Statistics of modifier distributions in mixed network glasses

The constituents of any network glass can be broadly classified as either network formers or network modifiers. Network formers, such as SiO₂, Al₂O₃, B₂O₃, P₂O ₅, etc., provide the backbone of the glass network and are the primary source of its rigid constraints. Network modifiers play a supporting role, such as charge stabilization of the network formers or alteration of the network topology through rupture of bridging bonds and introduction of floppy modes. The specific role of the modifiers depends on which network formers are present in the glass and the relative free energies of modifier interactions with each type of network former site. This variation of free energy with modifier speciation is responsible for the so-called mixed network former effect, i.e., the nonlinear scaling of property values in glasses having fixed modifier concentration but a varying ratio of network formers. In this paper, a general theoretical framework is presented describing the statistical mechanics of modifier speciation in mixed network glasses. The model provides a natural explanation for the mixed network former effect and also accounts for the impact of thermal history and relaxation on glass network topology.