We describe a numerical model of faceted crystal growth using a cellular automata method. The model was developed for investigating the diffusion-limited growth of ice crystals from water vapor, when the surface boundary conditions are determined primarily by strongly anisotropic molecular attachment kinetics. We restricted our model to cylindrically symmetric crystal growth with relatively simple growth morphologies, as this was sufficient for making quantitative comparisons between models and ice growth experiments. Overall this numerical model appears to reproduce ice growth behavior with reasonable fidelity over a wide range of conditions. More generally, the model could easily be adapted for other material systems, and the cellular automata technique appears well suited for investigating crystal growth dynamics when strongly anisotropic surface attachment kinetics yields faceted growth morphologies. 1. Introduction The formation of crystalline structures during solidification yields a remarkable variety of morphological behaviors, resulting from the often subtle interplay of nonequilibrium physical processes over a range of length scales. In many cases, seemingly small changes in surface molecular structure and dynamics at the nanoscale can produce large morphological changes at all scales. Some examples include free dendritic growth from the solidification of melts, where small anisotropies in the interfacial surface energy govern the overall characteristics of the growth morphologies [1, 2], whisker growth from the vapor phase initiated by single screw dislocations and other effects [3], the formation of porous aligned structures from directional freezing of composite materials [4], and a range of other pattern formation systems [5, 6]. Since controlling crystalline structure formation during solidification has application in many areas of materials science, much effort has been directed toward better understanding the underlying physical processes and their interactions. We have been exploring the growth of ice crystals from water vapor in an inert background gas as a case study of how complex faceted structures emerge in diffusion-limited growth. Although this is a relatively simple monomolecular physical system, ice crystals exhibit columnar and plate-like growth behaviors that depend strongly on temperature, and much of the phenomenology of their growth remains poorly understood [7–9]. Ice has also become something of a standard test system for investigating numerical methods of faceted crystal growth [10, 11]. A better understanding of ice
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