Origin of thec/avariation in hexagonal close-packed divalent metals

Abstract

The origin of the $c/a$ variation in hcp divalent metals (Be, Mg, Zn, and Cd), which ranges from 1.568 to 1.886, has been investigated by first-principles full-potential calculations in the framework of the density functional theory. We find that the ideal hcp structure $(c/a=1.633)$ is electronically unstable to $c/a$ distortions for all elements, however the distortion driving band energy is countered by the electrostatic part of the total energy, which favors the ideal close packing. In particular, Zn and Cd with $c/a$ ratios $g$ ideal follow the bonding principle of optimum hybridization between s and p valence bands, a situation similar to the metallic elements in the neighboring group-IIIa in the Periodic Table. For Mg the electronic instability is not effective because the electrostatic part of the total energy dominates over the band energy. However, under expansion a distortion to $c/a$ ratios $g$ ideal occurs. Finally, Be represents a special case. Typically of second-row elements, s and p valence bands mix intimately which creates an electronic structure quite distinguished from the other divalent metals. A $c/a$ distortion cannot improve $s\ensuremath{-}p$ band hybridization but $p\ensuremath{-}p$ bonding is increased for $c/al$ ideal.