Chapter 22: Ceramic Structures I

The Madelung constant emerges as a critical quantitative tool for calculating lattice energy from electrostatic Coulombic interactions, enabling prediction of structural stability. Pauling's rules serve as the conceptual framework for assessing ceramic stability, with the core principle that structures minimize edge and face sharing between coordination polyhedra when high-charge cations are present. Radius ratio analysis provides geometric predictive power by correlating cation-to-anion size ratios with preferred coordination numbers and polyhedron shapes including tetrahedral, octahedral, and cubic arrangements. The chapter systematically surveys major structure prototypes beginning with simple binary compounds like cesium chloride, sodium chloride, and calcium fluoride, then progresses to sulfide and oxide structures including zinc blende and its wurtzite polymorph. Technologically significant complex oxides receive substantial coverage, particularly corundum as the prototype for alumina applications, perovskites relevant to ferroelectric functionality and multiferroic materials, and spinels displaying both normal and inverse cation ordering in magnetic oxide systems. Additional structure families including nickel arsenide, cadmium iodide, and rutile illustrate non-cubic packing arrangements, while layered superlattice phases such as magnetoplumbites, Aurivillius phases, and Ruddleson-Popper phases demonstrate how anion and cation layers can be systematically stacked. The chapter concludes by transitioning from ideal structures to real materials through point defect analysis, introducing Kroeger-Vink notation as the standard formalism for describing native point defects including Schottky and Frenkel defects that maintain charge neutrality within the crystal lattice.