Properties of materials: Anisotropy, symmetry, structure

Contents......Page 8
1.1 Outline......Page 14
1.2 Structure”property relationships......Page 16
1.3 Symmetry of physical properties......Page 17
1.4 Atomistic arguments: Density......Page 18
2.2 Axis transformations......Page 22
2.3 Orthogonality conditions......Page 23
2.4 General rotation (Eulerian angles)......Page 25
3.1 Symmetry operations......Page 27
3.2 Symmetry elements and stereographic projections......Page 28
3.3 Point groups and their stereograms......Page 30
3.5 Point group populations......Page 33
4.1 Transformation operators for the crystallographic symmetry elements......Page 36
4.2 Transformation operations for the thirty-two crystal classes......Page 38
4.4 Curie group symmetries......Page 39
5.1 Physical properties......Page 43
5.2 Polar tensors and tensor properties......Page 44
5.3 Axial tensor properties......Page 45
5.4 Geometric representations......Page 46
5.6 Analytical form of Neumann’s Principle......Page 47
6.1 Linear systems......Page 50
6.2 Coupled interactions: Maxwell relations......Page 51
6.3 Measurement conditions......Page 53
7.1 Heat capacity of solids......Page 56
7.2 Lattice vibrations......Page 59
7.3 Entropy and the magnetocaloric effect......Page 61
8.2 Symmetry limitations......Page 63
8.3 Polar axes......Page 65
8.4 Geometric representation......Page 66
8.6 Primary and secondary pyroelectric effects......Page 67
8.8 Temperature dependence......Page 68
8.9 Applications......Page 70
9.1 Origins of the dielectric constant......Page 71
9.2 Dielectric tensor......Page 73
9.3 Effect of symmetry......Page 75
9.4 Experimental methods......Page 76
9.5 Geometric representation......Page 80
9.7 Structure”property relationships......Page 82
10.1 Mechanical stress......Page 85
10.2 Stress transformations......Page 87
10.3 Strain tensor......Page 88
10.4 Matrix transformation for strain......Page 90
11.1 Effect of symmetry......Page 92
11.2 Thermal expansion measurements......Page 94
11.3 Structure–property relations......Page 95
11.4 Temperature dependence......Page 98
12.1 Tensor and matrix formulations......Page 100
12.2 Matrix transformations and Neumann’s Law......Page 102
12.3 Piezoelectric symmetry groups......Page 104
12.4 Experimental techniques......Page 106
12.5 Structure–property relations......Page 107
12.6 Hydrostatic piezoelectric effect......Page 110
12.7 Piezoelectric ceramics......Page 112
12.8 Practical piezoelectrics: Quartz crystals......Page 113
13.1 Tensor and matrix coefficients......Page 116
13.2 Tensor and matrix transformations......Page 118
13.3 Stiffness-compliance relations......Page 119
13.4 Effect of symmetry......Page 120
13.5 Engineering coefficients and measurement methods......Page 122
13.6 Anisotropy and structure–property relations......Page 123
13.7 Compressibility......Page 126
13.8 Polycrystalline averages......Page 127
13.9 Temperature coefficients......Page 129
13.10 Quartz crystal resonators......Page 131
14.1 Basic ideas and units......Page 135
14.2 Magnetic structures and time reversal......Page 137
14.3 Magnetic point groups......Page 138
14.4 Magnetic axial vectors......Page 143
14.5 Saturation magnetization and pyromagnetism......Page 144
14.6 Magnetic susceptibility and permeability......Page 147
14.7 Diamagnetic and paramagnetic crystals......Page 148
14.8 Susceptibility measurements......Page 150
14.9 Magnetoelectricity......Page 151
14.10 Piezomagnetism......Page 155
14.11 Summary......Page 159
15.1 Nonlinear dielectric properties......Page 160
15.2 Nonlinear elastic properties......Page 161
15.3 Electrostriction......Page 164
15.4 Magnetostriction......Page 166
15.5 Modeling magnetostriction......Page 167
15.6 Magnetostrictive actuators......Page 172
15.7 Electromagnetostriction and pseudopiezoelectricity......Page 173
16.1 Free energy formulation......Page 175
16.2 Ferroelasticity......Page 178
16.3 Ferromagnetism......Page 181
16.4 Magnetic anisotropy......Page 183
16.5 Ferroelectricity......Page 187
16.6 Secondary ferroics: Ferrobielectricity and ferrobimagnetism......Page 190
16.7 Secondary ferroics: Ferrobielasticity and ferroelastoelectricity......Page 192
16.8 Secondary ferroics: Ferromagnetoelectrics and ferromagnetoelastics......Page 195
16.9 Order parameters......Page 196
17.1 Tensor and matrix relations......Page 201
17.2 Resistivity measurements......Page 202
17.3 Electrode metals......Page 204
17.4 Anisotropic conductors......Page 206
17.5 Semiconductors and insulators......Page 207
17.6 Band gap and mobility......Page 209
17.7 Nonlinear behavior: Varistors and thermistors......Page 212
17.8 Quasicrystals......Page 215
18.1 Tensor nature and experiments......Page 216
18.2 Structure–property relationships......Page 219
18.3 Temperature dependence......Page 221
18.4 Field dependence......Page 223
19.1 Definition and tensor formulation......Page 224
19.2 Structure–property relationships......Page 225
19.3 Ionic conductivity......Page 230
19.4 Superionic conductors......Page 232
19.5 Cross-coupled diffusion......Page 233
20 Galvanomagnetic and thermomagnetic phenomena......Page 236
20.1 Galvanomagnetic effects......Page 237
20.2 Hall Effect and magnetoresistance......Page 239
20.3 Underlying physics......Page 240
20.4 Galvanomagnetic effects in magnetic materials......Page 242
20.5 Thermomagnetic effects......Page 245
21.1 Seebeck Effect......Page 247
21.3 Thomson Effect......Page 248
21.4 Kelvin Relations and absolute thermopower......Page 249
21.5 Practical thermoelectric materials......Page 251
21.6 Tensor relationships......Page 252
21.7 Magnetic field dependence......Page 253
22.1 Tensor description......Page 256
22.2 Matrix form......Page 257
22.3 Longitudinal and transverse gages......Page 258
22.4 Structure–property relations......Page 260
23.1 The Christoffel Equation......Page 262
23.2 Acoustic waves in hexagonal crystals......Page 265
23.3 Matrix representation......Page 268
23.4 Isotropic solids and pure mode directions......Page 269
23.5 Phase velocity and group velocity......Page 271
24.1 Acoustic impedance......Page 274
24.2 Ultrasonic attenuation......Page 275
24.3 Physical origins of attenuation......Page 277
24.4 Surface acoustic waves......Page 278
24.5 Elastic waves in piezoelectric media......Page 279
24.6 Nonlinear acoustics......Page 283
25.1 Electromagnetic waves......Page 287
25.2 Optical indicatrix and refractive index measurements......Page 289
25.3 Wave normals and ray directions......Page 291
25.4 Structure–property relationships......Page 293
25.5 Birefringence and crystal structure......Page 295
26.1 Dispersion......Page 299
26.2 Absorption, color, and dichroism......Page 301
26.3 Reflectivity and luster......Page 304
26.4 Thermo-optic effect......Page 305
27.1 Basic concepts......Page 307
27.2 Photoelasticity......Page 308
27.3 Static photoelastic measurements......Page 309
27.4 Acousto-optics......Page 311
27.6 Material issues......Page 313
28 Electro-optic phenomena......Page 315
28.1 Linear electro-optic effect......Page 316
28.2 Pockels Effect in KDP and ADP......Page 317
28.3 Linear electro-optic coefficients......Page 321
28.4 Quadratic electro-optic effect......Page 322
29.1 Structure–property relations......Page 326
29.2 Tensor formulation and frequency conversion......Page 328
29.3 Second harmonic generation......Page 329
29.4 Phase matching......Page 331
29.5 Third harmonic generation......Page 335
30.1 Molecular origins......Page 338
30.2 Tensor description......Page 340
30.3 Effect of symmetry......Page 342
30.4 Relationship to enantiomorphism......Page 344
30.5 Liquids and liquid crystals......Page 346
30.6 Dispersion and circular dichroism......Page 350
30.7 Electrogyration, piezogyration, and thermogyration......Page 353
31.1 The Faraday Effect......Page 355
31.2 Tensor nature......Page 356
31.3 Faraday Effect in microwave magnetics......Page 358
31.4 Magneto-optic recording media......Page 359
31.5 Magnetic circular dichroism......Page 361
31.6 Nonlinear magneto-optic effects......Page 363
31.7 Magnetoelectric optical phenomena......Page 364
32.1 Crystal morphology......Page 367
32.2 Growth velocity......Page 369
32.3 Crystal growth and crystal structure......Page 371
32.4 Surface structures and surface transformations......Page 373
32.5 Etch figures and symmetry relations......Page 374
32.6 Micromachining of quartz and silicon......Page 376
32.7 Tensor description......Page 379
Further Reading......Page 382
E......Page 388
N......Page 389
T......Page 390
W......Page 391