Entropy and enthalpy catastrophe as a stability limit for crystalline material

Abstract

The transition from a crystalline material with long-range order to a glass-like disordered structure has been observed in several metal alloys and minerals using experimental techniques such as solid-state reaction, mechanical alloying, pressure application, ion-beam mixing and hydriding^1–3. In all these examples the vitrification occurs below the glass transition temperature, and because the glass can be thought of as a highly undercooled liquid, one may draw an analogy between the vitrification process and melting. The melting process is often viewed as a catastrophic instability of the crystal lattice^4–6, although none of these theories predicts the melting temperature correctly. The transition from crystal to glass could also be triggered by some type of instability⁷; indeed, Kauzmann⁸ has argued that an undercooled liquid whose entropy falls below that of the crystalline phase must undergo massive freezing to a glass. Applying an 'inverse' Kauzmann argument to the problem of melting, an entropy catastrophe is predicted when the entropy of a superheated crystal exceeds that of the liquid phase. We propose that this temperature represents an ultimate stability limit for superheated or supersaturated crystals.