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.