Chemical modeling of mixed occupations and site preferences in anisotropic crystal structures: case of complex intermetallic borides.

Transition-metal borides show not only promising physical properties but also a rich variety of crystal structures. In this context, quantum-chemical tools can shed light on important facets of the chemistry within such intermetallic borides. Using density-functional theory (DFT), we analyze in detail two phases of significant structural-chemical importance: the recently synthesized Ti(1+x)Os(2-x)RuB(2) and the isotypical Ti(1+x)Os(3-x)B(2). Starting from the observation of different Ti/Os occupations in X-ray crystal structure analysis, we assess suitable computational models and rationalize how the interplay of Ti-Ti, Ti-Os, and Os-Os bonds drives the site preferences. Then, we move on to a systematic investigation of the metal-boron bonds which embed the characteristic, trigonal-planar B(4) units within their metallic surroundings. Remarkably, the different Ti-B bonds in Ti(1+x)Os(2-x)RuB(2) (and also in its ternary derivative) are of vastly different strength, and the strength of these bonds does not correlate with their length. The tools presented in this work are based on simple and insightful chemical arguments together with DFT, and may subsequently be transferred to other intermetallic phases--transition-metal borides and beyond.