VOLUME 83, NUMBER 8 PHYSICAL REVIEW LETTERS 23 AUGUST 1999 Ab Initio Study of Metastability in Refractory Metal Based Systems C. Berne, 1 A. Pasturel, 2 M. Sluiter, 3 and B. Vinet 1 1 Commissariat à l’Energie Atomique, CEREM – Département d’Etudes des Matériaux, 17 rue des Martyrs, 38054 Grenoble-Cedex 09, France 2 Laboratoire de Physique et Modélisation des Milieux Condensés, Maison des Magistères, BP 166 CNRS, 38042 Grenoble-Cedex 09, France 3 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan (Received 3 May 1999) The interplay between local atomic environment and phase stability properties for tetrahedrally close packed (tcp) structures in transition metals has been examined using first-principles methods. The most probable transitory metastable tcp phases solidifying from undercooled transition metal melts and the sequence as a function of composition of tcp phases observed in the phase diagrams of many transition metal alloys are shown to have a common origin. These phenomena are explained in terms of atomic coordination and level splitting of the d-like states. PACS numbers: 64.70.Dv, 64.60.My, 71.20.Be, 81.30.Bx Under nonequilibrium conditions, the solidification of metallic melts may lead to the formation of metastable crystal structures. Among melt undercooling methods, undercooling experiments performed in a high drop- tube facility are one avenue to realize nonequilibrium solidification processes at moderate cooling rates. In particular, the discovery of a double recalescence phenomenon for Re and Ta metals gives the first experi- mental evidence of an undercooling-induced metastable phase transformation in pure transition metals [1]. Unfor- tunately, the metastable phases of pure refractory metals recorded in these experiments are transitory during the so- lidification process. Therefore, first-principles based total- energy calculations appear to be essential to evaluate the possibility of obtaining metastable phases and to get some insight into the physics of the nucleation path. Crystal structures of elemental metals tend to have certain sequences when viewed as a function of atomic numbers. Using qualitative tight-binding arguments, it was shown that for the transition metals the structural energy differences are given by the d-band energy dif- ferences only, assuming that the dominant term which minimizes the total energy of a given structure is as- sociated with the shape and the filling of canonical d bands [2]. The canonical hcp-bcc-hcp-fcc sequence of structures observed across the nonmagnetic 4d and 5d transition series can be understood from the fact that the topology of the lattice is reflected in powers of the Hamiltonian [3]. These results are now well supported by detailed quantum-mechanical calculations [4]. In a pre- vious contribution [1], we assumed that the mechanism which favors undercooling-induced metastable phases is not based on the idea of electron transfer from the s band to the d band, as required for pressure-induced phase transformation [5], but rather on the complex structure of the highly undercooled liquid. In fact, the speculations by Frank [6] about a possible preference of an icosahedral short-range order in undercooled metal- lic melts have been supported by computer simulations experiments [7]. Such an icosahedral short-range order in the under- cooled melt is similar to the short-range order found in quasicrystalline solids or partially in the tcp structures. Such structures are those which are built entirely out of tetrahedral packing units [8]. In contrast, the fcc struc- ture consists of both tetrahedral and octahedral units while the bcc structure is an intermediate case with the octa- hedra containing second-neighbor bonds. The tetrahedral packing in tetrahedrally close packed (tcp) phases leads to characteristic polyhedra which are labeled Z12, Z14, Z15, and Z16, where the numbers refer to the coordina- tion number of the atom centering the polyhedron. The simplest example of a tcp structure is the A15 structure which has eight atoms per unit cell. Two of these are surrounded by Z12 polyhedra, which are icosahedra, and the remaining six by Z14 polyhedra. This phase has been used as a possible candidate phase to interpret the occur- rence of a metastable phase in Ta metal brought on by drop-tube undercooling [1]. Considering that the icosahe- dral local order found in highly undercooled liquids can be the driving force for metastable phases in undercooling experiments, we present a systematic study of the ener- getics of the 4d and 5d refractory metals using the first- principles full-potential linear muffin-tin orbitals method (FPLMTO) [9]. This approach, one of the most accu- rate within the local-density approximation (LDA), is an all-electron method, which does not require any shape ap- proximation for the charge density or for the potential. In this work, particular care is taken for the total-energy convergence with regard to the k -space integration. The Methfessel-Paxton k -points technique [10] with a smear- ing parameter of 0.1 eV has been used. The number of irreducible k points is 182, 190, 150, 56, 18, and 20 for fcc, bcc, hcp, A15, sigma, and chi, respectively. The wave functions are expanded with 34 aug- mented Hankel functions per transition metal site; 0031-9007 99  83(8)  1621(3)$15.00 © 1999 The American Physical Society 1621