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Ice crystal

An ice crystal is a solid form of water in which H₂O molecules are arranged in a highly ordered, repeating crystalline lattice through hydrogen bonding, typically exhibiting a hexagonal symmetry under ambient conditions.^[1] This structure, known as ice Ih, features oxygen atoms positioned at the vertices of open hexagonal rings, with each oxygen atom forming tetrahedral bonds to four neighboring oxygens at a distance of approximately 2.75 Å, resulting in a density of about 0.917 g/cm³ at 0°C.^[2] The hydrogen atoms occupy positions along these bonds according to the Bernal-Fowler rules, ensuring two protons are close to each oxygen nucleus while maintaining overall disorder in proton orientations that is consistent with the second law of thermodynamics.^[2] Ice crystals form primarily through two mechanisms: the direct deposition of water vapor onto a suitable nucleus (deposition nucleation) or the freezing of supercooled liquid water droplets around an ice nucleus (freezing nucleation).^[3] In the atmosphere, heterogeneous nucleation dominates between 0°C and -36°C, catalyzed by particles such as mineral dust, black carbon, or biological materials like bacteria, which lower the energy barrier for crystallization.^[3] Below -36°C, homogeneous nucleation can occur in pure water without nuclei, driven by thermodynamic instability in supercooled states.^[3] Once initiated, crystal growth proceeds via the addition of water molecules to the lattice, influenced by factors like temperature, supersaturation, and supercooling degree, often yielding shapes such as plates, columns, or dendrites depending on environmental conditions.^[1] These crystals play critical roles in natural phenomena, including the formation of snowflakes, cirrus clouds, and precipitation, while also impacting fields like food science through freeze-concentration effects and atmospheric science via their influence on cloud reflectivity and radiative forcing.^[3] Ice Ih is the stable phase at standard pressures and temperatures below 0°C, though other polymorphs exist under extreme conditions, such as high pressure or low temperature.^[2] The unique open lattice structure, with voids larger than in liquid water, accounts for ice's lower density compared to water, enabling phenomena like ice flotation.^[1]

Structure and Morphology

Basic Crystal Structure

Ice Ih, the predominant form of ice in the Earth's atmosphere, exhibits a hexagonal crystal lattice with space group P6₃/mmc.^[4] The oxygen atoms are arranged in a wurtzite-like structure, forming a slightly distorted hexagonal close-packed array where each oxygen is tetrahedrally coordinated to four neighboring oxygens via hydrogen bonds.^[4] This arrangement creates a framework of puckered hexagonal rings stacked along the c-axis, with four water molecules per unit cell.^[4] The unit cell dimensions of ice Ih at 0°C are a = 4.5190 Å and c = 7.3616 Å, yielding a c/a ratio of approximately 1.629.^[4] The nearest-neighbor oxygen-oxygen distance is 2.76 Å, and the hydrogen bonds contribute to the overall stability of the lattice.^[4] Within this structure, the positions of the hydrogen atoms are disordered, adhering to the Bernal-Fowler rules, which stipulate that each oxygen atom has two hydrogen atoms covalently bonded to it (at ~0.96 Å) and two hydrogen atoms from adjacent molecules forming hydrogen bonds, ensuring one proton per O-O bond across the lattice.^[5]^[4] This proton disorder results in a residual entropy of R \ln \frac{3}{2} per mole at 0 K, reflecting the multiple possible configurations consistent with the ice rules.^[4] In contrast to other ice phases, such as the rhombohedral ice II or tetragonal ice III, which form under high pressure and exhibit more ordered or differently coordinated structures, ice Ih remains the stable polymorph at ambient atmospheric pressures and temperatures above approximately 200 K.^[4] The hexagonal symmetry of the ice Ih lattice underpins the common macroscopic habits observed in atmospheric crystals, including hexagonal prisms bounded by {0001} basal planes and {10\bar{1}0} prism planes, as well as thin plates that develop preferentially on the basal faces due to the layered stacking along the c-axis.^[4]

Growth Habits and Variations

Ice crystals exhibit a variety of macroscopic growth habits, primarily plates, columns, and dendritic forms, which arise from the underlying hexagonal lattice structure that allows preferential growth along specific crystallographic planes.^[6] These habits are observed in atmospheric conditions and laboratory settings, with shapes ranging from simple hexagonal plates to complex branched structures.^[7] The primary habits transition with temperature, as documented in empirical growth diagrams such as the Magono-Lee classification, which categorizes natural snow crystals based on observed morphologies and environmental conditions.^[7] At temperatures between -5°C and -10°C, plate-like crystals predominate, forming thin, hexagonal plates due to faster growth perpendicular to the c-axis.^[6] Between -10°C and -15°C, columnar (prismatic) habits become favored, resulting in elongated prisms that grow parallel to the c-axis.^[7] A more comprehensive diagram by Bailey and Hallett extends this to lower temperatures, showing plates from 0°C to -4°C and -8°C to -22°C, columns from -4°C to -8°C and below -40°C, and platelike polycrystals like stellar plates between -20°C and -40°C.^[6] Supersaturation, the relative humidity with respect to ice, significantly influences the complexity and branching of these habits, promoting dendritic growth at higher levels.^[6] Low supersaturations (1%-15%) yield compact forms such as short columns or simple plates, while intermediate levels (~25% at -40°C to -45°C) lead to assemblages like bullet rosettes, consisting of multiple columnar bullets radiating from a central core.^[6] High supersaturations enhance branching in dendritic crystals, such as fernlike or sector plates around -15°C, and can cause aggregates where multiple crystals cluster together during fall, forming irregular spatial structures.^[7] Examples include stellar plates, which develop broad, six-armed dendritic patterns at moderate supersaturations between -12°C and -16°C, and hollow columns, which form at low temperatures below -30°C with internal cavities due to vapor diffusion limitations.^[6] Rare forms deviate from the hexagonal norm under specific laboratory conditions, often due to confinement or rapid formation processes that introduce stacking disorders. Trigonal crystals, exhibiting threefold symmetry, arise from interlaced hexagonal and cubic stacking sequences in stacking-disordered ice, observed in clouds from -84°C to -5°C but replicated in labs via controlled nucleation.^[8] Square ice, a highly ordered two-dimensional phase with square lattice arrangement, forms in nanocapillaries between graphene sheets at room temperature under hydrophobic confinement.^[9] Cubic ice (ice Ic), with diamond cubic structure, forms through freezing of supercooled aqueous droplets under conditions relevant to the upper troposphere, such as those involving specific ammonium-to-sulfate ratios below 200 K, where hexagonal stacking faults are minimized.^[10]

Formation Processes

Nucleation Mechanisms

Nucleation mechanisms represent the initial stage in ice crystal formation, where stable ice embryos emerge from supercooled water or water vapor, overcoming thermodynamic barriers to initiate crystallization. In atmospheric contexts, such as cloud formation, these processes determine the onset of ice phase in mixed-phase or cirrus clouds, influencing precipitation and radiative properties. Two primary pathways dominate: homogeneous nucleation, which occurs spontaneously in pure phases without foreign substrates, and heterogeneous nucleation, which is facilitated by impurities like aerosols acting as ice nuclei. Homogeneous nucleation in supercooled liquid water or pure vapor proceeds via the formation of small ice clusters that must surpass a critical size to avoid dissolution. According to classical nucleation theory (CNT), the free energy change for forming a spherical embryo of radius r is given by

\Delta G = -\frac{4}{3}\pi r^3 \Delta \mu + 4\pi r^2 \sigma,

where \Delta \mu is the chemical potential difference driving supersaturation (positive for undercooling or supersaturation), and \sigma is the ice-vapor or ice-liquid interfacial energy.^[11] The critical embryo radius r^* occurs at the energy maximum, derived from \frac{d\Delta G}{dr} = 0, yielding r^* = \frac{2\sigma}{\Delta \mu}, beyond which clusters grow stably.^[11] This barrier height \Delta G^* = \frac{16\pi \sigma^3}{3 (\Delta \mu)^2} exponentially suppresses nucleation rates at modest undercoolings, with rates increasing dramatically below approximately -38°C for liquid water, where homogeneous freezing becomes probable without nuclei.^[12] In vapor, similar principles apply, though rates depend on supersaturation relative to ice, with direct simulations confirming CNT's applicability for small embryos in molecular models of water.^[12] Heterogeneous nucleation predominates in the atmosphere, occurring on foreign particles such as mineral dust, soot, or biological materials like bacteria, which lower the energy barrier by providing a template for ice embryo attachment. CNT extends to this mode via a contact angle \theta in the interfacial energy term, reducing \Delta G^* by a factor of f(\theta) = \frac{(2 + \cos \theta)(1 - \cos \theta)^2}{4} for spherical substrates, where \theta reflects wetting properties—smaller angles indicate more efficient nuclei. Dust aerosols, for instance, enable nucleation at warmer temperatures through immersion (within supercooled droplets) or deposition (direct from vapor) modes, with bacterial ice-nucleating proteins promoting activity up to -2°C.^[13] Parameterizations based on CNT fit laboratory data for these nuclei, showing heterogeneous rates that allow ice formation between -10°C and -20°C, far above homogeneous thresholds, thus initiating glaciation in clouds.^[14] In supercooled liquid droplets prevalent in mixed-phase clouds (typically -10°C to -20°C), heterogeneous nucleation seeds the first ice crystals, which then drive the Bergeron process by growing via vapor diffusion at the expense of surrounding droplets due to the ice-vapor equilibrium being lower than liquid-vapor at these temperatures.^[15] This initiation is crucial, as the sparse ice nuclei ensure few but rapidly growing crystals, with nucleation temperatures dictating cloud evolution—homogeneous events below -38°C glaciate entire cirrus layers, while heterogeneous modes sustain mixed-phase persistence higher up.^[16] The resulting embryo orientation on nuclei can influence early crystal habits, such as prismatic or platelike forms. Recent molecular studies as of 2025 have provided deeper insights into these mechanisms using techniques like in-situ cryogenic transmission electron microscopy (cryo-TEM) and atomic force microscopy (AFM). For instance, heterogeneous nucleation on substrates like graphene involves adsorption layers of amorphous ice leading to spontaneous formation of hexagonal (Ih) and cubic (Ic) ice nuclei without a classical critical size barrier, with growth proceeding via Ostwald ripening and oriented aggregation.^[17] Additionally, nucleus-free crystallization pathways have been observed in two-dimensional amorphous ice on graphite, where fractal dendritic growth transitions to compact structures driven by ad-molecule dynamics, challenging traditional CNT by demonstrating kinetic, barrierless processes at low temperatures (70-120 K).^[18] These findings enhance understanding of early-stage ice formation in atmospheric and surface environments.

Vapor Deposition and Growth

Ice crystals grow after nucleation primarily through the direct deposition of water vapor molecules from supersaturated air onto their surfaces, a process governed by both vapor transport in the gas phase and molecular attachment kinetics at the interface. This depositional growth expands the crystal lattice layer by layer, with the rate determined by the interplay between diffusion-limited supply of vapor and surface-specific attachment mechanisms. Environmental conditions in clouds, such as supersaturation levels, play a crucial role in sustaining this growth, enabling individual crystals to reach millimeter sizes before further processes like aggregation occur.^[19] The transport of water vapor to the crystal is typically limited by diffusion across a boundary layer of air surrounding the particle, particularly for slowly moving crystals. The vapor flux J to the surface can be approximated as J = \frac{D (\rho_v - \rho_s)}{\delta}, where D is the diffusion coefficient of water vapor in air (approximately $2 \times 10^{-5} m²/s at atmospheric temperatures), \rho_v is the ambient vapor density, \rho_s is the equilibrium vapor density over the ice surface, and \delta is the boundary layer thickness, which decreases with increasing ventilation from crystal fall speed or turbulence. This diffusion-limited regime dominates for larger crystals or in quiescent conditions, leading to mass growth rates proportional to the crystal's capacitance (a shape factor analogous to radius for spheres). For ventilated crystals falling through clouds, the effective flux increases via a ventilation coefficient, often on the order of 1.1 to 2 depending on Reynolds number.^[19] At the surface, water molecules attach via step growth mechanisms, where new layers form by the propagation of monolayer steps across faceted planes. These steps originate from screw dislocations, producing characteristic spiral patterns as described by the Burton-Cabrera-Frank theory adapted to ice, or from two-dimensional nucleation of new islands when supersaturation exceeds a critical threshold (typically 0.5-1% for ice faces). Growth proceeds via surface diffusion of adsorbed water molecules (admolecules) to step edges, with the step velocity v given by v = \beta \sigma, where \beta is the kinetic coefficient and \sigma is the supersaturation. Kinetic coefficients vary significantly between facets: prism faces (a-axes) often show higher \beta values (up to 10 times faster attachment) than basal faces (c-axis) at temperatures between -10°C and -20°C, due to differences in surface free energy and molecular bonding; for instance, at -15°C, the critical supersaturation for prism growth is about 0.6%, compared to higher values for basal planes. These facet-specific kinetics lead to anisotropic expansion, though detailed habits are determined elsewhere.^[21]^[22] Environmental factors modulate these growth processes profoundly. Supersaturation, driven by humidity relative to ice (often 10-20% above ice saturation in mixed-phase clouds), directly scales the driving force \rho_v - \rho_s, with higher values accelerating deposition. Temperature gradients around the crystal, arising from latent heat release during growth, can reduce local supersaturation by up to 30% at -15°C, effectively slowing growth unless compensated by diffusion. Ventilation from falling or turbulent motion thins \delta, enhancing flux by factors of 1.5-3 for crystals with Reynolds numbers around 10-100, as seen in plate-like habits descending at 20-50 cm/s. These factors collectively determine growth trajectories in atmospheric conditions.^[19]^[22] As crystals enlarge via deposition, aggregation becomes significant, where colliding particles stick to form branched snowflakes. This process is most efficient for dendritic or plate-like crystals at temperatures of -10°C to -20°C, where branching increases collision cross-sections. Collision efficiencies range from 0.1 for small columns to 0.8-0.9 for larger dendrites, influenced by relative velocities (typically 10-100 cm/s from differential sedimentation) and turbulence. Sticking efficiency, the probability of adhesion upon impact, peaks near -15°C (up to 0.7) due to optimal surface roughness and quasi-liquid layers, but drops at warmer temperatures (> -5°C) from reduced sticking or colder ones (<-25°C) from brittle fracture; it is parameterized as E_s = \exp\left[ -\beta(T) \frac{K_c}{A} \right], with K_c as collision kinetic energy and A as contact area. Aggregation thus rapidly scales particle size beyond individual deposition limits, contributing to precipitation formation.^[24]^[25] In addition to primary growth and aggregation, secondary ice production (SIP) mechanisms multiply ice crystal numbers in mixed-phase clouds, often producing 10^3 to 10^5 additional particles per primary crystal. Key processes include the Hallett-Mossop rime splintering (active at -3°C to -8°C, generating splinters from freezing droplets), ice-ice collisional breakup (dominant at -10°C to -20°C during dendritic growth), droplet shattering upon freezing, and sublimational breakup in subsaturated conditions. These enhance ice concentrations, accelerating glaciation and precipitation, and are crucial for accurate cloud modeling as of 2024 observations.^[26]

Physical Properties

Density and Mechanical Properties

Ice Ih, the common form of ice crystals, has a density of 0.917 g/cm³ at 0°C.^[27] This value reflects the open hexagonal structure, which incorporates voids compared to liquid water. Snow crystals, however, are highly porous due to air trapped within their branched or dendritic forms, resulting in effective densities ranging from 0.05 to 0.3 g/cm³, with porosity reducing the overall mass per volume.^[28] Mechanically, ice crystals display Vickers hardness values between 10 and 50 MPa, influenced by factors such as temperature, strain rate, and crystal orientation; for instance, at −12°C, hardness measures around 22 MPa.^[29] The material's elasticity is anisotropic owing to its hexagonal lattice, with Young's modulus of approximately 12 GPa along the c-axis, the direction of highest stiffness.^[30] This directional variation affects deformation under stress, where loading perpendicular to the basal plane yields lower compliance. Fracture in ice crystals preferentially occurs via cleavage along the basal (0001) planes, where interlayer bonding is weakest, leading to brittle failure modes.^[31] At −10°C, the tensile strength typically ranges from 0.7 to 3.1 MPa, limiting the structural integrity of individual crystals under pulling forces.^[32] For practical applications in atmospheric modeling, the mass m of ice crystals is often estimated from their maximum diameter D using the power-law relation m = \alpha D^\beta, where \beta \approx 2 for plate-like habits and \alpha, \beta are empirical coefficients varying by crystal type.^[33]

Thermal and Electrical Properties

Ice crystals, composed of hexagonal ice (Ih), display anisotropic thermal conductivity arising from their crystal lattice structure. Measurements on single crystals indicate that the thermal conductivity parallel to the c-axis is approximately 2.2 W/m·K near 0°C, while the value perpendicular to the c-axis is slightly lower, around 1.9 W/m·K, reflecting a modest anisotropy of about 5%.^[34]^[35] Below 0°C, the thermal conductivity of ice increases with decreasing temperature and follows an inverse proportionality to temperature, expressed as k \propto T^{-1}, due to reduced phonon scattering in the lattice.^[36] The specific heat capacity of ice at 0°C is approximately 2.1 J/g·K, representing the energy required to raise the temperature of 1 gram of ice by 1 K without phase change.^[34] Additionally, the latent heat of sublimation for ice crystals is 2.83 MJ/kg, the energy absorbed during the direct transition from solid to vapor phase, which plays a key role in atmospheric heat transfer processes.^[37] Electrically, ice crystals have a low intrinsic dielectric permittivity of approximately 3.2 at high frequencies (above ~1 kHz), compared to 1 for air, creating a significant contrast that enhances radar reflectivity in ice-bearing clouds.^[38] The intrinsic electrical conductivity of pure ice is very low, on the order of $10^{-12} S/m at temperatures around -10°C, limited by minimal free charge carriers in the lattice.^[39] However, this conductivity can be substantially enhanced by impurities, such as acids or salts, or through collisional charging mechanisms in thunderstorms, where ice crystals and graupel particles exchange charge during collisions, leading to electrification and increased conductivity in mixed-phase regions.^[40]

Optical Properties

Refraction and Birefringence

Ice crystals in their hexagonal Ih form exhibit birefringence arising from the anisotropic arrangement of water molecules along the optic axis. This optical anisotropy results in distinct refractive indices for the ordinary ray (n_o = 1.309) and the extraordinary ray (n_e = 1.313) at 0°C across visible wavelengths.^[41] The refractive indices display dispersion, with values slightly higher for shorter (blue) wavelengths than longer (red) ones, influencing the wavelength-dependent bending of light.^[42] The birefringence magnitude, \Delta n = n_e - n_o \approx 0.004, leads to double refraction in these non-cubic crystals, where an incident light ray splits into two orthogonally polarized components that propagate at different velocities and follow divergent paths within the crystal.^[41] This phenomenon is observable under polarized light and depends on the orientation of the crystal's c-axis relative to the light's propagation direction.^[43] Refraction at the prism-like faces of hexagonal ice crystals obeys Snell's law, n_1 \sin \theta_1 = n_2 \sin \theta_2, where n_1 \approx 1 for air and n_2 is the ice refractive index, determining the deviation angle of rays entering and exiting the crystal. For a 60° prism angle typical of these crystals, the ray deviation exhibits a minimum near 22°, corresponding to the geometry and refractive index that concentrates light rays at this angle.^[44]

Scattering and Absorption

Ice crystals interact with electromagnetic radiation primarily through scattering and absorption processes, which govern their role in atmospheric optics and radiative transfer. For small ice crystals where the size parameter x = \frac{2\pi r}{\lambda} (with r as the particle radius and \lambda as the wavelength) is less than approximately 10, scattering is accurately described by Mie theory, which solves Maxwell's equations for spherical approximations of the particles. As crystal size increases and x > 10, the scattering transitions to geometric optics approximations, accounting for ray tracing and diffraction effects in nonspherical shapes like hexagonal prisms and plates.^[45] The asymmetry factor g, which quantifies the degree of forward versus backward scattering, typically ranges from 0.8 to 0.9 for hexagonal plate ice crystals in the visible and near-infrared spectrum, promoting efficient forward scattering that influences radiative transfer in cirrus clouds.^[46] This high g value arises from the plate-like geometry and aspect ratio, directing most scattered light into the forward hemisphere and reducing backscattering.^[47] Absorption by ice crystals is negligible in the visible spectrum, with coefficients on the order of \alpha \approx 0.001 cm^{-1}, allowing deep penetration of sunlight through pure ice.^[43] In the infrared, absorption strengthens significantly due to vibrational modes of water molecules, particularly the O-H stretching band near 3 μm, where coefficients can exceed 100 cm^{-1}, leading to rapid attenuation of thermal radiation.^[48] Polarization signatures from ice crystal scattering provide a key diagnostic for distinguishing them from spherical aerosols, with the linear depolarization ratio \delta typically ranging from 0.3 to 0.5 at backscattering angles for nonspherical ice particles, compared to near-zero values for spheres.^[49] This depolarization arises from the irregular shapes and orientations of crystals, such as hexagonal plates and columns, which alter the polarization state of lidar or scattered light.^[50]

Atmospheric Role

Involvement in Precipitation

Ice crystals play a central role in the formation of precipitation through the Bergeron-Findeisen process, in which they grow by vapor diffusion at the expense of surrounding supercooled liquid droplets in mixed-phase clouds. This mechanism arises because the saturation vapor pressure over supercooled water exceeds that over ice at temperatures below 0°C, leading to a net transfer of water vapor from the droplets to the ice crystals. The saturation vapor pressure over water can be approximated by the formula e_w = 6.11 \times 10^{(7.5T)/(237.3 + T)} mbar, where T is in °C, while the corresponding value over ice (e_i) is lower, typically by 5-20% depending on temperature, driving the diffusional growth of ice crystals until they become large enough to fall as snowflakes.^[51] This process, first experimentally confirmed by Findeisen in 1938, is essential for precipitation in mid- and high-latitude clouds where mixed-phase conditions prevail.^[52] In addition to vapor growth, ice crystals contribute to precipitation via riming, the accretion of supercooled liquid droplets onto their surfaces, which rapidly increases particle mass and forms denser aggregates like graupel. Riming efficiency is high, with collection efficiencies E typically ranging from 0.5 to 1, depending on droplet size, relative velocity, and crystal habit, allowing ice particles to scavenge droplets effectively in regions of high liquid water content.^[53] This process accelerates fallout, transitioning pristine crystals into rimed particles that can further aggregate or melt into rain.^[54] As ice particles descend into warmer layers near 0°C, melting and shedding occur, where the crystals partially melt, shedding liquid water and often disintegrating into smaller fragments that coalesce into raindrops. This shedding enhances precipitation efficiency by breaking apart large aggregates and promoting the formation of spherical raindrops through collision and coalescence.^[55] Different growth habits of ice crystals influence their terminal fall speeds, with planar dendrites falling more slowly than columnar types, thereby affecting the depth of the melting layer they traverse.^[56] Regionally, ice crystal involvement in precipitation varies; in mid-latitude storms, dendritic and stellar crystals dominate snow formation via the Bergeron-Findeisen process in frontal systems, leading to widespread snowfall.^[57] In contrast, tropical anvil clouds feature more irregular ice crystals and bullet rosettes that riming and aggregation turn into heavy precipitation, often contributing to intense convective rain.^[58]

Influence on Clouds and Climate

Ice crystals significantly influence the radiative balance of the atmosphere through their role in cirrus clouds, which are composed primarily of ice particles at high altitudes. These clouds scatter incoming shortwave solar radiation via complex ice crystal shapes that enhance scattering efficiency through submicron surface roughness and mesoscopic deformations, flattening the angular scattering phase function and increasing backscattering compared to smooth hexagonal prisms.^[59] While cirrus clouds also trap outgoing longwave radiation, leading to a net warming in many cases, the enhanced shortwave scattering by ice crystal morphology provides a counterbalancing cooling influence on the overall radiative forcing.^[59] Globally, 30-50% of clouds contain ice phases, either as pure ice or mixed-phase configurations, profoundly affecting planetary albedo and greenhouse trapping. In mixed-phase clouds, where supercooled liquid droplets coexist with ice crystals, a greater fraction of liquid particles generally leads to higher cloud albedo, as liquid droplets reflect more shortwave radiation than ice particles.^[60] Conversely, ice crystals enhance the greenhouse effect by absorbing and re-emitting longwave radiation more efficiently in the upper atmosphere, particularly in high-altitude cirrus where optical properties favor infrared trapping over shortwave reflection.^[61] This dual role modulates the Earth's energy budget, with glaciated clouds reducing surface insolation while amplifying atmospheric warming, thereby influencing regional and global climate patterns.^[62] Aerosol indirect effects mediated by ice nuclei further amplify the climatic impact of ice crystals by altering cloud microphysics. Ice-nucleating particles, such as mineral dust or black carbon, serve as substrates for heterogeneous ice formation, increasing ice crystal concentrations in mixed-phase clouds and thereby depleting supercooled liquid water through the Bergeron process.^[63] This shift prolongs cloud lifetime in some scenarios by suppressing warm rain processes but often reduces overall cloud cover due to enhanced precipitation efficiency via rapid ice growth and fallout.^[61] Consequently, these effects can diminish cloud albedo, allowing more solar radiation to reach the surface, while simultaneously modifying the vertical distribution of ice, which influences longwave radiative transfer.^[63] Recent assessments, such as those in the IPCC Sixth Assessment Report (2021), highlight that uncertainties in mixed-phase cloud processes and ice nucleation contribute significantly to estimates of equilibrium climate sensitivity, with improved representations potentially reducing projected warming by 0.5–1 K.^[64] In global climate models (GCMs), accurate parameterization of ice processes is essential for simulating these influences. Schemes in models like ECHAM6-HAM2 employ two-moment microphysics to predict ice crystal number and mass, incorporating heterogeneous nucleation from aerosols and autoconversion rates that convert cloud ice to snow in mixed-phase regimes.^[65] Autoconversion rates, often tuned via parameters such as γ_s ≈ 1.0 for ice aggregation, control the rate at which small ice crystals coalesce into precipitating snowflakes, directly affecting cloud lifetime and radiative feedbacks in midlatitude mixed-phase clouds.^[65] These parameterizations reveal that uncertainties in ice autoconversion can alter equilibrium climate sensitivity by up to 1-2 K, underscoring the need for refined representations to capture the climatic role of ice crystals.^[65]

Detection and Study

Laboratory Techniques

Laboratory techniques for studying ice crystals involve controlled environments that simulate conditions conducive to nucleation, growth, and structural analysis, enabling precise measurements of crystal formation and properties. These methods allow researchers to isolate variables such as temperature, pressure, and vapor supersaturation, providing insights into microscopic behaviors that are challenging to observe in natural settings. Key approaches include chamber-based simulations for dynamic processes and advanced imaging for static structural characterization. Cloud chambers, particularly expansion types like the Wilson chamber, have been instrumental in visualizing ice nucleation by rapidly creating supersaturated vapor conditions that promote the formation of ice crystals from supercooled water droplets. In these setups, adiabatic expansion cools the air, leading to condensation or deposition onto nuclei, with the resulting crystal tracks or particles observable through optical means, thus revealing nucleation sites and initial growth patterns. Diffusion chambers, often employing thermal gradients, measure ice crystal growth rates by maintaining a controlled vapor flux toward a cold substrate, where crystals develop under steady-state conditions; for instance, experiments in such chambers have quantified dimensional growth of columnar ice at temperatures below -40°C, showing rates influenced by supersaturation levels. These chamber techniques validate nucleation mechanisms by demonstrating heterogeneous ice formation on aerosols under varying humidity and temperature profiles. Electron microscopy techniques, including scanning electron microscopy (SEM) and transmission electron microscopy (TEM), provide atomic-scale resolution of ice crystal facets and defects. Environmental SEM allows in-situ observation of ice growth at surface imperfections like steps or pores, where crystals preferentially form due to enhanced vapor deposition. Cryo-TEM, using liquid-cell setups, has imaged ice crystallization from liquid water, resolving lattice defects and grain boundaries at molecular resolution, confirming that ice formation tolerates nanoscale irregularities without disrupting overall hexagonal structure. X-ray diffraction (XRD) is widely used to confirm lattice parameters of ice crystals and investigate phase transitions under applied pressure. High-pressure XRD experiments have mapped the transition from ice VI to ice XV, revealing changes in lattice constants during hydrogen ordering, with precise measurements of unit cell volumes at gigapascal pressures. This technique elucidates pressure-induced shifts, such as the kinetics of superionic phases in ice VII, by analyzing diffraction patterns that indicate structural reordering. Historical developments in laboratory techniques include photomicrography pioneered by Wilson A. Bentley in the late 19th and early 20th centuries, culminating in the 1931 publication of over 2,000 images that classified ice crystal habits into categories like plates, columns, and dendrites based on morphological variations observed under controlled magnification.

Remote Sensing Methods

Remote sensing methods enable the observation of ice crystals in the atmosphere from afar, providing insights into their distribution, phase, and properties without physical sampling. These techniques leverage interactions between ice crystals and electromagnetic radiation, such as scattering and depolarization, to detect and characterize crystals in clouds like cirrus and convective systems. Key approaches include lidar, radar, aircraft-based imaging probes, and satellite infrared measurements, each offering complementary data on crystal morphology, concentration, and dynamics. Lidar systems, particularly the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) aboard the CALIPSO satellite, detect ice crystals by measuring attenuated backscatter and depolarization ratios at 532 nm. The depolarization ratio, defined as the ratio of perpendicular to parallel polarized backscatter, is typically higher for non-spherical ice crystals (around 0.3–0.5) compared to spherical liquid droplets (near 0), allowing discrimination of ice phase in clouds. Vertically integrated layer depolarization and backscatter are used in phase assignment algorithms to identify ice-dominated layers, with backscatter coefficients aiding in optical depth estimation for thin cirrus. These measurements have been validated globally, revealing ice crystal orientations and habits in various cloud types. Dual-polarization Doppler radar observes ice crystal fall speeds and habits by analyzing reflectivity, differential reflectivity (Z_DR), and Doppler velocity spectra. Z_DR, the ratio of horizontal to vertical reflectivity, varies with crystal orientation and shape—pristine plates or columns show positive Z_DR (>0 dB), while aggregates exhibit near-zero or negative values—enabling habit classification in winter storms. Doppler spectra provide terminal fall speeds, typically 0.2–1 m/s for pristine crystals and up to 2–3 m/s for rimed aggregates, revealing growth processes like riming or aggregation. The equivalent radar reflectivity factor Z_e, which quantifies backscatter from ice crystals and is often 10–20 dBZ in ice clouds, is defined as Z_e = \int N(D) D^6 \, dD where N(D) is the size distribution and D is particle diameter (typically in mm, yielding Z_e in mm<sup>6</sup> m<sup>-3</sup>); in the radar equation relating received power to Z_e, factors such as wavelength \lambda (via \lambda^{-4} for Rayleigh scattering) and the dielectric factor |K|^2 (≈0.18 for ice at microwave frequencies) are included.^[66]^[67] Aircraft-mounted probes, such as the Cloud Particle Imager (CPI), capture high-resolution 2D images of ice crystals during in-flight sampling to determine morphology and size distribution. The CPI uses a charge-coupled device camera with 2.3 μm pixel resolution to image particles from approximately 10 μm to 2 mm, achieving sizing accuracy on the order of 10 μm for small crystals by analyzing shadow projections and laser-illuminated silhouettes. These images reveal habits like plates, columns, and dendrites, supporting studies of crystal evolution in convective updrafts, with automated classification tools enhancing habit identification accuracy beyond 80%. Satellite infrared observations detect cirrus clouds containing ice crystals through brightness temperature (BT) differences in the 11–12 μm atmospheric window. Thin ice clouds exhibit positive BT differences (BT_{11μm} - BT_{12μm} > 0–2 K) due to stronger ice absorption at 12 μm compared to 11 μm, contrasting with near-zero differences over clear skies or liquid clouds. This method, applied to instruments like MODIS and ABI, identifies subvisual cirrus with optical depths <0.3, providing global coverage for climate monitoring, though it is less sensitive to thick ice layers. As of 2025, the EarthCARE satellite (launched in 2024) enhances these capabilities with its Cloud Profiling Radar (CPR) providing Doppler measurements of ice crystal fall speeds and the Atmospheric Lidar (ATLID) for depolarization-based habit discrimination in global cloud profiles.^[68]

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Mar 25, 2015 · Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement.
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Strong dependence of cubic ice formation on droplet ammonium to ...
Aug 23, 2007 · We also show that the amount of cubic ice formed in the aqueous solution droplets at temperatures below 200 K is independent of droplet size, ...
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Classical nucleation theory of homogeneous freezing of water
The sensitivity is governed by one parameter – the interfacial tension between ice and water, which determines the energetic barrier of the nucleation process.Missing: crystals | Show results with:crystals
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Direct calculation of ice homogeneous nucleation rate for a ... - PNAS
We use a path sampling approach to perform, to our knowledge, the first direct rate calculation of homogeneous nucleation of ice in a molecular model of water.
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A Classical-Theory-Based Parameterization of Heterogeneous Ice ...
The parameterization treats immersion, contact, and deposition nucleation by mineral dust, soot, bacteria, fungal spores, and pollen in mixed-phase clouds.
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An Empirical Parameterization of Heterogeneous Ice Nucleation for ...
Heterogeneous nucleation of ice, by which crystals are formed on the insoluble components of aerosol particles, is one of the processes to be represented when ...
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Brief Overview of Ice Nucleation - PMC - PubMed Central
Jan 13, 2021 · Classical nucleation theory in the broadest sense refers to a theoretical framework that allows temporary formations of spatially non-uniform ...
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Predicting global atmospheric ice nuclei distributions and their ... - NIH
Ice nucleation in clouds occurs via two primary pathways: homogeneous freezing of liquid particles below about -36 °C and heterogeneous ice nucleation, ...
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Including Surface Kinetic Effects in Simple Models of Ice Vapor ...
In cloud modeling, difficulties solving the diffusion equations are the reason for the near universal use of the capacitance method (Pruppacher and Klett 1997, ...Missing: formula | Show results with:formula
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https://www.nature.com/articles/s41467-025-63664-z
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In situ observations of spiral growth on ice crystal surfaces
Sep 10, 2018 · The spiral growth of crystals, mediated by their screw dislocations, is a general crystal-growth mechanism observed over a large variety of crystalline solids.
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https://doi.org/10.1175/1520-0469(1994)051
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https://link.aps.org/doi/10.1103/PhysRevMaterials.2.093402
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A Parameterization of Sticking Efficiency for Collisions of Snow and ...
Dec 1, 2015 · Aggregation of ice crystals in collisions to form snowflakes is one of the important processes in the growth of precipitation particles in ...
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https://doi.org/10.1175/1520-0469(1998)055
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[PDF] Structure of Ordinary Ice Ih. Part 1 - DTIC
This report examines the defect-free structure of ordinary \h reviewing experimental results and theoretical models of the arrangement of oxygen and hydrogen.<|control11|><|separator|>
[25]
Evaluation of Ten Fresh Snow Density Parameterization Schemes ...
As fresh snow density varies widely, roughly 0.1~0.35 g/cm3 [29], it is challenging to parameterize it in the land surface processes models. A study has shown ...
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Ice hardness in winter sports - ScienceDirect.com
Ice hardness at athletic ice surfaces was 22 ± 7 MPa at − 12 °C, a value that falls between the results of previous studies.
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Ice - Properties - The Engineering ToolBox
Youngs modulus of elasticity E (GPa): 9.1 · Fracture of toughness Kc (MPa m1/2): 0.12 · Ultimate tensile strength σu (MPa): 1 · Compressive strength σc (MPa): 6 ...
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Measurement of Cleavage Strength in Ice Crystals by a Laser ...
For crack growth along the basal planes, the intrinsic toughness values of (0.206±0.032) J/m2 at −10°C and (0.214±0.032) J/m2 at −40°C were obtained using a ...
[29]
Ice Particle Mass–Dimensional Relationship Retrieval and ...
Mar 1, 2017 · A Bayesian optimal estimation methodology is applied to retrieve the time-varying ice particle mass–dimensional (M–D) relationships.
[30]
Ice - Thermal Properties - The Engineering ToolBox
Thermal and thermodynamic properties of ice like density, thermal conductivity and specific heat at temperatures from 0 to -100 o C.Missing: parallel axis
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Effective thermal conductivity of reservoir freshwater ice with ...
Jul 26, 2017 · Landauer and Plumb (1956) found that the conductivity of monocrystal ice is a little higher (by 5%) parallel to the c-axis than perpendicular to ...
[32]
[PDF] THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL ...
The thermal conductivity value of pure water ice is inversely proportional to the temperature and decreases about 5-fold as the temperature increases from the ...
[33]
Field observations on spatial variability of surface hoar at the basin ...
Hence their shape and growth rate depend on temperature and on the excess vapour density over ice. ... (= 2.83 MJ kg−1) is the latent heat of sublimation, equation ...
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Use of dielectric spectroscopy to estimate ice content in frozen ...
Apr 22, 2004 · At frequencies larger than the relaxation frequency of ice (≈1 to 10 kHz), the dielectric permittivity of ice is about 3.2, at frequencies ...
[35]
The role of acids in electrical conduction through ice - AGU Journals
Jan 24, 2013 · The high input impedance (1014 Ω) enables measurement of conductivities as low as 10–12 S m–1. Measurement temperatures varied between –90°C and ...
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The Ice Crystal–Graupel Collision Charging Mechanism of ...
The ice crystal-graupel collision charging mechanism involves charge transfer when ice crystals collide with graupel, and is strongly affected by relative ...
[37]
Radio frequency ice dielectric permittivity measurements using ...
Feb 27, 2016 · At optical frequencies, Ih ice has an extraordinary index of 1.313 and an ordinary index of 1.309, corresponding to a wave speed asymmetry ...
[38]
Refractive index of CRYSTALS - ice - RefractiveIndex.INFO
Ice, the solid state of water, also has specific optical characteristics like birefringence and is studied for its role in atmospheric optics. Water vapor, on ...<|separator|>
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Optical properties of ice and snow - Journals
Apr 15, 2019 · Ordinary ice has a hexagonal crystal structure, so it is birefringent; refraction depends on the angle between the c-axis of the crystal and the ...
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Polarimetry of a 22° halo - Optica Publishing Group
a The 22° halo angles were calculated using the indices of refraction of ice given by Hobbs23 which are valid with respect to vacuum and a given are the ...
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Light Scattering by Quasi-Spherical Ice Crystals in - AMS Journals
The radii r of the ice crystals range from about 8 to 90 μm (see Table 1), so the size parameter x = 2πr/λ ranges from about 90 to 1000. Given these size ...
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[PDF] Light Scattering by Nonspherical Particles
... Mie theory or its modifications. However, many natural and artificial small particles have nonspherical overall shapes or lack a spherically symmetric ...
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A New Parameterization of an Asymmetry Factor of Cirrus Clouds for ...
The asymmetry factor of hexagonal ice particles in the solar spectrum is dominated by its aspect ratio, D/L, where D and L are the particle width and length, ...
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[PDF] Dependence of ice crystal optical properties on particle aspect ratio
This study is intended to provide an in-depth analysis of the dependence of the single- scattering properties of hexagonal ice crystals on their aspect ratios; ...
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[PDF] Optical properties of ice and snow - PSI Indico
Jan 12, 2018 · The absorption coefficient varies by ten orders of magnitude from the near-UV (300 nm wavelength) to the near-IR (3 micrometers). The blue and ...
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A global survey of CALIPSO linear depolarization ratios in ice clouds ...
Nov 14, 2009 · The linear depolarization ratio δ is commonly used in the lidar field to quantify changes in the backscattered polarization state, and is ...
[47]
Mishchenko and Sassen 1998: Depolarization of lidar ... - NASA GISS
We show that ice crystals with effective radii as small as several tenths of a micron can already produce δ exceeding 0.5 at visible wavelengths. This may ...
[48]
[PDF] Review of the vapour pressures of ice and supercooled water for ...
This review covers vapor pressures of ice and supercooled water for atmospheric applications, including cirrus clouds and ice crystal growth. Parametrizations ...
[49]
Limitations of the Wegener–Bergeron–Findeisen Mechanism in the ...
Findeisen (1938) provided experimental confirmation of enhanced growth of ice crystals in clouds containing both ice crystals and supercooled liquid droplets.
[50]
Collision Efficiencies of Ice Crystals at Low–Intermediate Reynolds ...
The riming rate hinges on two quantities: the collision efficiency between ice particles and supercooled droplets, and the coalescence efficiency of the ...
[51]
Riming of Graupel: Wind Tunnel Investigations of Collection Kernels ...
Aug 1, 2009 · The latter process involves the collection of supercooled liquid droplets by ice particles and proceeds very efficiently, leading to the ...
[52]
Evaporation and melting of ice crystals: A laboratory study
Neither columns nor plates fragmented during evaporation; melting columns shed only water, while no water-shedding at all took place during melting of plates.
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Snow Size Distribution Parameterization for Midlatitude and Tropical ...
In this study a moment estimation parameterization applicable to both midlatitude and tropical ice clouds is proposed.
[54]
[PDF] A global classification of snow crystals, ice crystals, and solid ...
'Dendrite-type' refers to snow crystals similar in shape to dendrites. This crystal type is the most typical shape of crystals found in the mid-latitudes. It is ...
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A Lagrangian Perspective on Tropical Anvil Cloud Lifecycle in ...
Jan 21, 2021 · Accretion is the removal of ice crystals by collisions with snowflakes and is an important sink of ice in the precipitating stage of the anvil ...
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https://journals.ametsoc.org/view/journals/atsc/64/12/2007jas2344.1.xml
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Radiative effect of thin cirrus clouds in the extratropical lowermost ...
Jan 29, 2024 · ... cirrus radiative forcing (of ∼ 0.1 W m−2). The radiative effect is also dependent on the cloud vertical extent and consequently the ...
[58]
In Situ Aircraft Measurements of the Vertical Distribution of Liquid ...
Recent studies indicate that 40%–60% of clouds in the temperature range between 0° and −30°C are mixed phase and 30%–60% are supercooled liquid water clouds ( ...
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[PDF] Global indirect aerosol effects: a review - ACP
Mar 3, 2005 · Because the precipitation formation via the ice phase is more efficient than in warm clouds, these glaciated clouds have a shorter lifetime than ...
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Space observations of cold-cloud phase change - PNAS
... cloud radiative effects. At -20 °C, the global average fraction of supercooled clouds in the total cloud population is found to be about 50% in the data period.
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Predicting global atmospheric ice nuclei distributions and their ...
Jun 7, 2010 · In addition, since ice nucleation is tied to the action of specific aerosol particles, natural and human impacts on ice nucleation in the ...
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The importance of mixed-phase and ice clouds for climate sensitivity in the global aerosol–climate model ECHAM6-HAM2
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