The effect of proximity of the Fermi level to singularities in the electron state density on elastic and thermodynamic properties of metals and alloys

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Abstract
The authors investigate the effect of the proximity of the Fermi surface (FS) to a singularity in the electron state density on atomic properties of a nearly free-electron metal. Expressions for thermodynamic potentials in the improved version of the pseudopotential perturbation theory are given which generalise the conventional formulae to the case of small distances eta between the FS and the Brillouin zone (BZ) face and also take into account the Fermi liquid interaction effects. The case of the FS proximity to the BZ edge is also considered. The character of the eta dependence of atomic properties is illustrated by model calculations for disordered Li1-xMgx alloys in the BCC, FCC and HCP structures. They calculate the concentration dependencies of the elastic constants cik and their volume derivatives delta cik/ delta u, the low-temperature phonon and electron contributions to the specific heat Cv and to the thermal expansion coefficient beta T, and the equilibrium lattice parameters. All the quantities have peculiar anomalies at small eta which can be rather large, especially in delta cik/ delta u and beta T. The results are compared with the available experimental data.