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 Na3V2(PO4)2F3, 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 Na3V2(PO4)2F3 in which enumeration methods are first used to generate a large number (∼3000) 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 Na3V2(PO4)2F3 is best described as belonging to the space group A21am with unit cell dimensions of a = 9.01928(4), b = 27.1379(1), and c = 10.73307(5). The 100 K unit cell has a large volume of 2627.07(2) Å3 with Z = 12 and 33 independent crystallographic sites (9 Na, 3 V, 3 P, 12 O, and 6 F) that is 3× and 6× larger than the room- and high-temperature polymorphs of this phase, respectively. The novel methods described here will be generally applicable for the solution of the complex cation-ordered structures that commonly occur for battery materials.尽管粉末衍射（powder diffraction）方法已被常规用于优化已知晶体结构化合物的结构模型，但解析未知晶体结构的难度要大得多。当未知结构较为复杂时，采用标准结构解析方法几乎难以完成结构解析，尤其是在空间群（space group）无法被明确解析的情况下。其中一类典型体系为极具应用前景的钠离子电池正极材料Na₃V₂(PO₄)₂F₃，其高温和室温结构此前已被解析，但更为复杂的低温结构始终未能确定。本文展示了一种新颖的材料组学方法（materials genomic approach），用于解析Na₃V₂(PO₄)₂F₃的100 K低温结构：首先基于钠离子的合理有序排布，通过枚举法（enumeration methods）生成约3000个试探结构（trial structure），随后对每个试探结构开展自动化Rietveld精修（Rietveld refinement）以完成结构优化。基于对优化后试探结构集合的分析，以及对部分精选试探结构的密度泛函理论（Density Functional Theory）能量最小化计算，最终确定Na₃V₂(PO₄)₂F₃的100 K结构最适宜归属为空间群A2₁am，晶胞参数为a=9.01928(4)、b=27.1379(1)、c=10.73307(5)。该100 K晶胞体积达2627.07(2) ų，Z=12，包含33个独立晶体学位点（9个Na、3个V、3个P、12个O以及6个F），其晶胞尺寸分别是该物相室温与高温多晶型（polymorph）的3倍和6倍。本文所报道的新颖方法，可广泛适用于电池材料中常见的复杂阳离子有序结构的解析。