ceramic stoichiometry
Stoichiometry is the fixed, whole-number recipe of a compound, how many of each kind of atom go into its formula. For an ionic ceramic the recipe is not arbitrary: it is forced by electroneutrality, the strict rule that the crystal must carry no net charge. Add up the positive charges of all the cations and the negative charges of all the anions, and the two must exactly cancel.
That single rule generates the whole family of ceramic formulas. If cation and anion charges are equal in size you get AX (Mg2+ with O2- gives MgO; Na+ with Cl- gives NaCl). If the cation carries twice the anion's charge you get AX2 (Ti4+ with two O2- gives TiO2); if the anion is doubly charged and the cation singly, you get A2X (two Li+ with one O2- gives Li2O). A 3+ cation with 2- oxygen gives M2O3 (two Al3+ balance three O2- in Al2O3). Mix two cations and the sums still must balance the oxygens: in ABO3 the A and B charges add to 6 (BaTiO3: 2 + 4), in AB2O4 they add to 8 (MgAl2O4: 2 + 2 times 3).
So stoichiometry and structure are two sides of one coin: the formula tells you the ratio of ions, and the structure tells you which holes they occupy to realise that ratio while packing efficiently. Honest caveat: real ceramics are often deliberately nonstoichiometric. Oxides like wustite (Fe(1-x)O), urania (UO2+x) and titania (TiO2-x) drift off the ideal recipe by creating vacancies or changing a cation's charge, and that controlled cheating on stoichiometry is exactly how we tune their electrical and diffusion behaviour.
Why is titania TiO2 and not TiO? Titanium here is Ti4+ and oxygen is O2-, so it takes two oxygens to soak up one titanium's four positive charges, forcing the AX2 formula, and the rutile structure that houses it.
Charge balance fixes the formula; the formula points to the structure.
A chemical formula is the equilibrium, defect-free ideal. Real ceramics tolerate small departures from it through point defects, and those nonstoichiometric deviations are often what make a ceramic electrically useful.