The Electronic Structure of Grain Boundaries in NB
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THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES IN NB ERIK C. SOWA,* A. GONIS* AND X. -G. ZHANG** * Lawrence Livermore National Laboratory, L356, Livermore, CA 94551 ** Lawrence Berkeley Laboratory, Berkeley, CA 94720
ABSTRACT We present first-principles calculations of the electronic structure of Nb grain boundaries. These are the first such calculations for a bcc metal using the real-space multiple-scattering theory (RSMST). Local densities of states near a F5" twist grain boundary are compared to those for bulk Nb.
INTRODUCTION The real-space multiple-scattering theory (RSMST) has been used [1, 2] to perform electronic-structure calculations at Z5 grain boundaries in fcc Cu. In this paper, we present the results of RSMST electronic-structure calculations at the E5S (100) 36.90 twist grain boundary in bcc Nb. This represents a significant extension of the method, because the bcc structure is more open than the fcc structure, and in Nb the Fermi level lies inside the d-bands. Since the RSMST has been described in previous publications[l, 2, 3, 4], we shall forgo all but a very brief description of this method here. The RSMST is based on the concept of semi-infinite periodicity (SIP), defined as the regular repetition along a given direction of a scattering unit (atom, planes of atoms, etc.), or a set of such units. Systems with SIP possess the property of removal invariance, which states that the scattering properties (scattering matrices) of any such system remain invariant when an integral number of scattering unit 3 is removed from, or added to, the free end of the system. Using this property in conjunction with multiple-scattering theory, one can determine the electronic Green function, and hence all one-particle quantities such as the density of states (DOS), directly in real space, bypassing often cumbersome reciprocalspace (k-space) integrations, and avoiding artificial periodic boundary conditions. This formalism provides a unified treatment of the electronic properties of a broad spectrum of systems that includes, but is not limited to, pure elemental solids, compounds, ordered alloys, surfaces and interfaces, and other low-symmetry systems. Only systems with no recognizable periodic structure, e.g. amorphous materials and liquids, fall outside the scope of the RSMST method. The essence of the method consists in a prescription for the proper renormalization of the scattering properties of the boundary sites of a cluster of atoms. Unrenormalized or "bare" sites in the interior of the cluster describe the region of interest, such as a grain boundary, while the renormalized boundary sites represent the infinite medium surrounding the cluster. This "dressing up" of the cluster is done independently for each part of a system that is characterized by its own SIP, so that grain boundaries between essentially arbitrary crystal structures can be treated. At its present stage of development, our codes can be applied to known atomistic configurations with known electronic one-particle potentials. Work currently in pr
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