Vapour pressure/solubility of small and big grain surfaces and corners

[snorkack]

When a condensed phase - solid or liquid - is in an immiscible fluid (gas or liquid), it has surface energy. Several small pieces of condensed phase have bigger combined surface than one bigger piece of the phase of the same volume, and thus bigger energy.

In case of liquid, the surface of a drop is curved and smooth. Due to surface tension, the curvature of a liquid drop equalizes. Which means that the surface energy is equal everywhere on the drop, and so is the vapour pressure or solubility.

But a solid grain possesses crystal faces, edges and corners. These must always enclose the volume of the crystal.
How does a crystal ensure that the binding energy of a molecule to a corner is identical to the binding energy of the same molecule to any other corner, edge or face of the same crystal - BUT smaller than binding energy of the same molecule to equally flat face of a bigger crystal?

 

[Lord Jestocost]

Different crystallographic faces of crystals have in general different surface energies, due to differences in bonding or atom density. The equilibrium shape of a crystal corresponds to a minimization of the total surface energy.

 

[snorkack]

Different crystallographic faces of crystals have in general different surface energies, due to differences in bonding or atom density. The equilibrium shape of a crystal corresponds to a minimization of the total surface energy.

The paradox I see here is the issue of total/local energy minimization. In case of a spherical liquid drop, the matter is easy - the drop adopts curvature which ensures uniform surface energy at every specific point. But in case of crystal - the action of a molecule evaporating or dissolving from a surface, edge or corner or depositing at another such place should respond only to local conditions, therefore how does it manage to minimize the total surface energy?

 

[Lord Jestocost]

One possibility is surface diffusion at higher temperatures.

 

[snorkack]

This does not resolve the paradox. Because since the equilibrium is between initial state of molecule attached to one place on the crystal and final state with the molecule attached to another place on the same crystal, it is irrelevant whether the intermediate state has the molecule in a gas phase, dissolved in a solvent or moving around along the surface.

 

[Lord Jestocost]

The paradox I see here is the issue of total/local energy minimization.

Where is here a paradox.

In case of solids, surface energy minimization can be attained if the constituents are mobile enough to rearrange themselves in reasonable times (normally at high temperatures).

The Wulff construction is a method to determine the equilibrium shape of a crystal of fixed volume inside a separate phase (usually its saturated solution or vapor). Energy minimization arguments are used to show that certain crystal planes are preferred over others, giving the crystal its shape.

https://en.wikipedia.org/wiki/Wulff_construction