Phenomenological bond length-bond number correlations for Ti, Zr and Hf: assessment and applications to metastable structures

This paper deals with (i) the establishment of Pauling's bond length vs. bond number relation (BLBNR) for Ti, Zr and Hf, and (ii) the analysis of the connections between the parameters entering into the BLBNR and the experimental interatomic distances (IDs) in the known solid phases of these elements. Recently assessed ID data on the hcp structure, which is the stable phase at room temperature and atmospheric pressure (RTAP) as well as on the bcc and omega (Ω) structures, which are metastable at RTAP, are treated in terms of the BLBNR, and various approaches are tested for the evaluation of the univalent metallic bond-length parameter, D(1), of Ti, Zr and Hf. Next, a comparison is made with Pauling's method, which is based on determining an optimum D(1) parameter. With these results, a new interpretation is presented of the so-called Jamieson correlation, which involves the possibility of a connection between D(1) and the shortest ID in the Ω phase. Finally, the BLBNR is applied to the metastable fcc structure of Ti, Zr and Hf, and a new evaluation is performed of the difference between metallic bond lengths for coordination numbers 12 (D(12)) and 8 (D(8)), which is compared with early generalisations on D(12)-D(8). (orig.)