Revisiting nonequilibrium characterization of glass: History dependence in solids

TL;DR

This paper reexamines the nature of glass as a nonequilibrium material, emphasizing the importance of appropriate state variables like time-averaged atomic positions to understand its history dependence.

Contribution

It proposes that time-averaged atomic positions serve as proper state variables for solids, including glass, clarifying the role of microstructures and relaxation times in nonequilibrium thermodynamics.

Findings

Time-averaged atomic positions are invariant state variables.

History dependence in glass relates to microstructure and relaxation times.

Equilibrium states are local and metastable in solids.

Abstract

Glass has long been considered a nonequilibrium material. The primary reason is its history-dependent properties: the obtained properties are not uniquely determined by two state variables alone, namely, temperature and volume, but are affected by the process parameters, such as cooling rates. However, closer observations show that this history dependence is common in solid; in crystal growth, the properties of an obtained crystal are affected by the preparation conditions through defect structures and metallurgical structures. The problem with the previous reasoning of history dependence lies in the lack of appropriate specification of state variables. Without knowledge of the latter, describing thermodynamic states is impossible. The guiding principle to find state variables is provided by the first law of thermodynamics. The state variables of solids have been searched by requiring that the internal energy $U$ is a state function. Detailed information about the abovementioned microstructures is needed to describe the state function $U$. This can be accomplished by specifying the time-averaged positions R_{j} of all atoms comprising the solids. Therefore, R_{j} is a state variable for solids. Defect states, being metastable states, represent equilibrium states within a finite time (relaxation time). However, eternal equilibrium is nonexistent: the perfect crystal is thermodynamically unstable. Equilibrium states can only be considered at the local level. Glass is thus in equilibrium as long as its structure does not change. The relaxation time is controlled by the energy barriers by which a structure is sustained, and this time restriction is intimately related to the definition of state variables. The most important property of state variables is their invariance to time averaging. The time-averaged quantity R_{j} meets this invariance property.