1.6.1 Pauling’s Rules

• Anions being the larger ions form the base lattice and lead to the formation of coordinated polyhedrons around cations. The co-ordination is determined by the radius ratio of cations (r_c) to anions (r_a) i.e. (r_c/r_a). Also, another point to note is that the ionic radius of each ion is also dependent on its co-ordination.

• The structure will be stable when it preserves the charge neutrality (Electrostatic valence rule).

• Corner linking of polyhedrons is preferred over face or edge sharing to ensure larger separation between cations. This is especially true for solids with smaller cations and cations with bigger charges e.g. Ti⁴⁺ and Zr⁴⁺. For example, in SiO₂, due to +4 charge on Si atoms, corner linking of tetrahedrons is preferred.

• In a crystal containing different cations, those of high valence and small coordination number tend not to share the polyhedron elements with one another such as in materials like BaTiO₃.

• The number of essentially different kinds of constituents in a crystal tends to be small. The repeating units will tend to be identical because each atom in the structure is most stable in a specific environment. There may be two or three types of polyhedra, such as tetrahedra or octahedra, but there will not be many different types (Rule of parsimony).