Physical Properties of Crystals: Their Representation by Tensors and Matrices |
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Page 12
... transform to the nine coefficients T. We have proved that the relation between them , the transformation law for second - rank tensors , is ( 22 ) . This is a most important result ; it is essential that its meaning and significance be ...
... transform to the nine coefficients T. We have proved that the relation between them , the transformation law for second - rank tensors , is ( 22 ) . This is a most important result ; it is essential that its meaning and significance be ...
Page 13
... Transformation laws for tensors Name Scalar Vector Transformation law tensor New in terms of old Old in terms of new 01234 = φ $ = & ' - = a¿jPj TisakajiTkl ( 13 ) Pi = ( 22 ) 3 Τ ijk = T1jkl = аilajmаknimn aimajnako iptmno Ti Tijkl Tij ...
... Transformation laws for tensors Name Scalar Vector Transformation law tensor New in terms of old Old in terms of new 01234 = φ $ = & ' - = a¿jPj TisakajiTkl ( 13 ) Pi = ( 22 ) 3 Τ ijk = T1jkl = аilajmаknimn aimajnako iptmno Ti Tijkl Tij ...
Page 112
... law ( 5 ) , for deciding how the components transform on change of axes . If it were not so , the definition would be merely circular . The transformation laws for first- and second - rank tensors are the same , respectively , as those ...
... law ( 5 ) , for deciding how the components transform on change of axes . If it were not so , the definition would be merely circular . The transformation laws for first- and second - rank tensors are the same , respectively , as those ...
Contents
THE GROUNDWORK OF CRYSTAL PHYSICS | 3 |
EQUILIBRIUM PROPERTIES | 51 |
ELECTRIC POLARIZATION | 68 |
18 other sections not shown
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 dijk direction cosines dummy suffix elastic electric field ellipsoid equation example force given grad H₁ H₂ heat flow Hence hexagonal homogeneous indicatrix isothermal isotropic k₁ magnetic magnitude matrix notation measured moduli monoclinic number of independent Onsager's Principle optical activity orientation orthorhombic Ox₁ P₁ parallel Peltier permittivity perpendicular photoelastic effect piezoelectric effect plane plate polarization principal axes produced pyroelectric pyroelectric effect quantities radius vector referred refractive index relation representation quadric represented right-handed rotation S₁ scalar second-rank tensor set of axes shear strain stress suffix notation surface susceptibility symmetry elements Table temperature gradient thermal expansion thermodynamics thermoelectric effects Thomson heat tion transformation law triclinic trigonal uniaxial values x₁ Young's Modulus zero