Pauling's rules

From Wikipedia, the free encyclopedia

Pauling's rules are five rules developed by Linus Pauling for determining the molecular structures of complex crystals.

1. A coordinated polyhedron of anions is formed about each cation, the cation-anion distance determined by the sum of ionic radii and the coordination number (C.N.) by the radius ratio.

° Common coordination polyhedra are: C.N. = 2 (linear, bent), C.N. = 3 (trigonal planar, pyramidal), C.N. = 4 (tetrahedral, pyramidal, square planar), C.N. = 5 (trigonal bypiramidal, squere pyramidal), C.N. = 6 (trigonal prysmatic, octahedral), C.N. = 7 (capped trigonal prismatic), C.N. = 8 (square anti-prismatic, cubic, dodecahedral), C.N. = 9 (tri-capped trigonal prysmatic), C.N. = 12 (cuboctahadral, anti-cuboctahedral).

2. An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an anion equal the charge on that anion.

° i.e. A stable ionic structure must be arranged to preserve Local Electroneutrality.

3. The sharing of edges and particularly faces by two anion polyhedra decreases the stability of an ionic structure.

° Effect is largest for cations with high charge and low C.N (especially when r+/r- approaches the lower limit of the polyhedral stability).

4. In a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with one another.

5. The number of essentially different kinds of constituents in a crystal tends to be small.

° Similar environments for chemically similar atoms.