Monte Carlo Simulations of Commensurate-incommensurate Transitions

We have extended the work of Frank and van der Merwe on the commensurate-incommensurate transition (C-IC transition) of a one-dimensional harmonic system in the field of a periodic potential by computer simulation. Our system includes: 1) a finite range of temperatures covering the entire range of the stable solid, 2) a full consideration of the anharmonicity, and 3) the consideration of both temperature and pressure-driven C-IC transitions. For the system without the periodic substrate, we have found the sublimation line, triple line, critical temperature, and the existence of the liquid state in one-dimension. The pressure driven transition studies show equilibrated solid phases that are registered, heavy walled, and free floating. Two-phase coexistence regions appear to occur between these phases. We found, for the temperature driven process at low pressure, registered and light walled structures. These phases are apparently separated by a two phase coexistence region. A free floating phase is preempted by traditional melting to a fluid phase.