an anion

An anion is an atom that has gained one or more electrons and so carries a negative charge. In the oxide ceramics that dominate the field the anion is almost always oxygen, O2-, which has grabbed two electrons; in other families it is nitrogen (N3-), carbon (as carbide), fluorine or chlorine. Gaining electrons puffs an atom up, because the extra electrons crowd and repel one another around the same nucleus, so anions are the big partners in a ceramic, and it is usually the anions that form the roomy scaffold.

Because the anions are large and the cations small, the natural way to picture most ceramic crystals is upside-down from how we name them: the anions pack together like stacked oranges (close packing), and the little cations drop into the gaps between them. Oxygen ions, being big and only doubly charged, are fairly squishy (polarizable), which is part of why real oxides are never perfectly ionic. Counting how many cations surround each anion, and demanding that their pulls add up to neutralise the anion's charge, is the heart of Pauling's electrostatic-valence rule.

The anion sublattice sets the stage. In MgO, Al2O3, and spinel the oxygen ions sit in essentially the same close-packed arrangement, and the different minerals are just different ways of filling the cation gaps, a powerful unifying idea. Anion movement matters too: in a solid-oxide fuel cell it is O2- ions that hop through the ceramic electrolyte to carry the current, and oxygen vacancies (missing anions) are among the most important defects in all of ceramics.