  The dynamical properties and mechanical functions of amorphous materials are
governed by their microscopic structures, particularly the elasticity of the
interaction networks, which is generally complicated by structural
heterogeneity. This ubiquitous heterogeneous nature of amorphous materials is
intriguingly attributed to a complex role of entropy. Here, we show in
disordered networks that the vibrational entropy increases by creating
phase-separated structures when the interaction connectivity is close to the
onset of network rigidity. The stress-energy, which conversely penalizes the
heterogeneity, finally dominates a smaller vicinity of the rigidity threshold
at the glass transition and creates a homogeneous intermediate phase. This
picture of structures changing between homogeneous and heterogeneous phases by
varying connectivity provides an interpretation of the transitions observed in
chalcogenide glasses.
