Polyamorphism and the universal liquid-liquid critical point in the supercooled state

The physics of critical phenomena is well established in systems as diverse as molecular fluids, crystalline alloys and magnetic materials. As the critical point is approached, the susceptibility increases anomalously and fluctuations give rise to dramatic opalescence. Evidence has recently emerged for the existence of a second critical point in the liquid state at supercooled temperatures, below which polyamorphic phases coexist differing in density but sharing the same composition. Whilst much attention has been paid to supercooled water, polyamorphic phases have been observed in many elemental and oxide liquids potentially offering routes to low-entropy glasses. Our recent direct observation of a polyamorphic phase transition in levitated molten yttria-alumina offers the first opportunity to study the associated critical point in a real supercooled system. In situ small-angle X-ray scattering records sharp rises in the average correlation length of density fluctuations and in the compressibility as the transition is approached. Both increases approximate to the universal power-law relations predicted by the three-dimensional Ising model in common with all critical point phenomena. The observation brings the second critical point predicted in liquids into line with other critical phenomena. 1. Introduction Supercooled liquids are antecedents of the vitreous and crystalline states and their vast application, which stretches from glass making and ceramic fabrication to steel production (Zarzycki 1991), derives from the increasingly complex structural behaviour that develops as liquids that are initially homogeneous cool below the melting point with rising viscosity and density (Greaves & Sen 2007). In particular, statistical fluctuations in density, which generally decrease in amplitude as the temperature falls and the bulk modulus rises (Landau & Lifshitz 1969), become non-ergodic in the supercooled state (Scopigno et al. 2003) with the emergence of slow processes which bifurcate from the fast processes of the thermodynamic liquid and influence the onset of the glass transition (Greaves & Sen 2007; Götze 1999).