Structure–entropy relationship in repulsive glassy systems

The entropy of glass can be evaluated from the experimental structure data and given laws of intermolecular forces. The method is based on the functional relation ∂2S/∂E2=− (ΔE)2 −1, which connects the entropy function S=S(E) to structure via the energy E and the spatial energy fluctuations (ΔE)2 . This method, previously applied to a model cohesive system, is extended to strong repulsive systems. In cohesive systems at low thermal temperature, E is mainly potential energy which can be determined from pair potentials and molecular pair distributions. In contrast, in strong repulsive systems, characteristic of systems subject to high external pressure, E is mainly kinetic and its dependence on structure can be derived only by quantum mechanics which relates the strong repulsive forces to an effective volume available for molecular motion. This dependence has a form peculiar to the wave nature of the particles, and is illustrated by a cell model treatment of a disordered dense packed hard spheres system. In the low thermal temperature limit, it leads to an entropy independent of Planckʹs constant and of the particle mass. To integrate the above equation we use a model of the radial distribution g(r) in the form of an analytic function, g(r)=g(r;L,D), where L is a set of parameters specifying a lattice characterizing the dominant local configurations of atoms and D is a “structural diffusion” parameter providing a measure of the degree of spatial decay of coherence between local structures in the amorphous system and the degree of structural disorder. The model provides a representation of structure by a point in the low dimensional parameter space {L,D}. Integration is performed along a path connecting the ordered state (L,0) to (L,D). Whereas S=S(D) increases with D, for strongly repulsive systems E=E(D) decreases with D, leading to an ordered state with highest energy. This implies a transition from an ordered to a more stable amorphous phase, in accordance with the observed phenomenon of high pressure induced amorphization, a transition under high pressure and low temperatures from a crystalline to an amorphous state.