Growth habits and growth rates of snow crystals
Growth habits and growth rates of snow crystals
复制标题
雪晶的生长习性和生长速度
DOI：
10.1098/rspa.1993.0045
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
B. J. Mason
中科院分区：
文献类型：
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作者：
B. J. Mason
本文根据大气温度、过饱和度及其终端速度导出了雪晶在大气中下落时的生长速率方程。预测的正六边形板（0.84 mm）、扇形板（约1.5 mm）、2毫米）和恒星树突（3.5毫米）是在良好的协议与观测的基础上Nakaya的大量收集的雪晶照片。Mason等人（Phil. Mag.8，505（1963））通过实验确定了作为温度的函数的水分子扩散穿过冰晶基底表面的平均迁移距离xB。这些xB的测量现在已经通过从小生长晶体的极限c/a比的测量中计算棱镜面的相应量xp来补充，小生长晶体的形状主要由xp和xB的值决定。枝晶生长开始的理论处理导致的结果是，当其直径dc超过1.6 × 105 × 2 p/Dv时，固定的薄正六边形板开始在拐角处发芽，其中Dv是水蒸气在空气中的扩散系数。平板在-8 °C至-23 °C的温度范围内生长，其直流范围为-15 °C时的50 µm至-8 °C时的670 µm。对于下落的通风板，在50 µm和940 µm处的dc值分别相当大，因为晶体周围的蒸汽浓度梯度增强了。这些后者的值分别同意与观察到的最小尺寸的薄板在恒星树枝状晶体的中心，并与观察到的最大尺寸的定期板。观察到的树枝状晶体中心扇形板的最大直径（1.2 mm）与基于以下假设的计算结果吻合得很好，即这些晶体起源于约-20 °C水平，只有在低于-16 °C水平后才发展成树枝状晶体。一种机制，基于外部蒸汽扩散场之间的相互作用，它非常迅速地响应于晶体几何形状的局部变化，和更缓慢的过程中的表面扩散，建议占对称的树枝状生长的每一个恒星晶体的六个臂，也解释观察到，一旦不对称是偶然引入的一个臂的一侧，它往往会持续。
Equations are derived for the growth rates of snow crystals as they fall through the atmosphere in terms of the air temperature, supersaturation and their terminal velocities. The predicted maximum attainable diameters of regular hexagonal plates(0.84 mm), sector plates (ca. 2 mm) and stellar dendrites (3.5 mm) are in good agreement with observations based on Nakaya’s large collection of snow crystal photographs. Mason et al. (Phil. Mag. 8, 505 (1963)) determined experimentally the average migration distance xB for water molecules diffusing across the basal surface of ice crystals as a function of temperature. These measurements of xB have now been supplemented by calculations of the corresponding quantity xp for the prism faces from measurements of the limiting c/a ratios of small growing crystals whose shape is largely determined by the values of both xp and xB. A theoretical treatment for the onset of dendritic growth leads to the result that a stationary thin regular hexagonal plate starts to sprout at the corners when its diameter dc exceeds 1.6 x 105 x2p/Dv, where Dv is the diffusion coefficient of water vapour in air. Plates grow in the temperature range –8 °C to –23 °C, for which dc ranges from 50 µm at –15 °C to 670 µm at –8 °C. For falling ventilated plates the corresponding values of dc are rather larger at 50 µm and 940 µm respectively, because the vapour concentration gradients around the crystal are enhanced. These latter values agree respectively with the observed minimum sizes of thin plates found at the centres of stellar dendritic crystals, and with the observed maximum size of regular plates. The observed maximum diameter (1.2 mm ) of sector plates at the centre of dendritic crystals agrees well with calculations based on the assumption that these originate at about the –20 °C level and develop into dendrites only after falling below the –16 °C level. A mechanism, based on the interplay between the external vapour diffusion field, which responds very rapidly to local changes in crystal geometry, and the much more sluggish process of surface diffusion, is suggested to account for the symmetrical dendritic growth of each of the six arms of a stellar crystal and also to explain the observation that once asymmetry is accidentally introduced on one side of an arm, it tends to persist.