The hardness of silicon and germanium

It is generally accepted that the hardness of silicon and germanium at low temperature is limited by a phase transformation under the indenter, as the measured hardness is equal to the transformation pressure. However, observations of the deformation under indents using transmission electron microscopy indicate that, in addition to the phase transformation, there is also plastic flow both in the transformed region and outside it. An analysis based on the spherical cavity model for indentation was developed to quantify the effect of a phase transformation on the measured hardness. This predicts that plastic deformation will extend beyond the transformed zone when the transformation pressure is greater than two-thirds of the yield stress. The analysis also predicts that the hardness can only be approximately equal to the transformation pressure if the yield strength of the transformed material is low, consistent with the experimental observations of substantial plastic deformation of the transformed phase, as well as with estimates of its lattice resistance.