Statistical mechanical model of the self-organized intermediate phase in glass-forming systems with adaptable network topologies

Non-equilibrium systems continuously evolve toward states with a lower free energy. For glass-forming systems, the most stable structures satisfy the condition of isostaticity, where the number of rigid constraints is exactly equal to the number of atomic degrees of freedom. The rigidity of a system is based on the topology of the glass network, which is affected by atomistic structural rearrangements. In some systems with adaptable network topologies, a perfect isostatic condition can be achieved over a range of compositions, i.e., over a range of different structures, giving rise to the intermediate phase of optimized glass formation. Here we develop a statistical mechanical model to quantify the width of the intermediate phase, accounting for the rearrangement of the atomic structure to relax localized stresses and to achieve an ideal, isostatic state.