Physical Properties of Crystals: Their Representation by Tensors and MatricesFirst published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects. |
Contents
THE GROUNDWORK OF CRYSTAL PHYSICS | 3 |
EQUILIBRIUM PROPERTIES | 51 |
ELECTRIC POLARIZATION | 68 |
Special forms of the stress tensor | 87 |
THE STRAIN TENSOR AND THERMAL EXPANSION | 93 |
PIEZOELECTRICITY THIRDRANK TENSORS | 110 |
Reduction in the number of independent moduli by crystal | 116 |
Results for all the crystal classes | 122 |
TRANSPORT PROPERTIES | 193 |
THERMOELECTRICITY | 215 |
NATURAL AND ARTIFICIAL DOUBLE REFRACTION | 235 |
OPTICAL ACTIVITY | 260 |
A Summary of vector notation and formulae | 275 |
Summary of crystal properties | 289 |
E Matrices for equilibrium properties in the 32 crystal classes | 295 |
F Magnetic and electrical energy | 302 |
Summary | 130 |
THE MATRIX METHOD | 150 |
THERMODYNAMICS OF EQUILIBRIUM PROPERTIES | 169 |
| 310 | |
SOLUTIONS TO THE EXERCISES WITH NOTES | 320 |
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Common terms and phrases
angle anisotropic antisymmetrical applied axial vector birefringence centre of symmetry Chapter coefficients components conductivity constant couple crystal classes crystal properties crystal symmetry cubic crystals defined denoted density diad axis diamagnetic dielectric dijk direction cosines dummy suffix elastic electric field ellipsoid equation example follows force given grad H₁ H₂ heat flow Hence hexagonal hyperboloid indicatrix isothermal isotropic left-handed length m.k.s. units magnitude matrix measured moduli Mohr circle construction monoclinic number of independent optic axis optical activity orientation orthorhombic Ox₁ P₁ parallel Peltier permittivity perpendicular photoelastic photoelastic effect piezoelectric effect plane polarization principal axes pyroelectric quantities radius vector referred refractive index relation representation quadric represented right-handed rotation S₁ scalar set of axes shear strain stress suffix notation surface susceptibility symmetrical second-rank tensor symmetry elements Table thermal expansion thermodynamical thermoelectric thermoelectric effects transformation law trigonal uniaxial values wave normal x₁ zero