Relationship between solubility and solubility product: The roles of crystal sizes and crystallographic directions

Grain size- and crystallographic direction-dependence are among the fundamental characteristics of crystal solubility. However, such important material properties are routinely ignored and solubility is often conveniently approximated by a solubility product. In this study, we attempt to outline the relationship between solubility and solubility product using thermodynamic arguments, and to provide observations that demonstrate the occurrence of circumstances where the solubility product cannot properly approximate crystal solubility. Theoretical analysis shows that solubility is always greater than solubility product, but the difference is inversely related to the grain size. Furthermore, the difference can be crystallographic direction specific if the total surface energy change upon the attachment of an individual growth unit is nonequivalent for each symmetrically unrelated crystal faces. In situ AFM experiments conducted on the cleavage face of calcite demonstrate that the steps exhibit direction- and length-dependent behavior. Specifically, the measured critical step lengths are consistent with the predicted inverse relationship to saturation states. Moreover, step retreat at and advance at are observed simultaneously in a narrow range of saturation at near equilibrium conditions, indicating the existence of direction specific solubility. Whereas these findings justify the rationale for approximating solubility by solubility product in cases where large crystals are concerned, the results imply that the size and direction effect should not be ignored if nanocrystal growth/dissolution is the subject of interest.