Cation Disorder in Ferroelectric Ba₄M₂Nb₁₀O₃₀ (M = Na, K, and Rb) Tetragonal Tungsten Bronzes

The crystal structure of tetragonal tungsten bronzes, with the general formula A1₂A2₄C₄B1₂B2₈O₃₀, is flexible both from a chemical and structural viewpoint, resulting in a multitude of compositions. The A1 and A2 lattice sites, with different coordination environments, are usually regarded to be occupied by two different cations such as in Ba₄Na₂Nb₁₀O₃₀ with Na⁺ and Ba²⁺ occupying the A1 and A2 sites, respectively. Here, we report on a systematic study of the lattice site occupancy on the A1 and A2 sites in the series Ba₄M₂Nb₁₀O₃₀ (M = Na, K, and Rb). The three compounds were synthesized by a two-step solid-state method. The site occupancy on the A1 and A2 sites were investigated by a combination of Rietveld refinement of X-ray diffraction patterns and scanning transmission electron microscopy with simultaneous energy-dispersive spectroscopy. The two methods demonstrated consistent site occupancy of the cations on the A1 and A2 sites, rationalized by the variation in the size of the alkali cations. The cation order-disorder phenomenology in the tungsten bronzes reported is discussed using a thermodynamic model of O'Neill and Navrotsky, originally developed for cation interchange in spinels.