The inorganic structural chemistry of boron and its compounds can be characterized by a remarkable complexity which is due to the preferentially formed one-, two- and three-dimensional arrangements of covalently bonded boron atoms. This is mainly driven by the need of saturation of the valence requirements of the constituting electron-deficient boron atoms. The topological dimension of these aggregates can be correlated with the element-to-boron ratio. This relation has been particularly explored for compounds composed of metal atoms (transition elements, rare earth metals, actinides) and boron. There, depending on the metal content the boron substructure evolves from isolated boron atoms to boron pairs, fragments of chains and infinite chains followed by formation of two-dimensional frameworks.

SrPd₄B and isotypic BaPd₄B crystallize with a new structure type, which shows a similar arrangement of trigonal prisms consisting of palladium atoms and centred by boron as those observed in the borides from homologous series of derivatives of the CaCu₅ type. Both synthesised borides are diamagnetic in the whole temperature range and show low metallic conductivity and no superconductivity above 0.35 K.

Figure 1. Boron-centred trigonal prisms in the CeCo₃B₂, CeCo₄B and SrPd₄B structure types: a) common fragments consisting of two edgesharing three-capped trigonal prisms [BT₆R₃] b) arrangement of the fragments [BT₆R₃] highlighted in Figure a and c) spatial arrangements of trigonal prisms [BT₆] centred by boron atoms.

Thus, they are metals with a low electronic density of states at the Fermi level, which is confirmed for SrPd₄B by theoretical calculations (1.7 eV^–1 f.u.^–1 at E_F). From the electronic band structure no itinerant magnetism can be expected, even not for realistic amount of doping.

Figure 2. Total and partial (atom resolved) electronic density of states for SrPd₄B (top). Orbital resolved DOS per atom for palladium and boron (bottom).
Gumeniuk R., Schmitt M., Schnelle W., Burkhardt U., Rosner H., Leithe-Jasper A. Z. Anorg. Allg. Chem. 636 (2010) 954.

Further increase of the boron fraction gives rise to the formation of three-dimensional covalently bonded boron frameworks. Here the type and degree of connectivity of boron polyhedra as well as the occupation of the interstitial sites by metal atoms become the structure governing elements.

Figure 3. Electron localizability indicator (ELI-D, Y) in YRhB₄: (a) crystal structure view along [001]; (b) isosurface of Y = 1.73 visualize positions of ELI-D attractors revealing the two-center bonding within the boron network
I.Veremchuk, T. Mori, Yu. Prots, W.Schnelle, A. Leithe-Jasper, M. Kohout, Yu. Grin, J. Solid State Chem. 181 (2008) 1983-1991

Figure 4. Temperature dependence of the inverse magnetic susceptibility for TmRhB₄ and YbRhB₄

Figure 5. X-ray absorption spectrum at the Yb L_III edge of YbRhB₄ in comparison with the reference Yb₂O₃ indicating the 4f¹³ state of ytterbium.

There, depending on the metal content the boron substructure evolves from isolated boron atoms to boron pairs, fragments of chains and infinite chains followed by formation of two-dimensional frameworks.

Figure 6. Isosurface of the electron localization function (η=0.75) of AlB₂ (blue spheres, aluminum; green, boron; unit cell is given by black lines; view tilt from [001])
U. Burkhardt, V. Gurin, F. Haarmann, H. Borrmann, W. Schnelle, A. Yaresko, Yu. Grin, J. Solid State Chem. 177 (2004) 389-394

Figure 7. Crystal orientation EBSD maps and pattern quality images of sections of a Spark Plasma Sintered TiB₂ sample
J. Schmidt, M. Boehling, U. Burkhardt, Yu. Grin, Science and Technology of Materials 8 (2007) 376-382

Research at the MPI-CPfS is focused on the relationship of the crystal structure ( ref.1,  ref.2) / electronic structure ( ref.1,  ref.2) to  physical properties in such compounds as well on the study of the  chemical bonding situation in position space.