Electronic basis of hardness and phase transformations (covalent crystals)
Several electronic parameters measure the stabilities of covalent crystals, including minimum energy band gap densities, inverse polarizabilities, plasma frequencies, transverse vibrational frequencies and elastic shear moduli. Convenient is the band gap density (energy/volume; called the 'bond modulus' For a given bonding type, the indentation hardness is proportional to the bond modulus. Examples are the group IV elements, III V compounds; and II VI compounds. The motion of dislocation kinks requires the excitation of bonding electrons into anti bonding states. The bond modulus measures this together with the work done by the applied stress when a kink moves.In addition to hardness, the bond modulus measures the compressive strain (pressure) needed to transform an ambient structure into a more dense structure. Activation of such transformations also requires the excitation of bonding electrons into anti bonding states together with the work done by the compressive stress.