A Comparative Atomistic Study of the Structure of Grain Boundaries in Tungsten
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A COMPARATIVE ATOMISTIC STUDY OF THE STRUCTURE OF GRAIN BOUNDARIES IN TUNGSTEN A. MARINOPOULOS, M. SOB, V. VITEK AND A. E. CARLSSON* Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6202, U.S.A. *Department of Physics, Washington University, St. Louis, MO 63130-4899, U.S.A. ABSTRACT Most atomistic studies of grain boundaries have been carried out using central forces to describe atomic interactions. However, in transition metals with unfilled d-bands the angular dependence of interatomic forces may be important. The purpose of this paper is to investigate the significance of angular forces in the case of Tungsten. The calculations have been performed for the E5(210) symmetrical tilt grain boundary using two alternate approaches. First are the central-force many-body potentials of the Finnis-Sinclair type. The second are the angular dependent potentials obtained via a moment analysis of the electronic density of states. The results of these two approaches are compared by analyzing the boundary structures, the relative displacements of the adjoining grains and the expansion. Differences in structural characteristics are discussed in terms of the effect of angular forces. INTRODUCTION A number of interatomic potentials suitable for studying various local or extended defects in metallic materials have been constructed. Recently, most frequently used are the Finnis-Sinclair [1-2] and EAM [3] potentials which are central-force potentials of physically appropriate form with empirically fitted parameters. No angular-dependent interactions are included in these potentials and this might be a drawback especially when describing the structures and energetics of defects in transition metals. To overcome this possible drawback, interatomic potentials including angularly dependent interactions have been proposed recently [4-7]. All these schemes include some angular-dependent contribution to the electronic cohesive energy. Very recently a first-principles tight-binding LMTO method was also developed [8], in which the angular forces and directional bonds are automatically taken into account in the band-structure energy. Carlsson [5] [9] used the moment expansion of the local density of states up to the fourth moment to construct angular-dependent potentials for some transition metals. These potentials are capable to predict correctly structural-energy differences in transition metals with half-filled d-bands. Using these potentials he studied the c(2x2) reconstruction on the W(100) surface. The results gave a good agreement with the corresponding ab-initio estimates for bcc-fcc energy difference, relaxation and surface energy as well as for the first surface layer contraction. The purpose of this paper is to compare the results of an atomistic study of a grain boundary obtained for the angularly dependent potentials based on the moment analysis, and for the central-force Finnis-Sinclair potentials. The boundary studied is the E5(210) symmetrical tilt boundary in Tungsten. RELAXAT
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