## 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. |

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### Contents

THE GROUNDWORK OF CRYSTAL PHYSICS | 3 |

EQUILIBRIUM PROPERTIES | 51 |

ELECTRIC POLARIZATION | 68 |

THE STRESS TENSOR | 82 |

VI THE STRAIN TENSOR AND THERMAL EXPANSION | 93 |

PIEZOELECTRICITY THIRDRANK TENSORS | 110 |

ELASTICITY FOUKTHRANK TENSORS | 131 |

THE MATRIX METHOD | 150 |

THERMOELECTRICITY | 215 |

NATURAL AND ARTIFICIAL DOUBLE REFRACTION | 235 |

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 |

310 | |

SOLUTIONS TO THE EXERCISES WITH NOTES | 320 |

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### Common terms and phrases

angle anisotropic applied axial vector birefringence centre of symmetry Chapter coefficients conductivity couple crystal classes crystal properties crystal symmetry cube cubic crystals defined deformation denoted density diad axis dielectric constant difk direction cosines displacement dummy suffix electric field ellipsoid equal equation example expression follows force given heat flow Hence hexagonal homogeneous indicatrix isothermal isotropic left-handed length longitudinal magnetic magnitude matrix notation measured moduli Mohr circle construction number of independent optical activity orientation parallel Peltier permittivity perpendicular piezoelectric effect plane plate polarization positive principal axes produced pyroelectric effect quantities radius vector referred refractive refractive index relation representation quadric represented right-handed rotation scalar set of axes shear strain stress suffix notation surface susceptibility symmetry elements Table temperature gradient tensile stress thermal expansion thermodynamics thermoelectric effects Thomson heat tion transformation law trigonal uniaxial unit volume values written zero