Solid State Communications 151 (2011) 1873–1876 Contents lists available at SciVerse ScienceDirect Solid State Communications journal homepage: www.elsevier.com/locate/ssc Prediction of a bcc–hcp phase transition for Sn: A first-principles study Yansun Yao ∗ , Dennis D. Klug Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, K1A 0R6, Canada article info Article history: Received 17 May 2011 Received in revised form 3 October 2011 Accepted 4 October 2011 by S. Scandolo Available online 12 October 2011 Keywords: A. Metals C. Crystal structure and symmetry D. Phase transitions E. Strain, high pressure abstract The high-pressure structural transformation of elemental Sn is studied using an ab initio density functional theory implementation of the metadynamics method that predicts with sufficient compression, Sn will transform from the bcc structure into an hcp structure. The low-free-energy pathway associated with this phase transition is characterized as the Burgers transition mechanism. The superconducting properties of Sn under pressure are also investigated. Both bcc and hcp structures of Sn exhibit very weak electron–phonon coupling and therefore would not sustain superconductivity at high pressure. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved. 1. Introduction Tin occupies a special position in the elements of Group IVa. The lighter group IVa elements (C, Si, and Ge) have a tendency to form strong sp 3 tetrahedral bonds at ambient conditions. Since in these elements s and p states are sufficiently close in energy to drive an s 2 p 2 → sp 3 hybridization, C, Si, and Ge are able to form covalent diamond structures at ambient conditions [1]. As one descends the Group IVa list in the periodic table, the sp 3 tetrahedral bonds become weaker and their metallic character increases simultaneously. In the heavy element Pb, relativistic effects become significant, which increases the s → p promotion energy and prohibits the formation of sp 3 bonds [2]. As a result, Pb forms a metallic fcc structure at ambient conditions. Sn is located at the borderline between the two distinctly different bonding patterns. The sp 3 bond formation energy in Sn is nearly equal to the s → p promotion energy, and therefore Sn can only form weak sp 3 bonds at low temperatures [3]. The diamond structure of Sn, or α-Sn, is unstable upon increasing temperature and Sn transforms to a metallic phase (β -Sn) at approximately 286 K. This phase transition was suggested as being attributed to significant entropy contributions to the free energy. Upon compression, β -Sn is stable up to 9.5 GPa and then transforms to a body-centered tetragonal structure (bct) [4,5]. Near 45 GPa, the bct structure further transforms to a bcc structure, and the latter remains stable ∗ Correspondence to: Steacie Institute for Molecular Sciences, National Research Council of Canada, Room 2007, 100 Sussex Drive, Ottawa, ON, K1A 0R6, Canada. Tel.: +1 613 991 1237; fax: +1 613 947 2838. E-mail address: Yansun.Yao@nrc.ca (Y. Yao). up to at least 120 GPa [6], the highest pressure achieved in previous experiments. The structures of Sn above 120 GPa are however still unknown, and this provided the motivation for the present study. Since pressure usually weakens directional forces and drives crystalline structures toward close-packed forms, it is reasonable to suggest the hcp structure as a post-bcc form of Sn. Density functional theory (DFT) [7] calculations, however, showed that the bcc and hcp structures of Sn have very close energies and therefore their relative ordering could not be determined [8]. Several calculations suggested that the bcc → hcp transition cannot occur in Sn [3,9], while others suggest that the transition can occur but the predicted transition pressures in reported calculations differ by more than 100 GPa [10,11]. Since the bcc and hcp structures are very close in energy, examining the phase transition via energetics alone may therefore not be adequate. In order for this phase transition to occur, an energy barrier has to be crossed and this requires knowledge of the free-energy surface. In the present study, we use a recently developed structural search algorithm, the metadynamics method [12,13], to explore the free-energy surface of Sn and search for its structures at high pressure, starting from the initial free-energy minimum for the bcc structure. This enables us to directly simulate the structural transformations of Sn under experimental conditions. In addition, we investigated the superconducting properties of Sn under pressure, using phonon-mediated Eliashberg theory [14] based on the Bardeen–Cooper–Schrieffer (BCS) model [15]. 2. Theoretical details All calculations in the present study were performed using the pseudopotential method with ab initio implementations of DFT. 0038-1098/$ – see front matter Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2011.10.003