Anisotropic thermal expansion in the divalent HCP metals

The HCP metal Mg has a nearly ideal c/a ratio which is almost independent of temperature. By contrast, the other divalent HCP metals Zn and Cd have c/a ratios which are larger than ideal at 0K and increase further as the temperature is raised. It is shown that while the absolute c/a values for Zn and Cd are to be understood in terms of d band influence, once this effect is recognised, the thermal variations are largely explainable via the anisotropy of the phonon spectra. The thermal vibrations can be largely accounted for in terms of an Einstein model in which, at all temperatures, the frequency of vibrations along the c axis is about half those transverse to it.