Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium

The elastic coefficients for an arbitrary rectangular coordinate system are calculated as a function of direction cosines in the crystal. Young's modulus, shear modulus, and Poisson's ratio are defined in general and values tabulated for some of the more important directions in the crystal. Graphs of these moduli are also plotted as a function of crystal direction for orientations in the (100) and (110) planes as well as planes determined by the [110] direction and any perpendicular direction.