Nanocluster model of intermetallic compounds with giant unit cells: beta, beta'-Mg(2)Al(3) 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. 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. 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. 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 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). 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 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. Thus, the nanoclusters A, A1, and A2 can be considered as "determinants" of the corresponding structures.