Most clouds that have regions below about -5 Celsius contain small ice crystals. Once they form, how do these crystals grow? Standard models used heretofore by the atmospheric sciences community contain serious deficiencies including an incorrect crystal shape and an incorrect surface boundary condition. The work presented here instead starts with the assumptions of the terrace, ledge, kink model of crystal surfaces and models the ice crystal with flat crystal faces. Three such models are proposed, each designed for specific conditions that depend on the values of presently poorly constrained surface parameters. The model likely to be applicable to the widest range of environmental conditions involves coupled surface and vapor diffusion to a cylindrically shaped crystal, which is a good approximation to a hexagonal prism. For this model, some of the predictions for the evolution of crystal shape are shown to be consistent with observations. Also presented are models for the influence of impurities on growth and sublimation as well as a model for the behavior of surface parameters when the adsorbed surface layer includes lateral interactions. The latter model predicts a sharp transition in the mean surface diffusion distance similar to that found by Mason et al. in 1963.
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