An energy-landscape-based crossover temperature in glass-forming liquids

The systematic identification of temperature scales in supercooled liquids that are key to understanding those liquids' underlying glass properties, and their formation-history dependence, is a challenging task. Here, we study the statistics of particles' squared displacements δr² between equilibrium liquid configurations at temperature T and their underlying inherent states, using computer simulations of 11 different computer glass formers. We show that the relative fluctuations of δr² are nonmonotonic in T, exhibiting a maximum whose location defines the crossover temperature T_X. Therefore, T_X marks the point of maximal heterogeneity during the process of tumbling down the energy landscape, starting from an equilibrium liquid state at temperature T down to its underlying inherent state. We extract T_X for the 11 employed computer glasses, ranging from tetrahedral glasses to packs of soft elastic spheres, and demonstrate its usefulness in putting the elastic properties of different glasses on the same footing. Interestingly, we further show that T_X marks the crossover between two distinct regimes of the mean ⟨δr²⟩: a high temperature regime in which ⟨δr²⟩ scales approximately as T^0.5 and a deeply supercooled regime in which ⟨δr²⟩ scales approximately as T^1.3. Further research directions are discussed.