Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids
Lattice mismatch - the difference in natural bond length between two species comprising a solid is a common occurrence in modern materials. Spatial patterns in certain nanocrystal heterostructures, for instance, are thought to be a result of elastic forces arising from lattice mismatch. However, the role of lattice mismatch in mediating the arrangement of atoms in such materials is incompletely understood. Here we consider a simple microscopic model for lattice mismatch, in which the difference in natural lengths between bonded atoms produces interactions mediated by elastic strain. Computer simulations reveal that the model exhibits rich phase behavior, including structures with periodic order and unusual coexistence scenarios. To explain this phase behavior, we derive an effective pairwise interaction potential between atoms, revealing preferred spatial arrangements of atoms driven by spatial variations in the interaction potential. We then develop a mean field theory based on this effective interaction which qualitatively captures observed transition to phases with modulated order. Finally, we explain the observed scenarios of coexistence between using a graphical construction, based on the realization that the free energy cost of phase separation in elastic systems grows with system size. Here, 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.
- Research Organization:
- University of California, Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1572233
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 13 Vol. 123; ISSN 0031-9007; ISSN PRLTAO
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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