Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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20<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, 3<br />
• Thus by repeated applications of the<br />
symmetry operators, one can demonstrate<br />
(for cubic crystal symmetry) that one can<br />
reduce the 81 coefficients down to only 3<br />
independent quantities. These become two in<br />
the case of isotropy.<br />
! C11 C12 C12 0 0 0 $<br />
#<br />
&<br />
# C12 C11 C12 0 0 0 &<br />
#<br />
&<br />
# C12 C12 C11 0 0 0 &<br />
#<br />
0 0 0 C44 0 0<br />
&<br />
#<br />
&<br />
# 0 0 0 0 C44 0 &<br />
#<br />
&<br />
" # 0 0 0 0 0 C44% &
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