Growth habits and growth rates of snow crystals

Abstract

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. Masonet al. (Phil. Mag. 8, 505 (1963)) determined experimentally the average migration distancexBfor water molecules diffusing across the basal surface of ice crystals as a function of temperature. These measurements ofxBhave now been supplemented by calculations of the corresponding quantityxpfor the prism faces from measurements of the limitingc/aratios of small growing crystals whose shape is largely determined by the values of bothxpandxB. 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 diameterdcexceeds 1.6 x 105x2p/Dv, whereDvis the diffusion coefficient of water vapour in air. Plates grow in the temperature range –8 °C to –23 °C, for whichdcranges from 50 µm at –15 °C to 670 µm at –8 °C. For falling ventilated plates the corresponding values ofdcare 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 ) ofsectorplates 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.