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The A2BX4 family of compounds manifest a wide range of physical properties, including transparent conductivity, ferromagnetism, and superconductivity. A 98% successful diagrammatic separation of the 44 different crystal structures of 688 oxide A2BX4 compounds (96% for 266 oxide-only) is described by plotting the total radius of the A atom RA versus the radius of the B atom RB for many A2BX4 compounds of known structure types and seeking heuristically simple, straight boundaries in the RA versus RB plane that best separate the domains of different structure types. The radii are sums RA = Rs(A) + Rp(A) of the quantum-mechanically calculated “orbital radii” Rs(Rp), rather than empirical radii or phenomenological electronegativity scales. These success rates using first-principles orbital radii uniformly exceed the success rates using classic radii. Such maps afford a quick guess of the crystal structure of a yet unmade A2BX4 compound by placing its atomic orbital radii on such maps and reading off its structure type.

Stable oxide topological insulators (TIs) have been sought for years, but none have been found; whereas heavier (selenides, tellurides) chalcogenides can be TIs. The basic contradiction between topological insulation and thermodynamic stability is pointed out, offering a narrow window of opportunity. The electronic motif is first identified and can achieve topological band inversion in ABO3 as a lone-pair, electron-rich B atom (e.g., Te, I, Bi) at the octahedral site. Then, twelve ABO3 compounds are designed in the assumed cubic perovskite structure, which satisfy this electronic motif and are indeed found by density function theory calculations to be TIs. Next, it is illustrated that poorly screened ionic oxides with large inversion energies undergo energy-lowering atomic distortions that destabilize the cubic TI phase and remove band inversion. The coexistence windows of topological band inversion and structure stability can nevertheless be expanded under moderate pressures (15 and 35 GPa, respectively, for BaTeO3 and RbIO3). This study traces the principles needed to design stable oxide topological insulators at ambient pressures as a) a search for oxides with small inversion energies; b) design of large inversion-energy oxide TIs that can be stabilized by pressure; and c) a search for covalent oxides where TI-removing atomic displacements can be effectively screened out.