The double perovskites Cs 2 AgBiBr 6 and Cs 2 AgBiCl 6 have been synthesized from both solid state and solution routes. X-ray diffraction measurements show that both compounds adopt the cubic double perovskite structure, space group Fm3̅ m, with lattice parameters of 11.2711(1) Å (X = Br) and 10.7774(2) Å (X = Cl). Diffuse reflectance measurements reveal band gaps of 2.19 eV (X = Br) and 2.77 eV (X = Cl) that are slightly smaller than the band gaps of the analogous lead halide perovskites, 2.26 eV for CH 3 NH 3 PbBr 3 and 3.00 eV for CH 3 NH 3 PbCl 3 . Band structure calculations indicate that the interaction between the Ag 4d-orbitals and the 3p/4porbitals of the halide ion modifies the valence band leading to an indirect band gap. Both compounds are stable when exposed to air, but Cs 2 AgBiBr 6 degrades over a period of weeks when exposed to both ambient air and light. These results show that halide double perovskite semiconductors are potentially an environmentally friendly alternative to the lead halide perovskite semiconductors.

The 23 Glazer tilt systems describing octahedral tilting in perovskites have been investigated. It is shown that in tilt systems a + a + a −, a + b + b −, a + a + c −, a + b + c −, a 0 b + b − and a 0 b + c − it is not possible to link together a three-dimensional network of perfectly rigid octahedra. In these tilt systems small distortions of the octahedra must occur. The magnitude of the distortions in the a + a + a − and a 0 b + b − tilt systems are estimated. A table of predicted space groups for ordered perovskites, A 2 MM′O6, for all 23 tilt systems is also given.

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Group-theoretical methods are used to enumerate the structures of ordered double perovskites, A(2)BB'X(6), in which the ordering of cations B and B' into alternate octahedra is considered in combination with the ubiquitous BX(6) (or B'X(6)) octahedral tilting. The cation ordering on the B-cation site is described by the irreducible representation R(1)(+) of the Pm3;m space group of the cubic aristotype, while the octahedral tilting is mediated by irreducible representations M(3)(+) and R(4)(+). There are 12 different structures identified, and the corresponding group-subgroup relationships are displayed. Known structures are briefly reviewed.

The 23 Glazer tilt systems describing octahedral tilting in perovskites have been investigated. The various tilt systems have been compared in terms of their A-cation coordination and it is shown that those tilt systems in which all the A-cation sites remain crystallographically equivalent are strongly favored, when all the A sites are occupied by the same ion. Calculations based on both ionic and covalent models have been performed to compare the seven equivalent A-site tilt systems. Both methods predict that when the tilt angles become large, the orthorhombic a+b-b -tilt system will result in the lowest energy structure. This tilt system gives the lowest energy structure because it maximizes the number of short A---O interactions. The rhombohedral a-a-a-tilt system gives a structure with a slightly lower Madelung energy, but increased ion-ion repulsions destabilize this structure as the tilt angles increase. Consequently, it is stabilized by highly charged A cations and small to moderate tilt angles. The ideal cubic a°a°a° tilt system is only observed when stabilized by oversized A cations and/or M---O 7r-bonding. Tilt systems with nonequivalent A-site environments are observed when at least two A cations with different sizes and/or bonding preferences are present. In these compounds the ratio of large-to-small cations dictates the most stable tilt system.