$6\mathrm{.}12$ As noted in Section $3\mathrm{.}15,$ for single crystals of some substances, the physical properties are anisotropic$-$that is$,$ they depend on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a general uvw direction, $E_{\text{u}\text{v}\text{w}},$ is described by the relationship

$\frac{1}{E_{\text{u}\text{v}\text{w}}}=\frac{1}{E_{(100)}}-3(\frac{1}{E_{(100)}}-\frac{1}{E_{(111)}})$

$({}^2{}^2+{}^2{}^2+{}^2{}^2)$