# Elasticity and Thermodynamics of Metallic Liquids, Glasses, and Crystals

Glasses exhibit continuum elasticity and thermodynamic properties well described by the traditional Debye-Gruneisen theory of solids. In the corresponding liquids, atoms sample many stable configurational states, each corresponding to a particular stable "solid" arrangement with its own characteristic elastic properties. Metallic liquids sample these configurations through thermally activated hopping events in which local atomic clusters jump between pairs of stable conformations. This configurational hopping is kinetically frozen out at the glass transition. The high frequency (exceeding the hopping rate) elastic properties of real liquids can be experimentally probed by ultrasonic measurements that measure "iso-configurational" elasticity constants. These data are surveyed in the talk. A simple two-state "buckle mode" model is proposed to describe the elementary configurational entropy of the liquid. The stable conformations of the liquid are built up from a sequence of these spatially localized "string-like" buckling events. The model divides the splitting energy of the two-state "buckle mode" into a "free buckle" transformation energy plus an "Eshelby" elastic compatibility strain energy term. The latter is associated with embedding the "free buckle" into an "average" linear elastic medium having temperature dependent elastic constants. A self-consistent "mean-field" approach is then used to solve for the temperature-dependent thermodynamics and elasticity of the liquid. The model predicts a liquid-liquid phase transition in the limit where the Eshelby compatibility strain energy dominates the "free buckle" transformation energy. This corresponds to limit of a "fragile liquid".

**Series:**Materials Research Lecture Series