Pauling's Rules

Question 1

Pauling’s first rule:

Answer 1

A coordinating polyhedron of anions is formed about each cation. The sum of the radii determines the cation-anion distance, and the radius ratio determines the coordination number. (Assumes ions are hard spheres).

Question 2

Pauling’s second rule:

Answer 2

In a stable coordinated structure the total strength of the valency bonds which reach an anion from all the neighbouring cations is equal to the charge of the anion. (i.e. electrical neutrality is preferred).

Question 3

Pauling’s third rule:

Answer 3

The existence of edges, and particularly faces, common to two anion polyhedra in a coordinated structure decreases its stability; this effect is large for cations with high valency and small coordination number, and is especially large when the radius ratio approaches the lower limit of the stability of the polyhedron.
eg: CsCl (large coordination) – polyhedra share faces.
NaCl (intermediate coord.) – polyhedra share edges.
ZnS (small coord.) – polyhedra share corners.
Violation of this rule usually means structure is not ionic.

Question 4

Pauling’s fourth rule:

Answer 4

In a crystal containing different cations, this of high valency and small coordination tend not to share polyhedron elements with each other. (Only displayed in more complex structures such as perovskite. High temperature semiconductors are an example).

Question 5

Pauling’s fifth rule:

Answer 5

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