In this Article, we present PRINCEPS, an algorithm based on a new coordination environment projection scheme that facilitates the structural analysis and comparison of such crystal structures. Making sense of the often complex crystal structures that arise here, developing a clear structural description, and identifying connections to other phases can be laborious and require an encyclopedic knowledge of structure types. Intermetallic crystal structures offer an enormous structural diversity, with an endless array of structural motifs whose connection to stability and physical properties are often mysterious. The localization of two Mg atoms in the pores of the framework is determined.
The basic 3D network, which characterizes the location of the gravity centers of the K63 clusters, corresponds to a hexagonal closely packed network (HCP, Mg type) with CN = 12. There are six neighboring K63 clusters in the local environment of the K63 cluster in the layer.
The center of a K63 cluster occupies the position with the point symmetry 3̅ in the unit cell. A quasi-spherical deltahedron shell made from 50 atoms is formed on the template. A new type of nanocluster-precursor of the crystal structure, which is formed on the internal 13-atomic cluster, which represents a template and consists of two bound ridged rings Mg–Al–Mg–Al–Mg–Al with the central Mg atom, is discovered. The symmetric and topological codes of the cluster self-assembly of the crystal structure are determined: primary chain S 3¹ → microlayer S 3² → microframework S 3³. The geometrical and topological analysis of the crystal structure of intermetallide ε-Mg23Al30 (ToposPro program) with V = 3098.0 ų and space group R-3 is carried out. Thus, the nanoclusters A, A1, and A2 can be considered as "determinants" of the corresponding structures. The nanocluster A was found only in two Pearson classes: cF464 and hP238, while the nanoclusters A1 and A2 occur in beta'-Mg(2)Al(3) only.
Using the TOPOS procedure of searching for finite fragments in infinite nets we found that nanocluster B is a typical fragment of intermetallic compounds: it exists in intermetallics belonging to 42 Pearson classes. The self-assembly scheme proves the similarity of beta, beta'-Mg(2)Al(3) to other extremely complicated Samson's phases, NaCd(2) and ZrZn(22) the spatial arrangement of the centers of nanoclusters in these structures as well as the topology of the corresponding network conform to the Laves phase MgCu(2). The self-assembly of the beta, beta'-Mg(2)Al(3) crystal structures was considered within the hierarchical scheme: 0D primary polyhedral clusters (coordination polyhedra) -> 0D two-shell primary nanoclusters A, A1, A2, or B -> 0D supracluster-precursor AB(2) -> 1D primary chain -> 2D microlayer -> 3D microframework. The nanocluster model interprets structural disordering in beta-Mg(2)Al(3): the disordered atoms form the inner shell of the nanocluster A, while the outer shells of all nanoclusters are preserved. Using the TOPOS program package that implements the method, we separated two types of two-shell primary nanoclusters A, A1, A2, and B consisting of 57-63 atoms that completely compose the structures of the polymorphs. A novel method for the computational description of intermetallics as an assembly of nanoclusters was improved and applied to extremely complicated crystal structures of beta, beta'-Mg(2)Al(3) polymorphs.