Modeling Intermetallic Structures: The Topological Alloying Approach

We
propose an approach for the interpretation of crystal structures
of intermetallic compounds and mechanisms of solid-state reactions
in metallic systems. This approach is based on a topological representation
of the crystal structures as periodic nets. One of the metals is considered
as a matrix (host net) for incorporating atoms of other (guest) metal(s).
A crucial point is that the structure of the host net and possible
positions of the guest atoms are determined by topological methods,
which are independent of the geometrical distortions and chemical
composition of the structures. The host net is defined as a substructure
(subnet) of the whole structure of the host metal. Two possible mechanisms
of incorporating guest atoms are considered: (i) substitution of a
part of the atoms in the host net where the atoms form one or more
interpenetrating subnets and (ii) insertion in the cages of the matrix,
which appear after breaking some interatomic contacts in the host
structure. The positions of the guest atoms are determined as centers
of natural tiles constructed for the host net. Since the mechanisms
are similar to the formation of substitutional and interstitial solid
solutions, we called this approach topological alloying. We showed
that many structure types of intermetallic compounds can be elucidated
by this approach. The topological alloying method can also be used
to find structural similarities between different intermetallic motifs,
to assess the possibility of topotactic solid-state reactions, and
to generate structural models for hypothetical intermetallics.

本研究提出一种用于解析金属间化合物晶体结构及金属体系中固态反应机制的方法。该方法基于将晶体结构拓扑表示为周期性网格（periodic nets）的思路。其中一种金属被视作基体，其对应的网格为主体网格（host net），用于容纳其他（客体）金属原子。核心要点在于，主体网格的结构与客体原子的可能占位可通过拓扑方法确定，该方法不受结构的几何畸变与化学组成影响。主体网格被定义为基体金属整体结构的子结构（子网格，subnet）。本研究考虑了两种客体原子嵌入的可能机制：(i) 取代主体网格中的部分原子——此时主体网格的原子会形成一个或多个互穿的子网格；(ii) 嵌入基体的笼状结构中，该笼状结构通过断裂主体结构中的部分原子间接触而形成。客体原子的占位被确定为针对主体网格构建的天然拼块（natural tiles）的中心。由于该机制与置换型和间隙型固溶体的形成过程相似，我们将此方法命名为拓扑合金化（topological alloying）。研究表明，诸多金属间化合物的结构类型均可通过该方法得以解析。拓扑合金化方法还可用于：探寻不同金属间结构基元间的结构相似性，评估拓扑导向固态反应的可行性，以及为假想金属间化合物生成结构模型。