## Physical Properties of Crystals: Their Representation by Tensors and Matrices |

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Page 9

The angular relations between the axes may be specified by drawing up a table

of

The angular relations between the axes may be specified by drawing up a table

of

**direction cosines**: 'Old' 'New' u. (11). «32 Thus, for example, the**direction****cosines**of x'2 with respect to xl, xs, xs are a21, a22, a23, and the**direction****cosines**of ...Page 26

Let lt now be the

The component of j parallel to E is (j.E)/E, or in suffix notation (jtEt)/E.^ Therefore

the conductivity in the direction lt is or, a This is the general expression for a, ...

Let lt now be the

**direction cosines**of E referred to general axes, so that Et = Elt.The component of j parallel to E is (j.E)/E, or in suffix notation (jtEt)/E.^ Therefore

the conductivity in the direction lt is or, a This is the general expression for a, ...

Page 33

Relations between the

that, for a transformation from one orthogonal set of axes Oxi to another set Oxi

given by il OlJ a13 21 aM a23 (1) the nine coefficients ati are not independent.

Relations between the

**direction cosines**ati. We remarked in § 2. 1 of Chapter Ithat, for a transformation from one orthogonal set of axes Oxi to another set Oxi

given by il OlJ a13 21 aM a23 (1) the nine coefficients ati are not independent.

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### Contents

THE GROUNDWORK OF CRYSTAL PHYSICS | 3 |

EQUILIBRIUM PROPERTIES | 51 |

ELECTRIC POLARIZATION | 68 |

15 other sections not shown

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### Common terms and phrases

angle anisotropic applied axial vector centre of symmetry Chapter coefficients conductivity constant crystal classes crystal properties crystal symmetry cube cubic crystals defined denoted diad axis dielectric 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 monoclinic number of independent Onsager's Principle optical activity orientation parallel Peltier permittivity perpendicular photoelastic effect piezoelectric effect plane plate polarization positive principal axes produced pyroelectric pyroelectric effect quantities radius vector referred refractive refractive index relation representation quadric represented right-handed rotation scalar second-rank tensor set of axes shear 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 Young's Modulus zero