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

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Page 119

us consider what effect a diad axis has on the

parallel to x3. Then the transformation is a?1 — > x1, Xf —> x2, x3 — > x3, or,

more compactly, 1->-1, 2->-2, 3->3. (23) We must now take the

one, ...

us consider what effect a diad axis has on the

**moduli**. Suppose the diad axis isparallel to x3. Then the transformation is a?1 — > x1, Xf —> x2, x3 — > x3, or,

more compactly, 1->-1, 2->-2, 3->3. (23) We must now take the

**moduli**one byone, ...

Page 122

and, for a 6-fold axis, dni = dn2 = ~dn2 = dsn = ^212 = ^222 = °- (27) The

conditions on the other

to be, for a 3-fold or a 6-fold axis, <*113 = »223, *123 — — *213, ^311 = <*322, ^

133 ...

and, for a 6-fold axis, dni = dn2 = ~dn2 = dsn = ^212 = ^222 = °- (27) The

conditions on the other

**moduli**are derived in a straightforward way and are foundto be, for a 3-fold or a 6-fold axis, <*113 = »223, *123 — — *213, ^311 = <*322, ^

133 ...

Page 319

... 158-68. method, 150-69. multiplication, 151. non-singular, 155. notation for

elastic coefficients, 134-5. — for electro-optical coefficients, 247-8. — for

photoelastic coefficients, 248-9. — for piezoelectric

reciprocal ...

... 158-68. method, 150-69. multiplication, 151. non-singular, 155. notation for

elastic coefficients, 134-5. — for electro-optical coefficients, 247-8. — for

photoelastic coefficients, 248-9. — for piezoelectric

**moduli**, 113-15. null — , 153.reciprocal ...

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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