Predicting glass properties from structure data and intermolecular forces

Beside energy, entropy is a basic property determining the relative stability of different states of matter. For glass both properties cannot be determined by measuring energy exchange with the surroundings. However, given interaction potentials, both energy and entropy can be determined from molecular distributions. The entropy function S=S(E) is related to structure by ∂2S/∂E2=−〈(ΔE)2〉−1, where 〈(ΔE)2〉 are the spatial energy fluctuations, expressible in terms of low order molecular distributions. The functional dependence on E implies certain constraints kept fixed while the energy E is varied. Such constraints are controllable by external forces when the system is in internal equilibrium, or can be explicitly introduced in computer experiments, but are only assumed to exist in the case of glass, practically preventing it from changing with time, although the glass phase is unstable in principle. Integration of the differential equation for S(E) is performed with the aid of a modeling of the radial distribution g(r) in form of a parametrized analytic function, g(r)=g(r;L,D), where L is a lattice characterizing the dominant local configurations of atoms and D is a `structural diffusionʹ parameter specifying the degree of spatial decay of coherence between local structures. The modeling provides a representation of structure by a point in the low dimensional parameter space {L,D}. This space includes also the ordered state (L)≡(L,0), for which S=S(L)=0, as follows from the third law of thermodynamics. Thus integration can be performed along a (virtual) path connecting (L,D) to (L,0). The method is illustrated by evaluating the entropy of a model metal in the liquid and glass state.