Title: 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,
Abstract: Using the formalism of the classical nucleation theory, we derive an
expression for the reversible work $W_*$ of formation of a binary crystal
nucleus in a liquid binary solution of non-stoichiometric composition
(incongruent crystallization). Applied to the crystallization of aqueous nitric
acid (NA) droplets, the new expression more adequately takes account of the
effect of nitric acid vapor compared to the conventional expression of
MacKenzie, Kulmala, Laaksonen, and Vesala (MKLV) [J.Geophys.Res. 102, 19729
(1997)]. The predictions of both MKLV and modified expressions for the average
liquid-solid interfacial tension $\sigma^{ls}$ of nitric acid dihydrate (NAD)
crystals are compared by using existing experimental data on the incongruent
crystallization of aqueous NA droplets of composition relevant to polar
stratospheric clouds (PSCs). The predictions based on the MKLV expression are
higher by about 5% compared to predictions based on our modified expression.
This results in similar differences between the predictions of both expressions
for the solid-vapor interfacial tension $\sigma^{sv}$ of NAD crystal nuclei.
The latter can be obtained by analyzing of experimental data on crystal
nucleation rates in aqueous NA droplets and exploiting the dominance of the
surface-stimulated mode of crystal nucleation in small droplets and its
negligibility 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 to
100 dyn/cm, while the MKLV expression predicts it in the range from 95 dyn/cm
to 105 dyn/cm. The predictions of both expressions for $W_*$ become identical
in the case of congruent crystallization; this was also demonstrated by
applying our method to the nucleation of nitric acid trihydrate (NAT) crystals
in PSC droplets of stoichiometric composition.