I examine a variety of snow crystal growth measurements taken at a temperature of -5 C, as a function of supersaturation, background gas pressure, and crystal morphology. Both plate-like and columnar prismatic forms are observed under different conditions at this temperature, along with a diverse collection of complex dendritic structures. The observations can all be reasonably understood using a single comprehensive physical model for the basal and prism attachment kinetics, together with particle diffusion of water vapor through the surrounding medium and other well-understood physical processes. A critical model feature is structure-dependent attachment kinetics (SDAK), for which the molecular attachment kinetics on a faceted surface depend strongly on the nearby mesoscopic structure of the crystal.
I examine a variety snow crystal growth experiments performed at temperatures near -2 C, as a function of supersaturation, background gas pressure, and crystal morphology. Although the different experimental data were obtained using quite diverse experimental techniques, the resulting measurements can all be reasonably understood using a single comprehensive physical model for the basal and prism attachment kinetics, together with particle diffusion of water vapor through the surrounding medium and other well-understood physical processes. As with the previous paper in this series, comparing a…
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 behavio…
In this paper I examine snow crystal growth near -14 C in comparison with a comprehensive model that includes Structure-Dependent Attachment Kinetics (SDAK). Analyzing a series of ice-growth observations in air, I show that the data strongly support the model, which stipulates that basal growth is described by classical terrace nucleation on faceted surfaces in this temperature region. In contrast, prism growth exhibits a pronounced "SDAK dip" that substantially reduces the nucleation barrier on narrow prism facets (relative to that found on broad prism facets). I use these measurements to fur…
We present experimental data demonstrating the presence of structure-dependent attachment kinetics (SDAK) in ice crystal growth from water vapor near -5 C. Specifically, we find that the nucleation barrier on the basal edge of a thin-walled hollow columnar crystal is approximately ten times smaller than the corresponding nucleation barrier on a large basal facet. These observations support the hypothesis that SDAK effects play an important role in determining the growth morphologies of atmospheric ice crystals as a function of temperature.
I examine the molecular dynamics of ice growth from water vapor, focusing on how the attachment kinetics can be augmented by edge-dependent surface diffusion. Although there are significant uncertainties in developing an accurate physical model of this process, it is possible to make some reasonable estimates of surface diffusion rates and admolecule density enhancements, derived from our basic understanding of ice-crystal growth processes. A quantitative model suggests that edge-dependent surface diffusion could substantially enhance terrace nucleation on narrow faceted surfaces, especially a…
In this paper I examine snow crystal growth near -4 C in comparison with a comprehensive model that includes Structure-Dependent Attachment Kinetics (SDAK). Together with the previous paper in this series that investigated growth near 14 C, I show that a substantial body of experimental data now supports the existence of pronounced 'SDAK dips' on basal surfaces near -4 C and on prism surfaces near -14 C. In both cases, the model suggests that edge-associated surface diffusion greatly reduces the nucleation barrier on narrow facet surfaces relative to that found on broad facets. The remarkable …
Snow crystals growing from water vapor occasionally exhibit morphologies with three-fold (trigonal) symmetry, even though the ice crystal lattice has a molecular structure with six-fold symmetry. In extreme cases, thin platelike snow crystals can grow into faceted forms that resemble simple equilateral triangles. Although far less common than hexagonal forms, trigonal snow crystals have long been observed both in nature and in laboratory studies, and their origin has been an enduring scientific puzzle. In this paper I describe how platelike trigonal structures can be grown on the ends of slend…
We present measurements of the diffusion-limited growth of ice crystals from water vapor at a temperature of -5 C, in air at a pressure of $p_{air}=1$ bar. Starting with thin, c-axis ice needle crystals, the subsequent growth morphologies ranged from solid prismatic columns to hollow columns to complex "fishbone" dendritic structures as the supersaturation was increased. We modeled the simpler morphologies using analytical techniques together with a cellular-automata method that yields faceted crystalline structures in diffusion-limited growth. We found that the molecular attachment coefficien…
This monograph reviews our current understanding of the physical dynamics of ice crystal growth, focusing on the spontaneous formation of complex structures from water vapor (called snow crystals) as a function of temperature, supersaturation, background gas pressure, and other extrinsic parameters. Snow crystal growth is a remarkably rich and rather poorly understood phenomenon, requiring a synthesis of concepts from materials science, crystal-growth theory, statistical mechanics, diffusion-limited solidification, finite-element modeling, and molecular surface processes. Building upon recent …
We examine ice crystal growth from water vapor at temperatures near the melting point, when surface premelting creates a quasiliquid layer at the solid/vapor interface. Recent ice growth measurements as a function of vapor supersaturation have demonstrated a substantial nucleation barrier on the basal surface at these temperatures, from which a molecular step energy can be extracted using classical nucleation theory. Additional ice growth measurements from liquid water as a function of supercooling exhibit a similar nucleation barrier on the basal surface, yielding about the same molecular ste…
I describe a new approach to the classification of snow crystal morphologies that focuses on the most common growth behaviors that appear in normal air under conditions of constant applied temperature and water-vapor supersaturation. The resulting morphological structures are generally robust with respect to small environmental changes and thus should be especially amenable to computational modeling. Because spontaneous structure formation depends on initial conditions, the choice of seed crystal can be an important consideration, and I have found that slender c-axis ice needles provide an exc…
We describe a comprehensive model for the formation and morphological development of atmospheric ice crystals growing from water vapor, also known as snow crystals. Our model derives in part from empirical measurements of the intrinsic ice growth rates as a function of temperature and supersaturation, along with additional observations and analyses of diffusion-driven growth instabilities. We find that temperature-dependent conformational changes associated with surface melting strongly affect layer nucleation dynamics, which in turn determines many snow-crystal characteristics. A key feature …
We present observations of the formation of plate-like snow crystals that provide evidence for an edge-enhancing crystal growth instability. This instability arises when the condensation coefficient describing the growth of an ice prism facet increases as the width of the facet becomes narrower. Coupled with the effects of particle diffusion, this phenomenon causes thin plate-like crystals to develop from thicker prisms, sharpening the edges of the plates to micron or sub-micron dimensions as they grow. This sharpening effect is largely responsible for the formation of thin plate-like ice crys…
The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to blame for this failure. Here, we study the growth of fractal nanostructures in a two-dimensional (2D) system, intercalated between mica and graphene. Based on our Scanning Tunneling Spectroscopy (STS) data we provide compelling evidence that these fractals are 2D ice. They grow while they are in material contact with the atmosphere at 20 $^{\circ}$C and with…
We describe a novel crystal growth instability that enhances the development of thin edges, promoting the formation of plate-like or hollow columnar morphologies. This instability arises when diffusion-limited growth is coupled with structure-depdendent attachment kinetics, specifically when the nucleation barrier on a facet surface decreases substantially as the facet width approaches atomic dimensions. Experimental data are presented confirming the presence of this instability in the growth of ice from water vapor at -15 C. We believe this edge-enhancing effect plays an important role in det…
We present measurements of the diffusion-limited growth of ice crystals from water vapor at different supersaturation levels in air at a temperature of -15 C. Starting with thin, c-axis ice needle crystals, the subsequent growth morphologies ranged from blocky structures on the needle tips (at low supersaturation) to thin faceted plates on the needle tips (at high supersaturation). We successfully modeled the experimental data, reproducing both growth rates and growth morphologies, using a cellular-automata method that yields faceted crystalline structures in diffusion-limited growth. From thi…
I describe an adaptable apparatus for making precision measurements of the growth of faceted ice prisms from water vapor as a function of temperature, supersaturation, and background gas pressure. I also describe procedures for modeling growth data to disentangle a variety of physical effects and better understand systematic errors and measurement uncertainties. By enabling precise ice-growth measurements over a broad range of environmental conditions, this apparatus is well suited for investigating the molecular attachment kinetics at the ice/vapor interface, which is needed to understand and…
We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed for investigating the diffusion-limited growth of ice crystals in air from water vapor, where the combination of bulk diffusion and strongly anisotropic molecular attachment kinetics yields complex faceted structures. We restricted the present model to cylindrically symmetric crystal growth with relatively simple growth morphologies, as this was sufficient …
We present a series of experiments investigating the growth of ice crystals from water vapor in the presence of a background gas. We measured growth dynamics at temperatures ranging from -2 C to -25 C, at supersaturations between 0.5 and 30 percent, and with background gases of nitrogen, argon, and air at a pressure of one bar. We compared our data with numerical models of diffusion-limited growth based on cellular automata to extract surface growth parameters at different temperatures and supersaturations. These data represent a first step toward obtaining precision ice growth measurements as…
We have investigated the morphological evolution of laboratory new snow under isothermal conditions at different temperatures $T=-3,-9,-19 ^{\circ}C$ by means of X-ray tomography. The collective dynamics of the bicontinuous ice-vapor system is monitored by the evolution of the two-point (density) correlation function $C(\mathbf{r},t)$ and a particular thickness distribution which is similar to a pore size distribution. We observe the absence of dynamic scaling and reveal fundamentally different classes of length scales: The first class comprises the mean ice thickness and the (inverse) specifi…
Ice crystals growing in highly supersaturated air at temperatures near -5 C exhibit a distinctive, nonplanar dendritic morphology that has not been previously documented or explained. We examine this structure and identify its most prominent features in relation to the ice crystal lattice. Developing a full 3D numerical model that reproduces this robust morphology will be an interesting challenge in understanding diffusion-limited crystal growth in the presence of highly anisotropic surface attachment kinetics.
We describe how surface interactions can affect the growth of ice crystal facets in contact with a substrate by lowering the normal nucleation barrier on the ice surface. We also describe how the resulting enhanced growth rates can produce systematic errors even when measuring the growth of facets not contacting the substrate. From an analysis of the diffusion dynamics we then develop a simple procedure for approximately correcting ice growth data, thus substantially reducing these systematic errors. We have found this technique to be quite useful for interpreting ice growth data and extractin…
We examine the molecular dynamics of crystal growth in the presence of surface melting and surface impurities, and from this propose a detailed microscopic model for the growth of ice from the vapor phase. Our model naturally accounts for many aspects of the experimental data that are otherwise difficult to explain, and it suggests a variety of measurements that can provide further confirmation. Although additional work is needed to refine these ideas, we believe that the combined influences of surface melting and impurities provide a viable solution to the 60-year-old mystery of why snow crys…
Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and anisotropic attachment kinetics. It is by now well understood that the morphological stability of ice crystals strongly depends on supersaturation, crystal size and temperature. Until very recently it was very difficult to perform numerical simulations of this highly anisotropic crystal growth. In particular, obtaining facet growth in combination with dendritic bran…
We examine the shape of a an isolated, dislocation-free ice crystal when it is in equilibrium with the vapor phase in an isothermal closed environment, as a function of temperature. From our analysis we draw the following conclusions: 1) The equilibrium shape has not yet been definitively measured for ice crystals; 2) The surface energy anisotropy is likely cusp-like near the facet angles, and the size of the cusps can be estimated from crystal growth measurements; 3) The equilibrium shape is likely nearly spherical with only small faceted regions; 4) The time needed to reach equilibrium is li…
We propose a new type of morphological instability in the diffusion-limited growth of faceted crystals from the vapor phase that can explain the formation of thin ice plates at temperatures near -15 C. The instability appears when the attachment kinetics for facet growth depends strongly on the morphology of the facet surface. In particular, we propose that the condensation coefficient for growth of ice prism facets increases dramatically when the width of the facet approaches atomic dimensions. This model reconciles several conflicting measurements of ice crystal growth, and makes additional …
With climate modeling predicting a raise of at least 2 C by year 2100, the fate of ice has become a serious concern, but we still do not understand how ice grows (or melts). In the atmosphere, crystal growth rates of basal and prismatic facets exhibit an enigmatic temperature dependence, and crossover up to three times in a range between 0 and -40 C. Here we use large scale computer simulations to characterize the ice surface and identify a sequence of novel phase transitions on the main facets of ice crystallites. Unexpectedly, we find that as temperature is increased, the crystal surface tra…
We present measurements of the growth rates of the principal facet surfaces of ice from water vapor as a function of supersaturation over the temperature range -2 C > T > -40 C. Our data are well described by a dislocation-free layer-nucleation model, parameterized by the attachment coefficient as a function of supersaturation α(σ) = Aexp(-σ_0/σ). The measured parameters A(T) and σ_0(T) for the basal and prism facets exhibit a complex behavior that likely originates from structural changes in the ice surface with temperature, in particular the onset and development of surface melting for T > -…
Water wetting on a hydrophobic surface at ambient conditions is disallowed by the nonpolar nature of the surface and high vapor pressure of water. However, the presence of sub-millimeter sized hydrophilic patches allows the waxy wings of desert beetles to become wettable by morning mist. Here, we show that a sprinkle of graphene oxide nanoflakes (nanoGOs) is effective in condensing water nanodroplets and seeding ice epitaxy on graphite at ambient conditions. By controlling relative humidity and nanoGO density, we are able to study the formation of a complete ice wetting layer on a time scale o…
