Polyamorphism and liquid-liquid phase transitions: challenges for experiment and theory

Phase transitions in the liquid state can be related to pressure-driven fluctuations developed in the density (i.e., the inverse of the molar volume; ρ = 1/V) or the entropy (S(T)) rather than by gradients in the chemical potential (μ(X), where X is the chemical composition). Experiments and liquid simulation studies now show that such transitions are likely to exist within systems with a wide range of chemical bonding types. The observations permit us to complete the trilogy of expected liquid state responses to changes in P and T as well as μ(X), as is the case among crystalline solids. Large structure-property changes occurring within non-ergodic amorphous solids as a function of P and T are also observed, that are generally termed 'polyamorphism'. The polyamorphic changes can map on to underlying density- or entropy-driven L-L transitions. Studying these phenomena poses challenges to experimental studies and liquid simulations. Experiments must be carried out over a wide P-T range for in situ structure-property determinations, often in a highly metastable regime. It is expected that L-L transitions often occur below the melting line, so that studies encounter competing crystallization phenomena. Simulation studies of liquid state polyamorphism must involve large system sizes, and examine system behaviour at low T into the deeply supercooled regime, with distance and timescales long enough to sample characteristic density/entropy fluctuations. These conditions must be achieved for systems with different bonding environments, that can change abruptly across the polyamorphic transitions. Here we discuss opportunities for future work using simulations combined with neutron and x-ray amorphous scattering techniques, with special reference to the behaviour of two polyamorphic systems: amorphous Si and supercooled Y₂O₃-Al₂O₃ liquids.