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

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Page 6

A scalar such as density is written without subscripts (for

components of a vector have one subscript (for

components of a second-rank tensor have two subscripts (for

number ...

A scalar such as density is written without subscripts (for

**example**, density />); thecomponents of a vector have one subscript (for

**example**, E2) ; and thecomponents of a second-rank tensor have two subscripts (for

**example**, tr12). Thenumber ...

Page 8

For

and k, l are dummy suffixes. Note that the order of the members of a product does

not matter in this notation; for

For

**example**, we might have an equation of this sort: , t, j are free suffixes hereand k, l are dummy suffixes. Note that the order of the members of a product does

not matter in this notation; for

**example**, the second term on the left in the above ...Page 142

found to be isotropic. We now see that the elastic properties of cubic crystals,

given by fourth-rank tensors, are not isotropic. (iv) Numerical

numerical

22m).

found to be isotropic. We now see that the elastic properties of cubic crystals,

given by fourth-rank tensors, are not isotropic. (iv) Numerical

**example**. For anumerical

**example**we choose ammonium dihydrogen phosphate (ADP) (class22m).

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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