Entropy catastrophe and superheating of crystals

Abstract

Kauzmann1 has pointed out that at a temperature (Tk) far below the melting temperature (Tm) of a crystal, the entropies of an undercooled liquid and its corresponding equilibrium crystal tend to become equal. At temperatures below Tk, the crystal would have a greater entropy than its liquid. Such a catastrophe is avoided through a glass transition of the liquid above Tk. Fecht and Johnson2 have shown that such a transition should occur for aluminium at 0.23 Tm. A similar entropy catastrophe can also arise at a temperature, TiS, above Tm. Above TiS, the crystalline solid is once again expected to have an entropy greater than that of the liquid. Cahn3 has considered the implications of this idea with respect to the superheating of a solid. Here we present an alternative evaluation of the two temperatures of instability, Tk and TiS, from experimentally measurable parameters. Results for alkali metals show that the Kauzmann-type entropy catastrophe occurs at about half the absolute melting temperature, whereas we find that the entropy catastrophe as described by Fecht and Johnson2 occurs at twice the absolute melting temperature. For most solids, vaporization will probably intervene before the entropy catastrophe temperature above the melting temperature is reached.