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Thermodynamic Stability and Activity Volcano for Perovskite-
based Oxide as OER Catalyst
by
Xi Rong
S.B., Mechanical Engineering, Washington University, St. Louis (2012)
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINERING IN PARTIALFULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2014
02014 Massachusetts Institute of Technology
All rights reserved.
Signature redacted
Signature of Author.....
Certified by ............
I......................................................
Department of Mechanical EngineeringMay 9, 2014
Signature redacted/
.......................................Alexie M. Kolpak
Assistant Professor, Department of Mechanical EngineeringThesis Supervisor
Signature redactedAccepted by .............. .........................................
David E. HardtProfessor, Department of Mechanical Engineering
Chairman, Committee for Graduate Students
-1
MASSACHUSETTS INSTMTJTE,OF TECHN voLoGY
A UG -1 5 2014
LIBRARIES
V
2
Thermodynamic Stability and Activity Volcano for Perovskite-based
Oxide as OER Catalyst
by
Xi Rong
Submitted to the Department of Mechanical Engineering on May 9, 2014 in Partial Fulfillment
of the Requirements for the Degree of Master of Science in Mechanical Engineering
Abstract
Design of efficient and cost-effective catalysts for the oxygen evolution reaction (OER) is crucial
for the development of electrochemical conversion technologies. Recent experiments show that
perovskite transition-metal oxides can exhibit high electro-catalytic activity for OER. Both
binding strength of reaction intermediate and a*-antibonding (eg) orbital filling of transition-
metal ions in the clean surface prove to be descriptors of perovksite activity. Plotting of activity
vs. a descriptor gives a volcano curve. However, little is known about the thermodynamic
stability and the catalytic activity of perovskite surface reconstructions. Reconstructions such as
defect, adsorbate, and steps are widely detected in experiments. They are caused by realistic
environment during fabrication, measurement, and eventual device operation. In this work, we
apply first-principles density functional theory and ab initio electro-thermodynamics to
investigate the environment-dependent surface reconstructions of perovskite, particularly those
based on LaMnO 3. We develop a surface stability phase diagram as a function of pH and
electrode potential, and compare those catalytic activities under realistic liquid environment of
electrolysis device. Our results show that values of pH and electrode potential can greatly affect
surface structure and its activity. The new approach developed in this work is applicable to other
oxide catalysts.
Thesis Supervisor: Alexie M. KolpakTitle: Assistant Professor, Department of Mechanical Engineering
3
Acknowledgements
I would first and foremost like to acknowledge my advisor Alexie M. Kolpak for her continuous
support of my S.M. study and research, for her patience, motivation, and enthusiasm. Coming to
MIT to do my graduate work with her is definitely one of the best decisions I have ever made.
Without her thoughtful encouragement and careful supervision, this thesis would never have
taken shape.
I would also like to thank the funding for this work. This work is supported by both Pappalardo
Fellowship from Department of Mechanical Engineering at MIT and the Center of
Electrochemical Energy jointly founded by MIT and Skolkovo Institute of Science and
Technoloy at Russia.
Many thanks of course go to the members of the Kolpak group. Both present and past, the
students and postdoctoral researchers in this group are the best I could ever imagine working
with. To Brian Kolb, for introducing me density functional theory and quantum espresso, and
probably lots of other things I don't remember; to Nongnuch Artith, for discussing
thermodynamics in my work and providing insight in our joint work; to Kevin J. May, for
teaching me experimental work related to this theoretical work; to Babatunde 0 Alawode and
Levi C. Lentz, for all of our discussions.
I also thank my parents for their love and support, for making me the person I am today and also
for giving me all the opportunities I needed to succeed. Finally, I would like to thank my
girlfriend, Qing Zhao, who is also a master student at Mechanical Engineering Department at
MIT, to her love, encouragement and accompany throughout my study here. Thank you for being
who you are and for being who you make me am.
4
Table of Contents
A b stract..........................................................................................................3
A cknow ledges............................................................................................... 4
Table of C ontents............................................................................................ 5
L ist of Figures............................................................................................... 7
L ist of T ables................................................................................................. 9
1 Introduction ............................................................................................. 10
1.1 Introduction to electrolysis.......................................................................10
1.2 Sate of art research on catalysis and its limitations...........................................11
1.3 Objectives and scope of this thesis.................................................................14
2 Current approach to surface stability and its limitations..........................................16
2.1 Method of analysis for surface stability........................................................16
2.2 Method of analysis for bulk stability.............................................................18
2.3 Correlation between stab-ility and realistic environment.....................................19
2.4 Results by this approach and its limitations..................................................21
3 Introduction to density functional theory (DFT)..................................................24
3.1 Basic framework of DFT........................................................................24
3.2 DFT computational details in this thesis......................................................27
4 A new approach for ab initio prediction of realistic surface reconstruction.....................29
4.1 Determination of 0 vacancy formation energy...............................................31
4.2 Determination of Mn vacancy formation energy........................................... 33
4.3 Experimental standard hydrogen electrode free energy.....................................35
4.4 Formation energy of surface reconstruction: a general form.............................. 37
4.5 Verification of the new approach..............................................................38
5 Results and discussions based on our new approach........................................... 39
5.1 Stability of surface with vacancy..............................................................39
5.2 Stability of surface with adsorption...............................................................41
5.3 Stability of surfaces with different terminations.............................................42
5.4 A global surface phase diagram...................................................................44
5.5 Bulk stability and equilibrium condition.....................................................45
5
6 Electrocatalytic activity of surface reconstruction..................................................49
7 Summary and future work..............................................................................54
R eferences....................................................................................................55
6
List of Figures
Figure 1.1: Schematic of alkaline electrolysis cell....................................................11
Figure 1.2: OER catalytic activity vs. intermediate binding energies3 5 .......... .. . . . . . . . . . . . . . . 12
Figure 1.3: OER catalytic activity vs. eg fillings of transitional metal 39......... . . . . . . . . . . . . . . ..13
Figure 1.4: LaMnO 3 crystal structure................................................................14
Figure 1.5: Main structure of this thesis..............................................................15
Figure 2.1: Phase diagram of surface structure and bulk stability in gas environment (SOEC)
by current approach...................................................................................... 21
Figure 2.2: Phase diagram of bulk stability in liquid environment (AEC and PEM) at T=250C
by current approach from our work....................................................................22
Figure 3.1: Procedures of DFT calculations with constant lattice parameters.................27
Figure 4.1: Three possible (001) ideal surfaces....................................................30
Figure 4.2: A hypothetical mechanism of vacancy formation...................................31
Figure 4.3: Mn phase diagram constructed by A GU,pH ----- -------................................ 38
Figure 5.1: Stability of surface with Mn vacancy................................................ 40
Figure 5.2: Stability of surface with 0 vacancy....................................................40
Figure 5.3: Configuration of surface with cation adsorbate.................................... 41
Figure 5.4: Stability of surface with cation adsorbate........................................... 42
Figure 5.5: Configuration of termination transition..................................................43
Figure 5.6: Stability of termination.................................................................43
Figure 5.7: Representative surface configurations................................................44
Figure 5.8: A global surface diagram..................................................................45
Figure 5.9: Bulk stability.............................................................................46
Figure 5.10(a): Surface structures and bulk stability at ions concentration of 10-3 M..... 47
Figure 5.10(b): Surface structures and bulk stability at ions concentration of 10~6 M..... 47
Figure 5.10(c): Surface structures and bulk stability at ions concentration of 10-9 M..... 48
Figure 6.1: Surface structures during OER reaction. For example, the second surface is LMO-
O H ...................................................................................................... . . .. 50
Figure 6.2: Free energy diagram of ideal catalyst at standard condition......................51
7
Figure 6.3:
Figure 6.4:
Figure 6.5:
Free energy diagram of the reference surface at standard condition.............52
Free energy diagram of the reference surface at U=1.23+q...........................52
Catalytic activities of reconstructions................................................53
8
List of Tables
Table 2.1: Experimental Gibbs formation energies of crystals at standard condition ....... 23
Table 3.1: Standard formation energies AGO, standard hydrogen electrode free energies AGSHE,
and electrochemical reaction energies AGu,pH..........................................................36
9
1 Introduction
1.1 Introduction to electrolysis
Hydrogen is often considered as one of the best carriers to store energy coming from renewable
and intermittent power sources. 1-8 It has high energy-to-weight ratio. The product of it as fuel is
environmentally friendly. Currently, natural gas is the dominant source and contributes as large
as 95% of hydrogen production.9 In this approach, bulk hydrogen is usually produced by the
steam reforming, where steam (H2 0) reacts with methane (CH4) or ethanol (C2H 50H) in an
endothermic reaction at high temperatures (700-1 lOOOC). 10 l 5 However, the steam reforming of
natural gas produces a high concentration of carbon monoxide as by-product. 16-18 Its dependence
on fossil fuels further accelerates the development of alternative approaches to hydrogen
production that is green, efficient and cost-effective.
Direct splitting of water is a promising alternative of hydrogen production. 1,19-24 Water is
plentiful in nature. Driven by input electricity, high-quality hydrogen (z100% hydrogen) can be
produced by the direct electrochemical water splitting with by-product of oxygen. Hydrogen
production from water splitting is clean and efficient, on the condition that the input electricity is
from a sustainable method such as wind, hydro and solar power.
Thermodynamically, it requires 1.23 eV per electron transfer to drive water splitting at
250C and pH 7. Experimentally, it requires over-potential (that is, more than 1.23 eV) to
overcome any kind of energy loss and nonideality in the electrochemical process such as reaction
barrier.
H 2 0(1) + 2.46eV = H 2 (g) + 10 2 (g) (1.1)2
At present, there are three main types of cells for water splitting: solid oxide electrolysis
cells (SOEC), polymer electrolyte membrane cells (PEM), and alkaline electrolysis cells (AEC).'
SOEC operates at high temperature, typically around 800 "C, requiring a significant amount of
thermal energy (heat). However, PEM and AEC typically operate around room temperature
and become increasingly available commercially. The big advantage of PEM and AEC is that
they have comparatively simple structure, accepting variety of power inputs.20, 26
10
Both PEM and AEC are characterized by having two electrodes connected by electrolyte.
Driven by electricity, hydrogen gas is generated at anode (HER) while oxygen is generated at
cathode (OER). OER catalysts for both are immersed in solution. The big difference between
PEM and AEC is that the former uses proton exchange membrane and the latter uses alkaline
liquid (KOH) as electrolyte. Proton exchange membrane conducts H+ while being impermeable
to gases and electrons; diaphragm immersed in alkaline liquid conducts OH~ while also being
impermeable to gases and electrons. Mechanisms for the two water splittings are similar except
that H2 and 02 come from decomposition of H20 in PEM but OH~ in AEC. In particular, pH
environments of OER for these two are very different. Fig. 1.1 shows the schematic of alkaline
electrolysis cell.
Figure 1.1: Schematic of alkaline electrolysis cell
1.2 State of art research on catalysis and its limitations
For both PEM and AEC, hydrogen evolution reaction (HER) takes place at anode while oxygen
evolution reaction (OER) occurs at cathode. Rate of HER is relatively fast by using a good
catalyst. Unfortunately however, splitting H20 molecule (PEM) or OH ion (AEC) is more
difficult, and this causes significant electric losses. A good catalyst can effectively accelerate
11
H20 02/H4/
Catalyit
L + i
rate of OER by reducing reaction activation energy. Platinum is a good option because of its
very high catalytic activity. Due to its high cost, a lot of work has been done to optimize the size
and shape of the platinum particles by designing nanoparticles that can provide a larger amount
of reactive sites for OER or alloying platinum with other metals. 27-34
Much fundamental work has been done to elucidate the OER mechanism and find
descriptors that govern catalytic activity of different materials. Discovery of a new descriptor
can lead to convenient design of both efficient and cost-effective catalysts. Norskov's group
found that this activity can be described by binding energies of OER intermediates (that is,
binding energies of -0, -OH, -OOH on catalyst surface).3 -38 The trend forms a volcano curve
because reaction intermediate can neither bind too strong nor too weak on catalyst surface, as
shown in Fig. 1.2. The volcano is constructed based on linear relationships among binding
energies of reaction intermediates. Materials close to the top of the volcano exhibit high
catalytic activity. By using this volcano, Norskov's group found that perovskite-based oxide
which is cost-effective may have good activity. Motivated by the d-band theory as a descriptor
for metal surfaces, Shao-hom's group found that activity of transition metal oxide including
perovksite-based oxide can be described by eg fillings of surface transition metal, as shown in
Fig. 1.3.19-40 eg orbital of surface transition metal participates in o-binding with reaction
intermediates. Its fillings can greatly influence binding energies of reaction intermediates.
0.0SrCoO3 rNI
-0.5LaCoOa rId-0.5 - 4 o 3 -
-1.0 SrMnO mO,
LaMnO
-1.5
-2.0SrVO 3j
-2.5 vo3
i 0-3.0 [ I
-1 0 1 2 3 4AG - AGHO. / eV
Figure 1.2: OER catalytic activity vs. intermediate binding energies 35
12
1 4.........................................-
@/,50 pA cm.X'Ba.Sr.Co,.Fe.03,
1.5 1 LaN10 L ca oo0*.LaCO3aCa~~Ui ~LaCa, MVIOLWM0
X Lari,,u.0Laingcafe,
1.6 .4n n Lsae
?.14 17 Lamno~ LaMnO,
.7LOCrO3
1.81 j-0.0 0.5 1.0 1.5 2.0 2.5
e electron
Figure 1.3: OER catalytic activity vs. eg fillings of transitional metal-'-
State of art research always assumes ideal surface that has the same structure as bulk.
However, surface reconstruction of oxides is widely found in nature.42 Substantial
experimental and theoretical work shows that transition metal oxides have a wide variety of
surface structures that have different surface energies.434 These include different surface
orientations, surface vacancies and adsorptions, kinks and steps. Surface reconstructions are
caused by realistic operating environment such as temperature, gas pressure, and ion
concentration. As medium between bulk and environment, a surface is thermodynamically
stable if it has the lowest surface energy among possible structures and satisfies the equilibrium
condition between bulk and environment. If the bulk structure is unchanged, change of the
realistic environment breaks the old equilibrium condition and drives the surface to switch
towards a more stable structure. A new surface presents a different electronic structure, giving
different binding energies of reaction intermediates. This will change its catalytic activity. It is
experimentally found that transition metal oxide with oxygen vacancy in surface has higher
catalytic than ideal surface.4
To date, trend of catalytic activities for different perovskite-based oxides under same
environment is well studied both theoretically and experimentally. The trend is fundamentally
determined by electronic structure of bulk or ideal surface, as demonstrated above. However,
little is known about surface structure as a function of realistic environment and its resulting
1 4
13
activity. This unknown impedes discovery of the optimal operating environment for a certain
perovskite catalyst.
1.3 Objectives and scope of this thesis
This thesis focuses on perovskite-based oxide as OER catalyst because it is generally efficient
and cost-effective. Its surface structure is sensitive to environment. Surface reconstruction of it
is widely detected in experiments. Among lots of perovskite, LaMnO 3 is first studied. LaMnO 3
attracts our interest because LaMnO 3 exhibits lower activity in oxygen evolution reaction (water
splitting) than in oxygen reduction reaction (fuel cell), which may be caused by surface
reconstruction. 39-40 Fig. 1.4 shows the crystal structure of LaMnO 3. Around room temperature,
LaMnO 3 presents orthorhombic structure (very close to cubic) due to Jahn-Teller effect. 48 Each
Mn atom is surrounded by six 0 atoms to form an octahedral structure.
Figure 1.4: LaMnO 3 crystal structure
The objectives of this thesis are to apply first-principles density functional theory and
electrochemical principles: (1) to develop a new method for ab intio prediction of surface
reconstruction under operating environment of electrolysis cell, (2) to determine bulk stability
and correlate it to surface structure, and (3) to compare OER catalytic activities of different
surface structures. Fig. 1.5 shows the main structure of this thesis. In this work, we do not
explicitly include water molecules on the surface, but incorporate its effects by considering
14
exchange of atoms between surface and solution. We develop a surface stability phase diagram
as a function of pH and electrode potential. Our results show that values of pH and electrode
potential can greatly affect surface structure and its activity. The new approach developed in this
work is applicable to other oxide catalysts.
Realistic'\environment \
U! /
4-,
3U
descriptor
L MnO
surface
Bulk
4
Figure 1.5: Main structure of this thesis
15
2 Current approach to surface stability and its limitations
State of art theoretical research on surface reconstruction of oxides is often restricted to surface
orientation and oxygen anion vacancy or adsorption. Most of the work focuses on SOEC where
OER catalyst is in gas environment. Partial pressure of oxygen gas in environment can greatly
influence equilibrium of exchange of oxygen atoms between environment and surface, leading to
oxygen anion vacancy or adsorption. Little work is done on surface reconstruction in a more
complex liquid environment (PEM and AEC). For both gas and liquid environment, we have to
take into account exchange of atoms among the bulk crystal, its surface, and the environment,
into our analysis of surface stability. Such processes are included into the Gibbs free energies at
the thermodynamic level of description. Therefore, we have to calculate the Gibbs free energy
of surface reconstruction formation. The Gibbs free energy of surface formation is a measure of
the excess energy of a semi-infinite crystal in contact with environment with respect to the bulk
crystal.49 It can be expressed as a function of chemical potentials of different atomic species.
The most stable surface has a structure, orientation and composition with the lowest surface
Gibbs free energy among all possible surfaces. Surface stability can be correlated to
environment if chemical potentials of atomic species can be expressed as functions of
environment. Here we introduce the current approach to surface stability.
2.1 Method of analysis for surface stability
The Gibbs free energy of surface formation can be straightforwardly expressed as the difference
between the slab Gibbs free energy, GsIab, and the chemical potentials of atomic species, YLa,
/Mn, and yIo:
AG = [Gslab - NLaILa - NMnIIMn - Nolto] (2.1)2
where NLa, NMn, and No are the numbers of respective atoms in the slab.
Equilibrium of bulk LaMnO 3 gives:
blk 3L (2.2)gLaMno3 = Yf Im + 2 Mto2
16
Thus the Gibbs free energy of surface formation can be expressed as the chemical
potentials of only Mn and 0:
AG = [Gslab - NLa La nO3 - AN llM/n - ANoyo] (2.3)
where ANMn and ANO are the relative numbers of the corresponding atoms with respect to the
number of La atoms in the slab. Here ANMn and ANO can be determined based on the numbers
of respective atoms in bulk LaMnO 3 in one unit cell, NLja 9, N/nlk, and Noulk-
bulk
ANMn = NMn - NLa .ulk4)NLa
bulkANo = No - NLa Nulk (2.5)
By using relative chemical potentials of atomic species with respective to their standard
states, AyLa, AjMn, and Ago, we can express the equilibrium of bulk LaMnO 3 in terms of Gibbs
free energy of bulk formation, Agan0 3 :
APLa = PIa - 9La (2.6)
Apmn - yMn - YMn (2.7)
Apo= Io - 2 Ito, (2.8)
buga"l 3 = La + A/Mn + 3Apo (2.9)
where gLja and g9,, are the Gibbs free energies of respective bulk metals at 250C, and go is the
Gibbs free energy of oxygen gas at 25'C and latm. Using the relative chemical potentials can
reduce the number of parameters in AG to only two, AIpMn and Apo:
AG = [Gslab - NLaLa$anoQ3 ANmn9Mn - ANgop 2 - ANmnAMn - ANoAoI (2.10)
The Gibbs free energies of the slab and the crystal metal can be split into:
g = E + Evib + pv - T s (2.11)
17
where E is the static component of the crystal energy, Evib is the vibrational contribution to the
crystal energy, v is the volume, and s is the entropy. For solids, pv can be negligible compared
to E. As it is commonly practiced, we will neglect the very small vibration contributions to g.
Ts of the slab and the crystal metals will be offset into a negligible amount during the calculation
of Gibbs free energy of surface formation, AG. Thus, we approximate the Gibbs free energy
with the total energy obtained from density functional theory (DFT) calculations which will be
introduced later:
g ~ E (2.12)
Therefore, we can determine the Gibbs free energy of surface formation from DFT
calculations and values of the relative chemical potentials ALmn and A to:
AG = Esab - NLaAE bnOu - AN nE bulk - ANOE - ANufAIIf - ANoAIlo] (2.13)
2.2 Method of analysis for bulk stability
The values of the chemical potentials are limited by existence and stability of the bulk LaMnO 3.
In particular, other possible crystals including metals and metal oxides cannot precipitate inside
the bulk LaMnO 3. Thermodynamically, the sum of chemical potentials of the respective atomic
species must lower than the Gibbs free energy of the metals and metal oxides:
PLa < gLa (2.14)
PMn <gMn (2.15)
2 Ika + 3pio <gLa2Q 3 (2.16)
XPUmn + YlIo < gMnfol (2.17)
where MnXOy represents MnO, Mn 30 4 , Mn2O 3, and MnO 2. Again, we use the relative chemical
potentials in consistent with the Gibbs free energy of surface formation:
AIPLa < 0 (2.18)
18
4IyMn <0 (
2AMLa + 3yo <AgL203 (2.20)
XAMn + yAgo < AgMnx0 (2.21)
It is obvious that the above bulk stability criterion defines a 2D region as a function of
AIIMfn and A po.
2.3 Correlation between stability and realistic environment
As medium between bulk and environment, a surface structure is stable if it has the lowest
surface energy among possible structures and satisfies the equilibrium condition between the
bulk and the environment. Thermodynamically, exchange of atoms between surface and
environment must achieve equilibrium. Such an exchange is a key factor in many
electrochemical and catalytic processes. In gas environment (SOEC), an exchange of 0 atoms
occurs. The equilibrium in exchange with 0 atoms gives the equality of oxygen chemical
potentials in the surface and atmosphere:
1o= 0o 2 (T, p) (2.22)
Chemical potential of oxygen gas at any pressure can be expressed with respective to that
at standard pressure, p = latm:
"02(T, p) = p (T, po) + kT In ( (2.23)
Thus relative chemical potential of oxygen atom at any pressure and temperature is:
Alo = [Io, (T, po) -- y02 + kT in () (2.24)
where 02 (T, p0 ) can be obtained from experiments.
In liquid environment (PEM and AEC), however, both exchange of anions and cations
occur. The exchange of cations (La and Mn) is more difficult to determine. This will be
19
(2.19)
discussed in Chapter 4. The equilibrium in exchange with 0 atoms gives the equality of oxygen
chemical potentials in the surface and solution. To determine its chemical potential in the
solution, we have to revisit oxygen evolution reaction and determine its Gibbs free energy
change, ALGOER:
1H 2 0(1) = 2H+ + 2e- + 0 2 (g) (2.25)
AGOER= 2 H+ + 21e- + -02 ~ PH2 0 (2.26)
where PH+ is the chemical potential of proton, yte- is the chemical potential of electron, and pH2 0
is the chemical potential of liquid water. Both PH+ and Pe- can be expressed with respect to
their standard states g40+ and g -:
pH+= po+ + kBTInaH+ (2.27)
Pe- = po- - eU (2.28)
where go + is at pH=O and T=250C, and go- is at electrode potential U=O; Since chemical
potential of liquid water is little affected by temperature, we treat it as constant that is equal to
the chemical potential at T=250C:
1 0 H0 (2.29)PH,20 = H20-
At standard condition where pH=O, U=O, and T=25 0C, the Gibbs free energy change per
electron transfer for OER is 1.23eV from experiments:
0 0 l 0 0
2P,+ + 2P e- + p0 - PH2 0 = 2.46eV (2.30)
Combining the above equations gives AMO in liquid environment (PEM and AFC):
Alo = 2eU + 4.6kBT -pH - 2.46eV (2.31)
20
2.4 Results by this approach and its limitations
We use Mastrikov's work to show part of results by this approach.50 It is a representative work
on LaMnO 3 surface structure in SOEC. In this work, stability of LaMnO 3 surfaces with different
terminations (LaO- and MnO2- terminated (001) surfaces without and with adsorbed 0 atom, 02-
and 0- terminated (011) surfaces) is correlated to the temperature and partial pressure of oxygen.
However, surface reconstruction such as vacancy is not adequately considered. Since this thesis
more focuses on the new approach in Chapter 4 and 5, we use Mastrikov's results to demonstrate
the work and limitations by this approach, as shown in Fig. 2.1.
In Fig. 2.1, different colored region represents different stable terminations. The
encircled numbers point to lines, where metals or their oxides begin to precipitate: (1) metal La,
(2) La2 0 3 , (3) MnO, (4) Mn 30 4, (5) Mn2O 3, (6) MnO 2, and (7) metal Mn. The bright region
restricted by the Lines 2, 4 and 6 is the stable bulk region. The right side of the figure shows
Alo as a function of temperature and partial pressure of oxygen gas. From the picture, we can
see that (001) surface occupies most of the stable bulk region.
AP1., OV T, K-6 -5 -4 -3 -2 -1 0 400 800 1200 1600 2000
-1 -1
-2 - --- ---- --- 2
0 -3-3 0
-4 -440 .30 -20 10
-6 -5 -4 -3 -2 -1 0 400 800 1200 1600 2000
Apu, eV T, K
MnO2 * LaO LaO+O 0 U0
Figure 2.1: Phase diagram of surface structure and bulk stability in gas environment (SOEC)by current approach. This phase diagram considers stability of LaMnO 3 surfaces with differentterminations (LaO- and MnO 2- terminated (001) surfaces without and with adsorbed 0 atom, 02-
21
and 0- terminated (011) surfaces). The encircled numbers point to lines, where metals or theiroxides begin to precipitate: (1) metal La, (2) La20 3 , (3) MnO, (4) Mn304, (5) Mn2O 3, (6) MnO 2 ,and (7) metal Mn. The bright region restricted by the Lines 2, 4 and 6 is the stable bulk region.The right side of the figure shows djto as a function of temperature and partial pressure ofoxygen gas. The labels m on the lines specifies the pressure according to: P(0 2) = 1 0 ' atm.Figure adapted from Mastrikov et al., 2009.
This approach is suitable for the investigation of surface stability in gas environment
(SOEC). Here we construct a phase diagram of bulk stability in liquid environment (AEC and
PEM) at T=250C by current approach. Stable bulk region is constructed based on experimental
formation energies [Table 2.1].5152 dyo is plotted by Eq. (2.31) as a function of electrode
potential U and pH. From Fig. 2.2, we can see that po as a function of U and pH does not
adequately indicate the operating condition that satisfies the stable bulk. For example, U has a
broad range at pH=0 for the stable bulk.
0N .
0-2 -pH=Bulk pH=4
-3 Stability -pH=7-pH=10-pH=14
-41-6 -4 -2 0-1 0 1
AjIMn/eV U/V
Figure 2.2: Phase diagram of bulk stability in liquid environment (AEC and PEM) at T=25Cby current approach from our work. Formation energies to construct bulk stability aresummarized in Table 2.1. The right side of the figure shows Apo as a function of electrodepotential U and pH.
22
Crystal Gibbs formation energy (eV) at
standard condition (T=250 C, Po 2= atm)
LaMnO 3 -14.07
La2O 3 -17.90
MnO -3.79
MnO 2 -4.85
Mn30 4 -13.35
Table 2.1: Experimental Gibbs formation energies of crystals atstandard condition5 1 5 2
In a gas environment (SOEC), exchange of metal atoms between surface and atmosphere
has a very high reaction barrier. It is adequate to only consider the thermodynamic equilibrium
of exchange of 0 atoms. In solution (AEC and PEM), however, metal atoms in the surface can
be ionized into solution at a much lower reaction barrier. Consideration of only exchange of 0
atoms gives limited information on the surface and bulk stabilities. Thermodynamic equilibrium
of exchange of both metal and oxygen atoms need to be taken into account. However, it is not
easy to correlate chemical potentials of metal atoms in the surface to the environment.
Determination of them requires information of bulk and surface structures, and factors such as
electrode potential and ions composition in solution. Without a realistic or simulated mechanism
of reconstruction, correlation between surface stability and liquid environment is hard to achieve.
23
3 Introduction to density functional theory (DFT)
3.1 Basic framework of DFT
It is stated in Chapter 2 that density functional theory (DFT) is used to determine the static
component of crystal energy. As approximation of Gibbs free energy, this static energy is used
to determine the Gibbs free energy of surface formation and the LaMnO 3 bulk stability. In fact,
DFT is widely used in physics, chemistry and materials science as a computational quantum
modeling tool to investigate the electronic structures and properties of molecules. Nowadays,
advance in DFT calculations with better model of the exchange and correlation interactions
makes it possible to accurately determine surface structures and properties that are sometimes
hard to obtain from experiments. The fundamental idea of DFT is that wavefunctions and
properties of a many-electron system can be determined by its electron density. The electron
density can be solved by Kohn-Sham equation which treats the many-electron system as non-
interacting electrons moving in an effective potential. The effective potential includes the
external potential and the effects of the Coulomb interactions between the electrons. Here we
introduce the basic framework of DFT. More details can be viewed in [Ref 53].
A stationary electronic sate can be described by a wavefunction 'P satisfying the many
electron time independent Schr6dinger equation:
RY = [T + I + Upv = Ew (3.1)
where H is the operator of Hamiltonian; T is the kinetic energy; V is the potential energy due to
positively charged nuclei, which we name as external potential; and U is the electron to electron
interaction energy; and E is the total energy. Hohenberg-Kohn theorems54 prove that the ground
state properties of a many-electron system are uniquely determined by an electron density. In
principle, the ground state wavefunction WO is a unique functional of the ground-state density po:
To = '1 [Po] (3.2)
Consequently, the ground-state expectation value of an observable 0 is also a functional
of po. This can be applied to the ground-state energy EO:
24
O[pO] = (Y[pO]IaIw[po]) (3.3)
EO = E[po] = (W[po]IT + V' + UIW[po]) (3.4)
Both the ground-state and general external potentials can be expressed explicitly as a
function of electron density:
V[po] = f V()po(r')d3r (3.5)
V[p] = f V(?)p(-)d3r (3.6)
DFT uses Kohn-Sham equation to solve electron density. The main difference between
Kohn-Sham equation and Schr6dinger equation is that the former treats the many-electron
system as non-interacting electrons moving in an effective potential V (r').
[T + Vs(??)]ci(i?) = Eioi() (3.7)
Vs(r) = V() + f e PVr)d33'r + Exc[p(r)] (3.8)
where qi is the wavefuction of orbital i; eL is the total energy of orbital i; f I d3 is the
electron-electron Coulomb repulsion; and Exc is the exchange correlation potential, which
includes all the many-particle interactions. An unfortunate compromise in the computational
tractability in the DFT method is to have to approximate Exc since we do not know its analytic
form. The simplest approximation is the local density approximation (LDA). Here, Exc only
depends on the value of the electron density and not on its derivative. The functional depends on
the density at the coordinate where the functional is estimated.
Ex A[p] = f exc(p)p(r)d3 r (3.9)
where exc is the exchange-correlation energy of a homogenous electron gas. The local spin-
density approximation (LSDA) is a straightforward generalization of the LDA to include electron
spin:
E'jDA[pT,P] = f EXC(pt,p)p(r')d3r (3.10)
25
Generalized gradient approximation (GGA) is still local but also considers the gradient of
the density at the same coordinate. This method is more accurate than LDA. GGA can give very
good results for molecular geometries and ground-state energies.
EA [pT, p1] = f exc(Pt, PI, VPT, Vpl)p(r)d3 r (3.11)
Figure 3.1 shows the procedures of DFT calculations with constant lattice parameters:
" Construct the nuclear potential given the atomic types and positions in the system;
" Give a initial guess of electron density and determine the corresponding potential;
" Solve the Kohn-Sham to obtain a new electron density;
" Stop the self-consistent calculation if the difference between the old and the new
energies are sufficiently small;
" Calculate the forces on each atom, and move the atoms accordingly;
" Repeat the self-consistent calculation;
* Move the atoms until the forces are almost zero;
* Determine the system's properties based on its geometry and charge density;
In this thesis, we are only interested in the minimum total energy from DFT calculation.
26
H1! = EW ) DFT ) Nsingle-particle equations(Kohn-Sham equations)
DeteSmine V(r) 4
Solve K-S equations for pXr)
V2V(r = P Set V(r)= V.(r)
110Vne(r) =Vr)
yes
Compute forces; moveatonis accordingly
no
Figure 3.1: Procedures of DFT calculations with constant lattice parameters
Several GGA functional have proved useful in applications to molecules and solids, but
Perdew, Burke, and Ernzerhof (PBE) have developed a simplified GGA that best satisfies many
of the physical and mathematical requirements of DFT." PBE from our DFT calculations can
well predict formation energies of transition metal oxide with respect to water and hydrogen gas
at standard condition. Trend of adsorption energy for different materials by PBE is generally
accurate.
3.2 DFT computational details in this thesis
DFT calculations are performed within the generalized gradient approximation (GGA) of
Perdew-Burke-Emzerho (PBE) formulation using Vienna ab initio simulation package (VASP)
and the projector-augmented-wave (PAW) methods with a 550eV cutoff energy [Ref]. Due to
open electronic shells on Mn ions, the spin-polarized calculations together with dipole
corrections are performed. All supercells are (001) orientated and symmetrical 7-layer thick with
27
16 A vacuum gap in the direction perpendicular to the surface. Lattice constant of LaMnO 3
crystal tested by above calculations is within 3% error from experiments. 56
We only consider vacancy and adsorption at concentrations of 2 and ML because of
limited computational resource. A smaller concentration of reconstruction needs a larger surface
consisting of more unit cells, making it computationally unfeasible. These two concentrations
are enough for us grasp the trend of surface change as a function of environment factors.
28
4 A new approach for ab initio prediction of realistic surface
reconstruction
Due to the limitation of conventional method for liquid environment (PEM and AEC), we
develop a new approach to model the thermo-chemistry of electrochemical reactions on surface
reconstructions. We determine the formation energy of surface reconstruction by assuming a
natural and computationally convenient mechanism. Such mechanism enables us to combine
DFT calculations and electrochemical principles to express the formation energy as a functional
of pH and electrode potential. In this work, we do not include explicitly include water molecules
on the surface, but incorporate its effects by considering exchange of atoms between surface and
solution. Factors of environment that are considered to affect surface structure include pH,
temperature, electrode potential, and concentrations of cation species. Cation species of La and
Mn in liquid is considered because their concentrations influence equilibrium of exchange of
metal atoms between surface and environment. Partial pressures of hydrogen and oxygen are
functions of pH, temperature, and electrode potential. Our objective is to construct a phase
diagram that describes surface structure as a function of environment factors.
We only consider (001) oriented surface because it is generally taken as the most stable
orientation.5 0 This orientation gives three possible ideal surfaces: MnO2-LaO terminated
asymmetric surface, MnO 2 terminated surface, and LaO terminated surface. The dipole moment
in asymmetric surface can largely increase its surface energy. Thus we focus on the more stable
symmetric surfaces. We use MnO 2 terminated surface as our reference. Surface reconstructions
will be based on this reference.
29
Asymmetric
- MMnn2
E
+ MnO2 LaO
+ L0 a Mn02 Li0
Figure 4.1: Three possible (001) ideal surfaces
Surface reconstruction in this work includes vacancy, adsorption and transition of
termination. The following schematic shows the mechanism of 0 and Mn vacancy formation.
Specifically, both reactants are reference surfaces, protons, electrons and water in liquid. For 0
vacancy, the final products are reconstructed surface and water. For Mn vacancy, the products
are reconstructed surface and certain Mn ion species (Mn 2+, Mn(OH)+, Mn(OH) 2, HMnO2,
Mn 30 4, Mn2O 3, MnO 2 , MnO 4 2-, or MnO4). Our goal is to determine Gibbs free energy change
of the two reactions, which we name as total vacancy formation energies. The mechanism of 0
and Mn vacancy is that the respective atom first escapes the reference surface, and then reacts
with protons, electrons and water in solution to form the final product. In realistic environment,
mechanism of vacancy maybe much more complicated. Fortunately, we are only interested in
vacancy formation energy which is only dependent on reactants and products. This mechanism
is natural, and computational convenient. This will be discussed below.
30
Symmetric Symmetric
LMO +
H+/e-
LMOH /
/%r~
H+/e/H 20
j I
+ AG 2
Figure 4.2: A hypothetical mechanism of vacancy formation
4.1 Determination of 0 vacancy formation energy
The total vacancy formation energy AG is the summation of AG1 and AG2 . Here, AG, is the
energy of 0 atom escaping from the reference surface; and AG 2 is the energy of that atom
reacting with protons and electrons to form water molecules:
AG1 = Gvac + Po - Gref
0 + 2H+ + 2e- = H 20()
(4.1)
(4.2)
(4.3)AG 2 = PH 2 0 ~ MO - 2 PH+ - 2 pe
where Gvac is the Gibbs free energy of slab with vacancy; Gref is the Gibbs free energy of the
reference slab; p0, PH2 0' MH+ and le are the chemical potentials of the escaped 0 atom, water
molecule, proton and electron. The chemical potential of that escaped 0 atom is hard to
determine. It depends on varieties of factors such as Mn-O bond strength and solution
temperature. Fortunately, that escaped 0 atom is a transitional product during vacancy
31
L
AG = AG1
+ Mn0z
formation. We introduce the relatively chemical potential ipo with respect to liquid water and
hydrogen gas at standard condition:
A1o = o - (H20 11H2) (4.4)
where p4120 is the chemical potential of water at T=250C; and /1 2 is the chemical potential of
hydrogen gas at T=250 C and P=latm; Substitution of the above equation into AG1 and AG2 leads
to cancellation of A yo in the determination of AG. Consequently, AG can be calculated based on
liquid water and hydrogen gas at standard condition instead of that escaped 0 atom. This can be
shown in the following:
AG = AGf + AGU,pH (4.5)
AGf = Gvac + (4H20 - Po) - Gref (4.6)
AGU,pH = ~ 20 - 020 - H2) - 1H+- 2Pe (4.7)
where A Gf and A GU,pH are the vacancy formation energy and electrochemical reaction energy
based on liquid water and hydrogen gas at standard condition. As stated in Chapter 2, the Gibbs
free energy of crystal is approximately equal to their static component energy from DFT
calculations:
AGf ~ Evac + (E Ho - EH2) Eref (4.8)
By setting standard hydrogen electrode as reference, we can relate the chemical potentials
of proton and electron to that of hydrogen gas. At standard condition, proton and electron is in
equilibrium with hydrogen gas. This standard condition is pH=O, T=250C, P(H2)=latm, and
electrode potential U=O.
0 0 (49H2 =H+ + Me (4.9)
At a pH different from 0, we can correct the chemical potential of proton by the
concentration dependence of the entropy. The effect of a bias involves an electron in the
electrode, shifting its energy away from standard state by -eU. Chemical potential of liquid
water can be treated as constant.
32
PH+= MH+ + kBT in aH+
Ye- = go- - eU (4.11)
H2 0 (4.12)
where aH+ is the concentration of protons. Substitution of the above equations into A GU,pH gives
the following form as a function U, T, and pH:
LIGU,pH = 2eU + 4.6kT -pH (4.13)
Obviously, the above form gives A GU,pH = 0 at T=0 and pH=0, in consistent with
equilibrium condition of standard hydrogen electrode. At T=25"C, the form reduces to
A GU,pH = 2eU + 0. 118pH (4.14)
4.2 Determination of Mn vacancy formation energy
The fundamental ideal to determine Mn vacancy formation energy is the same as that of 0
vacancy except that Mn ion species in solution needs to be considered. Mn ions in solution can
resist Mn atom from leaving surface. We consider varieties of ion species: Mn 2+, Mn(OH)+,
Mn(OH) 2, HMnO2, Mn30 4, Mn2O 3 , MnO 2, MnO 4 2 , or MnO4 -. The general form of
electrochemical reaction is:
Mn + nH+H+ + nH2 OH 20 + nee- = nMnxOyz- (4.15)
Similar to Chapter 4.1, the energy of Mn atom escaping from the reference surface is
AG1 = Gvac + pMn - Gref (4.16)
And the energy of that atom reacting with protons and electrons to form ion is
AG 2 = nyMnxoyz - (Mmn + nH+/UH+ + nH2 OIH2 0 + nele) (4.17)
Again, we introduce the relatively chemical potential AIMn with respect to bulk metal at
standard condition:
33
(4.10)
Alln = YMn - 9Mn (4.18)
where g9, is the Gibbs free energy of bulk Mn at T=250C. Substitution of the above equation
into AG 1 and AG 2 leads to cancellation of AIyMn in the determination of AG. Consequently, AG
can be calculated based on bulk metal at standard condition instead of that escaped Mn atom.
This can be shown in the following:
AG = AG +,AGU,pH (4.19)
A Gf Gvac + gmn - Gref (4.20)
AGU,pH ~ n/Mnxoyz- - (g~on + nH+H+ + nH2OIH20 + nele) (4.21)
where A Gf and A GU,pH are the vacancy formation energy and electrochemical reaction energy
based on bulk Mn. As stated in Chapter 3, the Gibbs free energies of slab and crystals are
approximately equal to their static component energies from DFT calculations:
AGf ~ Evac + EMn - Eref (4.22)
Again, we use standard hydrogen electrode as reference, where protons and electrons are
in equilibrium with hydrogen gas at standard condition.
PH, = PH+ + Ye (4.23)
Chemical potentials of proton and electron are shifted by pH and electrode potential
respectively:
11H+ = p%+ + kT In aH+ (4.24)
le = I - eU (4.25)
Chemical potential of ion is shifted by its concentration aMfxoyz-:
/lMnxoyz- = itMnOyz- + kT In aMnxoyz- (4.26)
where yMmnxoyz- is the standard chemical potential at aMfxoyz- = 1.
34
H20 ~ PH20
Substitution of the above equations into A GU,pH gives the following form as a function U,
T, pH, and amnlo z-:
0 0 [aMnxOyz-]nA GU,pH = - gMf -n - nH,0 PH, O-n fee +kT in [a~- + ne(eU)Gnxyz- - go -- H+YH+ -- H H ~~ [aH+InH+
(4.28)
where the term in bracket is the Gibbs free energy change at standard condition. We name it as
standard hydrogen electrode free energy, A GHE, which can be obtained from experiments. This
energy is related to standard hydrogen electrode potential. Thus, the final form of A GU,pH is
AGU,pH = AGSHE+ ne(eU) + 2.3nH+kT -pH + kT In[amnXoyz-]n (4.29)
It can be seen that A GUpH is contributed by four parts: (1) the free energy change at
standard condition; (2) the driving force from electrode potential; (3) the driving force from pH;
and (4) the effect from cation species. At T=250 C, A GU,pH can be reduced to
A GUpH = AGE + ne(eU) + 0. 05 9 nH+pH + 0.026 In[amnXoz-]" (4.30)
Similarly, the electrochemical reaction energy of La metal is:
La + nH+H + nH 2OH 2 0 + nee- = nLa.Oyz (4.31)
A GU,pH = AGSHE + ne(eU) + 0. 05 9 nH+pH + 0. 026 In[aLaxoyz-]n (4.32)
4.3 Experimental standard hydrogen electrode free energy
Standard hydrogen electrode (SHE) free energies are obtained from experiments. Due to limited
data of SHE potentials from literatures, we use standard formation energies based on oxygen gas
A G and correct them to SHE free energies A GSHE -57 Such correction is the change of free
energy reference from oxygen gas to liquid water and hydrogen gas at standard condition. For
35
(4.7)
the reaction of H 2 0(1) = H 2 (g) + 1 0 2 (g), the Gibbs free energy change per electron transfer is
1.23eV at standard condition. Therefore, the correction can be generalized as
A GSHE = AG+2.46noeVni
(4.33)
where no is the number of oxygen atoms in the formula of ion species. For example, no of
Mn(OH)+ is 1. ni is the number of metal atoms in the formula of ion species. For example, ni of
Mn30 4 is 3. Presence of ni in the correction is because AG" is the formation energy per ion
species formula while A G0HE is the free energy per metal atom. Note that standard hydrogen
electrode potentials derived from A GSHE are in consistent with those from experiments. The
following table shows AG, A GSHE, and AGUH for all ions considered in this work.
Table 4.1: Standard formation energies A G 0, standard hydrogen electrode free energies A GSHE,
and electrochemical reaction energies A GUpH
36
Ion species AG0 /eV AG;HE/eV AGU,pHleV
Mn2+ -2.36 -2.36 -2eU + 0.026 In amfl2+ - 2.36
Mn(OH)+ -4.20 -1.74 -2eU - 0.059pH + 0.0 2 6 In aMn(OH)+ - 1.74
Mn(OH) 2 -6.37 -1.45 -2eU - 0.118pH - 1.45
HMnO 2 -5.24 -0.32 -2eU - 0.177pH + 0.026 In aHMnOi - 0.32
Mn30 4 -13.30 -1.15 -2.667eU - 0.157pH - 1.15
Mn2O 3 -9.13 -0.88 -3eU - 0.177pH - 0.88
MnO 2 -4.82 0.1 -4eU - 0.236pH + 0.1
MnO 42 -5.24 4.60 -6eU - 0.472pH + 0.026 In aMflO- + 4.60
MnO 4 -4.64 5.20 -7eU - 0.472pH + 0.026 In amflO- + 5.20
La'+ -7.09 -7.09 -3eU + 0.026 In aLa3+ - 7.09
La2O 3 -17.68 -5.15 -3eU - 0.177pH - 5.15
4.4 Formation energy of surface reconstruction: a general form
Chapter 4.1 and 4.2 give the total vacancy formation energies for 0 and Mn. Besides vacancy,
adsorption, transition of surface termination, change of surface orientation, and surface steps and
kinks commonly take place in experiments. We develop a general form for formation energy of
surface reconstruction based on the idea of vacancy formation. In particular, Mechanism of
atomic adsorption is the process of ion species being reduced into respective neutral atom and
the atom attaching to the reference surface. Therefore, adsorption formation energy is the
summation of (1) adsorption energy based on bulk metal or liquid water and hydrogen gas at
standard condition and (2) electrochemical reaction energy from ion species to respective neutral
atom. Other more complicated reconstructions such as transition of termination can be viewed
as a combination of losing some atoms (vacancy) and getting other atoms (adsorption). This will
be discussed with more details in Chapter 5. With new slab free energy from DFT calculations,
we are able to estimate formation energy for varieties of surface reconstructions by summing
formation energy based on bulk metal and electrochemical reaction energy. The general form is
in the following.
AG = (Enew - Eref + Z i ni [Ebulk ]t) + Z i ni [AGU,pHi (4.34)
where (Enew - Eref + Z ni [Ebulk ]) is the reconstruction formation energy based on bulk metal,
liquid water and hydrogen gas at standard condition. Zj nj[AGU,pH] is the summation of
electrochemical reaction energies. Enew is the new slab energy. ni is the number of exchange of
atoms between surface and solution. It has positive sign for vacancy and negative sign for
adsorption. [A GU,pH], is the electrochemical reaction energy per respective atom, as shown in
Table 4.1. This form is fundamentally in consistent with surface formation energy based on
chemical potentials of atomic species, as developed from Chapter 2.
37
4.5 Verification of the new approach
Electrochemical reaction energy AGU,PH can be used to construct phase diagram of bulk metal
and its ion species. The lowest AGU,pH among all species gives the most stable state. As
verification, we construct the phase diagram of Mn. With the same experimental data, our phase
diagram is the same as pourbaix diagram based on Nernst equation. Note that we use UsHE in
place of U to emphasize electrode potential vs. standard hydrogen electrode.
U-IICd,
D)
2
0
-1
-2
Ion activity - 10-6
0 5 pH
MnO 42
10
Figure 4.3: Mn phase diagram constructed by AGU,pH
38
MnO4
VnO . .
Mn2+, fi 0,;
Mn 2 +
Mn
5 Results and discussions based on our new approach
In Chapter 4, we develop a new approach to determine formation energy of surface
reconstruction as a function of T, pH and ions concentrations. We use MnO 2 terminated surface
as reference. Negative formation energy indicates favored reconstruction on the reference. The
most negative formation energy among varieties of reconstructions gives the most favorable and
stable one. Therefore, we have to calculate formation energies of varieties of possible
reconstructions and compare their stabilities. In this work, reconstructions of step and kink are
neglected. In realistic environment, reconstruction such as vacancy and adsorption could take
place at numerous concentrations, and ions concentrations in solution could change greatly at
different operating environment of PEM and AEC. In this work, we only consider vacancy and
adsorption concentration at 2 and ML. Charged ions concentrations are fixed at 10-6 M in
consistent with pourbaix diagram. In our later discussion, we will investigate the influence of
ions concentration on surface structure. Our goal is to grasp the trend of surface change as a
function pH and U with limited computational resource. The trend of surface change can give us
the trend of its catalytic activity as a function of environment.
5.1 Stability of surface with vacancy
Figure 5.1 shows Mn vacancy formation energy AG vs. UsBE and pH at charged ions
concentrations of 10-6 M. The vacancy concentration is % ML (that is, one vacancy per 2x2 unit
cell). Different inclined line represents different ion specie in solution. The horizontal line
represents the reference surface. The lowest AG gives the most stable surface and ion species in
solution. In other words, it presents stabilities of both surface and ion. It shows that the
reference surface is stable at low UsB. As UsB increases, oxidation of surface takes place and
surface with Mn vacancy becomes favorable. High UsB can also oxidize ion species in solution.
It also shows that stability of surface with Mn vacancy shifts to a lower UsH at higher pH. This
means that high pH can also oxidize surface, though its effect is small.
39
pH=715
10
5
0
-5
-10--1 0 1USHE/V
1
-1
-1
pH=14
0 1USHE/V
2
Figure 5.1: Stability of surface with Mn vacancy
Figure 5.2 shows 0 vacancy formation energy AG vs. UsHE and pH. The vacancy
concentration is 1/4 ML. The inclined line represents the surface with 0 vacancy and the escaped
0 atom becomes H20 in solution. It shows that 0 vacancy is not favorable at positive electrode
potential. This is because solution has a very oxygen atom rich environment. Equilibrium
between surface and solution makes surface hard to lose oxygen atom.
6
4
2
0
-2
pH=7
O,,, Ref
0USHE/V
6
4
0
-2
pH=14
-- ------------
v /R e f
0USHE/V
---- Ref-H2 0
2
Figure 5.2: Stability of surface with 0 vacancy
40
2
Ref Mn V
5
0 ---------- ----------.
0 Ref Mn
5
<w
----- Ref- Mn2 +-MnOH*
Mn(OH) 2- HMnO~
2Mn3O4Mn203
- MnO2
---- MnO&4----- MnO-4
-1
2-
-2
5.2 Stability of surface with adsorption
In this section, we investigate the possibility of cation adsorbte on surface. In Mn pourbaix
diagram, different UsH and pH defines the most stable Mn ions in solution. The formation
energy for these ions becoming cation adsorbate on surface is demonstrated in Chapter 4.
Negative formation energy indicates stable surface with cation adsorbate. In this work, we only
consider one Mn adsorbate or MnO 2 adsorbate per 2x2 unit cell, as shown Fig. 5.3. MnO as
adsorbate is tested by DFT and proves to be unstable. Unlike Fig. 5.1, we do not show formation
energies for different ions in our later results and discussions. We only show the formation
energy from the most stable ion in solution.
Mn adsorbate MnO2 adsorbate
Figure 5.3: Configuration of surface with cation adsorbate
Figure 5.4 shows cation adsorbate formation energy AG vs. UsHE and pH. The red line
represents the surface with Mn adsorbate, and the blue line represents the surface with MnO 2
adsorbate. It shows that AG is positive. Therefore, cation adsorbate is not favorable in PEM and
AFC. This is because the small amount of ions in solution can not provide enough driving force
to the growth of surface. However, this suggests that we could add transition metal ion to the
water and get to different surfaces, which could be useful for some applications.
41
pH=7 pH=14-- Mn--- MnO 2
10 10
5 5
0 0-1 0 1 2
USHE/V USHE/V
Figure 5.4: Stability of surface with cation adsorbate
5.3 Stability of surfaces with different terminations
Different surface termination presents different electronic structure and binding energies with
intermediates. Transition of termination can greatly influence catalytic activity. Thus, it is very
important to know the realistic termination under operating environment. In experiments, people
often use microscopic techniques such as scanning electron microscope and transmission
electron microscopy to examine the surface termination. However, surface environment may
change during the detection of surface. Detection results do not adequately prove the realistic
termination in operation. To date, little theoretical work is reported to express termination
transition as a function of environment as we know. Here, we take the benefits of the new
approach. We describe terminate transition on a thermodynamic level.
We consider the surface in equilibrium with both bulk and environment. The equilibrium
gives the equalities of atomic chemical potentials in bulk, surface and environment. Therefore,
termination transition with respect to bulk is the same as that with respect to environment.
Termination transition with respect environment can be viewed as a process of exchange of
atoms between surface and solution. Thus, we can use the new approach to model termination
transition. It must be noted that we need information of La-based ions concentrations (La 3 and
La2O 3) to define its chemical potential. We fix charged La ions at the same concentration of
42
charged Mn ions (10-6 M). Due to the stoichiomerty of La and Mn in the bulk LaMnO 3, we
believe ion concentrations of La and Mn are close even in the presence of surface reconstruction.
This assumption must be based on no additive La and Mn ions in solution.
M1nO 2 HO
M nO2 O
Figure 5.5: Configuration of termination transition
Figure 5.6 shows stability of termination. It shows that LaO termination is only stable at
a very reduced environment. MnO 2 termination occupies most of the operating region. Our
DFT calculations indicate that LaO termination has a very strong binding energy with
intermediates. The strong binding dis-stabilizes LaO termination at normal operating
environment. High stability of MnO 2 termination is in consistent with experiments. Our
approach provides a theoretical proof to experimental detection.
2
1
MnO2
LaO ----05 10
pH
Figure 5.6: Stability of termination
43
5.4 A global surface phase diagram
Here we construct a global surface diagram. The construction includes varieties of
reconstructions. First, we consider stabilities of La and Mn based ion species. Surface only
exchanges atoms with the most stable ions. Secondly, we consider transition of terminations,
and vacancy and adsorbate of both anions and cations. Finally, we consider reconstruction
concentration at '2 and 1/4 ML. Charged ions are fixed at 10-6 M. Figure 5.7 shows some
representative surface configurations.
Ad
x
xs
Ideal Surface 0 Mn
sorbate Vacancy
MnO MnO2 Mn
TT /
Figure 5.7: Representative surface configurations
We generate a grid of surface formation energies and select the surface that has the
lowest energy at each point of UsHE and pH. Figure 5.8 presents different stable surfaces at
different environment. Below the red line, surface reconstruction based on LaO termination is
stable. Above the red line, surface reconstructions based on MnO 2 termination is stable. It can
seen that the reference surface is stable at UsHE=O and pH=7, in accordance with assumptions
from experiments. However, high UsHE and pH can oxidize surface. Surface experiences 0
coverage to Mn vacancy with rising UsHE. Our thermodynamic approach shows that surface
reconstruction may take place in realistic environment.
44
10-6 - aqueous ions concentration
2.Y, ML Mnvac
14 ML Mf YML Oads
> Y.- ML M vaLU
Y% ML LavaM
0 5 10pH
Figure 5.8: A global surface diagram
5.5 Bulk stability and equilibrium condition
Bulk stability is thermodynamically considered in terms of chemical potentials. Mathematically,
the summation of atomic chemical potentials must be larger than the Gibbs free energy of bulk
LaMnO 3. Again, we introduce the relative chemical potentials with respect to the phases of
elements at standard condition (bulk La, Mn, and oxygen gas). Then, the summation of the
relative chemical potentials must be larger than the formation energy of bulk LaMnO 3.
MLa + IMn + 3io GLamn 3 (5.1)
ALa + AMfn + 3Ato ;i AGLaMnO3 (5.2)
If the bulk is in equilibrium with the surface and solution, A/iu in the bulk is identical to
AGu,pH for any atom species i. This enables us to correlate bulk stability to UsHE and pH.
[6 Gu,pH]La + [AGU,pH] Mn + 3[ AGU,pH] AGLamno3 (5.3)
The following picture shows bulk stability as a function of UsHE and pH at different ion
concentrations. Inside the red line, bulk is stable. It can be seen that LaMnO 3 is only stable in
45
alkaline environment, in consistent with experiments. Larger ions concentration gives higher
bulk stability. The bold black line represents ideal oxygen evolution reaction without over
potential. Realistic operating condition will be above that line.
In equilibrium condition, the sum of chemical potentials in solution must be equal to the
formation energy of bulk LaMnO 3. Namely, the red line represents equilibrium condition at
respective ions concentration. Change of UsHE and pH away from that the line shifts the system
to a new equilibrium where a different ions concentration is adapted. Thus, the system is self-
adjusted to achieve equilibrium. However, large amount of ions dissolved from bulk can greatly
interrupt oxygen evolution reaction.
210-X - aqueous ions concentration
OER>1
LU
D%104 -0 \1o- \ Stable Bulk-
0-% % %%
-10-0 5 10 14
pH
Figure 5.9: Bulk stability
Here, we merged surface and bulk stabilities into one phase diagram. Both USHE and pH
have to satisfy bulk stability. Meanwhile, they have to be above ideal OER operating line to
simulate realistic environment. Our goal is to find surface structure under above criterions. We
also investigate ions concentration's effect on surface structure.
It can be seen from Fig 5.10 (a) to (c) that ions concentration does not greatly influence
surface structures. The trends of surface change as a function of USHE and pH are the same. The
factor that significantly affects surface structure is UsHE. This can be explained by UsHE s great
46
influence on atomic chemical potentials, as developed in Chapter 3. Fig 4.9 (a) to (c) also show
that 0 coverage and Mn vacancy may take place at high UsHE.
12
u-ir
0
-1
10-3 - aqueous ions concentration
) 5pH
% ML Oads
10
Figure 5.10(a):
2
LU
MDn
0
-1C
Figure 5.10(b):
Surface structures and bulk stability at ions concentration of 10-3 M
10- - aqueous ions concentration
Y2 ML Mnvac
M LMvac a M
Ref. \ StableBulk
% ML Lavac
5pH
10
Surface structures and bulk stability at ions concentration of 10-6 M
47
AML Mnvac
0---
ML a4Y ML Mnvalc
d%*4,f t
'% Ref. \ Stable Bulk
YMLLavac
i
YWML Oads
10-9 - aqueous ions concentration
Y2ML Mnva
Y4 ML ..
Ln %
Z 0 % Ref. \Stable Bulk % MLOads
Y ML Lavat s
0 5 10pH
Figure 5.10(c): Surface structures and bulk stability at ions concentration of 10-9 M
48
6 Electrocatalytic activity of surface reconstruction
Electrocatalytic activity of perovskite-based oxide with ideal surface is well studied by
Norskov.35-38 The activity is determined by the binding strength of the reaction intermediates on
the ideal surface. Plotting the activity as a function of binding energy forms a volcano curve.
This implies that reaction intermediates can neither bond too strong nor too weak on an active
surface. Here, we combine density functional theory and electrochemical principles to determine
thermodynamic overpotential of surface reconstruction. The overpotential is used to compare
activity. This method proves to well grasp the trend of catalyst activity of ideal surface.35
Here, we use a generally accepted OER mechanism that consists of four consecutive
proton and electron transfer steps. Reaction intermediates of -OH, -0, and -OOH are formed in
this mechanism. The four steps are shown in the following:
LMO + H20 = LMO-OH + H+ + e (6.1)
LMO-OH = LMO-O + H+ + e- (6.2)
LMO-O + H20= LMO-OOH + H+ + e (6.3)
LMO-OOH = LMO+02+ H + e- (6.4)
where LMO is the ideal surface; LMO-OH is the surface with OH adsorbate; LMO-O is the
surface with 0 adsorbate; and LMO-OOH is the surface with OOH adsorbate. Surface structures
during OER reaction are schematically shown in Fig. 6.1.
49
I
4-
Figure 6.1: Surface structures during OER reaction. For example, the second
surface is LMO-O
We calculate free energy change of each reaction step AG1, AG 2 , AG 3, and AG4 based on
standard hydrogen electrode (SHE) in the following equations. These equations are developed
with electrochemical principles. First, we assume standard condition (USHE=O, pH=O, T=250 C,
PH2=latm) where proton and electron are in equilibrium with hydrogen gas. Secondly, we
calculate formation energy of each step based on liquid water and hydrogen gas at standard
condition, which we name as binding energy. AGOH, AGO, and AGOOH are the binding energies
of LMO-OH, LMO-O, and LMO-OOH respectively. Finally, formation energy of each step is
shifted by the chemical potentials of proton and electron at finite USHE and pH. Details of
derivation can be seen in [Ref 35].
AG1 = AGOH - eUSHE - 2.3kT -pH
AG 2 = AGO - AGOH - eUSHE - 2.3kT -pH
AG 3 = AGOOH - AGOH - eUSHE - 2.3kT -pH
AG4 = AG0) -AGOOH - eUSHE - 2.3kT -pH
(6.5)
(6.6)
(6.7)
(6.8)
50
Here, we determine the thermodynamic overpotential 77 based on the free energy changes
of all reaction steps at standard condition (AGO, AG , AG , AGO) when there is no input driving
power from pH and U. The maximum A Gmax among the standard free energy changes indicates
the power needed from the input with finite pH and U to drive the four reactions. The
thermodynamic overpotential is calculated by the power relative to the thermodynamic ideal
power 1.23eV. Less overpotential shows less power needed from input, presenting higher
activity of a surface. A realistic overpotential may include other factors such as reaction barrier.
However, the thermodynamic overpotential is adequate to compare activities of different
surfaces.
AGmax = max(AG ,AG0,AG ,AGO) (6.9)
= LGmax (6.10)
The OER free energy change is totally 4.92eV. For an ideal catalyst, the four reaction
steps share /4 of the total free energy change, as shown in Fig. 6.2. Its thermodynamic
overpotential is 0. For a realistic surface, however, the binding energies of reaction
intermediates can never give the equality of free energy change in each step, leading to a finite
overpotential, as shown in Fig. 6.3. The step that has the largest free energy change is the
potential-determining step. By applying U=1.23V+ q to the system, the potential-determining
step has zero free energy change and the rest of steps become downhill, as shown in Fig. 6.4.
Ideal catalyst, U=O 1.23eV(D 1.1.23eV<3 1.23eV
kD 1.23ev
Figure 6.2: Free energy diagram of ideal catalyst at standard condition
51
Ref surface, U=0 G4 1
AG3 -Determiningster
< 0 - A G II2 10
Figure 6.3: Free energy diagram of the reference surface at standard condition
> 0a)-2
< -4 Ref surface, U=1.23+
Figure 6.4: Free energy diagram of the reference surface at U=1.23+r
By DFT calculations, we obtained binding energies of reaction intermediates for all
surface reconstructions considered in this work. We determine their thermodynamic
overpotentials by using the above method. From Fig. 6.5, we can see that adsorbate and vacancy
on the reference surface can give rise to different catalytic activities. Both oxygen vacancy and
adsorbate can improve perovskite's performance. However, Mn vacancy will reduce its activity
to a large extent.
52
1.8 1 1 1 1
1.6- Higher activity
> 1.4 -a)0% 1.2 -
0.8-
Figure 6.5: Catalytic activities of reconstructions on the (001) MnO 2 terminated surface
Back to the surface stability phase diagram in Chapter 5, we can see that the surface
around the OER operating condition maybe the MnO 2 terminated surface with 1/2 ML 0
adsorbate. This surface has higher activity than the reference surface. In other words, operating
condition with an appropriate UswE optimizes the performance of LaMnO 3. However, a large
UsHE may cause Mn vacancy, shifting the surface to a highly inactive state. Here we extend our
discussion to oxygen reduction reaction (ORR) for the fuel cell. The difference between the
operating conditions of ORR and OER is that the former operates below and the latter operates
above the thermodynamically ideal line. This is caused by overpotential. Below the line, we can
see that the surface around the ORR operating condition is the reference surface. Based on the
above comparison, we conclude that LaMnO 3 may experience Mn vacancy in OER, presenting
lower activity than ORR. This is in accordance with results from experiment. 39
53
7 Summary and future work
In this thesis, we developed a new method for ab initio prediction of realistic surface
reconstructions by using density functional theory (DFT) and electrochemical principles. By
using this method, we constructed a surface structure phase diagram as a function of pH and
electrode potential under the liquid environment of electrolysis devices. Our results show that
environment can affect surface structure and its resulting electro-catalytic activity. In particular,
a high electrode potential can cause Mn vacancy in surface, shifting the ideal surface to a very
inactive state. This may be one of the reasons for LaMnO 3's lower activity in OER than in ORR,
as found by experiment.
Work in this thesis sheds light upon my future work as a Ph.D. candidate. Future work
includes but not limited to:
" Consider the rate of reconstruction and OER reaction;
" Apply this method to ORR and other catalytic reactions in solution;
" Apply this method to other metal oxides as electrochemical catalysts;
" Investigate the descriptor of surface reconstruction activity by examining its electronic
structure.
54
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