Physical Properties of Crystals: Their Representation by Tensors and Matrices |
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Page 113
... dijk = аuajm akn dimn ( 10 ) ( 11 ) It follows that the dijk transform according to equation ( 5 ) , and there- fore constitute a third - rank tensor . The above proof of the tensor character of the dijk is a general one . It may be ...
... dijk = аuajm akn dimn ( 10 ) ( 11 ) It follows that the dijk transform according to equation ( 5 ) , and there- fore constitute a third - rank tensor . The above proof of the tensor character of the dijk is a general one . It may be ...
Page 121
... dijk the result is a set of simultaneous equations . We find , for example , that after using the symmetry property of dijk , d'111 is a function of the six dijk : d111 , d112 , d122 , d211 , d212 , d222 . By putting d'111 d111 an ...
... dijk the result is a set of simultaneous equations . We find , for example , that after using the symmetry property of dijk , d'111 is a function of the six dijk : d111 , d112 , d122 , d211 , d212 , d222 . By putting d'111 d111 an ...
Page 130
... dijk are the piezoelectric moduli ; they form a third - rank tensor . If body - torques are neglected , σij = ( 3 ) σji , and we put for convenience dijk = diki . This reduces the number of independent dijk to 18 . Matrix notation . The ...
... dijk are the piezoelectric moduli ; they form a third - rank tensor . If body - torques are neglected , σij = ( 3 ) σji , and we put for convenience dijk = diki . This reduces the number of independent dijk to 18 . Matrix notation . The ...
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