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

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Page 39

(19) Quantities which transform according to (18) are called

true vectors that transform according to (19) may be called polar vectors when it

is necessary to make an explicit distinction. Our conclusions up to this point may

be ...

(19) Quantities which transform according to (18) are called

**axial vectors**. Thetrue vectors that transform according to (19) may be called polar vectors when it

is necessary to make an explicit distinction. Our conclusions up to this point may

be ...

Page 40

where 1 is a unit vector perpendicular to p and q, such that p, q, 1 form a right-

handed set. Or, alternatively ... A method of representing

not depend on any convention about a positive screw motion is shown in Fig. 2.2

b.

where 1 is a unit vector perpendicular to p and q, such that p, q, 1 form a right-

handed set. Or, alternatively ... A method of representing

**axial vectors**that doesnot depend on any convention about a positive screw motion is shown in Fig. 2.2

b.

Page 54

I and B are also

prove that, since both Ii and Hj in (6) transform as the components of

, the 1/1^ transform as the components of an ordinary (polar) second-rank tensor

...

I and B are also

**axial vectors**, by equation (1) above. The reader may easilyprove that, since both Ii and Hj in (6) transform as the components of

**axial vectors**, the 1/1^ transform as the components of an ordinary (polar) second-rank tensor

...

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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