Introduction

After the nucleation of an ice-water particle or crystal, the addition of ice mass to the particle or crystal owing to supersaturation with respect to ice is called deposition. Furthermore, the loss of ice mass from an ice-water particle or crystal owing to subsaturation with respect to ice is called sublimation. Together these are called vapor diffusion of ice-water particles and crystals that are both governed by the same equation, which is nearly identical in form to that for diffusion of liquid-water particles except for some constants and shape parameters. The derivation for the vapor diffusion equation follows much the same path as that for deriving a basic equation to represent vapor diffusion for liquid-water particles. The main differences are related to the enthalpies of heat (enthalpy of sublimation instead of enthalpy of evaporation), and the particular shape factors for ice crystals, which include, for example: spheres; plates; needles; dendrites; sectors; stellars; and bullets and columns that can be either solid or hollow, etc. (see Pruppacher and Klett 1997 for habits at temperatures between 273.15 and 253.15 K, and Bailey and Hallet 2004 for habits at temperatures colder than 253.15 K).

Typically, for diffusion growth of ice-water particles and crystals, the electrostatic analog is invoked. This is similar to stating that the vapor diffusion growth of the various ice-water crystal shapes is related to the capacitance of the various shapes. The main shapes that are representative of the various ice-water particles include spheres, thin plates, oblates, and prolates.