Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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19<br />
Objective<br />
Linear<br />
Ferromagnets<br />
Non-linear<br />
properties<br />
Electric.<br />
Conduct.<br />
Tensors<br />
Elasticity<br />
Symmetry<br />
Effect of symmetry, 2<br />
• Using P’ = P, we can equate coefficients <strong>and</strong><br />
find that:<br />
C 11 =C 22 , C 13 =C 23, C 44 =C 35 , C 16 =-C 26,<br />
C 14 =C 15 = C 24 = C 25 = C 34 = C 35 = C 36 = C 45 = C 46<br />
= C 56 = 0.<br />
C ! =<br />
# C1 1 C1 2 C1 3 0 0 C1 6 &<br />
% C1 2 C1 1 C1 3 0 0 "C1 6(<br />
% C1 3<br />
% 0<br />
%<br />
0<br />
%<br />
$ C1 6<br />
C1 3<br />
0<br />
0<br />
"C1 6<br />
C3 3<br />
0<br />
0<br />
0<br />
0<br />
C4 4<br />
0<br />
0<br />
0<br />
0<br />
C4 4<br />
C4 6<br />
0<br />
0<br />
C4 6<br />
C6 6<br />
(<br />
(<br />
(<br />
(<br />
'