Structural Chirality from Short-Range Order in Heteroanionic Materials

Abstract

Established routes to structural chirality in inorganic crystals predominantly depend on symmetry-lowering atomic displacements of an achiral parent structure. We show that chirality can instead be forced by the short-range order of two anion species over the sites of an achiral parent, independent of atomic displacements. ReO${}_3$-type oxyfluorides with a 2:1 anion stoichiometry, such as NbO${}_2$F, exhibit two ordering patterns, cis octahedral coordination and period-three anion-chain ordering, both of which are rooted in the off-centring of $d^0$ cations. By direct enumeration, we prove that every arrangement combining both orderings on the smallest commensurate cell is chiral, belonging to a Sohncke space group. For NbO${}_2$F, density-functional theory (DFT) calculations predict a homochiral $P{3}_{1}21$ ground state. Wang-Landau Monte Carlo simulations of a DFT-trained cluster-expansion model predict that the chiral phase remains the equilibrium state up to a first-order transition at 494 K. We also identify three known vacancy-ordered compounds, BaZnO${}_2$, BaCoO${}_2$ and $\beta$-Fe${}_2$SeO, whose structures each map onto one of the enumerated chiral arrangements. Together, these results establish short-range order as a route to structural chirality, and mark heteroanionic and vacancy-ordered materials in which both orderings are active as candidates for new chiral phases.