Why are the close-packed structures of the noble metals cubic?

Abstract

It is shown that the method of Blandin, in which the energy difference between various close-packed metallic structures is expressed as the sum of interplanar interactions, is not restricted to non-degenerate second order perturbation theory. If the latter theory is applied to the case of the noble metals, assuming one valence electron per atom, the hexagonal close-packed structure is calculated to be stable, whereas the face-centered cubic structure is found experimentally. The result is not improved, if one includes in the theory the estimated influence of the dependence of the pseudopotential matrix elements on scattering vector and - angle. However, if the interplanar interactions are calculated numerically with the help of degenerate perturbation theory (2 OPW approximation for the one-electron energy levels) results in agreement with the experimental data are obtained. The improvement can be ascribed to the fact that allowance is made for the deformations of the Fermi sphere by the perturbation. The results of degenerate and non-degenerate perturbation theory agree with each other at valence electron concentrations exceeding 1.5 electron per atom, provided that an exponential “smearing” factor is inserted in the formulas of the non-degenerate second order perturbation theory.