『Abstract
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 〈441〉（最初の4の頭に-）±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 〈441〉+（最初の4の頭に-）
and advance at 〈441〉-（最初の4の頭に-) and 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.』
1. Introduction
2. Theoretical consideration
2.1. Dependence of Kb on crystal size
2.2. Dependence of Kb on crystallographic
directions
3. Material and methods
3.1. Sample and solution preparation
3.2. Imaging by fluid contact AFM
3.3. Critical step length and step velocity measurement
4. Experimental observations
4.1. Saturation states vs. step lengths
4.2. Saturation states vs. step directions
5. Discussion
5.1. Possibilities for imaging distortion and impurity effect
5.2. Size effect on solubility
5.3. Direction effect on solubility
6. Concluding remark
Acknowledgments
References