Modulated order and unconventional phase coexistence in a model for lattice mismatched solids

Lattice mismatch is a common occurrence in modern materials, but just how it influences the arrangement of atoms in materials is incompletely understood. Here we consider a simple microscopic model for lattice mismatch, in which the difference in natural bond lengths between atoms produces interactions mediated by elastic strain. Monte Carlo simulations reveal that the model exhibits rich phase behavior, supporting structures with modulated order and unusual coexistence scenarios. To explain this phase behavior, we derive an effective pair potential between atoms, revealing preferred spatial arrangements of atoms driven by spatial variations in the interaction energy. Based on this effective interaction, we then develop a mean field theory, which captures the modulated structures observed in our simulations. Finally, we explain the observed coexistence scenarios using a modified Maxwell construction, which is based on the realization that the free energy cost of phase separation in elastic systems is extensive. These results clarify the equilibrium effects of lattice mismatch in macroscopic solids and suggest a role for lattice mismatch in creating spatially heterogeneous compositions in nanoscale materials.