Enumeration as a Tool for Structure Solution: A Materials Genomic Approach to Solving the Cation-Ordered Structure of Na₃V₂(PO₄)₂F₃

While powder diffraction methods are routinely utilized to optimize structural models for compounds whose crystal structures are known, the determination of unknown structures is far more challenging. When the unknown structure is large, structure solution can become a virtually intractable problem using standard structure solution methodologies, especially when the space group cannot be unambiguously resolved. One such system is the promising Na-ion battery cathode material Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>2</sub>F<sub>3</sub> whose high temperature and room temperature structures were previously solved, but whose more complex low-temperature structure could not be determined. Here, a novel materials genomic approach is demonstrated for the solution of the unknown 100 K structure of Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>2</sub>F<sub>3</sub> in which enumeration methods are first used to generate a large number (~3,000) of trial structures based on plausible orderings of Na ions and then automated Rietveld refinements are carried out to optimize each of these trial structures. Based on both the analysis of the ensemble of optimized trial structures and the density functional theory energy minimization of selected trial structures, the 100 K structure of Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>2</sub>F<sub>3</sub> is best described as belonging to the space group A2<sub>1</sub>am with unit cell dimensions of a = 9.01928(4), b = 27.1379(1), c = 10.73307(5). The 100 K unit cell has a large volume of 2627.07(2) Å<sup>3</sup> with Z = 12 and 33 independent crystallographic sites (9 Na, 3 V, 3 P, 12 O, and 6 F) that is 3x and 6x larger than the room- and high-temperature polymorphs of this phase, respectively. Finally, the novel methods described here will be generally applicable for the solution of the complex cation-ordered structures that commonly occur for battery materials.