Statement of Electroneutrality (part 1): If the total
charge on a cation is divided by the number of anions immediately
surrounding it (the Coord #), the fraction is the amount of charge
the cation contributes to satisfying each anion.
Statement of Electroneutrality (part 2): The fraction of
charge received by an anion from neighboring cations, must equal (or
approximately equal) it's valency.
Common edges, and especially common faces, between polyhedra
diminish stability
Shared corners between polyhedra are most common.
In this configuration the central cations remain ~ far
apart.
Shared edges are less common.
Usually only occur for cubes and octahedrons
Very rare for tetrahedrons because central cations of
neighboring tetrahedrons come too close together.
Repulsion between the positive cation charges creates
instabilty.
Shared faces are uncommon.
will occur for cubes
NEVER occurs for tetrahedrons
Corollary to #3: In a crystal containing different cations,
those with high valence and low coordination number tend NOT to share polyhedral elements
because the repulsive forces are too great.
i.e., high valence => high charges => strong repulsive forces
low CN => few surrounding ions => few shielding anions
Principle of Parsimony: The number of essentially
different polyhedral constituents in a crystal structure tends to be
small (minerals avoid complexity - generally contain 2-3 polyhedra at
most).
