Ideal and cooperative bond-lattice representations of excitations in glass-forming liquids: Excitation profiles, fragilities, and phase transitions

We use the one-component equivalent of an ideal solution to show how an "el ementary excitations" treatment of the thermal behavior of a glass-forming liquid can reproduce the observations of experiments and computer simulatio ns on the excitation of simple liquids and also provide a testable explanat ion of the origin of so-called "fragile-liquid" behavior. We then introduce a treatment of interacting excitations in the one-component system, which is formally similar to the regular-solution treatment of nonideal binary so lutions, in order to model co-operativity in the excitation process. This r efinement permits us to understand the changes in liquid properties in cova lently bonded binary systems such as Ge-Se, which occur as the average numb er of bonds per atom exceeds the value of 2.4. The bond density of 2.4 has been identified by the constraint-counting theory as the rigidity percolati on threshold, and overconstraining at higher bond densities induces coopera tivity in the thermal excitation process. The treatment further predicts a liquid-liquid phase transition for strongly overconstrained networks, which we identify with the amorphous-phase "melting" phenomenon reported by expe rimentalists for Ge and Si. The treatment suggests that glasses formed in t hese systems by various routes, of which cooling through the liquid-liquid transition is only one, may be in very low states of configurational excita tion, which would correlate with the remarkable absence of the "ubiquitous" boson peaks and tunneling excitations from such glasses.