Eur. Phys. J. B 45, 39-46 (2005)
https://doi.org/10.1140/epjb/e2005-00162-y

Automatic procedure for stable tetragonal or hexagonal structures: application to tetragonal Y and Cd

Department of Materials Science and Engineering State University of New York, Stony Brook, NY 11794-2275, USA

Corresponding author: ^a franco.jona@sunysb.edu

Received: 28 September 2004
Revised: 17 December 2004
Published online: 16 June 2005

Abstract

A simple effective procedure (MNP) for finding equilibrium tetragonal and hexagonal states under pressure is described and applied. The MNP procedure finds a path to minima of the Gibbs free energy G at T=0 K (G=E+pV,  per atom, , per atom) for tetragonal and hexagonal structures by using the approximate expansion of G in linear and quadratic strains at an arbitrary initial structure to find a change in the strains which moves toward a minimum of G. Iteration automatically proceeds to a minimum within preset convergence criteria on the calculation of the minimum. Comparison is made with experimental results for the ground states of seven metallic elements in hexagonal close-packed (hcp), face- and body-centered cubic structures, and with a previous procedure for finding minima based on tracing G along the epitaxial Bain path (EBP) to a minimum; the MNP is more easily generalized than the EBP procedure to lower symmetry and more atoms in the unit cell. Comparison is also made with a molecular-dynamics program for crystal equilibrium structures under pressure and with CRYSTAL, a program for crystal equilibrium structures at zero pressure. Application of MNP to the elements Y and Cd, which have hcp ground states at zero pressure, finds minima of E at face-centered cubic (fcc) structure for both Y and Cd. Evaluation of all the elastic constants shows that fcc Y is stable, hence a metastable phase, but fcc Cd is unstable.