Physical Properties of Crystals: Their Representation by Tensors and Matrices |
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Page 113
... dijk = аuajm akn dimn Comparing ( 10 ) with ( 7 ) we find ( 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 = аuajm akn dimn Comparing ( 10 ) with ( 7 ) we find ( 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 ...
Page 118
... dijk аuajm akn dimn = Sjm -Süd jm Skn dimn = - -dijk › by the substitution property of 8. But since the crystal has a centre of symmetry Therefore , dijk = dijk . dijk = 0 . With other symmetry operations the working is not quite as ...
... dijk аuajm akn dimn = Sjm -Süd jm Skn dimn = - -dijk › by the substitution property of 8. But since the crystal has a centre of symmetry Therefore , dijk = dijk . dijk = 0 . With other symmetry operations the working is not quite as ...
Page 130
... dijk are the piezoelectric moduli ; they form a third - rank tensor . ( 3 ) = σji , and we put for convenience dijk = dikj • This reduces the number of independent dijk to 18 . Matrix notation . The second and third suffixes in dijk ...
... dijk are the piezoelectric moduli ; they form a third - rank tensor . ( 3 ) = σji , and we put for convenience dijk = dikj • This reduces the number of independent dijk to 18 . Matrix notation . The second and third suffixes in dijk ...
Contents
THE GROUNDWORK OF CRYSTAL PHYSICS | 3 |
3 | 29 |
EQUILIBRIUM PROPERTIES | 51 |
23 other sections not shown
Common terms and phrases
angle anisotropic applied axial B₁ biaxial birefringence centre of symmetry Chapter coefficients components conductivity constant crystal classes crystal properties crystal symmetry cube cubic crystals D₁ defined denoted diad axis dielectric dijk direction cosines displacement electric field ellipsoid equal equation example expression follows forces given grad H₁ H₂ heat flow Hence hexagonal indicatrix isothermal isotropic k₁ magnetic magnitude matrix notation measured moduli monoclinic number of independent Onsager's Principle optic axis optical activity orientation orthorhombic Ox₁ P₁ parallel Peltier permittivity perpendicular photoelastic photoelastic effect piezoelectric effect plane plate polarization positive principal axes produced pyroelectric effect quadric radius vector referred refractive index relation representation quadric represents right-handed rotation S₁ scalar second-rank tensor shear shown strain stress symmetry elements Table temperature gradient thermal expansion thermodynamics thermoelectric effects Thomson heat tion transformation law triclinic trigonal uniaxial values wave normal x₁ zero әт