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

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Page 7

Equations (5) may be

more compactly, as Pi We now leave out the summation sign: Pi = Tijqi (i,j= 1,2,3)

, (9) and introduce the Einstein summation convention: when a letter suffix occurs

...

Equations (5) may be

**written**i-i 3 P2 = 2Tv9i 3 m -lTij9f (»= 1,2,8). i— l (8) or,more compactly, as Pi We now leave out the summation sign: Pi = Tijqi (i,j= 1,2,3)

, (9) and introduce the Einstein summation convention: when a letter suffix occurs

...

Page 115

The array of dij

this matrix correspond to the layers in the arrangement (13). The matrix notation

has the advantage of greater compactness than the tensor notation, and it makes

...

The array of dij

**written**out as (18) is a matrix. It will be observed that the rows ofthis matrix correspond to the layers in the arrangement (13). The matrix notation

has the advantage of greater compactness than the tensor notation, and it makes

...

Page 158

Before we can use the rule of matrix multiplication we have to bring the repeated

suffixes together. This may be done by

transposing, thus: K'ij = aikKkl(at)lj\ so that we may write x' = axat. (25) It is also ...

Before we can use the rule of matrix multiplication we have to bring the repeated

suffixes together. This may be done by

**writing**the ajl term after the Kkl term andtransposing, thus: K'ij = aikKkl(at)lj\ so that we may write x' = axat. (25) It is also ...

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### Contents

THE GROUNDWORK OF CRYSTAL PHYSICS | 3 |

EQUILIBRIUM PROPERTIES | 51 |

ELECTRIC POLARIZATION | 68 |

69 other sections not shown

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### Common terms and phrases

angle anisotropic applied biaxial birefringence centre of symmetry Chapter coefficients conductivity crystal classes crystal properties crystal symmetry cube cubic crystals defined denoted diad axis dijk direction cosines electric field electro-optical effect ellipsoid equal equation example expression follows force given gives heat flow Hence hexagonal indicatrix isothermal isotropic lattice left-handed magnetic magnitude matrix notation measured moduli monoclinic number of independent Onsager's Principle optic axis optical activity orientation permittivity perpendicular photoelastic effect piezoelectric effect plane plate point group positive principal axes produced pyroelectric effect quadric quantities radius vector referred refractive index relation representation quadric represents right-handed rotation scalar second-rank tensor set of axes shear shown shows strain stress suffix notation symbol symmetry elements Table temperature gradient thermal expansion thermodynamics thermoelectric effects Thomson heat tion transformation law trigonal uniaxial unit volume values wave normal wave surface written zero