On the Definition of a Monte Carlo Model for Binary Crystal Growth

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.

Long-timescale simulations of diffusion in molecular solids

“…These restructuring processes are central to many fields and environments, e.g., ice layers on dust particles in the atmosphere and enantiomer separation 2 . In all cases, understanding the restructuring mechanism will shed light on the nature of the entire system 3 . In atmospheric chemistry it is well recognized that small aerosol particles and a Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.…”

“…2 In all cases, understanding the restructuring mechanism will shed light on the nature of the entire system. 3 In atmospheric chemistry it is well recognized that small aerosol particles and ice crystals are involved as catalysts in the conversion of many molecules. Understanding these reactions is crucial to gain insight into greenhouse-gas chemistry.…”

Quantification of segregation dynamics in ice mixtures

“…Monte Carlo simulations are used to qualitatively investigate ice segregation through two different diffusion mechanisms. The stochastic method employed here builds on the lattice-gas Monte Carlo technique used by Los et al (2006Los et al ( , 2007 and Cuppen & Herbst (2007). In the simulations CO 2 and H 2 O molecules are followed individually as a function of time, both position and environment, as they diffuse through the ice and desorb from it.…”

Growth of Crystal Faces Enhanced by 3D Nuclei Deposition: A Monte Carlo Simulation

“…This is the socalled "random rain model" introduced by others. 2,29 Here, the number of arrivals per unit time and surface area is only determined by the concentration and the diffusion coefficient of the growth units in the mother phase. If the number of available sites varies during growth and/or the probability of addition depends on the type of surface site, another approach is needed to evaluate time.…”

“…As the rate of creation, k + , is assumed to be independent of the type of surface site and, in addition, due to the SOS condition, the number of surface sites available for creation is constant, the number of additions is proportional with time. This is the so-called “random rain model” introduced by others. , Here, the number of arrivals per unit time and surface area is only determined by the concentration and the diffusion coefficient of the growth units in the mother phase. If the number of available sites varies during growth and/or the probability of addition depends on the type of surface site, another approach is needed to evaluate time …”