Crystal structures of Ti, Zr, and Hf under compression: Theory

Publisher Website
Google Scholar
Abstract
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→ω→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 ω structure agrees well with measurement. The chemical bonding of the ω 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 ω 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.