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.