Layered Atom Arrangements in Complex Materials

In this report, we develop an atom layer stacking model to describe systematically the crystal structures of complex materials. To illustrate the concepts, we consider a sequence of oxide compounds in which the metal cations progress in oxidation state from monovalent (M{sup 1+}) to tetravalent (M{sup 4+}). We use concepts relating to geometric subdivisions of a triangular atom net to describe the layered atom patterns in these compounds (concepts originally proposed by Shuichi Iida). We demonstrate that as a function of increasing oxidation state (from M{sup 1+} to M{sup 4+}), the layer stacking motifs used to generate each successive structure (specifically, motifs along a 3 symmetry axis), progress through the following sequence: MMO, MO, M{sub r}O, MO{sub r/s}O{sub u/v}, MOO (where M and O represent fully dense triangular atom nets and r/s and u/v are fractions used to describe partially filled triangular atom nets). We also develop complete crystallographic descriptions for the compounds in our oxidation sequence using trigonal space group R{bar 3}