Free energy of formation of a crystal nucleus in incongruent solidification: Implication for modeling the crystallization of aqueous nitric acid droplets in type 1 polar stratospheric clouds

摘要

Using the formalism of the classical nucleation theory, we derive anexpression for the reversible work $W_*$ of formation of a binary crystalnucleus in a liquid binary solution of non-stoichiometric composition(incongruent crystallization). Applied to the crystallization of aqueous nitricacid (NA) droplets, the new expression more adequately takes account of theeffect of nitric acid vapor compared to the conventional expression ofMacKenzie, Kulmala, Laaksonen, and Vesala (MKLV) [J.Geophys.Res. 102, 19729(1997)]. The predictions of both MKLV and modified expressions for the averageliquid-solid interfacial tension $\sigma^{ls}$ of nitric acid dihydrate (NAD)crystals are compared by using existing experimental data on the incongruentcrystallization of aqueous NA droplets of composition relevant to polarstratospheric clouds (PSCs). The predictions based on the MKLV expression arehigher by about 5% compared to predictions based on our modified expression.This results in similar differences between the predictions of both expressionsfor the solid-vapor interfacial tension $\sigma^{sv}$ of NAD crystal nuclei.The latter can be obtained by analyzing of experimental data on crystalnucleation rates in aqueous NA droplets and exploiting the dominance of thesurface-stimulated mode of crystal nucleation in small droplets and itsnegligibility in large ones. Applying that method, our expression for $W_*$provides an estimate for $\sigma^{sv}$ of NAD in the range from 92 dyn/cm to100 dyn/cm, while the MKLV expression predicts it in the range from 95 dyn/cmto 105 dyn/cm. The predictions of both expressions for $W_*$ become identicalin the case of congruent crystallization; this was also demonstrated byapplying our method to the nucleation of nitric acid trihydrate (NAT) crystalsin PSC droplets of stoichiometric composition.