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 functio nal relation partial derivative S-2/partial derivativeE(2) = - <(DeltaE)(2) > (-1), which connects the entropy function S = S(E) to structure via the e nergy E and the spatial energy fluctuations <(DeltaE)(2)>. This method, pre viously applied to a model cohesive system, is extended to strong repulsive systems. In cohesive systems at low thermal temperature, E is mainly poten tial 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 dep endence 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 part icles, and is illustrated by a cell model treatment of a disordered dense p acked hard spheres system. In the low thermal temperature limit, it leads t o an entropy independent of Planck's 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 se t of parameters specifying a lattice characterizing the dominant local conf igurations of atoms and D is a "structural diffusion" parameter providing a measure of the degree of spatial decay of coherence between local structur es in the amorphous system and the degree of structural disorder. The model provides a representation of structure by a point in the low dimensional p arameter 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 strong ly 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 s table amorphous phase, in accordance with the observed phenomenon of high p ressure induced amorphization, a transition under high pressure and low tem peratures from a crystalline to an amorphous state. (C) 2001 Elsevier Scien ce B.V. All rights reserved.