The University of New South Wales Faculty of Science and Technology School of Materials Science and Engineering

Electrical Properties of CaTi03

A Thesis

in

Ceramic Engineering

by

Mei-Fang Zhou

Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy

March 2004 U N b W 2 7 JAN 2005

LIBRARY CERTIFICATE OF ORIGINALITY

I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, nor material which to a substantial extent has been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis.

I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged.

(Signed) ACKNOWLEDGMENTS

The author would like to express her thanks to the following people for their contributions to the completion of this work:

Prof. J. Nowotny, my supervisor, for sparking my interest in this thesis project and for providing valuable advice on various aspects of the project. I am grateful for his constant encouragement and great assistance with the research plan, thesis corrections and valuable discussion. In particular, he contributed exceptional expertise in the defect chemistry of amphoteric semiconducting oxides.

Prof. C. C. Sorrell, my supervisor, for his quality supervision. The scholarship provided by him has been a key factor in the completion of the project. I am grateful for his valuable advice, helpful discussions and training in scientific research approaches. In particular, he guided me on the crystal chemistry aspects of this work.

Dr. T. Bak, my co-supervisor, for his every day guidance in performing this project and many valuable discussions that were so essential for me to understand defect chemistry and the impact of defect disorder on electrical properties.

Dr. Lou Vance, ANSTO Materials, for his cooperation in many aspects of this research project, which was performed as part of a collaborative program between UNSW and ANSTO.

Mr. J. W. Sharp for contributing his considerable technical and experimental expertise.

Ms. Jane Gao for her support with computing and IT-related matters. I also am grateful for her support for my permanent resident application.

II Dr. Y. Wang and Ms. I. Bolkovsky for the help with X-ray diffraction and Laser Roman Spectrometric analysis; Dr. C. H. Kong, Ms V. Piegerova and Mr. J. Budden for assistance with application of optical and electron microscopy.

Other staff and my friends in the School of Materials Science and Engineering at the University of New South University, for various technical or practical support during the course of my study.

Interlibrary Loan Section, Physical Science Library, UNSW for the acquisition of many papers otherwise unavailable.

Commonwealth Department of Education, Science and Training, Australia for providing financial support in the form of International Postgraduate Research Scholarship (IPRS).

My family members for their constant support and encouragement.

Ill For my family ABSTRACT

The present thesis studied semiconducting properties of polycrystalline CaTiC>3 at elevated temperatures and in controlled gas phase environment. The research included the determination of both electrical conductivity and thermoelectric power in the gas phase of well defined oxygen activity. The aim of research was the determination of the effect of processing conditions, including temperature and oxygen activity, on semiconducting properties of CaTiC>3, and related charge transport.

The present work was performed as a collaborative project between UNSW and

ANSTO. The CaTiC>3 specimen used in this study has been used for the fabrication of SYNROC at ANSTO.

The measurements of electrical conductivity and thermoelectric power of CaTi03 in the ranges of temperature 973 - 1323 K and under oxygen partial pressure lO'-Kf Pa were applied in this work. These two properties were determined simultaneously in the condition of gas/solid equilibrium.

The electrical conductivity data were used for (i) isothermal monitoring of the re­ equilibration kinetics after a new oxygen activity was imposed in the measuring chamber, and (ii) establishment of the equilibrium state. The thermoelectric power (Seebeck coefficient) data were used for the assessment of the conductivity type.

The determined experimental data were used for the following assessments/analyses:

• Verification of the gas/solid equilibrium

• Verification of defect disorder models • Determination of the conductivity components related to different charge carriers (electrons, electron holes and ions) • Verification of the effect of oxygen activity on the n-p transition

The obtained experimental data and their analysis result in the following conclusions:

V 1. The electrical conductivity within the n-p transition range should be considered in terms of the conductivity components corresponding to electrons, electron holes and ions. The latter may assume a substantial value (up to 50% of the total value of the electrical conductivity). 2. The temperature dependence of the electrical conductivity includes both the mobility and the formation terms. The determined activation energy of the formation of defects and their mobility is 125.3 kJ/mol at 10 Pa and 94.4 kJ/mol at 72 kPa, respectively.

3. It was found that the p(C>2) corresponding to zero value of the thermoelectric power differs substantially from the minimum of electrical conductivity as a

function of p(C>2). Therefore, the latter cannot be considered as corresponding to the n-p transition. This phenomenon indicates that the semiconducting properties of CaTiCb differ essentially from other oxide semiconductors which exhibit a good agreement between the minimum of the electrical conductivity and zero value of thermoelectric power. The discrepancy between the two is likely due to different mobility of electrons and electron holes.

The possibilities of incorporation of different impurities into lattice structure of CaTiCb to form substitutional solid solution or interstitial solid solution are assessed. Three atom contact models describing the CaTiCb structure are considered and the total effective concentration of the impurity elements affecting electrical properties of CaTiCb was determined.

The obtained experimental data were used to derive an equation that can be used for prediction of the electrical conductivity of CaTiCb as a function of temperature and oxygen partial pressure:

vpredia = e-'wmll,T(p(O2)x\0rry + 27.81x10''" e~m,MIRT(p(02)x\tfrY + 68.67xl03+r" g-15®10"”'

VI NOMENCLATURE

A Sum of concentration of foreign ion A' Concentration of acceptors [atomic ratio] An Kinetic constant related to scattering of electrons Ap Kinetic constant related to scattering of electron holes e Elementary charge [ 1.60206x 10'19C] Ea Activation energy [kJ/mol] Ec Energy of the bottom of the conduction band [eV]

Ef Fermi energy [eV] Ev Energy of the top of the valence band [eV] F Faraday constant [96500C] AG Change of free energy [J] h Electron holes AF1 Change of enthalpy [J] AHf Formation enthalpy of the predominant defects [J] k Boltzmann constant [8.6167x10'5eV/K, 1.3807x10'23J/K] K Equilibrium constant m Parameter related to defect disorder n Concentration of electrons [atomic ratio] Nn Density of states for electrons [atomic ratio] Np Density of states for holes [atomic ratio] p Concentration of electron holes [atomic ratio] p(C>2) Oxygen partial pressure [Pa] R Electrical resistance [Q] S Thermoelectric power, S [V/K] Sn Seebeck coefficient components related to electrons [V/K] Sp Seebeck coefficient components related to electron holes [V/K] AS Change of entropy [J] T Absolute temperature [K]

VII AT Temperature change across a specimen [K] t Transfer number tj Transport number of ions tn Transfer number of electrons tp Transfer number of electron holes AV Change of potential difference across a specimen [V] z Valency of defects [Tixi] Concentration of Ti ions in their lattice site [Vii””] Concentration of fully charged Ti vacancies [atom ratio] [ ] Concentration of defects n Mobility [mVS'1] p Specific resistivity [Q-cm] g Electrical conductivity [cnf'Q'1] Qj Ionic conductivity component [cnf’Q'1] an Electron conductivity component [cnf'Q"1] gp Electron hole conductivity component [cnf’Q'1]

VIII TABLE OF CONTENTS

SECTION______PAGE

CERTIFICATE OF ORIGINALITY...... I

ACKNOWLEDGMENTS...... II

ABSTRACT...... V

NOMENCLATURE...... VII

TABLE OF CONTENTS...... IX

LIST OF FIGURES...... XIII

LIST OF TABLES...... XIX

LIST OF APENDICES...... XXI

1 INTRODUCTION...... 1

1.1 Nonstoichiometry...... 1 1.2 Electrical Properties...... 2 1.3 Amphoteric Semiconducting Properties...... 3 1.4 Aims...... 4 1.5 Outline of the Thesis...... 4

2 DEFINITION OF TERMS...... 5

2.1 Effect of Oxygen Pressure...... 5 2.2 Basic Terms, Definitions and Equations...... 5 2.2.1 Electrical Conductivity...... 5 2.2.2 Thermoelectric Power...... 6 2.2.3 Electrical Conductivity versus Thermopower...... 12 2.2.4 The Formation of Point Defects...... 13

3 LITERATURE SURVEY...... 15

3.1 Phase Equilibria in the Ca0-Ti02 System...... 15

IX 3.2 Crystal Structure of CaTI03...... 20 3.3 Lattice Parameter of CaTiCL...... 23

3.3.1 Lattice Parameter of Undoped CaTiO 3...... 23 3.3.2 The Effect of Impurities on the Lattice Parameter...... 25 3.3.3 The Effect of Temperature on the Lattice Parameter...... 30 3.4 Preparation of CaTiCL...... 32

3.4.1 Preparation of CaTiO3 Powders...... 32 3.4.1.1 Solid State Reaction...... 36 3.4.1.2 Wet-chemical Processes...... 37 3.4.1.3 Comparison of Preparation Methods...... 41

3.4.2 Preparation of Pellet of CaTiO 3...... 43 3.4.2.1 Powder Consolidation...... 43 3.4.2.2 Sintering Process...... 43

3.5 Micro structure of CaTiC>3...... 44 3.5.1 Phase Transformations...... 44 3.5.1.1 The Effect of Temperature on Phase Transformations...... 44 3.5.1.2 The Effect of Dopant on Phase Transformation...... 46 3.5.2 Grain Size...... 49 3.5.2.1 The Effect of Preparation Methods on Grain Size...... 49 3.5.2.2 The Effect of Mechanical Activation on Grain Size...... 50 3.5.2.3 The Effect of Sintering on Grain Size...... 51 3.5.3 Density/ Porosity...... 51 3.5.3.1 The Effect of Preparation Methods on Density...... 51 3.5.3.2 The Effect of Mechanical Activation on Density/Porosity...... 52 3.5.3.3 The Effect of Sintering on Density...... 53 3.5.4 Grain Boundary...... 54

3.6 Defect Chemistry of CaTi03...... 56

3.6.1 Defect Reactions for Undoped-CaTiOi...... 56 3.6.1.1 Extremely Reducing Conditions...... 57 3.6.1.2 Reducing Conditions...... 58 3.6.1.3 Oxidising Conditions...... 63

3.6.2 Defect Reactions for Doped-CaTiOj...... 63

X 3.6.2.1 Acceptor-type Ions...... 63 3.6.2.2 Donor-type Ions...... 64

3.6.3 Conclusions...... 70

3.7 Electrical Properties of CaTi03...... 71

3.7.1 The Electrical Conductivity of Undoped-CaTiOj...... 71

3.7.2 The Electrical Conductivity of CaTlOi Doped with Aliovalent Ions...... 76

3.7.2.1 Gd-doped CaTi03...... 76

3.7.2.2 Y- and Nb-doped CaTi03...... 76 3.7.2.3 La-doped CaTiCb...... 77 3.7.2.4 Fe-doped CaTiCb...... 79

3.7.2.5 Cr-and Al-doped CaTi03...... 81

3.7.3 Summary...... 82

4 EXPERIMETAL...... 84

4.1 Raw Materials...... 84

4.1.1 Chemicals...... 84

4.1.2 Gases...... 85

4.2 Preparation of CaTiC>3 Pellets...... 85

4.2.1 CaTiOz Powder...... 86

4.2.2 CaTiO3 Pellets...... 86

4.3 Characterization of CaTiC>3 Pellets...... 86

4.3.1 Field Emission Scanning Electron Microscopy (FESEM)...... 86

4.3.2 Density...... 87

4.3.3 Electron Probe Microanalysis (EPMA)...... 87

4.3.4 Inductively Coupled Plasma Mass Spectrometry (ICP - MS)...... 88 4.3.5 Inductively Coupled Plasma Atomic Emission Spectrometry (ICP

-AES)...... 88 4.4 Experimental Set-up...... 88

4.4.1 High Temperature See beck Probe (HTSP)...... 88

4.4.2 Measurement of Electrical Conductivity and Thermopower...... 89

4.4.3 Ancillary Equipment...... 92

4.4.4 Gas System...... 94

4.4.5 Temperature Measurement...... 97

XI 4.4.6 Experimental Procedures...... 97

5 RESULTS AND DISCUSSION...... 101

5.1 Microstructure...... 101 5.2 Electrical Conductivity...... 101 5.2.1 Effect of Oxygen Partial Pressure...... 103 5.2.2 Effect of Temperature...... 107 5.3 Thermopower...... 113 5.3.1 Effect of Oxygen Activity...... 113 5.3.2 Effect of Temperature...... 113 5.3.3 Effect of Temperature on Electrical Conductivity at Constant Thermopower...... 117 5.3.4 Conductivity vs. Thermopower...... 118 5.4 Impurities...... 126 5.4.1 Analysis of Impurities in CaTiOs...... 126 5.4.2 Investigation of Impurities Incorporating into the Lattice Structure of CaTiOi...... 127

5.4.2.1 Lattice Structure of Cubic CaTi03...... 128 5.4.2.2 Substitutional Solid Solution...... 129 5.4.2.3 Interstitial Solid Solution...... 130 5.4.3 Mechanisms Impurities Affecting Electrical Properties of CaTiOi...... 147 5.4.3.1 Electron Transferring Mechanisms...... 147 5.4.3.2 Determination of Effective Concentration of Donors and Acceptors...... 147 5.5 Verification of Defect Chemistry Models using Electrical Conductivity...... 148 5.5.1 Electrical Conductivity Components...... 150 5.5.2 Electrical Conductivity Transfer Numbers...... 152 5.6 Model Equation of Electrical Conductivity for CaTiCE...... 161 5.6.1 Determination of Parameter erf crup and cr. in Equation...... 161

5.6.2 Verification of Parameter in Equation Describing o vs. piOj)...... 165

6 SUMMARY AND CONCLUSIONS...... 171

7 REFERENCES...... 173

XII LIST OF FIGURES

Figure 2-1. Electrical Conductivity of Barium Titanate...... 7 Figure 2-2. Generation of Thermopower...... 8 Figure 2-3. Schematic Illustration of the Plot of AV vs. AT...... 9 Figure 2-4. Thermopower of Barium Titanate...... 11

Figure 2-5. The Effect of p(C>2) on Both o and S...... 12 Figure 2-6. Variation of Gibb’s Free Energy of a Crystal with the Number of Defects...... 14 Figure 3-1. CaO-TiCE Binary Phase Diagram According to R. C. DeVries...... 15 Figure 3-2. Ca0-Ti02 Binary Phase Diagram According to R. S. Roth...... 16 Figure 3-3. CaO-TiCE Binary Phase Diagram According to Jongejan and Wilkins..... 17

Figure 3-4. CaO-TiC>2 Binary Phase Diagram ...... 18 Figure 3-5. CaO-TiCE Binary Phase Diagram According to [26]...... 19 Figure 3-6. Crystal Structure of CaTiCE...... 22

Figure 3-7. The Three Identified Ordered Phases of Can+iTin03n+i...... 22

Figure 3-8. Summary of the Lattice Parameters of Undoped Orthorhombic CaTi03 Reported in Literature...... 23 Figure 3-9. The Change of Lattice Parameter a as a Function of Impurities ...... 27 Figure 3-10. The Change of Lattice Parameter b as a Function of Impurities ...... 27 Figure 3-11. The Change of Lattice Parameter c as a Function of Impurities ...... 28 Figure 3-12. Summary of the Lattice Parameter a of Pure and Doped Cubic

CaTi03 Reported in Literature ...... 28

Figure 3-13. The Change of the Lattice Parameter of CaTi03 with Temperature...... 31

Figure 3-14. The Evolution of Preparation Method for CaTi03 with Year...... 36

Figure 3-15. Summary of Phase Transitions for Pure CaTi03 ...... 45 Figure 3-16. Phase Transformation in Fe-doped CaTiCE...... 46 Figure 3-17. Phase Transformation of Sr-doped CaTiCE...... 47

Figure 3-18. Phase Transformations in Nd-doped CaTi03 for x between 0 and 0.78...... 48 Figure 3-19. Phase Transformation in Nd-doped CaTiCE for x between 0.78 and 0.96...... 48

XIII Figure 3-20. SEM Images of Ca/CTO:Pr Particles Prepared by Solid State Reaction (a) and Sol-gel Method (b) Sintered at 1200°C...... 50 Figure 3-21. SEM Images of the Fracture Surface for the (a) Non-activated and (b) Activated Sample...... 51 Figure 3-22. The Dependence of Mean Particle Diameter of CaTiCE on the Calcination Conditions of the Powder Obtained from Sol-gel Method.... 52 Figure 3-23. Bulk and Grain Boundary Conductivity as a Function of Temperature ...... 55 Figure 3-24. Isothermal Plot of Electrical Conductivity of Undoped CaTi03 as a Function of p(02) According to Balachandran and Eror...... 57 Figure 3-25. Maximum Reversible Weight Change as a Function of Donor Concentration (derived according to data of Balanchandran and Eror.... 67 Figure 3-26. Schematic the Plot of Conductivity vs. Oxygen Partial Pressure...... 71 Figure 3-27. Plots of Electrical Conductivity vs. p(02)...... 73 Figure 3-28. Room Temperature AC Electrical Conductivities of CaTi03 Specimens with Excess CaO or Ti02 Sintered at 1400, 1500 and 1600°C and Subjected to Reduction Treatment in Ar + 5% H2 at 1150°C for 6h...... 74 Figure 3-29. Plots of Electrical Conductivity vs. p(02)...... 75 Figure 3-30. Temperature Dependence of the dc Conductivity of As-prepared Single-crystal Samples. Cai.xYxTi03: Solid Lines; CaTii_xNbx03: Dotted Lines; A Dopant-free Sample: Dashed Line...... 77 Figure 3-31. The Electrical Conductivity of Lanthanum-doped Calcium Titanate as a Function of Oxygen Partial Pressure at 1000°C ...... 78 Figure 3-32. The Electrical Conductivity of Lanthanum-doped Calcium Titanate as a Function of Oxygen Partial Pressure at 1050°C ...... 79 Figure 3-33. Arrhenius plots of the Total Conductivity of CaTii.xFex03.a Measured in Air...... 80 Figure 3-34. Transport Number of Oxide Ion Measured by Oxygen Concentration

Cell for CaTii.xFex03-a...... 80 Figure 3-35. Dependence of the Total Conductivity of CaTii_xFex03.§on the Oxygen Partial Pressure at 1000°C...... 81

XIV Figure 4-1. Procedures for Preparation of CaTiC>3 Bulk by Sol-gel Process...... 85 Figure 4-2. High-Temperature Seebeck Probe External View...... 90 Figure 4-3. Sample Holder for Imposition of a Temperature Gradient along a Rectangular Specimen and Related Electrical Connections for the Determination of Thermopower and Electrical Conductivity...... 91 Figure 4-4. Experimentally Recorded Data of the Thermovoltage as a Function of

Temperature Difference at 972K at p(C>2) = 6.15 kPa and Resulting Thermopower Determined from the Slope of This Dependence...... 93 Figure 4-5. High Temperature Seebeck Probe Functional Diagram...... 95 Figure 4-6. Flowsheet of Gas Flowing Through the Reaction Chamber...... 96 Figure 4-7. An Example of the Standard Monitoring Sheet, Involving p(02), T and EC, in Oxidation Atmosphere at 1273K...... 100 Figure 5-1. SEM Image (magnification x 500) of Polished Surface of Undoped CaTi03...... 102 Figure 5-2. SEM Image (magnification xlOOO) of the CaTiOs Specimen Thermally Etched at 1300K for 1 hour...... 102 Figure 5-3. The Dependence of Conductivity on Oxygen Partial Pressure at Different Temperatures...... 104 Figure 5-4. The Experimental Data of Electrical Conductivity Obtained in This Work vs. log p(02) along with Those of Eror et al...... 106 Figure 5-5. The Dependence of Conductivity on Temperature in Gas with the Oxygen Partial Pressure in the Range of 10-105 Pa...... 108

Figure 5-6. Activation Energy (Ea) of Electrical Conductivity for CaTi03 as a Function of Oxygen Partial Pressure p(02)...... 109 Figure 5-7. The Temperature Dependence of log a Obtained in the Present Work at 21 kPa with Error Bar...... 110 Figure 5-8. The Temperature Dependence of log a Obtained in the Present Work (interpolated for oxygen activity equal to 21 kPa) Along with the Data of Balachandran et al. [13], Dunyushkina et al. [15], Iwahara et al. [174], and Ueda et al. [172] (for the Sake of Comparison Our Data in This Figure are Limited to the Temperatures at 1073K and above)...... Ill

XV Figure 5-9. Enthalpy of Defects Formation Term, AHf, as a Function of Oxygen Partial Pressure...... 112 Figure 5-10. Thermopower (S) of CaTi03 vs. Logarithm of the Oxygen Partial Pressure (log p02) at Different Temperatures...... 114 Figure 5-11. Thermopower of CaTiOs as a Function of 1/T at p(02) = 72 kPa...... 115 Figure 5-12. Thermopower of CaTi03 as a Function of 1/T at p(02) = 10 kPa...... 116 Figure 5-13. Activation Energy of the Electrical Conductivity of Undoped CaTi03 at Constant Thermopower as a Function of Thermopower...... 118 Figure 5-14. Schematic Illustration of the Effect of Symmetry (solid lines) of Thermopower vs. log p(02) and logcr vs. log p(02) Plots and the

Discrepancy between the p(C>2) at S = 0 and that at amjn (broken line)... 120 Figure 5-15. Electrical Conductivity and Thermopower of CaTiCE at 973 and 1073K as a Function of Oxygen Partial Pressure...... 121 Figure 5-16. Thermopower (S) and the Logarithm of Electrical Conductivity (Logcr) of CaTi03 at 1173K vs. Logarithm of the Oxygen Pressure log p(02)...... 122 Figure 5-17. Electrical Conductivity and Thermopower of CaTi03 at 1223K as a Function of Oxygen Partial Pressure...... 123 Figure 5-18. Electrical Conductivity and Thermopower of CaTi03 at 1273K as a Function of Oxygen Partial Pressure...... 124 Figure 5-19. Electrical Conductivity and Thermopower of CaTi03 at 1323K as a Function of Oxygen Partial Pressure...... 125 Figure 5-20. Schematic Diagram of Substitutional Impurities and Interstitial Impurities in Lattice Structure...... 128 Figure 5-21. Phase Transformation of CaTi03...... 128 Figure 5-22. Cubic Perovskite Structure of CaTi03...... 129 Figure 5-23. Solubility of Impurities by Substitution into Ti Position in CaTi03...... 133 Figure 5-24. Schematic Structure of Perovskite CaTi03...... 134 Figure 5-25. The Overlap of Atoms Following 0-0 Contact Model...... 137 Figure 5-26. The Arrangement of Atoms Following Ti-0 Contact Model...... 138 Figure 5-27. The Arrangement of Atoms Following Ca-0 Contact Model...... 138

XVI Figure 5-28. Schematic Diagram of Three Possible Interstitial Sites, Comer Void (CV), Face Void (FV) and Volume Void (VV), in the Cubic Lattice Structure of the CaTiCL...... 139

Figure 5-29. Summary of Possible Location of Impurities in Cubic CaTiC>3...... 146

Figure 5-30. EC Components Including an, ap and 2) at 973K..... 154 Figure 5-31. EC Components Including on, opand

Figure 5-32. EC Components Including on, apand Oj Plots vs. log p(C>2) at 1173K .... 155

Figure 5-33. EC Components Including on, ap and o\ Plots vs. log p(C>2) at 1223K .... 155

Figure 5-34. EC Components Including an, apand o\ Plots vs. log p(C>2) at 1273K .... 156 Figure 5-35. EC Components Including on, apand Oj Plots vs. log p(02) at 1323K .... 156 Figure 5-36. Transfer Number of Electrons, Electron holes, Ions and Total Conductivity Plots vs. p(02) at 973K...... 157 Figure 5-37. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(02) at 1073K...... 157 Figure 5-38. Transfer Number of Electrons, Electron Holes, Ions and Total

Conductivity Plots vs. p(C>2) at 1173K...... 158 Figure 5-39. Transfer Number of Electrons, Electron Holes, Ions and Total

Conductivity Plots vs. p(C>2) at 1223K...... 158 Figure 5-40. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(02) at 1273K...... 159 Figure 5-41. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(02) at 1323K...... 159 Figure 5-42. Comparison of Electrical Conductivity Components between This Study and Eror’s Results at 1323K...... 160 Figure 5-43. Comparison of Transfer Number between This Study and Eror’s Results at 1323K...... 160

Figure 5-44. Temperature Dependence of lncr", In a" and In cr(° for Undoped

CaTi03...... 162

Figure 5-45. Comparison of Electrical Conductivity of CaTi03 in Verified Model (solid lines) Experimental Data (marks) at Different Temperatures...... 163 Figure 5-46. Comparison of Calculated Electrical Conductivity with Experimental Data from Dunyushkina [15]...... 164

XVII Figure 5-47. Comparison of Calculated Electrical Conductivity with Experimental Data from Eror [13]...... 165 Figure 5-48. Schematic of the Change Tendency of Electrical Conductivity of CaTiCE with Acceptor or Donor Doped CaTiCE, ya = Alogcr , yp = Alogp(02)...... 166

Figure 5-49. Comparison of Calculated Electrical Conductivity of CaTiCE (modified by parameter y) with Experimental Data from Dunyushkina et al. [15]...... 169 Figure 5-50. Comparison of Calculated Electrical Eonductivity of CaTiCE (Modified by Parameter j) with Experimental Data from Eror et al. [13]...... 170

XVIII LIST OF TABLES

Table 3-1 Reported Ca0-Ti02 Binary Phase Diagrams...... 20 Table 3-2 Lattice Parameters of Undoped CaTiCE Reported in Literature...... 24 Table 3-3 The Changes of the Lattice Parameter of CaTiCE with Impurities...... 25 Table 3-4 Cell Parameters of CaTiCb Perovskite as a Function of Temperature ...... 29 Table 3-5 Cell Parameters for Strem Sample of CaTiCE Perovskite as a Function of Temperature ...... 30 Table 3-6 Cell Parameters for Aldrich Sample of CaTiCb Perovskite as a Function of Temperature ...... 31 Table 3-7 Evolution of Methods for Preparation of CaTiCE Powders between 1911 and 2003...... 33 Table 3-8 The Isobaric-Isothermic Potentials for the Reactions of Calcium Oxide with Anhydrous and Hydrated Oxides...... 40

Table 3-9 Comparison of Preparation Methods for CaTi03 Powder...... 42 Table 3-10 Summary of Particle Size Derived from Various Preparation Methods..... 49 Table 3-11 Summary of Relative Density Obtained by Different Preparation Methods...... 53 Table 4-1 Raw Materials Specification...... 84 Table 4-2 Gases Specification...... 84 Table 5-1 Reciprocal of the p(02) Exponent of Electrical Conductivity...... 105

Table 5-2 The Activation Energy of CaTi03 in the Temperature Range of 10°-105 Pa...... 107 Table 5-3 Oxygen Partial Pressure Corresponding to the n-p Transition in

Undoped CaTi03 According to Thermopower (S = 0) and Electrical

Conductivity (cfmjn)...... 126 Table 5-4 Concentrations of impurities according to the ICP/MS method...... 127 Table 5-5 Concentrations of impurities according to the ICP/AES method...... 127 Table 5-6 Classification Criteria of Substitutional Solid Solubility for Metallic Impurity Element (X) in Metal (M)...... 129

Table 5-7 Solubility of Impurities into Ti Position in CaTi03...... 131

XIX Table 5-8 Solubility of Impurities into Ca Position in CaTi03...... 132 Table 5-9 Parameter a of CaTi03 from Different Models...... 136 Table 5-10 The Relationship of Radius Ratio and Coordination Number...... 140

Table 5-11 The Radius Ratio (Rca2+/Ro2-) of different models and corresponding Coordination number (CN), Coordination Polyhedron in Cubic CaTi03...... 141

Table 5-12 The Radius Ratio (Rii4+/Ro2-) of different models and corresponding Coordination number (CN), Coordination Polyhedron in Cubic CaTi03...... 141

Table 5-13 The Radius Ratio (RVOid/ R02-) of different models and corresponding Coordination number, Coordination Polyhedron in CaTi03...... 142 Table -5-14 Calculation of Radius for interstitial void in Cubic CaTi03...... 143 Table 5-15 Possibility of Impurities Located in Interstitial Void in Cubic CaTi03 from Ca - O Model:...... 145 Table 5-16 Number of Interstitial Voids in 1 gram CaTi03...... 146 Table 5-17 Number of Impurity Atoms in 1 gram CaTi03...... 146 Table 5-18 The Effective Concentration of Donors and Acceptors...... 149 Table 5-19 Parameter y0 and yp Obtained from Different Set of Experiment Data..... 168

XX LIST OF APPENDICES

Appendix A Calculation of The Radius Ratio for Cation Ions Ca2+ and Ti4+ Appendix B Calculation of The Radius Ratio for Interstitial Voids in CaTiC>3 Appendix C List of Publications

XXI 1 INTRODUCTION

1. INTRODUCTION

1.1 Nonstoichiometry

It is well known that most compounds are nonstoichiometric [1]. This means their chemical formula cannot be described by whole numbers, such as NiO and Ti02. In the case of metal oxides, the nonstoichiometry can be imposed by oxygen partial pressure during processing at elevated temperatures. The nonstoichiometry in metal oxides consists of either metal deficit (in the case of NiO) or oxygen deficit (in the case of Ti02). Therefore, their correct formulae are Nii_xO and Ti02-X, respectively. A consequence of nonstoichiometry is the presence of point defects, such as cation vacancies (in the case of NiO) and oxygen vacancies (in the case of Ti02). The deviation from stoichiometry is determined by the temperature and oxygen partial pressure according to the following general expression [1]:

i -AH j x = const ■ p(02)" exp(^—-—) (1-1) where AH , is the formation enthalpy of the predominant defects, n is the parameter determined by the valency of the defects, T is the absolute temperature, R is the gas constant and p(02) is the oxygen partial pressure. When one type of defects is the predominant lattice defects x in Eq. (1-1), it may be replaced by the concentration of these defects.

The effect of temperature and oxygen partial pressure on the concentration of ionic point defects can be examined by measuring weight changes vs T and p(C>2). Unfortunately, in most cases the effects are below the sensitivity limit of commercial thermobalances. It appears, however, that the point defects that exhibit an electric charge, have a substantial effect on electrical properties, and consequently, these electrical properties are very sensitive to the presence of point defect and the change of their concentration as a function of T and p(C>2).

1 1 INTRODUCTION

The present study will apply the electrical conductivity measurements in studies of defect chemistry of CaTiC>3.

1.2 Electrical Properties

Electrical properties, such as electrical conductivity and thermopower (Seebeck coefficient), have been widely applied in studies of defect chemistry at elevated temperatures [1]. Moreover, the measurements of these properties can also be applied for in situ monitoring of changes of defects concetration when the gas/solid system is in the transition from one equilibrium state to another [1]. Therefore, the electrical properties may be applied for in situ monitoring of defect structure during materials processing at elevated temperatures.

Changes of nonstoichiometry have an effect on electrical properties only when point defects, such as metal vacancies or oxygen vacancies, are ionised leading, in consequence, to the formation of both ionic and electronic charge carriers:

V0 — Va + 2e' (1-2) Eq. (1-2) represents ionisation of oxygen vacancies resulting in the formation of doubly ionised oxygen vacancies and electrons where, according to the notation of Kroeger- Vink [2], V0 and Va denote a neutral and doubly ionised oxygen vacancy, respectively.

The relationship between the concentration of defects of different charge (both ionic and electronic), that exhibit an electric charge, is governed by the lattice charge neutrality, which requires that positive charge be compensated by negative charge. Therefore, the charge neutrality for the reaction represented by Eq. (1-2) requires that:

2 lK] = [e]' (1-3) where the brackets [] denote concentrations. Although in most cases the electronic defects are substantially more mobile than the ionic defects, knowledge of the concentration of both types of defects is required for derivation of defect chemistry that is described by defect equilibria and the lattice charge neutrality for all the defects involved. The contribution of ionic defects on conduction assumes the highest value at the n-p transition when the concentration of electronic defect assumes a minimum. This

2 1 INTRODUCTION is the reason why the present work, focussed on the evaluation of the electrical conductivity components related to both ionic and electronic defects will be concentrated on the oxide materials that exhibit the n-p transition.

1.3 Amphoteric Semiconducting Properties

When the predominant electronic defects are electrons or electron holes, the material exhibits n-type and p-type semiconducting properties, respectively. In most cases, one type of charge carriers is predominant and then the material is either an n- or p-type semiconductor. In some cases, however, both electronic charge carriers have a comparable effect on electrical properties. Then both charge carriers have to be taken into account. This is the case, e.g. for undoped BaTi03 under an oxygen partial pressure corresponding to the minimum of electrical conductivity [3].

There has been a considerable amount of reports on the defect chemistry of BaTi03 [4- 9]. So far, however, little is known about the defect chemistry of CaTi03, which is an analogue compound to BaTi03. The literature on defect chemistry of undoped CaTi03 is limited to the reports of George et al. [10], Balachandran et al. [11-13], Eror et al. [14], Dunyushkina [15] and Udayakumar [16]. These reports consider the electrical properties of CaTi03 at elevated temperatures in equilibrium with the gas phase of controlled oxygen partial pressure, p(Oi). These data have shown that electrical conductivity vs. p(02) exhibits a minimum which corresponds to a transition between n- and p-type properties. Specifically, the electrical properties of CaTi03 at p(02) lower and higher than that corresponding to the minimum have been considered in terms of n- and p-type properties, respectively. These electrical conductivity data were then used for the verification of defect chemistry models of CaTi03. So far, these models have failed to explain the impact of defect chemistry on the physical meaning of the electrical conductivity in terms of its specific components with respect to different defects. The minimum of the electrical conductivity has not been verified by measurement of the Seebeck coefficient (thermoelectric power). This issue will be addressed in this thesis. Consequently, the aim of this study is the verification of the electrical conductivity data and their analysis in terms of the electrical conductivity components related to electrons, electron holes and ions.

3 1 INTRODUCTION

1.4 Aims

1 To understand the effect of defect disorder on charge transport 2 To derive defect disorder models of CaTi03

3 To verify defect chemistry models of CaTi03 at high p(02) using the electrical

conductivity measurement

1.5 Outline of the Thesis

The present thesis involves the following integral parts:

• Definition of basic terms to be used in the thesis and basic relationships between different properties and quantities

• Brief overview of the experimental and theoretical material reported in the literature

on the subject of the present thesis concerning CaTi03

• Summary of present knowledge on the defect chemistry of CaTi03

• Description of the experimental methods used and the procedures applied

• Results and their discussion

• Summary and conclusions

4 2 DEFINITION OF TERMS

2. DEFINITION OF TERMS

2.1 Effect of Oxygen Pressure

The importance of oxygen as a component of the gas phase surrounding oxide materials during their processing or/and annealing is that it is also the lattice component of these materials. Their nonstoichiometry, and specifically the metal-to-oxygen ratio, is determined by p(02). On the other hand, the nonstoichiometry may be closely related to the concentration of defects in all sub-lattices and related semiconducting properties. However, the gas phase composition, with specific respect to p(02), may have an impact on nonstoichiometry and related properties only at elevated temperatures when the gas/solid equilibrium may be reached. On the other hand, the changes of p(02) below the temperature corresponding to equilibrium either do not have an effect on nonstoichiometry or this effect is not well defined. Therefore, only the properties corresponding to the gas/solid equilibrium are suitable for verification of defect chemistry models.

This thesis studies the determination of defect-sensitive properties, including the electrical conductivity and thermopower of CaTiCb at elevated temperatures at which the gas/solid equilibrium can be reached.

2.2 Basic Terms, Definitions and Equations

2.2.1 Electrical Conductivity

The electrical conductivity, a, is a product of the concentration of the charge carriers, c,

and their mobility, p:

where e is elementary charge and [] denotes the concentration of the defects taking part in conduction.

5 2 DEFINITION OF TERMS

Electrical conductivity involves the components related to the species involved in the conduction, such as electrons, electron holes and ions. Therefore:

(2-2) V = °n+°P+(Ji where

cr„ - epinn (2-3)

°P = ePPP (2-4) cr;. = zjut[i] (2-5)

where n, p and [i] denote the concentration of electrons, holes and ions, respectively, pn, ppand pi are their respective mobilities, and z is the valency of ions. Figure 2-1 shows

isothermal plots of log a vs p(C>2) for undoped BaTiCE [6] within the n-p transition regime.

The determination of the electrical conductivity components an and gp has been usually made through analysis of electrical conductivity within either n-type regime or p-type regime and assuming that the concentration of minority electronic charge carriers is negligibly low. At this assumption, the equation (2-2) assumes the following forms for n- and p-type regime, respectively:

cr = a „+ cr, (2-6)

a = crp+ (Jj (2-7)

2.2.2 Thermoelectric Power

Thermoelectric power is the temperature coefficient of the electrical potential that is generated along a temperature gradient imposed on a solid. The thermoelectric power is also known under different terms, such as the thermopower and the Seebeck coefficient.

The Seebeck coefficient is a basic quantity in the characterisation of electronic structure of materials as well as their thermoelectric properties. This quantity may be related to the concentration of electronic charge carriers. Combined Seebeck coefficient and

6 2 DEFINITION OF TERMS electrical conductivity data can be used for the determination of their mobility terms. These data may be used for derivation of defect chemistry models and evaluation of the transport of charge and matter at elevated temperatures corresponding to the conditions of processing or performance of materials.

The principle of the determination of the Seebeck coefficient is illustrated in Figure 2-2.

BaTiO

1310K

1275K

1160K

1090K

log P0 [pQ in Pa] ^2 2

Figure 2-1. Electrical Conductivity of Barium Titanate

7 2

DEFINITION

TEMPERATURE [ARB. UNITS]

OF

TERMS DISTANCE Figure 5 = 2-2.

SPECIMEN

Generation O

[ARB. Al/ 8

of O

Thermopower UNITS]

MICROHEATER 2 2 DEFINITION OF TERMS

Imposition of a temperature gradient, AT, across a specimen (using micro-heaters) results in generation of a potential difference, AV, which is termed the Seebeck voltage or thermovoltage. Knowledge of both AT and AV are required for the determination of the Seebeck coefficient (thermopower), S [17, 4]:

S = ~[VK-'} (2-8) AT

TEMPERATURE, AT

Figure 2-3. Schematic Illustration of the Plot of AV vs. AT

Figure 2-3 shows a typical experimental plot of AV as AT within both orientations of the temperature gradient.

The following equations describe the relationship between S and the semiconducting properties of materials:

9 2 DEFINITION OF TERMS

o v„S„ +

k N Sn=-[\n(-^) + An] (2-10) e n

k N Sp - [ln( -) + A ] (2-11) e p where k is the Boltzmann constant (8.6167xlO''eVK'1); e is the elementary charge

(1.60206x10‘19C); Sn and Sp denotes the Seebeck coefficient components related to electrons and electron holes, respectively; Nn and Np denote density of states in the conduction band and valence band, respectively; An and Ap are kinetic constants related to scattering of electrons and electron holes, respectively; n and p are concentrations of electrons and electron holes, respectively.

Assuming that the electron distribution satisfies Maxwell-Boltzmann statistics, the following expressions may be written between the concentration of electric charge carriers and the Fermi energy, Ef: n = Nn exp( 1 ) (2-12) kT p = Npexp( ^ y) (2-13) where Ec is the energy of the bottom of the conduction band and Ev is the energy of the top of the valence band. Therefore, S may be directly related to Ep:

_EF- Ec k n rp Al (2-14) el e

Sp = Ef~ E' + k A (2-15) p eT e p

Figure 2-4 shows the plot of thermopower, S, as a function of oxygen partial pressure, p(C>2), for undoped BaTi03 within the n-p transition regime at 1090-1310K [3].

10 2 DEFINITION OF TERMS

As seen, the thermopower exhibits rapid changes within the n-p transition regime. The slope within both n- and p-type regimes may be used for verification of defect chemistry models [6, 7].

n=5.5 BaTiO n=5.2 _ n=5.4 n=5.3

• 1090K A 1160K ■ 1275K O131OK

log Pn [pQ in Pa] ^2 2

Figure 2-4. Thermopower of Barium Titanate

ll 2 DEFINITION OF TERMS

2.2.3 Electrical Conductivity versus Thermopower

The determination of both o and S within the n-p transition regime of amphoteric oxide semiconductors, such as Ti02, BaTiCE and CaTiCE, allows evaluation of the impact of the mobility terms on conduction and the impact of minority charge carriers on the conduction process [4].

MIXED PUREn-TYPE CONDUCTIVITY PUREp-TYPE REGIME REGIME REGIME

log p(02)

Figure 2-5. The Effect of p(02) on Both a and S

12 2 DEFINITION OF TERMS

Figure 2-5 illustrates that the effect of p(C>2) on both a and S when the mobility of electrons is equal to that of electron holes. As seen, the minimum of a coincides with S

= 0. The change of thermopower along with logp(C>2) in the n-p transition regime is complex. There is a steep part passing through the point at which S=0. The p(C>2) range in the vicinity of S = 0 (Aps), in which S exhibits non-linear changes vs p(C>2), is much larger than that demarcated by the changes of o (Apa).

2.2.4 The Formation of Point Defects

The Crystal is in equilibrium when its Gibb’s free energy is at a minimum:

AG = AH -TAS = 0 (2-16) where AH and AS denote enthalpy and entropy terms, respectively.

Formation of point defects results in increase of the enthalpy and entropy of the system. As shown in Figure 2-6, when the point defects are few, the entropy term in Eq. (2-16) decreases. The increase in entropy overrides the increase in enthalpy, which results in the decrease in Gibb’s free energy (AG < 0). When a large number of point defects exist in the material, the increase in entropy due to new point defect formation is much less significant, and its contribution to the free energy change is less important than that of the enthalpy, which results in an increase in Gibb’s free energy (AG > 0). In consequence, crystals of compounds are nonstoichiometric and the number of defects assumes the value which corresponds to the minimum Gibb’s free energy (AG = 0), that is a balance between the entropy and the enthalpy terms.

Great varieties of point defects have been considered, however, the main types of defects in ionic crystals include oxygen vacancies, cation vacancies, and cation interstitials. These defects are responsible for the formation of either donor states (oxygen vacancies and cation interstitials) or acceptor states (cation vacancies). At elevated temperatures these defects may be ionised leading, in consequence to the formation of ionic defects of different electrical charge and electronic defects, such as electrons and electron holes [17].

13 2

DEFINITION Figure

2-6.

Variation Free Energy, OF

TERMS of

Gibb Number ’ s

Free

of

Energy

Defects of a

Crystal with the

Number of

Defects 3 LITERATURE SURVEY

3. LITERATURE SURVEY

3.1 Phase Equilibria in the CaO - TiC>2 System

The CaO - UO2 phase diagram was first investigated in 1954 and the result is shown in Figure 3-1 [19]. The following features can be observed in the diagram:

1 The system contains two compounds with the CaO to UO2 ratio of 3:2, and 1:1. 2 The phase 3:2 decomposes at 1750°C and the phase 1:1 melts congruently at 1970°C. 3 There are two eutectics at 1695°C and 1460°C, respectively.

4 The low mutual solubilities of CaO in CasT^Oy and CasT^Oy in CaTi03 were supposed.

2000

Liquid /

/ CoTiO, Liquid

CoTiO

CoO ♦ 3CoO ETiOjjs

Wt %

Figure 3-1. CaO - UO2 Binary Phase Diagram According to R. C. DeVries [19]

15 3 LITERATURE SURVEY

Roth [20] later revised the above phase diagram, as illustrated in Figure 3-2. The major difference between their work [20] and that of DeVries [19] is that the new compound Ca^^Oio with a peritectic decomposition at 1755°C was found to exist as a stable phase in the Ca0-Ti02 system.

Both compounds, Ca^^Oio and CasT^Oy, are pseudotetragonal with only a few weak lines indicating a departure from tetragonality. The c axis equals 19.505 for CasT^Oy and 27.147 for CaTT^Oio. The dimensions indicate that CasTCOy has double perovskite layers interleaved with CaO, whereas Ca^^Oio has triple perovskite layers interleaved with CaO.

mol %

Figure 3-2. CaO - TiOy Binary Phase Diagram According to R. S. Roth [20]

16 3 The temperatures Figure the with cone-fusion reported phase checked, Temperature [°C] significant

LITERATURE

composition

phase an

of 2000 3-3.

Ir-Ir40Rh

by composition which

discontinuity

CaO diagrams Roth

methods. in

SURVEY Ca0-Ti02

- of are

[20]

TiC thermocouple, C 43

g

consistent

O >2 mentioned

and Ca^BOio

and

Binary Jongejan

+ in

Kimura

Liquid 81.5 system the

Phase

liquidus

with wt%

at above, as

and and using

1870°C illustrated

Diagram TiC^

the

4CoO'3Ti0 Muan

Wilkins

curve

Figure a results

+

Griffin-Telin 17 at

instead

Liq. [22].

temperatures

is According in

3-1

the [21], of Figure 2

of 1989 incongruently and DeVries

1752°C

however, hot-stage 3-3.

Figure to

of

Ti02 Jongejan

The

[19] 1740°C or 146

3-2,

+ 1720°C, two microscope 0°

melting determined and Co0TiO2

1L-

and

were and eutectic

Roth

(81.5%)

Wilkins

as + 1460°C point obtained

Liq. previously

[20]. modified points liquidus

for

[21]

were The

the

by at

3 LITERATURE SURVEY

Tulgar [25] later found that the phase reported as Ca^^Oio is, in fact, CasTUOn, as shown in Figure 3-4. Ca5Ti40i3 melts incongruently at 1840°C.

Limar et al. [23] and Savenko [24] reported that some phases made from aqueous solution exist between CaTiC>3 and TiC>2 area in the Ca0-Ti02 binary phase diagram.

For example, a CaTUC^ compound was stable up to 700°C, while a Ca2TisOi2 phase was stable up to 1000°C.

CaO + Ljq.

ct + no2

Figure 3-4. CaO - Ti02 Binary Phase Diagram According to Tulgar [25]

18 3 LITERATURE SURVEY

In 1993, Kaufman [26] calculated phase relations in Ca0-Ti02 system based on published phase diagram data and lattice stability data [27]. Although the calculated diagram (Figure 3-5) indicates that the decomposition temperature of Ca^TOio and both eutectic temperatures are higher, it is in general agreement with Figure 3-2 and Figure 3-3.

CoO + liq.

Rt + Liq.

Rt + CaftO

mol%

Figure 3-5. CaO - TiC>2 Binary Phase Diagram According to Kaufman [26]

A summary of all of the different phase equilibrium investigations of the CaO - Ti02 system is given in Table 3-1. The important features of these diagrams are the low mutual solubilities of CaO in Ca3Ti20? and CasT^O? in CaTi03, two eutectic points

19 3 LITERATURE SURVEY

located at the two sides of the diagram, the two peritectic decomposition of Ca3Ti207 and Ca4Ti3Oio or Ca5Ti40i3, respectively, and the open melting of CaTi03 only.

Table 3-1 Reported CaO - HO2 Binary Phase Diagrams

Reported Phase

0 m O

1954 V V [19]

1958 V V V [20]

1970 V V V [21]

1976 V V V a [25]

1988 V V V b [26]

a. C5T4 was observed rather than C4T3 b. Phase relations in the system have been calculated based on [20] (1958) and [21] (1970)

3.2 Crystal Structure of CaTI03

Calcium titanate, AB03 perovskite structured CaTi03, discovered by Gustav Rose, a Russian mineralogist in 1830 [28], has the most interesting dielectric properties amongst compounds within the Ca0-Ti02 system. It was determined to be a monoclinic structure in 1943 [29], but Megaw pointed out that an orthorhombic cell could be derived from the monoclinic lattice in 1946 [30]. Kay and Bailey [31] confirmed the orthorhombic cell, having space group Pcmn by analysis of single-crystal CaTi03 in 1957. The volume of the orthorhombic cell is approximately four times that of an ideal cubic perovskite (Pm3m symmetry), and is analogous to tetragonal KCuF3 [32].

20 3 LITERATURE SURVEY

When CaTiOs exhibits an orthorhombic structure (Pnma) [Figure3-6 (a)], it causes tilting of the titanium, centred octahedra. The deviations of its unit cell dimensions from the primitive cubic structure are very small [33,34]. This distortion is driven by the mismatch between the size of the cubo-octahedral cavity in the comer sharing octahedral network and the ionic radius of the undersized Ca2+ ion. The octahedral tilting distortion [35] lowers the coordination number of the A-site cation Ca2+ from 12 to 8. There is very little perturbation of the local octahedral coordination of the Ti4+ ion. The tolerance factor equation describes the fit of the A-cation in the comer sharing octahedra. The Goldshmidt tolerance factor [36] is defined as:

RCa + Rc (3-1) j2(RTi + Ro) where Rca, Rn and Ro indicate the radius of A-site metal ion, B-site metal ion, and oxygen ion respectively. For the ideal perovskite structure ABO3, t = 1. When t < 1, with decreasing of t, the perovskite structure deforms towards a structure with lower symmetry.

When CaTiCb exhibits a cubic structure (Pm3m) [Figure 3-6 (b)], it is composed of a three-dimensional framework of corner sharing TiC>6 octahedra. The Ca-site cation fills the twelve coordinate cavities formed by the TiC>3 network and are surrounded by twelve equidistant O2" ions.

CaTiC>3 may accommodate a large excess of CaO resulting in the formation of a homologous oxide series of the formula Can+iTin03n+i (where n is the number of perovskite blocks between single CaO layers) which are also called the Ruddleson- Popper phase [37,38,39]. Figure 3-7 shows the three identified ordered phases of

Can+iTin03n+i involving Ca3Ti207 (n = 2), Ca4Ti3Oi0(n = 3) and CaTi03 (n = 00) [40]. As seen, this compound consists of a coherent intergrowth of n perovskite blocks with single layers of CaO showing a disordered rock-salt configuration. In both cases, the

Ti06 octahedra are tilted and distorted in a similar fashion to that in CaTi03 [41, 42].

21 3 LITERATURE SURVEY

Ca2+ ion

Ti4+ ion O2" ion Ca2+ ion

(a) Orthorhombic (b) Cubic Perovskite

Figure 3-6. Crystal Structure of CaTiOs

The thermodynamic values of CaTiOs formation from the elements were: AH°i3oo = -

385.8 kcal/mole, AG°i3oo = -314.7 kcal/mole and S°i3oo = 72.6 e.u. Under standard conditions at 298K, these values were -370, -389, and 26.8, respectively [43].

PEROVSKITE BLOCKS

Figure 3-7. The Three Identified Ordered Phases of Can+iTin03n+i

22 3 LITERATURE SURVEY

3.3 Lattice Parameter of CaTiCU

3.3.1 Lattice Parameter of Undoped CaTiCU

From a comprehensive literature survey, the lattice parameters of undoped CaTiC>3 reported in the literature are compiled in Table 3-2. Except for the data from calculation, the experimental lattice parameters of undoped CaTiCE are summarised as following: • For the orthorhombic phase, the values of parameters, a, c and b, vary with 0.53670 ~ 0.54043nm, 0.54368 ~ 0.5447nm and 0.76352 ~ 0.76540nm, respectively, as shown in Figure 3-8. • For the tetragonal phase, the values of parameters, a and b, are located 0.36606 ~ 0.38370nm and 0.41400 ~ 0.42862nm, respectively. • For the cubic phase, the value of parameter, a, is between 0.3896 ~ 0.378nm.

0.546

0.541 - 0.765

0.536

0.755 0.531

CaTiO Calculation Data

Year

Figure 3-8. Summary of the Lattice Parameters of Undoped Orthorhombic CaTi03 Reported in Literature [44-62] (Ref. Table 3-2)

23 3 LITERATURE SURVEY

Table 3-2 Lattice Parameters of Undoped CaTiC>3 Reported in the Literature

Crystal Phase a (A) h (A) c (A) Year Reference

Orthorhombic 5.4043(8) 5.4224(7) 7.6510(12) 2002 44

5.1724 5.3596 7.4020 2001 45a

5.3804 5.4422 7.6417 2001 46

5.382 5.442 7.642 2001 47

5.3810(3) 5.4440(1) 7.6412(3) 2000 48

5.28 5.35 7.51 2000 49b

5.4671(2) 5.4823(2) 7.7461(3) 1999 50

5.383(2) 5.445(2) 7.649(2) 1998 51c

5.3814(1) 5.4418(1) 7.6409(2) 1998 52

5.378(1) 5.444(1) 7.637(3) 1997 53

5.381 5.442 7.642 1997 54

5.3812(2) 5.4342(2) 7.6379(3) 1995 55

5.3766(1) 5.4368(1) 7.6352(1) 1995 55

5.3785(2) 5.4419(2) 7.6400(3) 1993 56

5.388(1) 5.447(1) 7.654(1) 1992 57

5.381(1) 5.449(1) 7.647(1) 1988 58

5.3796(1) 5.4423(3) 7.6401(5) 1987 34

5.3829(3) 5.4458(3) 7.6453(3) 1983 59

5.3812(3) 5.4405(2) 7.6436(5) 1971 60

5.37 5.44 7.64 1960 61

5.3670(1) 5.4439(1) 7.6438(1) 1957 62

Rhombohedral 3.912 1999 50

Tetragonal 3.6606 4.2862 2001 45a

3.837 4.140 1999 50

Cubic 3.8251 2001 45a

3.78 2000 49b

3.822 1957 62

Note: a - ab initio calculation result; b - The result of quantum-chemical studies; c - Single crystal phase

24 3 LITERATURE SURVEY

3.3.2 The Effect of Impurities on the Lattice Parameter

The lattice parameters of CaTiCE are affected by doped impurities. Table 3-3 summarises the lattice parameters of CaTiOs materials with different types of and various contents (x) of impurities, obtained in literature. Although these samples were not all prepared at the same conditions, the data indicated that lattice parameters a and c tend to increase with increasing impurity (Pr, Sr, Nd, Pu, Ce, Gd, U and Fe) content in the range of x < 0.2, except for La, as shown in Figure 3-9 and Figure 3-11. Figure 3-10 shows that the lattice parameter b of CaTiCE increases with increasing the contents of some impurities as Pr, Pu, Gd, Ce and Nd, while decreases with increasing the contents of other impurities like U, Fe and La when x < 0.1. Except for Pu, further increasing the dopant contents to x > 0.1 decreases the lattice parameter b. According to the Figure 3-9 -Figure 3-11, the lattice parameters a, b and c do not change monotonically with increasing Ce, Nd and U content when x > 0.3, which may be attributed to the formation of second phases which were identified by X-ray diffraction pattern to be CeCE and

Ti02 for Ce and Nd2TL07 for Nd. CaU04 as the second phase was obtained after doping 3 mol% of U [54].

Table 3-3 The Changes of the Lattice Parameter of CaTiCb with Impurities

Crystal Impurity Material X a h (A) ci. A) Year Ref Phase (A) Pr CaTi03:Pr3+ 0.5 O* 5.381 5.443 7.654 2003 63

0.25 O 5.4440(8) 5.4591(8) 7.7213(11)

0.50 O 5.4677(9) 5.4713(7) 7.7390(10) Sr (Cai.xSrx)Ti03 2002 04 0.60 O 5.4784(10) 5.4791(8) 7.7517(13)

0.65 "p* 5.4801(7) 5.4801(7) 7.7619(10)

0.125 C* 3.78 CaTiOf 2002 OD 0.125 0 5.28 5.35 7.51

? 3.84 La-doped c CaTi03 9 0 5.37 5.44 7.64 1960 61

0.05 0 5.389 5.448 7.652

0.1 0 5.394 5.454 7.664 Pu Ca,.xPuxTi03 2001 00 0.15 0 5.403 5.458 7.674

0.2 0 5.404 5.467 7.680

0 5.4151(1) 5.4461(1) CaTio.9Feo.1O2.95 n 1 7.6786(1) Fe u. 1 2002 67 T 5.4927(1) 5.4927(1) 7.7703(2)

25 3 LITERATURE SURVEY

Table 3-3 The Changes of the Lattice Parameter of CaTiCb with Impurities (Continue)

X Crystal Impurity Material a b (A) c (A) Year Ref. mol% Phase (A) O 5.4037(1) 5.4359(1) 7.6623(2) Fe CaTi0 gFe02O2.90 0.2 T 5.4726(1) 5.4726(1) 7.7412(4) 2002 67 C 3.8767(1) 0.050 O 5.3854(2) 5.4429(2) 7.6465(2) 0.109 O 5.3918(3) 5.4401(3) 7.6534(4) 0.142 O 5.3953(3) 5.4391(3) 7.6557(5) 0.150 O 5.3977(6) 5.4394(6) 7.6579(9) Fe CaTi1JtFe^03jty2 0.188 O 5.4013(2) 5.4353(2) 7.6600(3) 2000 68 0.222 T 3.8327(1) 0.279 C 3.8335(1) 0.322 C 3.8348(1) 0.376 C 3.8356(1) 0.15 O 0.5388 0.5439 0.7652 0.25 O 0.5398 0.5438 0.766 0.4 O 0.5408 0.5437 0.7667 0.5 O 0.5418 0.5436 0.767 Nd Cai.xNd2x/3Ti03 0.6 O 0.543 0.543 0.7675 1997 69 0.7 O 0.5432 0.543 0.7678 0.8 O 0.384 0.3839 0.3843 0.85 0 0.3838 0.384 0.385 0.925 o 0.3837 0.3838 0.3858 0.1 o 5.388 5.446 7.657 0.2 o 5.402 5.440 7.664 Nd Cai.xNdxTi03 0.3 o 5.401 5.430 7.653 54 1997 0.4 0 5.418 5.423 7.648 0.5 0 5.410 5.426 7.642 0.1 o 5.399 5.450 7.688 0.2 o 5.399 5.451 7.688 Ca!.xCexTi03 1997 0.3 0 5.448 5.449 7.701 54 0.4 o 5.449 5.458 7.711 0.5 o 5.435 5.459 7.702 0.03 0 5.382 5.445 7.639 0.05 0 5.388 5.444 7.637 u Ca[.xUxTi03 1997 54 0.07 0 5.389 5.445 7.642 0.1 o 5.393 5.442 7.646 0.075 0 5.381(1) 5.449(1) 7.647(1) 1988 70 0.15 0 5.3853(5) Gd 5.4530(4) 7.6504(5) Ca!.xGdxTi03 1996 71 0.3 0 5.377(1) 5.442(1) 7.642(1) Note:

X - Amount of dopant; 0* - Orthorhombic; T* - Tetragonal; C* - Cubic; a - Calculation result.

26 3 LITERATURE SURVEY

0.5445 - - Pr

- - Nd 0.5425 - - Ce e—Gd - -A - u a 0.5405

0.5385 -

0.5365

Figure 3-9. The Change of Lattice Parameter a as a Function of Impurities (Refer to Table 3-3)

0.547

0.546

0.545

0.544

- - Pr

0.543 - - Nd

- -A - U 0.542

Figure 3-10. The Change of Lattice Parameter b as a Function of Impurities (Refer to Table 3-3)

27 3 LITERATURE SURVEY

CaTiO

0.7695 - - Pr

0.7675 - -Jk - U

- ••

0.7655

0.7635

Figure 3-11. The Change of Lattice Parameter c as a Function of Impurities (Refer to Table 3-3)

0.385 g 0.384 s ~ 0.383 0.382 0.381

0.379

0.378

0.377 0.125 0.279 0.322 0.376

Fe-Doped Nd-Doped

Calculated Experimental data value Dopant Content, x

Figure 3-12. Summary of the Lattice Parameter a of Pure and Doped Cubic CaTiCb Reported in Literature (Refer to Table 3-3 and [72])

28 3 LITERATURE SURVEY

Table 3-4 Cell Parameters of CaTi03 Perovskite as a Function of Temperature [73]

Temperature (K) a (A) b (A) £' (A) Crystal phase 293 5.3849 5.4449 7.6460 Orthorhombic 323 5.3883 5.4460 7.6490 Orthorhombic 373 5.3924 5.4474 7.6532 Orthorhombic 423 5.3968 5.4487 7.6578 Orthorhombic 473 5.3999 5.4501 7.6622 Orthorhombic 523 5.4040 5.4521 7.6668 Orthorhombic 573 5.4076 5.4528 7.6724 Orthorhombic 623 5.4264 5.4548 7.6760 Orthorhombic 673 5.4168 5.4565 7.6812 Orthorhombic 723 5.4199 5.4579 7.6852 Orthorhombic 773 5.4242 5.4597 7.6896 Orthorhombic 823 5.4276 5.4616 7.6938 Orthorhombic 873 5.4313 5.4631 7.6984 Orthorhombic 923 5.4354 5.4648 7.7032 Orthorhombic 973 5.4395 5.4668 7.7080 Orthorhombic 1023 5.4440 5.4686 7.7130 Orthorhombic 1073 5.4497 5.4709 7.7192 Orthorhombic 1123 5.4539 5.4733 7.7228 Orthorhombic 1173 5.4586 5.4751 7.7282 Orthorhombic 1223 5.4655 5.4771 7.7330 Orthorhombic 1273 5.4689 5.4805 7.7392 Orthorhombic 1323 5.4800 5.4869 7.7446 Orthorhombic 1373 5.4873 5.4914 7.7496 Orthorhombic 1423 3.8837 Cubic* 1473 3.8859 Cubic* 1523 3.8881 Cubic*

* Tetragonal cell parameters above 1373K were refined as cubic since the tetragonal strain was below the resolution of the diffractometer

As shown in Figure 3-12, doping with La, Fe and Nd increases lattice parameter a of cubic CaTi03, although the value of a keeps in a narrow range of 0.383-0.384 for

29 3 LITERATURE SURVEY different dopants and various doping levels. Calculated values of the parameter a for undoped CaTi03 and doped with La (0.125) are also marked in Figure 3-12, which show almost the same values but are significantly lower than experimental data.

3.3.3 The Effect of Temperature on the Lattice Parameter

Redfern [73] and Kennedy et al. [50] systematically studied the change of the lattice parameters of CaTiCb samples with temperature, as listed in Table 3-4, Table 3-5 and Table 3-6. As shown in Figure 3-13, the parameters, a, b and c of CaTiCb, increased with temperature up to 1530K when CaTiCb was in the orthorhombic phase, kept constant within 1530 ~ 1580K when the phase was tetragonal, and sharply decreased when the phase transformed to the cubic structure at temperatures above 1580K.

Table 3-5 Cell Parameters for Strem Sample of CaTiCb Perovskite as a Function of Temperature [50]

Temperature(K) a (A) b (A) c (A) Space group

295 5.3888(5) 5.4393(5) 7.6482(7) Pbnm 773 5.4253(4) 5.4559(4) 7.6931(6) Pbnm 1023 5.4460(3) 5.4678(3) 7.7181(5) Pbnm 1273 5.4678(6) 5.4821(6) 7.7436(10) Pbnm 1323 5.4724(6) 5.485(6) 7.7499(9) Pbnm 1373 5.4765(6) 5.487(6) 7.7552(1 1) Pbnm 5.4795(6) 5.4896(5) 7.7601(10) Pbnm 1398 7.7545(10) 7.7597(10) 7.7601(10) Cmcm 5.4825(6) 5.4916(6) 7.7626(11) Pbnm 1423 7.7582(12) 7.7614(11) 7.7639(9) Cmcm 5.4847(7) 5.4935(6) 7.7659(10) Pbnm 1448 7.7621(8) 7.7641(9) 7.7674(8) Cmcm 5.4895(7) 5.4957(6) 7.7674(10) Pbnm 1473 7.7659(9) 7.7698(8) 7.7683(8) Cmcm 5.4935(7) 5.4941(5) 7.7685(10) Pbnm 1493 7.7662(8) 7.7756(9) 7.7693(9) Cmcm 1513 5.4944(4) 7.7812(6) I4/mcm 1533 5.4962(3) 7.783(6) I4/mcm 1553 5.4988(4) 7.7843(8) I4/mcm 1573 5.5022(3) 7.7829(9) I4/mcm 1593 3.8923(2) Pm3m 1613 3.8933(2) Pm3m 1633 3.8950(2) Pm3m

30 3 LITERATURE SURVEY

Table 3-6 Cell Parameters for Aldrich Sample of CaTi03 Perovskite as a Function of Temperature [50]

Temperature(K) a (A) b (A) c(A) Space group

295 5.3810(1) 5.439(1) 7.6404(2) Pbnm 623 5.4131(1) 5.452(1) 7.6804(2) Pbnm 1003 5.4429(2) 5.4674(2) 7.7169(3) Pbnm

1273 5.4671(2) 5.4823(2) 7.7461(3) Pbnm 1373 5.4766(2) 5.4883(2) 7.757(2) Pbnm 5.4879(3) 5.4948(3) 7.7671(5) Pbnm 1473 7.7642(6) 7.7674(4) 7.7667(4) Cmcm 1523 5.4938(2) 7.7815(3) I4/mcm 1623 3.8933(1) Pm3m

7.78

7.76

Orthorhombic Area 7.74 Mq

- 7.68

CT 7.66

7.64 800 1000 1200 1400 1600 Temperature [K]

Figure 3-13. The Change of the Lattice Parameter of CaTiCL with Temperature

31 3 LITERATURE SURVEY

3.4 Preparation of CaTiC>3

Electronic ceramics must meet very specific electrical property requirements, and therefore their chemical composition and microstructure must be well controlled. A variety of methods of preparation of CaTiCE ceramics have been explored. The preparation of bulk CaTiCE ceramics involves three steps shown as follows:

mechanical process Step 1: Starting materials------^ CaTi03 powder or chemical process

consolidation Step 2: CaTiCb powder------CaTiCE pellet

sin lering Step 3: CaTi03 pellet------^ CaTiCE bulk ceramics

The key point is to fabricate a desirable starting powder, which has important consequences for both the consolidation step and calcination step to control the microstructure of the fired body.

3.4.1 Preparation of CaTi<>} Powders

The important powder characteristics for electronic ceramics are as follows [74]: Fine particle size (~1 micron) Narrow particle size distribution Spherical or equiaxial particle shape No agglomeration or soft agglomerates state High purity chemical composition Single phase composition These characteristics strongly depend on the preparation method of CaTiCE powder.

Since 1911, big progress has been made in the preparation of CaTiCb powder. Table 3-7 and Figure 3-14 summarises the synthesis mechanism of different CaTiCE powder preparation methods first reported with various starting materials between 1911 and

2003 (Data collected from SciFinder Scholar based on preparation of CaTi03).

32 3 LITERATURE SURVEY

Table 3-7 Evolution of Methods for Preparation of CaTi03 Powders between 1911 and 2003

Year Starting Materials Method Reaction Reference11

1911 Ti oxide + phosphate SS Phospate rock -f Ti02 [75] 1500°C —> CaTiO, + P2051 rock

1929 Ca3(P04)2 + ilmenite ss Ca, (POA )2 + ilmenit [76] high lemperalutt ------> CaTiO3

1941 CaO + Ti02 SS CaO + 7702 -> CaTiO , [77]

1956 CaCl2-2H20 + Ti02 wc- 1. Ti02 + H2SOA + (NHa)2SOa [78] -> Ti(SOA )2 + 2NHAOH Sulfate 2. CaCl2 ■ 2H20 + H2SOa -> CaSOA + 2HCI + 2 H20

3. Ti(SOA )2 + CaSOA —> CaTi(SOA), + SO,

A 1400“ C. 2/i ^ • CaTi(S04 )3 -> CaTiO, + SO,

1957 TiCl4 + H2C204 + WC- 1- CaCI2 -2H 20 + TiCI A + 2H 2C2Oa + H20 [79] 45 “C CaCl2-2H20 Oxalate -> CaTiO {C2Oa)2 ■ 4H 20 + 6HCI

2. 1 Klin'c CaTi0(C20t)2+-02 -> CaTiOj +CO +2C02

573 'C 1961 Ca(OH)2 + Ca(N03)2 HT Ca(OH )2 + Ca(NO, )2 + Ti02 -> [80] CaTiO2 +2HNO, + Ti02

IIOO'C 1972 Ca(N03)2 + Ti02 WC- Ca(NO, )2 + Ti02------> CaTiO, + NO, + N02 [81] Nitrate

IIOO'C 1974 Ca(N03)2 + TiCL, WC- Ca(NO, )2 +7702------> CaTiO, + NO, + N02 [82] Nitrate

1974 CaC03 + TiCl4 + WC- CaCO2 +TiClt + 2(NH A)2CO, -> [83] Car/Oj +4NH tCI +3C02 NH3 + (NH4)2C03 Carbonate

200 -900* C 1974 Ca(OEt)2 + Ti(OEt)4 WC-SG Ca(OEt)2 +Ti(OEt)A +3 H 20------> [84] 700- 900*C Caf[77(0£/)6 ]------> Caf/0 j + 6EtOH

1975 CaC03 + TiC 14 + WC- CaCO, + 77C/4 +2(NH,)iC01 -> [85] Car/Oj + 4NH ,CI + 3CO, NH3 + (NH4)2C03 Carbonate

C6//,o, 1982 (iso-PrO)4Ti + - WC -SG CaCOj + (/so - Pr 0)4 Ti------> [13] CaO • 7702 • 3C6//606 • 3//20 CaC03 + C6 H8 07 Citrate CaO • r/O, • 3C6//606 • 3tf20-> Ca7VOj + CO + co2 + //20

33 3 LITERATURE SURVEY

Table 3-7 Evolution of Methods for Preparation of CaTi03 Powders between 1911 and 2003 (continue)

Year Starting Materials Method Reaction Reference3

ca//,o, 1982 (iso-PrO)4Ti + WC - SG - CaC02 + (iso - Pr 0)4 Ti------> [13] CaCC>3 + C6 Hs O7 Citrate CaO ■ Ti02 ■ 3CbHbOb ■ 3H20

CaO ■ Ti02 ■ 3C6HbOb ■ 3 H20-> CaTiOy + CO + C02 + H20

TmC 1985 CaC03 + Ti02xH20 SS CaCOs + Ti02 xH 20------>CaTiOi +xH 20 [86]

1985 Ti(OC3H7)4 + CaCl2 WC -SG- Ti^OC.HO, +CaCI2 + H202 +(x + 2)H20-> [87] Ca02 TiO, ■ xH20 + 2NH2CI + 4C,H2OH + H202 HP

1987 Ti(OH)4 + CaO HT <400"C [88] 77(0//) 4 +CaO -► CaTiO, +2H20

Toluene 1988 CaC03, TiCl4, WC- TiCl, + 3C5 Ha (OH) 2 [89] C6H4(OH)2 Catecholat H2(Ti(CbHA02)2) + 4HCl H,0 e H2[Ti(C6HA02)} + CaC02 Ca(Ti(CbHA02\ ]+H20 + C02

600" C Ca[Ti(C6H A02 )3 ] -► CaTi02 + 2H 20 + 6C02

240“ C 1988 Ca(OH)2+ HT Ca(OH)2+Ti(OH)A -*• [90] Ti02nH20 CaTiO, + H20

ice Bath 1989 CaCl2+TiCl4+H202+ WC-HP TiCl4 + 3 H202 + 2 NH,------> [91] nh3 (NHA)2TiOb + \HCl ice Bath (NHt )2Ti06 + Ca2*------>

CaTiOb + NHl

CaTi06->CaTi02 + 02 t

2 4)2 Ti(C 0 + WC- E CaCI2 -2H 20 + TiCI A + 2H2C2Oa + H20 4J'C 2 CaCl -2H20 Oxalate -> CaTi0(C20A)24H20 + 6HCI 1992 [92] 2. | IOM*C CaTiO(C2Ot)2 +-0, ->•

CaTiO, +C0 + 2C02

1992 CaOnH20 + HT Ca(OH)2 + Ti(OH)A -+CaTiO3 + H20 [93] Ti02nH20 H-O 3 1992 CaC0 + SG CaC02 + H02CCR20H -►

ho2ccr2oh+ Ca(02C(CR2 )OH)2 + H20 + C02

Ti(OR')4 Ca(02C(CR2)OH)2+Ti(OR')A -> Ca(02CCR20)2Ti(0R')2 +2HOR [94]

Ca(02CCR20)2Ti(0R')2 + 2 HOR'

1 Hydrolysis Z.JnermolysB ------> CaTi03

1994 Ca(C204) + WC - SG - Ti(OCiH1)t +CaCI2 + H 202 +(x + 2)H20-> [95] (iso-PrO)4Ti Oxalate CaO 2 ■ TiO, xH20 +2 NH 4C/ + 4C, // 7 OH

34 3 LITERATURE SURVEY

Table 3-7 Evolution of Methods for Preparation of CaTiC>3 Powders between 1911 and 2003 (continue)

Year Starting Materials Method Reaction Reference1*

<70"C 1994 CaO or Ca(OH)2 MC CaO + TiO2 -> CaTiO, [96] +Ti02 or H2Ti03 <70° C Ca(OH)1 +TiO2 -> CaTiO, + H10

<70°C CaO+ H2TiO, -> CaTiO,

<70 “C Ca(OH)1 + H-JiO, ->

CaTiOj + 2 H20

1995 Ca2+ + Ti4+ SG pH>10 CaTi03 [971 ice Bath 1996 H2Ti03, H202, NH3, WC-HP HJiO, + H202 + NH,------>(NH,)2Ti [98] Ca(N03)2 ice Bath (NHA)JiO(t + Ca2+------>

CaTiO6 + NH;

CaTiOb 4 CaTiO, + 02 t 10 h 1998 CaO or Ca(OH)2 + MC CaO -I- TiOl^CaTiO3 [99] Ti02 at room temperature <70 °C 1998 CaO + Ti02 MC CaO + T\Ol -> CaTiO, [100]

<70 “C 2001 CaO + Ti02 MC CaO + TiO2 —> CaTiO, [101] 2002 Ca(N03)2+ (iso- SG+ MC [102] PrO)4Ti ice Bath 2003 H2Ti03+H202+NH3 WC-HP HJiO, + H^O, + NH,------> [103] + (AW4)27706 Ca(N03)2 ice Bath (NH4)JiOb+Ca2t------>

CaTiOb + NH;

CaTiO6 4 CaTiO, + 021

2003 CaC03+Ti02 MC CaCO,+Ti02 —”7- _► CaTiO, +C02 [104]

Note: a — Data collected from SciFinder based on preparation for CaTiCE (1911 - 2003); SS— Solid state reaction; WC— Wet-chemistry; HT— Hydrothermal synthesis; SG— Sol-gel process; HP — Hydrogen peroxide; MC— Mechanochemical Synthesis

35 3 LITERATURE SURVEY

1985 -

1965 -

1945 -

Method

Figure 3-14. The Evolution of Preparation Method for CaTi03 with Year SS—Solid state reaction; WC—Wet-chemistry; HT—Hydrothermal synthesis; SG—Sol-gel process; HP—Hydrogen peroxide; MC—Mechanochemical Synthesis (according to Table 3-7)

As shown in Figure 3-14, preparation methods of CaTiC>3 powder can be divided into two categories: solid state reaction and wet-chemical methods.

3.4.1.1 Solid State Reaction

In 1911, CaTi03 was first synthesised by Peacock [75] through the solid solution route - — heating the mixture of titanium oxide and phosphate rock in a single operation. Then,

Urbain [76] mixed Ca3(P04)2 with ilmenite and Carbon to fabricate calcium titanate in 1929. In 1941, Tanaka started to study the reaction between CaO and TiCh powders and

36 3 LITERATURE SURVEY found that one additional compound, CaTiOs, exists in the system Ca0-Ti02 system.

The reaction between CaO and TiC>2 begins at about 500°C [105].

Solid state reaction is a traditional process to fabricate CaTiOs, including comminution of metal oxides, or their acid salts and calcination at high temperatures. Comminution involves operations such as crushing, grinding and milling to reduce the particle size of a coarse material. Calcination involves chemical decomposition reactions, in which a solid reactant is heated to promote the inter-diffusion of constituent cations, the solid state reaction and the formation of the required compound.

The disadvantages of solid state reaction process are bigger grain size and composition variation that is caused by insufficient control of the preparation procedure or introduced during subsequent handling, often taking place unrecorded or undetected. However, their effects on the microstructure and electrical properties of the fabricated material can often be quite profound.

In 1970, Limar et al. [106] first gave a comparative evaluation for the powders prepared by various methods and found that all the techniques based on composition of Ca and Ti from the solutions give CaTiC>3 with a particle size of <1 pm and with better ceramic properties than those of powder synthesized from mechanical mixtures of Ca and Ti compounds. This has resulted in greater use of chemical methods for powder preparation.

3.4.1.2 Wet-chemical Processes

Wet-chemical process is a chemical method involving chemical reactions under carefully controlled conditions. The pure CaTiC>3 powder may be synthesised intensively by several wet-chemical routes, such as oxalates, citrate, hydrogen peroxide, Sol-gel process, hydrothermal synthesis, and mechanochemical synthesis.

37 3 LITERATURE SURVEY

3.4.1.2.1 Oxalate Route

In 1957, Lynd and Merker [79] were the first investigators to employ the oxalate method into processing of CaTi03 powder. It was demonstrated that the high purity stoichiometric CaTi03 powder with particles size of 0.1 ~ 1 pm could be prepared by pyrolising calcium titanyl oxalate. A calcium titanyl oxalate precipitate can be obtained by different starting materials, such as calcium chloride and titanium tetrachloride with oxalic acid [107], Ca(N03)2 with potassium titanyl oxalate [108], (NH4)2C204 and CaCl2 with TiO2[109].

3.4.1.2.2 Citrate Route

Pechini [110] was the first to develop the citrate method for preparing barium titanates. It was also employed in fabricating calcium titanate by Balachandran [13].

Calcium titanate may be synthesized by a modified sol-gel method using citrate [111]. Titanium alkoxide was dissolved in a citric solvent initially and then mixed with the stoichiometric amount of calcium compound.

3.4.1.2.3 Peroxide Route

Pfaff [112,113] applied the hydrogen peroxide route to prepare CaTi03. Different nanometer-sized CaTi03 powders were prepared by the chemical coprecipitation method [114,115]. The best molar ratio of H2Ti03:H202:NH3 was 1:8:2 and the nanometer-sized powders were obtained by calcination at different annealing temperatures (400-650°C) and for different time. These powders were studied by TEM and XRD and a reaction mechanism was proposed.

3.4.1.2.4 Sol-gel Processing

In 1974, it was the first time that Barabanshchikova et al. [84] employed alcoholates as starting materials to obtain CaTi03 at 700-900°C. The advantage of using double

38 3 LITERATURE SURVEY

alkoxide is that complete atomic mixing of the Ca and Ti cations is achieved in the initial solution. CaTiCb powder prepared by the pyrolysis of alcoholates has the finest particle size [116]. The main advantage of the mixed-alkoxide route is the high homogeneity and purity of the end product. The main disadvantage of the mixed- alkoxide process is that considerable difficulties are encountered in handling the raw materials which are highly sensitive to atmospheric moisture that hydrolyses the solution. Recently, many researchers have made efforts to modify some wet-chemical routes, such as oxalate [117,87], citrate [118,13], mechanochemical synthesis [119] etc. Unfortunately, powders obtained via these routes often exhibit undesirable morphologies due to high calcination temperatures required to completely remove residual carbonate phases (similar to high temperature solid-state reactions). Fine powders may be obtained by modified wet-chemical routes (combination with sol-gel process), which can be sintered to close to theoretical density at temperatures as low as 1150°C. Another benefit from sol-gel method is the wide range of flexible chemical components. It is especially suitable to make doped CaTiCb [120].

3.4.1.2.5 Hydrothermal Synthesis

Brcic et al. [121] developed a hydrothermal route in 1961. Hydrothermal synthesis of CaTiCb powder has been achieved at much lower temperatures (150-200°C) by reaction between relatively inexpensive raw materials, such as calcium and titanium hydroxides in strongly alkaline (pH > 12) solutions in an autoclave at pressures > 5MPa [122,123]. Kutty [124] reported that fine CaTiCb powders consisting of 0.1-0.5pm crystallites were prepared by the hydrothermal method starting from hydrated titania gel and reactive calcium oxide suspended as an aqueous slurry in an autoclave. The so-obtained powders were sintered to high-density ceramics at temperatures below 1400°C.

Powders prepared via hydrothermal routes are often unagglomerated, anhydrous and crystalline. Consequently, the as-prepared powders do not have to be calcined or milled, which reduces energy costs. They therefore remain unagglomerated and substantially free of impurities subsequent to formation.

39 3 LITERATURE SURVEY

However, the materials produced by this method exhibit some anomalous behaviour thought to be derived from the incorporation of water and the presence of hydroxyl groups in the crystal lattice [125].

3.4.1.2.6 Mechanochemisrty Route

Mi et al. [99] reported that crystalline CaTi03 can be mechanochemically synthesised by grinding at room temperature the mixture of CaO with both forms of Ti02 (anatase or rutile) through a planetary ball mill, but it is difficult to obtain from the mixtures of

Ca(OH)2 and TiC>2. These observations are in contradiction to the results of Avvakumov et al. [96] and in agreement with the thermodynamic data [100]. The values of Gibbs free energy change for all cases are negative (Table 3-8), suggesting that the mechanochemical reactions of these mixtures are able to take place under certain conditions. The reactivity of CaO or Ca(OH)2 is slightly higher with anatase than with rutile. Heating of the ground mixtures at 900-1200K is found to be effective for producing crystalline CaTiOs.

Table 3-8 The Isobaric-Isothermic Potentials for the Reactions of Calcium Oxide with Anhydrous and Hydrated Oxides

No. Reaction AG298 revcS^1 m0l\ Reference

-89.80 [96] 1 CaO + TiOz (anatase) —> CaTiO, -88.47 [99]

2 CaO + Ti02 (rutile) -> CaTiO, -82.33 [99]

3 CaO+ HJiO, CaTiO, + H20 -164.2 [96] -33.90 [96] 4 Ca(OH)2 + Ti02 (anatase)-* CaTiO, + H 20 -30.65 [99]

5 Ca(OH)2 + Ti02(rutile)-> CaTiO, + H 20 -24.51 [99]

6 Ca(OH)2 + HJiO, -> CaTiO, + 2H20 -108.0 [96]

40 3 LITERATURE SURVEY

Wu and Zhang [101] studied the mechanochemical process occurring during grinding a Ca0-Ti02 mixture in a planetary-mill. The results showed that in the first stage, the particle size of the mixture decreases, the lattice distorts, and the mixture transfers into the amorphous phase (0-2 h); in the second stage, the crystal nuclei were formed then the crystal particles of CaTi03 grow (2-10 h). Finally, growing and decreasing of crystal particle size are in a dynamically-balanced state (>10 h). Anatase can be transformed into rutile and has a higher activity compared with rutile. The crystal size of nano-sized CaTi03 synthesised by the mechanochemical process is 20-30 nm, as identified by XRD and TEM.

Lee and Lee [102] fabricated pure and nano-sized Ti02 and CaTi03 powders combining a polymeric steric entrapment route and planetary milling process. Titanium isopropoxide and calcium nitrate were dissolved in liquid ethylene glycol. The dried precursor ceramic gels were turned to porous powders through calcination process. The porous powders were crystallised at low temperature and the crystal powders were planetary milled to nano-sized particles.

The disadvantage of the wet-chemical process is agglomeration. Normally, as the size decreases below ~ 1 micrometer, the particles exhibit a greater tendency to interact, giving rise to the formation of agglomerates. One consolidated powder can be quite nonuniform. The overall effect is that during the firing stage little benefit is achieved over that of a coarse powder with a particle size corresponding to the agglomerate size of the fine powder. The use of fine powder therefore requires proper control of the handling and consolidation procedures in order to minimise the deleterious effects due to the presence of agglomerates. Such procedures may be quite demanding and expensive.

3.4.1.3 Comparison of Preparation Methods

The advantages and disadvantages of different preparation methods for CaTi03 are compared in Table 3-9.

41 3 LITERATURE SURVEY

In conclusion, the use of the wet-chemical route for the preparation of calcium titanate powder is an attractive alternative to the solid state reaction route. The impurity contents are considerably lower in powder prepared by the former route than by the latter route. Submicron powders are easily obtained. Unfortunately, for the routes of oxalate, citrate, catecholate and hydrogen peroxide, CaTiC>3 does not form directly during the calcination process, but via the decomposition of the carbonate or hydrates to yield the final products, i.e. solid-state reactions between CaC03 or Ca(OH)2 and various titanium-rich phases. The formation mechanism is similar to the conventional solid state reaction process in this respect. Recently, combinations of sol-gel process and mechanochemical synthesis were most intensively studied. However, particle agglomeration is difficult to avoid.

Table 3-9 Comparison of Preparation Methods for CaTiCb Powder [126]

Powder Preparation Advantages Disadvantages

Method

Limited purity, Inexpensive, wide limited homogeneity, Solid State Reaction applicability agglomerated powder, large particles Oxalate, citrate, High purity, small catecholate, particles, composition Expensive, hydrogen peroxide, control, chemical powder agglomeration sol-gel, homogeneity

Inexpensive raw Hydrothermal Pressure (~15Mpa), materials, high purity, synthesis Ca/Ti <1

Wet-Chemical unagglomeration

Inexpensive, fine particle Limited purity, Mechanochemical size, low temperature limited homogeneity for synthesis route multicomponent powders

42 3 LITERATURE SURVEY

3.4.2 Preparation of Pellets of CaTi(>3

3.4.2.1 Powder Consolidation

The consolidation of ceramic powder to produce a shaped specimen is referred to as forming. The main consolidations include: 1. dry or semidry pressing of powder 2. mixing of powder with water or organic polymers to produce a plastic mass that is shaped by pressing or deformation 3. casting from slurry 4. Colloidal methods: The powders are dispersed in a liquid (water) and stabilized to prevent agglomeration through the use of electrolytes or polymers that are dissolved in the liquid. The suspension is then made to settle by itself, by filtration, or by centrifuging. The deposit forms the green body for subsequent firing. Colloidal methods have not made inroads into many industrial applications where mass production is desired and fabrication cost is a serious consideration.

3.4.2.2 Sintering Process

In the sintering stage, the shaped powder pellet is heated to produce the desired microstructure. For some materials, polymorphic transformation between different crystalline structures can also be a source of severe difficulties for microstructure control. The transformation from one phase to another phase results in rapid grain growth and a severe retardation in the densification rate. Chemical reactions between incompletely reacted phases can also be a source of problems. It would be best to have no chemical change in the powder during sintering.

43 3 LITERATURE SURVEY

3.5 Microstructure of CaTiOs

The microstructure of the fabricated article is significantly dependent on the processing method. The examination of the microstructure may therefore serve as a test of successful processing. The control of the powder quality such as phase component, the size of individual grains, the amount of impurities and pores, the nature of the grain boundaries and second-phase particles has an influence on the development of the microstructure.

3.5.1 Phase Transformations

3.5.1.1 The Effect of Temperature on Phase Transformations

The structure of the CaTiOs phase as a function of temperature has been studied several times. Figure 3-15 compiles the phase transformation of CaTiC>3 as a function of temperature reported in the literature. In 1946, Naylor and Cook [127] measuring the heat capacity, reported the presence of one phase transition. Vogt and Schmahl [128] and Liu et al. [129, 56] also reported only one phase transition using differential thermal analysis and x-ray diffraction, respectively. This phase transformation represents the phase change from orthorhombic at lower temperature to cubic at higher temperature.

Wang and Liebermann [130] proposed the existence of two phase transitions: orthorhombic to tetragonal P4/mbm and then a cubic phase along with an increase in temperature. Guyot et al. [131] inferred two phase transitions from the heat capacity measurement, and suggested the orthorhombic Pmnb and Cmcm symmetries for the low- and intermediate-temperature phases, respectively. Crystallographic studies by Sasaki et al., [34], Buttner and Maslen [57] and Arakcheeva et al. [53] concluded that the low-temperature phase and the phase above 1530 K are orthorhombic Pbnm structure and the cubic Pm3m structure, respectively.

Matsui et al. [132] recently confirmed the presence of two phase transitions at about 1390 and 1530 K. Their x-ray diffraction patterns suggest the Pbnm-Cmcm-Pmm

44 3 Figure diffraction temperature tetragonal The sequence temperature first structure. changes orthorhombic Cmcm Year LITERATURE 2001

first transition

3-15. to 1200

i

from

of Matsui transformation cubic

I4/mcm measurements

dependence X-ray phase Summary |

Orthorhombic Cmcm

Pbnm SURVEY Pm3m at

et

diffraction transitions.

structure, 1300 al. 1390

structure

of to [73] structure.

of

was Phase and K Cmcm

the re-investigated

was

suggested and

and due but Redfern cell

Transitions

1400

Rhomb Kennedy

the at it differential to volume due Temperature

is

the 1380K

second still

[73]

another to ohe

change

45

et

was the

unclear,

for the dr

1500 carried

al.

al

at thermal

one phase

Pure

observed.

sequence: change [50]

which

from Tetrahedral was

and out

CaTi

transition confirmed

[K] analysis.

the from high-temperature the from 1600 a 03

Pbnm-I4/mcm-Pmm.

slight orthorhombic second [133,

I4/mcm

of orthorhombic

They that

pure | 56,

discontinuity

Cubic one

the

1700 proposed 73,

to CaTiC

at

phase

the

132, powder

Pbnm 1530

>3 cubic

Pbnm

50].

structure by

that K

in

to

1800

high- x-ray from

Pm the the the to

3 LITERATURE SURVEY

The above results are summarised in Figure 3-15. CaTiCb undergoes three polymorphic transitions and, correspondingly, has four polymorphic modifications upon heating. A possible sequence of transitions is as follows:

Pbnm <------> Cmcm <—> 74/mcm <—> Pm3m

1380-1390K 1500-1525K 1520-1650K

All the polymorphic transformations are reversible [134]. It is concluded that the cubic

(Pm3m) CaTiCb phase exists at temperatures higher than 1650 K.

3.5.1.2 The Effect of Dopant on Phase Transformation

The amount of impurities in CaTiCb samples may significantly affect the phase transition. Consequently, phases of cubic symmetry with the lattice parameter a may replace those of orthorhombic symmetry with a, b and c. For example, phases in the system CaFexTii.x03-x/2 (0 < x < 0.40), with randomly distributed oxygen vacancies, undergo at least two displacive phase transitions with increasing x at room temperature.

0.3836

CaFexTi 0.3S35 “

s 7 / J3 0.3S34 * ct -1

** 0.3S33 _ * m J C Pbnm 14/mcm Pm3rn 0.3832 ------i 0.2 0.25 0.3 0.35 0.4

x

Figure 3-16. Phase Transformation in Fe-doped CaTiCb

46 3 LITERATURE SURVEY

As seen in Figure 3-16, Fe-doped CaTi03 transformed from the orthorhombic Pbnm to the tetragonal M/mcm structure at x = 0.205 ± 0.017, and then to the cubic Pm3m polymorph at x = 0.251 + 0.029 [135].

The lattice parameters of the solid solutions of (Cai_xSrx)Ti03 are illustrated in Figure 3-17 [136]. The orthorhombic lattices are continuous between x = 0 and x = 0.6 in which a and b approach the same value, and at x = 0.65, a and b are identical, which indicates a tetragonal lattice.

0.7S2

0.777

0.550 *

0.772

14/rncm 0.767 a 0.546

0.762

0.542 0.757

0.540 0.752

Figure 3-17. Phase Transformation of Sr-doped CaTiC>3

Figure 3-18 and Figure 3-19 [72] showed the lattice parameters of (Cai.xNd2x/3)Ti03 for 0 < x < 0.78 and 0.78 < x < 0.93, respectively. In the former region, lattice parameters a and c increase while b decreases as x increases. In the latter region, however, the lattice parameter c increases as x increases while a and b remain nearly constant. A phase transformation in (Cai.xNd2x/3)Ti03 occurs from the orthorhombic GdFe03-type to the cubic La2/3TiC>3 type structure in the range of 0.69 < x < 0.78.

47 3 LITERATURE SURVEY

0.545 0.7680

0.544 ^ - 0.7675

0.543 - 0.7670

- -Jk - a 0.542 - - 0.7665 b - 0.7660

0.541 - [nm]

c 0.54 - 0.7655

0.539 - 0.7650

0.538 A 0.7645

0.537 0.7640

Figure 3-18. Phase Transformations in Nd-doped CaTiC>3 for x between 0 and 0.78.

0.3860

0.3855 - - -A - a

■Q— b

0.3850

«8 0.3845

0.3840

0.3835

X

Figure 3-19. Phase Transformation in Nd-doped CaTiC>3 for x between 0.78 and 0.96.

48 3 LITERATURE SURVEY

3.5.2 Particle Size

3.5.2.1 The Effect of Preparation Methods on Particle Size

Table 3-10 summarises particle sizes prepared from different methods. The particle size of samples prepared by solid state reaction route is as large as 2.7 pm, the largest among all the samples. Samples prepared by wet-chemical and hydrothermal routes have much smaller particle sizes, which change in the range of 0.015-1.5 pm. Sol-gel process may produce samples with particle size of about 0.03 pm.

Table 3-10 Summary of Particle Size Derived from Various Preparation Methods

Method Particle size [pm] Year Reference

SS 2.7 1990 [137]

WC*- Oxalate 0.1-1 1957 [138] o o r o WC-Carbonate l 1975 [139]

WC- Catecholate 0.05-0.1 1988 [89]

WC- hydrogen Peroxide 0.015 2003 [140] o o l 1987 [141] HT 0.1~ 1.5 1988 [142]

SG 0.03 1992 [143]

WC- SG-Citrate 0.03 1993 [144]

<2 1998 [145]

0.02-0.05 1999 [146,147] MC 0.02-0.03 2001 [148]

0.07 2003 [104]

SG + MC nano 2002 [149]

Note: SS — Solid state reaction; WC — Wet-chemistry; HT — Hydrothermal synthesis; SG — Sol-gel process; HP — Hydrogen peroxide; MC — Mechanochemical Synthesis

49 3 LITERATURE SURVEY

Diallo et al. [150] compared particle quality of 0.2 mol% Pr-doped titanates which were prepared by solid-state reaction route and by sol-gel procedure. The results of SEM micrographs showed that there are finer and denser particles prepared by sol-gel procedure than by solid-state reaction route (Figure 3-20).

Figure 3-20. SEM Images of Ca/CTO:Pr Particles Prepared by Solid State Reaction (a) and Sol-gel Method (b) Sintered at 1200°C

3.5.2.2 The Effect of Mechanical Activation on Particle Size

Evans et al. [104] studied the effect of mechanical activation on crystallite size of calcium titanate. The average crystallite size of non-activated sample is about 90 nm at room temperature and exceeds 200 nm when heated to 1100°C. The corresponding activated samples have crystallite sizes of about 70 nm and 120 nm, respectively. Figure 3-21 compares the SEM images of non-activated and activated samples subjected to thermal treatment at 1100°C. The changes in particle shapes and sizes caused by mechanical activation are remarkable. The activated sample consisted of fine particleed and non-agglomerated crystallites with nearly spherical shapes and almost uniform particle size (Figure 3-2lb). This contrasts to the bigger and irregular shaped particles of the non-activated sample (Figure 3-2la).

50 3 LITERATURE SURVEY

Figure 3-21. SEM Images of the Fracture Surface for the (a) Non-activated and (b) Activated Sample

Degtyareva and Verba [151, 152] also investigated the effect of raw material activity and preheating conditions (CaCOi at 800-1750°C, Ti02 at 1100-1550°C) on the kinetics of formation, the sintering (1100-1600°C) and growth of calcium titanate particles.

Their results showed that the amount of formed CaTiC>3 decreases with decreasing raw material activity and increasing particle size of the starting materials. The CaTiC>3 formation occurs at reciprocal diffusion of Ti4+ and Ca2+, with Ti4+ prevailing.

3.5.2.3 The Effect of Sintering on Particle Size

Figure 3-22 showed the results of the calculated mean particle sizes for the powder formed during the thermal degradation of the gel precursor for CaTi03. Increasing sintering temperature results in an increase of the particle size of CaTi03.

3.5.3 Density/ Porosity

3.5.3.1 The Effect of Preparation Methods on Density

Samples prepared by different methods may have different porosity and hence their relative densities also are different. Table 3-11 summarises the densities of samples prepared by different methods relative to the theoretical density of calcium titanate.

51 3 LITERATURE SURVEY

Solid state reaction route produced samples with the lowest relative density and hence the highest porosity, while sol-gel processes produce the densest samples.

3.53.2 The Effect of Mechanical Activation on Density /Porosity

The effect of the reactivity of the starting materials on the sinterability of calcium titanate has been studied [152,153], and it has been found that open porosity decreases with increasing sintering temperature, reaching 5% at 1600°C, when the most reactive starting compounds were used.

400 500 600 700 800 900 1000 1100 1200 1300 Temperature [K]

Figure 3-22. The Dependence of Mean Particle Diameter of CaTiCb on the Calcination Conditions of the Powder Obtained from Sol-gel Method [153].

52 3 LITERATURE SURVEY

Table 3-11 Summary of Relative Density Obtained by Different Preparation Methods

Sintering Condition Relative Method Year Ref. Temp. [°C] Time [h] Density [%]

Not SS 1200 83 1990 [154] mentioned HT 1250-1450 3-6 93-98 1988 [155] WC - Catecholate 1450 2 >92 1988 [89] WC - SG - Citrate 1350 14 94 1982 [13] WC - SG - Oxalate 800 0.16 >98.3 1985 [87] 1200 4 83 WC - SG - Oxalate 1994 [156] 1400 4 99

As shown in Figure 3-21, open porosity is evident for non-activated and mechanically activated samples. However, the porosity is significantly less pronounced in the mechanically activated samples.

3.5.3.3 The Effect of Sintering on Density

Pfaff [112] reported that the highest density after 4 h at 1200°C is 3.36 g cm'3 for

CaTi03 (relative density 83%). Sintering at 1400 °C for 4 h leads to a very strong shrinkage of samples with density values close to theoretical density. The highest reached density at 1400°C is 4.00 g cm'J for CaTiC>3 (99%).

Pickup [157] studied the densification and microstructure of calcium titanate. The results showed that higher sintering temperatures and longer sintering times resulted in a reduction in density because of grain boundary cracking which occurred on cooling through a phase transformation at 1240°C.

53 3 LITERATURE SURVEY

3.5.4 Grain Boundaries

The microstructure strongly affects electrical conductivity of polycrystalline ceramic. Electrical conductivity is measured as a function of oxygen partial pressure at high temperature to understand material properties, especially for defect structure of ceramic materials. It is important to understand the knowledge of the effect of grain boundaries on electrical conductivity.

For polycrystalline ceramic, the total electrical conductivity consists of bulk conductivity and grain boundary conductivity as shown in Equation (3-2):

+ <7g (3-2) Where crlol denotes total electrical conductivity, crb denotes bulk conductivity,

<7g denotes grain boundary conductivity.

The true grain boundary (or specific grain boundary) conductivity can be defined as (grain boundary consist of a continuous blocking layer) [158]:

^ gb ^ gh (y 1 Cjgb - X c7 . = —------X------(3-3) ^ * dgbA Rsh where tgh refers to the thickness of the grain boundary layer, d h the average grain size, ts the sample thickness, A the electrode area and Rgh the grain boundary resistance.

It is found that the grain boundary conductivity

54 3 LITERATURE SURVEY

The grain boundary conductivity is also a function of temperature. Figure 3-23 shows the Arrhenius plots of the grain boundary conductivity and bulk conductivity of calcium titanate materials. It is observed that the activation energy of grain boundary conductivity is 1.5 times higher than that of bulk conductivity, and the bulk conductivity is consistently much higher than the conductivity through grain boundaries. This illustrates that the main conduction mechanism is through the bulk of calcium titanate materials during measurement temperatures.

ia(buik) = 74kJ/mol

.S -8

CaTiO ' s Ea(gb) = 116kJ/mol

- Grain Boundary

1000/T [T in K]

Figure 3-23. Bulk and Grain Boundary Conductivity as a Function of Temperature [160]

At high temperature, the influence of the grain boundaries on the conductivity is usually small because the oxygen diffusion rate is lower in grain boundaries than in the bulk [1]. Consequently, the conductivity measured can be defined as the bulk (inter-grain) conductivity at high temperature.

55 3 LITERATURE SURVEY

3.6 Defect Chemistry of CaTiOj

The most common way of the verification of defect disorder models of metal oxides is

based on the dependence of a on oxygen partial pressure, p(02):

i cr = const ■ p(02) ",

where:

1 _ d In cr (3-5) d\np(02)

where a is electrical conductivity. The parameter mCT is reciprocal of the exponent of the

p(C>2) dependence of a that can be used for the verification of defect models [4]. Equation (3-5) is valid when the (VCaTiCE system is in an equilibrium state. This may

be achieved when oxygen non-stoichiometry imposed by p(C>2) at crystal surface is propagated into the bulk.

Kofstad [1] proposed that ma is a constant dependent on the nature of the lattice defects. In the presence of double-ionized oxygen vacancy defects, the value of mCT can vary from 4 to 6 depending on whether the conduction process is extrinsic or intrinsic (i.e., depending on the amount of impurities in the lattice).

3.6.1 Defect Reactions for Undoped-CaTiOj

The effect of oxygen partial pressure, p(C>2), on electrical properties may be considered

within several ranges of p(C>2) in which the effect of p(C>2) on electrical conductivity exhibits different slopes. As seen from Figure 3-24 [14] which shows the plot of electrical conductivity vs. log p(02) for undoped CaTiCE at 1223K, the defect chemistry models (that are characterised by the slope) may be considered within the following three regimes:

• Extremely reducing conditions • Reducing conditions

• Oxidising conditions

56 3 LITERATURE SURVEY

x=0.008 x=0.000 x=0.002 ^ Eror & Balachandran, 1982 x=0.005

x=0.008

* x=0.005

x = 0.008 f'/y x=0.000

x = 0.005 •/ x=0.002 x = 0.000 x = 0.002

Logp(02) [p(02) in Pa]

Figure 3-24. Isothermal Plot of Electrical Conductivity of Undoped CaTiCE as a Function of p(02) According to Balachandran and Eror [14]

3.6.1.1 Extremely Reducing Conditions

Application of extremely reducing conditions led to reduction of CaTiCE which, according to the Kroeger-Vink [161] notation, may be described by the following equilibrium [162, 13]:

0:^~02+V0"+ 2e’ (3-6) where 00 is oxygen on its lattice site, VJ* is a doubly ionised oxygen vacancy and e’ is an electron. The equilibrium constant of the reaction (3-6) is:

^={v:’WP{o2y 0-7) where n represents the number of free electrons. Then, assuming that oxygen vacancies are the predominant lattice defects, the lattice charge neutrality requires that:

2[V0"] = n (3-8)

57 3 LITERATURE SURVEY

The concentration of oxygen vacancies may also be considered in terms of the deficit of oxygen in the oxygen sublattice, 5. The correct formula of CaTiC>3 is CaTi03-8 where both n and 5 may be expressed as the following functions of p(02): n = {2Kxyp(02Y* (3-9) s = (^-)~6p(o2P (3-10) where

8 = [V0' ] (3-11)

Assuming that the mobility of electrons is independent of p(02), the parameter mCT may be determined from the relationship between electrical conductivity and p(02):

The p(C>2) regime corresponding to the extremely reducing conditions is demarcated by the p(C>2) range in which the log a vs log p(C>2) slope is equal to -6 (Figure 3-24) [13, 14].

3.6.1.2 Reducing Conditions

At higher p(C>2) but still in the p(C>2) range corresponding to the n-type regime, other defects also are formed besides doubly ionised oxygen vacancies. These defects include singly ionised oxygen vacancies and trivalent Ti ions on the Ti sites. There is no agreement with respect to which defects may play a major role in this regime because all of them lead to similar dependence on the electrical conductivity on p(02).

3.6.1.2.1 Singly Ionised Oxygen Vacancies

Singly ionised oxygen vacancies are formed according to the following equilibrium [163]:

58 3 LITERATURE SURVEY

0x0~^02+v;+e' (3-13)

The equilibrium constant of the reaction (3-13) is:

k; = n[v;]p(o2yV2 (3-i4)

Then the charge neutrality condition is:

[v;] = n (3-15)

Therefore:

I _I n = (K;yP(o2y (3-16)

3.6.1.2.2 Trivalent Ti Ion

The trivalent Ti ions are formed according to the equilibrium [163]:

2Tir, + O. ~ 2Ti„ + V" + i 02 (3-17)

Then the charge neutrality is:

w:;]=[TiT,} (3-i8)

Then, the combination of Eqs. (3-6) and (3-17) results in the following relation between n and p(02):

2k i -I ^(t^t)2^) 4 (3-19) [Th]

Dunyushkina et al. [163] claims that the concentration of trivalent ions is independent of p(C>2). As can be seen from Eq.3-17, this is incorrect.

59 3 LITERATURE SURVEY

3.6.1.2.3 Acceptor-Type Contaminations

This defect model assumes that the predominant negatively charged defects are acceptor-type impurities while the predominant ionic defects are oxygen vacancies [13,12,165,167]. Then the lattice charge neutrality condition is:

A = 2[V0-] (3-20) where A is defined as an excess of acceptors over donors:

A = [A']-[Dm] (3-21)

Then, taking into account Eq. (3-6), the concentration of electrons is the following function of p(C>2):

9 v - _! " = (—L)2/>(02) 4 (3-22) A

Again, also in this case the p(C>2) exponent (of the n vs p(C>2) dependence) is -1/4.

Eror and Balachandran [13,167] have shown that cation nonstoichiometry does not have a marked effect on the electrical conductivity of CaTi03 (their studies were performed for cation nonstoichiometry in the range 0.992 > [Ca]/[Ti] > 1.008, Figure 3-24). In their study of well-defined CaTiCE specimens with respect to the concentration of acceptor- type impurities, Ueda et al. [164] claimed that this model is not suitable for explaining the electrical conductivity data.

3.6.1.2.4 Ca Ions on Ti Sites

This model assumes the formation of anti-site defects consisting of Ca2+ ions on the Ti sites. The anti-site defect, CaTj, may be formed according to the following reaction:

2CaO -> CaCa + CaTi + 200 + V” (3-23)

In this case, the charge compensation requires that:

[V0"] = [CaTi] = S (3-24)

60 3 LITERATURE SURVEY

where the concentration of the CaTi defects, determined by the solubility of CaO in

CaTiCb, S, is independent of p(02). Then: n = (-^-yP{o2y (3-25) [CaTi]

Therefore, in this case the exponent of p(C>2) is also equal to -1/4.

Udayamakumar and Cormack [165] claimed that the concentration of these defects is very small because their formation enthalpy is very high (4.80eV).

3.6.1.2.5 Schottky-Type Defects

The Schottky-type defects are formed according to the following equilibrium [167]: nil^V'Ca+ V;;+3V0" (3-26)

Its equilibrium constant is:

Ks=[Vcaw;w;:f (3-27)

Application of the conservation condition of the site ratio in both metal sublattices results in:

W'ca\ = r + {r + W*] (3-28) where r = ([Ca]-[Ti])/[Ti\ (3-29)

The charge compensation requires that: s = [v;-}=iv-a]+2 [v;;] 0-30)

Combination of Eqs. (3-28)-(3-30) results in the following expression for 5 as a function of the parameter r:

61 3 LITERATURE SURVEY

(3-31) r + 1 where r is defined by Eq. (3-29). Because the partial pressure of both Ca and Ti over CaTiCE is extremely low even at high temperatures [166], one may assume that the ratio r remains unchanged and, therefore, the concentration of oxygen vacancies, 5, is independent of p(02). Then the concentration of electrons is the following function of

P(02):

n = (~tY pioS * (3-32)

Application of theoretical methods indicated that the formation enthalpy of Ti vacancies is extremely high (86.26eV) [165] and, therefore, this model is an unlikely alternative for the consideration of properties of CaTiC^.

3.6.1.2.6 Ca Vacancies

The formation of Ruddlesden-Popper type phases, involving excess Ca ions accommodated between CaTi03 blocks, may lead to the establishment of pairs of Ca and oxygen vacancies according to the following reaction [165, 167]:

Ca^+O^ VCa+V0"+(CaO)layer (3-33)

Its equilibrium constant is:

(3-34)

Then the charge neutrality condition is: w'c}=w:i=k} (3-35)

Combination of Eq. (3-8) and Eq. (3-35) results in: n = K?K2>p(02) * (3-36)

62 3 LITERATURE SURVEY

3.6.1.2.7 Summary

As seen from sections 3.6.1.2.1 - 3.6.1.2.6, all the derived defect models of CaTi03 lead to the same p(02) dependence of the concentration of electrons. Therefore, the experiment data based on p(C>2) dependence of electrical conductivity do not allow to distinguish the predominant defects related to these models. Accordingly, the verification of defect models requires the determination of another defect-sensitive property, such as diffusion coefficients.

3.6.1.3 Oxidising Conditions

While the section 3.6.1.2 considered defect models of CaTi03 that exhibits n-type properties, this section considers p-type CaTi03.

Essentially, all the defects considered in section 3.6.1.2 and related defects models may also be considered in this regime. The determination of the concentration of holes for all the models requires knowledge of the intrinsic equilibrium constant, Kji

K,=np (3-37)

All the models may be represented by the following general equation:

K i p = — = constp(02Y (3-38) n

As seen from Eq. (3-38), by analogy to the defect models considered for the n-type regime, the experimental dependence of the electrical conductivity as a function of p(C>2) does not allow us to distinguish between the defect models because all of them result in the p(C>2) exponent m = 4. Therefore, additional variables are required for understanding which defects are the predominant defects.

3.6.2 Defect Reactions for Doped-CaTiOj

3.6.2.1 Acceptor-type Ions

63 3 LITERATURE SURVEY

Incorporation of acceptors into the CaTi03 lattice results in p-type conductivity over the entire range of p(02). Incorporation of acceptor-type ions, such as Cr ions, may be represented by the following reaction:

Cr203 + 2CaO -> 2CrTi + 5Oxa + V" + CaCa (3-39)

Its equilibrium constant is:

KCr = [^»2p(.o2y (3-40)

The charge neutrality condition requires that:

2 [V0“] = [CrTi] (3-41)

Therefore:

IK- - (-—h)2p(o2) * (3-42) [CrTi]

Electrical properties of Al- and Cr-doped CaTiCE were reported by Balachandran et al.

[12]. The p-type conductivity of CaTi03 may only be observed at elevated temperatures at which the acceptor levels are ionised. It is interesting to note that at lower temperatures than that required to ionise the defects, CaTiC>3 exhibits good insulating properties. Accordingly, CaTiCE never exhibits p-type properties at room temperature.

3.6.2.2 Donor-type Ions

Incorporation of donors into CaTiCE results in n-type conductivity over the entire range of p(02). The materials based on donor-doped CaTi03 have an application in the fabrication of dielectrics and, specifically, grain boundary barrier-layer capacitors [42]. This is why a substantial number of studies have been reported on properties of donor- doped CaTiC>3.

Donor-doped CaTiC>3 is also a component of the materials for immobilization of nuclear wastes, such as SYNROC [167, 168].

64 3 LITERATURE SURVEY

3.6.2.2.1 Charge Neutrality

Donors may be formed either as a result of the incorporation of tri-valent ions into the Ca sites or pentavalent ions into the Ti sites. Incorporation of donor-type ions, such as La3+ and Ta3+, results in the formation of donors only when incorporated into Ca and Ti sites, respectively.

While the incorporation mechanism of donors into the lattice of CaTiC>3 is relatively well known, there is no agreement with respect to the charge-neutrality condition of the donor-doped CaTiCb lattice. Specifically, three different models on the charge compensations have been considered:

• Electronic compensation. This model assumes that the positive charge of the donors is compensated by quasi- free electrons, which, as has been assumed [169], are localized on Ti ions thus forming tri-valent defects, Ti3+ [167].

• Ionic compensation. The positive charge caused by the donors is compensated by cation vacancies, such as Ca and Ti vacancies [170]

• Self-compensation.

It appears that in most cases, the donor-doped CaTiC>3 may be described by a model that involves all the above-mentioned three charge-compensation mechanisms. Moreover, the compensation condition may change with temperature and oxygen partial pressure.

3.6.2.2.2 Oxygen Nonstoichiometry

Balachandran and Eror [171, 169] observed that isothermal changes of oxygen partial pressure over CaTi03 doped with both La and Ta result in weight changes indicating

65 3 LITERATURE SURVEY that oxygen is either involved or consumed by the specimen according to the following hypothetical reactions:

La.Ca^TiO, + - 02 - LaxCa,_xTiOx (3-43) ^ +2

CaTi,_xTaxOy +j02*±CaTil_xTax0 (3-44) * o

Figure 3-25 shows the effect of p(02) on weight change of undoped and donor-doped CaTiOs according to Balachandran and Eror [171, 169]. As can be seen, weight change is proportional to the concentration of donors. This weight change assumes reversible (positive and negative) values for oxidation and reduction experiments, respectively.

These results clearly indicate that reduction and oxidation of CaTiC>3 specimen results in oxygen release and consumption, respectively. As can also be seen, the amount of the oxygen (released or consumed) for the doped specimens is substantially higher than that corresponding to undoped CaTiCL (indicated by the dashed line). The following relation can be established between the experimental data of the weight change and the content of the donor dopant:

A[02]=Aa[ZT] (3-45) where [O2] is the weight change related to the amount of oxygen (consumed or released).

The reaction (3-43) and (3-44) indicate that in oxidizing conditions two dopant ions are neutralized by one excess oxygen ion. However structure does not allow an accommodation of additional nonstoichiometric oxygen as, for example, interstitial oxygen, while the presence of additional phases was not detected. The most plausible explanation of the observed effect is that the mechanism of incorporation of the donors (La and Ta) depends on oxygen partial pressure. Specifically, the effect observed by Balachandran and Eror indicates that incorporation of the donors is governed by different charge compensations.

66 3 LITERATURE SURVEY

CaTiO

0 La-DOPED ~ EXPERIMENTAL T Ta-DOPED - EXPERIMENTAL ----- THEORETICAL

C£ *—*

MAXIMUM OXYGEN NONSTOICHIOMETRY IN UNDOPED CaTiO,

DONOR CONCENTRATION [AT. %]

Figure 3-25. Maximum Reversible Weight Change as a Function of Donor Concentration (derived according to data of Balanchandran and Eror [179, 180])

The transition between the low p(02) and high p(C>2) form may be represented by the following equilibrium:

D- + nri •+102 - D- + TiTI + i 00 +1VJ"+ i VT;""" (3-46) 4 2 6 6

Where D* denotes a donor-type foreign ion, such as La3+ ion in the Ca site or Ta3+ ion in the site. According to the equilibrium (3-46) the lattice charge neutrality assumes the following respective forms at low and high p(C>2):

[D'] = n (3-47) m = hKc/"] + f[V"] 0-48)

67 3 LITERATURE SURVEY

Accordingly, the formulae of La-doped and Ta-doped CaTi03 assume the following respective forms:

[{Ca^La^MTi^-ATirnMO^ + ^O, - (3-49)

6+ ^[(CaCa)(6_6_r)/(6+6j)(-^^Ca)6;t/(6+^)(^Ca )t/(6>jr) 1 * [(^Yi)6/(6+jr) (^7T ) x/(6+x) MOM

[(CaCa)Wir,\^{W)J[(0„)3] + J02 ~

6 +1 l(Cac„ )6/(Mx) (V/"),,(6„, ] * [(T’/J7)(6_6jt)/(6„) (Ta; )„,,„, ][(0. )3 ] (3-50)

3.6.2.23 Low Oxygen Partial Pressure

Incoporation of La and Ta into the CaTi03 lattice at low p(02) may be represented by the following reactions:

La/), + 2770, « 2 La/ + 277;, + 60,) + i O, + 2e' (3-51)

Ta2Os + 2CaO - 27a.;, + Car„ + 60^ + ^ O, + 2e' (3-52)

Accordingly, the charge compensation of donor-doped CaTi03 at low p(02) assumes the following electronic forms:

[La'cA = n (3-53)

[Tari] = n (3-54) According to Eq. (3-54), the concentration of electrons is determined by the concentration of donors and, therefore, is independent of p(C>2).

3.6.2.2.4 High Oxygen Partial Pressure

Incorporation of La and Ta into the CaTi03 lattice at high p(02) may be represented by the following respective reactions:

68 3 LITERATURE SURVEY

La20, + 2Ti02 ~ 2LaCa + iF„'"'+70„ + 27Y„ + VCo" (3-55)

7a20, +CaO-2r«;( +iK7.i""+2Cac<, +70; +iKCo" (3-56)

Accordingly, the charge compensation at high p(C>2) assumes the following respective forms:

[ia^] = t[KCo"] + |PV'"] (3-57)

[7’a;] = i[Fc;'] + |[Fn""] (3-58)

Taking into account that the vapor pressure of both Ca and Ti over CaTi03 is very low and assuming the same filling of both metal sublattices - as indicated by the formulas expressed by Equation (3-49) and (3-50) - the concentration of electrons may be expressed by the following function of p(02): n = (K,)''\~)mp(02ym (3-59) Ks where

V = [VI,""] = lVCo"] (3-60)

3.6.2.2.5 Self Compensation Mechanism

Balachandran and Eror [171, 169] proposed that the mechanism of incorporation of aliovalent ions, such as La3+ and Ta5+, resulting in the formation of both donors and acceptors when introduced onto Ca and Ti sites:

La‘ca + Tiri'+102 = i o; + i VCa' ■+ \ Lar,'+1 LaCa + 77' (3-61) 4 2 3 6 6

To* +nTl'+\o2~±-(yo +\vrr+X7Tdri +| Tan + 77' (3-62) 4 2 3 6 6

69 3 LITERATURE SURVEY

3.6.2.2.6 Phases of Ruddledson-Popper

It has been proposed that Ca vacancies may form as a result of oxygen incorporation into the CaTi03 lattice:

\ Ca’a, + Tir,'+ i 02 - ± CaO + ± Kc„' '+7Y' (3-63)

3.6.2.2.7 Summary

The charge compensation of donor-doped CaTi03 depends on oxygen partial pressure and temperature. Donor-type defects are predominantly compensated by electrons at very low p(C>2). Increase of p(C>2) results in the formation of cation vacancies, in both Ca and Ti sublattice, that are responsible for the predominantly ionic-charge compensation.

It appears, therefore, that CaTiC>3 exhibits a tendency to escape from the electronic compensation at higher p(C>2) resulting in the formation of cation vacancies.

The ionic-compensation mechanism was also claimed by Larson et al. [58] and Vance et al. [167] for Ga-doped and Ce-doped CaTiC>3 in an oxidizing atmosphere.

3.6.3 Conclusions

Defect chemistry of undoped CaTiCb may be considered within three different regimes with respect to equilibrium p (O2) [Figure 3-26]:

• Extremely reductive regime, characterised by the p (O2) exponent, m = - 6, in which the predominant defects are doubly ionised oxygen vacancies. • Reductive regime, characterised by the parameter m = - 4, in which several defect chemistry models. • Oxidation regime, characterised by the parameter m = 4, in which several defect chemistry models.

70 3 LITERATURE SURVEY

The charge compansion of donor-doped CaTiC>3 depends on oxygen partial pressure.

The electronic and ionic compensation predominates at low and high p(C>2), respectively.

CaTiO

reducing regime

extremely reducing oxidizing regime

log p(02) [p(02) in Pa]

Figure 3-26. Schematic the Plot of Conductivity vs. Oxygen Partial Pressure

3.7 Electrical Properties of CaTiOj

3.7.1 The Electrical Conductivity of Undoped-CaTiOj

Eror and his co-workers [13,11, 14, 12, 171,169] extensively studied the defect chemistry of CaTiOs and related electrical properties. Their studies, including the determination of electrical conductivity within a wide range of p(02) (10’17 - 103 Pa), and temperatures (1073K - 1373K), have shown that the defect chemistry of undoped

CaTi03 may be considered within the following regimes (Figure 3-27):

71 3 LITERATURE SURVEY

1. The regime corresponding to extremely reducing conditions (10*-17 Pa - 10'-11 Pa ), m

which CaTiC>3 exhibits n-type properties and the parameter mCT is equal to - 6.

2. The regime corresponding to reducing conditions (10‘10 Pa - 10"4 Pa) in which

CaTi03 exhibits n-type properties and the parameter ma is equal to - 4.

3. The regime corresponding to oxidsing conditions (10‘4 Pa - 105Pa ) which involves two sub-regimes:

3.1 The sub-regime in which CaTiCE exhibits p-type properties and the parameter mCT is equal to 4.

3.2 The sub-regime in which CaTiCb exhibits a transition between n- and p-type properties and the parameter mCT exhibits a change between + 4 to - 4.

Balachandran et al. [13] explained the conductivity of the semiconductor CaTiCE in the range the slope has a value of (-1/6) by the doubly ionised oxygen vacancy model. While in the zone the slope has a value of (-1/4), the defect chemistry of the undoped

CaTiC>3 is dominated by accidental acceptor impurities and their related oxygen vacancies for p(C>2) >10'16 atm. In this range, the band gap is as high as 3.46eV (determined from the minimum of electrical conductivity), which keeps intrinsic electronic disorder below the net acceptor impurity content of the material, and intrinsic ionic disorder does not play a significant role. In the p-type zone of p(C>2) > 10'4atm, the incorporation of oxygen into the impurity related oxygen vacancies results in the observed semiconducting behaviour.

Balachandran and Eror also reported that the electrical conductivity of undoped CaTiCE is insensitive to cation nonstoichiometry including both calcium deficit [14] and calcium excess [11].

72 3

Loga [a in S/m] LITERATURE 1073K 1123K Figure 1173K

SURVEY 1223K 1273K, 1323K, 1373K

3-27. \

Plots Log

of tl

Electrical

p(0 ■ 73 2 )

Conductivity [p(0 Balachandran 2 )

in

CaTi0 vs.

Pa]

p(C>

and 2 )

[13] 3 Eror, 1/4

1982 3 LITERATURE SURVEY

Yang et al. [87] investigated electrical conductivity of CaTi03 with excess TiC>2 or CaO shown in Figure 3-28. The results showed that electrical conductivities decrease drastically with increasing amount of excess CaO, and then become constant while Ti/Ca>l.

7T 0.35

•£» 0.3 -

TJ 0.25 1673K

n 0.2 - 1773K 1873K W 0.15 -

Ti/Ca Ratio

Figure 3-28. Room Temperature AC Electrical Conductivities of CaTi03 Specimens with Excess CaO or Ti02 Sintered at 1400, 1500 and 1600°C and Subjected to Reduction Treatment in Ar + 5% H2 at 1150°C for 6h

Studies involving the electrical conductivity measurements of CaTi03 within a wide range of p(02) were also reported by Dunyashkina et al. [163]. Their studies were limited to one temperature: 1273K.

Figure 3-29 shows the data of Balanchandran and Eror (1982), Ueda et al. (1997), George and Grace (1969), Iwahara et al. (1988) and Dunyaushkina et al. (1999). As can be seen, their data differ in terms of their absolute values and the values of p(02) at the minimum electrical conductivity. The difference is specifically substantial in the p-type regime. This difference may be caused by different levels of impurities in their

74 3 LITERATURE SURVEY specimens that, unfortunately, were not reported. The characteristics of the electrical conductivity changes as a function of p(C>2) reported by these research groups suggest that the specimen of Eror et al. involves a substantial amount of acceptor-type impurities.

2.5 Undoped CaTi03 1373K □ Balanchandran and Eror, 1982 2 O Ueda et al, 1997 A George and Grace, 1969 1.5 A Iwahara et al, 1988 • Ueda et al, 1997

— 1 ■ Balanchandran and Eror, 1982 a O Dunyushkina et al, 1999 55 .a o.5 JD 1373K c n b£ W 1273K o

-0.5 Act = 2.4 S/m

-1

-1.5 Ap(02)mi„ = 10 Pa

-2 1 ' I r -17 -12 -7 -2 3 8 log p(02) [p(02) in Pa]

Figure 3-29. Plots of Electrical Conductivity vs. p(02) [10, 11, 15, 173, 174]

75 3 LITERATURE SURVEY

The difference between the results reported by Eror et al. and Dunyaushkina et al. may also be related to different experimental approaches in the determination of the electrical conductivity. While Eror et al. applied the four probe method which measured the entire electrical conductivity including both ionic and electronic components, Dunyashkina et al. applied the Hebb-Wagner polarisation method.

3.7.2 The Electrical Conductivity of CaTI03 Doped with Aliovalent Ions

3.7.2.1 Gd-doped CaTiOj

Bak et al. [172] reported the effect of 15mol% Gd on the electrical conductivity of CaTi03 at 1273K in air. The result showed that Gd introduced into CaTi03 results in a decrease of the resistance by more than one order of magnitude because of the formation of donors. Incorporation of Gd into CaTi03 caused a transition from p-type to n-type semiconductor. This phenomenon indicated that a minimum point corresponding to an n-p transition shifted to a higher p(02) value which was determined by measurements of thermopower of samples (+1000pV/K for undoped-CaTi03 and -800pV/K for Gd doped CaTi03).

3.7.2.2 Y- and Nb-doped CaTi03

Ueda et al. [164] investigated electrical properties of Cai_xYxTi03 and CaTii_xNbx03 (x = 0, 10'4, 10'3, and 10'2) single crystals at temperature range of 500 tol700K in air (Figure 3-30). The electrical conductivity first decreased with an increase in dopant concentration from x = 0 to 10‘3, and remarkably increased with a further increase in the concentration up to x = 10'2.

76 3 LITERATURE SURVEY

x = 0.01(Y)

- -» - x = 0.01(Nb)

■A— x = 0.001(Y,Nb)

- x = 0.0001(Nb)

&—x= 0.0001(Y)

0.5 1 1.5 2 2.5 looo/T [ic1]

Figure 3-30. Temperature Dependence of the dc Conductivity of As-prepared Single­

crystal Samples. Cai-xYxTi03: Solid Lines; CaTii.xNbx03: Dotted Lines; A Dopant-free Sample: Dashed Line [173]

3.7.2.3 La-doped CaTiC>3

Balachandran and Eror [173] reported the electrical properties of Lanthanum-doped calcium titanate LaxCai.xTi03. The conditions were as follows: the doped amounts of Lanthanum were 0.15, 0.2, 0.4, 0.5 and 0.8 at%; temperatures were 1000°C and 1050°C; and the p(C>2) was in the range of 10° to 10‘18 atm. Results are shown in Figure 3-31 and Figure 3-32. There were two kinds of charge compensation, electronic and ionic. In the range of p(C>2) < 10‘15 atm, the carrier concentration was fixed by the amount of lanthanum added and hence the conductivity was found to be independent of oxygen partial pressure but increased with lanthanum concentration. A plateau region (electronic compensation) was found for the samples with lanthanum concentration greater than 0.2 at.%. In the range of p(C>2) >10'l3atm, the extra charge of the lanthanum was compensated by doubly ionised calcium vacancies (ionic compensation).

77 3 LITERATURE SURVEY

-a—x = 0.0015 - -A - X = 0.002 —x = 0.004 " ■ x = 0.005 —O— x = 0.008

Figure 3-31. The Electrical Conductivity of Lanthanum-doped Calcium Titanate as a Function of Oxygen Partial Pressure at 1000°C [173]

—O—x= 0.0015 • -A - x = 0.002 —£r- x = 0.004 —O— x = 0.008 - *• - x = 0.005

-20 -16 -12 -8 -4 0 logp(02> [atm]

Figure 3-32. The Electrical Conductivity of Lanthanum-doped Calcium Titanate as a Function of Oxygen Partial Pressure at 1050°C [173]

78 3 LITERATURE SURVEY

3.7.2.4 Fe-doped CaTi03

Iwahara et al. [174] reported that mixed conduction of oxide ions and electron holes was observed in the sample of Fe-doped CaTiC^ measured in air at the temperature range of

600-100°C. The total conductivity of CaTii.xFex03.a increased with increasing content of the substituent Fe as shown in Figure 3-33, which showed that the ionic transport number became bigger with increasing temperature at each composition x = 0, 0.1, 0.2,

0.3, 0.4 in CaTii_xFex03_a.

Xie et al. [175] studied the transport mechanism in Fe-doped CaTi03 through oxygen permeation and electrical conductivity measurements. The electrical conductivity of Fe- doped CaTiC>3 decreased slightly with decreasing temperature. Higher oxygen permeation flux was achieved with decreased thickness of membranes and increased temperature. The high oxygen permeability for CaFeo.2Tio.803-s reported by Iwahara et al. [174] was confirmed.

0.2 or 0.3

1000/T [K ]

Figure 3-33. Arrhenius plots of the Total Conductivity of CaTii_xFex03.a Measured in Air [174]

79 3 LITERATURE SURVEY

- - x=0.1 —A—x=0.2 - -Jr - x=0.3 —O—x=0.4

X = 0.0

800 900 1000 1100 1200 1300

Temperature [oC]

Figure 3-34. Transport Number of Oxide Ion Measured by Oxygen Concentration Cell

for CaTii_xFex03-a

However, the oxygen flux observed in this study was almost one order of magnitude lower than that reported by Iwahara et al.

Dunyushkina et al. [15] studied electrical properties of the system CaTii.xFex03.5 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) over a wide range of oxygen partial pressure (10 to O' atm) at 900 and 1000°C. The results showed that considerable increases in both ionic and electronic conductivity were obtained when Ti was substituted by Fe. A wide region of primarily ionic conductivity appeared independent of p(02). They obtained higher values of electrical conductivity and wider horizontal plateaux on the graphs of conductivity vs. p(02) in the system of CaTio.9Feo.1O3.5and CaTio.8Feo.203-5.

80 3 LITERATURE SURVEY

„ -1

- x=0.0 x=0.1 -2.5 - ’ -A - x=0.2 x=0.3 - -♦ - x=0.5

Logp(02) [p(02) in atm]

Figure 3-35. Dependence of the Total Conductivity of CaTii_xFex03.5on the Oxygen Partial Pressure at 1000°C [15]

3.7.2.5 Cr- and Al-doped CaTi03

Balachandran and Eror [12] reported the effect of acceptor (A1 and Cr) on the conductivity of CaTi03 at 1000°C and 1050°C in p(02) range of 10'24 ~10° atm. In the n- type region (p(02) < 10'10 atm), the electrical conductivity of A1 or Cr-doped CaTi03 was lower than that of undoped CaTi03 and the values decreased with increase in concentration of A1 or Cr. In the p-type region (p(02) > 10'7 atm), the electrical conductivity increased with acceptor concentration and the conductivity minima shifted to lower oxygen partial pressure. The electrical conductivity values were observed to be the same in doped-CaTi03 with A1 or Cr of same concentration and this indicated both these elements were equally effective as acceptor impurities.

Tochenaya [176] reported that addition of Cr3+ to ceramic CaTi03 strongly increased the electrical conductivity. The electrical effects disappeared on addition of > 0.2 wt. % Cr203 to CaTi03.

81 3 LITERATURE SURVEY

3.7.3 Summary

Analysis of the literature reports on the electrical conductivity leads to the following general conclusions:

1. The defect chemistry of acceptor-doped CaTiC>3 may be considered within two regimes involving n-type regime at low p(02), in which the parameter ma = - 4, and the p-type regime at high p(02), in which the parameter mCT = 4.

2. The defect chemistry of donor-doped CaTi03 may be considered within two regimes in which the following charge compensations apply:

1. The regime corresponding to low p(C>2) in which the concentration of electronic charge carriers is fixed by the amount of the donor and, therefore, electrical

conductivity is independent of p(C>2).

2. The regime corresponding to high p(C>2) in which the donors are compensated by cation vacancies and the parameter mCT is equal to - 4.

3. At elevated temperatures, undoped CaTiC>3 is an amphoteric semiconductor which

exhibits both n-type and p-type conduction at low and high p(C>2), respectively.

Addition of acceptors results in a shift of the p(C>2) correspoding to the n-p transition to lower values. This is the case when electrical conductivity exhibits a minimum of electrical conductivity. On the other hand, addition of donors leads to a shift of the minimum of the electrical conductivity to higher p(02) values (above 1045 Pa).

Consequently, p-type conductivity of donor-doped CaTi03 could be achieved experimentally using a high p(02) reaction chamber. So far, such data have not been produced.

4. So far, undoped CaTi03 has been considered as a predominantly electrical conductor [9-18]. Consequently, defect chemistry models have been verified against the electrical conductivity data assuming that the charge carriers are limited to electrons

82 3 LITERATURE SURVEY

and electron holes while, the role of ions in conduction has been ignored. This assumption, however, requires verification.

5. There is a substantial discrepancy between absolute values of the electrical conductivity as well as their dependence on temperature and oxygen partial pressure reported by different authors.

An important issue in the studies of the effect of p(C>2) on electrical conductivity concerns the imposition of a well defined p(C>2) and its correct determination. Variable oxygen activity has been achieved by the application of gas mixtures, such as argon- oxygen, CO-CO2, and H2O/H2. Although the oxygen partial pressure corresponding to the Ar-C>2 mixture may be determined by its composition, the oxygen activity of such mixtures may differ from the oxygen partial pressure. The difference may be considerable especially at lower values of p(02). This is the reason that application of an electrochemical oxygen sensor is essential for the determination of oxygen activity.

Substantial complications may be expected when using such gas mixtures as CO-CO2 and H2O-H2 mixtures that have been frequently applied for imposition of very low p(C>2). The first complication is that a well defined oxygen activity requires that the gases forming the mixtures are in equilibrium. This is frequently not the case, especially when the gas flow rate is high and the contact between the gas phase components is short. The oxygen activity of such mixtures flowing through reaction chambers is position dependent. Moreover, the gases forming these mixtures include reactive elements, such as carbon and hydrogen. Their impacts on defect chemistry and related electrical conductivity data may be substantial due to incorporation into the lattice. In consequence, the application of these gas mixtures may lead to the electrical conductivity data that are not well defined. Due to above complications, the most reliable way in imposition of p(02) is the application of the argon-oxygen mixture in which the only reactive element, oxygen, is well defined in terms of its p(02). Low values of p(C>2) may also be achieved by using pure argon in which the oxygen content is lowered using an electrochemical oxygen pump [20].

83 4 EXPERIMENTAL

4. EXPERIMENTAL

This chapter presents the characteristics of raw materials, description of the experimental set-up and experimental procedures, methods employed for sample characterisation.

4.1 Raw Materials

4.1.1 Chemicals

The raw materials employed in the CaTi03 preparation and some of their technical data are summarised in Table 4-1.

Table 4-1 Raw Materials Specifications Molecular Purity Molecular No Chemicals Supplier formula (wt %) Weight (g/mol) Titanium(IV) 1 Ti[OCH(CH3)2]4 97% 284.26 isopropoxide Sigma- Aldrich 2 Isopropanol (CH3)2CHOH 99.5% 60.10 Pty Ltd Calcium 3 Ca(N03)2-4 H20 99% 236.15 Australia nitrate

Table 4-2 Gases Specifications

Molecular Molecular Gas Purity (wt %) Supplier Formula Weight (g/mol)

Oxygen o2 32.00 99.6 BOC Gases, Australia Argon Ar 39.95 99.998

84 4 EXPERIMENTAL

4.1.2 Gases

The electrical conductivity and thermopower were measured in a gas environment of which different oxygen partial pressures were achieved by changing the flow rates of oxygen and argon (provided by BOC Gases, Australia, in gas cylinders). The specification of the gases is listed in Table 4-2.

4.2 Preparation of CaTiC>3 Pellets

The preparation of CaTiCb pellet was carried out by a coprecipitation reaction between titanium dioxide and calcium nitrate. The procedures are summarised in Figure 4-1.

Ca(N03)2 Ti(OC3H7)4

(CH3)2CHOH

Ca2+ + Ti4+ precipitate

1 ’ Drying

' f Calcination

at 1023K for lh in air

CaTi03 powders Cold press and Calcination at 1573K for 2 h and w at 1773K for 24 h

CaTi03 pellet

Figure 4-1. Procedures for Preparation of CaTiCb Bulk by Sol-gel Process

85 4 EXPERIMENTAL

4.2.1 CaTi03 Powder

CaTi03 Powder was prepared by the following steps.

(1) An aqueous solution of calcium nitrate was added to isopropanol while heating (<70°C) and stirring with a magnetic stirrer (solution I). (2) A stoichiometric amount of titanium (IV) isopropoxide was added to isopropanol whilst stirring at room temperature for several minutes (solution II). (3) Solution I and solution II were mixed together while stirring and the precipitate dried in an oven overnight at about 383K. (4) Samples were calcined in air atmosphere in a tube furnace at 1023K for 1 h to remove organic species and nitrates.

4.2.2 CaTiOj Pellets

Calcined samples were cold pressed isostatically by 20MPa to form circular pellets with 25mm diameter, and then sintered at 1573K for 2h to obtain the CaTi03 crystal phase. In order to obtain high density CaTi03 pellet, the sintered specimen was crushed into powder in an agate mortar, then pressed again as before and fired again at 1773K for 24h.

A slab of the size 2.75mm x 3.11 mm x 12.15mm was cut off the sintered ceramic blocks with a diamond saw and then polished with diamond powder of 1 pm.

4.3. Characterization of CaTi03 Pellets

4.3.1 Field Emission Scanning Electron Microscopy (FESEM)

Field emission scanning electron microscopy (Hitachi S-4500II, Japan) was used to observe the microstructure of specimens. Usually, the accelerating voltage was set at 20KV, and the magnification was from 500x to 5000x.

86 4 EXPERIMENTAL

4.3.2 Density

Bulk density (Db) and apparent porosity (Pa) were determined by the boiling water method according to the Australia Standard AS 1774.5-2001.

A test specimen is dried at 110°C to constant mass (mD) and then boiled in water until saturated. After reweighing the saturated specimen suspended in cold water (m,) and the in air (ms), the bulk density and apparent porosity may be calculated.

Density Calculations is as follows: a) Bulk Density (Dh) — in kilograms per cubic meter, from the following equation:

D„ = xD i7i„ - m b) Apparent Porosity (Pa) — in percent, from the following equation:

Pa =^ m° xlOO ms - mi Notation for the equations above is as follows: mD - Mass of dried specimen, in grams ml = Mass of test specimen, saturated with and suspended in water, in grams

ms = Mass of test specimen, saturated with water and suspended in air, in grams

Di = Density of water at the temperature prevailing during the test, in kilograms per cubic meter

4.3.3 Electron Probe Microanalysis (EPMA)

Electron probe microanalysis (Cameca SX50 EPMA) was used for identification of main impurity elements present in bulk CaTiCE specimen. This was carried out at ANSTO, Lucas Heights Laboratories in Sydney.

87 4 EXPERIMENTAL

4.3.4 Inductively Coupled Plasma Mass Spectrometry (ICP - MS)

The HP4500 Inductively Coupled Plasma - Mass Spectrometry (ICP - MS) techniques were used to analyse the composition of the CaTiCb pellet. This was carried out at ANSTO, Lucas Heights Laboratories in Sydney.

4.3.5 Inductively Coupled Plasma Atomic Emission Spectrometry (ICP - AES)

The Vista Simultaneous Inductively Coupled Plasma - Atomic Emission Spectrometry (ICP-AES) was selected to analyse the concentrations of several ions, i.e. S, Si, P and K more accurately, because the concentration of these ions in the sample were below the detection limits of the ICP - MS method. The ICP-AES analysis was carried out at ANSTO, Lucas Heights Laboratories in Sydney.

4.4 Experimental Set-up

Experimental-setup for electrical property and thermopower measurements includes four parts: high temperature seebeck probe, ancillary equipment, gas system and temperature measurement system.

4.4.1 High Temperature Seebeck Probe (HTSP)

The HTSP (Figure 4-2) incorporates probe chamber (including sample holder, microheaters and thermocouples), and probe head (including electrical outlets and printed circuit board).

The key elements of the sample holder are two Pt electrodes (forming also Pt-PtRh thermocouples) which have the following three functions:

• Acting as thermocouples: o The determination of the temperature in the probe

88 4 EXPERIMENTAL

o The determination of temperature gradients along specimen

• Acting as voltage and current probes o Imposition of a voltage along the specimen leading, in consequence, in the imposition of a current required for the electrical conductivity measurements o The determination of the Seebeck voltage along the imposed temperature gradient (when acting as electrodes in the absence of the current imposed in the external circuit)

The Pt electrodes are not used simultaneously as thermocouples and current probes and so whether interference exists is beyond consideration.

The sample was placed between two Pt electrodes. The microheaters, located at an extreme position, were pushed against the sample by a spring mechanism (located outside the high temperature zone). The microheaters were used for imposition of a temperature gradient along the specimen. The arrangement of the electrodes for the determination of both electrical conductivity and thermopower is shown in Figure 4-3.

4.4.2 Measurement of Electrical Conductivity and Thermopower

Both electrical conductivity and thermopower were detemined using a high temperature Seebeck probe (HTSP).

The electrical conductivity was measured using the four-probe method. The external (current) probes were formed of Pt electrodes attached to both sides of the slabs of rectangular-shaped specimen. A spring mechanism, located outside the high temperature zone, was applied to maintain good galvanic contact between the plates and the specimen. The internal (voltage) electrodes were formed of two electrodes wrapped around the specimen and welded to the Pt connecting wires. The distance between these electrodes was 8.41mm.

89 4

EXPERIMENTAL

HIGH-TEMPERATURE SEEBECK PROBE Figure

4-2.

High-Temperature o

Seebeck

Probe

External

1100mm

View 4 Figure

EXPERIMENTAL MICROHEATERS

4-3.

Determination Rectangular Sample

Holder

Specimen

of

Thermopower for

LU Imposition

and

91 Related

and

of

Electrical

a

Electrical Temperature

Conductivity

Connections

Gradient

along for

CURRENT CIRCUIT the

a

4 EXPERIMENTAL

The thermopower was measured along the temperature difference of two different polarities, A T and - A T. The thermopower, obtained at 20-40 different temperature gradients in the range 0-5K, was determined from the slope of approximately 20-30 independent measurements of thermovoltage which is plotted vs. the temperature gradient. The resulting dependence of AT' vs AT is shown in Figure 4-4. As seen, the thermovoltage data exhibit a good linear dependence as a function of the applied temperature gradient within the temperature gradients of different orientations, A T and -AT (the procedure of imposition of the temperature gradient will be discussed below).

The thermopower of the oxide specimen, S, was determined by adding the absolute thermopower of the Pt electrode to the experimentally measured value of the thermopower:

S = S^ + SPI (4-1) The absolute value of thermopower of the Pt electrode in the range (100-2000K) was determined by Cusack and Kendall [177]:

SPl =-2.63-0.01457 [juV / K\ (4-2) Taking into account the uncertainty in the determination of AT (±0.1K) and the Seebeck voltage (±1%), the standard deviation of the individual determinations was within ±1%.

4.4.3 Ancillary Equipment

The measuring electrical circuitry and the gas system are schematically drawn in Figure 4-5 and Figure 4-6. As seen, several ancillary equipment items are required for the determination of the electrical conductivity and thermopower in the gas/solid equilibrium at elevated temperatures and also in its monitoring as a function of time during equilibration. The equipment items include:

• Scanner for switching current in the current circuit and routing signals from thermocouples, oxygen sensor and voltage electrodes. • Scanner for collecting the Seebeck voltage at several combinations of probes

92 4 EXPERIMENTAL AT[K] 2.0

I- CL CO

GRADIENT,

0.0

2.0 - TEMPERATURE

[AW]av ‘30VHOA N03333S

Figure 4-4. Experimentally Recorded Data of the Thermovoltage as a Function of

Temperature Difference at 972K at p(C>2) = 6.15 kPa and Resulting Thermopower Determined from the Slope of This Dependence

93 4 EXPERIMENTAL

• Current source for the determination of electrical conductivity • Electrometer for the determination of electrical conductivity • Temperature sensor for monitoring temperature in the reaction chamber • Temperature controller for imposition of desired temperature in the reaction chamber • Gas system for imposition of desired oxygen activity of the reaction chamber and its maintenance during the experiment • Oxygen sensor for the determination of oxygen activity of the reaction gas mixture at the exit of gases from the reaction chamber • Personal computer and software for data acquisition and processing

4.4.4 Gas System

The desired p(02) in the probe was imposed by an oxygen/argon mixture flowing through the reaction chamber (Figure 4-6) under atmospheric pressure. A constant flow rate (100 mL/min) was imposed by mass flow controllers. The controllers (Tylan General) were able to automatically regulate flow in response to an input voltage command and the stability of the preset mass flow was within ± 0.25% of the full scale flow and the response time was 6s. Different p(02) values within the range of 101 Pa - 72 kPa in the probe were achieved through imposition of different argon to oxygen ratios.

Oxygen activities in the gas phase were determined using a zirconia-based electrochemical oxygen sensor installed at the gas exit of the measuring chamber. The oxygen activity was recorded as a function of time during the experiment through monitoring of the electromotive force of the sensor. The extreme oxygen activities applied in this study, determined from sensor, were as follows: o p(O2)=10Pa (99.998% argon) o p(02) = 72kPa (99.6%% oxygen) The experiments in which oxygen activity was increased and decreased are termed oxidation and reduction experiment, respectively.

94 4

Gas Outle EXPERIMENTAL Figure

4-5.

High

Temperature

Seebeck 95

Probe

Functional aojnos PZSAeiwey

Diagram

iusjjpq 4 EXPERIMENTAL

C/1 p CD I—I rH O P -P

u a> -P no a> £ g rH O 'H ooo -P rH rH

C/1 C/1 C/1 C/1 cO

h (N m H H rl

ai o P cd a) G r—1 p rH G o Ch p 4J 0 G 43 O G CJ ai Eh 43 P ai o a> i—i p p -p (d G P-T G .p -p G fd G O p ai t N

rH Cl a ai a p P G P O

Figure 4-6. Flowsheet of Gas Flowing Through the Reaction Chamber

96

o •H C/1 •H i—i u id

4.4.5 Temperature Measurement

Six temperatures were selected: 973K, 1023K, 1173K, 1223K, 1273K, and 1323K. The highest temperature was determined by the equipment specification while the lowest temperature was selected as the minimum temperature at which the gas/solid equilibrium could be reached due to the kinetic reason. The temperature was measured using two thermocouples attached to both sides of the specimen and the average temperature value was used in data processing.

4.4.6 Experimental Procedures

Both electrical conductivity and thermopower were determined simultaneously, using a high temperature Seebeck probe (HTSP), in the temperature range of 973-1323K. Before the measurement, the specimen was heated to temperature of the measurements in Ar (purity: 99.998%) at a rate of 400K/h. At each temperature the specimen was initially annealed in reducing conditions (Ar) until the electrical conductivity reached a constant value, then electrical conductivity and thermopower were determined and finally a new p(C>2) was imposed isothermally. The experiments were performed at several oxygen activities in the range of 10 Pa - 72 kPa involving both oxidation and reduction experiments.

The measurements of the two electrical properties were performed using the following three procedures:

1. The measurement of resistance during oxidation and reduction experiments. The measurements, taken as a function of time, aimed at monitoring the gas/solid equilibration kinetics. It was assumed that the specimen was in equilibrium after the electrical conductivity reached a constant value as a function of time. These measurements were taken at lOpA imposed in 50ms cycles involving different current direction (in order to avoid polarisation effects of the specimen). The time gap

97 4 EXPERIMENTAL

between the cycles was 1 s while the time gap between subsequent measurements was in the range 30s and 15 min. The latter depends on the rate of the electrical conductivity changes and was automatically adjusted by appropriate software.

2. The measurements in equilibrium. These measurements aimed at the determination of the electrical conductivity with a specifically high accuracy and these data were then taken for quantitative analysis of electrical properties. These measurements were taken at 10-15 different currents, in the range of lOnA and 1mA, of two polarities while the overall voltage over the specimen remained within 5V. The measurements involved the determination of the dependence of the voltage as a function of current. The slope of linear part of this dependence, aimed also at the verification of applicability of the Ohms law, served for the determination of the equilibrium value of the electrical conductivity and thermopower.

3. Temperature gradients. The temperature gradients along the specimen, used for the determination of thermopower, were determined using two thermocouples at both sides of the specimen. These gradients were achieved by providing a current impulse to a microheater on one side and resulting, in consequence, in imposition of a maximum temperature gradient and achieve a steady value of AT (not using transient values of AT). Then, thermovoltage was measured while the temperature of this microheater was reduced to the background temperature level and the temperature gradients were assumed to successively decrease. Thermopower was determined for several temperature gradients and related thermovoltage values. The same procedure was applied when the temperature gradient of opposite polarity was imposed. In this case a current impulse was provided to the microheater on the opposite side of the specimen.

98 4 EXPERIMENTAL

Oxidation experiment involved introduction of a new gas mixture, of increased oxygen activity, into the reaction chamber. The oxidation experiments were monitored using the electrical conductivity measurements, temperature and p(02), since the moment when new gas mixture entered the measuring chamber. Reduction experiments were performed in a similar manner. The electrical conductivity data obtained during oxidation were then verified during reduction experiments. The data taken for quantitative analysis was the average value obtained during oxidation and reduction.

Figure 4-7 shows a standard monitoring sheet showing the changes of p(02), T and resistance (R) during two subsequent oxidation experiments at 1223K. As seen in Figure 4-7(a), imposition of a new gas phase results in a very rapid increase of p(02) to the level of 95% of a final value (within several seconds) and then assumes its nominal value within 30 min. According to Figure 4-7(b) the temperature during the experiment remains constant within ± 0.5K. Taking into account that the change of temperature by IK leads to the change of electrical conductivity Figure 4-7(c) by approximately 1 % (at the highest experimental temperature level, 1323K), the observed fluctuation of T in time have negligible effect on the measured electrical conductivity data.

99 4 Figure

TIME [h] EXPERIMENTAL

4-7. =fTTm

11111 An in [ed]

Oxidation

Example

i

i i

i

(2 o)d

of Atmosphere

the

Standard i

i

i

at i

M

I

1273K Monitoring i

i

100

i

i i

I

i

i

i

Sheet, i

111

Involving M i

i

i

i

1111 i

|

i

m a i

i

i

p(02), i

|

1 ii 1

i

i i

T

and

EC, TIME [ks]

5 RESULTS AND DISCUSSION

5. RESULTS AND DISCUSSION

5.1 Microstructure

Figure 5-1 and Figure 5-2 shows the scanning electron micrographs of the CaTiOs specimen after polishing and after subsequent thermal etching at 1300K for 1 h, respectively.

As can be seen, the polycrystalline specimen is dense with occasional pores. The relative density of the specimen sintered at 1773K for 24 hours was 96% of the theoretical density (4.14 g/cm3) and the apparent porosity was 1.17%.

Point analysis by Energy Dispersive Spectroscopy (EDS) showed that two phases, TiC>2

(rutile) and Ca3(P04)2, existed along the grain boundary shown in Figure 5-1. Rutile

TiC>2 was formed on the grain boundary as Ti atoms were expelled from the crystal structure due to their lattice positions being occupied by some impurity atoms. Impurity

P ions, once formed (PO4)3' groups of big size, were difficult to incorporate into the

CaTi03 lattice structure, and the (PO4)3' group extracted Ca2+ from the lattice structure to form Ca3(P04)2 phase located on the grain boundary.

The SEM image shown in Figure 5-2 was taken from a small cavity on the surface of the specimen, which displayed that the specimen consisted of individual grains with an average grain size of 30-40 pm.

5.2 Electrical Conductivity

Electrical conductivity is the most commonly studied defect-sensitive property of semiconducting materials. Their semiconducting properties have been mainly considered in terms of the electrical conductivity and its dependence on p(C>2) and temperature.

101 5 RESULTS AND DISCUSSION

Figure 5-1. SEM Image (magnification x 500) of Polished Surface of Undoped CaTiC>3

Figure 5-2. SEM Image (magnification xlOOO) of the CaTiCU Specimen Thermally Etched at 1300K for 1 hour

102 5 RESULTS AND DISCUSSION

5.2.1 Effect of Oxygen Partial Pressure

The electrical conductivity of CaTi03 were measured at 973, 1073, 1173, 1223 1273 and 1323K and in gas environment with oxygen partial pressure in the range of 101 *~ 103 Pa. The results are shown in Figure 5-3. Electrical conductivity constantly increased with increase in temperature. At constant temperatures, the slope of the loga vs. log p(02) curves at 1323K and 1273K exhibit a minimum at approximately 100 Pa and 20 Pa, respectively, while the electrical conductivity at 1223K has a tendency to assume a minimum at even lower p(02). At lower temperatures the minimum is not observed within the experimental range of p(02) and has a tendency to be achieved at p(02) lower than 10 Pa.

Assuming equality of the mobility terms, these minimum values in the electrical conductivity corresponded to the n-p transition. With increasing temperature, the n-p transition shifted towards higher p(C>2).

According to defect models, the p(C>2) exponent, l/mCT, varies. Consequently, the electrical conductivity vs p(C>2) curves may be divided into three regimes for CaTiC>3, as seen in section 3.6.3, the n-type regime in which the p(02) exponent is -1/6, the other n- type regime in which the p(C>2) exponent is -1/4, and the p-type regime in which the p(02) exponent is 1/4. In this study, however, the slopes of the curves obtained from experiments deviated from the above defect models.

1 ^ Jq qj The values of the parameter mCT in Eq. (5-2) (— =------) at low and high p(C>2) m„ 8 log p(02) range are listed in Table 5-1. The reciprocal of the p(02) exponent, mCT, increases from

4.1 to 5.3 at high p(C>2) and from 6.0 to 24 at lower p(02). The observed change tendency of mCT should be considered in terms of an increasing impact of minority charge carriers (electrons) on conduction [8]. Ultimately, the effect of both electrons and holes on conduction in the lower p(C>2) range at 1323K becomes comparable and, therefore, the conduction assumes a minimum.

103 at

Pa) 5 -10 0 (10

CaTiO Pressure

Pa]

Partial

in

[p

) 2 Oxygen

on

104 logp(0 Conductivity

of Temperatures

1073K 1173K 1223K 1273K 1323K DISCUSSION Dependence

Different AND The

5-3.

RESULTS

D) 6 0 | Uj [Ui/S Figure 5 5 RESULTS AND DISCUSSION

Table 5-1 Reciprocal of the p(02) Exponent of Electrical Conductivity Tenperature mCT

[K] 1 < log p(02) < 2.5 2.5 < log p(02) < 4.5 4.5 < log p(02) < 5 973 6.0 4.3 4.1 1073 7. 1 4.3 4.1 1173 15.3 5.1 4.3 1223 17.6 5.7 4.5 1273 24.0 6.0 4.6 1323 - 6.2 5.3

Figure 5-4 shows the effect of oxygen partial pressure on electrical conductivity, in the form of loga vs. log p(02) plots, including the data obtained in the present work (solid lines) along with those reported by Balachandran et al. [13] (broken lines). As can be seen, these two sets of data differ essentially in both their absolute values and the slope of the loga vs. log p(02) dependence.

As can be seen in Figure 5-4, the reciprocal of the slope of logs vs. log p(02) of the data of Balachandran et al. [13] is close to four in the entire range of temperatures. This means that the electrical conductivity of their specimen, that is well described by the

A 1 1 theoretical model expressed by Eq. (5-35) (p = Kj(----)12p(0 2Y), is substantially less 2 K affected by minority charge carriers. This seems to be a consequence of the fact that, as seen in Figure 3-11, the minimum of electrical conductivity determined in their work is assumed at the p(02) in the range 10'2 Pa - 1 Pa. The observed discrepancy may be considered in terms of one of the following two tentative models:

(1) The specimen of Balachandran et al. involves a higher concentration of acceptor- type impurities, which are responsible for substantially stronger p-type behaviour. Although this model is the most plausible explanation of the observed effect, however, its verification is not possible because Balachandran et al. [13] did not provide their impurity analysis.

105 Figure log a [a in Q 5

RESULTS

5-4. 1173K 1323K 1073K 1223K 1273K

vs. 973K The

AND

log

1 i Experimental

DISCUSSION p(0 i 2

This Balachandran )

log along

work

2

Data i with

p(0 of

Those i

Electrical 2 )

and

of 106 [

3

I Eror p(0

Eror,

Conductivity

et i

2 al.

) 1982

[13] in 4 i

CaTiO

Pa] Obtained i

in

5 i This 1273K 1173K 1223K 1323K 1073K

Work

5 RESULTS AND DISCUSSION

(2) The specimen of Balachandran et al. involves a higher concentration of acceptor- type intrinsic defects, such as Ca and/or Ti vacancies, which are responsible for shifting the conduction regime deeper into the p-type regime. These defects are formed according to the following reaction:

nil ~ 3V0+VCa' + Vn"" (5-1)

However, by analogy with BaTiCb, this model, if valid, should result in the reciprocal of p(C>2) exponent 5.33 [178]. The presence of this model is also in consistent with the sintering temperature reported by Balachandran et al. (1623K [11]) and that applied in the present study (1773K), because one should expect that the higher the sintering temperature, the higher concentration of cation vacancies formed during the sintering.

5.2.2 Effect of Temperature

The electrical conductivity of CaTiCh was studied as a function of temperature. Figure 5-5 showed the electrical conductivity of CaTiCb in the temperature range 973-1323K and in equilibrium with the gas phase with oxygen partial pressures between lO'-lO3 Pa. The values of the activation energy, which was calculated from the slope of the Arrhenius plots in Figure 5-5, are listed in Table 5-2 and Figure 5-6.

Table 5-2 The Activation Energy of CaTi03 in the Temperature Range of 10°-105 Pa

p02 [Pa] 14 58 130 550 2.51 6.25 1.89 3.95 7.05 xlO3 xlO3 xlO4 xlO4 xlO4 Activation Energy 125 116 113 108 103 100 97 97 94 [KJ/mol K] Activation Energy 1.29 1.20 1.17 1.11 1.06 1.03 1.00 1.00 0.97 [eVl

Figure 5-6 shows the change of the activation energy of the electrical conductivity obtained in the present study as a function of p(02). As seen, the activation energy varies with p(C>2) from 125.3 kJ/mol at 10 Pa to 94.4 kJ/mol at 72 kPa. Figure 5-7 shows that the error for the activation energy is within ±4.5 at 21 kPa.

107 5 RESULTS AND DISCUSSION

-0.75

-1.25

-1.75

—p(O2)=70.5KPa -2.25 - -A - p(02)=39.5KPa —p(02)=18.9KPa - -» - p(02)=6.25KPa —o-p(02)-2.51KPa -2.75 - - p(O2)=550Pa —o— p(O2)=130Pa - -♦ - p(02)=58Pa —O— p(Q2)=T4Pa -3.25

104/T [K1]

Figure 5-5. The Dependence of Conductivity on Temperature in Gas with the Oxygen Partial Pressure in the Range of 10-105 Pa

108 5 RESULTS AND DISCUSSION

CaTiO

logp(02) [p(02) in Pa]

Figure 5-6. Activation Energy (Ea) of Electrical Conductivity for CaTiCE as a Function of Oxygen Partial Pressure p(02)

There is an excellent agreement between the results determined in this work at 21 kPa and those reported by Iwahara et al. [174] in terms of the activation energy (88.8 kJ/mol and 9l.6±4.5 kJ/mol, respectively) as well as the absolute values of the electrical conductivity (Figure 5-8). Although the activation energy reported by Balachandran et al. is slightly larger (104.6kJ/mol), their absolute values of the electrical conductivity are almost one order of magnitude larger than those reported in this study. The difference is consistent with the explanation that the undoped (but not pure) specimen of Balachandran et al. [13] may include acceptor-type impurities, which may be responsible for an elevation of the conduction in the p-type regime.

Because electrical conductivity involves both terms: concentration and mobility, the activation energy of the electrical conductivity, Eff, has a complex physical meaning involving both terms [1]:

109 5 RESULTS AND DISCUSSION

S -1

^1.6 ± 4.5 kJ/mol K

0.7 0.75 0.8 0.85 0.9 0.95 1 1000/T [T in Kj Figure 5-7. The Temperature Dependence of log a Obtained in the Present Work at 21 kPa with Error Bar.

Ea=—AH/+AHm (5-2) ma where AHf denotes the enthalpy of the formation of defects, AHm is the enthalpy of the mobile ion charge carriers and ma is the parameter describing the p(02) dependence of the electrical conductivity:

1 _ diner (5-3) mtr d\np(02)

Correct determination of the mobility term AHm is essential for assessment of the conduction mechanism.

Assuming that the mobility terms remain constant within a wide range of oxygen partial pressure, the observed changes of the activation energy with p(02) may be considered in terms of the changes of the formation term. Assuming after Xie et al. [175] that

AH/;J =22 kJ/mol within the range of p(C>2) the parameter ma = 4, this study obtained

110 5 RESULTS AND DISCUSSION that the formation term changes from 206 kJ/mol at lOPa to 146 kJ/mol in air (Figure 5-9). This conclusion, however, is in conflict with the report of Eror et al. [13] who claim that the formation term within the regime of p(C>2) corresponding to p-type conductivity remains independent of p(C>2).

104.6 kJ/mol K

-=• -0.6

66.9 kJ/mol K

▲ This work

■ Balachandran and Eror, 1982 91.6 kJ/mol K -1.4 • Dunyushkina et al, 1999

-1.6 - □ Ueda et al, 1997

O Iwahara et al, 1988 88.8 kJ/mol K

1000/T [Tin K|

Figure 5-8. The Temperature Dependence of log a Obtained in the Present Work (interpolated for oxygen activity equal to 21 kPa) Along with the Data of Balachandran et al. [13], Dunyushkina et al. [15], Iwahara et al. [174], and Ueda et al. [173] (for the Sake of Comparison Our Data in This Figure are Limited to the Temperatures at 1073K and above)

111 5 RESULTS AND DISCUSSION Pa]

in

[p

) 2 p(0

■c E CD log D O

C/) X X < < <3 E

CVJ C\J T- [iouu/r>i] (°a)'hv

Figure 5-9. Enthalpy of Defects Formation Term, AHf, as a Function of Oxygen Partial Pressure

112 5 RESULTS AND DISCUSSION

5.3 Thermopower

5.3.1 Effect of Oxygen Activity

Figure 5-10 shows isothermal dependencies of the thermopower as a function of oxygen partial pressure in the temperature range of 973 - 1373K. In the temperature range between 973 - 1373K, the thermopower exhibits high positive values within the entire p(02) range, between 500 and 1125 pVK'1, which is consistent with p-type properties. At 1173K, thermopower assumes values between 900 pVK'1 at high p(02) and -110 pVK'1 at low p(02) while the slope of the loga vs. log p(C>2) varies between 5.1 and 15.3, respectively. These data still exhibit p-type properties which, however, are already affected by minority charge carriers (electrons), especially at low p(C>2) when S exhibits a change from positive to negative values. In the range of 1223 - 1323K, the thermopower assumes values from positive, 800 pVK'1 at high p(C>2) to negtive, -1000 pVK'1 at lower p(C>2), which are consistent with mixed-type semiconductivity, while one should expect that the predominant charge carriers of the CaTiC>3 specimen that exhibit positive and negative S values are electron holes and electrons, respectively. The experimental data of thermopower in the p(C>2) range of 10* - 105 Pa indicates that the

CaTiC>3 specimen used in this study remains within the n-p transition regime (II) in which thermopower of CaTi03 is affected by both type of charge carriers.

5.3.2 Effect of Temperature

As seen in Figure 5-11 and Figure 5-12, the temperature dependence of the thermopower depends substantially on the equilibrium p(C>2) resulting in the activation energy 133.9 kJ/mol and 753.2 kJ/mol at 72 kPa and 10 Pa, respectively. The temperature dependence of thermopower for reduced CaTi03 has been considered by George and Grace [162] in terms of the enthalpy of formation of oxygen vacancies. Assuming that the temperature dependence of the thermopower data determined in the present work has the same physical meaning, the formation term should be related to the specific defect disorder of the studied specimens in oxidising conditions.

113 5 RESULTS AND DISCUSSION

a B-g

1073K ■

1223K'

CaTiO 1273K.C

1323K

0.5 1.5 2.5 3.5 4.5

logp(02) [p(02)in Pa]

Figure 5-10. Thermopower (S) of CaTi03 vs. Logarithm of the Oxygen Partial Pressure (log p02) at Different Temperatures.

□ 973K ■ 1073K D1173K A1223K o 1273K • 1323K

114 5

RESULTS Figure 1300 1200 1100 1000

AND

5-11.

DISCUSSION

Thermopower [>l/ATl]

S of

‘

CaTi d3A/\OdOI/\ld3H± 03 115

as

a

Function

of

1/T

at

p(02)

=

72 CD O o in LO d CD co o d co in o r- LO kPa

1000/T [K ] 5

RESULTS Figure 1300 1200 1100 1000

AND

5-12.

DISCUSSION

O Thermopower [»/ATi]

"

S

of

‘

CaTi d3A/\OdOlAld3H± 03 116

as

a

Function

of

1/T

at

p(02)

=

10

kPa

1/000 1 1 ] > [, 5 RESULTS AND DISCUSSION

Applying the same procedure as George and Grace [162] and assuming that at 72 kPa the reciprocal of the p(02) exponent ms = 4 leads to the formation term equal to 268 kJ/mol. However, defect disorder of CaTi03 at 72 Pa is more complicated than that of reduced CaTi03 and should be considered in terms of several types of defects, such as oxygen vacancies and cation vacancies [179]. Therefore, the correct evaluation of the defect disorder of oxidised specimens is required for understanding of the physical meaning of the activation energy term.

The physical meaning of the activation energy of thermopower at 10 Pa is much more complicated. The complication is due to the fact that these data correspond to the n-p transition regime. As seen in Figure 5-10, the thermopower data at this specific p(02) correspond to p-type and n-type regimes at 973 and 1323K, respectively. Although application of the same procedure as George and Grace [162] results in the formation enthalpy term 1506.4kJ/mol, the physical meaning of this value cannot be considered in terms of specific defects because of the complex physical meaning of thermopower in this regime.

5.3.3 Effect of Temperature on Electrical Conductivity at Constant Thermopower

The obtained thermopower data were also used for the determination of the electrical conductivity at constant thermopower.

Mason et al. [180] reported a method of the determination of the mobility term AHm using the analysis of the temperature dependence of the electrical conductivity at constant thermopower. This method is based on an assumption that this dependence is determined by the mobility term according to the following relation:

_aino- din// _ AH„ (5-4) 5(1 IT)’’ d(VTy^ k P According to this method, the determined activation energy depends on S and assumes

119 kJ/mol and 146 kJ/mol at -500 pVK'1 (S < 0, electrons predominant) and 750 pVK’1 (S > 0, electron holes predominant), respectively. Figure 5-13 shows that the activation

117 5 RESULTS AND DISCUSSION

energy of electrical conductivity at S = constant steadily increases with an increase in thermopower from -500 pVK'1 to 400 pVK'1, accompanied by the effect of minor defect (electron holes) when S > 0. It sharply increases at 400 - 450 pVK'1 where electron holes become the predominant defects. These values are substantially larger than the mobility term AHm reported by George and Grace (16.7 kJ/mol) [10] and Xie et al. (22 kJ/mol) [175]. This discrepancy indicates that the method based on the relationship described by Eq. (5-4) cannot be applied to CaTiCb. It seems that this is due to invalidity of the condition Np/p = constant in this case.

.O'

7 [h] ~

[e'+h] ;

j6

S>0, p-type

-400 -200 0 200 400 600 800 THERMOPOWER, S [jtV/K]

Figure 5-13. Activation Energy of the Electrical Conductivity of Undoped CaTiCb at Constant Thermopower as a Function of Thermopower

5.3.4 Conductivity vs. Thermopower

The minimum of electrical conductivity vs. p(02) corresponds to the situation when both n- and p-type conductivity components are the same. Then the following condition applies:

"Mn = PPP (5-5)

118 5 RESULTS AND DISCUSSION

In the case when the following condition applies for the n-p transition point: n-p (5-6) and

Mn=M„ (5-7) where n and p denote the concentrations of electrons and electron holes.

When the mobilities of electrons and electron holes are the same then the p(C>2 ) values at which electrical conductivity exhibits a minimum and the thermopower assumes zero should overlap as for Ti02 single crystals reported by Nowotny [181]. Both electrical conductivity and thermopower change as a function of p(C>2) with an effect of symmetry, i.e. the p(02) corresponding to amjn is identical to the p(02) at which S = 0 (shown in Figure 5-14 ). When the mobilities of electrons and electron holes exhibit different values the effect of symmetry is absent (see the broken line in Figure 5-14), in which the electrical conductivity vs p(C>2) exhibits amjn at a p(C>2) different from that corresponding to S = 0. This is the case for polycrystalline TiC>2 [182].

Figure 5-15 ~ Figure 5-19 show electrical conductivity and thermopower as a function of oxygen partial pressure for CaTiC>3 polycrystalline ceramics at 973, 1073, 1173, 1223, 1273, 1323K. It is obvious that the minimum of electrical conductivity does not coincide with the point at which the thermopower equals zero. As seen in Table 5-3, there is a discrepancy between the p(02) values corresponding to the n-p transition obtained in this work at S = 0 and those corresponding to minimum of electrical conductivity data.

This result indicates that at S = 0, when the concentrations of both charge carriers are expected to be the same, the electrical conductivity is substantially larger than that at the minimum. The p(C>2) at which S = 0 is higher than that at which electrical conductivity exhibits a minimum, amin. The discrepancy between the p(02)[CTmin] and the p(C>2)[s=o] at 1223K and 1323K is approximetely one order of magnitude.

119 5 RESULTS AND DISCUSSION

D 6o| ) 2 p(0

log

S ‘U3M0dlAIU3Hl Figure 5-14. Schematic Illustration of the Effect of Symmetry (solid lines) of

Thermopower vs. log p(02) and logcr vs. log p(C>2) Plots and the

Discrepancy between the p(02) at S = 0 and that at

120 5 Figure

RESULTS Thermopower [ pV/K] logo [c in S/m]

5-15. 1200 1000 ------200 400 600 800 2.4 2.2 2.8 2.6 1.4 1.6 1.8 -2 -3

AND

0 Electrical a

-2 Function -2

DISCUSSION

s=o Conductivity

□ ■ of CaTiO

Oxygen 973K 1073K logp(0 0 0

Partial

and

Thermopower

2 Pressure 121 )

[ P 2 2 0

2

of in

CaTiC Pa] >3 4 4

at

973

and

1073K 6 6

as

Figure Thermopower [ pV/K] logo [o in S/m]

5-16.

Thermopower CaTiCE

at

1 173K

(S) logp(0

and vs.

Logarithm the

Logarithm 2 122 )

CaTiO

1173K [p0 of

the

of

2 Oxygen

Electrical

in

Pa]

Pressure

Conductivity

log

p(02)

(Loga)

of

5 Figure

Thermopower[uV/K] log a [ a in S/m] RESULTS

5-17.

AND

Electrical Function

DISCUSSION

of Conductivity

Oxygen logp(0

Partial

and

Thermopower Pressure 123 2 )

[p0 2

of in

CaTiC

Pa] >3

at

1223K

as

a

5 Figure

Thermopower[uV/K] log a [ a in S/m] RESULTS -1000

5-18.

AND

Electrical Function

DISCUSSION CaTiO o

1273K

of Conductivity

Oxygen logp(0

Partial

and

Thermopower Pressure 2 124 )

[p0 2

of in

CaTiCE

Pa]

at

1273K

as

a

Figure 5

RESULTS

5-19. Thermopower[uV/K] log a [ a in S/m] -1200 -1000

AND Electrical Function

DISCUSSION

o \ of Conductivity n

s Oxygen \ CaTi0

• Logp(0 Partial l°gp(0

and 1323K

Thermopower Pressure 3 125 2 2 ) )

[p0 [ P 0

of 2 2

CaTiCE

in in

Pa] Pa]

at

1323K

as

a

5 RESULTS AND DISCUSSION

It seems that this disagreement between the p(C>2) value corresponding to the minimum of the electrical conductivity and that corresponding to the zero value of thermopower can be explained assuming that there are different mobilities and different transport mechanisms between electron holes and electrons in CaTiCb polycrystalline ceramics. So far, little is known about this transport.

Table 5-3 Oxygen Partial Pressure Corresponding to the n-p Transition in Undoped

CaTi03 According to Thermopower (S = 0) and Electrical Conductivity (amjn)

S = 0 ^min Temperature [K] p(02) [Pa] 1173 15 _* 1223 70 Below 10 1273 190 20 1323 450 65

* No minimum of electrical conductivity detected in the p(02) range 101 ~ 10' Pa.

5.4 Impurities

Impurities present in ceramics affect the electrical properties of the ceramic materials. Difference in the position of the impurity elements located in the lattice structure results in various changes of the properties. For example, acceptor [12] and donor [173] impurities in CaTiCE shift amjn to lower or higher p(C>2), respectively. It is necessary to determine the effect of total effective concentration for donor and acceptor minor impurities in CaTiCE ceramics on its electrical properties. This section of the thesis focuses on analysing the amount of impurities in CaTiCE, investigating incorporation of these impurities into lattice structure of CaTiCE and determining the total effective concentration of the impurity elements affecting electrical properties of CaTiC^.

5.4.1 Analysis of Impurities in CaTiC>3

The concentrations of impurities were determined using the following methods:

126 5 RESULTS AND DISCUSSION

1. Electron probe microanalysis (EPMA) 2. Inductively coupled plasma mass spectrometry (ICP/MS) 3. Inductively coupled plasma atomic emission spectroscopy (ICP/AES)

EPMA was used for identification of the main impurity elements present in the bulk CaTiCE specimen. Their concentrations were then analysed using ICP/MS or ICP/AES. The results of the ICP/MS analysis are presented in Table 5-4. Because the concentrations of several ions, i.e. S, Si, P and K, were below the detection limits of the ICP/MS method, the ICP/AES method was selected to analyse these ions more accurately. The analysis results are given in Table 5-5.

Table 5-4 Concentrations of impurities according to the ICP/MS method Element A1 Co Cr Cu Fe Mg Concentration 0.06 0.0014 0.004 0.013 0.06 0.12 [wt %1 Element Mn Ni Sc V Zn Concentration 0.003 0.001 0.0004 0.004 0.05 [wt %1

Table 5-5 Concentrations of impurities according to the ICP/AES method Element S Si P K Concentration [wt %] 0.015 0.6 <0.02 <0.006

5.4.2 Investigation of Impurities Incorporating into the Lattice Structure of CaTi03

Impurities in cubic CaTiCE may be classified as the following forms: 1. Substituting ions of Ca or Ti to form a substitutional solid solution 2. Locating in interstitial voids to form interstitial solid solution 3. Locating in the grain boundary area

Figure 5-20 is a schematic diagram showing substitutional and interstitial impurities in lattice structure. The ability of each impurity to locate in a particular position in lattice structure of CaTiCE is determined by Hume-Rothery’s Rules [183] and Radius Ratio [184] for substitutional solid solution and interstitial solid solution, respectively.

127 5 RESULTS AND DISCUSSION

Substitutional impurity ion

Interstitial impurity ion

Figure 5-20. Schematic Diagram of Substitutional Impurities and Interstitial Impurities in Lattice Structure

5.4.2.1 Lattice Structure of Cubic CaTi03

As shown in section 3.5.1.1, there are three kinds of lattice structure of CaTiCb shown in Figure 5-21 The specimen employed in this study was sintered at 1773K for 24h, indicating that the structure of CaTiCb was cubic perovskite structure which can be presented in two types of cells as shown in Figure 5-22: • Ca and O ' form a cubic close packing CaOn - cuboctahedra (A cell) • Ti4+ and O2" form TiC>6- octahedral (B cell).

1380 -1500K 1520 -1650K Orthorhombic ^ Tetragonal —^ Cubic

Figure 5-21. Phase Transformation of CaTiCb

The A cell is a cubic structure with a calcium atom sitting in the center, 8 titanium atoms at each comer and 12 oxygen atoms in the center of each edge. The B cell is a cubic structure with a titanium atom sitting in the center, 8 calcium atoms at each comer and 6 oxygen atoms in the center of each face.

128 5 RESULTS AND DISCUSSION

A Cell: Ca012 Cuboctahedra B Cell: Ti06 Octahedra

Figure 5-22. Cubic Perovskite Structure of CaTi03

5.4.2.2 Substitutional Solid Solution

According to the Hume-Rothery’s rules [184], including relative size factor, electrochemical factor, and valency factor, the solubilities of impurity elements in the form of substitution into Ti position (6-coordination) and Ca position (12-coordination) in CaTi03 were investigated. The solubility of impurities was classified into three levels: favourable, low concentration and no substitutional solid solution. Table 5-6 gives the classification criteria of the solubility according to the differences in radius, valence and electronegativity between cation ions and impurities.

Table 5-6 Classification Criteria of Substitutional Solid Solubility for Metallic Impurity Element (X) in Metal (M)

Difference in Radius Difference in Difference in Solubility Electronegative (Rx - Rm)/Rm x 100% Valence (ENx-ENm) V < 15% 0 <0.1 o 15% ~ 20% 1 ~ 2 0.1 ~0.5

X > 20% 3 >0.5 Note: V----- favourable substitutional solid solution o----- low concentration substitutional solid solution x----- no substitutional solid solution

129 5 RESULTS AND DISCUSSION

5.4.2.2.1 Ti Position Substitutional Solid Solution

Figure 5-23 and Table 5-7 illustrate the solubilities of impurity elements in the form of substitution into the Ti position (6-coordination) in CaTiCb. Ions such as Al3+, Mn2+(LS), and V5+ are favourable to form solid solutions. Ions such as Co2+(LS), Co2+(LS), Cr3+, Cu2+, Fe3+(LS), Fe3+(HS), Mg2+, Ni2+, Sc3+ and Zn2+ are likely to form minor solid solutions. Other ions, such as Na+, K+, S4+, S6+, Si4+, P5+, and Mn2+(HS), are unable to substitute for Ti to form solid solutions.

5.4.2.2.2 Ca Position Substitutional Solid Solution

Table 5-8 illustrates the solubilities of impurity elements in the form of substitution into

Ca position (12-coordination) in CaTi03. According to the FIume-Rothery’s rules, the investigation found that only two ions, Na+ and K+, were considered to be able to substitute for Ca ion to form solid solutions. Na ion is favourable to form a solid solution, while K+ ion is likely to form a low concentration solid solution in the lattice structure of CaTi03.

5.4.2.3 Interstitial Solid Solution

Interstitial sites are the spaces between ions or atoms that can be occupied by other ions or atoms. Such formed solutions are called interstitial solid solutions. This section evaluates the possibility of formation of interstitial solid solutions between different impurity oxides and CaTi03. Possible interstitial sites are identified and their sizes are evaluated through radius ratio, and then the possibility of various impurity cations fitting into the interstitial sites is assessed. Implicit in this standard methodology is hard spheres in point contact.

130 5 RESULTS AND DISCUSSION

Table 5-7 Solubility of Impurities into the Ti Position in CaTiC>3

Radii in 6 Difference in Difference Element Coordination Radius in ENx ~ ENji Solubility (Rx-RTi)/Rii [nm] xl00% Valency

A1J+ 0.0675 -9.396 V 1 o 0.07 V V 0.0885 (HS) 18.792 o 2 o 0.34 o o Co2+ 0.0790

0.0970(HS) 30.201 X 2 o 0.016 V X Mn 2+ 0.0810(LS) 8.725 V 2 o 0.016 V V

Nil* 0.0830 11.409 o 2 o 0.37 o o Sc J+ 0.0885 18.792 o 1 o -0.18 o o Zn i+ 0.088 18.121 o 2 o 0.111 o o

Na ,+ 0.116 55.705 X 3 X -0.61 X X v>+ 0.068 -8.725 V -1 o 0.09 V V

K 1+ 0.152 104.03 X 3 X -0.72 X X

s6+ 0.0430 -42.282 X -2 o 1.04 X X

Si 4+ 0.0540 -27.517 X 0 o 0.36 o X

p5+ 0.0520 -30.201 X -1 o 0.65 X X Ti 4+ 0.0745 Note: V...... favourable substitutional solid solution o----- low concentration substitutional solid solution x----- no substitutional solid solution LS---- low spin HS-----high spin

131 5 RESULTS AND DISCUSSION

Table 5-8 Solubility of Impurities into the Ca Position in CaTiCE

Differs;nce in Radii in 12 Element Rac ius Difference in ENX- Solubility Coordination ENca Valency [nm] (Rx-Rc:a)/Rca xlO0%

A13+ ? ? ? -1 O 0.61 X X

Co 2+ ? ? ? 0 V 0.88 X X

Cr 3+ ? ? ? -1 O 0.66 X X

Cu 2+ ? ? ? 0 V 0.9 X X

Fe 3+ ? ? ? -1 O 0.83 X X

Mg 2+ ? ? ? 0 V 0.55 X X

Mn 2+ ? ? ? 0 V 0.556 X X

Ni 2+ ? ? ? 0 V 0.91 X X

Sc 3+ 9 ? ? 1 O 0.36 o X

Zn 2+ ? ? ? 0 V 0.651 X X Na + 0.153 3.38 V 1 O -0.07 V V

V5+ ? ? ? -3 X 0.63 X X K + 0.178 20.27 o 1 o -0.18 o o

S6+ ? ? ? -4 X 1.58 X X

Si 4+ ? ? ? -2 o 0.9 X X

P5+ ? 9 ? -3 X 1.19 X X Ca 2+ 0.148

Note: V------favourable substitutional solid solution o----- low concentration substitutional solid solution x----- no substitutional solid solution ? ----- data unavailable

132 5 RESULTS AND DISCUSSION

e 5-23. Solubility of Impurities by Substitution into Ti Position in CaTiCb 5 RESULTS AND DISCUSSION

A Cell

B Cell

O Ca Ti

Figure 5-24. Schematic Structure of Perovskite CaTiC>3

134 5 RESULTS AND DISCUSSION

5.4.2.3.1 Evaluation of possible interstitial void for interstitial ions in CaTiOs

In order to evaluate possible interstitial sites in lattice structure of CaTiC>3, the accommodation of Ca, Ti, and 0 ions needs to be verified. It is necessary to evaluate the practical values of radii of Ca or Ti because the effective ionic radii of Ti and Ca in the lattice are different from the values in pure CaO or TiC>2. This may be achieved by assessing three physical models of titanium - oxygen contact, calcium - oxygen contact, and oxygen - oxygen contact models and comparing the values with that calculated using PDF card[185]. Figure 5-24 illustrates schematic structure of CaTiCb (A Cell and B cell).

1. 0-0 Contact Model

Figure 5-25 shows the overlap of atoms when the CaTi03 structure follows the 0-0 contact model. It is well accepted that the radius of 02‘ is 0.126 nm for 6-coordination. Based on this value, the lattice parameter a can be calculated as 0.356 nm.

2. Ti -O Contact Model:

Figure 5-26 shows the arrangement of atoms in the Ti-0 contact model. From this model, the lattice parameter a can be calculated as 0.401 nm based on the radius of Ti4+ is 0.0745nm for 6-coordination.

3. Ca -O Contact Model:

Figure 5-27 shows the arrangement of atoms in the Ca-0 contact model. From this model, the lattice parameter a can be calculated as 0.387 nm based on the radius of Ca2+ being 0.148nm for 12-coordination.

4. PDF Model: From this model, the lattice parameter a can be obtained from the PDF card, which is 0.382.

135 RESULTS AND DISCUSSION

Table 5-9 Parameter a of CaTiCb from Different Models

Model a [nm]

PDF card (XRD measurement) 0.382

0-0 Contact Model 0.356

Ti - 0 Contact Model 0.401

Ca - 0 Contact Model 0.387

136 5 RESULTS AND DISCUSSION

e 5-25. The Overlap of Atoms Fo 5 RESULTS AND DISCUSSION

Rii4+= 0.0745 run

Ro2-= 0.126 nm

a— 2(RTi4++ R02-) = 0.401 nm

Figure 5-26. The Arrangement of Atoms Following Ti-0 Contact Model

Rca2+= 0.148 nm

Ro2-= 0.126 nm

a= V2 /2(Rca2++ R02-) = 0.387nm

Ca • Ti ® O

Figure 5-27. The Arrangement of Atoms Following Ca-0 Contact Model

138 5 RESULTS AND DISCUSSION

The values of the lattice parameter a of CaTi03 calculated from different models are compared in Table 5-9. The lattice parameter a from the O - 0 model is significantly lower than the value from XRD measurement, from the Ti - O Model it is quite bigger than the value from XRD measurement and the Ca-0 Contact Model is the closest to the real structure.

Based on these models, a schematic diagram describing three types of possible interstitial sites, comer void (CV), face void (FV) and volume void (VV), in the cubic lattice structure of CaTi03 are shown in Figure 5-28. White circles represent O atoms located in the centre of face planes, while grey and black circles show Ca and Ti atoms, respectively.

z A

X 001/

X

OCa • Ti O o

Figure 5-28. Schematic Diagram of Three Possible Interstitial Sites, Comer Void (CV), Face Void (FV) and Volume Void (VV), in the Cubic Lattice Structure of the CaTi03

139 5 RESULTS AND DISCUSSION

5.4.2.3.2 Investigation of the size of interstitial void in CaTiOs

The size of these interstitial voids that may be filled by interstitial ions can be determined via calculation of the radius ratio (^cation/^anion) with respect to different structural models in CaTi03. Consequently, the Coordination Number (CN) is determined by the radius ratio (Table 5-10).

Table 5-10 The Relationship of Radius Ratio and Coordination Number Radius Ratio Arrange of Anions around the Coordination Number cation (CN) 0.00 0-0.155 Linear 2 0.155 - 0.225 Equilateral Triangle 3 0.225 -0.414 Tetrahedron 4 0.225 -0.414 Trigonal Bipyramid 5 0.414-0.732 Octahedron 6 0.732- 1.000 Cube 8 1.000 Cuboctahedron (FCC) 12

FCC= Face Centred Cubic or Cubic Closest Packed

The Coordination Number is defined as the number of anions that can fit around a cation. This number increases as the radius ratio increases. When the radius ratio is small, then only a few anions can fit around a cation. When the radius ratio is large, then more anions can fit around a cation. When the CN is 4, it is known as tetrahedral coordination; when the CN is 6, it is octahedral; and when the CN is 8, it is known as cubic coordination.

5.4.23.2.1 Radius Ratio of Rcati0n/Ro2-and Coordination Number (CN)

The calculation results of Rca2+/Ro2- and RTj4+/Ro2., corresponding coordination number (CN) and coordination polyhedron in cubic CaTi03 are listed in Table 5-11 and Table 5-12, respectively. The detailed calculations are presented in Appendix A and B. From Table 5-11 and Table 5-12, the calculated radii of Ca2+ and Ti4+ from the Ca-0

140 5 RESULTS AND DISCUSSION

model are very close to those from the PDF card, which indicates that the Ca-0 model is most likely to be the real lattice structure of CaTiC>3 crystal.

Table 5-11 The Radius Ratio (Rca2+/Ro2-) of different models and corresponding

Coordination number (CN), Coordination Polyhedron in Cubic CaTiC>3

Contact Radius of Coordination Coordination Rca2+/R-02- Model Ca2+ [nm] number (CN) Polyhedron

0-0 1 0.126 12 Cuboctahedron (FCC)

Ti-0 1.25 0.158 12 Cuboctahedron (FCC)

Ca-0 1.175 0.148 12 Cuboctahedron (FCC)

PDF Card 1.143 0.144 12 Cuboctahedron (FCC)

Ca - oxide 0.148 12 Cuboctahedron (FCC)

Table 5-12 The Radius Ratio (Rxi4+/Ro2-) of different models and corresponding

Coordination number (CN), Coordination Polyhedron in Cubic CaTiC>3

Contact Radius of Coordination Coordination Rli4+/Ro2- Model Ti4+ [nm] number (CN) Polyhedron

0-0 0.414 0.0522 6 Octahedron

Ti-0 0.591 0.0745 6 Octahedron

Ca-0 0.536 0.0675 6 Octahedron

PDF Card 0.516 0.0650 6 Octahedron

Ti - oxide 0.0745 6 Octahedron

5.4.23.2.2 Radius Ratio of Rinterstitiai void/Ro2- and Coordination Number (CN)

The calculation results of Rinterstitiai/Ro2-, corresponding coordination number (CN) and

coordination polyhedron in cubic CaTiC>3 are listed in Table 5-13.

141 Table 5-13 The Radius Ratio (RVO id/ R0 2-) of different models and corresponding Coordination number, Coordination Polyhedron in CaTi0 3 ■2 2 ’ .2 4 X .2 X T u .2 X z U .a .2 X X X >' 5 cd C O O o C o

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■d (N - Table -5-14 Calculation of Radius for interstitial void in Cubic CaTiCb

R a d iu R s a tio o f P o sitio n R a d iu o s f P o sitio n[nm ] C o n ta cM t o d e l Rvoid/ Rq2- R Interstitial Void V > o > o n N" <3 © 1 § - 0 .0 5 2 2 o o o o P o o o O P > > O o h h

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The detailed calculations are presented in Appendix B. The calculated maximum radii of different interstitial voids with different atom contact models are listed in Table 5-14.

The sizes of interstitial voids is in the order of Rev > Rvv > Rfv-

5.4.2.3.3 Assessment of the possibility of impurities fitting into the interstitial sites

The possibility of impurities, such as P, Si and S, located in interstitial void were assessed using the Ca-0 contact model shown in Table 5-15 and Figure 5-29. As seen, P (CN=4) is favourable into comer and volume interstitial voids; P (CN=5) is favourable into corner interstitial void, but unfavourable into the volume interstitial void. S (CN=4) is favourable into comer and volume interstitial voids. Si (CN=4) is favourable into corner interstitial void, but unfavourable into volume interstitial void. None of the elements, such as P, S, Si is favourable into face interstitial void.

Comparisons of the number of interstitial voids, including comer void (CV) and volume void (VV), and the number of impurity atoms, including S, P, Si, in 1 gram CaTiCb are showed in Table 5-16 and Table 5-17. It is showed that there are enough numbers of interstitial voids (1.329 x 1022 voids/g for CV Voids and 3.543 x 1022 voids/g for VV Voids, respectively) to allow all impurities (1.358 xlO20 atoms/g) to incorporate in CaTi03.

144 Table 5-15 Possibility of Impurities Located in Interstitial Void in Cubic CaTiCb from Ca

Radii of Elements with Different CN Interstitial Radius Radius of Coordination Favourable Coordination [nm] Void Ratio of Interstitial Void Number Element > hH > > Polyhedron HH > Position Position Position [nm] (CN) * £ d O V V > a. £ cu £ h 0.031 0.043 Tetrahedron 4 • GO o o Ql d '3' O V 33 1 £ Comer 0.363 0.0458 1 i Void m Trigonal £ d C/3 04 V 1 £ 1 Bipyramid 0.026 1 £ P X X h £ 33 X X

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evarn 5 RESULTS AND DISCUSSION

Table 5-16 Number of Interstitial Voids in 1 gram CaTiCE CaTiOs Number of Unit Cell Number of CV Void Number of VV Void lmol 6.023 x 1023 lg 6.023 x 10^/136 3 x 6.023 x 1023/136 8 x 6.023 x 1023/136 = 4.429 x 1021 = 1.329 x 1022 = 3.543 x 1022 CV------Corner Void; VV------Volume Void

Table 5-17 Number of Impurity Atoms in 1 gram CaTi03

Element CaTiOs s P Si S, P, Si Weight M 1 0.00015 0.0002 0.006 Number 6.023 x 1023 0.00015/32 x 0.0002/31 x 0.006/28 x 1.358 of atoms /136 6.023 x 1023 6.023 x 1023 6.023 x 1023 xlO20 = 4.429 x 1021 = 2.823 xlO18 = 3.886 x 1018 = 1.291 x 102U

r > Elements can not be P: IV. V incorporated into the Si: IV voids l S: IV J / r

Elements can be ■5*4 incorporated into the voids

O c. Ti o °

Figure 5-29. Summary of Possible Location of Impurities in Cubic CaTiOs IV: CN = 4 V: CN = 5

146 5 RESULTS AND DISCUSSION

5.4.3 Mechanisms Impurities Affecting Electrical Properties of CaTiOs

The impact of impurities on electrical properties is determined by the mechanism of their incorporation into the lattice.

5.4.3.1 Electron Transferring Mechanisms

The following electron transferring mechanisms may be taken into account:

• Donor-type mechanism involving: 4 Incorporation into interstitial positions of ions of any positive valency 5 Incorporation into the lattice sites of ions whose the positive valency is larger than that of the host ions • Acceptor-type mechanism involving the incorporation of the ions, whose positive valency is smaller than that of the host ions, into lattice sites • Neutral mechanism involving the incorporation of isovalent ions into lattice sites

Assuming that donors and acceptors are fully ionized at elevated temperatures, their effective concentration is determined by the product involving the concentrations and the number of quasi-free electrons supplied to and removed from the lattice, respectively:

(5-8)

Where D is the effective concentration of donors, the brackets denote the concentrations of individual donors, [D], and acceptors, [A], a and b correspond to their respective valency values (in the case of interstitial position of ions) or the difference in valencies with host ions (in the case of lattice sites of ions).

5.4.3.2 Determination of Effective Concentration of Donors and Acceptors

According to the Hume Rothery’s Rules and calculation of radius ratio, the ionic radii with respect to specific coordination of the impurities in CaTiC>3 was investigated,

147 5 RESULTS AND DISCUSSION which results in the following assumptions concerning the mechanism of incorporation of impurities into the lattice of CaTiC^:

• The 3d metal ions principally enter the Ti4+ sites and, because of the valency, most of them are lower than that of the host lattice ion, their incorporation leads to the formation of acceptors. Similar electronic mechanism may be assumed for A1 and Zn. • Because of its small ionic radius, S6+ enters interstitial sites thus leading to the formation of donors • Because Si is small ionic radius as well, its dissolution in the lattice leads to the formation of four-valent ions located in interstitial sites. • Phosphorus may be confined to grain boundaries in the form of whitlockite, however, some P5+ ions may enter perovskite interstitial species.

Taking into account the above assumptions, the effective concentration of donors and acceptors are shown in Table 5-16. The total effective concentration of impurities in Eq. (5-8) is approximately 0.02 mol%. Even assuming that their vast majority is confined to grain boundary areas, the donor-type impurities seem to have a predominant effect on the electrical properties of the studied CaTiC>3 specimen, which may shift the minimum electrical conductivity to the high-p(02) direction.

5.5 Verification of Defect Chemistry Models using Electrical Conductivity

In essence, the problem of interpreting and controlling electrical conductivity in ceramics consists of characterizing the concentration and mobility of each possible current carrier and synthesizing these contributions to obtain the total conductivity.

It is the first time that this study quantified the electrical conductivity components of

CaTi03 in the regime of the n-p transition through verifying defect chemistry models using electrical conductivity measurement, so that one may determine the separated contributions of electron conductivity, electron hole conductivity and ionic conductivity.

This method is based on a comparative analysis of the electrical conductivity of CaTiC>3

148 5 RESULTS AND DISCUSSION

and its defect disorder models within the n-p transition regime in which the ionic component assumes its maximum values. Consequently, one also may predict the concentrations of electrons, holes and ions present in the defect structure of CaTi03 material.

Table 5-18 The Effective Concentration of Donors and Acceptors

Mol % WT% Effective Charges Concentration Difference [mol/mol] Elements Donor Acceptor [mg/g] [D] / [A] a[D] b [A] a[D]-b[A] [a] [b]

A13+ 6.47E-02 6.46E-04 1 6.46E-04 Co "+ 1.39E-03 6.36E-06 2 1.27E-05 Cr J+ 3.99E-03 2.07E-05 1 2.07E-05 Cu 2+ 1.26E-02 5.36E-05 2 1.07E-04 Fe 6.14E-02 2.96E-04 1 2.96E-04 Mg 1.19E-01 1.32E-03 2 2.64E-03 Mn 2+ 2.95E-03 1.45E-05 2 2.89E-05 Ni2+ 9.30E-04 4.27E-06 2 8.54E-06 Sc J+ 3.60E-04 2.16E-06 1 2.16E-06 Zn 2+ 4.94E-02 2.04E-04 2 4.08E-04 Na1+ 5.00E-04 5.86E-06 1 5.86E-06 V 4.19E-03 2.22E-05 1 2.22E-05 0.00E+00 K1+ 6.00E-03 4.13E-05 1 4.13E-05 S6+ 1.50E-02 1.26E-04 6 7.56E-04 Si 4+ 6.00E-01 5.76E-03 4 2.30E-02 P3+ 2.00E-02 1.74E-04 5 8.70E-04

Total: 2.47E-02 4.22E-03 2.05E-02

149 5 RESULTS AND DISCUSSION

5.5.1 Electrical Conductivity Components

Usually, more than one charge carrier can contribute to the electrical conduction in a single material. The individual charge carrier may be electrons, holes, or charged ions. In this case, a partial conductivity (electrical conductivity components) for each charge carrier is defined by:

= a. + ah + crim = ep,[e'] + eph[h ] + zepit\i\ (5-9) where atot denotes the total of conductivity, ae is electronic conduction, Oh is electron holes conduction and ajon is ionic conduction; [e'], [h] and [/] denote the concentration of electrons, electron holes and ions; jue, /Jh and /ut are mobility; z is the valency of ions and e is elementary charge.

1 & \ Taking into account that the parameter mCT in Eq. (5-3) (----=------), describing ma 5 log p(02) the effect of oxygen partial pressure on electrical conductivity, assumes values of -4 and 4 in the n- and p-type regimes, respectively. Therefore, the conductivity components in

CaTi03 can be expressed as the following respectively:

i =

i <7P =

Assuming that the ionic electrical conductivity component remains independent of p(C>2) within a wide range of p(02) [179], the electrical conductivity within the n-p transition regime is expressed in the following form:

i a = a“p(02) 4 +a-°pp(02y + is unity.

150 5 RESULTS AND DISCUSSION

Determination of electrical conductivity components on and op are usually made through analysis of electrical conductivity within either n-type regime or p-type regime and assuming that the concentration of the minor electronic charge carriers is negligibly low. In this study, the ionic component of electrical conductivity is supposed significant.

It was shown that in the n-p transition regime, both types of electronic charge carriers needed to be taken into account in explaining electrical properties of metal oxides [8]. Consequently, all the electronic components of electrical conductivity, on, op and Gi,

have an impact on the curvature of the electrical conductivity vs. log p(02).

In order to determine the electrical conductivity components, one may apply a curvalinear least squares analysis aimed at fitting the experimental data to Eq. (5-13).

The fitting analysis involves such adjustment of the constants a°i, o°n and o°p that a minimum of the following function is achieved:

\^o,-

The above analysis was used for the determination of the electrical conductivity

components including on, ap and Gj.

Plots of electrical conductivity components vs. p(C>2) are shown in Figure 5-30 to Figure 5-35 for 973K, 1073K, 1173K, 1223K, 1273K and 1323K, respectively. From these figures, it can be seen that:

• Increasing p(02) from 101 Pa to 105 Pa, resulted in an decrease, and gp increase,

while

conduction mechanism of semiconductor CaTiC>3 transfer from tri-mixed conduction (electrons, electron holes and ions) to bi-conduction (electron holes and ions). Electron holes are predominant in the oxidation regime.

Semiconducting properties of CaTiCb in this p(C>2) regime changed from n-p transition to p-type.

151 5 RESULTS AND DISCUSSION

• The inflection points between the cjn and gp lines, which corresponds to the n-p

transition point, shifted to the high p(C>2) direction with increasing temperature. This phenomenon is consistent with the shift direction of the n-p transition point obtained from electrical conductivity and thermopower.

• But the values of p(02) at which corresponding to inflection point of an and ctp lines, the minimum of electrical conductivity, and at which S = 0 are different.

• The

5.5.2 Electrical Conductivity Transfer Numbers

The fraction of total electrical conductivity contributed by each charge carrier is:

t k (5-14) alol where t^ is called the transfer number. Obviously, the sum of the individual transfer numbers must be unity:

(5-15)

The determination of transfer number of electrons, electron holes and ions using the following relations:

tn (5-16)

152 5 RESULTS AND DISCUSSION

t,=^~ (5-18) ®lot where tn, tp and tj are transport number of electrons, electron holes and ions, respectively.

Figure 5-36 to Figure 5-41 show the changes of the transport numbers of electrons, electron holes and ions along with change in p(C>2) at 973K, 1073K, 1223K, 1273K and 1323K respectively. It is concluded that:

• When p(02) = p(C>2) CTmin, the transfer number of ions is larger than that of electrons (tj > tn) and transfer number of ions is larger than that of electron holes as well (tj > tp); In this n-p transition regime, ionic conductivity is predominant. The transfer number of ions (tj) is as high as 0.5;

• When p(02)>p(02) CTmin, the transfer number of electron holes is larger than that of electrons (tp > tn) and the transfer number of electron holes is larger than that of ions (tp > tj); Electron holes conduction is predominant; CaTiCb exhibits a p-type conductor.

5 When p(C>2) < p(C>2) CTmin, the transfer number of electron is larger than that of electron holes (tn > tp) and the transfer number of electron is larger than that of ions

(tn> tj); Electron conduction is predominant; CaTiC>3 exhibits a n-type conductor.

The comparison of the electrical conductivity component and transfer number between this study and Eror in the p(C>2) range of 101 to 105Pa at 1323K showed in Figure 5-42 and Figure 5-43. It is obviously showed that:

• Electron holes predominate in this regime

• Ionic transfer number exhibited the tendency of increase quickly when p(02) goes into the n-p transition regime so that ionic conduction can not be ignored.

153 5

RESULTS

Figure log a [o in S/m] log 0 [o in S/m] ' igure

1

______5-31.

5-30. AND CaTiO 1073K

CaTiO 973K

DISCUSSION EC EC 1

Components Components 2 1

log log

Including Including

p(0 p(0 1

2 2 154 )

) a

o

[p(0 n n [p(0 , ,

3

1

a a

p p

and and 2 2 ) )

in in Oj Oj

I

Plots Plots Pa] Pa]

vs. vs. 4

1

logp(02)

log

p(02) \

at at

1073K 973K 5 5

RESULTS

Figure log a [a in S/m] log a [a in S/m] igure

5-32. 5-33.

AND j 1 ______

CaTiO 1173K

CaTiO, 1223K

EC EC DISCUSSION

Components Components \ ______2 | ______

log

loaptsy Including Including

p(0 i ______2 155

)

a a

[p(0 n n IP(0 , ,

o o 3 | p p ______

and and 2) 2

)

in

a\ o\ in

Plots Plots Pa] i

______Pa]

vs. vs.

4 log log | ______

p(C> p(02) 2 ) |

______at at

1 1223K 173K 5 5 RESULTS AND DISCUSSION

ocr"

CaTiO 1273K

log p(02) [p(02) in Pa]

Figure 5-34. EC Components Including an, op and o. Plots vs. log p(02) at 1273K

'O -1.5

CaTiO 1323K

log p(02) [p(o2) in Pa]

Figure 5-35. EC Components Including an, apand Oj Plots vs. log p(C>2) at 1323K

156 5 RESULTS AND DISCUSSION

CaTiO 973K

0.2

log p(02) [p(02) in Pa]

Figure 5-36. Transfer Number of Electrons, Electron holes, Ions and Total Conductivity Plots vs. p(02) at 973K

CaTiO. 1073K

H 0.2

log p(02) [p(02) in Pa]

Figure 5-37. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(02) at 1073K

157 5 RESULTS AND DISCUSSION

CaTiO. 1173K

£Q 0.6

log p(02) [p(02) in Pa]

Figure 5-38. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(02) at 1173K

CaTiO 1223K

CD 0.6

HI 0.4

log p(02) [p(02) in Pa]

Figure 5-39. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(02) at 1223K

158 5 RESULTS AND DISCUSSION

CaTiO. 1273K

log p(02) [p(02) in Pa]

Figure 5-40. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(C>2) at 1273K

CaTiO 1323K

log p(02) [P(02) in Pa]

Figure 5-41. Transfer Number of Electrons, Electron Holes, Ions and Total Conductivity Plots vs. p(C>2) at 1323K

159 5 RESULTS AND DISCUSSION

CaTiO 1323K -0.5 -

logp(02) [pC>2 in Pa]

Figure 5-42. Comparison of Electrical Conductivity Components between This Study and Eror’s Results at 1323K

CaTiO 1323K

S 0.6

a? 0.4

b 0.3

logp(02) [P02 in Pa]

Figure 5-43. Comparison of Transfer Number between This Study and Eror’s Results at 1323K

160 5 RESULTS AND DISCUSSION

• The value of p(02) CTmin of this study is higher than that of Eror’ s results, indicating that the n-p transition in this study is at higher p(02) than in Eror’s results. This discrepancy may be caused by different type of impurities existed

in different CaTiC>3 samples.

5.6 Model Equation of Electrical Conductivity for CaTiC>3

In order to predict electrical conductivity of CaTiC^, it is necessary to determine the parameters

= +o>(02)4+a-; (5-19)

In section 5.5.1, these electrical conductivity components were determined by fitting calculated results to the experimental data using a parameter estimation program at a certain temperature. It is shown that electrical conductivity components erf,

5.6.1 Determination of Parameter erf,

The Arrhenius plots of the electron component, erf, electron hole component, erf, and ionic component, erf, vs. reciprocal temperature give activation energies of electrical conductivity for different charge carriers (electrons, electron holes and ions) in Eqs. (5- 20 ~ 5-22), shown in Figure 5-44. The activation energy of electrons, electron holes and ions are 134.14, 86.56 and 156.21 kJ/mol, respectively.

161 5 RESULTS AND DISCUSSION

Consequently, the individual unit contribution of electrons, electron holes and ions to conductivity when the oxygen partial pressure is unity may be expressed by Eqs. (5-23 ~ 5-25):

a°n = 16.26x1 OV154140""' (5-23) o-;; = 79.29x1 oV86570""' (5-24)

C-; =28.16x10V156210""' (5-25)

CaTiO

(Ea)n= 134.14 kJ/mol

(Ea)p = 86.56 kJ/mol

A Electron □ Electron hole (Ea)j= 156.21 kJ/mol O Ion

0.7 0.8 0.9 1 1.1 1000/T [T inK]

Figure 5-44. Temperature Dependence of lncr", In

The total electrical conductivity, in terms of temperature and p(02) can be expressed as: crlol = \S.32x\03 e-'34m,RT p(02f* + 27.81*10V86560/*7'p(O2)? + 68.67*10V1562I0/*r

(5-26)

162 5 RESULTS AND DISCUSSION

The electrical conductivity of CaTiCE calculated using Eq. (5-26) in comparison with experimental data at different temperatures and oxygen partial pressures is shown in Figure 5-45. In the whole range of experimental conditions, the electrical conductivity predicted from Eq. (5-26) fits excellently to the experimental data of this study, with the maximum deviation of only 3.6% in the n-p transition range.

CaTiO

Solid line Calculation data Mark Experimental data (this work) 1323K 1273K 1223K 1173K 1073K

973K & -1.5

log p(02) [p(02) in Pa]

Figure 5-45. Comparison of Electrical Conductivity of CaTiCE in Verified Model (solid lines) Experimental Data (marks) at Different Temperatures.

The calculated electrical conductivity by Eq. (5-26) (solid lines) are compared with experimental data (marks) by Dunyushkina and Eror, as showed in Figure 5-46 and Figure 5-47, respectively. It is obvious that, although the electrical conductivity curves well describe the trend of experimental data from Dunyushkina and Eror, the values significantly deviate from the curves. This difference obviously is attributed to the

163 5 RESULTS AND DISCUSSION difference in the materials employed in this study and those by Dunyushkina and Eror in impurity types, impurity contents, density and grainboundary. Therefore, Eq. (5-26) needs to be modified if it is used to describe the electrical conductivity of materials other than employed in this study. Assuming that the slope remains the same, the modification should involve introduction of the parameters ya and yp describing the shifts along logo and log p(C>2) axis, respectively.

CaTiO 1273K o Dunyushkina

Calculation data

log p(02) [p(02) in Pa)

Figure 5-46. Comparison of Calculated Electrical Conductivity with Experimental Data from Dunyushkina [15].

164 5 RESULTS AND DISCUSSION

1323K CaTiO

1073K

o# 0«o 2® -0.5 0®0A 1323K 1273K 1223K 1173K 1073K

•ogp(02) [p(02) in Pa]

Figure 5-47. Comparison of Calculated Electrical Conductivity with Experimental Data from Eror [13].

5.6.2 Verification of Parameter in Equation Describing o vs. p(C>2)

Assuming parameter y is a function of 8 (Eq.5-27) which corresponds to those factors shifting electrical conductivity up or down (Aloga) and left or right (Alog p(02)) in Figure 5-48, but it is independence of p(02), such as acceptor impurities , donor impurities, density, grain boundary and so on. y = f(S) (5-27)

Ya ~ A logo- (5-28)

165 5 RESULTS AND DISCUSSION rp = A\og p(02) (5-29)

CaTiO

Undoped

Donor-doped

Acceptor-doped

Jog p(02) [p(02) in Pa]

Figure 5-48. Schematic of the Change Tendency of Electrical Conductivity of CaTiCh with Acceptor or Donor Doped CaTiCb, ya = A log cr ,yp = A log p(02)

where ya denotes the difference of logo value between experimental data and calculation data; y denotes the difference of log p(02) between experimental data and calculation data.

It is possible to determine parameters ya and y using at least two experimental data.

Assuming:

y = fW (5-30) where x = logp{02) ,y = \oga y-Ay = f(x-Ax) (5-31) where

166 5 RESULTS AND DISCUSSION

Ax = Alog p(02) = yp (5-32)

Ay = A log (J = ya

(5-33)

Assuming there are two sets of experimental data: (xei, yei), (xe2, ye2) According to Equation (5-31):

ye i “Ay = f(xei ~ Ax) (5-34)

ye2 AV = f (Xe2 - Ax) (5-35)

ye2 ~ yel = f(Xe2 ~ Ax) - f(Xel ~ Ax) (5-36)

So, Ax may be solved from Equation (5-36). Then Ay can be determined by Equation (5-37):

Ay = ye\ ~f(xe\ “Ax) (5-37)

Consequently,

y = f(x-Ax) + Ay (5-38)

Then

log

=1(5-40)

The corresponding oxygen partial pressure can be expressed as the following formula:

logp(02)pndic, = log p(02)Malio„ +yp (5-41)

P(Ql)pndicl = !°r' P(02)M,„„, (5-42)

167 5 RESULTS AND DISCUSSION

Finally, Eq. (5-19) modified by parameter ya and yp may be expressed as the following

18.32x1034''" e'134140"'7' (p(02 )x\0r' )’4 formula: predict (5-43) + 27.81x10''" e -86560IRT (p(O2)x\0r'Y +68.67xl03+r3 CT° e-156210/RT

So, Equation (5-43) may be used for predicting the electrical conductivity of CaTi03 in the p(02) range of near the n-p transition regime based on several experimental data for selected sample.

Table 5-19 presented parameter y0 and yp obtained from experiment data of Dunyushkina et al. and Eror et al.

Table 5-19 Parameter ya and yp Obtained from Different Set of Experiment Data

Author Temperature [K] yc (Aloga) yp(Alogp(02))

This work Any temperature 0 0 Dunyushkina et al. 1273 -0.068 +0.5 1073 -3.6 -0.3 1173 -2.9 -0.1 Eror et al. 1223 -2.4 0.05 1273 -2 0.1 1323 -1.6 0.2

Figure 5-49 and Figure 5-50 showed that the electrical conductivities predicted from Equation (5-43) are quite comparable to the experimental data obtained from Eror and Dunyushkina in the regime of near the n-p transition. ya and yp which are a function of temperature can be expressed as the following relationship according to the data obtained from Eror et al:

ya =0.00817-12.34 (5-44) yp =0.0027-2.45 (5-45)

168 5 RESULTS AND DISCUSSION

In conclusion, it is confirmed that the assuming Equation (5-19):

__L \_ cr = cr°p(02) *+<7

Parameters for this equation to predict electrical conductivity of CaTiCb were determined by this work.

CaTiU 3 1273K

o Dunyushkina

Calculation data

Near the n-p transition Regime

log P(0 2) [p(0 2) in Pa)

Figure 5-49. Comparison of Calculated Electrical Conductivity of CaTiCh (modified by parameter yj with Experimental Data from Dunyushkina et al. [15]

169 5 RESULTS AND DISCUSSION

2.5 -r~

CaTiO t Solid line------Calculation data 1.5 - Mark------Experimental data (Eror, 1982)

Near the n-p transition Regime

0.5 - 1323K 1273K 1223K 1173K

-1.5 -

logp(0 2) lp(0 2) in Pa]

Figure 5-50. Comparison of Calculated Electrical Eonductivity of CaTiCE (Modified by Parameter yj with Experimental Data from Eror et al. [13]

170 7 REFERENCES

6 SUMMARY AND CONCLUSIONS

The aim of the project was to understand the charge transport in the selected electronic material CaTiOs. For this aim, the effect of processing conditions (temperature, oxygen activity) on this transport was studied. The charge transport was quantitatively described through the determination of the charge transport related properties, such as electrical conductivity of specific charge carries (electrons, holes, and ions)

This chapter summarises the conclusions of this work, which are as follows:

1. Undoped CaTiCb is a p-type conductor in the p(C>2) range of 101 - 105 Pa and the temperature range of 973 -1373K.

2. The activation energy of the electrical conductivity at constant p(C>2) varies between 125.3 kJ/mol at 10 Pa to 94.4 kJ/mol at 72 kPa.

3. The n-p transition point determined according to the thermopower data for

undoped CaTiC>3 (corresponding to S = 0) significantly deviates from that determined according to the minimum of electrical conductivity amjn, i.e. p(02)s=o > p(02)amin- This discrepancy suggests that the mobility of electrons

is larger than the mobility of electron holes in polycrystalline CaTi03.

4. The activation energies of the electrical conductivity at constant thermopower are 119 kJ/mol and 146 kJ/mol at-500 pVK'1 and 750 pVK'1, respectively.

5. The possibilities of incorporation of different impurities into the lattice structure

of CaTi03 to form substitutional or interstitial solid solutions have been assessed. It is concluded that: • The 3d metal ions Al3+ and Zn2+ are likely to form Ti4+ substitutional solid solution; • K+ and Na+ ions are likely to form Ca2+ substitutional solid solution;

171 REFERENCES

• S6+, P5+ and Si4+ are likely to enter comer voids or volume voids to form interstitial solid solutions.

6. The predominant impurity elements affecting the electrical properties of the

CaTi03 specimen are donor-type impurities.

7. Increasing the p(C>2) from 101 Pa to 1(T Pa results in a decrease in the electrical conductivity component of electrons (an) and an increase in the electrical

conductivity component of electron holes (cjp), while the electrical conductivity

component of ions (<7j) remains constant at constant temperature.

8. The inflection points between the

transition points, shifts to the high-p(C>2) direction with increasing temperature.

The values of p(C>2) corresponding to the inflection points are similar to those of

p(C>2) when the electrical conductivity reaches a minimum, although they are

different from those of p(C>2) when the thermopower equals zero.

9. The electrical conductivity component of ions (Gj) cannot be ignored within the n-p transition range, but it is negligible for highly reduced or highly oxidised specimens. In the n-p transition regime, the transport number of ions is as high as 0.5.

10. The activation energies of different charge carriers, electrons, electron holes, and ions, were determined as 134.14, 86.56, and 156.21 kJ/mol, respectively.

11. Based on the defect models, the electrical conductivity of CaTiCb materials (near the n-p transition regime) can be predicted by the following equation:

aprtdic, = 18.32xl0J+''" e-mmlRT (p(02)x\0'r )*

+ 27.81x10''" e~S6560"!l\p(O2)x\0'r); + 68.67xl03+’'" g-'56210"'7'

172 7 REFERENCES

7 REFERENCES

1 P. Kofstad, “Nonstoichiometry, Diffusion, and Electrical Conductivity in Binary Metal Oxides” (Wiley Series on the Science and Technology of Materials) Wiley- Interscience, Wiley-Interscience, New York, N. Y. 1972 2 F. A. Kroeger and H. J. Vink, “Relations Between Concentrations of Imperfections in Crystalline Solids,” Solid State Physics, 3, 307-435 (1956). 3 J. Nowotny, M. Rekas, “Defect Structure, Electrical Properties, and Transport in Barium Titanate. V. Work Function”, Ceramics International, 20 [4] 251-5 (1994). 4 J. Nowotny, “Interface Electrical Phenomena in Ionic Solids,” pi21-59, in: The CRC Handbook of Solid State Electrochemistry, Edited by P. J. Gellings, J. M. Bouwmeester, CRC Press, Boca Raton, 1997. 5 J. Nowotny, M. Rekas, “Positive Temperature Coefficient of Resistivity for Barium Titanate (BaTi03)-based Materials,” Ceramics International, 17 [4] 227-41 (1991). 6 J. Nowotny, M. Rekas, in: Electronic Ceramic Materials, (Trans Tech Publishing, Zurich, 1992) pi. 7 J. Nowotny and M Rekas, “Defect Chemistry of Barium Titanate,” Solid State Ionics, 49, 135-54 (1991). 8 J. Nowotny, M. Rekas, H-I. Yoo, “Chemical Diffusion in BaTiCE: Effect of Minority Charge Carriers,” p283-96 in: Ceramic Interfaces: Properties and Applications, Edited by R St C Smart, J Nowotny, Institute of Materials, London, 1998. 9 J. Nowotny, M. Radeeka, M. Rekas, S. Sugihara, E. R.Vance, W.Weppner, “Electronic and Ionic Conductivity of TiCE Single Crystal Within the n-p Transition Range,” Ceram. International, 24 [8] 571-7 (1998). 10W. L. George, R. E. Grace, “Formation of Point Defects in Calcium Titanate,” J. Phys. Chem. Sol., 30 [4] 881-7 (1969). 11 U. Balachandran, N. G. Eror, “Electrical Conductivity in Calcium Titanate with Excess Calcium Oxide,” Mater. Sci. Eng. 54 [2] 221-8 (1982) 12 U. Balachandran, B. Odekirk, N. G. Eror, “Defect Structure and Acceptor-doped Calcium Titanate at Elevated Temperatures,” Journal of Materials Science 17 [6] 1656-62 (1982).

173 7 REFERENCES

13 U. Balachandran, B. Ode Kirk, N. G. Eror, “Electrical Conductivity in Calcium

Titanate,” Journal of Solid State Chemistry 41 [2] 185-94 (1982). 14 N. G. Eror and U. Balachandran, “On the Defect Structure of Calcium Titanate with

Nonideal Cationic Ratio,” J. Solid State Chemistry, 43 [2] 196-203 (1982). 15 L. A. Dunyushkina, A. K. Demin, B. V. Zhuravlev, “Electrical Conductivity of Iron-

doped Calcium Titanate,” Solid State Ionics, 116 [1,2] 85-88 (1999). 16 K. R. Udayakumar, A. N. Cormack, “Nonstoichiometry in alkaline earth-excess

alkaline earth titanates,” Journal of Physics and Chemistry of Solids, 50 [1] 55-60 (1989). 17 B. S. Hong, S. J. Ford, T. O. Mason, “Equilibrium Electric Property Measurements

in Electroceramics,” Key Engineering Materials, 125-126, 163-185 (1997). 18 T. Bak, J. Nowotny, C. C. Sorrell, E. r. Vance, “Effect of Gd on electrical

conductivity of CaTi03,” Journal of the Australasian Ceramic Society, 34 [1] 182- 186 (1998) 19 R. C. DeVries, R. Roy and E. F. Osbom, “Phase Equilibria in the System Lime-

Titanium Dioxide,” J. Phys. Chem., 58, 1069-73 (1954). 20 R. S. Roth, “Revision of the Phase Equilibrium Diagram of the Binary System Calcia-titania, Showing the Compound Ca^^Oio”, J. Research Natl. Bur.

Standards, 61 [5] 437-40 (1958). 21 A. Jongejan and A. L. Wilkins, “Reexamination of the system calcium oxide-

titanium dioxide at liquidus temperatures,” J. Less-Common Metals, 20 [4] 273-9 (1970). 22 S. Kimura and A. Muan, Contribution No. 69-36 from the College of Earth and

Mineral Sciences, Pennsylvania State University, University Park, PA, 1970. 23 T. F. Limar, N. G. Kisel, I. F. Cherednichenko and A. I. Savos’kina, “Calcium

Tetratitanate, ” Russ. J. Inorg. Chem. (Engl. Transl.), 17, 292 (1972). 24 V.G. Savenko and V. V. Sakharov, “Formation of Calcium Titanate (CaiTisO^) in the Thermolysis of Mixed Titanium and Calcium Hydroxides,” Zhurnal

Neorganicheskoi Khimii, 24 [5] 1389-91 (1979). 25 H. E. Tulgar, “Solid State Relationships in the System Calcium Oxide-titanium

Dioxide,” Istanbul Teknik Universitesi Bulteni, 29 [1] 111-29 (1976).

174 7 REFERENCES

26 L. Kaufman, “Calculation of phase diagrams for commercial materials,” Journal of Phase Equilibria, 14 [4] 413-17 (1993). 27 O. Kubaschewski and C. B. Alcock; International Series on Materials Science and Technology, Vol.24 (Metallurgical Thermochemistry); 5th ed.; pp. 1-449. Pergamon Press, Oxford, United Kingdom, 1979. 28 R. M. Hazen, “Life’s Rocky Start,” Scientific American, 284 [4] 76-85 (2001). 29 I. Naray-szabo, “The Structural Type of Perovskite (CaTiOs),” Naturwissenschaften 31,202-3 (1943). 30 H. D. Megaw, “Crystal structure of barium titanium oxide at different temperatures,” Experientia, 2, 183-4 (1946). 31 H. F. Kay, and P. C. Bailey, “Structure and Properties of CaTiOs” Acta Crystallographica, 10, 219-26 (1957). 32 R. H. Buttner, E. N. Maslen and N. Spadaconi, “Structure, Electron Density and Thermal Motion of Potassium Trifluorocuprate(II),” Acta Crystallographica, B46 [2] 131-38 (1990). 33 H. J. A. Koopmans, G. M. H. Van Der Velde and P. J. Gellings, “Powder Neutron Diffraction Study of the Perovskites Calcium Titanate(IV) and Calcium Zirconate(IV),” Acta Crystallographica, C69 [10] 1323-5 (1983) 34 S. Sasaki, C. T. Prewitt, J. D. Bass and W. A. Schulze, “Orthorhombic Perovskite

CaTiO 3 and CdTi03: Structure and Space Group,” Acta Crystallographica, Sect. C 43, 1668-74(1987). 35 P. M. Woodward, “Octahedral Tilting in Perovskites. II. Structure Stabilizing Forces” Acta Cryst. B53, 44-66 (1997). 36 V. M. Goldschmidt, “Laws of Crystal Chemistry,” Naturwissenschaften, 14, 477-85 (1926). 37 R. J. D. Tilley, “An Electron Microscope Study of Perovskite-related Oxides in the Strontium-Titanium-Oxygen System,” Journal of Solid State Chemistry, 21 [4] 293- 301 (1977). 38 K. R. Udayakumar and A. N. Cormack, “Nonstoichiometry in Alkaline Earth-Excess Alkaline Earth Titanates,” Journal of Physics and Chemistry of Solids, 50 [1] 55-60 (1989).

175 7 REFERENCES

39 R. C. Devries, R. Roy and E. F. Osborn, “Phase Equilibria in the System Lime- titanium Dioxide,” Journal of Physical Chemistry, 58, 1069-73 (1954). 40 L. W. Coughanour, R.S.Roth, V. A. De Prosse, “Phase Equilibrium Relations in the Systems Lime-titania and Zirconia-titania,” J. Research Natl. Bur. Standards, 52, 37-42 (1954).

41 M. Ceh and D. Kolar, “Solubility of CaO in CaTi03,” Journal of Materials Science, 29 [23] 6295-300 (1994) 42 J. Nowotny and M. Rekas, in “Electronic Ceramic Materials”, (Trans Tech Publishing, Zurich, 1992) pp45-144 43 A. N. Golubenko and T. N. Rezukhina, “Thermodynamic Properties of Calcium Titanates Determined from Electrochemical Measurements at High Temperatures,” Zhurnal Fizicheskoi Khimii, 38 [12] 2920-3 (1964).

44 T. Yamanaka, N. Hirai and Y. Komatsu, “Structure Change of Cai.xSrxTi03 Perovskite with Composition and Pressure,” American Mineralogist, 87 [8-9] 1183- 89 (2002).

45 K. Parlinski, Y. Kawazoe and Y. Waseda, “Ab Initio Studies of Phonons in CaTi03,” Journal of Chemical Physics, 114 [5] 2395-2400 (2001).

46 E. Cockayne, “Comparative Dielectric Response in CaTiC>3 and CaAli/2Nbi/203 from First Principles,” Journal of Applied Physics, 90 [3] 1459-68 (2001). 47 T. Sato, Y. Hanajiri, T. Yamashita, T. Matsui, T. Nagasaki, “Thermal Expansion of

(Cai.xPux)Ti03”, Journal of Nuclear Materials, 294 [1,2] 130-4 (2001). 48 A I Becerro, F Seifert, R J Angel, S Rios and C McCammon, “ Displacive Phase

Transitions and Spontaneous Strains in Oxygen Deficient CaFexTii.x03-x/2 Perovskites (0

49 F. Erazo, A. Stashans, “Quantum-chemical Studies of Nb-doped CaTi03”, Philosophical Magazine B: Physics of Condensed Matter: Statistical Mechanics, Electronic, Optical and Magnetic Properties, 80 [8] 1499-1506(2000). 50 B. J. Kennedy, C. J. Howard and B. C. Chakoumakos, “Phase Transitions in Perovskite at Elevated Temperatures—a Powder Neutron Diffraction Study,” Journal of Physics: Condensed Matter, 11 [6] 1479-88 (1999). 51 S. Oishi, M. Shibui, “Growth of Perovskite Crystals from Potassium Fluoride Flux,” Nippon Kagaku Kaishi, [6] 412-6 (1998).

176 7 REFERENCES

52 A. R. Chakhmouradian and R. H. Mitchell, “A Structural Study of the Perovskite Series CaTii.^FejNbXV’, Journal of Solid State Chemistry, 138 [2] 272-277 (1998).

53 A. V. Arakcheeva, D. Yu. Pushcharovskii, V. M. Gekimyants, V. A. Popov, G. U. Lubman, “Crystal Structure and Microtwinning of Natural Orthorhombic Perovskite CaTi03,” Crystallography Reports, 42 [1] 46-54 (1997).

54 Y. Hanajiri, H. Yokoi, T. Matsui, Y. Arita, T. Nagasaki and H. Shigematsu, “Phase Equilibria of CaTi03 Doped with Ce, Nd and U”, Journal of Nuclear Materials, 247, 285-8 (1997).

55 R. F. Garrett, D. J. Cookson, G. J. Foran, T. M. Sabine, B. J. Kennedy and S. W. Wilkins, “Powder Diffraction Using Imaging Plates at the Australian National Beamline Facility at the Photon Factory,” Review of Scientific Instruments, 66 [2, Pt. 2] 1351-3 (1995).

56 X. Liu and R. C. Liebermann. Physics and Chemistry of Minerals 20, 171 (1993).

57 R. FI. Buttner and E. N. Maslen, “Electron Difference Density and Structural Parameters in CaTi03”, Acta Crystallogr. Sect. B 48, 644-49 (1992). 58 E. M. Larson, P. G. Eller, J. D. Purson, C. F. Pace, M. P. Eastman, R. B. Greegor, F. W.Lytle, “Synthesis and Structural Characterization of Calcium Titanate Doped with 0.05-7.5 mole% Gadolinium(III),” Journal of Solid State Chemistry, 73 [2] 480-7 (1988). 59 H. J. A. Koopmans, G.M.H. Van De Velde, and P.J. Gellings, “Powder Neutron Diffraction Study of the Perovskites Calcium Titanate(IV) and Calcium Zirconate(IV),” Acta Crystallographica, C39 [10] 1323-5 (1983). 60 H. E. Swanson, H. F. McMurdie, M. C Morris, E. H. Evans, and B. Paretzkin, NBS Monogr. U.S. 25, Section 9 (1971). 61 R.W.G. WYCKOFF, Crystal Structures (New York: Interscience), 1960. 62 B r H. F. KAY AND P. C. BAILEY, “Structure and Properties of CaTi03 ” Acta Crystallogr aphica, 10, 219-26 (1957). 63 S. H. Shin, D. Y. Jeon, C. W. Park, and D. S. Zang, “Correlation of Cathodoluminescence of AB03:Pr3+ Phosphor with its Crystal Structure,” Japanese

177 7 REFERENCES

Journal of Applied Physics, Part 1: Regular Papers, Short Notes & Review Papers, 42 [6A] 3508-9 (2003). 64 T. Yamanaka, N. Hirai, and Y. Komatsu, “Structure Change of Cai.xSrxTi03 Perovskite with Composition and Pressure,” American Mineralogist, 87 [8-9] 1183- 89 (2002). 65 F. Erazo, and A. Stashans, “Structural and Electronic Properties of La-doped CaTi03 Crystal,” International Journal of Quantum Chemistry, 87 [4] 225-31(2002). 66 T. Sato, Y. Hanajiri, T. Yamashita, T. Matsui, T. Nagasaki, “Thermal Expansion of (Cai_xPux)Ti03”, Journal of Nuclear Materials 294 [1,2] 130-34 (2001). 67 A. I. Becerro, S. A. T. Redfem, M. A. Carpenter, K. S. Knight, F.Seifert, “Displacive Phase Transitions in and Strain Analysis of Fe-Doped CaTiCE Perovskites at High Temperatures by Neutron Diffraction”, Journal of Solid State Chemistry, 167 [2] 459-71 (2002). 68 A. I. Becerro, F. Seifert, R. J. Angel, S. Rios and C. McCammon, “ Displacive Phase Transitions and Spontaneous Strains in Oxygen Deficient CaFexTii.x03-x/2 Perovskites (0

71 E. R. Vance, R. A. Day, Z. Zhang, B. D. Begg, C. J. Ball, and M. G. Blackford, “Charge Compensation in Gd-Doped CaTi03,” Journal of Solid of State Chemistry, 124, 77-82 (1996). 72 M. Yoshida, N. Hara, T.Takada and A. Seki, "Structure and Properties of (Cai.xNd2x/3)Ti03," Japanese Journal of Applied Physics, 36, 6818-23 (1997) 73 S. A. T. Redfern, “High-temperature Structural Phase Transitions in Perovskite (CaTi03)”, Journal of Physics: Condensed Matter, 8, 8267-75 (1996).

178 7 REFERENCES

74 A. D. Hilton and R. Frost, “Recent Developments in the Manufacture of Barium Titanate Powders,” pi45-8 in “Electronic Ceramic Materials,” edited by J. Nowotny, Trans Tech Publications Ltd., 1992. 75 S. Peacock, “Producing P2O5 and CaTiOs,” US 995897 19110620 (1911). 76 E. Urbain, “Calcium Titanate and Ferro-phosphorus” FR 684889 19290213 (1929). 77 Y. Tanaka, “Reactions between Solid Oxides at Higher Temperatures. II. The Reaction between Calcium Oxide and Titanium Oxide and the Photosensitivity of

Calcium Titanate,” Bulletin of the Chemical Society of Japan, 16, 455-62 (1941). 78 L. Merker, “Calcium Titanate,” US 2751279 19560619 (1956). 79 L. E. Lynd, L. Merker, “Pure Calcium Titanates,” DE 1014972 19570905 (1957). 80 I. B. S. Brcic, S. Milicev, J. Siftar, “Synthesis of the Calcium Metatitanate at Low Temperature,” Croatica Chemica Acta, 33, 169-79 (1961). 81 T. F. Limar, F. N. Cherednichenko, M. A. Sokolova, “Synthesis of Calcium Metatitanate by the Spray Drying to Solutions, and its Properties,” Ukrainskii

Khimicheskii Zhurnal (Russian Edition), 38 [7] 665-8 (1972). 82 T. P. Maidukova, L. S. Voloshina, L. Y. Seraya, “Aging During the Preparation of

Calcium Titanate by Coprecipitation,” Neorganicheskie Materialy, 10 [2] 375-6 (1974). 83 T. P. Limar, A. V. Naumov, V. F. Getmanets, A. M. Gareev, P. I. Bochko, “Calcium Titanate,” SU 435193 19740705 (1974). 84 R. M. Barabanshchikova, T. F. Limar, M. V. Mokhosoev, “Synthesis of Calcium

Titanates from Alcoholates,” Neorganicheskie Materialy, 10 [9] 1665-8 (1974). 85 T. P. Maidukova, L. S. Voloshina, “Calcium Titanate,” SU 468890 19750430 Application: SU 71-1723843 19711208 (1975). 86 A. A. Dvemyakova, G. N. Novitskaya, M. V. Verkhovskaya, “Reaction of Calcium

Carbonate with Hydrated Titanium Dioxide,” Neorganicheskie Materialy, 21 [3] 442-5 (1985). 87 Z. Z. Yang, H. Yamada, G. R. Miller, “Synthesis and Characterization of High-purity

Calcium Titanate (CaTiOs),” American Ceramic Society Bulletin, 64 [12] 1550-4 (1985). 88 T. R. N. Kutty R., Vivekanandan, “Preparation of Calcium Titanate (CaTiOs) Fine

Powders by the Hydrothermal Method,” Materials Letters, 5 [3] 79-83 (1987).

179 7 REFERENCES

89 N. J. Ali, J. Bultitude, L. A. Xue, S. J. Milne, “Preparation of Stoichiometric M'Ti03 Powders (M' = barium, strontium, calcium) from Catecholate Complexes,” Materials

Research Society Symposium Proceedings, 121 (Better Ceram. Chem. 3), 269-74 (1988). 90 T. R. N. Kutty and R. Vivekanandan, “Precipitation of Rutile and Anatase (TiC^) Fine Powders and their Conversion to MTiC>3 (M = Ba, Sr, Ca) by the Hydrothermal

Method,” Materials Chemistry and Physics, 19, 533-46 (1988). 91 G. Pfaff, “Wet-chemical Synthesis of Strontium Titanate (SrTiC^) and Calcium Titanate (CaTi03) Sintered Powders from Precipitation of SrTi02(02).3H20 and CaTi02(02).3H20,” Zeitschrift fuer Chemie, 29 [1] 30-1 (1989). 92 G. Pfaff, “Preparation and Characterization of Titanate Powders of Different

S interability,” Jo urnal of Materials Science, 27 [5] 1222-6 (1992). 93 N. V. Kosova, E. G. Avvakumov, “Mechanochemical Synthesis of Calcium Titanate

from Hydrated Forms of Oxides,” Sibirskii Khimicheskii Zhurnal, (3), 121-7 (1992). 94 C. D. Chandler, M. J. Hampden-Smith, “Formation of Crystalline, Integral, and Nonintegral Stoichiometry Perovskite-phase Complex Metal Oxide Powders from Metal-organic Precursors,” Chemistry of Materials, 4 [6] 1137-9 (1992). 95 G. Pfaff, “Synthesis of Calcium Titanate Powders by the Sol-gel Process,” Chemistry of Materials, 6 [1] 58-62 (1994). 96 E. G. Avvakumov, E. T.Devyatkina and N. V Kosova, “Mechnochmical Reactions of

Hydrated Oxides,” Journal of Solid State Chemistry, 113, 379-83 (1994). 97 L. E. Kademina, A. N. Toropov, B. I. Zhelnin, O. V. Mel'nikova, “Study of the Interaction of Phases in Samples of the System Ca0-Ti02-H20, Produced by the

Sol-gel Method in Strongly Alkaline Media,” Zhurnal Neorganicheskoi Khimii, 40 [2] 297-99 (1995). 98 Z. Peng, G. Wang, W. Zhang, L. Zhang, “Nanometer-size CaTi03 Powder Prepared

by the Chemical Coprecipitation Method,” Gongneng Cailiao, 27 [5] 429-30 (1996). 99 G. Mi, F. Saito, S. Suzuki, Y. Waseda, “Formation of CaTi03 by Grinding from Mixtures of CaO or Ca(OH)2 with Anatase or Rutile at Room Temperature,”

Powder Technology, 97 [2] 178-82 (1998).

180 7 REFERENCES

100 O. Abe, “Mechano-synthesis of Alkaline-earth Titanate Powders,” World Congress on Particle Technology 3, Brighton, UK, July 6-9, 1998, 3905-14 (1998). Publisher: Institution of Chemical Engineers, Rugby, UK 101 Q. Wu, S. Zhang, “Study on Nano-crystalline CaTi03 Synthesized by Mechanochemistry,” Guisuanyan Xuebao, 29 [5] 479-83 (2001). 102 S. J. Lee, C. H. Lee, “Fabrication of Nano-sized Titanate Powder via a Polymeric Steric Entrapment Route and Planetary Milling Process,” Journal of the Korean Ceramic Society, 39 [4] 336-40 (2002). 103 Z. Peng, Y. Chen, “Preparation of BaTi03 Nanoparticles in Aqueous Solutions,” Microelectronic Engineering, 66 [1-4] 102-6 (2003). 104 I. R. Evans, J. A. K, Howard, T. Sreckovic, M. M. Ristic, “Variable Temperature in Situ X-ray Diffraction Study of Mechanically Activated Synthesis of Calcium Titanate, CaTi03,” Materials Research Bulletin, 38 [7] 1203-1213 (2003). 105 P. S. Mamykin, B. A. Loshkarev, “Titanates of Calcium and the Kinetics of their Formation,” Ogneupory, 15,215-21 (1950). 106 T. F. Limar, I. F. Cherednichenko, A. N. Sverdlova, Yu. N. Velichko, R. M. Barabanshchikova, “Properties of Calcium Titanate,” Neorganicheskie Materialy, 6 [10] 1829-34(1970). 107 I. B. S. Brcic, S. Milicev, J. Siftar, “Synthesis of the Calcium Metatitanate at Low Temperature,” Croatica Chemica Acta, 33, 169-79 (1961). 108 A. V. P. Rao, M. Suresh, “The pH Dependence of Formation of Stoichiometric Precursors for Calcium, Cadmium and Lead Titanates - a Thermal Study”, Ferroelectric,s 229 [1-4] 141-146(1999).

109 Z. Puff, K. Kufel, “Investigations of Preparation of Divalent Metal TitanateS in a Form of Ceramic Powders with High Degree of Purity and Dispersion,” Materialy Elektroniczne, 20 [4] 73-91(1992). 110 M. P. Pechini, US 3330697, 1967. 111 A. G. Andersen, T. Hayakawa, T. Tsunoda, H. Orita, M. Shimizu, K. Takehira, “Preparation and Characterization of Calcium Titanate (CaTi03)-based Perovskitic Oxides as Catalysts for Partial Oxidation of Light Hydrocarbons”, Catalysis Letters, 18 [1-2] 37-48 (1993).

181 7 REFERENCES

112 G. Pfaff, “Wet-chemical Synthesis of Strontium Titanate (SrTiOs) and Calcium Titanate (CaTiCb) Sintered Powders from Precipitation of SrTi02(02).3H20 and CaTi02(02).3H20,” Zeitschrift fuer Chemie, 29 [1] 30-1 (1989). 113 G. Pfaff, “Peroxide Route to Synthesize Calcium Titanate Powders of Different Composition,” Journal of the European Ceramic Society, 9 [4] 293-9 (1992). 114 Z. Peng, G. Wang, W. Zhang, L. Zhang, “Nanometer-size CaTi03 Powder Prepared by the Chemical Coprecipitation Method,” Gongneng Cailiao, 27 [5] 429-30 (1996). 115 Z. Peng, Y. Chen, “Preparation of BaTiOs Nanoparticles in Aqueous Solutions,” Microelectronic Engineering, 66 [1-4] 102-6 (2003). 116L. E. Kademina, A. N. Toropov, B. I. Zhelnin, O. V. Mel'nikova, “Study of the Interaction of Phases in Samples of the System Ca0-Ti02-H20, Produced by the Sol-gel Method in Strongly Alkaline Media,” Zhurnal Neorganicheskoi Khimii, 40 [2] 297-99(1995). 117 G. Pfaff, “Synthesis of Calcium Titanate Powders by the Sol-gel Process,” Chemistry of Materials, 6 [1] 58-62 (1994). 118 A. G. Andersen, T. Hayakawa, T. Tsunoda, H. Orita, M. Shimizu, K. Takehira, “Preparation and Characterization of Calcium Titanate (CaTi03)-based Perovskitic Oxides as Catalysts for Partial Oxidation of Light Hydrocarbons,” Catalysis Letters, 18 [1-2] 37-48 (1993). 119 S. J. Lee, C. H. Lee, “Fabrication of Nano-sized Titanate Powder via a Polymeric Steric Entrapment Route and Planetary Milling Process,” Journal of the Korean Ceramic Society, 39 [4] 336-40 (2002). 120 S. M. Kim, J. I. Goo, T. O. Kim, “The Synthesis and Properties of Red Phosphor CaTi03: Pr3+ by Sol-gel Method,” Yoop Hakhoechi, 36 [11] 1274-1279 (1999). 121 I. B. S. Brcic, S. Milicev, J. Siftar, “Synthesis of the Calcium Metatitanate at Low Temperature,” Croatica Chemica Acta, 33, 169-79 (1961). 122 D. Hennings, G. Rosenstien, H. Schreinemacher, “Hydrothermal Preparation of Barium Titanate from Barium-titanium Acetate Gel Precursors,” Journal of the European Ceramic Society, 8 [2] 107-15 (1991). 123 A. N. Christensen, S. E. Rasmussen, “Hydrothermal Preparation of Compounds of

the Type ABO3 and P&iOaG Acta Chemica Scandinavica, 17 [3] 845 (1963).

182 7 REFERENCES

124 T. R. N. Kutty R., Vivekanandan, “Preparation of Calcium Titanate (CaTi03) Fine

Powders by the Hydrothermal Method,” Materials Letters, 5 [3] 79-83 (1987). 125 C. J. Brinker; D. E. Clark; D. R. Ulrich; “Better Ceramics Through Chemistry II, III and IV,” Materials Research Society: Pittsburgh, 1984, 1986, 1988. 126 M.N Rahaman, “Ceramic Processing and Sintering”, p41, Marcel Dekker, Inc. New York, 1995. 127 H. F. Naylor and O. A. Cook, “High-temperature Heat Contents of the Metatitanates of Calcium, Iron, and Magnesium,” Journal of the American

Chemical Society, 68, 1003-5 (1946). 128 T. Vogt and W. W. Schmahl, “The High-temperature Phase Transition in

Perovskite,” Europhysics Letters, 24 [4] 281-5 (1993). 129 X. Liu, Y. Wang, R. C. Liebermann, P. D. Maniar, and A. Navrotsky, “Phase Transition in CaGe03 Perovskite: Evidence from X-ray Powder Diffraction,

Thermal Expansion, and Heat Capacity,” Physics and Chemistry of Minerals, 18 [4] 224-30 (1991).

130 Y. Wang and R. C. Liebermann, Physics and Chemistry of Minerals, 20, 147 (1993). 131 F. Guyot, P. Richet, Ph. Courtial, and P. Gillet, “High-temperature Heat Capacity and Phase Transitions of Calcium Titanate Perovskite,” Physics and Chemistry of

Minerals, 20 [3] 141-6 (1993). 132 T. Matsui, H. Shigematsu, Y. Arita, Y. Hanajiri, N. Nakamitsu, and T. Nagasaki, “High temperature phase transitions of CaTi03 and (Cao.85Ndo.i5)Ti03 by X-ray diffractometry and differential thermal analysis,” Journal of Nuclear Materials,

247, 72-5 (1997). 133 C. J. Ball, G. J. Thorogood and E. R. Vance. “Thermal Expansion Coefficients of Zirconolite (CaZrTLCL) and Perovskite (CaTi03) from X-ray Powder Diffraction

Analysis,” Journal of Nuclear Materials, 190, 298-301 (1992). 134 R. G. Grebenshchikov, V. F. Popova, A. K. Shirvinskaya, “Phase Diagrams of the LnA103-CaTi03 (Ln = Nd, Sm) Systems and Polymorphism of CaTi03”, Glass

Physics and Chemistry (Translation of Fizika i Khimiya Stekla) 29 [2] 194-9 (2003).

183 7 REFERENCES

135 A. I. Becerro, F. Seifert, R. J. Angel, S. Rios and C. McCammon, “ Displacive

Phase Transitions and Spontaneous Strains in Oxygen Deficient CaFexTii.x03.x/2

Perovskites (0

136 T. Yamanaka, N. Hirai, and Y. Komatsu, “Structure Change of Cai_xSrxTi03

Perovskite with Composition and Pressure,” American Mineralogist, 87 [8-9] 1183- 89 (2002).

137 D. A. Chang, T. Y. Tseng, “Humidity-sensitivity Characteristics of CaTi03 Porous

Ceramics,” Journal of Materials Science Letters, 9, 943-44 (1990). 138 L. E. Lynd, L. Merker, “Pure Calcium Titanates,” DE 1014972 19570905 (1957). 139 T. P. Maidukova, L. S. Voloshina, “Calcium titanate,” SU 468890 19750430 Application: SU 71-1723843 19711208 (1975).

140 Z. Peng, Y. Chen, “Preparation of BaTi03 Nanoparticles in Aqueous Solutions,”

Microelectronic Engineering, 66 [1-4] 102-6 (2003).

141 T. R. N. Kutty R., Vivekanandan, “Preparation of Calcium Titanate (CaTi03) Fine

Powders by the Hydrothermal Method,” Materials Letters, 5 [3] 79-83 (1987). 142 T. R. N. Kutty and R. Vivekanandan, “Precipitation of Rutile and Anatase (Ti02)

Fine Powders and Their Conversion to MTiC>3 (M=Ba, Sr, Ca) by the Hydrothermal

Method,” Materials Chemistry and Physics, 19, 533-46 (1988). 143 C. D. Chandler, M. J. Hampden-Smith, “Formation of Crystalline, Integral, and Nonintegral Stoichiometry Perovskite-phase Complex Metal Oxide Powders from

Metal-organic Precursors,” Chemistry of Materials, 4 [6] 1137-9 (1992). 144 A. G. Andersen, T. Hayakawa, T. Tsunoda, H. Orita, M. Shimizu, K. Takehira,

“Preparation and Characterization of Calcium Titanate (CaTi03)-based Perovskitic Oxides as Catalysts for Partial Oxidation of Light Hydrocarbons,” Catalysis Letters,

18 [1-2] 37-48 (1993). 145 O. Abe, “Mechano-Synthesis of Alkaline-Earth Titanate Powders,” World Congress

on Particle Technology 3, Brighton, UK, July 6-9, 3905-3914 (1998), Institution of Chemical Engineers, Rugby, UK.

146 G. Mi, Y. Murakami, D. Shindo, F. Saito, “Microstructural Investigation of CaTi03 Formed Mechanochemically by Dry Grinding of a CaO-Ti02 Mixture,” Powder

Technology, 104 [1] 75-79 (1999).

184 7 REFERENCES

147 G. Mi, Y. Murakami, D. Shindo, F. Saito, “Mechanochemical Synthesis of CaTi03

from a Ca0-Ti02 Mixture and its HR-TEM Observation,” Powder Technology, 105 [1-3] 162-6 (1999). 148 Q. Wu, S. Zhang, “Study on Nano-crystalline CaTi03 Synthesized by

Mechanochemistry,” Guisuanyan Xuebao, 29 [5] 479-83 (2001). 149 S. J. Lee, C. H. Lee, “Fabrication of Nano-sized Titanate Powder via a Polymeric Steric Entrapment Route and Planetary Milling Process,” Journal of the Korean

Ceramic Society, 39 [4] 336-40 (2002). 150 P. T. Diallo, K. Jeanlouis, P. Boutinaud , R. Mahiou, J. C. Cousseins,“Improvement of the Optical Performances of Pr in CaTi03,” Journal of Alloys and Compounds,

323-324 218-22 (2001). 151 E. V. Degtyareva, L. I. Verba, N. V. Gul'ko, “Kinetics of Calcium Titanate

Synthesis,” Neorganicheskie Materialy, 13 [10] 1913-15 (1977). 152 E. V. Degtyareva, L. I. Verba, “Effect of Raw Material Activity and Roasting Conditions on the Sintering and Growth of Calcium Titanate Grains,” Ogneupory,

19 [1] 39-44 (1978). 153 L. I. Verba, E. V. Degtyareva, N. M. Kvasman, “Sintering of Perovskite (CaTi03) in the Synthesis Process,” Izvestiya Akademii Nauk SSSR, Neorganicheskie

Materialy, 11 [9] 1622-5 (1975). 154 D. A. Chang, T. Y. Tseng, “Humidity-sensitivity Characteristics of CaTi03 Porous

Ceramics,” Journal of Materials Science Letters, 9, 943-44 (1990). 155 T. R. N. Kutty and R. Vivekanandan, “Precipitation of Rutile and Anatase (Ti02) Fine Powders and their Conversion to MTi03 (M=Ba, Sr, Ca) by the Hydrothermal

Method,” Materials Chemistry and Physics, 19, 533-46 (1988). 156 G. Pfaff, “Synthesis of Calcium Titanate Powders by the Sol-gel Process,”

Chemistry of Materials, 6 [1] 58-62 (1994). 157 H. Pickup, “The Densification and Microstructure of Calcium Titanate,” Diffusion

and Defect Data—Solid State Data, Pt. B: Solid State Phenomena, 25-26 (Sintering ’91), 251-8 (1992). 158 0. Johannesen, “Enhanced Ionic Conductivity in Inorganic Solids,” in Selected Topics in High Temperature Chemistry, Defect Chemistry of Solids, pp 169, Edited

185 7 REFERENCES

by O. Johannesen and A. G. Andersen, Elsevier, Amsterdam-Oxford-New York- Tokyo, 1989. 159 J. Nowotny, “Science of Ceramic Interfaces” in Materials Science Monographs, 75, ppl07, Elsevier Amsterdam-London-New York-Tokyo 1991. 160 E. Chinarro, J. R. Jurado, F. M. Figueiredo, J. R. Frade, “Bulk and Grain Boundary

Conductivity of Cao.97Tii-xFex03-8 Materials,” Solid State Ionics, 160 [1,2] 161-168 (2003). 161 F. A. Kroeger and H. J. Vink, in “Solid State Physics” Edited by F. Seitz and D. Turnbull (Academic Press, New York, 1956) p307 162 W. L. George, R. E. Grace and E. Richard, “Formation of Point Defects in Calcium Titanate,” Journal of Physics and Chemistry of Solids, 30 [4] 881-7 (1969). 163 L. A. Dunyushkina, A. K. Demin and B. O. Zhuravlev, “Electrical conductivity of iron-doped calcium titanate,” Solid State Ionics, 116 (1, 2) 85-88 (1999). 164 K. Ueda, H. Yanagi, H. Hosono and H. Kawazoe, “Carrier Generation and Compensation in Y- and Nb-doped CaTiCh Single Crystals,” Physical Review B: Condensed Matter, 56 [20] 12998-13005 (1997). 165 K. R. Udayamakumar and A. N. Cormack, “Nonstoichiometry in Alkaline Earth- excess Alkaline Earth Titanates,” Journal of Physics and Chemistry of Solids, 50 [1] 55-60 (1989). 166 I. Barin, Thermodynamical Data of Pur Substances, 2nd Edition, (VCH, Weinheim, Germany) (1993), 1834 pp. 167 E. R. Vance, R. A. Day, Z. Zhang, B. D. Begg, C. J. Ball and M. G. Blackford,

“Charge Compensation in Gd-Doped CaTiC>3,” Journal of Solid State Chemistry, 124 [1] 77-82(1996). 168 E. R. Vance, T. Bak, J. Nowotny, N. B. Manson and S. E. French, J. H. Hadley, F. H. Tsu, Y. Huand and V. Bellitto, in “Ceramic Interfaces” (IOM, London, 1998) p229 169 U. Balachandran , N. G. Eror, “Oxygen Nonstoichiometry of Tantalum-doped Calcium Titanate,” Physica Status Solidi A: Applied Research, 71 [1] 179-84 (1982). 170 G.Mandel, “Self-compensation limited conductivity in binary semiconductors. I. Theory,” Physical Review, 134 [4A] 1073-9 (1964).

186 7 REFERENCES

171 U. Balachandran , N. G. Eror, “Self-compensation in Lanthanum-doped Calcium

Titanate,” Journal of Materials Science, 17 [6] 1795-800 (1982). 172 T. Bak, J. Nowotny, M. Rekas, C. C. Sorrell, E. R. Vance, “Effect of Gd on Electrical Conductivity of CaTi03,” Journal of the Australasian Ceramic Society, 34 [1],182-6 (1998). 173 K. Ueda, H. Yanagi, H. Hosono, and H. Kawazoe, “Carrier Generation and

Compensation in Y- and Nb-doped CaTiOs Single Crystals,” Physical Review B, 56 [20] 12998-13005(1997). 174 H. Iwahara, T. Esaka, T. Mangahara, “Mixed Conduction and oxygen permeation in

the substituted oxides for CaTiCE” J. Applied Electrochemistry, 18, 173-7 (1988) 175 S. Xie, W. Liu, K. Wu, P. H. Yang, G. Y. Meng, C. S. Chen, “Oxygen Permeation and Electric Conductivity Study in CaFeo.2Tio.803_5” Proceedings of the China International Conference on High-Performance Ceramics, 1st, Beijing, China, Oct. 31-Nov. 3, 1998 (1999), Meeting Date 1998, 519-522

176 A. G. Tochenaya, “Dielectric and Electric Properties of Calcium Metatitanate

(CaTi03) with a Chromium(3+) Ion Impurity,” Elektron. Mashinostr., 21, 75-9 (1972). 177 N. Cusack, P. Kendall, M. Fielder, “Electron transport properties in a liquid alloy,”

Philosophical Magazine (1798-1977), 10 [107] 871-82 (1964). 178 J. Nowotny, M. Rekas, “Defect Structure, Electrical Properties and Transport in Barium Titanate. VII. Chemical Diffusion in Nb-doped BaTi03,” Ceramics

International, 20 [4] 265-75 (1994). 179 M. F. Zhou, T. Bak, J. Nowotny, M. Rekas, C. C. Sorrell, E. R. Vance, “Defect Chemistry and Semiconducting Properties of Calcium Titanate,” Journal of

Materials Science: Materials in Electronics, 13 [12] 697-704 (2002). 180 H. C. Chen, E. Garstein, T. O. Mason, “Conduction Mechanism Analysis for Iron Oxide (Fej-gO) and Cobalt Oxide (Coi-gO),” Journal of Physics and Chemistry of

Solids, 43 [10] 991-5 (1982). 181 J. Nowotny, M. Radecka, M. Rekas, “Semiconducting Properties of Ti02.”

International Ceramic Monographs, (1994), 1 (1, Proceedings of the International Ceramics Conference, 1994), 474-9.

187 7 REFERENCES

182 T. Bak, T. Burg, S.-J. L. Kang, J. Nowotny, M. Rekas, L. Sheppard, C. C. Sorrell, E. R. Vance, Y. Yoshida, M. Yamawaki, “Charge Transport in Polycrystalline Titanium Dioxide,” Journal of Physics and Chemistry of Solids, 64 [7] 1089-95 (2003).

183 W. Hume-Rothery, Atomic Theory for Students of Metallurgy, The Institute of Metals, London, 1969 (Fifth Reprint).

184 W. Hume-Rothery, R. W. Smallman and C. W. Haworth, The Structure of Metals and Alloys, The Institute of Metals, London, 1969.

185 Mcmurdie, Howard F. J. Research Natl. Bur. Standards (1941), 27(Research Paper No.1437), 499-505. PDF card No.02-0907 Calcium Titanium Oxide

188 APPENDIX A

Appendix A:

Calculation of The Radius Ratio for Cation Ions Ca2+ and Ti4+

1. The Structure of Perovskite CaTiC>3

A Cell

B Cell

O Ca • Ti O O

Figure A-l Schematic Structure of Perovskite CaTi03

189 APPENDIX A

2. Calculation of The Radius Ratio of Rca2+/Ro2-

Assuming: R02- = 0.126 nm

2.1 0-0 Contact Model-1

2(RCa2+ + Ro2-)2 —1Z2

3. ~ 2 V2 Ro2-

RCa2+/ Ro2- = 1

190 APPENDIX A

2.2 Ti-O Contact Model-1

2a2 — (2Rca2++2Ro2-)2 a=2(Rxi4++Ro2-)

Rca2+/ Ro2- = (2V2RTiA+ + 2a/2 - 2)/2

Rxi4+ = 0.0745

Rca2+/ Ro2-~ 1-25

191 APPENDIX A

2.3 Ca-O Contact Model-1

(2Rca2+ + 2Ro2-)2 — 2a2

a = y[2 (Rca2++Ro2-)

Rca2+/ R-02-= 1-175

2.4 PDF Card

a - J2 ( Ro2-+Rca2+)

Rca2+/ Rq2- = 1 -143

192 APPENDIX A

3. Calculation of The Radius Ratio of Rxi4+/Ro2-

3.1 O - OContact Model-2

2(2Ro2-)2 = (2Ro2- +2RTi4+)2

Rxi4+/Ro2-= V2 -1=0.414

a < >

193 APPENDIX A

3.2 Ti-O Contact Model-2

(J2/2 a)2 = 2(Ro2.+RTi4+)2 a = 2(Ro2-+R-Ti4+)

Rxi4+= 0.0745 nm

Rxi4+/ R02- = 0.591

Ro2-+Rli4+ <------>

194 APPENDIX A

3.3 Ca-O Contact Model-2

(V2/2 a)2 = 2(Ro2-+Rii4+)2

a = V2 ( Ro2-+Rca2+)

Rli4+/ R02- = ( V2 -2+ V2 Rca2+/Ro2-)/2 Rca2+ = 0.148 nm

Rxi4+/ R02- = 0.537

195 Appendix B: Calculation of The Radius Ratio for Interstitial Voids in CaTiC>3

B-l. Schematic Diagram of Three Possible Interstitial Sites, Comer Void (CV), Face Void (FV) and Volume Void (VV), in the Cubic Lattice Structure of the CaTiC>3 2.1 Schematic Diagram o f Interstitial Corner Void in CaTiO3 Structure with Different Models < CL CL w Z Q x fN ▼■H fS Ti-O Contact Model: Rxi4+= 0.0745 nm

Unstable packing as oo Ca-O Contact Model: Rra2+= 0.148 nm APPENDIX B

2.2 The Radius Ratio of Interstitial Corner Void (CV):

Assuming:

Rfv (ooi) = the maximum radius of interstitial corner void parallel to relative plane (001) in CaTiOs crystal shown in Figure B-l

Rfv (oio) = the maximum radius of interstitial comer void parallel to relative plane (010) in CaTiOs crystal shown in Figure B-l

Rfv (ioo) = the maximum radius of interstitial corner void parallel to

relative plane (100) in CaTiC>3 crystal shown in Figure B-l

R02- = the radius of oxygen ion

2.2.1 Calculation of Rev (ooi) / R02-

2(Rcv(ooi) + R02-)2 = (a/2/2a)2 a = 2 (R.Ti4++Ro2-)

(Rev (001) + R02-)2 = (Rli4++Ro2- )2

Rev (ooi) / R02-= Rri4+/Ro2-

When Rxi4+/Ro2- = 0.414 (0-0 Contact Model)

Rev (ooi) / Rq2-=0.414

• When RTi4+/Ro2- = 0.591 (Ti-0 Contact Model)

Rev (ooi) / Rq2-=0.591

• When Rji4+/Ro2- = 0.536 (Ca-0 Contact Model)

Rev (ooi) / Ro2-= 0.536

200 APPENDIX B

2.2.2 Calculation of Rev (oio) / R02- and Rev (ioo) / R02-

Assuming: Rev (oio) / R02- — Rev (ioo) / R02-

(Rca2++R02-)2 = (Rca2++ Rev (OIO))2 + (l/2a) 2

V2 a = 2 (Rca2++R02-)

Rev (010) / R02- = (a/2 /2-1) Rca2+/Ro2-+a/2/2

• When Rca2+/Ro2- = 1 (0-0 Contact Model) Riy /Ro = 0.414

• When Rca2+/Ro2- = 1 -25 (Ti-0 Contact Model) R[y /Ro = 0.341

• When Rca2+/Ro2- = 1-175 (Ca-0 Contact Model) Riy /Ro = 0.363

201 3.1 Schematic Diagram o f Interstitial Face Void in CaTiO3 Structure with Different Models

202 Ti-O Contact Model: Rxi 4+= 0.0745 nm o (N < eu w cu 5 X rn t n — H Ca-O Contact Model: Rca2+= 0.148 nm o3

204 APPENDIX B

3.2 The Radius Ratio of Interstitial Face Void (FV):

Assuming:

R-fv (ooi) = the maximum radius of interstitial comer void parallel to

relative plane (001) in CaTi03 crystal shown in Figure B-l

Rfv (oio) = the maximum radius of interstitial comer void parallel to

relative plane (010) in CaTi03 crystal shown in Figure B-l

Rfv (ioo) = the maximum radius of interstitial corner void parallel to relative

plane (100) in CaTiC>3 crystal shown in Figure B-l

R02- = the radius of oxygen ion

3.2.1 Calculation of Rfv (ooi) / R02-

(2 Rfv (ooi) + 2 R02-)2 = (>/2 /2a)"

a = 2 (Rti4++Ro2- )

Rfv (ooi) / R02- =

-J2 /2( RTi4+/Ro2-)+ -n/2 /2-1

• When Rxi4+/Ro2-= 0.414 (0-0 Contact Model)

Rfv (ooi) / R02- = 0.000

• When RTi4+/Ro2-= 0.591 (Ti-0 Contact Model)

Rfv (ooi) / R02- = 0.125

• When Rxi4+/Ro2- = 0.536 (Ca-0 Contact Model)

Rfv (ooi) / R02- = 0.0860

205 APPENDIX B

3.2.2 Calculation of Rev (oio> / R02- and Rev (ioo) / R02-

Assuming: Rev (010) / R02- = Rev (ioo) / R02-

Rcv(oio) = a a = 2 (RTi4++Ro2-)

Rev (010) / Ro2- = 2(RTi4+/R02-+l)

• When RTi4+/Ro2- = 0.414 (0-0 Contact Model) Rev (010) / R02- = 2.828

• When RTi4+/Ro2- = 0.591 (Ti-0 Contact Model) Rev (010) / R02- = 3.182

• When RTi4+/Ro2- = 0.536 (Ca-O Contact Model) Rev (010) / R02-= 3.072

206 APPENDIX B

4. Calculation of The Radius Ratio for Interstitial Volume Void (W)

4.1 Schematic Diagram of Interstitial Volume Void in CaTiO3 Structure with Different Models 1/8 unit cell

4.2 The Radius Ratio of Interstitial Volume Void (FV):

A

vt

X

207 APPENDIX B

x2 = y2 + z2 y = 1/3 [(V2 /2 a)2- (V2/4 a)2]1/2 =l/3(l/2a2-l/8a2)1/2 = V6/12 a

^■Ti4+~^o2- “ E2 a

Rca2++^c>2- “a/2 a

S = (V3 /2 a- Rjj4+-R-Ca2+)^+^Ti4+

=^/3 /2 a + RTi4++ Rq2_ - (Rca2+ + Rca2 =(V3 /2a+ 1/2 a V2 /2 a)/2 = (V3+l-V2)/4a t = [(l/2a)2- (2y)2]1/2= (l/4a2- 6/36 a2 ) 1/2 = V3/6 a z = t - s

= V3/6a-(V3 +I-V2 )/4a = (2/3 -3/3 -3+^2 )/12 a

x2=( V6/12a)2+[(2/3 -3a/3 -3 + 3^2 )/12 a]2 =0.0433 a2

208 APPENDIX B

(Rw+Ro2-)2 ~ X2 + (Rfv + R02-)2

= 0.0433 a2 + (V2 /4a)2 = 0.0433 a2+ 1/8 a2 = 0.168 a2 a = 2 (RTi4++Ro2-)

(Rvv+Ro2.)2“ 0.168x4 (RTi4+“t"Ro2- )2

(Rw+Ro2-) — 0.82 (RTi4++Ro2-)

Ryy / Ro2- = 0.82 RTi4+/Ro2- “0.18

• When RTi4+/Ro2- = 0.591 (Ti-0 Contact Model)

Ryv / Ro2- = 0.305

• When RTi4+/Ro2- = 0.414 (0-0 Contact Model)

Ryy / Rq2- = 0.1 60

• When RTi4+/Ro2- = 0.536 (Ca-0 Contact Model)

Ryy / Ro2- = 0.260

209 APPENDIX B JO JD *6 • .2 • 13 T u H CQ U 13 t _o P • CJ P H P^

'HJ o3 oa o »"H > O 3 c 0 03 r-H 3 C/3 CD a 4 3 1 h 1 ■<

R adius R atio o f P osition R adius o f P osition [nm] £ <1 £ £ a [nm] p & ‘ ■a 4 CN S* rs CN 4 £ + 5 R Interstitial Void

R ad iu so f 0.148 0.0745 »• C atio n 12-coordination 6-coordinaton U > u > O ni ne O ­ 0.0522 o o o o PP > PP 0-0 > o o o O O O o CN CN O r VO O in ni ne CN o m VO o o O in r o — 1 H

­ i £ P-C > OO CN oo C o n tact CN O O O 0.356 > > o M odel s © O o 1 0.0202 > u cj > o ON in O 0.0745 o > u > o m ne O O © T i-0 O 0.0429 PP O © o r» ne m > O ON m oo nf O CN o o in P ;> o CN m r-H in O O C o n tact h 0.0157 £ £ OO CN m O M odel O 0.401 o 1 o m in S 1 0 0.0384 cj CJ VO > o in cn O 0.0675 nf oo o O in cj > cj > VO o cn cn O O C a-0 O O oo o o o o o vo t"- in PP > cn VO o nT oo © rn oo © P o t> r- in in > o o oo VO O p C o n tact O Ph > pp > cn CN o r- O O © M odel © 0.387 £ O CN VO o © 1 © 1 0.0328 © o VO o in CJ > CJ VO > o in r — © O H o > CJ > o cn r- CN O O © © 0.0469 pp > O ne ne o r-H vo oo © cn in P > o o r- oo CN r-H nT cn O PDF card p 0.0650 0.00905 P > o O CN P > m p O o p O O 0.381 > > o (N cn N- O VV(ooi,oio,ioo) o CJ 0.0306

CV------C o m er V oid ; FV------Face V oid; VV------V olum eV oid; ) 100 ( ‘ ) (010 ‘ ) 001

(001), (010), (100 )( —■—p arallel to relative planes (001), (010), (100 ) in crystal show nin Figure B -l; CN o APPENDIX C

Appendix C: List of Publications

1. Zhou, M. F.; Bak, T.; Nowotny, J.; Rekas, M.; Sorrell, C. C.; Vance, E. R. “Defect chemistry and semiconducting properties of calcium titanate”, Journal of Materials Science: Materials in Electronics, 13 [12] 697-704 (2002) 2. Bak, T.; Nowotny, J.; Sorrell, C. C. and Zhou, M. F. “Charge Transport in

CaTiC>3 I. Electrical Conductivity”, Journal of Materials Science: Materials in Electronics, 15 [10] 635-644 (2004) 3. Bak, T.; Nowotny, J.; Sorrell, C. C. and Zhou, M. F. “Charge Transport in CaTi03 II. Thermoelectric Power”, Journal of Materials Science: Materials in Electronics, 15 [10] 645-650 (2004) 4. Bak, T.; Nowotny, J.; Sorrell, C. C. and Zhou, M. F. “Charge Transport in

CaTi03 III. Jonker Analysis”, Journal of Materials Science: Materials in Electronics, 15 [10] 651-656 (2004) 5. Zhou, M. F; Bak, T.; Nowotny, J.; Sorrell, C. C. and Vance, E. R. “Ionic Conductivity of CaTiCV’, International Conference on Materials for Hydrogen Energy, 27 August 2004, The University of New South Wales, Sydney, Australia. 6. Nakajima, T; Sheppard, L; Zhou, M. F.; Hossain, F; Ogawa, T; Murch. G and Nowotny, J. “Surface and Grain Boundary Segregation in TiOi”, International Conference on Materials for Hydrogen Energy, 27 August 2004, The University of New South Wales, Sydney, Australia.

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