Tensor properties of solids phenomenological development of the tensor properties of crystals

Tensor Properties of Solids......Page 1
ABSTRACT......Page 5
Preface......Page 6
Acknowledgments......Page 8
Contents......Page 10
PART I - Equilibrium Tensor Properties of Solids......Page 16
1.1 DEFINITION OF A TENSOR PROPERTY......Page 18
1.2 CONCEPTS OF EQUILIBRIUM AND REVERSIBILITY......Page 19
1.3 INTERACTION DIAGRAMS AND FIRST-ORDER EQUILIBRIUM PROPERTY NOMENCLATURE AND REPRESENTATION......Page 20
1.4 INTERACTION DIAGRAM FOR THE FIRST-ORDER NONEQUILIBRIUM TENSOR PROPERTIES......Page 24
2.1 INTRODUCTION TO TENSOR AND MATRIX NOTATION......Page 28
2.2 TRANSFORMATION OF TENSORS......Page 29
2.2.2 Transformation of Vectors......Page 30
2.2.3 Transformation of Second-Rank Tensors......Page 31
2.2.4 Symmetrical and Antisymmetrical Second-Rank Tensors......Page 32
2.2.5 Quadratic Transformation Forms......Page 34
2.2.6 Transformation of Third-Rank Tensors......Page 35
2.2.7 Transformation of Fourth-Rank Tensors......Page 37
2.3 INTRODUCTION TO TENSOR ALGEBRA......Page 40
2.3.2 Tensor Multiplication......Page 41
2.3.4 Tensor Contraction......Page 42
2.4 AXIAL TENSORS......Page 44
2.5 TAYLOR’S SERIES EXPANSION AND THE TENSOR DIFFERENTIATION LAWS......Page 45
2.6 TENSOR FIELDS AND TENSOR OPERATORS......Page 46
2.6.1 Gradient of a Tensor Field......Page 47
2.6.3 Kronecker Delta, Permutation Tensor, Vector Cross Product, and Tensorial Contraction......Page 48
3.1 INTRODUCTION......Page 52
3.2.2 Center of Symmetry......Page 53
3.3 SPACE LATTICES, UNIT CELLS, CRYSTALLOGRAPHIC PLANES, AND DIRECTIONS-MILLER INDICES......Page 56
3.5 NEUMANN’S PRINCIPLE AND ITS APPLICATION TO TENSOR PROPERTIES......Page 61
3.6 APPLICATION OF NEUMANN’S PRINCIPLE TO SYMMETRICAL SECOND-RANK PROPERTY TENSORS......Page 67
3.7 EFFECT OF NEUMANN’S PRINCIPLE ON THE 11 CENTROSYMMETRICAL CRYSTAL CLASSES......Page 71
3.8 LONGITUDINAL AND TRANSVERSE EFFECTS FOR SYMMETRICAL SECOND-RANK PROPERTY TENSORS......Page 72
4.1 Energy Representations and the Criteria for Thermodynamic Equilibrium......Page 76
4.1.1 Energy Density Representation......Page 79
4.2 Thermodynamic Definition of Parameters......Page 80
4.3 Generalized Compliance and Rigidity Matrices......Page 83
4.4 Symmetry of the General Compliance and Rigidity Matrices......Page 86
4.5.1 Principal Effects......Page 89
4.5.2 Independent Coupled Effects......Page 90
4.6 Effect of Measurement Conditions on the First-Order Tensor Properties......Page 93
5.1 THE DEPENDENT COUPLED EFFECTS......Page 100
5.2 INTERRELATIONSHIP BETWEEN FIRST-ORDER PROPERTIES-USE OF INTERACTION DIAGRAMS......Page 102
5.3 THE GRÜNEISEN TENSOR......Page 105
6.1.1 Direct Piezoelectric Effect......Page 110
6.1.2 Converse Piezoelectric Effect......Page 112
6.1.3 Crystal Symmetry Considerations......Page 114
6.1.4 Brute-Force Method for the Trigonal and Hexagonal Classes- The Piezoelectric Moduli......Page 115
6.1.5 Longitudinal Piezoelectric Effect......Page 121
6.2 ELASTICITY......Page 123
6.2.2 Bulk Elastic Behavior......Page 125
6.2.3 Transformation Laws......Page 127
6.2.5 Effect of Crystal Symmetry......Page 128
6.2.6 Homogeneous Elastically Isotropic Solids......Page 133
6.2.7 Young’s Modulus in a Particular Direction......Page 135
6.2.8 Shear Modulus and Poisson’s Ratio......Page 137
7.1 ELECTROSTRICTION AND MORPHIC EFFECTS......Page 138
7.1.1 Symmetry and Transformation Considerations of Fourth-Rank Tensors......Page 139
7.2 GENERALIZED DEVELOPMENT OF THE SECOND-ORDER EFFECTS......Page 140
7.3 PHENOMENOLOGICAL DEVELOPMENT OF THE OPTICAL EFFECTS......Page 144
7.3.1 Electro-Optical Effects......Page 147
7.3.2 Piezo-Optical and Elasto-Optical Effects......Page 149
7.3.3 Piezo-Optical Effect in Cubic Crystals Under Uniaxial Tension......Page 151
7.3.4 Magneto-Optical (Cotton-Mouton and Faraday) Effects......Page 154
7.3.5 Thermo-Optical Effects......Page 157
Part II - Transport Properties of Solids......Page 160
8.1 GRADIENTS, CURRENT DENSITIES, AND THE CONDUCTIVITIES......Page 162
8.3 CROSS OR INTERFERENCE CONDUCTIVITIES......Page 164
8.4.1 Markoff Processes......Page 165
8.4.3 Onsager’s Reciprocity Principle......Page 166
8.5 PROPER CHOICE OF PARAMETERS......Page 167
8.5.1 Further Restrictions on the Phenomenological Coefficients......Page 170
8.6 FLOW OF ELECTRONIC CHARGE AND HEAT- THE CONDUCTIVITIES......Page 171
9.1 SEEBECK EFFECT (THERMOCOUPLE EFFECT)......Page 174
9.2 PELTIER EFFECT (THERMOELECTRIC HEATER/REFRIGERATOR EFFECT)......Page 177
9.3 THOMSON EFFECT......Page 178
9.4 PIEZOTHERMOELECTRIC AND ELASTOTHERMOELECTRIC EFFECTS......Page 181
9.5 PIEZORESISTANCE EFFECT (STRAIN GAUGE EFFECT)......Page 184
9.6.1 Multiple Diffusing Species......Page 186
10.1 FIRST-ORDER THERMOMAGNETIC AND GALVANOMAGNETIC EFFECTS IN AN ISOTROPIC PLANE......Page 190
10.2 DEFINITIONS OF THE THERMOMAGNETIC AND GALVANOMAGNETIC EFFECTS IN AN ISOTROPIC x,y PLANE......Page 193
10.3 SECOND-ORDER EFFECTS IN A MAGNETIC FIELD- THE HALL AND MAGNETORESISTANCE TENSORS......Page 196
10.4 FIRST-ORDER THERMOGALVANOMAGNETIC EFFECTS IN ISOTROPIC CONDUCTIVE MEDIA......Page 199
10.5 OTHER HIGHER-ORDER MAGNETOTRANSPORT TENSOR PROPERTIES IN ANISOTROPIC MEDIA......Page 201
A.1 CONDITIONS FOR MAGNETOCRYSTALLINE CLASS APPLICATION......Page 204
A.2 COMBINED SPACE-TIME TRANSFORMATIONS......Page 205
A.3 APPLICATION OF NEUMANN’S PRINCIPLE TO MAGNETOCRYSTALLINE TRANSFORMATIONS......Page 207
A.4 THE MAGNETIC POINT GROUPS......Page 210
I. GENERAL TEXTS ON THE PHYSICAL (TENSOR) PROPERTIES OF SOLIDS......Page 216
III. GENERAL TEXTS FROM A THEORETICAL PHYSICS POINT OF VIEW......Page 217
VI. MAGNETIC PROPERTIES AND SYMMETRY CONSIDERATIONS......Page 218
VIII. MEASUREMENT TECHNIQUES AND DATA OF TENSOR PROPERTIES OF SOLIDS......Page 219
Author Biography......Page 244
Glossary of Terms and Expressions......Page 220
Glossary of Symbols and Abbreviations......Page 238
Greek Symbols......Page 242
Index......Page 246