METALLURGICAL AND MATERIALS TRANSACTIONS A U.S. GOVERNMENT WORK VOLUME 29A, JULY 1998—1845 NOT PROTECTED BY U.S. COPYRIGHT Ab Initio Studies of the Electronic Structure and Energetics of Bulk Amorphous Metals D.M.C. NICHOLSON, G.M. STOCKS, W.A. SHELTON, YANG WANG, and J.C. SWIHART Bulk amorphous metals (BAMs) are an interesting class of new materials possessing unique prop- erties that offer exciting possibilities for applications to a broad range of technologies. In contrast to the previous generation of amorphous metals, BAMs can be produced in bulk form at cooling rates as low as 1 K/s. The understanding of the structure, properties, and required cooling rates for BAM formation is hindered by the large number of constituents in typical alloys. In this article, we present the results of first principles local density approximation studies of the electronic structure and energetics of model Ni-Pd-P, Zr-Ni-Cu, and Zr-Ni-Al amorphous alloys that relate to two of the simplest BAMs, namely, Ni 0.4 Pd 0.4 P 0.2 and Zr 0.6 Al 0.15 Ni 0.25 . The calculations are based on large unit cell (300-atom) structural models for which the electronic structure is calculated using the first principles order–N locally self-consistent multiple scattering method. I. INTRODUCTION BY now, a large number of compositions have been found that exhibit bulk amorphous behavior; some of the ear- liest found include Zr 0.413 Ti 0.137 Cu 0.125 Ni 0.10 Be 0.225 , [1] La 0.55 Cu 0.10 Ni 0.05 Co 0.05 Al 0.25 , [2] Zr 0.60 Cu 0.15 Ni 0.10 Pd 0.05 Al 0.10 , [3] Zr 0.525 Cu 0.179 Ni 0.046 Ti 0.05 Al 0.10 , [4] Zr 0.57 Cu 0.154 Ni 0.026 Nb 0.05 Al 0.10 , [4] and Ni 0.4 Pd 0.4 P 0.2 . [5,6] Many bulk amorphous metals (BAMs) have excellent properties: high strength (2 GPa); ductility in compres- sion; low coefficient of friction; high wear resistance; high corrosion resistance; low shrinkage during cooling; ex- tended superplastic range between the glass transition tem- perature, T g , and the recrystallization temperature, T x ; and almost perfect as-cast surfaces. It is important to understand why these glasses form at such low cooling rates and how alternative compositions can be similarly stabilized. In gen- eral, the understanding of the structure, properties, and re- quired cooling rates for BAMs is hindered by the large number of constituents in the typical alloy. Thus, from the theoretical point of view, the two BAM systems, Ni 0.4 Pd 0.4 P 0.2 [5,6] and Zr 0.6 Al 0.15 Ni 0.25 , [7] are particularly attrac- tive in that they contain only three elements yet display the important characteristics of this class of materials. Further- more, the thoroughly studied structure of related binary glasses provides a useful starting point for theoretical in- vestigation. [8,9] Much of the progress in the calculation of ground state properties of crystalline metals can be attributed to the local D.M.C. NICHOLSON, Senior Research Scientist, G.M. STOCKS, Corporate Fellow, and W.A. SHELTON, Research Scientist, are with the Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114. YANG WANG, Senior Computational Scientist, is with Pittsburgh Super Computing Center, Pittsburgh, PA 15213. J.C. SWIHART, Professor, is with the Physics Department, Indiana University, Bloomington, IN 47405. This article is based on a presentation made in the ‘‘Structure and Properties of Bulk Amorphous Alloys’’ Symposium as part of the 1997 Annual Meeting of TMS at Orlando, Florida, February 10–11, 1997, under the auspices of the TMS-EMPMD/SMD Alloy Phases and MDMD Solidification Committees, the ASM-MSD Thermodynamics and Phase Equilibria, and Atomic Transport Committees, and sponsorship by the Lawrence Livermore National Laboratory and the Los Alamos National Laboratory. density approximation (LDA) to density functional the- ory [10] and translational symmetry. Density functional the- ory reduces the many-electron problem, which is intractable for all but the simplest systems, to a one-electron problem with no approximation. In practice, the density functional equations are solved numerically within some approxima- tion, typically the LDA. Translational symmetry allows the further reduction of the one-electron, but many atom, prob- lem to an N atom problem, where N is the number of atoms in the periodically repeated unit cell. In conventional elec- tronic (band) structure methods, the size of the matrices that must be manipulated to determine the electronic structure is proportional to N. Elemental metals are typically found in ground state structures such as fcc, bcc, or hcp that have only one or two atoms per unit cell. Ordered compounds typically require several atoms per unit cell, although there are rare exceptions that require many more. In the case of solid solution alloys and off-stoichiometric compounds, there is a well-established technique, the coherent potential approximation, [11] that restores translational symmetry through the introduction of effective scatterers, thereby yielding tractable calculations for configuration averaged properties. Because BAMs lack translational symmetry, their study does not benefit from the LDA electronic struc- ture techniques developed for periodic systems. Further- more, there is no completely satisfactory theory that restores translational symmetry for the purpose of calculat- ing configuration averaged properties. The most realistic approximation for the configuration averaged electronic structure of structurally disordered systems is the effective medium approximation (EMA), introduced by Roth. [12] Al- though the EMA has produced some promising results, it has been shown to give negative densities of electronic states [13] in some cases. Furthermore, the EMA is compu- tationally intensive, involving iterative solution of coupled integral equations that are not guaranteed to converge. In this article, we present the results of calculations of the electronic structure of BAMs that are obtained by straightforward first principles application of the LDA to models of BAMs that are large enough to give reliable elec- tronic structures. The calculations are facilitated by the re- cently developed order-N, O(N), locally self-consistent