Patterns in strained-layer heteroepitaxy: Beyond the Frenkel-Kontorova model

The second layer of Ag on Pt (111) is experimentally observed to form a striped dislocation pattern with Ag stripes alternating between fcc and hcp stacking. We address the origins of the stripes with a combination of density-functional theory and Monte Carlo simulations. We find that this dislocation pattern is driven by electronic and anisotropic substrate-mediated interactions associated with the Shockley surface state on Ag (111). Our simulations reveal the quantum mechanical underpinnings of strain-relief patterns, previously described phenomenologically by the classical Frenkel-Kontorova model that is widely used to describe such systems.