Coupling between cation and anion disorder in β-K2Ca3(CO3)4

Since the development of anionic group theory, the spatial arrangement of anionic groups in optical crystals has been believed to determine their functional, such as nonlinear optical, properties. At the same time, cation substitution, resulting in either the appearance of disordered cation sites in a crystal structure or the emergence of cation-ordered superstructures, has been widely used to control material properties. This work demonstrates the coupling between positional cation disorder and orientational disorder of (CO₃)²⁻ anions in the β modification of the recently described K₂Ca₃(CO₃)₄ material. In contrast to the α modification [P2₁2₁2₁, a = 7.39134 (18), b = 8.8153 (2), c = 16.4803 (4) Å], where the ordered cation sublattice favors the non-centrosymmetric orientationally ordered arrangement of (CO₃)²⁻ anionic groups, positional cation disorder in β-K₂Ca₃(CO₃)₄ [Pnma, a = 7.5371 (2), b = 16.1777 (5), c = 8.7793 (3) Å] within the cation sublattice of the same topology leads to orientational disorder of (CO₃)²⁻ groups and the appearance of an inversion center in the average structure.