Electronic structure and related properties of metallic glasses: Linear muffin-tin orbital approach
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INTRODUCTION
BY now, the linear muffin-tin orbital (LMTO) method[1,2] is about 20 years old and is a well-known and well-tested scheme for calculating the electronic structure of condensed matter based on density functional theory. One of the great advantages of the LMTOs is that they constitute a minimal basis in the sense that, per site, only one s, three p, and five d, and, for f-band materials, seven f orbitals are needed. Thus, with increasing computing power, the band structure method based on LMTOs could be applied to crystalline systems with larger and larger unit cells. Noncrystalline materials could be studied by treating them as crystalline systems with very large unit cells, typically consisting of 50 to 100 atoms. This so-called LMTO supercell method has been used extensively to study the electronic structure of metallic glasses,[3–8] quasicrystals,[9,10] and liquid metals.[11] The method allows self-consistency in charge density and potential, as dictated by the density functional theory, to be achieved for every atom. This selfconsistency at the local level seems to be important for reproducing and understanding the correlation between many local properties and the electronic structure. An important advancement in the LMTO method was achieved some 10 years ago by Andersen and co-workers with the introduction of short-ranged or tight-binding LMTOs.[12,13] The long range of the standard or traditional LMTOs prevented them from being used in conjunction with the real-space methods (such as the recursion method of Haydock[14]) of calculating the electronic structure. While the standard band structure methods can operate with both long- and short-ranged orbitals, the recursion method relies crucially on the existence of a basis in which the one-elecS.K. BOSE, Associate Professor, is with the Physics Department, Brock University, St. Catharines, ON, Canada L2S 3A1. 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. METALLURGICAL AND MATERIALS TRANSACTIONS A
tron Hamiltonian possesses nonzero matrix elements connecting a given atom to only a modest number of near neighbors. With the advent of the tight-binding linear muffin-tin orbital (TB-LMTO) recursion method, calculations involving large clusters (several hundred to thousand atoms), representing amorphous materials, became possible. Prior to this, recursion method calculations for amorphous systems were usually carried out using parameterized forms of the Hamiltonian matrix elements.[15] In spite of modest practical success, such calculations suffered from the lingering doubt about the transferability of these parameters from one system
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