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

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Page 111

Similarly, P2 = d2jk ajk, and P3 = d3jk ajk- Thus, the general statement of the

relationship between Pt and aij is Pt = dijkajk- (3) The

moduli. Let us consider the meaning of the various moduli. If a uniaxial tensile

stress ...

Similarly, P2 = d2jk ajk, and P3 = d3jk ajk- Thus, the general statement of the

relationship between Pt and aij is Pt = dijkajk- (3) The

**dijk**are the piezoelectricmoduli. Let us consider the meaning of the various moduli. If a uniaxial tensile

stress ...

Page 113

0<| Pi = 0<j d[mn amn = 0<j dimn Ujm akn ^ ( l 0) Comparing (10) with (7) we find

d'ijk = "tf ",m akn dlmn- (U) It follows that the

5), and therefore constitute a third-rank tensor. The above proof of the tensor ...

0<| Pi = 0<j d[mn amn = 0<j dimn Ujm akn ^ ( l 0) Comparing (10) with (7) we find

d'ijk = "tf ",m akn dlmn- (U) It follows that the

**dijk**transform according to equation (5), and therefore constitute a third-rank tensor. The above proof of the tensor ...

Page 121

We find, for example, that after using the symmetry property of

function of the six

nve more simultaneous equations may be written down for the same six

We find, for example, that after using the symmetry property of

**dijk**, d'ln is afunction of the six

**dijk**: duv dn2, d122, d2n, d212, d222. ... d'21v d'212 and d'222nve more simultaneous equations may be written down for the same six

**dijk**.### What people are saying - Write a review

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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