A thermodynamic description of the glass state and the glass transition

Many properties of solids, such as the glass state, hysteresis, and memory effects, are commonly treated as nonequilibrium phenomena, which involve numerous conceptual difficulties. However, few studies have addressed the problem of understanding equilibrium itself. Equilibrium is often assessed based on the assumption that its thermodynamic state should be solely determined using temperature and pressure. However, this assumption must be fundamentally reappraised from the beginning because no rigorous proof for this assumption exists. Previous work showed that for solids, the time-averaged positions of all constituent atoms of the solid are thermodynamic coordinates (TCs). In this study, this conclusion is further elaborated starting from the principles of solid-state physics. This theory is applied to glass materials, for which many challenges remain. Results show that first, the glass state, which is the state after freezing, is an equilibrium state under given constraints. Accordingly, the properties of a glass can be solely described using the present time-averaged atom positions, irrespective of their history, which is consistent with the definition of a state in the thermodynamic context. Any quantity that is determined using TCs can be used as an order parameter. Second, although the traditional view that the transition state during the glass transition is a nonequilibrium state is correct, whether it reaches the supercooled-liquid state given sufficient time is highly questionable. The final state must be an inhomogeneous mixture of solid and liquid phases. In the liquid phase, the atom positions are missing from the set of TCs. The degeneration of the state space occurs, which corresponds to an increase in configuration entropy. Conversely, when the phonon and structural parts of the atom positions are well separated, the time-averaged atom positions in the solid part remain as TCs. In this manner, the transition state can be described using a reduced set of TCs as a function of time. An important outcome of this theory is that the hysteresis of the glass transition can be described using the present values of TCs through the structural-dependent energy barrier. Complicated response functions describing the history, which are widely used in glass literature, are unnecessary. The expense of this simplification is that, in a rigorous sense, all the atom positions are needed for TCs. However, in most cases, only a few TCs are sufficient to describe the transition state, if these TCs are suitably chosen.