The trifluorides of the two high field strength elements yttrium and holmium are studied by periodic density functional theory. As a lanthanide, holmium also belongs to the group of rare earth elements (REE). Due to their equivalent geochemical behavior, both elements form a geochemical twin pair and consequently, yttrium is generally associated with the REE as REE+Y. Interestingly, it has been found that DFT/DFT+U describe bulk HoF₃ best, when the 4f-electrons are excluded from the valence region. An extensive surface stability analysis of YF₃ (PBE) and HoF₃ (PBE+U${}_{\mathrm{d}}$/3 eV/4f-in-core) using two-dimensional surface models (slabs) is performed. All seven low-lying Miller indices surfaces are considered with all possible stoichiometric or substoichiometric terminations with a maximal fluorine-deficit of two. This leads to a scope of 24 terminations per compound. The resulting Wulff plots consists of seven surfaces with 5–26% abundance for YF₃ and six surfaces with 6–34% for HoF₃. The stoichiometric (010) surface is dominating in both compounds. However, subtle differences have been found between these two geochemical twins.

中文翻译：

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YF3 和同构 HoF3 的第一原理表面分析

采用周期密度泛函理论研究了钇和钬两种高场强元素的三氟化物。作为一种镧系元素，钬也属于稀土元素 (REE) 族。由于它们具有相同的地球化学行为，两种元素形成地球化学孪生对，因此，钇通常与 REE 关联为 REE+Y。有趣的是，我们发现，当 4f 电子被排除在价区之外时，DFT/DFT+U 能够最好地描述体 HoF _{3 。YF 3} (PBE) 和 HoF ₃ (PBE+U)的广泛表面稳定性分析${}_{\mathrm{d}}$/3 eV/4f-in-core）使用二维表面模型（板）进行。所有七个低位米勒指数表面都被考虑为具有所有可能的化学计量或亚化学计量终止，最大氟缺陷为二。这导致每个化合物有 24 个终止点。_{生成的 Wulff 图由 YF 3}丰度为 5-26% 的七个表面和 HoF ₃丰度为 6-34% 的六个表面组成。化学计量 (010) 表面在两种化合物中占主导地位。然而，在这两个地球化学双胞胎之间发现了细微的差异。