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

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Page 7

The dummy

Equations (5) may be written pt or, more compactly, as (»=1,2,3). (8) We now

leave out the summation sign: Pi=Ttiqi (t,j=l,2,3), (9) and introduce the Einstein

summation ...

The dummy

**suffix notation**. It is convenient now to shorten our notation.Equations (5) may be written pt or, more compactly, as (»=1,2,3). (8) We now

leave out the summation sign: Pi=Ttiqi (t,j=l,2,3), (9) and introduce the Einstein

summation ...

Page 134

It is worth noting, as a reminder of the economy of the dummy

equation (11) typifies 34 equations each with 34 terms on the right-hand side,

making a total of 38 = 6,561 terms in all. The above proof is a general one.

It is worth noting, as a reminder of the economy of the dummy

**suffix notation**, thatequation (11) typifies 34 equations each with 34 terms on the right-hand side,

making a total of 38 = 6,561 terms in all. The above proof is a general one.

Page 150

The matrix and tensor

and VIII in the piezoelectric equations Pi = dtiai ... nature of the property, that is, its

tensor rank andhowit transforms, is indicated precisely by the number of

The matrix and tensor

**notations**THE matrix**notation**introduced in Chapters VIIand VIII in the piezoelectric equations Pi = dtiai ... nature of the property, that is, its

tensor rank andhowit transforms, is indicated precisely by the number of

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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