Elastic heterogeneity and phase stability under hydrostatic pressure

Structural phase transitions typically arise from differences in the average stiffness, nominal bond length and/or lattice topology between competing structures. We show how heterogeneity in the nominal bond lengths and stiffnesses can shrink and soften a material, thereby favoring a heterogeneous state, even when the average bond length and stiffness are unchanged. We quantify the relationship between lattice coordination, the variance of the local bond stiffnesses and the macroscopic rigidity. We also demonstrate that long-range order in three dimensions can survive perturbative disorder in the nominal bond length.