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 'elementary excitations' treatment of the thermal behavior of a glass-forming liquid can reproduce the observations of experiments and computer simulations on the excitation of simple liquids and also provide a testable explanation 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 solutions, in order to model co-operativity in the excitation process. This refinement permits us to understand the changes in liquid properties in covalently bonded binary systems such as Ge-Se, which occur as the average number 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 percolation threshold, and overconstraining at higher bond densities induces cooperativity 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 experimentalists for Ge and Si. The treatment suggests that glasses formed in these systems by various routes, of which cooling through the liquid-liquid transition is only one, may be in very low states of configurational excitation, which would correlate with the remarkable absence of the 'ubiquitous' boson peaks and tunneling excitations from such glasses.