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

Using the formalism of classical thermodynamics in the framework 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 droplets, the new expression more adequately takes account of the effects of nitric acid vapor compared to the conventional expression of MacKenzie, Kulmala, Laaksonen, and Vesala (MKLV) [J. Geophys. Res.: Atmos. 102, 19729 (1997)]. The predictions of both MKLV and modified expressions for the average liquid-solid interfacial tension σls of nitric acid dihydrate (NAD) crystals are compared by using existing experimental data on the incongruent crystallization of aqueous nitric acid droplets of composition relevant to polar stratospheric clouds (PSCs). The predictions for σls 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 σsv of NAD crystal nuclei. The latter can be obtained by using the method based on the analysis of experimental data on crystal nucleation rates in aqueous nitric acid droplets; it exploits the dominance of the surface-stimulated mode of crystal nucleation in small droplets and its negligibility in large ones. Applying that method to existing experimental data, our expression for the free energy of formation provides an estimate for σsv of NAD in the range ≈92 dyn/cm to ≈100 dyn/cm, while the MKLV expression predicts it in the range ≈95 dyn/cm to ≈105 dyn/cm. The predictions of both expressions for W* become identical for the case of congruent crystallization; this was also demonstrated by applying our method for determining σsv to the nucleation of nitric acid trihydrate crystals in PSC droplets of stoichiometric composition.