Microscopic theory of elasticity of the crystalline solid solution based on pseudopotential method

Abstract

A theoretical method is developed using the pseudopotential method of electron band theory for calculating the strain energy posed by a crystalline solid solution having solute and solvent atoms that differ in size. In the harmonic approximation, the expression of the strain energy obtained from the pseudopotential method is formally identical to that of the phenomenological theory of elasticity. However, it clarifies the physical significance of the phenomenological parameters (solute, solute-lattice and lattice coupling parameters), so that important characteristics of coupling parameters such as the concentration dependence, the effect of the Fermi surface and the effect of the phonon dispersion curves have been made clear. The analysis reveals the direct effect of the Kohn anomaly on the relaxation of the strain energy of a crystalline solid solution. By applying the result to β-brass, the occurence of spinodal decomposition is consistently explained in the scheme of elastic energy. The pair of concentration (deviation) waves, each of which arises in the α- and β-sublattice, respectively, is theoretically described as an acoustic mode of waves with amplitude ratio β Q( q) Q ( α q ) = 999 .