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Rules of structure formation for the homologous InMO3(ZnO)n compounds.

The formation mechanisms that lead to the layered M-modulated InMO3(ZnO){n} structures (M=In, Ga, and Al; n=integer) are revealed and confirmed by first-principles calculations based on density functional theory. We show that all ground state structures of InMO3(ZnO){n} satisfy the octahedron rule for the InO2 layers; they contain an inversion domain boundary located at the M and Zn fivefold trigonal bipyramid sites and maximize the hexagonality in the (MZn{n})O{n+1} layers. They also obey the electronic octet rule. This understanding provides a solid basis for studying and understanding the physical properties of this group of homologous materials.