal and theincoming signal generating an output the mean level of which is the DC output.When the two inputs multiplied are in phase a positive mean level is obtained,see Fig. 3.20, whereas a mean level of zero is obtained when the two signals arecompletely out of phase. In an experimental setup, the signal will not be noise-free, but as the noise has no fixed frequency or phase relationship with thereference it does not result in a change of the mean DC level. Mathematically,

Figure 3.20: Left: An incoming signal in phase with the reference signal will yielda demodulator output in the form of a sinusoidal wave with twice the referencefrequency and a mean level which is positive. Right: In the case of signal witha phase that is delayed 90◦ with respect to the reference the demodulator outputis still a sinusoidal wave with twice the reference frequency, but the mean level iszero [33].

the output voltage, Vout is given by

Vout = A cos(ωt) ·B cos(ωt+ θ) =12AB cos θ +

12AB cos(2ωt+ θ) (3.23)

where A cos(ωt) is the signal and B cos(ωt+ θ) is the reference signal with auser-adjustable phase-shift θ. If B is kept constant it should be appreciatedthat the mean DC level is proportional to the amplitude of the signal, A anda function of the phase angle, θ, between the signal and reference. The 2ωtcomponent is removed in a low-pass filter before the output leaves the lock-inamplifier as a DC signal.

42

Vibrating Sample Magnetometer (VSM)

Using this procedure, a high sensitivity is obtained as the measurementsare made insensitive to changes in the vibration amplitude, vibration fre-quency, small magnetic field instabilities, amplifier gain and amplifier linear-ity. Using a suitable configuration of the pick-up coils the measurements arealso insensitive to the exact sample position [31]. Indeed, the data sheet forthe LakeShore 7407 VSM used in this study specifies a moment measurementrange of 0.1× 10−6 emu to 1000 emu.

Calibration

A small standard reference sample is used for calibration of a VSM. Usually,a Ni sample is used as it has a high and well-known moment, so that a largesignal is obtained for a small sample. Other considerations are its chemicalstability, low saturation field, low cost, the availability in high purity and thefact that it is only slightly temperature sensitive even at 300 K [32].


In this study was used the LakeShore 7407 VSM located at the Department ofMicro and Nanotechnology (MIC), DTU. Assistance with the VSM was kindlyprovided by Associate Professor Mikkel Fougt Hansen.

3.4.2 Interpretation of VSM Data Obtained

A multitude of measurements can be made with a VSM. In this study hys-teresis loops or field sweeps are made. The applied magnetic field is driven tomaximum before starting the measurement of the magnetization. The mea-surement is started and, in incremental steps, the field is reversed and thendriven to maximum again all the while the magnetization is measured. In thisway the relation between the magnetization and applied field is determined.If irreversibilities such as domain wall shifting happens in the sample duringthe sweep of the magnetic field a hysteresis seen, see Fig. 3.21. In the fig-ure are seen the parameters most often extracted from a hysteresis loop tocharacterize the magnetic properties of the sample. The coercivity or coercivefield, denoted Hc in the figure, is the field at which the magnetization is zeroafter having been saturated. The remanence or remanent magnetization, Mr,is the magnetic moment at zero applied field. Finally, Ms is the saturationmagnetization. If the magnetization does not reach saturation at maximumfield the loop is said to be a minor loop.

A horizontal shift in the hysteresis loop may be seen when an antiferro-magnetic and ferromagnetic phase can interact via exchange and the sampleis field cooled from above the Neel temperature but below the Curie tempera-ture. In this case the ferromagnets magnetization will align with the field andas the sample is cooled through the Neel temperature the moments of the an-tiferromagnet will align with those of the ferromagnet. If the anisotropy of theantiferromagnet is large it will tend to hold its alignment against the sweeping

43


Figure 3.21: Hysteresis loop indicating the coercivity, Hc, the remanence, Mr andthe saturation magnetization, Ms. Figure from [27].

field as a hysteresis loop is recorded. Through exchange interaction the spinsof the ferromagnet will be given a preferential direction and are said to bepinned. To turn the spins away from the easy direction a higher magneticfield is required than to return the spins to the easy direction. Thus, thereis said to be exchange bias in the system and the hysteresis loop is shiftedhorizontally in the opposite direction of the easy direction. If not all spinsrotate to the harder direction there will also be a vertical shift. Exchangebias has been studied using thin films, but the effect was discovered in fer-romagnetic Co nanoparticles having an antiferromagnetic shell of CoO [34].Antiferromagnetic nanoparticles may display both coercivity and loop shiftsas the uncompensated spins couple to the antiferromagnetic core [35].

44

Four

Ferrihydrite and CoO

4.1 Ferrihydrite

Ferrihydrite is a poorly crystalline Fe(III) oxyhydroxide1, which typically oc-curs in nature, see Fig. 4.1, as the result of rapid oxidation of Fe(II). It may

Figure 4.1: Image from [36] with caption: Iron oxide formation in the environment:ferrihydrite formed by oxidation of Fe2+ in a ferriferous spring in Iceland. (Photocourtesy: Dr. Liisa Carlson, University of Helsinki).

also occur where inhibitors, be they organics, phosphate or silicate species,1An oxyhydroxide contains O and OH groups

45

4. Ferrihydrite and CoO

stabilize ferrihydrite and prevents it from transforming to more stable miner-als such as hematite. Thus, the typical environments in which ferrihydrite isfound are Fe containing springs, drainage lines, lake oxide precipitates, groundwater and stagnant-water soils and river sediments [36].

The chemical composition of ferrihydrite is not well-understood, but pos-sibilities given in literature are Fe5HO8 ·4H2O, 5Fe2O3 ·9H2O, Fe6(O4H3),Fe2O3 · 2FeOOH2.6H2O and Fe4.5(O,OH,H2O)12 [4]. As seen from thedifferent suggestions part of the trouble lies in determining the water content.Because ferrihydrite is poorly crystalline an XRD spectrum does not providea crystal structure to constrain the chemical formula.

Ferrihydrite comes in several different forms designated according to thenumber of peaks in their XRD spectra. The most common are 2-line and6-line ferrihydrite, see Fig. 4.2. As can be seen from the XRD spectra 6-lineferrihydrite is the more crystalline, while 2-line ferrihydrite shows an almostamorphous XRD spectrum. Despite the poorly crystalline structure apparent

Figure 4.2: XRD spectra (Co Kα) of 2-line and 6-line ferrihydrite [36].

in XRD, ferrihydrite is not amorphous and crystal structure is seen in TEMimages, see Fig. 6.3 on page 68.

The structure of ferrihydrite is believed to be at least partly similar to thatof hematite (α−Fe2O3). In hematite layers of edge- and face-sharing FeO6-octahedra are stacked in the c direction, see Fig. 4.3. The iron to oxygen ratiois lower in ferrihydrite than in hematite and one suggestion is that ferrihydritecontains a defect hematite-like component with vacancies in some of the Fepositions. Whereas the fundamental structure unit in hematite is the FeO6-octahedron, the fundamental structure unit in ferrihydrite is believed to be theFe(O,OH)6-octahedron. Another suggestion is that ferrihydrite is closer to

46

Ferrihydrite

Figure 4.3: Left: Idealized model of hematite showing the edge- and face-sharingoctahedra. The Fe3+ ions are located in the center of the octahedra. Where theoctahedra are face-sharing (shading) the centers of the octahedra are closer andthe repulsion between the cations move them off-center. Right: Idealized modelof goethite showing the edge-sharing octahedra linked by corner-sharing. Again theFe3+ ions are located in the center of the octahedra. The double lines represent Hbonds. [36].

goethite (α−FeOOH) in structure. In goethite double bands of edge-sharingFeO3(OH)3 octahedra are linked by corner-sharing to create tunnels, seeFig. 4.3. It seems that the hematite- or goethite-like structure is confined tothe core of ferrihydrite as results from EXAFS2 and XANES3 spectroscopyindicate that the surface of ferrihydrite contains a large number of Fe ionsin tetrahedral coordination [4]. Several models for the crystal structure offerrihydrite have been suggested, but none has so far been able to provide acalculated XRD pattern, which has been incontrovertible.

The poorly ordered crystals of ferrihydrite are between 2 and 7 nm in size.This leads not only to a smearing-out of XRD patterns, but also to a distribu-tion of quadrupole splittings in the superparamagnetic state and a distributionof magnetic hyperfine fields in the magnetically ordered state in Mossbauerspectra [37]. The spread in particle size also means that no temperature existsat which a sample of ferrihydrite orders magnetically rather the transition isgradual with superparamagnetism and magnetic ordering co-existing over awide temperature range. Ferrihydrite may remain superparamagnetic to tem-peratures as low as 23 K, but at 4.2 K all samples appear as sextets with nosuperparamagnetic doublet.

In Fe(III) the orbital angular moment is quenched, so that the magneticmoment is entirely from the spin of the electron. The electron configuration of

2Extended x-ray absorption fine-structure3X-ray absorption near-edge structure

47


Fe is [Ar]4s23d6, so Fe(III) has five unpaired electrons in the high-spin state.The magnetic moment, µ, of an ion given by

µ = (L+ gS)µB (4.1)

where L is the orbital angular momentum, S =√s(s+ 1) is the spin angular

momentum and g = 2.00232 is the Lande factor. Thus, with s = 52 we find

theoretically a magnetic moment of 5.92µB per Fe(III) ion.By examining Mossbauer spectra of ferrihydrite at 4.2 K in applied fields

up to 9 T, it has been determined that 6-line ferrihydrite is antiferromagnetic[38]. The Neel temperature as determined by neutron scattering is ' 330(20)K [39].

4.1.1 Ferrihydrite in Living Organisms

Ferrihydrite is part of the core of a protein called ferritin, which acts as an iron-storage in living organisms. Ferritin is a hollow sphere inside which ferrihydriteis attached to the inner walls. In humans, ferritin is primarily found in theliver, spleen, and bone marrow, but a small amount is also found in the blood.A test of the amount of ferritin in a blood sample is used as an indication ofthe amount of iron stored in the body. Ferritin acts to contain iron so that itdoes not react with other molecules, it acts as a buffer against iron deficiencyand as a means to release the iron in a controlled fashion. The body needsiron in the Fe(II) oxidation state, but the Fe in ferrihydrite is in the Fe(III)oxidation state. A reduction agent is used to change Fe(III) into Fe(II), beforeit leaves the protein via a 3-fold channel, see Fig. 4.4.

4.2 CoO

The transition metal oxide CoO is antiferromagnetic with a bulk Neel temper-ature of TN ' 293 K. Neutron scattering [41] and VSM [42] measurements onCoO nanoparticles find that their Neel temperature is close to the bulk value.The size of the nanoparticles in the two studies is 20 and 18 nm, respectively.

In the paramagnetic phase the crystal structure of CoO is simple cubic,see Fig. 4.5. The transition to the ordered antiferromagnetic state is coupledwith a large tetragonal contraction along the cubic [001] direction, i.e. the caxis is shortened so that c/a < 1. A smaller deformation along the cubic [111]direction was inferred from a high-resolution synchrotron powder diffractionstudy and found to scale with the tetragonal distortion [43]. This latter distor-tion is controversial as the magnetic ordering would be coupled with a cubic-to-monoclinic symmetry breaking making the paramagnetic-antiferromagneticphase transition of first order, which is not seen in other studies [44]. In Fig.4.6 is shown the relation between the paramagnetic and antiferromagnetic unitcell of CoO. Also shown in Fig. 4.6 is the magnetic structure. The electronconfiguration of Co is [Ar]4s23d7 and that of O is [He]2s22p4. In CoO two of

48

CoO

Figure 4.4: Molecular model of ferritin. Magenta subunits are farthest away, lightblue subunits are closest and dark blue subunits are in between. The circles labeled3-fold and 4-fold refer to hydrophilic and hydrophobic channels, respectively. AfterFe(III) has been reduced to Fe(II) it leaves the protein via a 3-fold channel [40]

Figure 4.5: The cubic, tetragonal and monoclinic Bravais lattices. Adapted from [45].

the electrons are paired with two of the 2p electrons in O. This leaves 3 un-paired electrons in a high-spin configuration and a magnetic moment arisingpurely from the spin of the Co ion would have a magnitude of 3.87µB per Coion. A magnetic moment of 3.98(6)µB per Co ion has been determined usingneutron scattering [43]. The larger magnetic moment measured is due to anincomplete quenching of the orbital magnetic moment.

CoO has a high anisotropy with the value of the first anisotropy constantcalculated to be K1 ' 2.7× 108 erg/cm3 [46].

49


Figure 4.6: The relationship between the paramagnetic crystal structure and themagnetically ordered monoclinic structure of CoO. [43].

50

The principle of science, thedefinition, almost, is thefollowing: The test of allknowledge is experiment.Experiment is the sole judge ofscientific “truth.”

Richard P. Feynman,Lectures on Physics

Experimental Results andConclusions

51

Five

Production of Ferrihydrite and CoONanoparticles

In the following the production of samples used in the Mossbauer and VSMstudies is described.

5.1 CoO

Two batches of CoO nanoparticles, CoO1 and CoO6, were made using a two-step procedure. A powder of as prepared Co3O4 was ball-milled to reducethe size of the particles and then reduced in hydrogen at a temperature of250◦C. The reverse procedure is more difficult because CoO will transforminto Co3O4 if ball-milled in air. An attempt was made with ball-milling CoOin an Ar atmosphere, but this unexpectedly lead to a transformation intoCo3O4. This is thought to be due to a lack of proper containment in thegrinding bowl used, so that air was introduced to the sample. As the two-stepprocedure of ball-milling with subsequent reduction in H2 was successful inproducing CoO nanoparticles, the milling of CoO in an atmosphere deprivedof oxygen was not pursued further.

An XRD spectrum of as prepared Co3O4 was refined using Fullprof2000, see Fig. 5.1, and a crystallite size of 27.6 nm was determined. Co3O4

is an antiferromagnet. Its has a bulk TN = 40 K and in 8 nm particles a Neeltemperature of 30 K has been determined [47].

5.1.1 Fritsch Pulverisette Ball Mill

In the production of CoO nanoparticles a ball mill is used to reduce the sizeof the particles. Following is a brief description of the working principle of aplanetary ball mill such as the Fritsch pulverisette 5 planetary mill used inthis study. The mill consists of a number of grinding bowls that rotate aroundtheir axis during operation of the ball mill. These grinding bowls are situatedon a counter-rotating disc. The powder to be ground is put inside a bowl with

53

5. Production of Ferrihydrite and CoO Nanoparticles

Figure 5.1: Refined XRD spectrum of as prepared Co3O4.

a number of grinding balls. When the ball mill is operating the balls will bothgrind and crush the powder. The grinding takes place as powder is caughtbetween the inner wall of the bowl and a ball driven along the inner wall.Due to the force from the large counter-rotating disc the balls will separatefrom the wall, cross the bowl and crush the powder against the inner wall, seeFig.5.2.

In all operations with the ball mill a WC (tungsten carbide) grindingbowl and nine WC grinding balls were used. The WC balls have an averagediameter of 19.47 mm and a combined weight of 514.86 g. The choice of bowland balls should be considered not only for its suitability in terms of hardness,but also with the consideration that material from the grinding bowl and ballsare mixed with the powder to be ground. An alternative in this study wasusing a stainless steel bowl, but this would contaminate the sample with Fe.Choosing a bowl and balls of WC, however, contaminates the sample withCo as this is used as a hardener in the alloy. The analysis of the grinding bowlprovided by Fritsch, see appendix C, states that the actual composition of theWC grinding bowl is 93.5% WC, 6.0 % Co and 0.5 % TaC (tantal carbide).

54

CoO

Figure 5.2: Left: Drawing of a Fritsch pulverisette 5 [48]. The drawing is of a newermodel than the one used in this study. Right: Drawing depicting the grinding andcrushing motion of the balls.

Thus, it cannot be avoided that some Co is introduced into the ball-milledsamples. The Co content of the WC grinding bowls and balls was not knownat the time of production.

In this study the ball mill was always run at 200 rpm.

5.1.2 Step One: Ball-Milling of Co3O4

During initial runs with the ball mill it was found that a continuous run doesnot reduce particle size as much as when a cooling off period is introducedbetween runs. When run continuously, the bowl heats up and this worksagainst the size reduction of the particles. To illustrate, the ball mill was runwith 1.0 g of as prepared Co3O4 for a total of 280 minutes with a break every20 minutes where an XRD spectrum of the grinding material was made. Thebreaks were of varying lengths with the shortest being 40 minutes. All thespectra were made with 2θ = 34◦−39◦, a stepping of 0.05◦ and a measurementtime of 4 seconds per step. This angle interval covers the most intense peakof Co3O4 at 2θ = 36.85◦ and a much less intense peak at 2θ = 38.55◦.After grinding in the ball mill the peaks recorded in the XRD spectra showbroadening. With only one peak it is not possible to discern size and strainbroadening, so even though the peak broadens visibly this broadening cannotbe translated into a crystallite size. The ball mill was then run continuouslyfor 220 minutes, again with 1.0 g of as prepared Co3O4. Without assumingthat the broadening of the peak at 2θ = 36.85◦ can be directly translated to aparticle size using Scherrer’s formula, we will use it to quantitatively estimatethe effect of ball-milling with and without cooling off periods. The peak isfitted with a Lorentzian and the FWHM plotted as a function of time, seeFig. 5.3. The FWHM of the peak at 2θ = 36.85◦ after a total ball-millingtime of 200 min disturbs what would otherwise look like a smooth broadening

55


Figure 5.3: Broadening of Co3O4 XRD peak after ball-milling with and withoutcooling off periods.

of peaks and may be an artefact possibly due to the short measurement timeof the XRD spectrum. If not, it is not correct to conclude that ball-millingwith cooling off periods leads to smaller particle sizes. Still, in the productionof the samples CoO1 and CoO6 it was decided to continue ball-milling withcooling off periods.

5.1.3 Step Two: Heating in H2

By heating Co3O4 in H2 it reduces to CoO and then to Co. To determineif it is possible to reduce to CoO without further reducing to Co 1.0 g ofas prepared Co3O4 was reduced in H2 at various temperatures and heatingtimes, see Fig. 5.4. It was found that heating at a temperature of 250◦C for45 minutes reduced the as prepared Co3O4 to CoO.

It was initially thought that the 45 minutes at 250◦C in a H2 flow needed toreduce the sample of as prepared Co3O4 would also be correct for reducing theball-milled Co3O4 nanoparticles to CoO. However, after heating a ball-milledsample of Co3O4 for 45 minutes in H2 at 250◦C, an XRD spectrum showedthat the sample contained a mixture of Co3O4 and CoO. It was decided thathigher temperatures should not be attempted as this might reduce the Co3O4

to Co and instead the Co3O4 nanoparticles were heated for a longer time.The reason for the extended heating time required to reduce the Co3O4

nanoparticles to CoO nanoparticles could be that it is more difficult for molec-

56

CoO

Figure 5.4: XRD of Co3O4 reduced in H2 at the temperatures and times indicated.The lines indicate the scattering angles for CoO. The successful production ofCoO without traces of Co3O4 or Co is shown in bold.

ular nucleation to take place. When particles transform, molecular nucleationstarts at a site and spreads from there. The smallness of the particles meansthat there are fewer sites where molecular nucleation can start. There arealso far more particles and the nucleation must start at a site in each. How-ever, molecular nucleation is more likely to start at surface defects and asthe nanoparticles have a higher surface to volume ratio, this would furthermolecular nucleation.

57


5.1.4 Production Details for Samples CoO1 and CoO6

CoO1

1.7 g of as prepared Co3O4 was ball-milled with cooling off periods for a totalball-milling time of 24 hrs and 12 minutes. The details of the ball-millingtimes and cooling off periods are given in Table D.1 in appendix D. Thesample CoO1 was made before a timer was installed to ease ball-milling withcooling off periods. After ball-milling the Co3O4 nanoparticles were heatedfor 45 min at 250◦C in H2. As this was not enough to reduce the Co3O4

nanoparticles to CoO, the sample was heated twice for 5 hours at 250◦C inH2. An XRD spectrum of the sample was refined using Fullprof 2000, seeFig. 5.5, and the CoO particle size estimate is 11 nm. It was also determinedthat the weight percentages of Co3O4 and WC in the sample are 3.3 and6.6%, respectively. No Co is seen in the XRD spectrum.

Figure 5.5: Refinement of XRD spectrum of sample CoO1.

58

CoO

CoO6

2.0 g as prepared Co3O4 was ball-milled with a timer programmed to run theball mill for 15 min then stop and wait 45 min before the next run. The ballmill was run in this manner for 4 days, which comes to a total ball-milling timeof 24 hours. 1.0 g of the ball-milled Co3O4 nanoparticles was heated twice for5 hours. Again, the XRD spectrum was refined using Fullprof 2000, see Fig.5.6. A size estimate of 9 nm is found for the CoO nanoparticles and weightpercentages of Co3O4 and WC in the sample are 0.2 and 8.3%, respectively.No Co is seen in the XRD spectrum.

Figure 5.6: Refinement of XRD spectrum of sample CoO6.

5.1.5 Samples CoO2, CoO3, CoO4 and CoO5

Samples CoO2, CoO3, CoO4 and CoO5 contained amounts of Co visiblein the XRD spectra and were discarded. One sample was heated longer to tryand remove more of the Co3O4, but the reduction went too far. In the caseof the other three samples it was discovered that the high energy ball-milling

59


had made a chemical reaction and that the powder, before any heating in H2,contained both Co3O4, CoO and Co.

5.2 Ferrihydrite

The sample of ferrihydrite was synthesized following the recipe given in [36]for 6-line ferrihydrite with the sole difference that the solution was put in acentrifuge before freeze-drying. Without the specific details, the recipe is asfollows:

• Crystals of ferric nitrate (Fe(NO3)3·9H2O) are added to distilled waterwhich has been heated to 75◦C in an oven. The solution is stirred,returned to the oven and left there for 10 − 12 minutes during whichtime the solution changes color. The solution is then cooled rapidly inice water and transferred to dialysis bags for 3 days of dialysis. Finally,the suspension is freeze-dried.

An XRD spectrum verified that the sample is 6-line ferrihydrite, see Fig.5.7. No refinement was made of the ferrihydrite XRD spectrum as no definite

Figure 5.7: XRD spectrum of ferrihydrite sample. Comparing the spectrum with Fig.4.2 verifies that the sample is 6-line ferrihydrite.

crystal structure is known.TEM images obtained of the ferrihydrite particles are of poor quality due

to agglomeration of the particles, see Fig. 5.8. However, the few particles

60

Ferrihydrite

Figure 5.8: TEM image of ferrihydrite showing agglomeration of the particles.

distinguishable in the image do appear to be ∼ 5 nm in size and spherical inshape.

61

Six

Mossbauer study

This chapter describes the results of Mossbauer spectroscopy on samples offerrihydrite, both the as prepared sample and samples treated by grindingand heating in H2. Ferrihydrite was mixed with CoO nanoparticles in variousways to determine the best procedure for facilitating inter-particle interaction.The interactions between the nanoparticles in the mixed samples were studiedusing Mossbauer spectroscopy.

• Section 6.1 gives an overview of samples.

• Section 6.2 describes the characterization of the ferrihydrite nanoparti-cles using Mossbauer spectroscopy.

• Section 6.3 describes the changes seen in Mossbauer spectra of ferrihy-drite after grinding by hand in an agate mortar, after heating in H2 andafter grinding with subsequent heating in H2. These treatments wereperformed on ferrihydrite for comparison with samples described in thefollowing section.

• Section 6.4 describes the results of Mossbauer spectroscopy measure-ments on a wide range of mixed samples of ferrihydrite and CoO nanopar-ticles. Mossbauer spectra and hyperfine field distributions of the differ-ent mixed samples are compared.

• Section 6.5 compares the room temperature spectra of ferrihydrite andthe mixed samples.

6.1 Overview of Samples

An overview of the samples produced is given in Table 6.1. The details of pro-duction for each sample is given in the following sections. The mixed samplesof ferrihydrite and CoO follow the naming scheme:FHCoO <mg ferrihydrite mg CoO> <comment on method of production>. Whenreferencing the sample in the text the middle part giving the mass is usuallyleft out.

63

6. Mossbauer study

Name Content

FH Ferrihydrite nanoparticlesCoO1 CoO nanoparticles, small amounts of Co3O4 and WC , see

section 5.1.4 for details.CoO6 CoO nanoparticles, small amounts of Co3O4 and WC , see

section 5.1.4 for details.

FH 50 GH 50 mg FH, ground by hand (GH) in agate mortar.FH 53 6H100CH2 53 mg FH, heated for 6 hours at 100◦C in H2.FH 50 GH 6H100CH2 50 mg FH, ground by hand (GH) in agate mortar and then

heated for 6 hours at 100◦C in H2.

FHCoO 5051 RTD 50 mg FH and 51 mg CoO1, mixed in water and room tem-perature dried (RTD).

FHCoO 5157 CD 51 mg FH and 57 mg CoO1, mixed in water and cold dried(CD) in refrigerator.

FHCoO 5050 RTD slow 50 mg FH and 50 mg CoO1, mixed in water and room tem-perature dried (RTD) slowly.

FHCoO 2250 RTD 22 mg FH and 50 mg CoO1, mixed in water and room tem-perature dried (RTD).

FHCoO 5655 RWC100 FD 56 mg FH and 55 mg CoO1, reflux water cooled (RWC) at∼ 100◦C and freeze dried (FD).

FHCoO 5151 RWC75 FD 51 mg FH and 51 mg CoO1, reflux water cooled (RWC) at∼ 75◦C and freeze dried (FD).

FHCoO 5050 GH 50 mg FH and 50 mg CoO6, ground by hand (GH) in agatemortar.

FHCoO 5050 Mix 50 mg FH and 50 mg CoO6, mixed with plastic spoon.FHCoO 5050 Mix XH100CH2 50 mg FH and 50 mg CoO6, mixed with plastic spoon and

heated for X (4 or 6) hours at 100◦C in H2.FHCoO 5050 GH 6H100CH2 50 mg FH and 50 mg CoO6, ground by hand (GH) in agate

mortar and heated for 6 hours at 100◦C in H2.FHCoO 5050 MW 6H100CH2 50 mg FH and 50 mg CoO6, mixed in water (MW) and

heated for 6 hours at 100◦C in H2.

FHCoO 5050 US3 RTD 50 mg FH and 50 mg CoO1, mixed in water, given ultra-sound for 3 hours (US3) and room temperature dried (RTD).

Table 6.1: Overview of samples.

64

Ferrihydrite and Sample CoO6

Hyperfine field distributions using distfit

Using the program distfit selected spectra of ferrihydrite and mixed sampleswere fitted with a hyperfine field distribution. By fitting a single sextet to thespectrum of ferrihydrite at 20 K with the program mfit an isomer shift, δ =0.478 mm/s, and quadrupole splitting, ∆ = −0.036 mm/s, were determined.These parameters were used as input for the program and hyperfine fielddistributions with fields ranging from 1 to 60 T were made. Smoothing is atfirst set to a low value and then increased until χ2 increases. Asymmetry ofthe lines, i.e. the differing lengths of the otherwise pairwise identical lines,means that the distribution fit must also contain an isomer shift distribution.This is achieved by making the isomer shift, δ, a function of the hyperfinefield, such that

δ = A1 +A2 ×Bhf (6.1)

where A1 and A2 are parameters to be fit. Further, the line area ratios are alsofitting parameters in the distribution model chosen. When plotting the hy-perfine field distributions they are normalized so that the sum of probabilitiesequals one.

6.2 Ferrihydrite and Sample CoO6

Mossbauer spectra of ferrihydrite, see Fig. 6.1, show magnetic splitting at 20and 50 K with broad lines. The broad lines indicate a distribution of hyperfinefields from the different atomic environments of the 57Fe ions. Zhao et al. [49]conclude, based on XAFS1, that the Fe atoms in the interior of ferrihydriteare octahedrally coordinated, while a significant number of surface Fe atomshave fewer than six (O,OH) ligands. The narrowness of lines 3 and 4 comparedto the other lines is also a characteristic of a hyperfine field distribution.

The onset of magnetic order in ferrihydrite takes place over a range of tem-peratures due to the broad distribution of particle size. As the temperatureincreases, larger and larger particles relax until finally no magnetic splittingis seen in the Mossbauer spectrum. The hyperfine field distributions as wellas the Mossbauer spectra show the progression from magnetic splitting to in-creasing superparamagnetic relaxation. At 20 K the magnetic splitting is pro-nounced and the hyperfine field distribution has a maximum at 48 T with thedistribution slightly skewed towards lower values. This is consistent with thehyperfine field distribution analysis performed by Murad and Schwertmann[37] on a natural sample of ferrihydrite at 4 K with a higher peak maximum,50 T, due to the greater splitting at the lower temperature. At 50 K thespectrum is beginning to collapse as the lines are broadened asymmetricallytowards the center of the spectrum due to more particles becoming super-paramagnetic. This causes the maximum in the hyperfine field distribution tomove towards lower values and the distribution is more spread out. At 80 K

1X-ray absorption fine-structure spectroscopy

65

6. Mossbauer study

Figure 6.1: Left: Mossbauer spectra of ferrihydrite at the temperatures indicated. The lines arefits to magnetic hyperfine field distributions. Right: Distributions of magnetic hyperfine fields offerrihydrite at the indicated temperatures. The distributions are shown on the same scale.

the spectrum is dominated by a doublet and at 120 K the magnetic splitting iscompletely gone. This is seen in the hyperfine field distributions as a gradualtransition towards lower fields.

The room temperature spectra of ferrihydrite and samples of ferrihydritemixed with CoO are studied in section 6.5.

66

Effects of Grinding and Heating on Ferrihydrite.

Sample CoO6

To be certain that no Fe is present in the samples of CoO nanoparticles aMossbauer spectrum was made of sample CoO6, see Fig. 6.2. We see from theMossbauer spectrum that the samples of CoO nanoparticles do not contain57Fe.

Figure 6.2: Mossbauer spectrum of sample CoO6 with a spectrum of ferrihydritesuperimposed to give scale. The lines are guides to the eye.

6.3 Effects of Grinding and Heating onFerrihydrite.

FH 50 GH

50 mg of ferrihydrite was ground by hand in an agate mortar for ∼ 5 minutes.

The grinding has an effect on the superparamagnetic relaxation as seenin the Mossbauer spectra in Fig. 6.5 on page 70. The untreated ferrihydriteshows an almost collapsed magnetic splitting at 80 K with a prominent dou-blet, whereas the ground ferrihydrite has an increased magnetic splitting at thesame temperature. This increase in magnetic splitting could result from inter-actions between the ferrihydrite nanoparticles or from an increase in particlesize, which would increase the relaxation time. To examine whether the effectwas due to an increase in particle size, TEM images were made of the groundferrihydrite, see Fig. 6.3. The micrographs do not show larger particles, butit cannot be ruled out that the mean particle diameter has increased due to

67

6. Mossbauer study

Figure 6.3: TEM image of ground ferrihydrite. No increase in particle size due to thegrinding is apparent.

the grinding. When goethite nanoparticles (α−FeOOH) are ground by handin an agate mortar for ∼ 10 minutes. they transform to hematite (α−Fe2O3)[50]. An XRD spectrum of ground ferrihydrite, see Fig. 6.4, shows that noor little transformation takes place after grinding for a short time. The XRDspectrum is limited in that it was obtained with a scattering angle up to 50degrees and a short measurement time. An XRD spectrum going to a higherscattering angle might show changes not visible in the obtained spectrum.

Comparing the hyperfine field distribution at 20 K for the sample of groundferrihydrite, Fig. 6.6 on page 70, with that of as prepared ferrihydrite, Fig.6.1 on page 66, shows that a shift has occurred in the maximum of the peak.For the sample of as prepared ferrihydrite the peak maximum is at 48 T, whileit has shifted to 50 T for the ground sample and also for the samples groundand heated in H2 to be described in the following. As the peak maximum isan indicator of crystallinity for different samples of ferrihydrite [51] it wouldappear that grinding and/or heating leads to a more crystalline ferrihydrite.To what degree this affects TEM images of the samples is unclear, but perhapsit is not a coincidence that lattice planes are seen in all images taken of theground ferrihydrite, whereas none are visible in the images of as preparedferrihydrite. That is not to say that the lattice planes are not there in the asprepared ferrihydrite, but that it may be less likely to see them due to thelower crystallinity.

68


Figure 6.4: XRD spectra of untreated ferrihydrite (left) and ground ferrihydrite(right). The XRD spectra show no apparent changes in the structure due to thegrinding.

FH 53 6H100CH2

53 mg ferrihydrite was put in a crucible and heated for 6 hours at 100◦C inH2.

Heating the ferrihydrite affects the magnetic properties as seen in theMossbauer spectra in Fig. 6.5 on page 70. The magnetic splitting is moreprominent in the spectrum at 80 K and the doublet gets rounded as themagnetic splitting is increased compared to the untreated ferrihydrite. Thehyperfine field distribution, see Fig. 6.6 on page 71, at 80 K also reflects thisas it is shows a slight increase in probabilities at high fields just as for thesample of ground ferrihydrite, FH GH.

69

6. Mossbauer study

Figure

6.5:M

ossbauerspectra

atthe

indicatedtem

peraturesof

ferrihydritetreated

bygrinding

andheating.

The

linesare

hyperfinefield

distributionfits

exceptfor

theroom

temperature

spectra,w

herethey

arem

erelyguides

tothe

eye.

70


Figure

6.6:H

yperfinefield

distributionsat

theindicated

temperatures

offerrihydrite

treatedby

grindingand

heating.T

hedistributions

areshow

non

thesam

escale.

71

6. Mossbauer study

When ferrihydrite is heated in H2 water is extracted from the structure.An XRD spectrum of sample FH 6H100CH2, see Fig. 6.7, shows changes athigh scattering angles. No distinct transformation has occurred as the spec-

Figure 6.7: XRD spectra of untreated ferrihydrite (left) and ferrihydrite heated inH2 for 6 hours (right). The XRD spectra show that changes occur in the structureat high scattering angles after heating.

trum still shows only poorly crystalline structures, but it may be the beginningof a transformation. No experiment was made with continued heating to seeif further changes occur or if the heating has simply lead to a slight reorderingin the structure, which does not progress further.

FH 50 GH 6H100CH2

50 mg ferrihydrite was ground by hand in an agate mortar for ∼ 5 min., putin a crucible and heated for 6 hours at 100◦C in H2.

The spectrum at 80 K of ferrihydrite both ground and heated in H2 alsoshows increased magnetic splitting. In contrast with the two previous samples,however, a distinct doublet with narrow lines is also seen in the spectrum.Thus, in the hyperfine field distribution there is an increase in both the highand low field part. The doublet appears shifted relative to the magneticsplitting, which is also seen in other spectra showing a distinct doublet, e.gsample RWC100 in Fig. 6.11 on page 78. It is not understood why thespectrum at 80 K has both a distinct doublet indicating a greater relaxation ofthe ferrihydrite and at the same time a greater magnetic splitting compared tountreated ferrihydrite, which means a decrease in relaxation. The spectrum at120 K shows a doublet much broader than that of the as prepared ferrihydritealso indicating a decrease in relaxation.

72

Study of Ferrihydrite Mixed with CoO

6.4 Study of Ferrihydrite Mixed with CoO

6.4.1 Samples Mixed in Aqueous Solutions

FHCoO 5051 RTD

50 mg ferrihydrite and 51 mg CoO1 were mixed in 100 mL demineralizedwater and given ultrasound for 20 minutes to further mix the powders. Thesolution was left in a petri dish with no cover to dry at room temperature.Drying time: ∼ 10 days.

The Mossbauer spectra of sample FHCoO RTD, see Fig. 6.8, show thatthe ferrihydrite nanoparticles are affected by the CoO nanoparticles in thatthe superparamagnetic relaxation has been slowed. The spectrum at 80 K,which shows prominent magnetic splitting and a small superparamagneticdoublet, should be compared with the spectrum of pure ferrihydrite in Fig.6.1 on page 66. The Mossbauer spectrum at 120 K of the mixed sample closelyresembles that of pure ferrihydrite at 80 K.

The hyperfine field distribution at 80 K shows a maximum around 52 T,which is surprisingly higher than the maximum seen at 20 K. When comparingthe Mossbauer spectra at 80 K of the three samples of dried aqueous solutionsit is found that the spectrum of FHCoO RTD is wider than the others. Asthis is not seen at any other temperature it is believed to be due to a mistakein calibration. Quantitatively we can say that a peak being present in thehigh field end of the distribution means a magnetic splitting is there as seenin the Mossbauer spectrum. The hyperfine field distribution at 20 K has apeak maximum at ∼ 48 T just as for pure ferrihydrite.

No Mossbauer spectra at 50 K or room temperature were obtained beforethe sample was used for VSM measurements.

FHCoO 5157 CD

51 mg ferrihydrite and 57 mg CoO1 were mixed in 100 mL demineralizedwater and given ultrasound for 25 minutes. The solution was kept in a petridish with no cover and put in a refrigerator to dry. During the time in therefrigerator, the solution froze and had to be taken out of the refrigerator tothaw. The solution was put back in the refrigerator afterwards. Drying time:∼ 20 days.

The sample FHCoO CD dried under cooler conditions and the dryingtime was twice as long compared to sample FHCoO RTD. The Mossbauerspectra of the mixed sample are very similar to that of the sample dried atroom temperature. The differing conditions under which the samples driedhave apparently not made a difference on the interaction between the nanopar-ticles.

73

6. Mossbauer study

Figure

6.8:M

ossbauerspectra

takenat

theindicated

temperatures

ofsam

plesm

ixedin

aqueoussolutions.

The

linesare

hyperfinefield

distributionfits

exceptfor

theroom

temperature

spectra,w

herethey

arem

erelyguides

tothe

eye.

74


Figure

6.9:H

yperfinefield

distributionsat

theindicated

temperatures

ofsam

plesm

ixedin

aqueoussolutions.

The

distributionsare

shown

onthe

same

scale.

75

6. Mossbauer study

FHCoO 5050 RTD slow

50 mg ferrihydrite and 51 mg CoO1 were mixed in 100 mL demineralizedwater and given ultrasound for 30 minutes to further mix the powders. Thesolution was left to dry at room temperature in a petri dish covered with asilver foil in which small holes had been made with a pin. Drying time: ∼ 44days.

With a much longer drying time, but otherwise produced in the samemanner as the sample FHCoO RTD, the Mossbauer spectra are much thesame at all temperatures. Again, the differing conditions during productionhave apparently not made much difference in the inter-particle interaction.The hyperfine field distribution at 120 K shows a larger peak in the low fieldend than that seen for the other samples of dried solutions, so it may be thatthe longer drying time is actually counterproductive in the attempt to makethe nanoparticles interact.

FHCoO 2250 RTD

22 mg ferrihydrite and 50 mg CoO1 were mixed in 100 mL demineralizedwater and given ultrasound to further mix the powders. The solution was leftin a petri dish with no cover to dry at room temperature. Drying time: ∼ 8days.

This sample was made to examine the effect of increasing the relativeamount of CoO nanoparticles compared to ferrihydrite nanoparticles. Un-fortunately, this made the sample so thin that the Mossbauer spectrum tookmuch longer than for the other samples and the statistics are not good. A com-parison of the Mossbauer spectrum at 80 K with those of the other mixed sam-ples produced by drying aqueous solutions shows that increasing the amountof CoO has not effected the suppression of the superparamagnetic relaxation,see Figs. 6.10 and 6.8.

Figure 6.10: Mossbauer spectrum of mixed sample FHCoO 2250 RTD at 80 K.The lines connecting the data points are guides to the eye.

76


Summary of results for dried aqueous solutions

Drying an aqueous solution of ferrihydrite nanoparticles and CoO nanopar-ticles is seen to suppress the superparamagnetic relaxation of ferrihydrite.Attempts at varying the drying time, drying temperature and increasing theamount of CoO relative to that of ferrihydrite all proved to have no greateffect. The spectra of the four mixed samples of dried aqueous solutions aresimilar.

6.4.2 Reflux Water-Condenser Samples

FHCoO 5655 RWC100 FD

56 mg ferrihydrite and 55 mg CoO1 were mixed in 100 mL demineralizedwater and given ultrasound for 25 minutes. Afterwards, the solution was putin a reflux water-condenser which was set to heat at ∼100◦C. 13 days laterthe sample was freeze-dried.

The Mossbauer spectrum taken at 80 K, see Fig. 6.11, shows magneticsplitting, but also a large distinct doublet. As the magnetic splitting is lessthan that seen in the sample dried at room temperature an XRD pattern ofthe mixture was obtained to determine if either the ferrihydrite or CoO hadbeen effected by the treatment. The XRD pattern showed mostly Co3O4

and only small peaks due to CoO. Apparently, the treatment has oxidizedthe CoO. The sample FHCoO 2250 RTD discussed above showed thatincreasing the relative amount of CoO did not increase the suppression of thesuperparamagnetic relaxation of ferrihydrite. Apparently, even small amountsof CoO leads to some suppression and the distinct doublet is probably dueto a large number of non-interacting ferrihydrite nanoparticles.

FHCoO 5151 RWC75 FD

51 mg ferrihydrite and 51 mg CoO1 were mixed in 100 mL demineralizedwater and given ultrasound for 25 minutes. Afterwards, the solution was putin a reflux water-condenser which was set to heat at ∼75◦C. 13 days later thesample was freeze-dried.

Just as for the sample FHCoO RWC100 FD the Mossbauer spectrumat 80 K shows some magnetic splitting, but again also a large doublet, seeFig. 6.11. The magnetic splitting appears, surprisingly, to be less than for thesample treated at a higher temperature. Surprisingly, because the oxidizationof CoO should be less, so that more particles can interact with the ferrihydrite.On the other hand, the higher temperature at which the nanoparticles inFHCoO RWC100 FD were heated may have caused more interaction. Todetermine the relative oxidation of CoO an XRD spectrum was made, againshowing a decrease in the amounts of CoO and an increase in the amountof Co3O4. As expected, less of the CoO is oxidized compared to the sampleheated at a higher temperature.

77

6. Mossbauer study

Figure 6.11: Mossbauer spectra at 80 K of mixed samples FHCoO RWC100 FDand FHCoO RWC75 FD heated in a reflux water-condenser at ∼ 100◦C and∼ 75◦C, respectively. Also shown is the spectrum of ferrihydrite at the sametemperature. The lines are guides to the eye.

Summary on reflux water-condenser samples

It might be possible to achieve a strong interaction between ferrihydrite andCoO nanoparticles, using the production method outlined above, if the heat-ing is set to a lower temperature. The two temperatures attempted were toohigh and led to a partial oxidization of the CoO nanoparticles. The suppres-sion of the superparamagnetic relaxation is less than that seen in other mixedsamples.

It should also be noted that these samples are the only ones subjected tofreeze-drying. This may also have an effect on the interaction between the

78


nanoparticles and possibly on the poorly crystalline, water-containing struc-ture of the ferrihydrite in the samples.

6.4.3 Sample Mixed with Ultrasound

FHCoO 5050 US3 RTD

50 mg ferrihydrite and 50 mg CoO1 were mixed in 100 mL demineralized wa-ter. The solution was then given ultrasound for 3 hours. As this causes heatingof the solution, the glass was kept in ice and water while being subjected tothe ultrasound. The ice was changed regularly, but when the ultrasound treat-ment was stopped the temperature of the solution was measured at ∼50◦Cand there were marks on the glass due to evaporation. The solution was leftovernight to precipitate and water was then removed with a pipette until ∼20mL were left. The remainder was left to dry at room temperature. Dryingtime: <14 days.

This mixed sample might not be reproducible because of the heating duringultrasound treatment. When comparing the spectrum at 80 K to that of amixed sample left to dry at room temperature which had only been given30 min. of ultrasound, they are similar, see Fig. 6.12. So either the longer

Figure 6.12: Mossbauer spectra at 80 K of two samples mixed using ultrasound andsubsequently dried at room temperature. The sample marked US3 RTD was givenultrasound for 3 hours, while the other sample, RTD slow, was given ultrasoundfor only 30 min.

79

6. Mossbauer study

ultrasound treatment did not have an effect on the interactions between thenanoparticles or the heating to ∼50◦C was counterproductive.

6.4.4 Samples Mixed by Grinding and Heating

FHCoO6 5050 Mix

50 mg of ferrihydrite and 50 mg of CoO6 were mixed gently with a plasticspoon.

The gentle mixing did not lead to interactions between the nanoparticlesvisible in the Mossbauer spectrum at 80 K, see Fig. 6.13. The spectrum ofthe mixed sample is of poor quality, but it can clearly be seen to resemblethat of the as prepared ferrihydrite.

Figure 6.13: Mossbauer spectrum at 80 K of the mixed sample FHCoO6 Mix. Alsoshown is the spectrum of as prepared ferrihydrite at 80 K.

FHCoO6 5050 GH

50 mg of ferrihydrite and 50 mg of CoO6 were mixed and then ground byhand in an agate mortar for ∼ 5 min.

The Mossbauer spectrum at 80 K of the sample ground by hand showsa spectrum very much like that of ground ferrihydrite, see Fig. 6.14. Thus,grinding alone does not create interaction between the CoO and ferrihydritenanoparticles.

80


Figure 6.14: Mossbauer spectrum at 80 K of the mixed sample FHCoO6 GH. Alsoshown is the spectrum of ground ferrihydrite (FH GH) at 80 K.

FHCoO6 5050 Mix XH100CH2

50 mg ferrihydrite and 50 mg CoO6 were mixed gently using a plastic spoonand heated for X (4 or 6) hours at 100◦C in H2

The Mossbauer spectra in Fig. 6.15 show little difference in interactionbetween the nanoparticles after 4 and 6 hours of heating in H2. Indeed, thespectra and hyperfine field distributions closely resemble those of ferrihydriteheated for 6 hours, see Fig. 6.5 on page 70. Thus, gentle mixing and subse-quent heating in H2 does not create interaction between the nanoparticles.

FHCoO6 5050 GH 6H100CH2

50 mg ferrihydrite and 50 mg CoO6 were mixed gently and then ground byhand in an agate morter for ∼ 5 mins. The sample was then heated for 6hours at 100◦C in H2

The Mossbauer spectra of this sample should be compared to those of theground and heated ferrihydrite sample, FH GH 6H100CH2, in Fig. 6.5 onpage 70. The spectrum of the mixed sample at 80 K closely resembles that of

81

6. Mossbauer study

Figure 6.15: Mossbauer spectra at 80 K of samples mixed and heated in H2 for 4 and6 hours. Also shown is the spectrum of ferrihydrite heated in H2 for 6 hours (FH6H100CH2)

ferrihydrite at 50 K. Also, the spectrum at 120 K shows magnetic splitting,which is only seen at this temperature in one other sample, FHCoO6 MW6H100CH2, described in the following subsection.

There is no sign of the distinct peak seen in the 80 K spectrum of groundand heated ferrihydrite, not even at 120 K.

The grinding and subsequent heating of the mixed powder has producedan effect in the Mossbauer spectra unlike that seen in mixed samples treatedwith either grinding or heating. This is reflected also in the hyperfine fielddistributions shown in Fig. 6.17 on page 85. At 80 K the distribution still

82


shows a peak, although its center has moved from ∼ 50 T at 20 K to ∼ 45T. Even at 120 K a small peak is seen at high fields in the hyperfine fielddistribution.

FHCo06 5050 MW 6H100CH2

50 mg ferrihydrite and 50 mg CoO6 were mixed in 20 mL demineralized water,shaken and given low intensity ultrasound for 2 min, shaken again and left toprecipitate in a closed plastic bottle. 14.5 mL of water was removed from thesample with a pipette and the remainder was transferred to a crucible. Thesample was then heated for 6 hour at 100◦C in H2

The Mossbauer spectrum at 80 K shows prominent magnetic splitting andthe Mossbauer spectra and hyperfine field distributions for this sample aremuch the same as those for sample FHCoO6 GH 6H100CH2 describedpreviously.

It should be noted that no examination was made of the effect of thistreatment on a sample containing ferrihydrite alone.

Summary on samples mixed by grinding and heating

The samples of ferrihydrite and CoO mixed gently or ground by hand did notshow interaction between the nanoparticles in the Mossbauer spectra. Neither,did the mixed samples that were heated for 4 and 6 hours in H2. However,when the nanoparticles were ground or mixed in water before being heatedinter-particle interactions were greatly enhanced compared to all other mixedsamples.

83

6. Mossbauer study

Figure

6.16:M

ossbauerspectra

atthe

indicatedtem

peraturesof

mixed

samples

heatedin

H2

with

varioustreatm

entsbefore

theheating.

The

linesare

hyperfinefield

distributionfits

exceptfor

theroom

temperature

spectra,w

herethey

arem

erelyguides

tothe

eye.

84


Figure

6.17:H

yperfinefield

distributionsof

spectraobtained

atthe

indicatedtem

peraturesof

samples

heatedin

H2 .

The

distributionsare

shown

onthe

same

scale.

85

6. Mossbauer study

6.5 Room Temperature Mossbauer Spectra

At 295 K the lines in the Mossbauer spectrum of ferrihydrite are still slightlyasymmetric and a fit with a single doublet is poor. Fitting with two doubletsgives a better fit as seen in Fig. 6.18. The values determined by the fit with two

Figure 6.18: Mossbauer spectrum of ferrihydrite at room temperature fitted with oneor two doublets.

doublets are given in Table 6.2 along with values determined for two naturalsamples of ferrihydrite [37]. The isomer shifts and quadrupole splittings of

Sample δ (mm/s) ∆EQ

Ferrihydrite in this study 0.35 0.940.36 0.54

Sample N162 from [37] 0.34(1) 0.89(2)0.35(1) 0.54(1)

Sample 31 from [37] 0.35(1) 0.85(3)0.36(1) 0.51(2)

Table 6.2: Isomer shift and quadrupole splitting of ferrihydrite at room temperatureas determined by fitting the Mossbauer spectrum with two doublets. Values givenfor two natural samples of ferrihydrite are also shown.

the two doublets fitted to the 6-line ferrihydrite used in this study are seento coincide well with the values quoted. The uncertainties on the fits made

86

Room Temperature Mossbauer Spectra

with mfit are unknown and the differences in the quadrupole splittings ofone of the doublets may be within the uncertainty of the fit. Fitting withtwo doublets should not be taken to mean that two discrete sites exist. It isa simplified representation of a distribution of quadrupole splittings due tothe continuous variation of parameters in ferrihydrite. The fitting with twodoublets was made to compare with available literature.

Fitting was also done using a distribution of isomer shift and quadrupolesplitting. As for the hyperfine field distributions, the program distfit is usedfor the fitting. In the model the isomer shift, δ, and the quadrupole splitting,∆, are related by

δ = B1 +B2 ×∆ (6.2)

whereB1 andB2 are parameters to be fit. Fig. 6.19 shows selected distributionfits of the room temperature Mossbauer spectra.

Figure 6.19: Mossbauer spectra at room temperature of ferrihydrite and two mixedsamples. Also shown are distributions of the isomer shift, δ, and the quadrupolesplitting, ∆. The lines in the Mossbauer spectra are distribution fits.

The results obtained for the distribution of the quadrupole splitting are

87

6. Mossbauer study

consistent with those found in literature [51] for a sample of natural 2-line fer-rihydrite even though it does not appear from the text that a related isomershift distribution was used. Nine room temperature spectra of ferrihydriteand mixed samples were fitted with a distribution of the isomer shift andquadrupole splitting. The distribution of the quadrupole splitting is the samefor all samples fitted. The value at peak maximum in the isomer shift dis-tribution varies slightly, but is ∼ 0.355 mm/s for all nine samples. Thus, weare left to conclude that the interaction between ferrihydrite and CoO seenat lower temperatures is not visible in the room temperature spectra.

88

Seven

VSM Measurements

This chapter describes the results of the VSM measurements performed on6-line ferrihydrite, sample CoO1 and the mixed sample FHCoO RTD.

• Section 7.1 compares the results for the three samples. It is shownthat the ferrihydrite nanoparticles and the CoO nanoparticles in themixed sample FHCoO RTD are interacting, confirming the results ofMossbauer spectroscopy.

• Section 7.2 discusses the fitting of a modified Langevin function to thefield curves of ferrihydrite.

• Section 7.3 describes the result of fitting the slope of the low field datato obtain the temperature dependence of the initial susceptibility offerrihydrite. A modified Curie law is used to estimate TN .

Contribution from sample holders

The sample holders for the VSM are made of BN (Boron Nitride), whichgives a diamagnetic contribution to the magnetization measurements. A fieldsweep from +16 kOe to −16 kOe of one of the sample cups is shown in Fig.7.1. The maximum contribution from the sample cup is seen to be less than1 memu and even though this is a very small contribution it might have beenprudent to deduct it from the magnetization measurements, but this was notdone. The data points for the cup holder cannot simply be subtracted fromthe other sets of data as the field sweeps are continuous meaning that thesoftware sweeps the field and measures the moment as the field continuouslychanges. Thus, the field values, while covering the same range, are differentfor all measurements. A fit of the data would be needed. It is not immediatelyclear which function should be used as the magnetization as a function of thefield is not linear. Why the magnetization of the sample holder is positive fora positive applied field < 4000 Oe is unknown.

89

7. VSM Measurements

Figure 7.1: Field sweep of empty sample cup. Note that the unit of the ordinate ismemu (milli-emu).

Experimental details

All field sweeps are continuous sweeps with applied magnetic fields rangingfrom +16 kOe to -16 kOe in steps of approximately 25 Oe and a measurementtime of 0.5 seconds/point. In the temperature range of 10−100 K field cooledsweeps were made by cooling the sample using liquid He in a field of 16 kOe.For measurements in the temperature range of 80− 300 K liquid N was usedas coolant. An oven mounted instead of the cryostat allowed measurementsto be made in the temperature range of 300 − 700 K. All field cooling wasdone from room temperature, which means ferrihydrite was not cooled fromT > TN .

None of the samples were measured in the full temperature range available.An overview of the temperature ranges of experimental data is given in Table7.1. The ZFC hysteresis loops of ferrihydrite were stopped at 35 K due to

Sample Field cooled (FC) Zero field cooled (ZFC)Ferrihydrite 20− 300 K 20− 35, 80− 160 and 300− 700 KCoO1 20− 280 K 80− 300 KFHCoO RTD 10− 300 K 10− 220 K

Table 7.1: Temperature ranges of fields sweeps made on three samples.

mechanical error and the measurements obtained in the temperature range

90

Interactions between Nanoparticles

20 − 35 K are very noisy as are the FC data in the range 60 − 80 K. Thesample rod holder had been twisted during mounting causing the sample rodto touch the inside of the cryostat. These measurements were not redoneimmediately and while making the measurements on CoO1 the liquid He ranout, which is why these measurements are not complete either.

The flow of He had to be controlled by hand for the 10 − 15 K mea-surements and field sweeps at these temperature were done only for sampleFHCoO RTD, while the rest of the field sweeps were programmed using thesoftware.

All the curves obtained are minor loops, i.e. none resulted in saturationof the magnetization.

7.1 Interactions between Nanoparticles

A short description of the results obtained for the three samples examined isgiven in the following. The results are plotted and compared in subsection7.1.1.

Ferrihydrite

Hysteresis is observed in both FC and ZFC loops of ferrihydrite up to ∼ 60 K.In the 20− 30 K ZFC and FC loops a step-like feature is seen in the low-fieldregion, see Fig. 7.2, which has also been reported for 2-line ferrihydrite [52]and is believed to be due to dipolar inter-particle interaction. With increasingtemperature the steps become smoother until they are no longer observed.Ferrihydrite was not FC from T > TN and no exchange bias or moment shiftof significance is seen.

Figure 7.2: Low-field part of ZFC and FC hysteresis loops for ferrihydrite sample at20 K showing the step-like feature.

91

7. VSM Measurements

Ferrihydrite transformed by heating in Ar

Around 400 K ferrihydrite began a transformation to magnetite. In the tem-perature interval 300 − 445 K the dependence of the magnetic moment offerrihydrite as a function of applied field is linear in the applied field rangeof ±16 kOe. At 450 K the magnetic moment at maximum field is larger atthe end of the sweep than it was in the beginning. This effect is present inthe remainder of the measurements on ferrihydrite. At 475 K the dependenceof the magnetic moment is no longer linear, but rather a Langevin curve isobtained, which becomes more and more S-like with temperature, see Fig. 7.3.At 590 K the sample becomes so magnetic, that the sensitivity level set for

Figure 7.3: Field sweeps at 480, 530 and 580 K showing the progression in magneticmoment at maximum field and S-like shape.

the measurements is too low and overflow in the magnetization measurementoccurs. The change in shape of the curve and sudden rise in magnetic momentis attributed to a transformation of the ferrihydrite upon heating in Ar. Thetransformation is thought to start around 450 K as changes in linearity andclosure of field sweep are first seen at this temperature. After cooling of thesample to room temperature a field sweep was made showing a curve muchdifferent from the one obtained of ferrihydrite at the same temperature. Atroom temperature the magnetic moment at maximum field went from 0.017emu for ferrihydrite to 0.863 emu after the transformation. Also, the depen-dence of the magnetic moment on the field is no longer linear and a hysteresisis present.

Mossbauer spectra of the transformed ferrihydrite reveal that most of thetransformed material is magnetite (Fe3O4), see Fig. 7.4. This explains the

92


rise in magnetic moment measured by VSM as magnetite is ferrimagnetic. Thedoublet(s) seen in the spectrum of transformed ferrihydrite at room temper-ature is not untransformed ferrihydrite unless the ferrihydrite is magneticallysplit at 80 K. It might be relaxing magnetite nanoparticles. An XRD spec-

Figure 7.4: Mossbauer spectra at 80 K and room temperature of transformed ferri-hydrite. The spectra show that ferrihydrite has transformed into magnetite.

trum of the transformed ferrihydrite was refined using Fullprof 2000 and aparticle size estimate of 12.5 nm was determined.

Sample CoO1

All field sweeps of the sample CoO1 show hysteresis. Even though the sampledoes not contain Co in amounts detectable by XRD small amounts may bepresent from ball-milling. Metallic Co is ferromagnetic with a Curie temper-ature of 1388 K and if present is certainly part of the cause of the hysteresis.Even though the CoO and Co3O4 nanoparticles are antiferromagnetic, theywill also show hysteresis due to coupling between the uncompensated momentsand the antiferromagnetic core.

In the field cooled measurements the sample was cooled from T > TN forboth CoO and Co3O4. Cooling from above the Neel temperature often leadsto exchange bias and moment shift in antiferromagnetic nanoparticles belowtheir blocking temperature [52]. Exchange bias is indeed observed in the FChysteresis loops. Also observed is a moment shift, whereby the hysteresis loopis shifted vertically. These effects are only observed in the FC loops and aredue to pinning of uncompensated spins. If Co is present in the sample thismay also affect the exchange bias and moment shift as the ferromagnetic Comay be pinned by the antiferromagnetic CoO.

93

7. VSM Measurements

Mixed sample FHCoO RTD

Hysteresis is observed in the loops of the mixed sample FHCoO RTD atall temperatures, but for temperatures higher than 90 K it is quite small.Exchange bias and a relatively large moment shift is seen in the FC data until∼ 60 K.

7.1.1 Comparison of the Three Samples

Comparison of hysteresis loops

If the ferrihydrite and CoO1 are not interacting in the mixed sample its hys-teresis curves should be a superposition of the hysteresis curves of ferrihydriteand CoO1. Hysteresis curves of the mixed sample at different temperatureswere compared with hysteresis curves created by adding together the curvesof ferrihydrite and CoO1 at the same temperatures. The values of magneticmoment for ferrihydrite and CoO1 were weighted in the creation of the addedhysteresis curves. Both the compared FC hysteresis loops in Fig. 7.5 and thecompared ZFC loops in Fig. 7.6 show that the nanoparticles are interactingas the loops are not identical. This supports the conclusion from Mossbauer

Figure 7.5: FC hysteresis curves of the mixed sample FHCoO RTD at the indicatedtemperatures compared with hysteresis curves created by adding together the FChysteresis curves of ferrihydrite and sample CoO1.

spectroscopy. It is surprising that the magnetization found for the mixedsample is smaller than the one found by addition of the data for ferrihydriteand sample CoO1. If the CoO nanoparticles are suppressing the superpara-magnetic relaxation of ferrihydrite one would expect the magnetization tobe higher. Perhaps the particle moments of ferrihydrite in the mixed sample

94


Figure 7.6: ZFC hysteresis curves of the mixed sample FHCoO RTD at the indicatedtemperatures compared with hysteresis curves created by adding together the ZFChysteresis curves of ferrihydrite and sample CoO1.

cannot align as easily with the field due to interaction with the CoO nanopar-ticles. As described in the following, when discussing the moment shift andexchange bias, some of the ferrihydrite moments are believed to be pinnedby inter-particle interactions with CoO up to 60 K. It could be that evenabove this temperature the interactions make ferrihydrite less susceptible tothe applied magnetic field.

Magnetic moment at maximum absolute field

The averaged values of the magnetic moments at fields of ±16 kOe are plottedin Fig. 7.7. No difference is seen between the FC and ZFC sweeps as expected.From the plots of the magnetic moment at maximum absolute field we see thatthe mixed sample FHCoO RTD has a temperature dependence much likethat predicted from a superposition of ferrihydrite and CoO1. However, themagnetic moment is smaller than predicted as seen also when comparing thehysteresis loops.

Moment shift

In all three samples the low temperature FC hysteresis loops are shifted bothvertically and horizontally. This is shown for the mixed sample in Fig. 7.8.

The moment shift, i.e. the shift vertically, is found as the difference inthe maximum and minimum absolute value of the magnetic moment and isplotted for all samples in Fig. 7.9. In the plot is also shown the value expected

95

7. VSM Measurements

Figure 7.7: Averaged values of the magnetic moment at maximum field (±16 kOe)for the FC sweeps (left) and ZFC sweeps (right). The lines are guides to the eye.

Figure 7.8: FC and ZFC hysteresis loops of mixed sample FHCoO RTD at 10 K.

for the mixed sample if its properties were simply a weighted superposition ofthose of ferrihydrite and the sample CoO1.

When a sample of antiferromagnetic nanoparticles is FC it is importantwhether it is cooled from above or below the Neel temperature. Above theNeel temperature the particle is paramagnetic and the spins will more easily

96


Figure 7.9: The moment shifts of ferrihydrite, sample CoO1 and mixed sample FH-CoO RTD. Also shown is a weighted sum of the values for ferrihydrite and CoO1.

align with the field. If the particle is then cooled through the Neel temperaturea preferred direction of the particle moment will come about depending on themagnetic anisotropy and temperature. The samples are all FC in a magneticfield of +16 kOe and the preferred direction will lead to an exchange bias tothe left, i.e. towards negative fields, and a moment shift upwards, i.e. in thedirection of positive magnetic moment.

We see from Fig. 7.9 that ferrihydrite, which was not FC from above itsNeel temperature, has no moment shift. The sample CoO1, however, whichwas FC through its Neel temperature shows a moment shift up to about 250 Kat which point the uncompensated moments are unpinned due to decreasinganisotropy and increasing temperature. The CoO nanoparticles have a highanisotropy allowing the antiferromagnetic core to retain a preferred directionof magnetization after being FC through the Neel temperature.

Although the moment shift is present in all the samples it is distinctlylarger for the mixed sample up to 60 K after which it follows the curve ex-pected for a weighted superposition. As ferrihydrite shows practically nomoment shift, the curve followed is actually the one expected for the amount

97

7. VSM Measurements

of CoO present in the sample. In antiferromagnetic nanoparticles the mo-ment shift is a result of coupling between the uncompensated spins and theantiferromagnetic core. In the mixed sample the additional moment shift atlow temperatures is believed to be due to inter-particle interactions, wherebysome of the ferrihydrite particles are pinned by the CoO nanoparticles.

All the samples show an increased moment shift at 20 K, which mustsomehow be an experimental artifact.

Exchange bias

As ferrihydrite was not cooled from above its Neel temperature it shows noexchange bias after field cooling.

Before calculating the exchange bias, i.e. the horizontal shift of the hys-teresis loop, the loops are corrected for the moment shift. The exchange biasof the sample CoO1 is shown in Fig. 7.10 and shows a more or less steadydecrease with temperature.

Figure 7.10: Exchange bias of sample CoO1. The line is a guide to the eye.

The exchange bias for the mixed sample FHCoO RTD shows a maximumat 25 K, see Fig. 7.11. However, we have seen that the moment shift isincreased at 20 K for all samples possibly due to an experimental artifact.Perhaps this is also true for the values obtained at 10 and 15 K for the mixedsample. If so, too much moment shift has been subtracted from the mixedsample, moving the curve too far down. This would explain why the exchangebias is smaller below 25 K.

98


Figure 7.11: Exchange bias of mixed sample FHCoO RTD. The line is a guide tothe eye.

The exchange bias of the mixed sample almost disappears around 60 K,which is the temperature at which the moment shift began following the curveexpected for the amount of CoO in the sample. It is believed to be the tem-perature at which the ferrihydrite moments are unpinned. The CoO nanopar-ticles in the mixed sample still cause an exchange bias above 60 K, but this ismuch smaller than the bias seen below 60 K and is not apparent in Fig. 7.11.

Coercivity

As all the samples show hysteresis at some temperature it might also be in-teresting to examine the coercivity. Because of the moment shift the size ofthe coercivity is underestimated unless the curves are corrected for the shift.

The curves were corrected for the moment shift and the coercivity calcu-lated by a linear interpolation between two readings that straddle the zeromoment value, see Fig. 7.12. The absolute value of the fields found at zeromagnetic moment are then averaged. In this way we also correct for anyexchange bias.

The coercivity of ferrihydrite is shown in Fig. 7.13. Ferrihydrite showshysteresis at temperatures up to ∼ 60 K. The measurements are generallyof poor quality, but do show the qualitative behavior of the coercivity forcomparison with the other samples. The temperature at which the coercivitydisappears is taken to be the blocking temperature, TB, where the relaxation

99

7. VSM Measurements

Figure 7.12: Diagram showing the linear interpolation of readings used to calculatethe coercivity as described in the text. The diagram is taken from the help file forthe LakeShore VSM software.

Figure 7.13: Coercivity of FC and ZFC ferrihydrite.

of the particle moments becomes fast compared to the characteristic time ofthe measurements.

The sample CoO1 has a dip in coercivity at ∼ 40 K, see Fig. 7.14. Itmay be that this dip is the effect of the transition from the antiferromagneticto the paramagnetic state of Co3O4. If so, we may explain the dip as the co-ercivity is a function of contributions from both CoO and Co3O4. When thetemperature gets near the Neel temperature of Co3O4 its coercivity decreasesand susceptibility increases, which makes the coercivity of the sample less, asillustrated in Fig. 7.15, for the case where the coercivity of Co3O4 is nearlygone. Above the Neel temperature of Co3O4 its susceptibility decreases with

100


Figure 7.14: Coercivity of CoO1 showing a dip at 40 K. A line is drawn at 40 K toshow this clearly.

Figure 7.15: Illustration of superposition of two curves and the effect on coercivity.

temperature and the coercivity of sample CoO1 increases until 80 K, wherethe contribution from Co3O4 must be vanishing.

The mixed sample shows a maximum in coercivity around 40 K, see Fig.7.16. The FC and ZFC coercivities have the same shape, but the FC coer-civity is higher at low temperatures up until about 60 K. This may be dueto the interaction between ferrihydrite and CoO. The maximum in the co-ercivity might again be due to Co3O4. However, it is not understood howthe transition of Co3O4 to the paramagnetic state can cause the temperaturedependency of the coercivity as seen for the mixed sample.

At 80 K the coercivity is about 100 Oe and becomes temperature inde-

101

7. VSM Measurements

Figure 7.16: Coercivity of mixed sample FHCoO RTD showing a maximum ∼ 40K. A line is drawn at 40 K to show this clearly.

pendent, which may be related to small amounts of Co not detectable inXRD.

7.2 Langevin Fit of Ferrihydrite Field Curves

In ideal superparamagnetic nanoparticles the average magnetization 〈M〉 ofthe particles are described by a Langevin function,

〈M〉 = M0L(µpB

kBT

)(7.1)

Here, µp is the magnetic moment per particle, M0 is the saturation magnetiza-tion and L(x) is the Langevin function, see section 2.2. Ferrihydrite, however,does not fit well with Eq. 7.1 due to the fitted line being too curved. Asin other studies on ferritin [53, 54, 55] and 2-line ferrihydrite [52, 55, 56], alinear component is added to Eq. 7.1. For comparison with other studiesthe data are fitted using CGS units such that [M0] = emu/g, [H] = Oe andkB = 1.380× 10−16 erg/K. Thus, the data is fitted with the equation

〈M〉 = M0L(µpH

kBT

)+ χaH (7.2)

where χa is the antiferromagnetic susceptibility. The data can be fitted withthis equation for temperatures between the blocking temperature, TB, and the

102

Langevin Fit of Ferrihydrite Field Curves

Neel temperature, TN . In systems with a particle size distribution, a distribu-tion of blocking temperatures is found. The maximum blocking temperatureis estimated to be ' 60 K as this is the temperature where the coercivity offerrihydrite becomes insignificant. This is consistent with the blocking tem-perature of 65 K determined for 2-line ferrihydrite [55]. The Neel temperatureof 6-line ferrihydrite has been estimated to be TN ' 330(20) K [39].

The curves are fit using the non-linear curve fitting analysis tool in Origin7.5. The high temperature data are difficult to fit using Eq. 7.2 as only thelinear part of the Langevin curve is obtained with the applied fields available.The fitted parameters of Eq. 7.2, viz. M0, µp and χa, for the temperatureinterval 70−160 K are found to vary with temperature as shown in Fig. 7.17.These results confirm the temperature dependence of the parameters as also

Figure 7.17: Plots showing the temperature dependence of the saturation magneti-zation, M0, the particle magnetic moment, µp, and the antiferromagnetic suscep-tibility, χa. The lines are guides to the eye.

determined for ferritin [53, 54, 55] and 2-line ferrihydrite [52, 55, 56]. However,the fits are very sensitive to the starting value chosen and, as mentionedabove, with the superparamagnetic part being far from saturation it becomesdifficult to separate the antiferromagnetic susceptibility component. As in theprevious studies M0 and χa are found to decrease with temperature, while theparticle magnetic moment, µp, increases. The values of µp found are muchlarger than expected. For both ferritin and 2-line ferrihydrite the values ofµp found were 350 − 400µB, while this study finds µp ' 950µB for 6-lineferrihydrite. One would expect the particle magnetic moment, which arisesfrom the uncompensated spins, to be less in 6-line ferrihydrite compared to2-line ferrihydrite as 6-line ferrihydrite has a higher structural order. It maybe that the 6-line ferrihydrite nanoparticles studied here are generally largerthan the 2-line ferrihydrite and ferritin nanoparticles studied elsewhere.

103

7. VSM Measurements

In an attempt to extend the fitted temperature range a series of fits weremade with the antiferromagnetic susceptibility, χa, kept at a constant value.χa does not vary much with temperature. However, with the values deter-mined in the fit outlined above we find that at maximum field the componentχaH does account for about half of the magnetization. The fits were found tobe very sensitive to the value of χa and the attempt was abandoned.

It has been theorized that the increase in µp with temperature could be theresult of a thermoinduced magnetization in nanoparticles of antiferromagneticmaterials [57, 58]. At temperatures too low for the particle magnetic momentto flip, it may fluctuate around the easy direction of magnetization. Thesefluctuations, known as collective magnetic excitations, are uniform precessionsof the magnetic moment and transitions between these precession states. Theuniform precession mode can be described as a spin wave with wave vectorq = 0 and is the predominant spin wave in nanoparticles. When the uniformmode is thermally excited an antiferromagnetic nanoparticle will have a netmagnetic moment as the two magnetic sublattices precess at different angleswith the easy direction, see Fig. 7.18. The absolute value of the average net

Figure 7.18: Illustration of the differing angles with which the sublattices magnetiza-tion vectors, MA

S and MBS , precess around the easy direction of magnetization in

an antiferromagnet leading to a net magnetic moment. The difference in θA andθB is exaggerated for clarity.

magnetic moment at low temperatures is found to be

〈|µAF |〉 ' 2gµBkBT

~ω0(7.3)

where g is the Lande factor and ω0 is the angular frequency of the q = 0spin wave. This thermoinduced magnetic moment is seen to increase with

104

Initial Susceptibility of Ferrihydrite

temperature.It has also been suggested that the temperature dependence of M0 and µp

may be a result of fitting without considering the particle size distribution [59].The authors demonstrate well the fault of fitting field curves using a Langevinfunction without including a magnetic moment distribution. They constructdata sets having a log-normal distribution of particle size and a constant valueof µp. When fitting these data with Eq. 7.1 they find that M0 decreases whileµp increases as a function of temperature as shown previously for ferritin,2-line ferrihydrite and, in this study, 6-line ferrihydrite. The authors alsoapplied a Langevin function with a magnetic moment distribution to data onferritin and found that µp decreases with temperature. If they are correctthen the previously held assumption that ferritin represents a monodispersesystem [53] is incorrect.

7.3 Initial Susceptibility of Ferrihydrite

The initial susceptibility of 6-line ferrihydrite is found in an attempt to obtainthe Neel temperature. Below the Neel temperature the susceptibility decreasesas the nanoparticles are superparamagnetic. Near the Neel temperature theantiferromagnetic susceptibility of the core will increase causing a rise in thecombined susceptibility. Above TN the now paramagnetic susceptibility willdecrease with temperature.

The low field data (-700 to +700 Oe) in the field sweeps were fitted witha linear regression to determine the initial mass susceptibility, χ = σ

H . Fieldsweeps of ferrihydrite in cryostat and in oven were made using two differentsample holders. The ferrihydrite is from the same sample, but the amountsin the sample holders are different. When comparing the field sweeps madeat 300 K with the cryostat in place before any cooling was done with thatof the measurement at 300 K with the oven mounted a discrepancy is seenbetween the two different samples as shown in Fig. 7.19. The reason for thediscrepancy is unknown. It may be due to an error in weighing one of thesamples and will result in a jump in the susceptibility at 300 K.

A plot of the susceptibility and inverse susceptibility versus temperatureis shown in Fig. 7.20. The jump anticipated at 300 K is seen in the plots. Asdescribed in subsection 7.1 ferrihydrite transformed to magnetite during theheating. The transformation is not visible in the field sweeps until reaching atemperature of 450 K, but the data for temperatures higher than about 400 Kmay be affected by the beginning of a transformation. The Neel temperaturewas expected to be found in the temperature range 300− 400 K, but nothingis seen in the plots in this range to indicate a change of state.

With the particles being superparamagnetic a linear increase in the inversesusceptibility would be expected if the particles followed a Curie-Weiss law.However, Seehra and Punnoose [55] have shown that a non-linear behavior ofχ follows from the magnetization being described by the modified Langevin

105

7. VSM Measurements

Figure 7.19: Field sweeps of ferrihydrite at 300 K with cryostat and oven mounted inthe VSM. The mass magnetization is seen to be different in the two setups.

Figure 7.20: Temperature dependence of the initial susceptibility (left) and inverseinitial susceptibility (right) of ferrihydrite.

function,

〈M〉 = M0L(µpH

kBT

)+ χaH (7.4)

as done in section 7.2. The modified Curie law is given by

χ = χ0 +C

T(7.5)

106

Initial Susceptibility of Ferrihydrite

where χ0 = χa − CTN

and C = µpM∗

3kBwith M∗ being the magnitude of the sat-

uration magnetization extrapolated to T = 0 K. By extrapolating to T = 0 Kthe values of M0 found by fitting the modified Langevin function in section7.2 we find M∗ = 1.109 emu/g, see Fig. 7.21. Using the values found from the

Figure 7.21: Extrapolation of M0 to T = 0 K. The value of M∗ thus found is 1.109emu/g.

fit with the modified Langevin function and the value of M∗, we may estimatethe Neel temperature. In this way, an estimate of TN ∼ 500 K is found, seeFig. 7.22, which is much higher than the Neel temperature of ' 330(20) Kfound using neutron scattering [39]. The validity of this estimate of the Neeltemperature for 6-line ferrihydrite is dependent on the validity of using themodified Langevin function when fitting the magnetization as a function ofapplied field as discussed in section 7.2. With neutron scattering data givinga much lower estimate this would seem to be more evidence suggesting thatthe modified Langevin function in Eq. 7.2 is incomplete.

107

7. VSM Measurements

Figure 7.22: Plot of the susceptibility and the result from Eq. 7.5 with TN = 500 K.Also shown is the result of using TN = 350 K.

108

Eight

Conclusions

Nanoparticles of CoO can be produced by high energy ball-milling and sub-sequent reduction by heating in H2 of Co3O4. The CoO nanoparticles pro-duced this way were found to have a diameter of ∼ 10 nm.

Two experimental methods, Mossbauer spectroscopy and VSM, were usedto examine the interactions between ferrihydrite and CoO nanoparticles inmixed samples.

In several mixed samples, the two nanoparticles were shown to interact,whereby CoO with its high anisotropy is able to suppress the superpara-magnetic relaxation of ferrihydrite. Mixing the nanoparticles in demineral-ized water and letting them dry was shown to create interactions between thenanoparticles. Grinding or mixing the nanoparticles in water and then heatingthem in H2 are possibly even better ways of getting the particles to interact.However, the effect of the latter treatment on ferrihydrite is unknown.

The room temperature Mossbauer spectra of ferrihydrite and selectedmixed samples were studied to see if the interaction seen at lower temper-atures would affect the spectra. This was found not to be the case.

Ferrihydrite, CoO and a mixed sample were studied using VSM and fromthe difference in behavior of the hysteresis loops from that expected of non-interacting nanoparticles, the conclusion from Mossbauer spectroscopy aboutinteraction between the nanoparticles is confirmed.

A suggestion is made where the relatively large moment shift of the mixedsample below 60 K is attributed to interaction between the nanoparticles asCoO may be pinning some of the ferrihydrite particles.

A dip in the coercivity as a function of temperature for sample CoO1could be explained by a transition of Co3O4 from the antiferromagnetic tothe paramagnetic state. A maximum at the same temperature in the coercivityof the mixed sample, however, could not be explained, but is thought to berelated to the same transition.

Fitting a modified Langevin function to the magnetization versus field datafor ferrihydrite showed an increase of µp, the magnetic moment per particle,with temperature. This is in line with conclusions from studies on 2-line ferri-hydrite and ferritin and may be the result of a thermoinduced magnetization.

109

8. Conclusions

However, the validity of using the modified Langevin function without con-sidering the particle size distribution is in question. Furthermore, from thefits µp ' 900µB is found, which is surprisingly high compared to both ferritinand 2-line ferrihydrite where µp ' 400µB has been found. The reason for thehigh magnetic moment per particle found is not clear.

A modified Curie law was used to estimate the Neel temperature of ferrihy-drite from the initial susceptibility and an estimate of TN ' 500 K was found.The modified Curie law is deduced from the modified Langevin function andit is uncertain to what extent the question of the validity of the modifiedLangevin function applies to the modified Curie law. However, with neutronscattering data giving TN ' 330(20) K it seems likely that the estimate ofthe Neel temperature is wrong further indicating a problem with the modifiedLangevin function.

8.1 Outlook

At present, no Mossbauer spectra of the two mixed samples showing thestrongest interaction have been made in the temperature range above 120K below room temperature. Therefore, the temperature at which the mag-netic splitting disappears is unknown. An XRD spectrum of the sample mixedin water and heated in H2 should be made to see if any changes in ferrihydritehas occurred due to the treatment.

It would also be interesting to study Mossbauer spectra of the mixed sam-ples with a magnetic field applied as this might shed further light on theinteractions between the nanoparticles.

VSM measurements have the potential of providing more information ifthe data sets were completed and in some cases redone. Measurements onferrihydrite FC through its Neel temperature might prove interesting. Newmeasurements should be made on a mixed sample to confirm that the magneti-zation is smaller than what is predicted by adding together the magnetizationof ferrihydrite and CoO. It would also be interesting if a sample of CoOnanoparticles without a contamination of Co3O4 was mixed with ferrihydriteto see the temperature dependence of the coercivity.

To get better values of the particle magnetic moment, magnetization mea-surements should be done with a larger magnetic field and the size distributionof the particles should be taken into account when fitting. In this way, it maybe possible to see experimentally the thermoinduced magnetization. Possibly,one might estimate how monodisperse the system must be in order for thedistribution to be insignificant in magnetization measurements.

110

Appendices

111

Appendix A

Units and Constants

Constants Gaussian SIµ0 1 4π × 10−7 H/m el. Tm/AµB 9.274015× 10−21 erg/G 9.274015× 10−24 Am2(J/T)

Numerical values

Velocity of light c = 2.99793× 108 ms−1

Planck’s constant h = 6.62554× 10−34 JsBoltzmann’s constant k = 1.38054× 10−23 JK−1

Atomic mass unit (amu) 1.6604× 10−27 kgNuclear magneton βn = 5.0505× 10−27 JT−1

Bohr magneton µB = 9.2732× 10−24 JT−1

Vacuum permittivity ε0 = 8.8544× 10−12 N−1m−2C2

Elementary charge e = 1.6021× 10−19 CVacuum permeability µ0 = 4π × 10−7 mkgC−2

Constants relevant for 57Fe Mossbauer spectroscopy.Mean lifetime τm = 141.1× 10−9 sg-factor, excited state ge = −0.10355g-factor, ground state gg = 0.181208Quadrupole moment, ground state Qg = 0Quadrupole moment, excited state Qe = 0.21× 10−28 m2

Cross section for resonant absorption σ0 = 2.57× 10−22m2

Transition Energy E0 = 14.41× 103 eV

113

Appendix B

Conversion Table between CGS Gaussian and SI

UNITS FOR MAGNETIC PROPERTIES

Quantity Symbol CGS Gaussian Conversion factor, C SI

Magnetic flux density, B Gauss (G) 10−4 Tesla (T)magnetic induction

Magnetic field strength H Oersted (Oe) 103/4π A/mMagnetic moment m emu 10−3 A· m2, J/TMagnetization M emu/cm3 103 A/mMass magnetization σ emu/g 1 A· m2/kgMass susceptibility χ emu/g 4π × 10−3 m3/kg

To convert a number from CGS Gaussian units to SI multiply by C.

115

Appendix C

Element Analysis of Fritsch Pulverisette WCGrinding Bowl

The following was obtained from Fritsch by e-mail in response to an inquiryabout the Co content in their WC grinding bowls.

Element analysis of grinding parts

”pulverisette 0””pulverisette 2””pulverisette 5””pulverisette 6””pulverisette 7”

Grinding bowl made of Tungsten Carbide

German Standard No. WZ 10, ISO G10

name total formula %

Tungsten Carbide (WC) 93.5Cobalt Co 6.0Tantalcarbide TaC 0.5

specific gravity: 14.89 g/cm3

hardness (Vickers): 1628 HV50

transverse rupture strength: 1500 N/mm2

particle size: 2 µm

117

Appendix D

Ball Milling Timetable for Sample CoO1

Ball milling time Cool off time Total ball milling time

30 min 36 min 30 min30 min 39 min 60 min30 min 18 hrs 9 min 1 hr 30 min30 min 46 min 2 hrs30 min 38 min 2 hrs 30 min22 min 40 min 2 hrs 52 min20 min 32 min 3 hrs 12 min20 min 1 hr 10 min 3 hrs 32 min20 min 33 min 3 hrs 52 min20 min 35 min 4 hrs 12 min20 min 63 hrs 56 min 4 hrs 32 min20 min 21 min 4 hrs 52 min20 min 30 min 5 hrs 12 min20 min 43 min 5 hrs 32 min20 min 42 min 5 hrs 52 min20 min 57 min 6 hrs 12 min20 min 43 min 6 hrs 32 min20 min 48 min 6 hrs 52 min20 min 39 min 7 hrs 12 min20 min 33 min 7 hrs 32 min20 min 15 hrs 15 min 7 hrs 52 min20 min 42 min 8 hrs 12 min20 min 46 min 8 hrs 32 min20 min 40 min 8 hrs 52 min20 min 40 min 9 hrs 12 min20 min 214 hrs 17 min 9 hrs 32 min20 min 40 min 9 hrs 52 min20 min 41 min 10 hrs 12 min20 min 15 hrs 44 min 10 hrs 32 min

119

D. Ball Milling Timetable for Sample CoO1

Ball milling time Cool off time Total ball milling time

20 min 42 min 10 hrs 52 min20 min 41 min 11 hrs 12 min20 min 38 min 11 hrs 32 min20 min 40 min 11 hrs 52 min20 min 39 min 12 hrs 12 min20 min 42 min 12 hrs 32 min20 min 65 hrs 2 min 12 hrs 52 min20 min 48 min 13 hrs 12 min20 min 40 min 13 hrs 32 min20 min 41 min 13 hrs 52 min20 min 51 min 14 hrs 12 min20 min 42 min 14 hrs 32 min20 min 20 hrs 44 min 14 hrs 52 min20 min 44 min 15 hrs 12 min20 min 40 min 15 hrs 32 min20 min 38 min 15 hrs 52 min20 min 44 min 16 hrs 12 min20 min 41 min 16 hrs 32 min20 min 17 hrs 19 min 16 hrs 52 min20 min 14 min 17 hrs 12 min20 min 39 min 17 hrs 32 min20 min 41 min 17 hrs 52 min20 min 49 min 18 hrs 12 min20 min 45 min 18 hrs 32 min20 min 20 hrs 37 min 18 hrs 52 min20 min 41 min 19 hrs 12 min20 min 53 min 19 hrs 32 min20 min 41 min 19 hrs 52 min20 min 42 min 20 hrs 12 min20 min 17 hrs 48 min 20 hrs 32 min20 min 40 min 20 hrs 52 min20 min 43 min 21 hrs 12 min20 min 43 min 21 hrs 32 min20 min 50 min 21 hrs 52 min20 min 29 min 22 hrs 12 min20 min 44 hrs 28 min 22 hrs 32 min20 min 40 min 22 hrs 52 min20 min 39 min 23 hrs 12 min20 min 40 min 23 hrs 32 min20 min 43 min 23 hrs 52 min20 min 24 hrs 12 min

Table D.1: Ball milling timetable for the sample CoO1.

120

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