Topology and symmetry analysis of rare earth borocarbides structural family,analogy to hexaferrites and relation to properties

The topology and symmetry analysis was applied to a series of rare earth borocarbide compounds, which have been gaining increasing interest due to their magnetic and thermoelectric properties. Using principles of OD theory, the crystal structures were deconvoluted into L(1) (B₁₂ icosahedra and C‐B‐C chain) layers and L(2) (rare earth and B₆ octahedral) layers. The arrangement of B₁₂ icosahedra in the L(1) layer is equal to close packed spheres, however, symmetry of the B₁₂ block lowers symmetry of the resulting layer from P 6/mmm to P 3m1. Both layers, L(1) and L(2) possess symmetry P 3m1 and the conjugation of L(1) with L(2) layers occurs in accordance with the symmetry elements. No disorder may appear here because of equal symmetry of single layers and layer pairs and it is not a classical OD family. Only the increasing of the amount of one type of layers, namely L(1), provides the structural variations. Close analogy to the hexagonal ferrites family has been found. Topology and symmetry analysis reveals principles in the building up of the structural family, gives an insight into the particular order‐disorder formation mechanism/criteria of these homologous borocarbide compounds and as the result relation to the properties (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)