Metastable tetragonal states of zirconium: Theory and experiment

The epitaxial Bain path of tetragonal zirconium has been calculated with the full-potential linearized-augmented-plane-wave method within both the nonrelativistic local-density approximation (LDA) and the relativistic generalized-gradient approximation (GGA). Both procedures yield three energy minima, corresponding to three tetragonal phases with different axial ratios c/a. For the LDA the three phases are face-centered cubic (fcc), body-centered cubic (bcc), and body-centered tetragonal (bct); all three are metastable, as determined by calculations of the corresponding elastic constants. For the GGA the three phases are fcc and two bct (the bcc phase is at a maximum and unstable). Experiments were carried out with the goal of stabilizing the fcc phase by pseudomorphic epitaxy of zirconium films on a {001} surface of tungsten. The structure of the zirconium films was determined by quantitative low-energy electron diffraction and found to be strained fcc, strained by the pseudomorphism. Agreements and disagreements with published results of other workers are discussed.