Pauling's rules
/ PAW-lings /
Pauling's rules are a set of five plain-language guidelines, published by Linus Pauling in 1929, for guessing how a complicated ionic crystal is put together, a kind of grammar for building oxides and silicates. Before computers could solve structures, these rules let a chemist reason out a plausible arrangement of ions from little more than their charges and sizes. They remain the single most useful mental toolkit in ceramic crystal chemistry.
The five rules in plain terms: (1) Each cation sits in a polyhedron of anions whose number and shape are set by the radius ratio, the coordination-polyhedron rule. (2) In a stable crystal the charge of each anion is balanced locally by the bonds reaching it from surrounding cations, the electrostatic-valence rule, the quantitative heart of the set. (3) Sharing edges, and especially faces, between two cation polyhedra is destabilising, because it brings the positive cations closer and they repel. (4) In a crystal with different cations, the highly charged, small ones tend not to share polyhedron elements with each other. (5) The rule of parsimony: the number of essentially different kinds of site in a structure tends to be small.
Together the rules explain why silicate structures are built from corner-sharing (not face-sharing) SiO4 tetrahedra, why certain compositions are stable and others are not, and how to sketch a candidate structure by hand. But they are guidelines distilled from ionic crystals, not laws: they weaken badly for covalent compounds and for very polarizable ions, and modern structure determination has found plenty of well-behaved exceptions. Think of them as an experienced builder's rules of thumb, extraordinarily good but not infallible.
Rule 3 in action: SiO4 tetrahedra in silicates almost always share only corners (single oxygens), never faces, because face-sharing would push the two Si4+ ions dangerously close and the electrostatic repulsion would tear the structure apart.
Why silicates link corner-to-corner, read straight off Pauling's third rule.
Pauling's rules are heuristics for ionic solids, not universal truths. They lose their grip as bonds become covalent, so do not expect them to govern SiC, Si3N4, or other strongly covalent ceramics.