First Principles Studies of the Surface Chemistry of NiFe2O4 ......First Principles Studies of the...

First Principles Studies of the Surface

Chemistry of NiFe2O4 and NixCo3-xO4 Spinel

Oxides

XIAO SHI

A DISSERTATION

PRESENTED TO THE FACULTY

OF PRINCETON UNIVERSITY

IN CANDIDACY FOR THE DEGREE

OF DOCTOR OF PHILOSOPHY

RECOMMENDED FOR ACCEPTANCE

BY THE DEPARTMENT OF

CHEMISTRY

ADVISERS ANNABELLA SELLONI

STEVEN BERNASEK

JUNE 2018

copy Copyright by Xiao Shi 2018

All rights reserved

iii

Abstract Nickel cobaltite NiCo2O4 and nickel ferrite NiFe2O4 are spinel oxides with interesting

catalytic properties Nickel cobaltite oxidizes carbon monoxide and methane while

nickel ferrite is an electrocatalyst for water oxidation These materials have been recently

the focus of intense research aimed at modifying their activities and improving their

performances This thesis describes our theoretical studies of the structural and electronic

properties of nickel cobaltite and nickel ferrite their surfaces and their interactions with

probe molecules

The inverse spinel nickel cobaltite is a promising technological material with complex

electronic and magnetic properties Understanding these properties is important for the

development of novel electronic devices and as a basis for the study of their surface and

catalytic properties We have investigated the bulk electronic and magnetic properties of

nickel cobaltite using Density Functional Theory (DFT) calculations augmented with on-

site Hubbard U repulsion on 3d electrons (DFT+U) Starting from an analysis of nickel

doped cobalt oxides we found that nickel acts as a p-type dopant in Co3O4 NiCo2O4 has

a ferrimagnetic half-metallic ground state with fractional valence on Ni and Co cations at

tetrahedral sites (Td) caused by the partial occupancy of Ni and Co(Td)rsquos eg states We

also determined the formation energies of two relevant defects namely NiharrCo(Td)

exchanges and oxygen vacancies as a function of the values of the U terms Facile

NiharrCo(Td) exchange as observed experimentally was obtained using U values that are

significantly smaller than those predicted by linear response theory Our computed bulk

O-vacancy formation energies suggest that NiCo2O4 is an active oxidant similar to

Co3O4

We next extend our study to NiCo2O4 (NCO) surfaces focusing on the structure defects

and reactivity of (001) surfaces Our results suggest that the formation of surface oxygen

vacancies (VO) on the NCO (001) surface is strongly affected by the neighboring cation

in the 3rd layer In particular Ni in the 3rd layer significantly reduces the VO formation

energy As a result VO formation is generally much easier on NCO (001) than on Co3O4

(001) surfaces suggesting that NCO may be a better catalyst than Co3O4 for oxidation

iv

reactions based on the Mars Van Krevelen mechanism VOs on reduced NCO surfaces

can be healed through dissociative water adsorption at room temperature In contrast

adsorption of molecular oxygen at VOs is energetically unfavorable under ambient

conditions suggesting that O2 adsorption may represent the thermodynamic limiting step

for oxidation reactions on NCO (001) surfaces

We again use DFT+U calculations to investigate the mechanism of the low temperature

CO oxidation reaction (COOR) on Co3O4(110)(001) and NiCo2O4(001) as well as

methane oxidation on NiCo2O4(001) Our results indicate that the COOR is controlled by

the thermodynamics of surface re-oxidation on (001) surfaces and by the kinetic barrier

for CO2 formation on the on Co3O4 (110) surface The COOR is inhibited by water

adsorption at surface oxygen vacancies For methane oxidation the computed barrier of

the first C-H bond agrees well with experimental observations

Nickel ferrite NiFe2O4 is another spinel oxide with interesting properties and

applications particularly as a catalyst for water oxidation We have used DFT+U

calculations to study the structure electronic properties and energetics of the

NiFe2O4(001) surface and its interaction with water both in the absence and in the

presence of surface oxygen vacancies In a humid environment water adsorbs

dissociatively on the surface oxygen vacancies leading to the formation of surface

hydroxyls At high temperature water desorbs leaving a surface containing oxygen

vacancies These defects could represent useful reactive sites for various catalytic

reactions CO and methane oxidation on NiFe2O4 are slightly less favorable in

comparison to NiCo2O4 even though the reaction pathways are similar

v

Acknowledgement

I would like to start by thanking my advisors Prof Annabella Selloni who offered me

the opportunity to work in theoretical and computational chemistry her genial and

kindness helped me a lot through my graduate school life and her altitude toward science

helped me a lot in building a solid and rigorous research altitude Prof Steven Bernasek

who offered me the opportunity to work on this project on spinel oxides his gentle nature

helped me a lot in practicing experiment and have a broader wide in research Without

their support and guidance this dissertation would not be possible

I thank the members in my thesis and general exam committees Prof Robert Cava Prof

Andrew Bocarsly and Prof Carnet Chan for their support on the general exam on the

dissertation and over the years

I would also like to thank Prof Zhenhua Li my mentor at Fudan University who brought

me to the field of computational chemistry

Irsquom also very grateful to the members of Selloni Car and Bernasek Groups especially

Dr Yefei Li Dr Sencer Selcuk Hsinyu Ko Jiming Sun Lukas Muechler Matt Vallon

and Matt Frith for their insightful discussions and helps I also enjoyed the friendship

with them Irsquom also thankful to Duyu Chen and Boxiao Zheng outside my group for

sharing and discussion their research and for their friendship

This list would be incomplete without Robert LrsquoEsperance who has been very helpful and

encouraging through and after my teaching career and Meredith LaSalle-Tarantin and

Meghan Krause who are always very optimistic and kind graduate administrators who

helped me a lot through the whole graduate school

Outside Frick I am also grateful to Ruixiang Zhang my old roommate to Xue Wu who

has almost identical driver license photo with mine to Chen Zhao to Jintao Zhang and

shared a lot of happy moment with them They made my life at graduate school more

wonderful than I could imagine

vi

In the end I would like to thank my family who are always with me and give me full

support regardless of the distance which is almost halfway round the world

vii

Table of Contents Chapter I Introduction 1

1 Nickel Cobaltite NiCo2O4 2

2 Surface Oxidation Reactions on Spinel Cobaltite (MCo2O4) 4

21 CO Oxidation 4

22 Methane Oxidation5

3 Nickel Ferrite NiFe2O4 5

4 Organization of this Thesis 7

5 References 9

Chapter II Method 14

1 Basics of Quantum Chemistry 14

2 Density Functional Theory 16

21 Basis Sets and Pseudopotentials 18

22 Self-Interaction Correction 19

23 Structural Optimization 21

3 Nudged Elastic Band Method 22

4 References 24

Chapter III Formation electronic structure and defects of Ni substituted spinel

cobalt oxide 26

1 Introduction 26

2 Computational details 27

3 Results and Discussion 28

31 Ni substitution in Co3O4 NixCo3-xO4 (x = 0 -1) 28

32 Structure bonding and electronic properties of NCO 31

33 NiharrCo exchanges 36

34 Oxygen vacancies 40

4 Conclusions 43

5 References 45

viii

Chapter IV Oxygen deficiency and reactivity of spinel NiCo2O4 (001) surfaces 49

1 Introduction 49

2 Methods and Models 50


31 Pristine (001) (100) surfaces 51

32 Surface oxygen vacancies 56

33 Water adsorption 65

34 Oxygen adsorption 69

4 Conclusions 73

5 References 75

Chapter V Mechanism and activity of the oxidation reactions (CO and methane)

cobaltite spinels (NCO and Co3O4) 78

1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81

311 CO adsorption 81

312 CO oxidation 83

32 NCO (001)(100) surfaces 87

33 Methane oxidation on NCO (100)mix surface90

331 Methane adsorption and first C-H bond breaking 90

332 Second C-H bond breaking 92

4 Conclusions 92

5 References 94

Chapter VI Structure of the NiFe2O4(001) surface in contact with gaseous O2 and

water vapour and oxidation reactions for CO methane 97

1 Introduction 97



ix

31 Bulk properties 101

32 NiFe2O4 (001) surface 104

321 Defect-free surface 104

322 Surface O vacancy 106


331 Water adsorption on the defect-free surface 108

332 Water adsorption on the defected surface 109

34 Phase diagram 112

35 CO oxidation 113

36 Methane oxidation 115

4 Summary and Conclusions 116

5 References 117

1

Chapter I

Introduction Spinel oxides with formula AB2O4 form a class of compounds that crystallize in the cubic

crystal system and include a variety of divalent trivalent and tetravalent cations Cations

of the iron group (Fe Co and Ni) - being earth abundant similar in chemical properties

and able to form magnetic materials - have an important place within this family For

example magnetite (Fe3O4) which is known as the most magnetic naturally-occurring

mineral on earth is widely used in audio recording Magnetite is also widely used as a

catalyst in ammonia synthesis

Recently there has been a lot of interest in the catalytic activity of Fe Co and Ni spinel

oxides After the discovery of low temperature CO oxidation on cobalt oxide Co3O4 by

Haruta and Shen1 numerous studies have focused on understanding and modifying the

properties of this material For example Gao et al studied the synthesis and activity of

doped and substituted cobalt oxides for low temperature methane oxidation2 Iron based

spinel oxides have also been investigated extensively For example the prediction that

Fe3O4 partially dissociates water3 has motivated several studies of both water-ferrite

interactions and the catalytic activity iron based spinel oxides Potential catalytic

applications range from harvesting solar energy to water gas shift reactions to reduce

exhaust gases 4-5

CO and methane oxidation on doped cobalt oxides is of special interest 6-7 Among the

different spinel cobaltites nickel cobaltite NiCo2O4 is the most promising material for

this purpose8 On the other hand nickel ferrite NiFe2O4 though not active for CO

oxidation was found to be quite active for water oxidation4 In the following sections we

will give a brief introduction to the properties of NiCo2O4 (denoted NCO in this thesis)

and NiFe2O4 (denoted NFO in this thesis) and their catalytic activities

2

1 Nickel Cobaltite NiCo2O4

Nickel cobaltite (NCO) crystallizes in the spinel structure The oxygen anions form a face

centered cubic lattice while octahedral and tetrahedral sites are partially occupied (12 of

octahedral and 18 of tetrahedral) by cations A B Spinel oxides can have two types of

structure normal spinel and inverse spinel Normal spinels (Figure 1a) have all the

tetrahedral sites occupied by cation A and octahedral sites occupied by cation B Inverse

spinels have all the tetrahedral sites occupied by cation B and octahedral sites equally

occupied by both A and B The symmetry on octahedral sites can further lead to either α

or β type inverse spinel (Figure 1b c) NCO is an inverse spinel and prefers the β type

structure The experimental lattice constant is 8115 Aring9 NCO decomposes into NixCo3-

xO4 and NiO at around 400~600 degC10-12 depending on the synthetic procedure used

Figure 1 Spinel AB2O4 a normal spinel where A cations occupy tetrahedral sites and B

cations occupy octahedral sites b α inverse spinel with B cations occupying tetrahedral

sites and A B occupying octahedral sites c β inverse spinel where octahedral sites

along [001] direction are occupied by either A or B

Being an inverse spinel NCO has Co at tetrahedral sites (Co(Td)) and a mixture of Ni

and Co at octahedral sites (Ni(Oh) and Co(Oh)) with both Co(Td) and Ni(Oh) showing

mixed 2+ and 3+ oxidation states13-14 However NiharrCo exchanges at tetrahedral sites

are frequent10 which leads to a reduced degree of inversion of the structure Co(Td) and

Ni(Oh) are in the high and low spin states respectively and contribute to NCOrsquos

magnetic properties NCO is usually found to be ferrimagnetic15 with Co(Td) and Ni(Oh)

having anti-parallel spins However the synthetic procedure can influence NCOrsquos

magnetic ordering16-17 for example high temperature growth may result in diamagnetic

3

order NCOrsquos electronic properties are also interesting as this material shows high

conductivity as well as an optical band gap of 197 eV Single crystal studies10 18-19 could

provide more detailed information on NCOrsquos electronic and magnetic properties but are

rare due to the difficulty of growing good NCO crystals

The surface properties of NCO are important for understanding its oxidation activity The

most stable surfaces of NCO are (001) (111) and (110) for which surface energies of

129 Jm-2 142 Jm-2 and 160 Jm-2 respectively have been computed20 The (001)

surface is the most common surface with predicted abundance of 548 while the

abundance is only 70 for the (110) surface In the following we shall thus focus on

NCO (001) surfaces to learn about active sites and reaction mechanisms Since NCO is β

type inverse spinel 16 of NCO (001) surfaces contain only Co(Oh) cations 16 contain

only Ni(Oh) cations and the remaining 23 contain 50 Ni(Oh) and 50 Co(Oh)

(Figure 2)

Figure 2 Side views of NCO (001)(100) surfaces a pure Ni(Oh) terminated b pure

Co(Oh) terminated and c mix of Ni(Oh) and Co(Oh) termination

2 Surface Oxidation Reactions on Spinel Cobaltites (MCo2O4) 21 CO Oxidation

CO oxidation on spinel Co3O4 was first discovered over 15 years ago and subsequently

similar studies were performed on other doped cobaltites as well1 21 The reaction was

first observed at room temperature for pre-oxidized Co3O422-23 when cobalt oxide was

heated and cooled in oxygen rich environment before being treated with CO the reaction

was found to occur at temperatures as low as 20 degC However the catalyst was found to

4

slowly deactivate over time and the mechanism of the deactivation remained

controversial hindering further development

As the techniques of growing Co3O4 crystals improved it was easier for researchers to

control their shape and exposed surfaces Co3O4 nanorods were later found to steadily

oxidize CO at temperature as low as -77 degC without significant deactivation1 The

nanorods expose both (110) and (001) surfaces (Figure 3) Co3+ ions originating from

octahedral sites are believed to have a key role in the CO oxidation reaction on the

surface The (110) surface was found to be about three times more active than the (001)

surface21

Figure 3 Side views of the Co3O4 (110) and (001) surfaces Both surfaces expose

Co(Oh) with 3+ charge and two types of oxygen sites On the (110) surface an oxygen

atom bonded to 2 (3) Co cations is denoted O2f (O3f) on the (001) surface oxygen atoms

bonded to 3 Co(Oh) are denoted O1 while oxygen atoms bonded to 2 Co(Oh) and 1

Co(Td) are denoted O2

DFT calculations of CO oxidation on the Co3O4(110) surface24-25 show a strong

dependence on the value of Hubbard U term (see also Ref 26) When U = 0 Co3+ is the

preferred adsorption site for CO27 When Hubbard U is applied to achieve a better

description of the thermodynamic and electronic properties CO tends to be adsorbed on

O2f while pointing toward Co3+ 28 Both O2f and Co3+ sites are crucial for the CO

oxidation reaction on the (110) surface In contrast to the numerous studies for the (110)

5

surface the mechanism of CO oxidation has not been studied for the most abundant (001)

surface

22 Methane Oxidation

In the case of methane oxidation Co3O4 is often used as a support for another catalyst29-30

that is more active at breaking the first C-H bond which is usually the rate determining

step of this reaction31 Co3O4 starts to oxidize methane at around 400 degC30 With Ni

doping notably for Ni05Co25O4 the activation barrier was found to be reduced by 35

KJmol2 Further doping leads to NCO which starts to oxidize methane from 200 degC7

Lattice oxygen atoms are involved in the formation of CO2 during the oxidation process

The activation barrier involving Ni on the (110) surface is lower and thus consistent with

the observation that doping Ni would make methane oxidation easier

A recent DFT study examined the methane oxidation activities of Co3O4 (110) and (001)

surfaces32 The (110) surface was found to be more active than the (001) one though the

first C-H bond breaking appears to be easier on (001) However the low activity of O2

sites on the (001) surface (Figure 3) hinders or even prevents further oxidation Methane

oxidation on the (001) surfaces of Co3O4 and NCO could therefore be of great interest for

achieving partial oxidation of methane

3 Nickel Ferrite NiFe2O4

Nickel ferrite (NFO) is an α-type inverse spinel33 with lattice constant of 833 Aring34

Similar to NCO NFO is also ferrimagnetic35 with the spin of Fe(Td) anti-parallel to

Ni(Oh) and Fe(Oh)36 according to DFT calculations The Neacuteel temperature is about 850

K37 An indirect band gap of 16 eV is observed possibly involving d-d and p-d charge

transfer transitions between the correlated bands of Ni2+ and Fe3+ sites Although NFO is

usually insulating tuning the growth conditions to oxygen free environment would

greatly increase its conductivity38

6

Studies of NFO surfaces are still scarce in comparison to those of bulk NFO The growth

direction of NFO crystals is controlled by the substrate39 eg films grown on MgAl2O4

(001) expose the (001) surface Other synthesis conditions like hydrothermal synthesis

lead to crystals preferentially exposing (111) surfaces NFOrsquos chemical properties are

altogether similar to those of Fe3O4 which is known to partially dissociate water on the

(001) surface and fully dissociate water on (111) surface40 However doping Ni into

Fe3O4 was found to substantially enhance the activity of two step water splitting

reactions41-42 suggesting that NFO might be generally more active than Fe3O4 for

reactions involving water For example this might be the case for the water gas shift

(WGS) reaction which was found to be controlled by water adsorption and dissociation

on the ferrite surface5 Recently NFO was shown to photocatalytically oxidize water with

the help of a photosensitizer and an oxidant4 Possible formation of high valence Ni

(Ni3+Ni4+) might be crucial for this photocatalytic reaction

Theoretical calculations can help understand the fundamentals of NFO interaction with

water and interpret how Ni increases the reactivity of Fe3O4 for catalytic reactions

involving water Previous DFT calculations for the NFO (111) surface showed that the

interaction of water with octahedral Fe sites is enhanced by the presence of Ni relative to

tetrahedral Fe and becomes favored thermodynamically43 Water dissociation on Fe(Oh)

is also a barrier free reaction The activity is believed to come from the strong interaction

between the OH σ orbitals and Fe d orbitals The NFO (001) surface also exposes

Fe(Oh) sites with one of its octahedral ligand site empty and able to bind a water

molecule or an OH group Our theoretical study of water adsorption on the NFO (001)

surface (Figure 4) is discussed in detail in Chapt VI

7

Figure 4 Water adsorption and dissociation on NFO (001) surface with water adsorbed

on oxygen vacancies and on top of Fe and Ni

4 Organization of this Thesis

In the next chapter we review the methods used for this work and will give a brief

summary of the relevant theoretical background

In chapter 3 we investigate the thermodynamic and electronic properties of bulk NCO

As mentioned above NCO exhibits interesting electronic and magnetic properties eg

coexistence of high conductivity with a large band gap whose origin was not well

understood Our results show the existence of fractional valence states for Co(Td) and

Ni(Oh) which largely determine NCOrsquos properties

In chapter 4 we extend our study to NCO (001)(100) surfaces which were predicted to

be the most abundant surfaces of this material20 A recent study of methane oxidation on

NCO7 suggests that the formation of surface oxygen vacancies might be a key to

understand NCOrsquos surface reactivity Focusing on the thermodynamics of (001)(100)

surfaces we show that Ni prefers to segregate to the surface The Ni (Oh) close to the

surface will significantly influence the formation of oxygen vacancies (VO) and thus

8

possibly improve the catalytic performance Furthermore re-oxidation of the reduced

surface is difficult and could possibly limit the activity on (001)(100) surfaces

Chapter 5 examines the mechanism of CO and methane oxidation on NCO (001)(100)

surfaces in comparison to Co3O4 Since experiments show that CO oxidation on Co3O4

is very efficient on the (110) surface whereas the (001) surface is less active21 previous

theoretical studies focused on the Co3O4 (110) surface27 and did not examine the

difference between (110) and (001) surfaces Our results indicate that CO is oxidized

more easily on Co3O4NCO (001) than on the (110) surface due to easier VO formation

On (001) however it is more difficult to recover the active surface after the first

oxidation Our additional study of methane oxidation on NCO (100) shows that the

kinetic barrier for the first C-H bond breaking (the well-known rate determining step of

methane oxidation) is smaller than that reported for doped CeO2 a well know low

temperature methane oxidation catalyst This result thus confirms the strong NCOrsquos

activity for methane activation

In chapter 6 we investigate the structure of the NFO (001) surface and its interaction

with water We study the thermodynamics of water adsorption including the effect of

surface oxygen vacancies Our results show that water adsorbs preferentially on VO sites

where it tends to dissociate Results for CO and methane oxidation on NFO (001) are also

presented

9

5 References

1 Xie X Li Y Liu Z-Q Haruta M Shen W Low-Temperature Oxidation of

Co Catalysed by Co3o4 Nanorods Nature 2009 458 746-749

2 Ren Z Botu V Wang S Meng Y Song W Guo Y Ramprasad R Suib

S L Gao P-X Monolithically Integrated Spinel Mxco3minusXo4(M=Co Ni Zn)

Nanoarray Catalysts Scalable Synthesis and Cation Manipulation for Tunable Low-

Temperature Ch4and Co Oxidation Angew Chem Int Ed 2014 126 7351-7355

3 Mulakaluri N Pentcheva R Wieland M Moritz W Scheffler M Partial

Dissociation of Water on Fe_3O_4(001) Adsorbate Induced Charge and Orbital

Order Physical Review Letters 2009 103

4 Hong D Yamada Y Nagatomi T Takai Y Fukuzumi S Catalysis of

Nickel Ferrite for Photocatalytic Water Oxidation Using [Ru(Bpy)3]2+and S2o82ndash

Journal of the American Chemical Society 2012 134 19572-19575

5 Reddy G K Gunasekera K Boolchand P Dong J Smirniotis P G High

Temperature Water Gas Shift Reaction over Nanocrystalline Copper Codoped-Modified

Ferrites The Journal of Physical Chemistry C 2011 115 7586-7595

6 Zhu J Gao Q Mesoporous Mco2o4 (M=Cu Mn and Ni) Spinels Structural

Replication Characterization and Catalytic Application in Co Oxidation Microporous

Mesoporous Mater 2009 124 144-152

7 Tao F F Shan J-j Nguyen L Wang Z Zhang S Zhang L Wu Z

Huang W Zeng S Hu P Understanding Complete Oxidation of Methane on Spinel

Oxides at a Molecular Level Nat Commun 2015 6 7798

8 Bitla Y et al Origin of Metallic Behavior in Nico2o4 Ferrimagnet Scientific

Reports 2015 5 15201

9 Nkeng P Characterization of Spinel-Type Cobalt and Nickel Oxide Thin Films

by X-Ray near Grazing Diffraction Transmission and Reflectance Spectroscopies and

Cyclic Voltammetry J Electrochem Soc 1995 142 1777

10 Iliev M N Silwal P Loukya B Datta R Kim D H Todorov N D

Pachauri N Gupta A Raman Studies of Cation Distribution and Thermal Stability of

Epitaxial Spinel Nico2o4 Films J Appl Phys 2013 114 033514

10

11 Cabo M s Pellicer E Rossinyol E Castell O Surinach S Baro M D

Mesoporous Nico2o4spinel Influence of Calcination Temperature over Phase Purity and

Thermal Stability Cryst Growth Des 2009 9 4814-4821

12 Lapham D P Tseung A C C The Effect of Firing Temperature Preparation

Technique and Composition on the Electrical Properties of the Nickel Cobalt Oxide

Series Nixco1 - Xoy Journal of Materials Science 2004 39 251-264

13 Marco J F Gancedo J R Gracia M Gautier J L Riacuteos E I Palmer H M

Greaves C Berry F J Journal of Materials Chemistry 2001 11 3087-3093

14 Marco J F Gancedo J R Gracia M Gautier J L Riacuteos E Berry F J

Characterization of the Nickel Cobaltite Nico2o4 Prepared by Several Methods An

Xrd Xanes Exafs and Xps Study J Solid State Chem 2000 153 74-81

15 Cui B Lin H Liu Y-z Li J-b Sun P Zhao X-c Liu C-j

Photophysical and Photocatalytic Properties of Core-Ring Structured

Nico2o4nanoplatelets J Phys Chem C 2009 113 14083-14087

16 Dileep K Loukya B Silwal P Gupta A Datta R Probing Optical Band

Gaps at Nanoscale from Tetrahedral Cation Vacancy Defects and Variation of Cation

Ordering in Nico2o4epitaxial Thin Films J Phys D Appl Phys 2014 47 405001

17 Zakutayev A Paudel T R Ndione P F Perkins J D Lany S Zunger A

Ginley D S Cation Off-Stoichiometry Leads to Highp-Type Conductivity and

Enhanced Transparency in Co2zno4and Co2nio4thin Films Phys Rev B 2012 85

085204-1 - 085204-8

18 Silwal P Miao L Stern I Zhou X Hu J Ho Kim D Metal Insulator

Transition with Ferrimagnetic Order in Epitaxial Thin Films of Spinel Nico2o4 Appl

Phys Lett 2012 100 032102

19 Silwal P Miao L Hu J Spinu L Ho Kim D Talbayev D Thickness

Dependent Structural Magnetic and Electronic Properties of the Epitaxial Films of

Transparent Conducting Oxide Nico2o4 J Appl Phys 2013 114 103704

20 Zasada F Gryboś J Indyka P Piskorz W Kaczmarczyk J Sojka Z

Surface Structure and Morphology of M[Comprime]O4(M = Mg Zn Fe Co and Mprime = Ni Al

Mn Co) Spinel NanocrystalsmdashDft+U and Tem Screening Investigations J Phys Chem

C 2014 118 19085-19097

11

21 Hu L Sun K Peng Q Xu B Li Y Surface Active Sites on Co3o4 Nanobelt

and Nanocube Model Catalysts for Co Oxidation Nano Research 2010 3 363-368

22 Jansson J Low-Temperature Co Oxidation over Co3o4Al2o3 Journal of

Catalysis 2000 194 55-60

23 Jansson J Palmqvist A E C Fridell E Skoglundh M Oumlsterlund L

Thormaumlhlen P Langer V On the Catalytic Activity of Co3o4 in Low-Temperature Co

Oxidation Journal of Catalysis 2002 211 387-397

24 Broqvist P A Dft Study on Co Oxidation over Co3o4 Journal of Catalysis

2002 210 198-206

25 Xu X L Li J Q Dft Studies on H2o Adsorption and Its Effect on Co

Oxidation over Spinel Co3o4 (110) Surface Surface Science 2011 605 1962-1967

26 Selcuk S Selloni A Dft+U Study of the Surface Structure and Stability of

Co3o4(110) Dependence on U J Phys Chem C 2015 119 9973-9979

27 Pang X-Y Liu C Li D-C Lv C-Q Wangthinsp G-C Structure Sensitivity of

Co Oxidation on Co3o4 A Dft Study ChemPhysChem 2013 14 204-212

28 Xu X-L Yang E Li J-Q Li Y Chen W-K A Dft Study of Co Catalytic

Oxidation by N2o or O2on the Co3o4(110) Surface ChemCatChem 2009 1 384-392

29 Liotta L F Di Carlo G Pantaleo G Deganello G Catalytic Performance of

Co3o4Ceo2 and Co3o4Ceo2ndashZro2 Composite Oxides for Methane Combustion

Influence of Catalyst Pretreatment Temperature and Oxygen Concentration in the

Reaction Mixture Applied Catalysis B Environmental 2007 70 314-322

30 Hoflund G B Li Z Surface Characterization Study of a PdCo3o4 Methane

Oxidation Catalyst Applied Surface Science 2006 253 2830-2834

31 Arndtsen B A Bergman R G Mobley T A Peterson T H Selective

Intermolecular Carbon-Hydrogen Bond Activation by Synthetic Metal Complexes in

Homogeneous Solution Accounts of Chemical Research 1995 28 154-162

32 Hu W Lan J Guo Y Cao X-M Hu P Origin of Efficient Catalytic

Combustion of Methane over Co3o4(110) Active Low-Coordination Lattice Oxygen and

Cooperation of Multiple Active Sites ACS Catalysis 2016 6 5508-5519

12

33 Ivanov V G Abrashev M V Iliev M N Gospodinov M M Meen J

Aroyo M I Short-Range B-Site Ordering in the Inverse Spinel Ferrite Nife_2O_4

Physical Review B 2010 82

34 Baltzer P K White J G Crystallographic and Magnetic Studies of the System

(Nife2o4)1minusX + (Nimn2o4)X Journal of Applied Physics 1958 29 445

35 Hutlova A Niznansky D Plocek J Bursik J Rehspringer J-L Journal of

Sol-Gel Science and Technology 2003 26 473-477

36 Perron H Mellier T Domain C Roques J Simoni E Drot R Catalette

H Structural Investigation and Electronic Properties of the Nickel Ferrite Nife2o4 A

Periodic Density Functional Theory Approach Journal of Physics Condensed Matter

2007 19 346219

37 Šepelaacutek V Baabe D Mienert D Schultze D Krumeich F Litterst F J

Becker K D Evolution of Structure and Magnetic Properties with Annealing

Temperature in Nanoscale High-Energy-Milled Nickel Ferrite Journal of Magnetism and

Magnetic Materials 2003 257 377-386

38 Luumlders U Bartheacuteleacutemy A Bibes M Bouzehouane K Fusil S Jacquet E

Contour J P Bobo J F Fontcuberta J Fert A Nife2o4 A Versatile Spinel Material

Brings New Opportunities for Spintronics Advanced Materials 2006 18 1733-1736

39 Luumlders U Bibes M Bobo J F Fontcuberta J Tuning the Growth Orientation

of Nife2o4 Films by Appropriate Underlayer Selection Applied Physics A 2005 80 427-

431

40 Zhou C Zhang Q Chen L Han B Ni G Wu J Garg D Cheng H

Density Functional Theory Study of Water Dissociative Chemisorption on the

Fe3o4(111) Surface The Journal of Physical Chemistry C 2010 114 21405-21410

41 Gokon N Murayama H Nagasaki A Kodama T Thermochemical Two-Step

Water Splitting Cycles by Monoclinic Zro2-Supported Nife2o4 and Fe3o4 Powders and

Ceramic Foam Devices Solar Energy 2009 83 527-537

42 Gokon N Mataga T Kondo N Kodama T Thermochemical Two-Step

Water Splitting by Internally Circulating Fluidized Bed of Nife2o4 Particles Successive

Reaction of Thermal-Reduction and Water-Decomposition Steps International Journal

of Hydrogen Energy 2011 36 4757-4767

13

43 Kumar P V Short M P Yip S Yildiz B Grossman J C High Surface

Reactivity and Water Adsorption on Nife2o4(111) Surfaces The Journal of Physical

Chemistry C 2013 117 5678-5683

14

Chapter II

Methods The development of computational methods has progressed enormously within the

scientific and engineering communities over the last few decades The increase in

computational power makes solving previous unpractical problems and questions viable

Nowadays computation has become an indispensable research tool alongside with

experiment

In this chapter we shall briefly introduce the computational methods used to obtain the

results presented in this thesis Our basic tool is Density Functional Theory (DFT)

currently one of the most important tools in the field of computational chemistryphysics

and materials science Our discussion is limited to the scope of this thesis and one should

refer to many other text books available for a more comprehensive presentation

1 Basics of Quantum Chemistry

Just as Newtonrsquos laws of motions offered fundamental principles to describe the

movement of classical objects like earth and moon the motion of quantum particles like

single atoms or molecules is described by Schroumldinger equation expressed as the

following in non-relativistic form

minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627

Here Ψ is the wave function a mathematical description of the quantum state of an

isolated system which contains all the information about this system and Ĥ is the

Hamiltonian operator which corresponds to the total energy of the system described by

Ψ

Without loss of generality Ψ can be written as a linear combination of wave functions

Ψn where Ψns are eigenvectors for Ĥ and satisfy

15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

Thus Ĥ contains all the system specific information For the systems of interest in

chemistry Ĥ is usually composed of the kinetic energies of nuclei and electrons and the

potential energies of the electrostatic interactions among nuclei between nuclei and

electrons and among electrons themselves

The first basic approximation used to reduce the complexity of chemical systems is the

BornndashOppenheimer approximation The success of this approximation is due to the huge

difference between the mass of the electron and that of the nuclei for example the

lightest nucleus the proton is 1835 times heavier than an electron while the O and Co

nuclei are over 20000 times heavier than electron As a result nuclei move at a much

smaller rate in comparison to electrons and their velocity is negligible Thus one can

separate the pure nuclear energy (nuclear kinetic energy and nuclei-nuclei electrostatic

interaction) in an adiabatic process where Ψ is decomposed into the product of an

electron Ψel and a nuclear Ψnu wavefunction As a consequence one only needs to

solve the electronic Schroumldinger equation as the first step The solution of Schroumldinger

equation can be used to construct the potential for the nuclei Schroumldinger equation In

most cases the nuclei can be treated classically and further reduce the computational cost

for the system

Solving the electronic Schroumldinger equation is the key to study chemical systems Except

for the simple case of a hydrogen atom one still needs to consider a many electron

system where an analytical solution is hard to achieve A common practice to solve the

problem is by mean field theory where an electron is treated as subjected to the mean

field created by all other particles Thus the current wave function Ψel determines the

electronic Hamiltonian Ĥel from which a new wave function Ψel can be calculated When

starting with a reasonable guess for Ψel one can iteratively update Ψel and Ĥel until

convergence is achieved This is known as the self-consistent field method Hartree-Fock

theory as one of the earliest realizations of this approach

16

2 Density Functional Theory

Even within Hartree-Fock theory calculating the electronic wave function can be still

difficult and computationally intensive For example a typical NCO model investigated

in this thesis involves around 600 electrons and around 1500 basis functions

Building on the ideas in the Thomas-Fermi model Walter Kohn and Pierre Hohenberg

rigorously demonstrated that the ground state properties of a many-electron system eg

interacting electron gas with external field like fixed nuclei from BornndashOppenheimer

approximation are uniquely determined by the 3-dimensional charge density as long as

the ground state is non-degenerate and there is no external magnetic field1 This is known

as the first Hohenberg-Kohn theorem They subsequently demonstrated the second

Hohenberg-Kohn theorem which states that the true ground state electron density

minimizes the systemrsquos total energy These theorems provide the foundation for Density

Functional Theory (DFT) where the number of degrees of freedom is reduced from 3N

(for N electrons) to 3 Soon afterward Hohenberg-Kohnrsquos results were generalized to

degenerate systems2 and systems in the presence of an external magnetic field3-4 Time

dependent DFT was also proposed in the attempt to describe excited states5

The two Hohenberg-Kohn theorems suggest that for a given number of electrons N

defined by 119873119873 = int119899119899(119903119903)119889119889119903119903 and charge density 119899119899(119903119903) = 119873119873int1198891198891199031199032 ∙∙∙ int 119889119889119903119903119899119899 120569120569lowast(119903119903 1199031199032∙∙∙

119903119903119899119899)120569120569(119903119903 1199031199032∙∙∙ 119903119903119899119899) there are universal functionals 119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)] that represent the

kinetic energy of the electrons and the potential energy of their interaction in the ground

state On the other hand the external field influence is described by a non-universal

functional 119881119881119890119890119890119890119890119890[119899119899(119903119903)] As a result the total energy can be expressed in the following

form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903

This equation can be solved variationally provided one is able to find proper forms of

119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]

An effective method to construct such functional was proposed by Kohn and Sham in

19656 They separated the electron-electron interaction 119880119880[119899119899(119903119903)] into two parts The first

17

part treats the classical Coulomb interaction of the electron density to account for

electron-electron repulsion The second part accounts for the exchange energy and

correlation effects that are ignored when electrons are treated as electron density Thus

119880119880[119899119899(119903119903)] can be expressed as

119880119880[119899119899(119903119903)] =12

119899119899(119903119903) ∙ 119899119899(119903119903prime)|119903119903 minus 119903119903prime|

119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]

Here the first term is the Coulomb interaction and the second term is the exchange-

correlation energy

The kinetic energy 119879119879[119899119899(119903119903)] being a unique functional of 119899119899(119903119903) can be solved exactly for

non-interacting electrons with the same density as the system of interest Thus only the

exchange-correlation term is unknown The original solution suggested by Kohn and

Sham is to borrow this term from the homogeneous electron gas (HEG) with the same

local density of the system of interest (note that HEGrsquos exchange energy can be

expressed analytically while its correlation part can be calculated numerically) This leads

to the following expression for the exchange-correlation energy

119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903

This expression is known as the local density approximation (LDA) and is still widely

used However the LDA fails in systems where rapid changes of density occur such as

in many small molecules In our work we applied another widely used approximation

the generalized gradient approximation (GGA) which improves the LDA exchange-

correlation functional by accounting for the spatial variation of the density and usually

offers better result

119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903

More detailed discussion of the GGA can be found in the article by Perdew Burke and

Ernzerhof7 where the so-called PBE functional is introduced

18

21 Basis Sets and Pseudopotentials

The analytical form of electronic wave function Ψel is not known for most chemical

systems Hence it is often convenient to use some basis set of know functions that can be

linearly combined to approximate the real wave function For periodic systems as

considered in this thesis plane waves 119890119890119894119894119896119896 119903119903 are a good choice according to Blochrsquos

theorem as any square-integrable continuous function can be expanded into an infinite

series of plane waves In practice however truncation of the plane waves is always

necessary to make the calculations feasible Usually good accuracy can be achieved with

careful selection of the truncation threshold

Figure 5 scheme of pseudopotential (PS) its corresponding wave function and compared

with all electron potential and wave functions where they converge at cutoff radius

19

For some system the like hydrogen atom the wave function is smooth and can be

described quite well with relatively few basis functions However when systems become

more complicated eg transition metals like Fe and Ni some wave functions start to

change rapidly and sharply One needs to include a huge amount of basis functions to

better describe the wave function Luckily for most chemical systems the region where

the wave function is rapidly changing is always close to the core electrons which form a

closed shell structure In the chemical relevant region for valence electrons the wave

functions are usually relatively smooth Thus the core electrons together with the nuclei

can be regarded as a pseudo core that can be conveniently described via pseudo potentials

for the valence electrons thus saving computational time and achieving smoother pseudo

wave functions (Figure 5)

The first type of pseudopotentials that were proposed for use within DFT were called

norm-conserving pseudo potentials (NCPPs)8 Three main criteria exist for constructing a

NCPP First the energy eigenvalues of the valence orbitals should be the same given by

all electron calculations second the wave function should replicate the all electron wave

function beyond a cut off radius as this is the key region where bonds form between

different atoms The last criterion for NCPP is that the total charge is preserved for the

valence electron density A drawback of NCPPs is that they often require a large basis set

to represent the wavefunction especially for 2 p and 3 d series elements Thus this thesis

will adopt another type of pseudo potentials the so-called ultrasoft pseudopotentials

(USPPs)9 With these pseudopotentials the shape of pseudo wave functions in softened

in the core region while conservation of the total charge is dealt with using some

reshaping operator As a consequence USPPs though more complicated to generate with

good transferability usually reduce the computational cost substantially by allowing the

use of significantly smaller basis sets

22 Self-Interaction Correction

The self-interaction error (SIE) is a common type of issue occurring in DFT and makes

many predictions less meaningful quantitatively It originates from the Hartree term

20

electrostatic potential that comes from the charge distribution for multiple electrons

system The expression

119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)

|119903119903 minus 119903119903prime|119889119889119903119903prime

represents the potential energy of an electron moving in the field generated by the

electronic charge density 119899119899(119903119903) However 119899119899(119903119903) also includes the electron itself thus

leading to unphysical repulsion between the electron and itself As a consequence this

repulsion would usually result in wrongly delocalized charge The effect of SIE is

significant in many strongly correlated materials like transition metal oxides that have d

electrons and results in smaller band gap than expected and also results in inaccurate

thermodynamic and kinetic properties

This thesis focuses on iron group spinel oxides where transition metals Fe Co and Ni are

studied in their 2+ and 3+ charge states All these cations contain 3 d electrons and thus

SIE will be a big issue Taking a step backward Hartree-Fock theory offers an exchange

term which exactly cancels the SIE influence Inspired by Hartree-Fock theory

researchers mixed the exact exchange with the DFT exchange and correlation in order to

handle the SIE error This is known as the hybrid functional DFT method where the

exact exchange usually accounts for 20-25 of the exchange energy as in the well-

known B3LYP and PBE0 functionals10-11 However due to the inclusion of exact

exchange hybrid functionals are quite computationally demanding for many systems For

the systems of interest in this thesis like NCO another method of correction called

DFT+U12 is more commonly used DFT+U is more than ten times computationally

cheaper than hybrid DFT while keeping sufficient accuracy and is thus more

convenient The idea of DFT+U comes from the Hubbard model and introduces on-site

Coulomb interaction for localized electrons especially d and f electrons This new

potential helps reduce SIE and is given by the following expression

119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21

Here λ is the occupation number for the orbital and spin lσ and varies between 0 and 1 l

is the index for orbital angular momentum σ represents the spin channel and i is the

atomic index 119899119899119897119897119897119897 is the charge density projected onto the specific lσ orbital As seen by

the formula when λ=10 meaning the orbital is either occupied or empty the Hubbard U

correction will have no contribution When λ is close to 05 the correction is maximized

As a consequence it will penalize those electrons especially d and f electrons which

become delocalized U can be determined ab initio by application of linear response

theory13-14 In practice however U is often determined empirically by fitting to

experiment typically to thermodynamic results15

23 Structural Optimization

In section 21 and 22 we introduced the general procedures of how to determine the

electronic structure within the BornndashOppenheimer approximation The problem of the

ionic motion such as the determination of the optimal atomic geometry still needs to be

addressed As mentioned earlier the ionic motion is usually regarded as a classical

problem That is the goal is to find the ionic coordinates 119877119877 that minimize the potential

energy defined by 119877119877 and the electron density 120569120569119890119890119897119897119877119877 2 This defines an optimization

problem Thus the minimized structure will be in some local minimum where nabla 119881119881119877119877 =

0 and nabla 2119881119881119877119877 gt 0 The first criteria equivalent to classic force equal to zero indicates

no tendency toward moving when in equilibrium and the second criteria indicates the

structure is in a stable state Optimization problems are widely seen in different fields in

science and engineering and are very well studied The simplest method to solve

optimization problem is by the steepest descent algorithm where the optimization goes

into the opposite direction of the gradient nabla 119881119881119877119877 However when the gradient is small

as it always is when close to the local minimum steepest descent is very slow and takes a

lot of time to converge This problem can be overcome by applying momentum or

Newtonrsquos method In Newtonrsquos method the second order derivative nabla 2119881119881119877119877 also known

as Hessian matrix is calculated to help determine the optimization step length and thus

greatly reduce the optimization steps However in many systems such as the NCO in this

22

thesis calculating the Hessian is too expensive and should be avoided Instead we

applied a quasi-Newton method called Broyden ndash Fletcher ndash Goldfarb ndash Shanno (BFGS)

algorithm16 where only the initial Hessian is calculated accurately and is successively

updated with previous step information

3 Nudged Elastic Band Method

Aside from structural optimization which explores thermodynamic properties it is often

desirable to determine the systemrsquos kinetic properties eg finding the reaction pathways

and activation energies These can be obtained from the total energies of transition states

which can be determined by DFT alongside the total energies of the reactants and

products A popular method for this purpose is the nudged elastic band (NEB) method an

improved algorithm derived from the elastic band method17 The elastic band method

starts with creating a number of intermediate structures also known as images linearly

interpolated and in most cases evenly distributed between the reactant and product Each

of these images is assumed to be connected to the closest images by springs thus

preventing them to relax into the same local minimum Thus as a result the springs add

additional forces onto the total force where the force of atom j in image i can be

expressed as shown below

119865119894119894119894119894 = minusnabla 119881119881119877119877 119894119894119894119894 + 119896119896119894119894+1119877119877 119894119894+1 minus 119877119877 119894119894 minus 119896119896119894119894119877119877 119894119894 minus 119877119877 119894119894minus1

However forces added by springs may shift the structure away from the minimum energy

path In the actual minimum energy path the force minusnabla 119881119881119877119877 119894119894119894119894 should be on the pathway

and the force perpendicular to the pathway should be 0 Thus in the NEB the force is

decomposed into two parts first the true force perpendicular to the pathway to optimize

the structure onto the pathway and second the spring force projected onto the direction

or tangent of the reaction pathway (Figure 6)

119865119894119894119894119894 = minusnabla 119881119881119877119877 119894119894119894119894perp + 119896119896119894119894+1119877119877 119894119894+1 minus 119877119877 119894119894 minus 119896119896119894119894119877119877 119894119894 minus 119877119877 119894119894minus1∥

23

Figure 6 NEB method showing the force and optimization path Forces on the 5th image

are shown in the enlarged region where the black arrow indicates the true force

However the force projected onto the path (blue arrow) is not used whereas the force

coming from the spring (red arrow) is used on the path

Though NEB constrains all the images onto the reaction path it still doesnrsquot give the

structure of the saddle point To determine the latter the climbing image technique is

applied to a single image to move it to the saddle point18 The force part perpendicular to

the path remains the same as in the NEB method while the parallel force is the inverse

of the true force projected onto the path Thus the image is climbing uphill toward the

saddle point and stopped there

24

4 References

1 Hohenberg P Kohn W Inhomogeneous Electron Gas Physical Review 1964

136 B864-B871

2 Levy M Universal Variational Functionals of Electron Densities First-Order

Density Matrices and Natural Spin-Orbitals and Solution of the V-Representability

Problem Proceedings of the National Academy of Sciences 1979 76 6062-6065

3 Vignale G Rasolt M Density-Functional Theory in Strong Magnetic Fields

Physical Review Letters 1987 59 2360-2363

4 Grayce C J Harris R A Magnetic-Field Density-Functional Theory Physical

Review A 1994 50 3089-3095

5 Runge E Gross E K U Density-Functional Theory for Time-Dependent

Systems Physical Review Letters 1984 52 997-1000

6 Kohn W Sham L J Self-Consistent Equations Including Exchange and

Correlation Effects Physical Review 1965 140 A1133-A1138

7 Perdew J P Burke K Ernzerhof M Generalized Gradient Approximation

Made Simple Physical Review Letters 1996 77 3865-3868

8 Hamann D R Schluumlter M Chiang C Norm-Conserving Pseudopotentials


9 Vanderbilt D Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue

Formalism Physical Review B 1990 41 7892-7895

10 Stephens P J Devlin F J Chabalowski C F Frisch M J Ab Initio

Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density

Functional Force Fields The Journal of Physical Chemistry 1994 98 11623-11627

11 Perdew J P Ernzerhof M Burke K Rationale for Mixing Exact Exchange

with Density Functional Approximations The Journal of Chemical Physics 1996 105

9982-9985

12 Anisimov V I Zaanen J Andersen O K Band Theory and Mott Insulators

Hubbarduinstead of Stoneri Physical Review B 1991 44 943-954

13 Cococcioni M de Gironcoli S Linear Response Approach to the Calculation of

the Effective Interaction Parameters in Thelda+Umethod Physical Review B 2005 71

25

14 Kulik H J Cococcioni M Scherlis D A Marzari N Density Functional

Theory in Transition-Metal Chemistry A Self-Consistent Hubbarduapproach Physical

Review Letters 2006 97

15 Wang L Maxisch T Ceder G Oxidation Energies of Transition Metal Oxides

within Thegga+Uframework Physical Review B 2006 73

16 Liu D C Nocedal J On the Limited Memory Bfgs Method for Large Scale

Optimization Mathematical Programming 1989 45 503-528

17 JOacuteNsson H Mills G Jacobsen K W Nudged Elastic Band Method for

Finding Minimum Energy Paths of Transitions 1998 385-404

18 Henkelman G Uberuaga B P Joacutensson H A Climbing Image Nudged Elastic

Band Method for Finding Saddle Points and Minimum Energy Paths The Journal of

Chemical Physics 2000 113 9901-9904

26

Chapter III

Formation electronic structure and

defects of Ni substituted spinel cobalt

oxide

1 Introduction

Nickel cobaltite NiCo2O4 (NCO) is an emerging technological material with a variety of

promising applications ranging from supercapacitors1-4 to catalysts for CH4 and low

temperature CO oxidation5-7 For instance a recent study has shown that NCO can

completely oxidize methane to CO2 and water in the temperature range of 350ndash550 C7

Considering that NCO is also a cheap material made of earth-abundant elements this result

suggests that NCO may be a better methane oxidation catalyst than typical precious-metal-

based catalysts8

NCO is generally considered to have an inverse spinel structure with mixed valence

typically expressed as 1198621198621198621198621198901198902+1198621198621198621198621minus1198901198903+ [1198621198621198621198623+1198731198731198941198941minus1198901198902+ 1198731198731198941198941198901198903+]1198741198744 where tetrahedral (Td) sites are

occupied by both Co2+ and Co3+ ions and octahedral (Oh) sites are occupied by Ni2+ Ni3+

and Co3+ ions9-11 However evidence for Ni(Td) ions is also reported indicating that

Ni(Oh)harr Co(Td) exchanges can take place rather easily9 Co(Oh) ions are non-magnetic

whereas Co(Td) and Ni(Oh) tend to have anti-parallel spins (see Figure 7c) so that the

material is usually found to be ferrimagnetic10 12 However synthesis conditions can

influence the magnetic order which has led to some contradictory results12-14 Only a few

studies on NCO single crystals have been conducted9 15-16 these confirmed that NCO is

ferrimagnetic and metallic and the electronic and magnetic behaviors are strongly

correlated with the concentration of Ni3+(Oh) ions17 NCO was also reported to become

unstable around 600 degC in vacuum and to partially decompose into NiO and NixCo3-xO49

The loss of oxygen suggests that oxygen vacancies would form in this process Oxygen

27

vacancies are common and important defects in metal oxides18 but their effects on NCO

are not clearly understood Theoretical studies on NCO are also scarce various bulk13 19

and surface7 20 properties have been investigated but many aspects of the behavior of this

material eg the origin of the half-metallic ferrimagnetic structure and the influence of

oxygen vacancies are still largely unexplored

With the growing interest in using NCO for various applications a more detailed and

complete understanding of the structure and electronic properties of this material would be

desirable This has motivated us to carry out first principles calculations on defect-free and

defected bulk of NCO using Density Functional Theory (DFT) with on-site Coulomb

repulsion (DFT+U) As a first step we have studied the evolution from Co3O4 to NCO by

determining the substitution energies and the atomic and electronic structures of NixCo3-

xO4 as a function of the doping ratio x from x=0 to x=1 Our results show that Ni acts as a

p-type dopant in Co3O4 and is fractionally occupied This leads to a half-metallic

ferrimagnetic structure for NCO consistent with previous calculations13 19 and recent

experiments14 17 Typical bulk defects notably Ni(Oh)harr Co(Td) exchanges and oxygen

vacancies have been studied using different U values Facile NiharrCo(Td) exchange as

observed experimentally can be reproduced using U values smaller than those determined

from first principles linear response theory Oxygen vacancies occur preferentially at sites

coordinated to a larger number of Ni ions with a computed formation energy similar to

that found for pure spinel cobalt oxide

2 Computational details

Spin-polarized DFT calculations were performed using the plane-wave-pseudopotential

scheme as implemented in the Quantum Espresso package21 Exchange and correlation

terms were described using the Perdew-Burke-Ernzerhof (PBE)22 functional with on-site

Coulomb repulsion U term on Co and Ni 3 d electrons Unless otherwise specified we used

the U values determined from first principles linear response theory23 denoted as ULR

notably ULR(Ni) = 66 eV for nickel and ULR(Co) = 44 eV and 67 eV for Co ions at Td

site and Oh sites respectively Ultrasoft pseudopotentials24 were generally employed

28

where valence electrons include O 2 s 2 p Co 3 d 4 s and Ni 3 d 4 s states Kinetic energy

cutoffs used were 50 Ryd and 500 Ryd for wave function and augmented density

respectively Selected calculations using norm-conserving pseudopotentials25 were also

performed in this case a kinetic energy cutoff of 100 Ryd was used Structural

optimizations were carried out by relaxing all atoms until forces were smaller than 1 times 10-

3 au Calculations were performed using the 56-atom conventional cubic cell containing 8

formula units (Figure 7) with a 3 times 3 times 3 Monkhorst-Pack k-point mesh to sample the

Brillouin zone All results eg total energies or magnetic moment that are reported in the

following will be referred to this conventional unit cell Wannier functions were calculated

using the wannier 90 code26

Figure 7 Conventional cell of (a) α type and (b) β type inverse spinel The β-type inverse

spinel structure was used in most calculations (c) Spin occupations of the 3d states of Ni

and Co ions in the β-type inverse spinel structure as obtained from our calculations (sect

32) red arrows for Ni and Co(Td) indicate fractional occupation of the corresponding

orbitals

3 Results and Discussion 31 Ni substitution in Co3O4 NixCo3-xO4 (x = 0 -1)

We studied the formation of NCO starting from the normal spinel Co3O4 and successively

substituting 8 Co at the octahedral sites of a 56 atom cubic supercell with Ni atoms thus

gradually increasing the doping ratio from x=0 to x=1 by steps Δx=18 By this procedure

the resulting NCOrsquos structure is an inverse spinel with tetrahedral sites occupied by Co

only For each x the lattice constant was determined from the Birch-Murnagham equation

29

of state and found to increase linearly with increasing doping ratio x by ~001 Aring per 18

change in x (see Table 1) For Co3O4 we determined a lattice constant of 8149 Aring which

is 09 larger than the experimental value 8085 Aring27 while the computed lattice constant

for NCO is 8237 Aring which is about 15 larger than the experimental value of 8115 Aring27

Doping energies were determined from the expression

119864119864119889119889119889119889119889119889119894119894119899119899119889119889 = 1198641198641198731198731198941198941199091199091198621198621198891198893minus1199091199091198741198744 minus 11986411986411986211986211988911988931198741198744 minus 119909119909120583120583119873119873119894119894 + 119909119909120583120583119862119862119889119889119909119909

Table 1 Lattice constant bulk modulus and doping energy of NixCo3-xO4 for different

values of x calculated using DFT+ULR The doping energies are determined for

different orderings of the spins on Co(Td) ions The preferred ordering is anti-parallel in

Co3O4 and parallel in NCO

Doping ratio x Lattice

constant a0 Aring

Bulk modulus B

GPa

Doping energy eV

Spin parallel Spin anti-

parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119

Whereas for the above formula 1198641198641198731198731198941198941199091199091198621198621198891198893minus1199091199091198741198744 and 11986411986411986211986211988911988931198741198744 are the total energies of NixCo3-

xO4 and Co3O4 respectively and μCo and μNi are the chemical potentials of Co and Ni at

Oh sites The latter were evaluated as 120583120583119872119872 = 119864119864119872119872119874119874 minus121205831205831198741198742 where 119864119864119872119872119874119874 is the computed

30

total energy per formula unit of the MO binary oxide (M= Co or Ni) and 1205831205831198741198742 is the

chemical potential of an oxygen molecule As a result 119864119864119889119889119889119889119889119889119894119894119899119899119889119889 can be rewritten as

119864119864119889119889119889119889119889119889119894119894119899119899119889119889 asymp 1198641198641198731198731198941198941199091199091198621198621198891198893minus1199091199091198741198744 minus 11986411986411986211986211988911988931198741198744 minus 119909119909119864119864119873119873119894119894119874119874 + 119909119909119864119864119862119862119889119889119874119874119909119909

Figure 8 Electronic density of states (DOS) of NixCo3-xO4 for different values of the doping

ratio x calculated using DFT+ULR The DOS is not affect by the spin ordering of Co(Td)

ions

The computed doping energies for different x values are reported in Table 1 We can see

that the doping energy is positive at x=18 indicating that doping Co3O4 with Ni is not

favorable at low concentration For xgt 14 however the doping energy becomes

increasingly negative with increasing doping ratio indicating that further doping is

favorable For xlt 34 the spins of Co ions at neighboring Td sites prefer to be anti-parallel

Both anti-parallel and parallel spins are present at x=78 while the spin ordering of Co(Td)

31

ions changes to parallel at x=1 (the spins of Ni(Oh) and Co(Td) are always antiparallel)

Together with the decrease of doping energies Table 1 shows a small increase of the lattice

constant with increasing x The bulk modulus decreases significantly with increasing x

reaches a minimum at x=58 and slightly increases afterwards

Figure 8 shows the evolution of the Density of States (DOS) of NixCo3-xO4 as a function

of x We can see that Ni doping gradually transforms Co3O4 an insulating material into

a half metal in which the majority spin channel remains insulating while the minority one

becomes conducting The valence bands for both spin channels thus shift toward the

Fermi level in comparison to Co3O4 These results also indicate that Ni (which prefers a

charge state Ni2+) substituting a Co3+ at an Oh site acts as p-type dopant in Co3O4

consistent with recent experimental findings14 19 The presence of Ni2+ at an octahedral

site causes indeed the formation of a Co(Td)3+ which has only one occupied e orbital in

the minority spin channel (see Figure 7) The other empty e orbital on Co(Td) gives

then rise to a hole (acceptor) state at the top of the valence band (note that the e states of

Co(Td) are part of the valence band in Co3O4) Similarly a Ni3+ at an octahedral site

(resulting in Co(Td) 2+) has an empty eg state which also leads to a hole state at the top of

or just above the valence band Hence in both cases empty states above or at the top of

the minority spin valence band are formed indicating that Ni acts as a p-dopant in Co3O4

32 Structure bonding and electronic properties of NCO

We considered two different symmetries known as α-type and β-type of the inverse spinel

crystal structure (Figure 7a-b) The β-type structure has alternating layers of -Co(Oh)-O-

and -Ni-O- along the z direction in Figure 7b whereas layers containing both Co(Oh) and

Ni ions are present in the α-type structure Total energy calculations are performed for

many possible magnetic configurations with these symmetries The β-type inverse spinel

is found to be slightly more stable by 005 eV per conventional cell in comparison to the

α-type structure For both symmetries the most stable state is half-metallic and

ferrimagnetic with anti-parallel spins on Ni(Oh) and Co(Td) ions and a total magnetization

of 16 microB per conventional unit cell (note that the Co(Oh) ions have always fully occupied

32

t2 states and no spin polarization) However the ferromagnetic state (total magnetization

of 32 microB) is only 007 eV higher in energy and also half metallic By contrast the

ferrimagnetic configuration with insulating behavior in both spin channels has much higher

energy (117 eV) The Densities of States of NCOrsquos ground state and excited ferromagnetic

and insulating ferromagnetic states are compared in Figure 9

Figure 9 DOS calculated for the insulating ferrimagnetic (I) (top panel) metallic

ferromagnetic (M) (middle panel) and metallic ferrimagnetic (M) (bottom panel)

configurations of NCO

Maximally Localized Wannier functions (MLWFs)28-29 are a useful tool for studying

bonding properties their centers provide information on the atomic oxidation states while

their shapes help understand the character of the bonds Calculation of the MLWFs for

NCOrsquos half-metallic ferrimagnetic ground state shows that there are 8 7 and 6 d-type

Wannier functions centered on the Ni Co (Td) and Co (Oh) ions respectively suggesting

33

oxidation state +3 for Co(Oh) and +2 for Ni and Co (Td) ions However this would

introduce a charge imbalance in NCO More detailed analysis of the band structure shows

indeed that the eeg states of Ni and Co(Td) ions in the minority spin channel cross the

Fermi energy and are not fully occupied (Figure 10a) The partial occupation of these states

gives rise to both the fractional valence and the metallic behavior of the minority spin states

consistent with recent XPS data showing that both +2 and +3 oxidation states are present

for Ni and Co in NCO12 17 As shown by the projected band structure (Figure 11) however

also the oxygen orbitals contribute to the states around the Fermi level suggesting the

presence of covalent interactions with the Ni and Corsquos ege states Due to the partial

occupation of the oxygen orbitals the fractions of Co2+ and Ni3+ states can be different and

therefore NCOrsquos composition can be better expressed as 1198621198621198621198621198901198902+1198621198621198621198621minus1198901198903+ 1198621198621198621198623+1198731198731198941198941minus1199101199102+ 1198731198731198941198941199101199103+1198741198744

For comparison we also calculated the MLWFs of the ferrimagnetic insulating state and

found that in this case one e orbital of Co(Td) is only singly occupied (see Figure 7 for

comparison) consistent with a perfect Co3+[Ni2+Co3+]O4 structure as reported in Ref9

Figure 10 (a) Band structure for the minority spin states and (b) Projected density of

state (PDOS) of NCO calculated using DFT+ULR The different colors in (a) reflect the

contribution of the e states of Co (Td)

34

Figure 11 Projected DOS calculated for the eg states of (a) Co (Td) and (b) Ni The

fractional valence calculated from this PDOS is ~21+ for both Co(Td) and Ni (c) Band

structure around the Fermi level different colors indicate the contribution of the oxygen

orbitals

The projected Density of States (PDOS) for NCO in its ferrimagnetic ground state is shown

in Figure 10b The main contribution to the states around the Fermi energy in the minority

spin channel comes from Ni and Co(Td) as well as O ions consistent with the presence of

a significant hybridization between cation 3d and oxygen 2p orbitals The computed atomic

magnetic moments are 239 and -112 μB for Co(Td) and Ni respectively in good

agreement with the corresponding experimental values of 218 and -149 μB 10 On the other

hand the contributions of Co(Td) and Ni to the conduction bands are very different Co(Td)

ions do not contribute to the majority spin conduction states whereas Ni ions do not

contribute to the minority spin states The detailed band structure plotted along several

symmetry directions is shown in Figure 12a and 12b There is an indirect band gap of about

20 eV along the Γ X direction for the majority spin states However the valence bands are

35

quite flat so that the direct gap found near X is very similar 21 eV The minority spin

bands show a stronger dispersion especially across the Fermi level

Figure 12 Band structure of NCO calculated using DFT+ULR (a) majority and (b)

minority spin states

To obtain insight into the absorption spectrum the Joint Density of States (JDOS) was also

calculated (Figure 13) The norm-conserving pseudopotentials used for these calculations

yield a band structure similar to the ultrasoft pseudopotential results of Figure 12a and 12b

with a somewhat larger bandgap of 24 eV for the majority spins The shapes of the JDOS

curves are similar for the majority and minority spin states except for the longer low energy

tail of the latter This is consistent with recent experiments indicating that there is optical

adsorption for NCO at relatively large wavelength (gt700nm) together with an optical band

gap around 26 eV17

36

Figure 13 Electronic structure of NCO calculated using norm conserving

pseudopotentials with U terms from linear response band structure for (a) majority and

(b) minority spins (c) Projected DOS and (d) Joint DOS The JDOS suggests an optical

band gap of ~ 25 eV for the majority spins and absorption at long wavelengths for the

minority spins

33 Ni harr Co exchanges

Motivated by the experimental evidence of Ni(Td) ions19 we have investigated the

stability of NCO with respect to Ni(Oh) harr Co(Td) exchanges by calculating the

formation energy (119864119864119904119904119904119904119904119904)

119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl

where 119864119864119890119890119890119890119909119909ℎ is the total energy of the crystal after exchanging Ni(Oh) and Co(Td) 1198641198640 is

the total energy of the defect free bulk in the inverse spinel structure and n is the number

of Ni sites exchanged Results with our standard DFT+ ULR setup predict however a

37

rather large (~ 13 eV) energy cost for the Ni harr Co(Td) exchange which seems at

variance with experiment10 19 Since it is known that the choice of U in DFT+U

calculations is not unique and different U values may perform better in different

situations30-31 we then decided to examine how the formation energy 119864119864119904119904119904119904119904119904 is affected by

the choice of U Results for different nrsquos and different choices of the Hubbard U terms

are reported in Table 2 Specifically we compare 119864119864119904119904119904119904119904119904 computed using our standard

linear response ULR values with results obtained using (i) pure PBE (U = 0) and (ii) U

values (Ueff) suggested by previous studies ie Ueff = 55 and 30 eV for Ni32 and both

types of Co ions30 33 respectively As a reference the DOS of NCO calculated with these

different choices of U are shown in Figure 14 We notice that all U values predict the

material to be ferrimagnetic with total magnetization of 16 μB per conventional unit cell

and the minority spin states to be conducting The shapes of the DOS obtained with

different U values are also similar but pure PBE shows no gap for the minority spin

states whereas a gap occurs in both DFT+ULR and DFT+Ueff calculations

Figure 14 DOS of pristine NCO calculated using different U values as indicated

38

As shown in Table 2 our computed substitution energies do not change monotonically

with increasing U value With PBE and intermediate U values (Ueff) the substitution

energies are very small which seems to provide the best agreement with the experimental

observation that intermediate structures between inverse spinel and normal spinel occur

frequently10 19 By contrast the Ni harr Co(Td) exchange is energetically very costly with

large U values (ULR) indicating that ULR does not predict well the thermodynamic

properties To make closer connection with experiment we also determined the formation

temperature 119879119879119904119904119904119904119904119904 = 120549120549119864119864119904119904119904119904119904119904∆119878119878 where 120549120549119864119864119904119904119904119904119904119904 is the formation energy difference due to the

exchange and ∆119878119878 is the corresponding change of configurational entropy (see Table 2)

This was determined from the expression ∆119878119878 = 11989611989611990411990411989711989711989911989911988211988211198821198820

where W0 and W1 are the number

of configurations corresponding to the initial and final values of the exchange ratio PBE

and PBE+Ueff predict moderate exchange formation temperatures whereas PBE+ULR

strongly overestimates the temperature Although PBE appears to well reproduce the

experimental observations9 one should notice that the results in Table 2 do not include the

changes of vibrational entropy which may give comparable contribution compared with

configurational entropy34 This and other sources of inaccuracy could lead to an error of

about 01 eV for 119864119864119904119904119904119904119904119904 and thus a ~ 300 K difference in 119879119879119904119904119904119904119904119904 Increase of the substitution

ratio R from 18 to 14 Ni gives slightly lower 119864119864119904119904119904119904119904119904 but higher 119879119879119904119904119904119904119904119904 due to a smaller ΔS

After the Ni harr Co(Td) exchange the Ni ions at the Td sites tend to be spin parallel to the

Co at the other Td sites The total magnetization does not change and the DOS changes are

also minor using both Ueff and ULR (Figure 15) Finally complete Ni harr Co(Td) exchange

(R=1 in Table 2) leads to NCO in the normal spinel structure for which the values of

119864119864119904119904119904119904119904119904 are similar to those at smaller exchange ratios

39

Table 2 Computed Ni(Oh)harrCo(Td) exchange energies 119864119864119904119904119904119904119904119904 and formation

temperatures Tsub (between parentheses) for different exchange ratios R and different U

values For example R = 18 corresponds to one Co(Td)harr Ni exchange per

conventional (56 atoms) cell

Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314

Figure 15 DOS calculated using Ueff (left) and ULR (right) with (ad) no substitution

(be) 18 substitution and (cf) 14 substitution

40

34 Oxygen vacancies

NCO is unstable and forms NiO and NixCo3-xO4 above 650 C9 The decomposition is

associated to a loss of oxygen and thus to creation of oxygen vacancies The formation

energy of oxygen vacancies is thus an important quantity for evaluating the thermal

stability of NCO

We considered 1 vacancy per conventional (56 atoms) unit cell and determined the

formation energy from the expression

119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879

Table 3 Oxygen vacancy formation energies (Eform) for NCO calculated using DFT+U

with various choices of U (see text) Two situations were considered (a) T = 0 K and

standard oxygen pressure and (b) T = 1000 K and 10-9 atm oxygen pressure (shown in

bracket) For comparison the O-vacancy formation energies in Co3O4 are also shown

For each U the corresponding optimized lattice constant was used For Co3O4 we were

not able to obtain a well converged ground state for the defected crystal using Ueff and

therefore the corresponding value of Eform is not reported

Material U (eV) Lattice

constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)

where 119864119864119889119889119890119890119891119891 and 1198641198640 are the total energies of the defected and pristine crystal

respectively 1205831205831198741198742 is the chemical potential of O2 and 119896119896119904119904119897119897119899119899119879119879 is the configurational entropy

Two inequivalent sites for oxygen vacancies exist in NCO site A which has 3 Co and 1

41

Ni neighbors and site B with 2 Co and 2 Ni neighbors to test the possible dependence of

their relative stabilities on the U term calculations for different choices of U as described

in Sec IIIC were performed Results are reported in Table 3 for two different conditions

namely (a) T= 0 K and standard oxygen pressure and (b) T = 1000 K and 10-9 atm oxygen

pressure (decomposition conditions) This shows that the O-vacancy formation energy at

site B is somewhat smaller than that at site A (independent of U) both being however

similar to the O-vacancy formation energy in Co3O4 Moreover both PBE+ULR and

PBE+Ueff predict negative O-vacancy formation energy for case (b) indicating that oxygen

vacancies form spontaneously under such conditions This is consistent with experiments

which indicate thermal decomposition of NCO under similar conditions (900 ndash 1000 K in

vacuum)19

Oxygen vacancies are known to have an important influence on the electrical properties of

metal oxides often causing the material to become a n-type semiconductor18 It is thus

interesting to study how this defect affects the structural and electronic properties of NCO

The atomic structure of an O-vacancy at site B is displayed in Figure 16b Analysis of the

atomic relaxations around the vacancy shows a large displacement of 026 Aring away from

the vacancy site for the Co(Td) bonding with the oxygen that was removed (Co1 in Figure

16b) On the other hand the displacements of the neighboring Co(Oh) Ni and O atoms are

moderate around 005 Aring with O1O2 and O3 moving toward the vacancy site As for the

electronic structure the formation of an oxygen vacancy gives rise to several low lying

states with different total magnetizations making the identification of the ground state

quite delicate The electronic Densities of States for defect free and defected NCO with A

and B-type oxygen vacancies are compared in Figure 16a For the majority spin states both

vacancy types result in the formation of additional states in the band gap For the minority

spin states the states at the Fermi level split in the case of an A-type vacancy leading to

the opening of a small band gap of ~ 03 eV here the low energy empty states originate

from Ni ions which do not contribute to the conduction bands of defect free bulk (Figure

17) In the case of a B-type vacancy the minority spin states remain conducting and the

overall changes in the electronic structure are minor Since B-type vacancies are favored

over A-type ones this suggests that at variance with other oxides oxygen vacancies have

only a minor influence on the conductivity of NCO The occupation of the d orbitals on the

42

Co(Td) Co(Oh) and Ni ions close to the vacancy are illustrated in Figure 16c Interestingly

although Co(Td) has a large displacement its occupation remains unchanged A change

occurs only for the Co(Oh) ion which becomes 2+ and assumes an anti-parallel spin with

respect to Ni (we note that the same results are obtained with DFT+ULR and DFT+Ueff)

Moreover the total magnetization remains unchanged in the presence of the vacancy

possibly because the hybridization between metal and oxygen states leads to compensation

of the spin polarization

Figure 16 (a) DOS of defect free (top) and reduced NCO containing an oxygen vacancy

either at site A (middle) or at site B (bottom) (b) Atomic structure of a B-type oxygen

vacancy the dark gray ball is the vacancy site (c) Occupation of Ni and Co d orbitals in

the presence of an oxygen vacancy the red arrow indicates a newly occupied orbital in

comparison to those in defect free NCO

43

Figure 17 PDOS of defect free bulk (a) oxygen vacancy on Site A (b) and oxygen vacancy

on Site B (c) where the PDOS changes a lot by creating oxygen vacancy on Site A

4 Conclusions

In this work we have used DFT+U calculations to investigate the electronic and

thermodynamic properties of spinel NiCo2O4 (NCO) and obtain insight into the origin of

the high conductivity and ferrimagnetic properties of this material We have studied the

formation of NCO from Co3O4 focusing on the electronic structure of NixCo3-xO4 as a

function of the doping ratio x Our results show that Ni acts a p-type dopant in Co3O4 and

gradually makes the minority spin channel metallic Of the two possible symmetries α-

type and β-type of inverse spinels NCO favors the latter but the energy difference

between the two structures is quite small Investigation of different possible magnetic

structures indicates that NCO has a ferrimagnetic ground state with a low lying

ferromagnetic excited state which may explain why different conditions of synthesis often

44

cause major differences in the observed magnetic properties7 Further analysis of the

ferrimagnetic ground state indicates that the ege states of Ni and Co(Td) are partially

occupied resulting in fractional valence and metallic behavior consistent with recent

experimental results17

We also studied the influence of two frequently observed defects Ni harr Co(Td) exchanges

and oxygen vacancies on the structural and electronic properties The computed energy

cost of Ni harr Co(Td) exchanges is largely independent of the value of the exchange ratio

consistent with the fact that significant cation disorder is usually observed in spinel oxides19

Oxygen vacancies are predicted to occur more frequently at sites coordinated to a larger

number of Ni ions and to form spontaneously under conditions of high temperature and

low oxygen pressure where thermal decomposition of NCO is actually observed to take

place On the other hand oxygen vacancies are found to have only a minor effect on the

magnetic and electronic properties and therefore do not modify the p-type character of the

conductivity

45

5 References

1 Zhang G Lou X W Controlled Growth of Nico2o4 Nanorods and Ultrathin

Nanosheets on Carbon Nanofibers for High-Performance Supercapacitors Scientific

Reports 2013 3 1470

2 Liu S Hu L Xu X Al-Ghamdi A A Fang X Nickel Cobaltite

Nanostructures for Photoelectric and Catalytic Applications Small 2015 11 4267-4283

3 Yu L Zhang G Yuan C Lou X W Hierarchical Nico2o4Mno2corendash

Shell Heterostructured Nanowire Arrays on Ni Foam as High-Performance

Supercapacitor Electrodes Chem Commun 2013 49 137-139

4 Liu X Shi S Xiong Q Li L Zhang Y Tang H Gu C Wang X Tu J

Hierarchical Nico2o4Nico2o4coreShell Nanoflake Arrays as High-Performance

Supercapacitor Materials ACS Appl Mater Interfaces 2013 5 8790-8795











8 Farrauto R J Low-Temperature Oxidation of Methane Science 2012 337 659-

660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201

18 Deml A M Holder A M OrsquoHayre R P Musgrave C B Stevanović V

Intrinsic Material Properties Dictating Oxygen Vacancy Formation Energetics in Metal

Oxides The Journal of Physical Chemistry Letters 2015 6 1948-1953

19 Ndione P F Shi Y Stevanovic V Lany S Zakutayev A Parilla P A

Perkins J D Berry J J Ginley D S Toney M F Control of the Electrical

Properties in Spinel Oxides by Manipulating the Cation Disorder Adv Funct Mater

2014 24 610-618



47


C 2014 118 19085-19097

21 Giannozzi P et al Quantum Espresso A Modular and Open-Source Software

Project for Quantum Simulations of Materials J Phys Condens Matter 2009 21

395502


Made Simple Phys Rev Lett 1996 77 3865-3868


the Effective Interaction Parameters in Thelda+Umethod Phys Rev B 2005 71 035105-1

-035105-16


Formalism Phys Rev B 1990 41 7892-7895


Phys Rev Lett 1979 43 1494-1497

26 Mostofi A A Yates J R Lee Y-S Souza I Vanderbilt D Marzari N

Wannier90 A Tool for Obtaining Maximally-Localised Wannier Functions Comput

Phys Commun 2008 178 685-699




28 Chen J Wu X Selloni A Electronic Structure and Bonding Properties of

Cobalt Oxide in the Spinel Structure Phys Rev B 2011 83 245204-1 -245204-7

29 Marzari N Vanderbilt D Maximally Localized Generalized Wannier Functions

for Composite Energy Bands Phys Rev B 1997 56 12847-12865


within Thegga+Uframework Phys Rev B 2006 73 195107-1 - 109107-6

31 Garciacutea-Mota M Bajdich M Viswanathan V Vojvodic A Bell A T

Noslashrskov J K Importance of Correlation in Determining Electrocatalytic Oxygen

Evolution Activity on Cobalt Oxides J Phys Chem C 2012 116 21077-21082

32 Shi X Li Y-F Bernasek S L Selloni A Structure of the Nife2o4(001)

Surface in Contact with Gaseous O2 and Water Vapor Surface Science 2015 640 73-79

48



34 Fultz B Vibrational Thermodynamics of Materials Prog Mater Sci 2010 55

247-352

49

Chapter IV

Oxygen deficiency and reactivity of spinel

NiCo2O4 (001) surfaces

1 Introduction

Spinel cobalt oxide (Co3O4) has recently attracted attention as a highly active catalyst for

various oxidation reactions1-3 Interest in this material has also generated efforts aimed at

tuning its catalytic activity through doping or substitution with selected transition metals

Among such substituted cobaltites NiCo2O4 (NCO) has emerged as a particularly

promising catalyst for low temperature methane and CO oxidation4-5 as well as the

oxygen evolution reaction6-7 For instance recent experiments have shown that NCO can

completely oxidize methane at 350-550 degC suggesting that in some cases NCOrsquos activity

could be higher than that of precious-metal-based catalysts8

NCO is a material with complex structural and electronic properties It is generally

considered to have an inverse spinel structure with mixed valence where tetrahedral (Td)

sites are occupied by Co2+ and Co3+ ions and octahedral (Oh) sites are occupied by Ni2+

Ni3+ and Co3+ ions9-13 However Ni(Oh)harr Co(Td) exchanges can take place rather

easily9 resulting in considerable cation disorder NCO is also generally described as

ferrimagnetic and metallic with much higher conductivity compared to other

cobaltites12 14-15 It was indeed suggested that NCO is a more efficient water oxidation

catalyst compared to pure Co3O4 due to its higher conductivity16

Despite the growing interest in the use of NCO in catalysis understanding of its

fundamental surface properties is still limited So far only few experimental and

theoretical studies on well-defined NCO surfaces have been reported5 17-19 The aim of

this work is to obtain insight into NCOrsquos surface structure and reactivity through Density

Functional Theory (DFT) calculations on the (001) surface which is one of the most

common surfaces of spinel materials20 Using DFT with the addition of on-site Coulomb

50

repulsion U terms on Co and Ni 3d shells (DFT+U)21 we investigate surfaces with

various CoNi ratios focusing on the formation of surface oxygen vacancies (VOs) which

have been proposed to play a key role in the oxidation of CO and methane on NCO4 We

also investigate the adsorption of two typical probe molecules water and O2 which are

important for characterizing the surface structure under ambient conditions and the

surface reoxidation process during catalytic reactions respectively Our results clearly

show that Ni has a major influence on the formation of surface oxygen vacancies leading

to VO formation energies significantly lower than those found for Co3O4 On the other

hand O2 adsorption is more difficult and is likely to represent the thermodynamic

limiting step of oxidation reactions on NCO(001)

2 Methods and Models

Spin polarized DFT+U calculations were performed using the plane-wave-

pseudopotential scheme as implemented in the Quantum Espresso package22 Exchange

and correlation terms were described using the Perdew-Burke-Ernzerhof (PBE)23

functional with on-site Coulomb repulsion U term on Co and Ni 3 d electrons We used

the values U(Co)=30 eV and U(Ni)=55 eV which we recently found to provide a better

description of NCOrsquos thermodynamic properties compared to the U values determined

from Linear Response theory24-25 Ultrasoft pseudopotentials26 were employed and the

valence electrons include O 2 s 2 p Co 3 d 4 s and Ni 3 d 4 s states Kinetic energy


respectively Structural optimizations were carried out by relaxing all atoms until forces

were smaller than 10 times 10-3 au

Of the two possible symmetries α-type and β-type of inverse spinels the latter is slightly

more stable20 and was thus chosen for studying the surface properties In this structure

the (100) and (001) surfaces are inequivalent the former exposing both Ni and Co

cations and the latter either Co or Ni only see Figure 18 These surfaces were modeled

using slabs of 11 layers terminated by oxygen and octahedral Co and Ni ions and a

vacuum region of 20 Aring was used to separate adjacent slabs We kept the same chemical

51

composition for the (100) and (001) slabs resulting in two different terminations for the

latter nonetheless the net polarization is zero in all cases because the system is metallic

(see below) We used theoretical lattice parameters20 and considered a square surface

unit cell of dimensions 8209 x 8209 Aring2 exposing 4 octahedral cations and 8 oxygens in

the outer layer and 2 Co(Td) in the second layer just below We sampled the surface

Brillouin zone using 2 times 2 times 1 k-point grid Oxygen vacancies and adsorbed molecule

were introduced only on one of the surfaces of the slab Dipole corrections were found to

have only minor effects (about 001 eV) and were not included in our standard setup

3 Results and Discussion 31 Pristine (001) (100) surfaces

Experimental control of the NCO stoichiometry is very challenging and in practice NCO

samples are always non-stoichiometric14 17 Nonetheless the perfectly stoichiometric

NCO surface remains a convenient reference system for the study of surface oxygen

vacancies which is the reason why we consider it here The structures of the defect-free

NCO (001) and (100) slabs are shown in Figure 18 We found an energy difference of

less than 001 eV between the two slabs which is consistent with the fact that they have

the same overall stoichiometries (Ni12Co22O48) All investigated surfaces are terminated

by oxygen anions and metal cations that are at Oh sites in the bulk both Ni and Co(Oh)

are present on the (100) surface (denoted noted as (100)mix Figure 18be) while either Ni

or Co(Oh) are present on the (001) surface (indicated as (001)Ni and (001)Co Figure

18acd) In addition two different types of surface oxygen anions exist O1 bonded to

two 1st layer metal cations and a 3rd layer cation at an Oh site and O2 bonded to two 1st

layer metals and a 2nd layer Co(Td) On the (100)mix surface O1 atoms can be further

distinguished in O1a and O1b bonded to 3rd layer Co and Ni cations respectively We

further calculate the surface energy difference of those surfaces by using the formula of

calculating surface energy from

120574120574 =(119864119864119904119904119897119897119904119904119904119904 minus 119899119899119864119864119904119904119904119904119897119897119896119896 minus 119909119909120583120583119862119862119889119889 minus 119910119910120583120583119873119873119894119894 minus 1199111199111205831205831198741198742)

119860119860

52

where E is the total energy calculated for slab and bulk respectively and μ is the chemical

potential of corresponding compounds We get

∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860

where the chemical potential of Ni and Co are refer to our previous paper20 ΔEslab were

calculated from extrapolating energies of different layered surface to have a more

accurate energy difference We found (001)Ni surface is more stable and (100)mix and

(001)Co surface has a surface energy of 0229 Jm2 and 0515Jm2 relative to (001)Ni

surface indicating NCO surface tends to be Ni rich in agreement with experiment that

when decomposed NiO will form on the surface9 27

Figure 18 Side views of (a) NCO(001) and (b) NCO(100) slabs blue gray and small red

spheres represent Co Ni and oxygen atoms respectively Top views of (c) (001)Ni (d)

(001)Co and (e) (100)mix surfaces only the atoms of the first and second layers are

represented by spheres O1 and O2 are defined in the text

53

Table 4 Average displacements of surface Ni and Co(Oh) and second layer Co(Td) from

their ideal bulk positions Positive (negative) out of plane displacements correspond to

outward (inward) displacements

Surface Type Atom type In-plane

displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084

Average displacements of surface and second layer atoms from their ideal bulk positions

are reported in Table 4 while in-plane and out of plane Co-O and Ni-O distances are

compared to computed and experimental10-11 17 bulk anion-cation bond lengths in Table

5 Surface oxygen atoms tend to have large in-plane and smaller out-of-plane

displacements especially on the (001)Co surface and O1 shows somewhat larger

displacements compared to O2 The metallic cations (Ni Co(Oh) and Co(Td)) exhibit

54

smaller in-plane and larger out-of-plane displacements compared to oxygen ions Co(Td)

in the 2nd layer relaxes outward whereas surface atoms relax inward ie toward the bulk

As a result the distance between 1st and 2nd layer is reduced by ~02 Aring

Table 5 Anion-cation bond lengths calculated for NCO bulk and (001)(100) surfaces

where computational value of O-Co(Td) was found to be falls within experimental results

between 188 and 1979 Aring However the increasing bond length in the out of plane

direction dues to the in-plane distortion when forming surface whereas bond length of O-

Co(Td) decreases in general indicating a closer top and 2nd layer distance

Structure type O-M cation type In-plane direction

Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882

In Figure 19 we compare the Densities of States (DOS) of the (100) and (001) slabs to

the DOS of bulk NCO Differences between the bulk and slab DOS are larger for the

minority-spin states than for the majority-spin ones As shown by the layer resolved DOS

55

(Figure 20) these differences originate mainly from the atoms in the surface layers For

the majority-spin states a band gap of 14 eV comparable to the bulk band gap is still

present on the (100) slab whereas the majority spin states of the (001) slab are

conducting due to surface states around the valence bands maximum These surface

states as well as those near the conduction band are mainly contributed by surface

Co(Oh) ions on the (001)Co surface On both (100)mix and (001)Co surfaces Co(Oh) ions

while remaining 3+ become spin polarized with their spin parallel to Ni cations and

anti-parallel to Co(Td) At the same time the 2nd layer Co(Td) ions change their bulk

fractional valence state to a 3+ high spin state

Figure 19 Computed projected DOS for (a) NCO (001) slab (b) NCO(100) slab and (c)

bulk NCO The majority spin states of the (001) slab is conducting due to surface states

on the (001)Co surface

56

Figure 20 layer resolved DOS for a (001)Ni b (001)Co and c (100)mix surfaces Each

layer includes a layer of Oxygen and Oh site cations and an inner layer of Td site cations

32 Surface oxygen vacancies

The formation of surface oxygen vacancies (VOs) has a key role in the oxidation activity

of metal oxide materials often based on the Mars-van Krevelen (MvK) mechanism4 28

We considered 1 and 2 VOs per surface unit cell corresponding to a coverage of 18 and

14 monolayer (ML) respectively The formation energies are calculated as

119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl

where 119864119864119889119889119890119890119891119891 and 1198641198640 are the total energies for the defected and pristine surfaces

respectively n is the number of surface oxygen vacancies 1205831205831198741198742 is the chemical potential

of O2 Our results are summarized in Table 6 (computed VOs formation energies) Figure

57

21 (geometries and electronic structures) and Figure 22 (surface stability diagrams as a

function of the oxygen chemical potential)

From Table 6 we can see that VOs at O1 sites (Eform ~ 11 eV on average) are about 06

eV more favorable than at O2 sites (Eform ~ 17 eV) in the case of one vacancy per unit

cell (18 ML) This can be explained by the fact that a VO at O2 would result in a 3-

cordinated Co(Td) which is quite unfavorable Formation of an O1 vacancy has a

particularly low energy cost on the (001)Co surface (040 eV) followed by O1b vacancies

on the (100)mix surface (082 eV) For comparison the computed VO formation energy is

much larger for bulk NCO (~ 23 eV)20 and for the Co3O4(100) surface (156 eV)

whereas a somewhat smaller VO formation energy 034 eV was obtained for the (100)

surface of NiFe2O4 a spinel catalyst with some similarity to NCO24 From the structural

point of view O1 vacancies on the NCO(001)Co surface are characterized by a strong

local relaxation such that the closest O1 oxygen moves to the middle between two metal

cations resulting in the formation of a so-called ldquosplit-vacancyrdquo The same effect is

observed also for O1a vacancies on the (100)mix surface (Figure 21c)

Table 6 (shown on next page) Average surface oxygen vacancy (VO) formation energies

(in eV) for different surfaces and different VO concentrations Both values at T= 0 K and

under ambient conditions (T=300K and p(O2) = 02 atm corresponding to the oxygen

partial pressure in air) are reported For the (100)mix and (100)exch surfaces inequivalent

O1 sites are denoted as lsquoabcdrsquo in the case of a single vacancy and lsquoaaabbbrsquo in the case

of two vacancies per surface cell (see Figs19e and 21d)

58

Surface Type Vacancy site Formation energy

(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053

Figures 21a and 21b show the electronic structure changes induced by the formation of an

oxygen vacancy on the (100)mix surface Both O1 and to a smaller extent O2 vacancies

generate new empty states in the majority-spin band gap which are primarily contributed

by Co(Oh) and both Ni and Co(Oh) ions respectively with a significant contribution by

oxygen The spin states of Co(Oh) and Ni on the defected surface remain the same as on

59

the pristine surface except for the case of a split-vacancy where Co(Oh) acquires a high

spin state

Figure 21 Projected DOS for the defected (100)mix surface with a VO at (a) O1 and (b)

O2 (c) Top view of the O1a split-vacancy on the (100)mix surface (d) (100)exch surface

obtained after exchanging the Co(Oh) and Ni metal sites on (100)mix inequivalent O1

sites are indicated

The exchange of surface Co(Oh) and Ni ions has a computed energy cost of only 003 eV

and is thus expected to occur quite frequently on NCO(100)mix On the resulting (100)exch

surface (see Figure 21d) four different types of O1 oxygen sites are present

characterized by 0123 Ni neighbors and denoted as O1abcd respectively Our

calculations show that the VO formation energy at O1b and O1d is similar to that at O1b

on the regular (100)mix surface whereas O1a and O1c have formation energies similar to

60

O1a on the (100)mix surface (Table 6) This indicates that 3rd layer ions have larger

influence on the formation of surface oxygen vacancies than surface cations In

particular the formation energy appears to be lower when the surface O1 is bonded to a

3rd layer Ni ion

To better understand the role of 3rd layer cations on O-vacancy formation energies we

performed calculations on (100) surfaces obtained by interchanging Co and Ni ions in the

surface and 3rd layer The resulting surfaces with 25 and 75 Ni cations are shown in

Figure 23 Interestingly the 75 Ni surface is found to be 02-03 eV more stable in

comparison to the (100)mix surface while the 25 Ni surface is 02 eV less stable This

suggests that it is thermodynamically favorable for Ni to segregate at the surface

consistent with the experimental observation that during high temperature decomposition

Ni moves to the surface and forms NiO on top of spinel NCO9 27 The average VO

formation energies and standard deviations on the 75 and 25 Ni surfaces are reported

in Table 7 As shown in Table 7 standard deviations are very small when formation

energies are grouped according to the 3rd layer cations neighboring the vacancy thus

confirming that 3rd layer cations have a major impact on VO formation This result can be

rationalized by considering that upon VO creation the less coordinated cations that are

formed on the surface can undergo significant displacements to partially compensate the

reduced coordination whereas displacements are more difficult for the 3rd layer cations

In particular our computed average VO formation energies are 126 088 and 050 eV for

O-vacancies coordinated to 3rd layer Co Ni and Ni neighboring another Ni ion

respectively It is clearly more favorable to create a VO coordinated to a 3rd layer Ni

compared to a vacancy coordinated to a Co(Oh)3+ because the excess electrons associated

with the vacancy can form a stable Ni2+ species from the original Ni fractional valence

between +2 and +3

61

Table 7 Average surface oxygen vacancy formation energies and corresponding standard

deviations on NCO(100) with 25 and 75 Ni surface concentrations (Figure 23) The

results refer to the different surfaces shown in Figure 23 (first four rows) or to the

different surface oxygen types (last three rows) where O1 is a surface oxygen bound to a

3rd layer Co O2 a surface oxygen bound to a 3rd layer Ni O3 a surface oxygen bound to

a 3rd layer Ni that has a neighboring Ni The standard deviations are significantly smaller

when formation energies are grouped according to the oxygen type indicating that the VO

formation energies depend mostly on the 3rd layer cation

Surface type Oxygen type Average VO

formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62

Figure 22 Phase diagram for VO formation on a (001)Ni b (001)Co and c (100)mix surfaces

as a function of the oxygen chemical potential (referred to an isolated O2 molecule at

T=0K) In all cases the black horizontal line represents the pristine surface Shaded

regions indicate ambient conditions (p(O2) = 02 atm T= 300 K ndash 350 K blue) and

typical conditions for CO and methane oxidation (02 atm at 600 K ndash 800 K yellow)

63

Figure 23 NCO (100) surfaces with different Ni cation concentrations (ab) 25 in the

surface and 75 in the 3rd layer (cd) 75 in the surface and 25 in the 3rd layer VO

sites are indicated as O1 O2 and O3 depending on the 3rd layer cation arrangement O1

oxygen bonding with 3rd layer Co O2 oxygen bonding with 3rd layer Ni O3 oxygen

bonding with 3rd layer Ni and a neighboring Ni similar to oxygen on (001)Co surface

We further investigated the possibility of stronger surface reduction and examined

models containing two O1 vacancies per unit cell As sites for creating the second

vacancy we choose O1 sites not bonding to 4-coordinated Co(Oh) and Ni cations

generated by the first vacancy in order to avoid the formation of 3-coordinated Co(Oh)

64

and Ni ions From Table 6 we can see that the first and second VO formation energies are

similar on the (100)mix and (001)Ni surfaces whereas Eform is much higher (119 eV) for

the second vacancy than for the first one (04 eV) on the (001)Co surface

Finally we combined the results in Table 6 with the temperature and pressure

dependence of the oxygen chemical potential to determine the surface stability diagrams

shown in Figure 22 Note that these diagrams account only for the relative energies of the

structures with 18 and 14 ML VOs and do not take into account the possibility that a

lower energy 18 ML concentration could be created by phase separating into surface

regions with no VOs and regions with frac14 ML VOs Moreover the range of variation of

Δμ(O2) (the oxygen chemical potential referred to an isolated O2 molecule at T=0K) has

been extended beyond the narrow range -081 eV le_Δμ(O2) le 0 that is determined

from the conditions of thermodynamic equilibrium of bulk NCO with O2 gas Co3O4 and

NiO (Table 8) with corrections on O2 binding energy29-30 This is done because NCO

nanoparticles are actually observed to be stable up to rather high temperatures8 As shown

in Figure 22 the behaviors of the three investigated surfaces are clearly quite different

VOs (18 ML) can form easily slightly above room temperature at ambient O2 pressure

on the (001)Co surface whereas VO formation is unlikely on the Ni terminated (001)Ni

surface even under typical oxidation conditions On the (100)mix surface formation of

18 and 14 ML VOs becomes favorable around 700 and 800 K respectively suggesting

that this surface should be quite active in high temperature oxidation reactions

65

Table 8 heat of formation (ΔH) was calculated for NCO Co3O4 and NiO to find the

lower bond of O2 chemical potential for stable NCO crystal structures by

3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0

Where ΔHMO is the heat of formation for metal oxides MO and ∆1205831205831198741198742is the chemical

potential of O2 Calculations are done with no binding energy correction for O2 and

binding energy corrections used by a Jia of 101 eV and b Ceder of 136 eV Results are

compared with experimental heat of formation for Co3O4 and NiO in combination with

O2 binding energy correction of 101 eV Where with corrections on O2 bind energy we

found the NCO will be stable around room temperature or some high temperature

situation

∆HNCO ∆HCo3O4 ∆HNiO Lower bond of

∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074

Experimental -929 -253

33 Water adsorption

Water adsorption free energies 119864119864119904119904119889119889119904119904 on pristine and reduced NCO(001)(100) containing

one oxygen vacancy per unit cell (18 ML) are reported in Table 9 Values at T = 0 K

and under ambient conditions (T = 300 K and water pressure pH2O = 002 atm) were

determined using 119864119864119904119904119889119889119904119904 = 1198641198641198671198672119874119874lowast minus 119864119864119904119904119904119904119903119903119891119891 minus 1205831205831198671198672119874119874 + 120549120549120549120549120549120549119864119864 where 1198641198641198671198672119874119874lowast and 119864119864119904119904119904119904119903119903119891119891 are the

computed total energies of the surface with adsorbed water and without water

respectively 1205831205831198671198672119874119874 is the water chemical potential and 120549120549120549120549120549120549119864119864 is the zero point energy

difference between adsorbed water and an isolated water molecule

66

As shown in Table 9 the values of 119864119864119904119904119889119889119904119904 are similar for the Ni and Co sites of pristine

surfaces However water adsorbs in molecular form on Ni sites whereas the adsorption

is dissociative on Co Moreover Nirsquos electronic structure is barely influenced by the

adsorption whereas Co is oxidized from 3+ to 4+ and its magnetization is reduced Water

adsorption on Ni and Co sites is not favorable (119864119864119904119904119889119889119904119904 gt 0) under ambient conditions

indicating that the pristine surface is very little affected by water The introduction of

Van der Waals interactions (not included in our calculations) is not expected to change

this conclusion even though it may slightly strengthen the adsorption at T = 0K

On oxygen-deficient surfaces water adsorption is easier at VO sites where it is

thermodynamically favorable (119864119864119904119904119889119889119904119904 lt 0) also at room temperature For water at a VO the

hydrogen atoms tend to form H-bonds of length 146-167Aring with neighboring lattice

oxygens (Figure 24b) Proton transfer to one of these oxygens is facile making

dissociative adsorption at VOs energetically more stable by about 040 eV relative to

molecular adsorption at the same site Water adsorption is obviously less favorable at the

reconstructed split-vacancy sites For instance even though water tends to remove the VO

reconstruction and dissociate on the (001)Co surface its adsorption energy is very small (-

005 eV) under ambient conditions By combining the results for VO formation (Table 6)

and water adsorption (Table 9) we can also estimate the energetics of hydroxyl formation

on NCO(100)(001) For example the formation energy of an O1b vacancy on the

(100)mix surface is +054 (+082) eV under ambient conditions (at T=0K) while the

dissociative water adsorption energy at VO1b is -049 (-115) eV under the same

conditions This indicates that the surface is likely to be partially hydroxylated at low T

and become pristine under ambient conditions (after desorption of the hydroxyl

hydrogens to form H2) A slightly different picture was obtained for the NiFe2O4(100)

surface24 for which the lower energy cost of VO formation makes hydroxylation highly

favorable also under ambient conditions

67

Figure 24 Water and O2 adsorption structures on the (100)mix surface (top views) (a)

water dissociatively adsorbed at a Co site (b) molecular water at a VO site (c) O2 at a

VO site (d) O2 adsorbed on a surface with two VOs per unit cell Oxygen atoms of

adsorbed molecules are shown in orange oxygen vacancy sites are indicated by a cyan

dotted line

68

Table 9 Computed water adsorption free energies at Co and Ni sites on pristine

(100)(001) and at VO sites on reduced surfaces Both results at T=0K and under ambient

conditions (T = 300 K and pH2O = 002 atm corresponding to the water partial pressure in

air) are reported All values refer to 025 monolayer coverage (ie one adsorbed molecule

per surface unit cell) and positive values indicate that adsorption is thermodynamically

unfavorable For water adsorbed at a VO M and D indicate molecular and dissociative

adsorption respectively VO1b denotes a vacancy at an O1b site Figures showing the

various structures are listed in the last column

Surface Type Adsorption site Eads (0 K)eV Eads (air)eV Figure

001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

Figure 25 Water adsorption structures on different (001)(100) surfaces with and without

oxygen vacancies (only non-split VOs are considered) a water adsorbed at a Ni site on

the pristine (001)Ni surface b water adsorbed at a VO site on the reduced (001)Ni surface

with 1 VOcell c water dissociatively adsorbed at VO on (001)Ni surface with 1 VOcell

d water dissociatively adsorbed at a Co site on the (001)Co pristine surface e water

adsorbed at VO on (001)Co surface with 1 VOcell f water dissociatively adsorbed at VO

site on (001)Co surface with 1 VOcell g water adsorbed at a Ni site on the (100)mix

pristine surface h water dissociatively adsorbed at VO on (100)mix surface with 1 VOcell

Adsorption energies for these structures are given in Table 9 of main text

34 Oxygen adsorption

O2 adsorption is the first step of surface reoxidation in catalytic processes based on the

MvK mechanism Computed O2 adsorption free energies on reduced NCO(100)(001)

surfaces are reported in Table 10 These were determined using 119864119864119904119904119889119889119904119904 = 1198641198641198741198742lowast minus 119864119864119904119904119904119904119903119903119891119891 minus121205831205831198741198742 where 1198641198641198741198742lowast and 119864119864119904119904119904119904119903119903119891119891 are the total energies of the surface with and without

adsorbed O2 and 1205831205831198741198742 is the chemical potential of O2 From Table 10 it appears that O2

can adsorb at a VO but not at a surface metal site at low T whereas adsorption is always

unfavorable under ambient conditions This suggests that surface re-oxidation may be the

70

thermodynamic limiting step for MvK oxidation reactions on NCO(100)(001) For O2

adsorbed at a Vo (Figure 24c) one oxygen atom of the molecule binds to a top layer

metal atom while the other binds to both a metal atom at the surface and a metal of the 3rd

layer The O-O bond length is 136 Aring suggesting the formation of a superoxide O2minus We

also examined whether the adsorbed molecule could dissociate (Figure 26) but found the

dissociated configuration to be less stable than the molecular one by 027 eV Unlike

water O2 does not adsorb on split vacancies notably on the (001)Co surface

Figure 26 O2 adsorption on reduced NCO (001)(100) surfaces a O2 adsorbed at a Ni site

on the (001)Ni surface with 1 VOcell b O2 adsorbed at VO on (001)Ni surface with

1VOcell c O2 adsorbed on (001)Ni surface with 2 VOscell d O2 adsorbed at a Co site

71

on (001)Co surface with 1 split VOcell e O2 adsorbed at non-split VO on (001)Co surface

with 1 split VO and 1 non-split VOcell f O2 adsorbed at Ni on (100)mix surface with 1

VO1bcell g O2 adsorbed at Co on (100)mix surface with 1 VO1bcell h O2 adsorbed at

VO1b on (100)mix surface with 2 VO1bcell i Oxygen transfer onto surface Co from Figure

24c If not specified VO (oxygen vacancies) is the non-split vacancy Adsorption energies

for these structures are given in Table 10 of main text

The adsorption of an O2 molecule on a surface with higher oxygen deficiency (2 VOs per

surface unit cell) is slightly more favorable than on a surface with only 1 VO per cell

However O2 adsorption remains unfavorable at room temperature and atmospheric

pressure When the 2 vacancies are close to each other (eg on the (100)mix surface with

O1a-O1b vacancies or on the (001)Co surface) O2 takes a different adsorption structure

(Figure 24d) where only one of the two oxygens binds to a neighboring surface cation

whereas the other oxygen points toward the vacancy site with an O-O bond length of

137 Aring Breaking of the O-O bond to recover the pristine surface is highly favored

thermodynamically and has a small activation barrier of only 025 eV with an O-O

distance of 139 Aring at the transition state (Figure 27) This suggests that the mechanism of

surface reoxidation by O2 would involve the diffusion of oxygen vacancies to form a

close pair as rate limiting step

72

Table 10 Computed O2 adsorption free energies at Co and Ni sites on pristine

(100)(001) and (non-split) VO sites on reduced (100)(001) surfaces Both values at

T=0K and under ambient conditions (T=300 K and p(O2) = 02 atm corresponding to the

O2 partial pressure in air) are reported All values refer to 025 monolayer coverage (ie

one adsorbed molecule per surface unit cell) and positive values indicate that adsorption

is not favorable VO (M) and VO(M) + VO indicate O2 adsorption at a vacancy site of a

reduced surface with 1 VO and 2 VOs per surface unit cell respectively Figures showing

the various structures are listed in the last column


(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73

Figure 27 Selected structures along the reoxidation pathway of a (100)mix surface with

2VOscell (a) initial state with O2 adsorbed at a VO and pointing toward the other VO

(b) transition state with slightly increased O-O distance (c) final state showing the

reoxidized (100)mix surface Relative energies are listed below the structures Calculations

were performed via constrained minimizations

4 Conclusions

In this work we have studied the structure and chemistry of NCO(100)(001) surfaces

with different CoNi terminations using DFT+U calculations Our results show that there

is a thermodynamic driving force for Ni to segregate to the surface which is consistent

with the experimental observation of NiO formation on the surface during thermal

decomposition27 On the other hand oxygen vacancy formation is considerably more

difficult on the purely Ni-terminated NCO(001)Ni surface than on the Co-terminated

(001)Co and mixed Ni and Co-terminated (100)mix surfaces (Figure 22) The latter are thus

expected to represent the active surfaces in oxidation reactions On these surfaces VO

formation is easiest at O1 sites which are not bound to 2nd layer Co(Td) and especially at

O1 sites that are bound to 3rd layer Ni atoms while VOs at O1 sites with more Co(Oh)

than Ni neighbors tend to reconstruct to form split-vacancies The computed formation

energy of a regular (ie non reconstructed) VO at O1 is approximately 08 ndash 09 eV at T =

0 K (Table 6) which is essentially half the value (156 eV) that we find for a VO on the

Co3O4(100) surface Easier VO formation on NCO suggests that this material may be a

74

better oxidation catalyst than Co3O4 under mild conditions (ie at temperatures below Ni

segregation to the surface takes place)

NCOrsquos surface reactivity has been further characterized by studying the adsorption of two

typical probe molecules water and O2 Both molecules preferentially adsorb at oxygen

vacancy sites at low temperature Under ambient conditions however VOs can be easily

healed via dissociative water adsorption whereas adsorption of O2 is not favorable These

results suggest that O2 adsorption is likely to represent the thermodynamic limiting step

for oxidation reactions on NCO(001)(100) surfaces

75

5 References



2 Ma C Y Mu Z Li J J Jin Y G Cheng J Lu G Q Hao Z P Qiao S

Z Mesoporous Co3o4and AuCo3o4catalysts for Low-Temperature Oxidation of Trace

Ethylene J Am Chem Soc 2010 132 2608-2613

3 Hu L Peng Q Li Y Selective Synthesis of Co3o4nanocrystal with Different

Shape and Crystal Plane Effect on Catalytic Property for Methane Combustion J Am

Chem Soc 2008 130 16136-16137








6 Chen S Qiao S-Z Hierarchically Porous Nitrogen-Doped Graphenendash

Nico2o4hybrid Paper as an Advanced Electrocatalytic Water-Splitting Material ACS

Nano 2013 7 10190-10196

7 Shi H Zhao G Water Oxidation on Spinel Nico2o4nanoneedles Anode

Microstructures Specific Surface Character and the Enhanced Electrocatalytic

Performance J Phys Chem C 2014 118 25939-25946


660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102

16 Lee D U Kim B J Chen Z One-Pot Synthesis of a Mesoporous Nico2o4

Nanoplatelet and Graphene Hybrid and Its Oxygen Reduction and Evolution Activities as

an Efficient Bi-Functional Electrocatalyst J Mater Chem A 2013 1 4754




C 2014 118 19085-19097

18 Kim J G Pugmire D L Battaglia D Langell M A Analysis of the Nico2o4

Spinel Surface with Auger and X-Ray Photoelectron Spectroscopy Appl Surf Sci 2000

165 70-84




20 Shi X Bernasek S L Selloni A Formation Electronic Structure and Defects

of Ni Substituted Spinel Cobalt Oxide A Dft+U Study J Phys Chem C 2016 120

14892-14898

77


Hubbarduinstead of Stoneri Phys Rev B 1991 44 943-954



395502












28 McFarland E W Metiu H Catalysis by Doped Oxides Chem Rev 2013 113

4391-4427





78

Chapter V

Mechanism and activity of the oxidation

of CO and methane on spinel Co3O4 and

NiCo2O4

1 Introduction

Various oxidation reactions are found to proceed very efficiently on Fe Co and Ni based

spinel oxides1-2 For example ferrites shows high catalytic activity for oxygen evolution3-

4 and is a potential catalyst for the water gas shift reaction5 (though limited by water

desorption6) while spinel cobaltites especially Co3O4 and NiCo2O4 (NCO) are very

active for CO oxidation7-8 and hold promise as catalysts for low temperature methane

oxidation9-10

Among oxidation reactions the oxidation of CO to CO2 is of great interest both as the

reaction typically used for reducing the amount of CO in waste gases and also as a

benchmark reaction for oxidation catalysts Following the work of Haruta et al8

numerous experimental studies have examined CO oxidation on Co3O48 11-13

The (110)

surface has been found to be the most active low-index surface of this material CO can

be converted to CO2 even at -70 degC and complete conversion takes place at around

150 degC8-9 On the theoretical side studies of CO oxidation on Co3O4 (110)14-16 have

predicted a Mars-van Krevelen mechanism with a major role of Co ions at octahedral

sites However room temperature CO oxidation on Co3O4 (110) gradually deactivates

during the reaction11 17 which has been attributed to surface reconstruction and water

adsorption Moreover (110) surfaces are not very common for the spinel structure (111)

and (001) surfaces have lower surface energies and thus generally make larger

contributions to the surface area18 For Co3O4 however the (111) and (001) surfaces

79

have been reported to be inactive for CO oxidation8 The origin of these different surface

activities is difficult to understand on the basis of simple structural differences

To obtain better insight we have carried out a comparative theoretical study of the

COOR 2CO + O2 2CO2 over pristine and defected Co3O4(110) Co3O4(001) and

NiCo2O4(001) surfaces using DFT calculations with the addition of on-site Coulomb

repulsion U terms on Co Ni and Fe 3d shells (DFT+U)21 Our results suggest different

rate determining steps for the different surfaces of COOR In particular surface

reoxidation is found to be rate limiting on (001) surfaces while CO2 formation is the

most difficult step on Co3O4 (110)

Methane is an abundant energy resource and there is currently enormous interest in

developing more efficient and environmentally benign strategies for its utilization A

better understanding of methane oxidation is essential for such development Numerous

studies have examined methane oxidation on Co3O4 It was found that methane is

completely oxidized on the Co3O4 (110) surface and lattice oxygen atoms are involved in

the oxidation process10 Recent theoretical studies indicate the possibility of incomplete

methane oxidation on the Co3O4 (001) surface19 which may lead to interesting

applications It was also reported that NCO is a better catalyst for methane oxidation

compared to Co3O49

Motivated by this finding we have investigated the first two steps

of methane oxidation on NiCo2O4(001) notably the first C-H bond breaking that is

commonly believed rate determining20 as well as the second C-H bond breaking An

interesting result is that methane oxidation on NiCo2O4(001) has a pseudo barrier

comparable to that found on doped CeO222 a well-known catalyst for low temperature

methane oxidation





functional with on-site Coulomb repulsion U term on Co Ni and Fe 3 d electrons We

80

used the values U(Co)=30 eV U(Ni)=55 eV and U(Fe)=35 and 34 eV for Fe at Oh and

Td sites which we found to provide a better description of Co3O4 and NCO and NFOrsquos

thermodynamic properties compared to the U values determined from Linear Response

theory25-26 Ultrasoft pseudopotentials27 were employed and the valence electrons include

O 2 s 2 p Ni 3 d 4 s Co 3 d 4 s and Fe 3 d 4 s states Kinetic energy cutoffs used were

35 and 350 Ryd for wave functions and augmented density on Co3O4 and NCO and 50

and 500 Ryd for wave functions and augmented density on NFO Structural optimizations

were carried out by relaxing all atoms until forces were smaller than 10 times 10-3 au

Co3O4 NCO and NFO (001) surfaces were modeled using slabs of 11 layers terminated

by oxygen and metal cations occupying octahedral sites in the bulk material The Co3O4

(110) surface was modeled using slabs of 7 layers with oxygen rich termination A

vacuum region of 20 Aring was used to separate adjacent slabs We kept similar chemical

composition for the different (001) slabs with 10 metal atoms at tetrahedral (Td) sites 24

metal atoms at octahedral (Oh) sites and 48 oxygens The Co3O4 (110) slab included 14

(6) Co atoms at Oh (Td) sites and 28 oxygens We employed theoretically optimized

lattice parameters and considered square (2 x 2) surface unit cells of dimensions 8136 times

8136 Aring2 8209 times 8209 Aring2 and 8447 times 8447 Aring2 for Co3O4 NCO and NFO (001)

surfaces respectively25-26 28 the unit cell dimensions for Co3O4 (110) were 8149 times

5762 Aring2 We sampled the surface Brillouin zone using a 2 times 2 times 1 k-point grid for both

(001) and (110) surfaces CO and O2 molecules were adsorbed only on one of the two

surfaces of each slab previous calculations showed that dipole corrections have minor

influence (001 eV) and were not included in our setup

Kinetic barriers for selected reaction steps were determined using the Climbing Image

Nudged Elastic Band (CI-NEB) method29 We typically used 9 images that we optimized

until forces were smaller than 005 eVAring

Adsorption energies of various species X (eg CO O2 etc) were calculated using

119864119864119904119904119889119889119904119904 = 119864119864119883119883lowast minus 119864119864119904119904119904119904119903119903119891119891 minus 120583120583119883119883

81

where 119864119864119883119883lowast and 119864119864119904119904119904119904119903119903119891119891 are the computed total energies of the surfaces with and without

adsorbed X respectively and 120583120583119883119883 denotes the chemical potential of X calculated from

JANAF Tables30

3 Results and Discussion 31 CO adsorption and oxidation on Co3O4 (001) and (110) surfaces

311 CO adsorption

CO adsorption energies on Co3O4(001) and (110) surfaces are reported in Table 11 For

Co3O4 (001) we considered both the pristine surface and the surface with one oxygen

vacancy (VO) per unit cell (Figure 28ab) as the VO concentration may influence further

VO formation and therefore also the energetics of CO oxidation through the Mars-van

Krevelen (MvK) mechanism The computed CO adsorption energy at Co(Oh) is Eads = -

092 eV (at T= 0K) The adsorbed CO is perpendicular to the surface with C-Co distance

of 175 Aring suggesting a rather strong interaction CO adsorption is less favorable at a VO

site (Eads = -065 eV) while it is much more favorable at the two nonequivalent O1 (Eads

= -186 eV) and O2 (Eads = -143 eV) oxygen sites31 (Figure 28a) When CO adsorbs at

the latter sites it actually forms a CO2 molecule without any apparent intermediate or

barrier The resulting adsorption configuration can be described as a CO2 at a surface VO

(see structure II in Figure 29) consistent with a MvK mechanism

82

Figure 28 a Top view of the (2x2) surface unit cell and b side view of the top few layers

of the Co3O4 (001) slab model used in our calculations Only the atoms of the top and

second layer are shown as balls The dashed orange circle in a indicates a surface oxygen

vacancy (VO ) other labels indicate Co cobalt at a surface octahedral site O1 surface

oxygen bonding with 3rd layer Co(Oh) O2 surface lattice oxygen bonding with 2nd layer

Co(Td) c Top view of the surface unit cell and d side view of the first few layers of the

pristine Co3O4 (110) slab model used in our study Labels indicate Co cobalt at a surface

octahedral site O1 surface oxygen bonding with 2 inner layer Co(Oh) and 1 surface

Co(Oh) O2 surface oxygen bonding with 1 inner layer Co(Td) and 1 surface Co(Oh)

For Co3O4 (110) we considered only the pristine surface (Figure 28cd) as the defected

(110) surface is found to reconstruct25 The computed adsorption energy for CO at the 4-

coordinated surface Co(Oh) is Eads = -180 eV thus more negative (favorable) than on

the (001) surface where Co(Oh) is 5-fold coordinated CO points toward one of the

Co(Oh)-O bonds forming an angle of 45 degrees with the surface In addition to

Co(Oh) two types of oxygen sites exist for CO adsorption (Figure 28c) notably O1

bound to three Co(Oh) where Eads = -149 eV and O2 bound to one Co(Oh) and one

Co(Td) where Eads = -191 eV thus slightly larger than on Co(Oh) At both O1 and O2

sites CO forms bridging bonds with the oxygen and a surface Co(Oh) with bond lengths

83

of 130 and 195 Aring respectively (see structure II in Figure 30 where all CO adsorption

structure on lattice oxygen is shown in Figure 31)

Table 11 Computed CO adsorption energies (in eV) at various surface sites on pristine

and defected Co3O4 (001) and (110) surfaces Adsorption energies are reported at both T

= 0 K and T = 300 K (in parentheses) with CO pressure of 1 atm

Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation

Our results for the intermediates and energetics of the COOR on Co3O4 (001) and

Co3O4(110) are summarized in Figure 29 Figure 30 and Table 12 The first three

structures in Figure 29 correspond to the bare (001) surface (I) the adsorption of a CO

molecule and formation of CO2 by abstraction of a surface oxygen atom (II) and the

surface with an oxygen vacancy after the desorption of CO2 (III) In the subsequent step

an O2 molecule adsorbs at the VO site with one of the oxygen atoms taking the position

of the missing lattice oxygen while the other oxygen stretches outwards (IV) the O-O

bond length is 1344 Aring suggesting a superoxide species O2minus The computed O2

adsorption energy is -042 eV at T = 0K and + 017 eV ie endothermic under ambient

conditions (Table 12) These results indicate that re-oxidation of the surface is difficult at

room temperature The last step in Figure 29 is the adsorption of a second CO molecule

which reacts with the protruding oxygen of O2 and leaves as CO2 (V) so that the surface

can recover its initial state The energy release for this process is large - 444 (-392) eV

at T=0 (300) K The presence of an additional VO on the (001) surface has only minor

84

influence on the various intermediates (Table 12) the main effect being to slightly

increase the likelihood of O2 adsorption

Figure 29 Intermediates (side views) and free energy changes (in eV) for the various

steps of the COOR on pristine Co3O4 (001) pristine surface (I) adsorbed CO forming a

CO2 molecule with a surface O atom (II) defective surface following CO2 desorption

(III) re-oxidized surface with an O2 molecule at the vacancy site (IV) pristine surface

with physisorbed CO2 formed upon adsorption of another CO (V) Free energy changes

are given at both T=0 K and T=300 K (between parentheses) with CO O2 and CO2

partial pressures of 1 atm 02 atm and 00004 atm respectively

The intermediates of the COOR on Co3O4(110) are shown for the case of adsorption at

the O1 site (Figure 30) After CO adsorption and CO2 formation desorption of CO2 to

form a surface VO has an energy cost of +013 eV at 0K (-064 eV at RT) close to the

analogous cost on the (001) surface At variance with the (001) surface however the

subsequent adsorption of O2 at the vacancy site on Co3O4 (110) is very favorable being

exothermic at both T = 0K (-140 eV) and RT (-081 eV) The O2 adsorption

configuration is characterized by one of the oxygen atoms occupying the missing lattice

oxygen site while the other oxygen stretches out toward a neighboring Co(Oh) with an

85

O-O bond length of 137 Aring This oxygen is very reactive when another CO molecule

arrives CO2 forms readily without barrier and with an energy release of -458 eV In the

case of CO adsorption at the O2 site CO2 formation does not involve the CO bridging

structure in Figure 30 and the COOR mechanism is more similar to the one on the (001)

surface As shown in Table 12 the energy release is -197 (-144) eV compared to -113

(-060) eV for the O1 site while CO2 desorption has an energy cost of +040 (-038) eV at

0 K (RT) which is higher than the value found for the O1 site Adsorption of O2 is also

very favorable -105 (-046) eV at 0 K (RT) and further CO oxidation occurs with an

energy release of -399 (-346) eV


steps of the COOR on Co3O4 (110) with initial CO adsorption at the O1 site The

sequence of intermediates is the same as in Figure 29 Free energy changes are given at

both T=0 K and T=300 K (between parentheses) with CO O2 and CO2 partial pressures

of 1 atm 02 atm and 00004 atm respectively

By comparing the free energy changes for the various steps of the COOR on Co3O4 (110)

and (001) surfaces (Table 12) we can see that the thermodynamic limiting step of the

COOR on Co3O4(001) is the adsorption of O2 which becomes unfavorable around room

86

temperature On Co3O4 (110) on the other hand the COOR is more likely controlled by

the kinetics of CO2 desorption which requires a significant structural rearrangement

whereas O2 adsorption is more favorable

Figure 31 CO adsorption structure on different spinel surfaces with a on Co3O4 (110)

pristine surface b on Co3O4 (001) pristine surface c on NCO (001)Ni pristine surface

d on NCO (001)Co surface with one splitted oxygen vacancy e on NCO (100)mix pristine

surface and f on NFO (001) pristine surface

87

Table 12 Computed free energy changes (in eV) for the various steps of the COOR on

the Co3O4 (001) and (110) surfaces The labels PD indicate pristine and defected (with a

VO) surface respectively Results are reported at both T= 0 K and T = 300K (between

parentheses) with CO and O2 pressure of 1 and 02 atm respectively

I II II III III IV IV V V I

O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)

32 CO oxidation on NCO (001)(100) surfaces

Different from normal spinel Co3O4 NCO has an inverse spinel structure where

tetrahedral (Td) sites are occupied primarily by Co2+ and Co3+ ions and octahedral (Oh)

sites by Ni2+ Ni3+ and Co3+ ions27 NCO (001)(100) surfaces can expose both Co(Oh)

and Ni cations or only one type of metal cation following Ref31 we denote (100)mix a

surface exposing both Co(Oh) and Ni while (001)Ni and (001)Co expose only Ni and

Co(Oh) respectively

Figure 32 and Table 13 show the computed intermediates and free energy changes for the

COOR on pristine and defected NCO(001)(100) By comparing these results to those in

88

Table 12 for Co3O4 we can see that the free energy release for CO adsorption and CO2

formation (step I II) on NCO is larger than on Co3O4 This free energy release is

indeed strongly correlated with the VO formation energy for which cations in the 3rd

layer play a key role Ni cations causing smaller VO formation energies31 On the other

hand computed O2 adsorption energies at VO sites (step IIIIV) on reduced

NCO(001)(100) with 18 and frac14 ML VO coverages are similar to those on Co3O4 (001)

ie are typically positive at RT (Table 13) This suggests that reoxidation is difficult also

on NCO On the Co-terminated NCO(001)Co surface in particular VOs tend to

reconstruct at low coverage31 which prevents O2 adsorption Thus the COOR cannot

continue on this surface except at high VO concentrations where non-reconstructed VOs

are also present Reduced surfaces always tend to adsorb O2 more easily than pristine

ones as expected


pristine (P) and defected (D) NCO (001)(100) surfaces Results are reported at both T= 0

K and T = 300K (between parentheses) with CO and O2 pressure of 1 and 02 atm

respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89


steps of the COOR on the NCO (100)mix pristine surface The sequence of intermediates

is the same as in Figure 29 Free energy changes are given at both T=0 K and T=300 K

(between parentheses) with CO O2 and CO2 partial pressures of 1 atm 02 atm and

00004 atm respectively

To further characterize the COOR on NCO we studied the kinetic pathways of two key

steps of the reaction the formation of the 1st CO2 (I II) and of O2 adsorption (III

IV) (Figure 33) For the 1st CO adsorptionCO2 formation NEB calculations give a

barrier of 011 eV (Figure 33a) The C=O bond length at the transition state is 112 Aring

while the distances of the C atom to surface oxygen and Ni atoms are 135 and 217 Aring

respectively For O2 adsorption on defected NCO (100)mix NEB calculations show a

smooth potential energy surface with a very small barrier of about 001 eV (Figure 33b)

The O-O bond length at the transition state is 1239 Aring and the distance of the lower

oxygen to the surface is 1403 Aring indicating that interaction with the surface is still weak

These results suggest that the COOR on NCO is controlled by the thermodynamics of O2

adsorption

90

Figure 33 pathways of a formation of CO2 (I rarr II) and b O2 adsorption (III rarr IV) with

their transition barrier shown in the middle of the panel The relative energy (in eV) with

respect to initial structure is display below the structures CO2 formation is accomplished

by CO adsorption to surface lattice oxygen and then leave as CO2 after itrsquos adsorbed

33 Methane oxidation on the NCO (100)mix surface 331 Methane adsorption and first C-H bond breaking

Our calculation indicate that methane can only physisorb on the NCO (100)mix surface

CH4 remaining more than 28 Aring away from the surface To determine the energy of C-H

bond breaking we calculated the adsorption energies of several configurations with

hydrogen and methyl groups at different adsorption sites The methyl group favors

adsorption at the surface O1 site (Figure 34a) with hydrogen adsorbed on an O1 site

away from the methyl the computed adsorption energy is -222 eV Possible intermediate

states were also studied (Figure 34) When the methyl group is adsorbed on a surface Ni

(Co) site and H on a neighboring O1 a formation energy of -040 (-051) eV is obtained

91

(Figure 34bc) for the intermediate state The C-M bond length is around 197 Aring

Intermediate states with a methanol like structure involving methyl and hydrogen

adsorbed on the same surface O1 and O2 sites were also studied (Figure 34d e) We

obtained formation energies of -128 and -046 eV at O1 and O2 respectively with a C-O

bond length of ~ 146 Aring The adsorption barrier was estimated by considering the

configuration shown in Figure 34f with hydrogen adsorbed on the surface and the methyl

radical in gas phase for which an adsorption energy of 048 eV is found Although the

true barrier may be slightly larger than our estimated (pseudo) barrier22 it would still be

comparable to that on doped CeO2 a well-known low temperature methane oxidation

catalyst indicating the ability to break C-H bond at relative low temperature After

adsorption of the methyl radical onto the surface hydrogen diffusion will be favored

thermodynamically over desorption of methanol and further oxidationdehydrogenation

should occur

Figure 34 first C-H bond breaking structures on NCO (100)mix surface a most stable

structure with methyl and hydrogen adsorbed on different O1 sites b methyl adsorbed

on Ni c methyl adsorbed on Co d methyl and hydrogen adsorbed on the same O1 site

to form methanol e methyl adsorbed and hydrogen adsorbed on same O2 site f gas

phase methyl radical and hydrogen adsorbed surface to approximate transition barrier

92

332 Second C-H bond breaking

To verify the viability of further methane oxidation we studied the energetics of the

second C-H bond breaking from the stable methyl adsorption structure After C-H bond

breaking the resulting methylene group (CH2) adsorbs forming a bridge between O1 and

neighboring surface sites When CH2 is bridging O1 with Ni and Co the total energy

decreases by 038 eV and 058 eV respectively the C-O bond is reduced to around 136 Aring

and C-M bond length is around 197 Aring CH2 bridging O1 with another O1 and O2 sites is

favored with formation energy of -142 eV and -132 eV respectively The average C-O

bond length is slightly reduced to 142 Aring for the O1-C-O1 bridge and is almost the same

for the O1-C-O2 bridge Unlike in the cases of CO oxidation and first C-H bond

breaking the reactivity of the O2 site in the 2nd C-H bond breaking is comparable to that

of the O1 site It is possible to create O2 site vacancies with the 2nd C-H bond breaking

which may facilitate the surface reoxidation

4 Conclusions

Our results show that the (001) surfaces of spinel Co3O4 NCO and NFO have all the

same mechanism for the CO oxidation reaction CO molecules adsorb strongly at lattice

oxygen sites and form CO2 readily while re-oxidation through O2 adsorption at VO sites

is thermodynamically unfavorable at room temperature or higher This may be the reason

why the Co3O4(100) surface has been reported to be rather inert in experiment On the

other hand our results show that the rate-limiting step of CO oxidation on the Co3O4

(110) surface which is found to be quite reactive in experiment is not the re-oxidation

but the formation of CO2 from adsorbed CO If the temperature is relatively low CO

oxidation on (001) surfaces is also limited by the hydroxylation of the surface upon

water adsorption and dissociation at a VO site surface OH groups are formed that hinder

the interaction of CO with lattice oxygens These results suggest that the COORrsquos activity

of Co3O4 and NCO (001) surfaces is determined by the weak interaction of O2 with the

surface and competing molecules like water can adsorb at the VO site and block the active

site Our calculations also suggest that the NCO (001) surface has potential catalytic

93

activity for low temperature methane oxidation with a transition barrier comparable to

various doped CeO2 for the first C-H bond breaking rate determining step

94

5 References

1 Liang Y Li Y Wang H Zhou J Wang J Regier T Dai H Co3o4

Nanocrystals on Graphene as a Synergistic Catalyst for Oxygen Reduction Reaction

Nature Materials 2011 10 780-786

2 Ma N Selective Oxidation of Styrene over Nanosized Spinel-Type

Mgxfe3minusXo4 Complex Oxide Catalysts Applied Catalysis A General 2003 251 39-47

























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097









22 Kumar G Lau S L J Krcha M D Janik M J Correlation of Methane

Activation and Oxide Catalyst Reducibility and Its Implications for Oxidative Coupling

ACS Catalysis 2016 6 1812-1821

96



395502











14892-14898




30 Malcolm W Chase Jr Nist-Janaf Thermochemical Tables Fourth edition

Washington DC American Chemical Society New York American Institute of

Physics for the National Institute of Standards and Technology 1998 1998

31 Shi X Bernasek S L Selloni A Oxygen Deficiency and Reactivity of Spinel

Nico2o4 (001) Surfaces The Journal of Physical Chemistry C 2017 121 3929-3937

97

Chapter VI

Surface chemistry of NiFe2O4(001)

surface structure in contact with O2 and

water vapor and reactivity toward CO

and methane

1 Introduction

The spinel ferrites with general formula AFe2O4 are materials of both fundamental and

technological interest1 In particular NiFe2O4 is a promising material for magnetic

storage systems2 magnetic-resonance imaging3 spintronics4-5 etc Recently NiFe2O4 has

also attracted significant attention for its catalytic activity for the oxygen evolution

reaction6 and as a potential catalyst for the Water Gas Shift (WGS) reaction7 where the

reactivity is limited by water desorption8 The interaction of NiFe2O4 surfaces with water

plays a key role in all the applications of this material in catalysis Understanding this

interaction is thus essential for the design of more efficient NiFe2O4 catalysts for the

WGS and other oxidation reactions

While numerous theoretical9 and experimental10-12 investigations of the bulk electronic

and magnetic properties of NiFe2O4 have been reported studies on the surfaces of

NiFe2O4 are still scarce NiFe2O4 exposes different surfaces depending on the growth and

preparation conditions11-12 the (111) and (001) surfaces being the most frequent ones For

instance hydrothermal synthesis of NiFe2O4 nanoparticles often leads to faceted

octahedra enclosed by (111) planes13 while films grown on MgAl2O4 or SrTiO3 expose

the (001) surface11-12 Recently DFT calculations have shown that H2O undergoes strong

dissociative adsorption on the metal terminated (111) surface13 Instead the structure of

the (001) surface and its interaction with water have not yet been studied

98

To help fill this gap we present here a computational study of the structure of the

NiFe2O4(001) surface exposed to molecular oxygen and water vapour the most common

gases with which a surface can be in contact Using the DFT+U method we start by

studying the electronic density of states (DOS) of bulk NiFe2O4 both in the absence and

in the presence of an oxygen vacancy These results are used as a reference in order to

understand the effects of the (001) termination on the electronic structure We next study

the adsorption of water on both the defect-free and defected NiFe2O4(001) surfaces Our

computed surface stability diagram predicts that the NiFe2O4(001) surface is

hydroxylated at ambient conditions while it exhibits surface oxygen vacancies in the

temperature range of 600-900 K that is often used for catalytic reactions

Another important aspect of the surface chemistry of NiFe2O4(001) that is discussed in

this chapter is the surface reactivity toward CO and methane The oxidation reactions of

CO and methane on NiFe2O4(001) are found to go through reaction paths similar to those

found for NiCo2O4 CO oxidation is limited by O2 adsorption on vacancies which is more

difficult than on NiCo2O4 Methane oxidation is found to have a slightly higher pseudo

transition barrier compared to NiCo2O4


DFT calculations were performed within the plane-wavendashpseudopotential scheme as

implemented in the Quantum Espresso package14 Spin polarization was always included

and exchange and correlation terms were described using the gradient corrected Perdew-

Burke-Ernzerhof (PBE)15 functional with the on-site Coulomb repulsion U term on the Fe

and Ni 3 d states We used the values U(Ni) =55 eV and U(Fe)=35 eV and 34 eV for

different Fe sites which were determined from linear response16 Ultrasoft

pseudopotentials17 were employed and the valence electrons included O 2 s 2 p Fe 3 d 4

s and Ni 3 d 4 s states Kinetic energy cutoffs of 50 Ry and 500 Ry were chosen for the

wave functions and augmented density respectively Structural optimizations were

carried out by relaxing all atomic positions until all forces were smaller than 1 times 10 minus3

au

99

Bulk calculations were performed using different unit cells The lattice constant was

determined using the 28-atom primitive cell (Figure 35a) with a 4 times 4 times 3 Monkhorst-

Pack k-point grid to sample the Brillouin zone To model a bulk oxygen vacancy we

used the conventional cubic cell (Figure 35b) with one oxygen atom removed and

sampled the Brillouin zone with a 3 times 3 times 3 k-point grid

As in previous studies of the surfaces of spinel oxides18-20 we modeled the NiFe2O4(001)

surface using symmetric slabs of 11 layers terminated by layers exposing oxygen and

octahedral Fe and Ni sites The slabs were separated by a vacuum region 20 Aring wide To

check the convergence of the slab thickness we calculated the surface oxygen vacancy

formation energy (see definition below) for slabs of different thicknesses we found the

formation energy difference between 11-layer and 13-layer slabs to be less than 001 eV

We considered 1 times 1 square unit cell which corresponds to the conventional cell We

sampled the surface Brillouin zone using a 3 times 3 times 1 k-point grid Adsorption calculations

and defected surface calculations were performed with adsorbed species and surface

defects present on one side only of the slab (Model I) To validate this approach we

performed test calculations with adsorbed species and defects symmetrically present on

both sides of the slab (Model II) We found that the two models predict very similar

results For instance the computed surface oxygen vacancy formation energy at T = 0K is

0342 eV with Model I and 0366 eV with Model II Moreover the value obtained for

Model I changed by less than 001 eV when dipole corrections were included Similarly

water dissociation at the surface vacancy yields an energy gain of 1026 eV with Model I

and 1025 eV with Model II

In order to study the surface phase diagram we computed the formation energy

119864119864119865119865119867119867(119879119879 119901119901119894119894 119899119899119894119894) of the surface in contact with various gases at temperature T as

follows21

119864119864119865119865119867119867(119879119879 119901119901119894119894 119899119899119894119894) = 119864119864119890119890119889119889119890119890(119899119899119894119894) minus 119864119864119875119875 minus sum 119899119899119894119894 times 119906119906119894119894(119879119879119901119901119894119894)119889119889119904119904119904119904 (1)

Here 119901119901119894119894 are the partial pressures of the gaseous species (oxygen and water) 119899119899119894119894 are

the corresponding numbers of adsorbeddesorbed molecules onfrom the surface

119864119864119890119890119889119889119890119890(119899119899119894119894) is the total energy of the slab with the adsorbeddesorbed species at 0 K (the

100

T-dependence of the chemical potential of the slab can be considered negligible) 119864119864119875119875 is

the total energy of the clean pristine (defect-free) surface and 119906119906119894119894(119879119879119901119901119894119894) is the chemical

potential of gas species i at temperature T and pressure 119901119901119894119894 For the latter the expression

given in Ref21 was used The zero point energy (ZPE) contribution of molecular water

and adsorbed water and hydroxide groups was included in the corresponding chemical

potential and total energies

As a special case of Eq (1) the formation energy of an oxygen vacancy at 0 K and

oxygen partial pressure of 1 atm was calculated using the expression 119864119864119865119865119867119867 = 119864119864119907119907119904119904119909119909 minus

119864119864119899119899119889119889minus119889119889119890119890119891119891 minus 121198641198641198741198742 where 119864119864119907119907119904119904119909119909 and 119864119864119899119899119889119889minus119889119889119890119890119891119891 denote the total energies of the systems with

and without vacancy respectively

Figure 35 Primitive cell (a) and conventional cell (b) of the α-type inverse spinel crystal

structure of NiFe2O4 (c) Local structure of an oxygen vacancy (black sphere) in the

conventional cell with different atoms labeled as in Table 14 Red gray and yellow

spheres represent oxygen Ni and Fe atoms respectively

101

3 Results and Discussion 31 Bulk properties

NiFe2O4 crystallizes in the α type inverse spinel (Figure 35a) which has a tetragonal

P4122P4322 symmetry22 Equal numbers of Ni and Fe atoms occupy octahedral sites

while the remaining Fe atoms occupy tetrahedral sites The conventional cell (Figure

35b) is a radic2 times radic2 times 1 primitive cell having 8 formula units The lattice constant was

determined by fitting the computed total energies to the Birch-Burnagham equation of

state We obtained a value of 845 Aring which is about 14 larger than the experimental

value of 833 Aring23

The computed DOS for the defect-free crystal (Figure 36a) shows an overall band gap of

10 eV The band gap is 15 eV for the majority bands (spin up) and 16 eV for the

minority bands in good agreement with the experimental value of the optical band gap of

16 eV24 Also in agreement with experiment10 24 we find NiFe2O4 to be ferrimagnetic

the octahedral (Oh) and tetrahedral (Td) sites being occupied predominantly by majority

and minority spins respectively The oxidation states of the metal ions computed using

the method in Ref25 are 2+ for Ni and 3+ for Fe

Figure 36 Density of states for (a) defect-free bulk NiFe2O4 (b) defective crystal with

an oxygen vacancy (Figure 35c)

102

As most oxidation reactions on metal oxides occur through a Mars-van Krevelen

mechanism the oxygen vacancy formation energy is usually considered a good

descriptor of the reactivity of these materials26 NiFe2O4 contains two inequivalent

oxygen anions OI bound to 2 Fe and 1 Ni at Oh sites and 1 Fe at Td and OII bound to 1

Fe and 2 Ni at Oh sites and 1 Fe at Td We found that an OI vacancy is slightly preferred

(less costly) with respect to an OII one Still the computed formation energy 287 eV is

rather high indicating that one may need high vacuum and high temperatures to create

oxygen vacancies in bulk NiFe2O4 For comparison we also computed the oxygen

vacancy formation energy in Co3O4 another well-studied spinel oxide using DFT+U

with U = 44 and 66 eV for Co ions at Td and Oh sites respectively27 The resulting

value 288 eV is very similar to that found for NiFe2O4

Table 14 Displacements of the atoms close to a bulk O-vacancy (Figure 235c) with

respect to their positions in the defect-free crystal (Figure 35b) Atoms are labelled as in

Figure 35c Only the atoms closest to the vacancy are considered

Displacement (Aring)

x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017

The displacements of several atoms around the oxygen vacancy are reported in Table 14

Fe2 the Fe(Td) cation closest to the oxygen vacancy (which was originally bonded to the

removed O atom) undergoes a large displacement 046 Aring with respect to its position in

the defect-free crystal Large displacements of about 01 Aring are present also for a few

oxygens (O2 O25 and O31) bonded to Fe2 The electronic DOS for the defective crystal

is shown in Figure 36b We can see that the DOS for the majority spin states is little

affected by the O-vacancy whereas additional bands are present for the minority spin

states in particular a new occupied state above the original minority band valence band

maximum This results in a smaller minority band gap of ~ 10 eV At the same time the

Fermi levels moves up in the band gap consistent with the fact that the O-vacancy is an

electron donor Analysis of the spin and charge distribution further shows that one of the

two excess electrons donated by the O-vacancy reduces the oxidation state of the

neighboring Fe2(Td) cation from 3+ to 2+ and at the same time reduces also its

magnetic moment The other excess electron is shared by the three neighboring Fe10

Fe13 and Ni6 cations at Oh sites and slightly reduces their magnetic moments Since Td

and Oh sites have different spin states the total magnetization remains unchanged in the

presence of the O-vacancy

104

32 NiFe2O4 (001) surface 321 Defect-free surface

The optimized structure of the NiFe2O4(001) surface is shown in Figure 37 while the

atomic displacements relative to the positions of the bulk-terminated surface are reported

in Table 15 We can see significant outward displacements of the atoms in the first three

layers in comparison to the positions of the bulk-terminated surface Particularly large

(gt01Aring) displacements along the [001] direction are present for Fe2(Td) in the second

layer and for O2 O3 O4 in the top three layers Large in plane displacements are also

present for O2 and O3 the surface oxygens that are not bonded to Fe2

Figure 37 Structure of the NiFe2O4 (001) surface (a) top view of the top three layers

and (b) side view Various O Fe and Ni atoms are indicated

105

Table 15 Displacements of the atoms in the first three layers of the relaxed (001) surface

relative to their positions at the bulk-terminated surface

Displacement Aring in plane (001) direction

O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082

The DOS (Figure 38a) for the defect-free NiFe2O4(001) surface shows the formation of

surface states in the band gap of the majority spin DOS which make the surface metallic

An analogous result was found for the Co3O4(110) surface18 By contrast the minority

spin band is almost unaffected by the presence of the surface and remains very similar to

the minority spin band in the bulk The computed work function was determined from

the analysis of the electrostatic potential profile and found to have a value of about 6

eV

106

Figure 38 DOS for (a) clean defect-free NiFe2O4(001) (denoted as P) (b) clean surface

with 1 oxygen vacancyunit cell (P + 1VO) (c) hydroxylated surface resulting from the

adsorption of 1 water moleculeunitcell on the surface in (b) (P + 1VO + 1H2O) (d) fully

water-covered surface resulting from the adsorption of 6 water moleculesunit cell on the

surface with 25 concentration of oxygen vacancies (P + 2VO + 6H2O)

322 Surface O vacancy

To determine the preferred structure of NiFe2O4(001) we studied the formation of 1 and

2 surface oxygen vacancies (VOrsquos) per unit cell corresponding to surface VO

concentrations of 18 (Figure 39a) and frac14 (Figure 39b) respectively The formation of 1

VO unit cell has an energy cost of 034 eV at 0 K and 1atm O2 pressure The most

favorable site for VO formation is the O3 site ie the oxygen that bonds to two Ni cations

(Ni1 and Ni2) and one Fe (Fe1) By comparing to the bulk formation energy of 287 eV

it is clear that creating an oxygen vacancy at the surface is much easier than in the bulk

This remains true also at higher VO concentrations even though the VO formation energy

107

increases significantly with increasing concentration The formation of 2 oxygen

vacancies per unit cell (Figure 39b) has indeed an energy cost of 143 eV which

corresponds to an average formation energy of 071 eV per vacancy The two oxygen

vacancies prefer to form both at O3 sites and all O3 anions are removed by forming 2

oxygen vacancies unit cell Formation of the second oxygen vacancy at O2 which binds

to 2 Fe(Oh) site and 1 Ni(Oh) has a slightly higher energy cost than at the O3 site

whereas O1 is much harder to remove Since O1 binds to Fe2(Td) removing O1 would

indeed result in a undercoordinated Fe(Td) which is much more unstable

Figure 39 Top views of the first three layers of the NiFe2O4(001) surface in the presence

of (a) 1 O-vacancy (P+ 1VO) (b) 2 O-vacancies (P+ 2VO) The oxygen vacancies are

indicated by the black spheres Atoms are labelled as in Figure 37

The DOS for the surface with 18 VO coverage is shown in Figure 38b We can see a

change in the majority spin surface state band which results in the opening of a narrow

band gap of ~01 eV at the Fermi level On the other hand the minority spin band does

not change significantly except for a small increase by 01 eV of the band gap The

108

computed work function 59 eV remains almost unchanged relative to the one for the

pristine surface

33 Water adsorption 331 Water adsorption on the defect-free surface

The adsorption structures of water on the pristine NiFe2O4(001) surface are found to vary

significantly with coverage At frac14 mono-layer (ML) coverage corresponding to 1 water

molecule per surface cell (Figure 40a) water adsorbs in molecular form on a Ni cation

whereas it dissociates on Fe resulting in an OH on top of the Fe ion and an H donated to

a surface oxygen The adsorption energy on Ni is 053 eV which is about 01 eV more

favorable that on Fe At frac12 ML coverage (Figure 40b) the two water molecules prefer to

adsorb both in molecular form one on a Ni site and one on a Fe site with an adsorption

energy of 044 eVH2O At frac34 ML coverage (Figure 40c) the most stable configuration

corresponds to two water molecules adsorbed in molecular form on Ni sites and one

dissociated water on a Fe site and the adsorption energy is 058 eV H2O Finally the

preferred configuration at full water coverage has all the 4 water molecules adsorbed in

molecular form (Figure 40d) two on Ni one on Fe and one forming an H-bond with an

O site with average adsorption energy of 052 eV H2O A mixed molecular-dissociated

structure with two intact and two dissociated water molecules adsorbed on Ni and Fe

sites respectively was found to be slightly higher in energy

109

Figure 40 Phase diagram of pristine NiFe2O4 (001) exposed to water vapour The two

vertical lines in cyan indicate the region of water chemical potential corresponding to

liquid water (300 K ndash 400 K) The side panels show the structures of adsorbed water at

different coverages (top views) (a) frac14 ML (b) frac12 ML (c) frac34 ML (d) 1 ML Reported

adsorption energies include the change of zero point energies

The phase diagram for the pristine surface exposed to water is shown in Figure 40 This

was obtained by considering the dependence of the computed surface formation energies

on the water chemical potential 12054912054911990611990611986711986721198741198741198791198791199011199011198671198672119874119874 = 1199061199061198671198672119874119874119879119879 1199011199011198671198672119874119874 minus 1198641198641198671198672119874119874 where EH2O

denotes the total energy (including ZPE) of a water molecule at T=0K This diagram

predicts that all water desorbs from the pristine surface at temperatures above ~ 300K

332 Water adsorption on the defected surface

Figure 41 shows some adsorption structures of water on defected NiFe2O4(001) surfaces

at various coverages From the reported adsorption energies (Eads) we can see that water

adsorption is much more favorable on the defected surface than on the pristine surface

110

(Figure 40) In the presence of a surface oxygen vacancy (Figure 39a structure P+1Vo)

a water molecule dissociates on the VO giving rise to two surface hydroxyls with Eads =

090 eV (Figure 41a structure P+1Vo+1H2O) By adsorbing three additional water

molecules to this structure the water molecule adsorbed on the Fe site dissociates into

OH groups while the other two molecules at Ni sites remain intact (Figure 41b

P+1Vo+4H2O) The average adsorption energy per molecule is 070 eV which is smaller

than the value for a single water molecule in Figure 41a On the surface with two oxygen

vacancies (P+2Vo) the configuration with two water molecules adsorbed dissociatively

on the two VOrsquos gives the highest adsorption energy 123eV molecule (structure

P+2Vo+2H2O Figure 41c) When two additional water molecules are adsorbed on this

surface one prefers to adsorb in molecular form on a Ni site while the other is

dissociatively adsorbed on a Fe site(Figure 41d P+2Vo+4H2O) The adsorption energy

086 eVmolecule is lower compared to Figure 41c but still quite higher than water

adsorbed on the pristine surface Finally the addition of two further water molecules

leads to a configuration where all metal sites are covered by adsorbed water (Figure 41e

P+2Vo+6H2O) The two added molecules dissociate on Fe1 sites and the average

adsorption energy is 072 eVmolecule Altogether it appears that mixed molecular-

dissociated configurations are favored at high coverages Water dissociation takes place

both at oxygen vacancies and at Fe sites whereas adsorption in molecular form is

preferred at Ni sites

111

Figure 41 Adsorption structures (top views) of water on defected NiFe2O4(001) surfaces

at different coverages (a) one water molecule adsorbed to a surface with 1 oxygen

vacancy (P+1VO+1H2O) (b) four water molecules adsorbed to a surface containing 1

oxygen vacancy (P+1VO+4H2O) (c) two water molecules adsorbed to two oxygen

vacancies (P+2VO+2H2O) (d) four water molecules adsorbed to a surface containing 2

oxygen vacancies (P+2VO+4H2O) (e) six water molecules adsorbed to a surface with two

oxygen vacancies (P+2VO+6H2O) All structures shown refer to a single surface cell

Reported adsorption energies per molecule include ZPE corrections

The DOS for the surface with an adsorbed water molecule at an oxygen vacancy site

(Figure 38c) is very similar to that of the bare surface with the VO (Figure 38b) Analysis

of the surface metal oxidation states shows that also these oxidation states remain

unchanged upon water adsorption Altogether this indicates that the influence of

adsorbed water on the surface electronic structure is rather limited Support for this

conclusion is also provided by the DOS for the fully hydrated surface (Figure 41e) which

is shown in Figure 38d Comparison to the DOS in Figure 38b and 38c for the clean

defective and hydroxylated surfaces indicates that the main effect of the adsorbed water

112

is the presence of additional bands for both spin states in the band gap near the Fermi

level

Figure 42 Phase diagram of NiFe2O4(001) exposed to H2O and O2 as a function of the

relative chemical potentials 120549120549119906119906119894119894(119879119879119901119901119894119894) = 119906119906119894119894(119879119879119901119901119894119894) minus 119864119864119894119894 referred to the their values at

T=0K The two horizontal lines in cyan indicate the region of water chemical potential

corresponding to liquid water P in the phase diagram indicates the pristine (001) surface

34 Phase diagram

In order to characterize the stability of the (001) surface in O2 and water vapour

environment we examined about 30 surface configurations without and with adsorbed

water and used them to determine the stability diagram of the NiFe2O4 (001) surface in

O2 and water vapor environment The resulting diagram is shown in Figure 42 We

113

identified eight favored structures in the relevant range of water and oxygen chemical

potentials Among these two structures ie P+1VO and P+2VO+2H2O are more

prominent In a wide range of conditions including ambient conditions the P+2VO+2H2O

structure corresponding to a surface with ~ 25 of hydroxyls is predicted to occur At

higher temperatures water desorbs and a dry surface with oxygen vacancies (~ 12

concentration) becomes more favorable The latter structure may be the one which is

typically present during catalytic reactions like the WGS and the CO oxidation reactions

35 CO oxidation

The interaction of CO with the (001) surface of NiFe2O4 (NFO) is weaker in comparison

to that with Co3O4 and NCO (001) surfaces We found indeed an average CO adsorption

energy of -011 and -042 eV on Fe and Ni sites of NFO (001) to be compared to -031

and -088 eV on Ni and Co sites of NCO (100)(001) and -092 eV on Co sites of

Co3O4(001) thus NFO tends to have inert cation-CO interaction On the other hand

NFO(001) has the lowest computed VO formation energy among these materials which

has important consequences on the COOR as identical reaction path is found compared

with NCO As shown in Table 16 the free energy change for the step of CO2 formation (I

II) of the COOR is in fact significantly more favorable on NFO(001) than on Co3O4

(100) and NCO (001)(100) surfaces with similar reaction pathway (Figure 43) while the

step of O2 adsorption at a VO (III IV) is less favorable on NFO(001) in comparison to

Co3O4(100) and NCO (001)(100) This could be a reason why NFO is a less efficient

COOR catalyst than Co3O4 and NCO

114


pristine (P) and defected (D) NFO (001) surfaces Results are reported at both T= 0 K and

T = 300K (between parentheses) with CO and O2 pressure of 1 and 02 atm respectively


P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)

Figure 43 Pathway of formation of CO2 (I rarr II) on NFO (001) surface from initial state

(IS structure I) to transition state (TS) and final state (FS structure II) The relative

energy (in eV) with respect to initial structure is display below the structures It shows

identical mechanism compared with NCO (001) surfaces with minor different being the

energy of transition barrier

As the NFO (001) surface tends to be hydroxylated in humid environment we also

investigated the influence of surface hydroxyls on CO adsorption We used the

P+2VO+2H2O structure where all O1 sites are changed into OH groups which represents

the stable surface in a wide range of temperatures and found that CO tends to remain at

115

least 25 Aring away from the surface This indicates only weak interaction between the

hydroxylated surface and gaseous CO which may be another reason of the low COOR

activity of NFO

36 Methane oxidation

As on the NCO (100)mix surface CH4 can only physisorb on the NFO (001)surface as

the molecule remains more than 28 Aring away from the surface in fact the computed

adsorption energy is only -009 eV The barrier of the first C-H bond breaking was first

estimated by the energy of the configuration where hydrogen is adsorbed on the surface

and the methyl radical is in gas phase In this way we obtained a pseudo barrier of 058

eV slightly larger than on NCO (100)mix indicating that the NFO (001) surface is slightly

less active compared with NCO (100)mix surface even though oxygen vacancies are easier

to form on NFO(001) We also determined the barrier with more accurate NEB

calculations which always gave transition states with a gas phase methyl radical like

structure (as used for the preliminary estimate) However the transition barrier obtained

with NEB is much larger 113 eV indicating an under estimation by around 055 eV

with the pseudo barrier approximation To determine the energy of the first C-H bond

breaking we examined configurations where both the methyl and hydrogen were

adsorbed on the surface Results are comparable to those for the NCO (100)mix surface

Methyl adsorbed on surface Fe and Ni results in a formation energy of -027 eV and -031

eV respectively Methyl on surface O1 sites results in a formation energy of -074 eV and

-244 eV respectively for hydrogen adsorbed on the same and different O1 sites NCO

(100)mix surface is likely to be more active when compared with NFO (001) surfaces due

to slightly lower C-H bond breaking barrier

As found for NCO (100)mix the second C-H bond breaking leads to an adsorbed CH2

bridging O1 and another surface site In the most favorable configuration with CH2

bridging two O1 sites the formation energy is -119 eV whereas CH2 bridging O1 and

O2 sites is much less favored with a formation energy of -032 eV All other structures

116

including CH2 bridging metal sites or forming an adsorbed CH2O species on VO are

energetically unfavored

4 Summary and Conclusions

We have studied the atomic structure electronic properties and reactivity of the bulk and

(001) surface of NiFe2O4 using the PBE+U method Our results show that unlike in the

bulk oxygen vacancies form quite easily on the nickel ferrite surface especially at

oxygen sites that are coordinated mainly to Ni ions Our results also indicate that

dissociative adsorption of water at vacancy sites is much more favorable than adsorption

at regular surface sites thus suggesting that a humid environment may help the creation of

oxygen vacancies From our computed surface phase diagram we infer that the

NiFe2O4(001) is hydroxylated at ambient conditions while water desorption should lead

to a defective surface containing a significant fraction of oxygen vacancies at higher

temperature

It is also interesting to notice that our computed phase diagram for NiFe2O4(001) in

Figure 42 is significantly different from that for the Fe3O4 (001) surface20 exposed to

water and oxygen despite the similarity of the two surfaces In comparison to

NiFe2O4(001) the Fe3O4 (001) surface shows a stronger tendency to adsorb water

whereas formation of an oxygen vacancy appears to be much more difficult CO

oxidation through the Mars-Van Krevelen mechanism and breaking of the methane C-H

bond on NiFe2O4 (001) are found to proceed through reaction pathways that are

qualitatively similar but energetically less favorable than those on the NCO (100)mix

surface

117

5 References

1 Brabers V A M Chapter 3 Progress in Spinel Ferrite Research 1995 8 189-

324

2 Han D-H Luo H-L Yang Z Remanent and Anisotropic Switching Field

Distribution of Platelike Ba-Ferrite and Acicular Particulate Recording Media Journal of

Magnetism and Magnetic Materials 1996 161 376-378

3 Cunningham C H Arai T Yang P C McConnell M V Pauly J M

Conolly S M Positive Contrast Magnetic Resonance Imaging of Cells Labeled with

Magnetic Nanoparticles Magnetic Resonance in Medicine 2005 53 999-1005

4 Worledge D C Geballe T H Magnetoresistive Double Spin Filter Tunnel

Junction Journal of Applied Physics 2000 88 5277

5 Hu G Suzuki Y Negative Spin Polarization of Fe3o4 in MagnetiteManganite-

Based Junctions Physical Review Letters 2002 89










9 Sun Q-C Sims H Mazumdar D Ma J X Holinsworth B S OrsquoNeal K

R Kim G Butler W H Gupta A Musfeldt J L Optical Band Gap Hierarchy in a

Magnetic Oxide Electronic Structure of Nife_2O_4 Physical Review B 2012 86





118

11 Lders U Bibes M Bobo J F Fontcuberta J Tuning the Growth

Orientation of Nife2o4 Films by Appropriate Underlayer Selection Applied Physics A

2004 80 427-431

12 Klewe C Meinert M Boehnke A Kuepper K Arenholz E Gupta A

Schmalhorst J M Kuschel T Reiss G Physical Characteristics and Cation

Distribution of Nife2o4 Thin Films with High Resistivity Prepared by Reactive Co-

Sputtering Journal of Applied Physics 2014 115 123903



Chemistry C 2013 117 5678-5683



395502




the Effective Interaction Parameters in the Lda+U Method Physical Review B 2005 71



18 Chen J Selloni A Electronic States and Magnetic Structure at the Co3o4(110)

Surface A First-Principles Study Physical Review B 2012 85

19 Mulakaluri N Pentcheva R Scheffler M Coverage-Dependent Adsorption

Mode of Water on Fe3o4(001) Insights from First Principles Calculations The Journal

of Physical Chemistry C 2010 114 11148-11156




21 Reuter K Scheffler M Composition and Structure of Theruo2(110)Surface in

Ano2and Co Environment Implications for the Catalytic Formation Ofco2 Physical

Review B 2003 68

119









2007 19 346219

25 Sit P H L Car R Cohen M H Selloni A Simple Unambiguous

Theoretical Approach to Oxidation State Determination Via First-Principles Calculations

Inorganic Chemistry 2011 50 10259-10267

26 McFarland E W Metiu H Catalysis by Doped Oxides Chemical Reviews

2013 113 4391-4427


Cobalt Oxide in the Spinel Structure Physical Review B 2011 83

copy Copyright by Xiao Shi 2018

All rights reserved

iii







probe molecules















Co3O4







iv























v

Acknowledgement


























vi



vii




21 CO Oxidation 4




5 References 9








4 References 24


cobalt oxide 26

1 Introduction 26







4 Conclusions 43

5 References 45

viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



iii







probe molecules















Co3O4







iv























v

Acknowledgement


























vi



vii




21 CO Oxidation 4




5 References 9








4 References 24


cobalt oxide 26

1 Introduction 26







4 Conclusions 43

5 References 45

viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



iv























v

Acknowledgement


























vi



vii




21 CO Oxidation 4




5 References 9








4 References 24


cobalt oxide 26

1 Introduction 26







4 Conclusions 43

5 References 45

viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



v

Acknowledgement


























vi



vii




21 CO Oxidation 4




5 References 9








4 References 24


cobalt oxide 26

1 Introduction 26







4 Conclusions 43

5 References 45

viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



vi



vii




21 CO Oxidation 4




5 References 9








4 References 24


cobalt oxide 26

1 Introduction 26







4 Conclusions 43

5 References 45

viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



vii




21 CO Oxidation 4




5 References 9








4 References 24


cobalt oxide 26

1 Introduction 26







4 Conclusions 43

5 References 45

viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



viii


1 Introduction 49







4 Conclusions 73

5 References 75



1 Introduction 78



31 Co3O4 (001) and (110) surfaces 81


312 CO oxidation 83

32 NCO (001)(100) surfaces 87




4 Conclusions 92

5 References 94



1 Introduction 97



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



ix









35 CO oxidation 113



5 References 117

1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



1

Chapter I

















exhaust gases 4-5







2
























3













(Figure 2)









4









surface21












5


surface
























6
























7

















8



















presented

9

5 References























Reports 2015 5 15201







10





















085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097

11




Catalysis 2000 194 55-60





2002 210 198-206





















12











2007 19 346219










431











13



Chemistry C 2013 117 5678-5683

14

Chapter II





experiment











minus119894119894ħ120597120597120597120597120597120597120627120627 = Ĥ120627120627




Ψ



15

Ĥ120569120569119899119899 = 119864119864119899119899120569120569119899119899

















for the system










16























form

119864119864[119899119899(119903119903)] = 119879119879[119899119899(119903119903)] + 119880119880[119899119899(119903119903)] + 119881119881119890119890119890119890119890119890[119899119899(119903119903)] ∙ 119899119899(119903119903) ∙ 119889119889119903119903


119879119879[119899119899(119903119903)] and 119880119880[119899119899(119903119903)]



17





119880119880[119899119899(119903119903)] =12


119889119889119903119903119889119889119903119903prime + 119864119864119890119890119909119909[119899119899(119903119903)]


correlation energy








119864119864119890119890119909119909119871119871119871119871119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903)]119889119889119903119903







119864119864119890119890119909119909119867119867119867119867119871119871[119899119899(119903119903)] = 119899119899(119903119903) ∙ 119907119907119890119890119909119909119867119867119867119867119867119867[119899119899(119903119903) |nabla119899119899(119903119903)|2]119889119889119903119903



18












19





























20



119907119907119867119867[119903119903119899119899(119903119903)] = 119890119890119899119899(119903119903prime)
























119864119864119880119880[119899119899119897119897119897119897] =11988011988021205821205821198941198941198971198971198971198971 minus 120582120582119894119894119897119897119897119897

119894119894119897119897119897119897

21





























22


























23











24

4 References


136 B864-B871







Review A 1994 50 3089-3095
















9982-9985





25













26

Chapter III



oxide

1 Introduction







based catalysts8














27





























28















orbitals







29












constant a0 Aring

Bulk modulus B

GPa

Doping energy eV


parallel

0 8149 203 - -

18 8162 190 0028 0031

14 8173 179 -0009 -0019

38 8184 175 -0056 -0067

12 8196 171 -0062 -0073

58 8199 136 -0086 -0093

34 8216 167 -0095 -0103

78 8227 170 -0113 -0113

1 8237 163 -0125 -0119




30






ions







31





























32














33


















34




orbitals












35












gap around 26 eV17

36





minority spins





119864119864119904119904119904119904119904119904 = (119864119864119890119890119890119890119909119909ℎ minus 1198641198640) 119899119899frasl




37
















38

























39





Esub eV (Tsub K)

Method R = 18 R= 14 R = 1

PBE 0157 (438) 0151 (672) 0113

DFT+Ueff 0044 (123) 0042 (185) 0062

DFT+ULR 1305 (3541) 1288 (5887) 1314



40

34 Oxygen vacancies




stability of NCO



119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 121205831205831198741198742 minus 1198641198640 minus 119896119896119904119904119879119879119897119897119899119899119879119879









constant Aring

Eform (eV)

site A

Eform(eV)

site B

NCO 0 8141 317 (076) 302 (061)

Ueff 8209 235 (-006) 226 (-017)

ULR 8237 180 (-061) 163 (-077)

Co3O4 0 8088 334 (093)

ULR 8149 159 (-082)




41











vacuum)19





















42













43



4 Conclusions











44














conductivity

45

5 References



Reports 2013 3 1470




















660






46













085204-1 - 085204-8



Phys Lett 2012 100 032102





Reports 2015 5 15201







2014 24 610-618



47


C 2014 118 19085-19097



395502





-035105-16




Phys Rev Lett 1979 43 1494-1497



Phys Commun 2008 178 685-699















48




247-352

49

Chapter IV



1 Introduction























50





























51



























119860119860

52



∆120574120574 = (∆119864119864119904119904119897119897119904119904119904119904 + 119899119899(120583120583119873119873119894119894 minus 120583120583119862119862119889119889))119860119860











53





displacementAring

out of plane

displacementAring

(001)Ni

Ni

Co(Td)

O1

O2

0029

0051

0133

0091

-0087

0146

-0118

-0046

(001)Co

Co(Oh)

Co(Td)

O1

O2

0026

0039

0170

0122

-0084

0093

0000

-0049

(100)mix

Ni

Co(Oh)

Co(Td)

O1

O2

0010

0035

0018

0137

0090

-0080

-0118

0106

-0073

-0084







54










Aring

Out of plane

direction Aring

bulk

Ni 2007

Co(Oh) 1944

Co(Td) 1933

(001)Ni Ni 1925 2022

Co(Td) 1882

(001)Co Co(Oh) 1892 1949

Co(Td) 1931

(100)mix Ni 1925 2024

Co(Oh) 1907 1993

Co(Td) 1882




55













56








119864119864119891119891119889119889119903119903119891119891 = 119864119864119889119889119890119890119891119891 + 11989911989921205831205831198741198742 minus 1198641198640 119899119899frasl




57






















58


(0 K)

Formation energy

(300 K 02 atm)

(001)Ni

O1

O2

O1-O1

138

173

141

110

144

112

(001)Co

O1

O2

O1-O1

040

191

079

011

162

051

(100)mix

O1a

O1b

O2

O1a-O1a

O1a-O1b

O1b-O1b

118

082

170

131

113

088

090

054

142

102

085

060

(100)exch

O1a

O1b

O1c

O1d

111

087

125

081

082

059

096

053






59


spin state




sites are indicated







60




3rd layer Ni ion





















between +2 and +3

61










formation energy

eV

Standard deviation

eV

Figure 23a

Figure 23b

Figure 23c

Figure 23d

078 033

075 022

119 027

121 020

O1 126 018

O2 088 006

O3 050 010

62






63










64





















65



3∆119867119867119873119873119862119862119874119874 minus 2∆11986711986711986211986211988911988931198741198744 minus 3∆119867119867119873119873119894119894119874119874 le12∆1205831205831198741198742 le 0







situation


∆microO2

No correction -699 -812 -169 062

Correction a -901 -1014 -219 -039

Correction b -971 -1084 -237 -074


33 Water adsorption








66



























67





dotted line

68










001)Ni

Ni

VO (M)

VO (D)

-042

-094

-157

024

-028

-091

Figure 25a

Figure 25b

Figure 25c

(001)Co Co

VO (M)

VO (D)

-043

-063

-071

022

003

-005

Figure 25d

Figure 25e

Figure 25f

(100)mix Ni

Co

VO1b (M)

VO1b (D)

-044

-033

-079

-115

022

033

-013

-049

Figure 25g

Figure 24a

Figure 24b

Figure 25h

69

















70











71



















72










(001)Ni Ni

VO (M)

VO (M) + VO

017

-040

-062

082

025

003

Figure 26a

Figure 26b

Figure 26c

(001)Co Co

VO (M) + VO

-001

-043

063

022

Figure 26d

Figure 26e

(100)mix Ni

Co

VO1b (M)

VO1a (M) + VO1b

VO1b (M) + VO1b

-003

005

-046

-055

-047

062

070

019

010

017

Figure 26f

Figure 26g

Figure 16c

Figure 16d

Figure 26h

73






4 Conclusions















74









75

5 References








Chem Soc 2008 130 16136-16137










Nano 2013 7 10190-10196





660






76





Reports 2015 5 15201







085204-1 - 085204-8



Phys Lett 2012 100 032102







C 2014 118 19085-19097



165 70-84






14892-14898

77





395502













4391-4427





78

Chapter V



NiCo2O4

1 Introduction






oxidation9-10





The (110)










79


















compared to Co3O49






methane oxidation






80




























81



JANAF Tables30


311 CO adsorption













82



















83






Co O1 O2 VO

Pristine 001 -095(-042) -186(-133) -143(-090)

Defected

001 -090(-038) -175(-122) -104(-052) -065(-013)

Pristine 110 -180(-128) -149(-097) -191(-139)

312 CO oxidation















84


















85


















86








87






O1 site (001)

P

-186(-133) 015(-062) -042(017) -444(-392) 004(-073)

O1 site (001)

D

-175(-122) 014(-063) -053(006) -458(-406) 019(-058)

O1 site (110)

P

-113(-060) 013(-064) -134(-075) -428(-376) 010(-068)

O2 site (110)

P

-197(-144) 040(-038) -105(-046) -399(-346) 009(-068)







Co(Oh) respectively



88












ones as expected




respectively


P - (001)Ni -217(-164) 028(-049) -039(019) -423(-370) -003(-080)

D - (001)Ni -203(-151) 020(-057) -062(-004) -322(-270) -085(-163)

D - (001)Co -217(-165) 009(-068) -043(016) -373(-320) -029(-107)

P - (100)mix -250(-197) 006(-072) -046(013) -342(-290) -021(-098)

D - (100)mix -210(-157) 027(-050) -055(004) -425(-372) 009(-068)

89
















adsorption

90














91













should occur






92














4 Conclusions















93



94

5 References






























95







Catalysis 2000 194 55-60


2002 210 198-206










C 2014 118 19085-19097












96



395502











14892-14898









97

Chapter VI




and methane

1 Introduction



















98




























au

99

























follows21





100















101


















102
















x y Z

O2 0071 -0044 -0048

O11 0008 0044 0045

O13 -0041 0005 0053

O14 0051 0012 -0047

O18 0057 0054 -0001

O19 -0033 -0011 -0004

O25 0077 0055 0075

O31 -0025 -0052 0056

Fe2 0281 -0242 0273

103

Fe10 -0029 0021 -0009

Fe13 -0036 0021 -0033

Ni6 -0010 0060 -0017


















104











105




O1 0098 0026

O2 0185 0126

O3 0185 0080

O4 0085 0108

Ni1 0026 0024

Ni2 0017 0062

Fe1 0049 0036

Fe2 0042 0196

Fe3 0062 0082







eV

106















107
















108


pristine surface

















109















110





















111

















112


level





34 Phase diagram





113








35 CO oxidation














114





P ndash (001) -302(-250) 010(-067) -022(037) -354(-302) 015(-062)

D ndash (001) -228(-175) 010(-068) -040(019) -390(-337) -006(-083)










115



activity of NFO

























116













temperature









surface

117

5 References


324



























118



2004 80 427-431







Chemistry C 2013 117 5678-5683



395502

















Review B 2003 68

119









2007 19 346219





2013 113 4391-4427



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