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
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.
PACS: 64.60.My – Metastable phases / 71.15.Nc – Total energy and cohesive energy calculations / 62.20.Dc – Elasticity, elastic constants
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005