Delta *

$\delta ^{*}$ was defined as :

$\delta ^{*}\equiv {\frac {1}{2(c_{33})^{2}}}\left[2(c_{13}+c_{44})^{2}-(c_{33}-c_{44})(c_{11}+c_{33}-2c_{44})\right]$

where $c_{\alpha \beta }$ indicate elements in the elastic stiffness matrix. It was used to derive $\delta$:

$\delta \equiv {\frac {1}{2}}{\frac {(c_{13}+c_{44})^{2}-(c_{33}-c_{44})^{2}}{c_{33}(c_{33}-c_{44})}}$

which is the most critical factor for Polar anisotropy: