Theory of Interplanar Interaction in Metals of Close-Packed Structures on Free Electron Model

Abstract

Interplanar interactions between the hexagonal net planes in close-packed metals are discussed as a function of the electron-atom ratio on the same model that Blandin et al. used. Now the expansions are done to second order, whereas those by Blandin et al. are only to first. The second order asymptotic expansions show that the anomaly in the interplanar interactions at ≈1.140, found by Blandin et al. , disappears. These expansions are applied to evaluate approximate values of the stacking fault energy, γ SF , and the difference Δ U HF in the binding energies between HCP and FCC lattices. Comparisons of these values with those accurately calculated show that the second order expansion is a good approximation. The approximate relation γ SF ≈2 N p Δ U HF holds in =1.0∼1.2, where N p is the density of lattice points on the net plane.