Dual properties of conjugate disclination segment networks in amorphous materials

Abstract

We extend some recent results concerning the structural properties of amorphous materials deduced from a model in which the frustration effects leading to non-crystallographic short-range order are described by curved spaces [1]. It is proposed that the final structure obtained from the « best » mapping from curved space consists in two conjugate irregular networks of straight segments, which are sources of distortions of opposite signs and of the elastic disclination type. Also, each network carries either spherical or hyperbolic curvature, in the sense that they correspond to different coordination numbers for the atoms. The typical size ξ of the network unit is estimated from a balance of (internal) elastic stresses and of core energies, at low temperature; at higher temperatures (above a typical To temperature definitely smaller than Tm) the networks are mobile and their entropy must be taken into account, which leads to a dependence of ξ with temperature. Analogy and differences with a usual Vogel-Fulcher law are outlined, and the existence of some sort of long-range orientational order stressed