skip to main content

Title: Approximate Models for Lateral Growth on Ice Crystal Surfaces during Vapor Depositional Growth
Abstract Measurements show that after facets form on frozen water droplets, those facets grow laterally across the crystal surface leading to an increase in volume and surface area with only a small increase in maximum dimension. This lateral growth of the facets is distinctly different from that predicted by the capacitance model and by the theory of faceted growth. In this paper we develop two approximate theories of lateral growth, one that is empirical and one that uses explicit growth mechanisms. We show that both theories can reproduce the overall features of lateral growth on a frozen, supercooled water droplet. Both theories predict that the area-average deposition coefficient should decrease in time as the particle grows, and this result may help explain the divergence of some prior measurements of the deposition coefficient. The theories may also explain the approximately constant mass growth rates that have recently been found in some measurements. We also show that the empirical theory can reproduce the lateral growth that occurs when a previously sublimated crystal is regrown, as may happen during the recycling of crystals in cold clouds.
Authors:
;
Award ID(s):
1824243
Publication Date:
NSF-PAR ID:
10250486
Journal Name:
Journal of the Atmospheric Sciences
Volume:
78
Issue:
3
Page Range or eLocation-ID:
967 to 981
ISSN:
0022-4928
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract. Ice growth from vapor deposition is an important process for the evolution of cirrus clouds, but the physics of depositional ice growth at the low temperatures (<235 K) characteristic of the upper troposphere and lower stratosphere is not well understood. Surface attachment kinetics, generally parameterized as a deposition coefficient αD, control ice crystal habit and also may limit growth rates in certain cases, but significant discrepancies between experimental measurements have not been satisfactorily explained. Experiments on single ice crystals have previously indicated the deposition coefficient is a function of temperature and supersaturation, consistent with growth mechanisms controlled by the crystal's surface characteristics. Here we use observations from cloud chamber experiments in the Aerosol Interactions and Dynamics in theAtmosphere (AIDA) aerosol and cloud chamber to evaluate surface kinetic models in realistic cirrus conditions. These experiments have rapidly changing temperature, pressure, and ice supersaturation such that depositional ice growth may evolve from diffusion limited to surface kinetics limited over the course of a single experiment. In Part 1, we describe the adaptation of a Lagrangian parcel model with the Diffusion Surface Kinetics Ice Crystal Evolution (DiSKICE) model (Zhang and Harrington, 2014) to the AIDA chamber experiments. We compare the observed ice water content andmore »saturation ratios to that derived under varying assumptions for ice surface growth mechanisms for experiments simulating ice clouds between 180 and 235 K and pressures between 150 and 300 hPa. We found that both heterogeneous and homogeneous nucleation experiments at higher temperatures (>205 K) could generally be modeled consistently with either a constant deposition coefficient or the DiSKICE model assuming growth on isometric crystals via abundant surface dislocations. Lower-temperature experiments showed more significant deviations from any depositional growth model, with different ice growth rates for heterogeneous and homogeneous nucleation experiments.« less
  2. There are few measurements of the vapor growth of small ice crystals at temperatures below -30°C. Presented here are mass-growth measurements of heterogeneously and homogeneously frozen ice particles grown within an electrodynamic levitation diffusion chamber at temperatures between -44 and -30°C and supersaturations ( s i ) between 3 and 29%. These growth data are analyzed with two methods devised to estimate the deposition coefficient ( α) without the direct use of s i . Measurements of s i are typically uncertain, which has called past estimates of α into question. We find that the deposition coefficient ranges from 0.002 to unity and is scattered with temperature, as shown in prior measurements. The data collectively also show a relationship between α and s i , with α rising (falling) with increasing s i for homogeneously (heterogeneously) frozen ice. Analysis of the normalized mass growth rates reveals that heterogeneously-frozen crystals grow near the maximum rate at low s i , but show increasingly inhibited (low α) growth at high s i . Additionally, 7 of the 17 homogeneously frozen crystals cannot be modeled with faceted growth theory or constant α. These cases require the growth mode to transition from efficient tomore »inefficient in time, leading to a large decline in α. Such transitions may be, in part, responsible for the inconsistency in prior measurements of α.« less
  3. Abstract
    Excessive phosphorus (P) applications to croplands can contribute to eutrophication of surface waters through surface runoff and subsurface (leaching) losses. We analyzed leaching losses of total dissolved P (TDP) from no-till corn, hybrid poplar (Populus nigra X P. maximowiczii), switchgrass (Panicum virgatum), miscanthus (Miscanthus giganteus), native grasses, and restored prairie, all planted in 2008 on former cropland in Michigan, USA. All crops except corn (13 kg P ha−1 year−1) were grown without P fertilization. Biomass was harvested at the end of each growing season except for poplar. Soil water at 1.2 m depth was sampled weekly to biweekly for TDP determination during March–November 2009–2016 using tension lysimeters. Soil test P (0–25 cm depth) was measured every autumn. Soil water TDP concentrations were usually below levels where eutrophication of surface waters is frequently observed (&gt; 0.02 mg L−1) but often higher than in deep groundwater or nearby streams and lakes. Rates of P leaching, estimated from measured concentrations and modeled drainage, did not differ statistically among cropping systems across years; 7-year cropping system means ranged from 0.035 to 0.072 kg P ha−1 year−1 with large interannual variation. Leached P was positively related to STP, which decreased over the 7 years in all systems. These results indicate that both P-fertilized and unfertilized cropping systems mayMore>>
  4. Abstract Theories of the Beaufort Gyre (BG) dynamics commonly represent the halocline as a single layer with a thickness depending on the Eulerian-mean and eddy-induced overturning. However, observations suggest that the isopycnal slope increases with depth, and a theory to explain this profile remains outstanding. Here we develop a multilayer model of the BG, including the Eulerian-mean velocity, mesoscale eddy activity, diapycnal mixing, and lateral boundary fluxes, and use it to investigate the dynamics within the Pacific Winter Water (PWW) layer. Using theoretical considerations, observational data, and idealized simulations, we demonstrate that the eddy overturning is critical in explaining the observed vertical structure. In the absence of the eddy overturning, the Ekman pumping and the relatively weak vertical mixing would displace isopycnals in a nearly parallel fashion, contrary to observations. This study finds that the observed increase of the isopycnal slope with depth in the climatological state of the gyre is consistent with a Gent–McWilliams eddy diffusivity coefficient that decreases by at least 10%–40% over the PWW layer. We further show that the depth-dependent eddy diffusivity profile can explain the relative magnitude of the correlated isopycnal depth and layer thickness fluctuations on interannual time scales. Our inference that the eddymore »overturning generates the isopycnal layer thickness gradients is consistent with the parameterization of eddies via a Gent–McWilliams scheme but not potential vorticity diffusion. This study implies that using a depth-independent eddy diffusivity, as is commonly done in low-resolution ocean models, may contribute to misrepresentation of the interior BG dynamics.« less
  5. Core–shell Ge/GeSn nanowires provide a route to dislocation-free single crystal germanium-tin alloys with desirable light emission properties because the Ge core acts as an elastically compliant substrate during misfitting GeSn shell growth. However, the uniformity of tin incorporation during reduced pressure chemical vapor deposition may be limited by the kinetics of mass transfer to the shell during GeSn growth. The balance between Sn precursor flux and available surfaces for GeSn nucleation and growth determines whether defects are formed and their type. On the one hand, when the Sn precursor delivery is insufficient, local variations in Sn arrival rate at the nanowire surfaces during GeSn growth produce asymmetries in shell growth that induce wire bending. This inhomogeneous elastic dilatation due to the varying composition occurs via deposition of Sn-poor regions on some of the {112} sidewall facets of the nanowires. On the other hand, when the available nanowire surface area is insufficient to accommodate the arriving Sn precursor flux, Sn-rich precipitate formation results. Between these two extremes, there exists a regime of growth conditions and nanowire densities that permits defect-free GeSn shell growth.