[ { "id": "authors:aqk2b-42c81", "collection": "authors", "collection_id": "aqk2b-42c81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210716-222542124", "type": "monograph", "title": "Triangular Snowflakes: Growing Structures with Three-fold Symmetry using a Hexagonal Ice Crystal Lattice", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 slender ice needles in air with high reliability at -14 C. I further suggest a physical model that describes how such structures can self-assemble and develop, facilitated by an edge-sharpening instability that turns on at a specific combination of temperature and water-vapor supersaturation. The results generally support a comprehensive model of structure-dependent attachment kinetics in ice growth that has been found to explain many of the overarching behaviors seen in the Nakaya diagram of snow crystal morphologies.", "doi": "10.48550/arXiv.2106.09809", "publisher": "arXiv", "publication_date": "2021-06-17" }, { "id": "authors:egqa7-9vm52", "collection": "authors", "collection_id": "egqa7-9vm52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201203-151015297", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth: 9. Characterizing Structure-Dependent Attachment Kinetics near -4 C", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 quantitative similarities in the growth behaviors near -4 C and -14 C suggest that these two SDAK features arise from essentially the same physical mechanism occurring at different temperatures on the two principal facets. When applied to atmospheric snow crystal formation, this comprehensive model can explain the recurrent morphological transitions between platelike and columnar growth seen in the Nakaya diagram.", "doi": "10.48550/arXiv.2011.02353", "publisher": "arXiv", "publication_date": "2020-11-04" }, { "id": "authors:2zr0w-x7b41", "collection": "authors", "collection_id": "2zr0w-x7b41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201005-101157249", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth: 8. Characterizing Structure-Dependent Attachment Kinetics near -14 C", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 further characterize and refine the SDAK model, which effectively explains the robust formation of platelike snow crystals in air near 14 C.", "doi": "10.48550/arXiv.2009.08404", "publisher": "arXiv", "publication_date": "2020-09-17" }, { "id": "authors:9kgwe-4qv96", "collection": "authors", "collection_id": "9kgwe-4qv96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200601-095929758", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth: 7. Ice Attachment Kinetics near -2 C", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 and reconciling different data sets at a single temperature yields significant insights into the underlying physical processes that govern snow crystal growth dynamics.", "doi": "10.48550/arXiv.2004.06212", "publisher": "arXiv", "publication_date": "2020-04-13" }, { "id": "authors:zrzzx-4vh43", "collection": "authors", "collection_id": "zrzzx-4vh43", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200227-094236760", "type": "monograph", "title": "A Versatile Apparatus for Measuring the Growth Rates of Small Ice Prisms from the Vapor Phase", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 model snow crystal growth dynamics.", "doi": "10.48550/arXiv.1912.09440", "publisher": "arXiv", "publication_date": "2019-12-19" }, { "id": "authors:0yrv1-77f33", "collection": "authors", "collection_id": "0yrv1-77f33", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200218-105526027", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth: 6. Ice Attachment Kinetics near -5 C", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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.", "doi": "10.48550/arXiv.1912.03230", "publisher": "arXiv", "publication_date": "2019-12-06" }, { "id": "authors:7jdjv-wce43", "collection": "authors", "collection_id": "7jdjv-wce43", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191216-161856301", "type": "monograph", "title": "A Quantitative Physical Model of the Snow Crystal Morphology Diagram", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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.", "doi": "10.48550/arXiv.1910.09067", "publisher": "arXiv", "publication_date": "2019-10-20" }, { "id": "authors:mg3aq-hdb02", "collection": "authors", "collection_id": "mg3aq-hdb02", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160523-110531636", "type": "monograph", "title": "Measurements of Cylindrical Ice Crystal Growth Limited by Combined Particle and Heat Diffusion", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "We present measurements of the growth of long columnar ice crystals from water vapor over a broad range of temperatures and supersaturation levels in air. Starting with thin, c-axis ice needle crystals, we observed their subsequent growth behavior in a vapor diffusion chamber,\nextracting the initial radial growth velocities of the needles under controlled conditions. Approximating the hexagonal needle crystals as infinitely long cylinders, we created an analytical growth model that includes effects from particle diffusion of water molecules through the surrounding air along with the diffusion of heat generated by solidification. With only minimal adjustment of model\nparameters, we obtained excellent agreement with our experimental data. To our knowledge, this is the first time that the combined effects from particle and heat diffusion have been measured in ice growth from water vapor. This analysis further provides an accurate method for calibration of the water-vapor supersaturation levels in experimental growth chambers.", "doi": "10.48550/arXiv.1602.02683", "publication_date": "2016-02-08" }, { "id": "authors:nza1m-94z13", "collection": "authors", "collection_id": "nza1m-94z13", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160510-082526689", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth: 4. Measurements of Diffusion-limited Growth at -15 C", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Miller", "given_name": "Christopher", "clpid": "Miller-Christopher" }, { "family_name": "Potter", "given_name": "Ryan", "clpid": "Potter-Ryan" }, { "family_name": "Budaeva", "given_name": "Nina", "clpid": "Budaeva-Nina" }, { "family_name": "Lemon", "given_name": "Cameron", "clpid": "Lemon-Cameron" }, { "family_name": "Thomas", "given_name": "Sarah", "clpid": "Thomas-Sarah" } ], "abstract": "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 this quantitative analysis of well-controlled experimental measurements, we were able to extract information about the attachment coefficients governing ice growth under different circumstances. The results strongly support previous work indicating that the attachment coefficient on the prism surface is a function of the width of the prism facet. Including this behavior, we created a comprehensive model at -15 C that explains all the experimental data. To our knowledge, this is the first demonstration of a kinetic model that reproduces a range of diffusion-limited ice growth behaviors as a function of supersaturation.", "doi": "10.48550/arXiv.1512.03389", "publication_date": "2015-12-11" }, { "id": "authors:p2vcg-s0z09", "collection": "authors", "collection_id": "p2vcg-s0z09", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160125-105810267", "type": "monograph", "title": "Incorporating Surface Diffusion into a Cellular Automata Model of Ice Growth from Water Vapor", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "We describe a numerical model of faceted crystal growth using a cellular automata\nmethod that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in\nthe medium surrounding the crystal. The model was developed for investigating the diffusion-limited\ngrowth of ice crystals in air from water vapor, where the combination of bulk diffusion and strongly\nanisotropic molecular attachment kinetics yields complex faceted structures. We restricted the present\nmodel to cylindrically symmetric crystal growth with relatively simple growth morphologies, as this\nwas sufficient for making quantitative comparisons between theoretical models and ice growth experiments.\nOverall this numerical model reproduces ice growth behavior with reasonable fidelity over\na wide range of conditions, albeit with some limitations. The model could easily be adapted for\nother material systems, and the cellular automata technique appears well suited for investigating\ncrystal growth dynamics when strongly anisotropic surface attachment kinetics cause faceted growth\nmorphologies.", "doi": "10.48550/arXiv.1509.08543", "publication_date": "2015-09-28" }, { "id": "authors:kekrg-sz716", "collection": "authors", "collection_id": "kekrg-sz716", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160201-152804474", "type": "monograph", "title": "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", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "We reanalyzed the measurements made by Asakawa et al. [1] of the growth velocities of single-molecule-high steps on basal ice surfaces, as we believe the authors made a number of incorrect assumptions regarding ice growth parameters and bulk diffusion in their experiments. Applying what we believe are more accurate assumptions, we used the data in [1] to derive a surface diffusion length of x_s \u2248 10 nm for\nwater molecules on basal ice surfaces at T = \u22128.4 C, about 500 times lower than what was reported in [1].\nMoreover, in our analysis we found that no information about the height of the Ehrlich-Schwoebel barrier\ncould be obtained from these measurements.", "doi": "10.48550/arXiv.1509.06609", "publication_date": "2015-09-22" }, { "id": "authors:m3x90-wxh86", "collection": "authors", "collection_id": "m3x90-wxh86", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150518-101608391", "type": "monograph", "title": "An experimental apparatus for observing deterministic structure formation in plate-on-pedestal ice crystal growth", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "We describe an experimental apparatus for making detailed morphological observations of the growth of isolated plate-like ice crystals from water vapor. Each crystal develops a plate-on-pedestal (POP) geometry, in which a large, thin, plate-like crystal grows out from the top edge of an initially prismatic seed crystal resting on a substrate. With the POP geometry, the substrate is not in contact with the growing plate (except at its center), so substrate interactions do not adversely affect the crystal growth. By controlling the temperature and supersaturation around the crystal, we can manipulate the resulting ice growth behavior in predictable ways, producing morphologies spanning the full range from simple faceted hexagonal plates to complex dendritic structures. We believe that the experimental apparatus described here will allow unprecedented investigations of ice crystal growth behaviors under controlled conditions, identifying and exploring robust morphological features in detail. Such investigations will provide valuable observational inputs for developing numerical modeling techniques that can accurately reproduce the faceted and branched structures that frequently emerge during diffusion-limited crystal growth.", "doi": "10.48550/arXiv.1503.01019", "publication_date": "2015-03-03" }, { "id": "authors:bmgwj-3x722", "collection": "authors", "collection_id": "bmgwj-3x722", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140721-082120941", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth: 3. The Correspondence Between Ice Growth from Water Vapor and Ice Growth from Liquid Water", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 step energy. These data suggest that ice growth from water vapor and from liquid water are both well described by essentially the same underlying nucleation phenomenon over a substantial temperature range. A physical picture is emerging in which molecular step energies at the solid/liquid, solid/quasiliquid, and solid/vapor interfaces create nucleation barriers that dominate the growth behavior of ice over a broad range of conditions. Since the step energy is an equilibrium quantity, just as surface melting is an equilibrium phenomenon, there exists a considerable opportunity to use many-body simulations of the ice surface structure and energetics at equilibrium to better understand many dynamical aspects of ice crystal growth.", "doi": "10.48550/arXiv.1407.0740", "publication_date": "2014-07-02" }, { "id": "authors:1yn0z-ja614", "collection": "authors", "collection_id": "1yn0z-ja614", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140519-102124085", "type": "monograph", "title": "A Dual Diffusion Chamber for Observing Ice Crystal Growth on c-Axis Ice Needles", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "We describe a dual diffusion chamber for observing ice crystal growth from water vapor in air as a function of temperature and supersaturation. In the first diffusion chamber, thin c-axis ice needles with tip radii ~100 nm are grown to lengths of ~2 mm. The needle crystals are then transported to a second diffusion chamber where the temperature and supersaturation can be independently controlled. By creating a linear temperature gradient in the second chamber, convection currents are suppressed and the supersaturation can be modeled with high accuracy. The c-axis needle crystals provide a unique starting geometry compared with other experiments, and the dual diffusion chamber allows rapid quantitative observations of ice growth behavior over a wide range of environmental conditions.", "doi": "10.48550/arXiv.1405.1384", "publication_date": "2014-05-06" }, { "id": "authors:zpan3-wjj35", "collection": "authors", "collection_id": "zpan3-wjj35", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130219-095515435", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth Dynamics:\n 2. Structure Dependent Attachment Kinetics near -5 C", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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.", "doi": "10.48550/arXiv.1302.1231", "publication_date": "2013-02-05" }, { "id": "authors:xdps7-mx982", "collection": "authors", "collection_id": "xdps7-mx982", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130122-144406629", "type": "monograph", "title": "Toward a Comprehensive Model of Snow Crystal Growth Dynamics: 1. Overarching Features and Physical Origins", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 in our model is the substantial role played by structure-dependent attachment kinetics, producing a growth instability that is largely responsible for the formation of thin plates and hollow columnar forms. Putting these elements together, we are able to explain the overall growth behavior of atmospheric ice crystals over a broad range of conditions. Although our model is complex and still incomplete, we believe it provides a useful framework for directing further investigations into the physics underlying snow crystal growth. Additional targeted experimental investigations should better characterize the model, or suggest modifications, and we plan to pursue these investigations in future publications in this series. Our model also suggests new avenues for the continued exploration of ice surface structure and dynamics using molecular dynamics simulations.", "doi": "10.48550/arXiv.1211.5555", "publication_date": "2012-11-23" }, { "id": "authors:b38pd-fej85", "collection": "authors", "collection_id": "b38pd-fej85", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121010-075243372", "type": "monograph", "title": "An Edge-Enhancing Crystal Growth Instability Caused by Structure-Dependent Attachment Kinetics", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 determining the growth morphologies of atmospheric ice crystals as a function of temperature, a phenomenon that has been essentially unexplained for over 75 years. Our model of structure-dependent attachment kinetics appears to be related to surface melting, and thus may be present in other material systems, whenever crystal growth from the vapor phase occurs near the material melting point.", "doi": "10.48550/arXiv.1209.4932", "publication_date": "2012-09-21" }, { "id": "authors:831hd-97083", "collection": "authors", "collection_id": "831hd-97083", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120917-091902007", "type": "monograph", "title": "Crystal Growth in the Presence of Surface Melting: Novel Behavior of the Principal Facets of Ice", "author": [ { "family_name": "Libbrecht", "given_name": "K. G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Rickerby", "given_name": "M. E.", "clpid": "Rickerby-M-E" } ], "abstract": "We present measurements of the growth rates of the principal facet surfaces of ice\nfrom water vapor as a function of supersaturation over the temperature range \u22122 \u2265 T \u2265 \u221240 C. Our\ndata are well described by a dislocation-free layer-nucleationmodel, parameterized by the attachment\ncoefficient as a function of supersaturation \u03b1(\u03c3) = Aexp(\u2212\u03c3_0/\u03c3). The measured parameters A(T)\nand \u03c3_0(T) for the basal and prism facets exhibit a complex behavior that likely originates from\nstructural changes in the ice surface with temperature, in particular the onset and development of\nsurface melting for T > \u221215 C. From \u03c3_0(T) we extract the terrace step energy \u03b2(T) as a function\nof temperature for both facet surfaces. As a basic property of the equilibrium ice surface, the\nstep energy \u03b2(T) may be amenable to calculation using molecular dynamics simulations, potentially\nyielding new insights into the enigmatic surface structure of ice near the triple point.", "doi": "10.48550/arXiv.1208.5982", "publication_date": "2012-08-29" }, { "id": "authors:3kzzh-tky11", "collection": "authors", "collection_id": "3kzzh-tky11", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120521-075926479", "type": "monograph", "title": "On the Equilibrium Shape of an Ice Crystal", "author": [ { "family_name": "Libbrecht", "given_name": "Kenneth G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" } ], "abstract": "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 likely prohibitively long, except under special circumstances; and 5) Surface energy effects likely play a relatively smaller role in ice crystal growth dynamics when compared to the role of attachment kinetics.", "doi": "10.48550/arXiv.1205.1452", "publication_date": "2012-05-07" }, { "id": "authors:my3pb-29a84", "collection": "authors", "collection_id": "my3pb-29a84", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111107-134141507", "type": "monograph", "title": "Measurements of Growth Rates of (0001) Ice Crystal Surfaces", "author": [ { "family_name": "Libbrecht", "given_name": "K. G.", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Rickerby", "given_name": "M. E.", "clpid": "Rickerby-M-E" } ], "abstract": "We present measurements of growth rates of the (0001) facet surface of ice as a function of water vapor supersaturation over the temperature range \u22122 \u2265 T \u2265 \u221240 C. From these data we infer the temperature dependence of premelting on the basal surface and the effects of premelting on the ice growth dynamics. Over this entire temperature range the growth was consistent with a simple 2D nucleation model, allowing a measurement of the critical supersaturation \u03c3_0(T) as a function of temperature. We find that the 2D nucleation barrier is substantially diminished when the premelted layer is partially developed, as indicated by a reduced \u03c3_0, while the barrier is higher both when the premelted layer is fully absent or fully developed.", "doi": "10.48550/arXiv.1110.5828", "publisher": "California Institute of Technology", "publication_date": "2011-10-26" } ]