Physical Properties of Crystals: Their Representation by Tensors and Matrices |
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Page 7
... dummy suffix notation . It is convenient now to shorten our notation . Equations ( 5 ) may be written P1 P2 = 3 ΣΤ ,,, T 3 T2j Ij P3 = Taj lj ( 7 ) or , more compactly , as 3 Pi = 19 ; ( i = 1 , 2 , 3 ) . ( 8 ) We now leave out the ...
... dummy suffix notation . It is convenient now to shorten our notation . Equations ( 5 ) may be written P1 P2 = 3 ΣΤ ,,, T 3 T2j Ij P3 = Taj lj ( 7 ) or , more compactly , as 3 Pi = 19 ; ( i = 1 , 2 , 3 ) . ( 8 ) We now leave out the ...
Page 11
... dummy suffix , ( 13 ) may be written Pi = aik Pk . ( 13 ) ' Using k as the free suffix and l as the dummy suffix , ( 9 ) takes the form = Pk Tk9i ; and , similarly , by changing the free suffix from i to l , ( 16 ) becomes Then ...
... dummy suffix , ( 13 ) may be written Pi = aik Pk . ( 13 ) ' Using k as the free suffix and l as the dummy suffix , ( 9 ) takes the form = Pk Tk9i ; and , similarly , by changing the free suffix from i to l , ( 16 ) becomes Then ...
Page 12
... dummy suffixes , while i and j are free . The reader may find it helpful , at first , to expand such expressions in two stages , first for one suffix and then for the other- the order is immaterial . Thus , expanding for 1 , Tij aikaji ...
... dummy suffixes , while i and j are free . The reader may find it helpful , at first , to expand such expressions in two stages , first for one suffix and then for the other- the order is immaterial . Thus , expanding for 1 , Tij aikaji ...
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