Dislocation-mediated melting is studied in a model of a free bilayer with an interlayer potential of the form -Vcos($p_1$${\theta }_1$-$p_2$${\theta }_2$). The model can describe the behavior of two adsorbed layers of different atoms, both layers being incommensurate with the substrate or a monolayer on a periodic substrate where elastic deformations of the substrate are also allowed. Depending on the ratio of the elastic constants, temperature, and lattice mismatch, a rich phase diagram with locked, unlocked, liquid, or partial liquid phases are possible. If the elastic constants of each layer are not too different, for $p_1$=$p_2$=1, a liquid phase separates the locked from the unlocked phase, even at low temperatures, and for $p_1$=1, $p_2$=2, a partial liquid phase, where only the second layer is melted, separates the locked from the unlocked phase at low temperatures.

• Received 21 July 1988

DOI:https://doi.org/10.1103/PhysRevB.39.4444