Statistical mechanics of permanent random atomic and molecular networks: Structure and heterogeneity of the amorphous solid state

Under sufficient permanent random covalent bonding, a fluid of atoms or sma ll molecules is transformed into an amorphous solid network. Being amorphou s, local structural properties in such networks vary across the sample. A n atural order parameter, resulting from a statistical-mechanical approach. c aptures information concerning this heterogeneity via a certain joint proba bility distribution. This joint probability distribution describes the vari ations in the positional and orientational localization of the particles, r eflecting the random environments experienced by them, as well as further i nformation characterizing the thermal motion of particles. A complete solut ion, valid in the vicinity of the amorphous solidification transition, is c onstructed essentially analytically for the amorphous solid order parameter , in the context of the random network model and approach introduced by Gol dbart and Zippelius [Europhys. Lett. 27, 599 (1994)]. Knowledge of this ord er parameter allows us to draw certain conclusions about the stucture and h eterogeneity of randomly covalently bonded atomic or molecular network soli ds in the vicinity of the amorphous solidification transition. Intel alia, the positional aspects of particle localization are established to have pre cisely the structure obtained previously in the context of vulcanized media , and results are found for the analog of the spin glass order parameter de scribing the orientational freezing of the bonds between particles. [S0163- 1829(99)12229-X].