I present a new set of new rules for Crystal Chemistry that greatly increases our understanding of the factors affecting the stereochemistry of mineral and inorganic crystal structures.

The electric field in a crystal is a vector field; bond strengths from cations to anions are positive and bond strengths from anions to cations are negative. The incident bond strengths at all ion sites must equal the formal charges at those sites. Bond strengths along non-degenerate paths between symmetrically equivalent ions in the structure must sum to zero. This leads to rule 1: the a priori bond-strength rule: “A priori bond-strengths may be calculated for all bonds in a structure by constructing a bond-strength table that includes all bond-strengths as unknown variables. The corresponding charge-conservation matrix can be solved for all the unknown bond-strengths”. The resultant bond strengths depend only on the formal charges of the constituent ions and the bond topology of the structure. However, they correlate strongly with bond lengths.

Ion radii derived from experimental bond lengths do not represent the radii of ions in crystals as we cannot objectively divide bond lengths into the radii of the constituent ions. This leads to rule 2, the ion-radius rule: “Ratios of ion radii have no physical meaning whereas sums of ion radii can be used in crystal chemistry (e.g. correlating site occupancies with observed mean bond lengths).”

The characteristic Lewis acidity of a cation is defined as its characteristic bond strength, which is equal to its charge/characteristic-coordination-number. The characteristic Lewis basicity of an anion is defined as the characteristic strength of the bonds formed by the anion. This leads to rule 3, the bond-strength-matching rule: “Stable structures will form where the Lewis acidity of the cation closely matches the Lewis basicity of the anion.” Cation and anion coordination numbers adjust to optimize matching of Lewis acidities and Lewis basicities.