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 hydriding1–3. 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 lattice4–6, 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.