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. bo nd number relation (BLBNR) for Ti, Zr and Hf, and (ii) the analysis of the connections between the parameters entering into the BLBNR and the experime ntal interatomic distances (IDs) in the known solid phases of these element s. Recently assessed ID data on the hcp structure, which is the stable phas e at room temperature and atmospheric pressure (RTAP) as well as on the bcc and omega (Omega) structures, which are metastable at RTAP, are treated in terms of the BLBNR, and various approaches are tested for the evaluation o f the univalent metallic bond-length parameter, D(1), of Ti, Zr and Hf. Nex t, a comparison is made with Pauling's method, which is based on determinin g an optimum D(1) parameter. With these results, a new interpretation is pr esented of the so-called Jamieson correlation, which involves the possibili ty of a connection between D(1) and the shortest ID in the Omega phase. Fin ally, 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 compare d with early generalisations on D(12)-D(8). (C) 2000 Elsevier Science S.A. All rights reserved.