An Approximate Criterion for Morphological Transformations in Small Vapor Grown Ice Crystals

Observations and measurements show that crystals remain relatively compact at low ice supersaturations, but become increasingly hollowed and complex as the ice supersaturation rises. Prior measurements at temperatures .2258C indicate that the transition from compact, solid ice to morphologically complex crystals occurs when the excess vapor density exceeds a threshold value of about 0.05 g m²³. A comparable threshold is not available at low temperatures. A temperature-dependent criterion for the excess vapor density threshold (Dr_thr) that defines morphological transformations to complex ice is derived from laboratory measurements of vapor grown ice at temperatures below 2408C. This criterion depends on the difference between the equilibrium vapor density of liquid (r_e‘) and ice (r_ei) multiplied by a measurement-determined constant, Dr_thr ≃ 0:27(r_e‘2 r_ei). The new criterion is consistent with prior laboratory measurements, theoretical estimates, and it reproduces the classical result of about 0.05 g m²³ above 2258C. Since Dr_thr defines the excess vapor density above which crystals transition to a morphologically complex (lower density) growth mode, we can estimate the critical supersaturation (s_crit) for step nucleation during vapor growth. The derived values of s_crit are consistent with previous measurements at temperatures above 2208C. No direct measurements of s_crit are available for temperatures below 2408C; however, our derived values suggest some measurement-based estimates may be too high while estimates from molecular dynamics simulations may be too low.