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

The formation mechanisms that lead to the layered M-modulated InMO(3)(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 InMO(3)(ZnO)(n) satisfy the octahedron rule for the InO(2) 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.