CRYSTAL-STRUCTURES OF TI, ZR, AND HF UNDER COMPRESSION - THEORY

We have studied the crystal structures of Ti, Zr, and Hf under pressure by means of first-principles, total-energy calculations. The three metals are shown to exhibit a crystal structure sequence hcp --> omega --> bcc, with increasing pressure. This is in good agreement with experiment for Zr and Hf, whereas the bcc structure for Ti is a prediction. The calculated transition volumes as well as transition pressures compare fairly well with experiment. Also, the computed c/a ratio for hcp Ti, Zr, and Hf is found to be in good agreement with experiment. Similarly the calculated c/a ratio for Zr in the omega structure agrees well with measurement. The chemical bonding of the omega structure is shown to be quite different from what is normally the case in the transition metals, with a large degree of covalency. A search for the omega structure in Tc and Ru was fruitless yielding a stable hcp structure. At zero temperature and zero pressure the bcc crystal structure is found to be mechanically unstable for Ti, Zr, and Hf.