Boron Substructures in Inorganic Borides: Network Topology and Free Space

Abstract

We have analyzed polymeric boron substructures in all 1154 robust inorganic borides from the Inorganic Crystal Structure Database using topological and geometrical models as implemented in the ToposPro program package. We have classified all boron substructures into 63 topological types of atomic networks depending on the method of connection and discriminated them by periodicity into molecular, chain, layer, or framework motifs. We have revealed topological relations between boron motifs of different topologies and periodicities and found the boron substructures that can serve as templates for assembling motifs of a more complicated topology and/or a higher periodicity. We have applied the natural tiling approach to find all cages in a particular boron substructure and estimated the size of these cages with Voronoi polyhedra. The sizes of all metal atoms, which occur in the inorganic borides, have also been calculated in the same way. As a result, we have explained the composition of some borides and showed that the combined geometrical−topological approach helps one to estimate the feasibility of possible new boride structures and to refine the conditions for the synthesis or to prepare initial structural data for the subsequent predictive modeling.

Topological Analysis and Structural Role of Silicon Motifs in Metal Silicides

“…Crystal structures of silicides are often considered along with the corresponding borides. , Since we have recently classified topological motifs of boron substructures, it would be interesting to compare that classification with the results of this work. In general, the silicide substructures with 112 topological types are topologically almost twice as diverse as the boron motifs with 63 types.…”

“…1 To explore the free space in three-periodic silicon motifs, we have used the model of natural tiling, 21 which was successfully applied to zeolites 22 and inorganic borides. 9 The natural tiling of a particular three-periodic net is composed of cages (natural tiles), which are generalized polyhedra whose faces are represented by rings of the net. This means that the faces can be curved, but nonetheless, the polyhedra form a partition of the space without intersections or gaps.…”

“…In this paper, we consider all metal silicides whose crystal structures were experimentally determined and classify topological motifs of silicon atoms by using rigorous algorithms. Recently, we overviewed boron substructures in inorganic borides with the same methods. Since many silicides are structurally similar to borides, , it was also interesting to compare the results of the topological analysis for these two groups of compounds.…”