On the
definition of a Monte Carlo model for binary crystal growth
Los JH (Los, J. H.), van Enckevort WJP (van Enckevort, W. J. P.),
Meekes H (Meekes, H.), Vlieg E (Vlieg, E.)
J. Phys. Chem. B 111 (2007) 782-791
Abstract:
We show that consistency of the transition probabilities in a lattice
Monte Carlo ( MC) model for binary crystal growth with the
thermodynamic properties of a system does not guarantee the MC
simulations near equilibrium to be in agreement with the thermodynamic
equilibrium phase diagram for that system. The deviations remain small
for systems with small bond energies, but they can increase
significantly for systems with large melting entropy, typical for
molecular systems. These deviations are attributed to the surface
kinetics, which is responsible for a metastable zone below the liquidus
line where no growth occurs, even in the absence of a 2D nucleation
barrier. Here we propose an extension of the MC model that introduces a
freedom of choice in the transition probabilities while staying within
the thermodynamic constraints. This freedom can be used to eliminate
the discrepancy between the MC simulations and the thermodynamic
equilibrium phase diagram. Agreement is achieved for that choice of the
transition probabilities yielding the fastest decrease of the free
energy (i.e., largest growth rate) of the system at a temperature
slightly below the equilibrium temperature. An analytical model is
developed, which reproduces quite well the MC results, enabling a
straightforward determination of the optimal set of transition
probabilities. Application of both the MC and analytical model to
conditions well away from equilibrium, giving rise to kinetic phase
diagrams, shows that the effect of kinetics on segregation is even
stronger than that predicted by previous models.