A Quantitative Physical Model of the Snow Crystal Morphology Diagram

I describe a semi-empirical molecular model of the surface attachment kinetics governing ice crystal growth from water vapor as a function of temperature, supersaturation, and crystal mesostructure. An important new hypothesis in this model is surface-energy-driven molecular diffusion enabled by a leaky Ehrlich-Schwoebel barrier. The proposed surface-diffusion behavior is sensitive to facet width and surface premelting, yielding structure-dependent attachment kinetics with a complex temperature dependence. By incorporating several reasonable assumptions regarding the surface premelting behavior on basal and prism facets, this model can explain the overarching features of the snow crystal morphology diagram, which has been an enduring scientific puzzle for nearly 75 years.

[1]  K. Libbrecht.  Physical Dynamics of Ice Crystal Growth , 2017 .

[2]  K. Libbrecht.  The Surface Diffusion Length of Water Molecules on Faceted Ice: A Reanalysis of "Roles of Surface/Volume Diffusion in the Growth Kinetics of Elementary Spiral Steps on Ice Basal Faces Grown from Water Vapor", by Asakawa et al , 2015, 1509.06609.

[3]  K. Libbrecht.  An experimental apparatus for observing deterministic structure formation in plate-on-pedestal ice crystal growth , 2015, 1503.01019.

[4]  K. Libbrecht.  Toward a Comprehensive Model of Snow Crystal Growth: 3. The Correspondence Between Ice Growth from Water Vapor and Ice Growth from Liquid Water , 2014, 1407.0740.

[5]  James G Kelly,et al.  Physical improvements to a mesoscopic cellular automaton model for three-dimensional snow crystal growth , 2013, 1308.4910.

[6]  K. Libbrecht,et al.  Measurements of surface attachment kinetics for faceted ice crystal growth , 2013 .

[7]  K. Libbrecht.  Toward a Comprehensive Model of Snow Crystal Growth Dynamics: 2. Structure Dependent Attachment Kinetics near -5 C , 2013, 1302.1231.

[8]  K. Libbrecht.  An Edge-Enhancing Crystal Growth Instability Caused by Structure-Dependent Attachment Kinetics , 2012, 1209.4932.

[9]  K. Libbrecht.  On the Equilibrium Shape of an Ice Crystal , 2012, 1205.1452.

[10]  M. Bailey,et al.  Ice Crystal Linear Growth Rates from −20° to −70°C: Confirmation from Wave Cloud Studies , 2012 .

[11]  M. Bailey,et al.  A Comprehensive Habit Diagram for Atmospheric Ice Crystals: Confirmation from the Laboratory, AIRS II, and Other Field Studies , 2009 .

[12]  D. Griffeath,et al.  Modeling snow-crystal growth: a three-dimensional mesoscopic approach. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Matthew Bailey,et al.  Growth Rates and Habits of Ice Crystals between −20° and −70°C , 2004 .

[14]  K. Libbrecht.  Explaining the formation of thin ice crystal plates with structure-dependent attachment kinetics , 2003 .

[15]  C. Knight,et al.  Snow Crystal Habit Changes Explained by Layer Nucleation , 1998 .

[16]  Kuroda,et al.  Pattern formation in growth of snow crystals occurring in the surface kinetic process and the diffusion process. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[17]  J. Hallett,et al.  Epitaxial ice crystal growth on covellite (CuS) II. Growth characteristics of basal plane steps , 1984 .

[18]  T. Kobayashi.  The growth of snow crystals at low supersaturations , 1961 .

[19]  B. J. Mason,et al.  The influence of temperature and supersaturation on the habit of ice crystals grown from the vapour , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  G. W Sears,et al.  A growth mechanism for mercury whiskers , 1955 .

[21]  Matthew Bierbaum,et al.  Physical Dynamics of Ice Crystal Growth , 2017 .

[22]  B. Sutherland.  The Influence of Temperature and Supersaturation on the Habit of Ice Crystals Grown from the Vapour , 2008 .

[23]  B. Mutaftschiev.  The atomistic nature of crystal growth , 2001 .

[24]  T. Kuroda,et al.  Rate Determining Processes of Growth of Ice Crystals from the Vapour Phase , 1984 .

[25]  T. Kuroda,et al.  Growth kinetics of ice from the vapour phase and its growth forms , 1982 .

[26]  T. Gonda.  The Growth of Small Ice Crystals in Gases of High and Low Pressures , 1976 .

[27]  D. Lamb,et al.  Linear growth rates of ice crystals grown from the vapor phase , 1972 .

[28]  Ukichirō . Nakaya,et al.  Physical Investigations on the Growth of Snow Crystals , 1958 .