Local Atomic Configurations in Intermetallic Crystals: Beyond the First Coordination Shell

We
have used a combined geometrical-topological approach to analyze
21,697 intermetallic crystal structures stored in the Inorganic Crystal
Structure Database. Following a geometrical scheme of close packing
of balls, we have considered the three most typical polyhedral atomic
environments of the icosahedral, cuboctahedral, or twinned cuboctahedral
shape as well as multi-shell (up to four shells) local atomic configurations
(LACs) based on these cores in 10,657 unique crystal structure determinations.
In total, half of intermetallic structures have been found to contain
one of these configurations, with the icosahedral LACs being the most
frequent. We have revealed that even a two-shell configuration strongly
predetermines the overall connectivity (topological type) of an intermetallic
crystal structure. The chemical and stoichiometric composition of
the multi-shell LACs generally obeys the close-packing model: the
number of atoms in the subsequent shells (Nk) varies around the value Nk = 10k2 + 2,
which is valid for the same size atoms, to reach the densest packing
for the kth shell. Deviations from the revealed regularities
often indicate inconsistencies in the crystallographic information,
unusual features of the structure, or the existence of more stable
phases that can be used for the validation of experimental and modeling
data.

本研究采用几何-拓扑联合分析方法，对存储于无机晶体结构数据库（Inorganic Crystal Structure Database）中的21697个金属间化合物晶体结构开展分析。基于球体密堆积的几何框架，本研究在10657个独立晶体结构解析结果中，考量了三类最典型的多面体原子配位环境——二十面体、立方八面体及孪晶立方八面体构型，同时也研究了基于这些核心结构的多壳层（最多四层）局域原子构型（local atomic configurations, LACs）。整体而言，有半数的金属间化合物晶体结构包含上述一类构型，其中二十面体型局域原子构型最为常见。本研究揭示，即便仅为双壳层构型，也会显著决定金属间化合物晶体结构的整体连接性（拓扑类型）。多壳层局域原子构型的化学组成与化学计量比通常符合密堆积模型：对于尺寸均一的原子，第k层壳层的原子数Nk围绕公式Nk=10k²+2波动，该公式可实现第k层壳层的最密堆积。与上述规律存在偏差的情况，通常意味着晶体学信息存在矛盾、晶体结构具有非常规特征，或是存在更稳定的物相——这类偏差可用于验证实验与模拟数据的可靠性。