Semiempirical Angular-Force Method for BCC Transition Metals
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SEMIEMPIRICAL ANGULAR-FORCE METHOD FOR BCC TRANSITION METALS A. E. Carlsson Department of Physics, Washington University St. Louis, Missouri 63130 ABSTRACT An angular-force method for bcc transition-metals is obtained by generating a functional form via a quantum-mechanical analysis, and subsequently fitting the parameters in this form to experimental and ab-initio theoretical inputs. The quantummechanical analysis uses a four-moment treatment of the electronic density of states (DOS) in a d-band tight-binding model. Calibration of the method gives excellent results for the bcc-fcc energy difference and the vacancy-formation energy in W. The method is used to treat relaxation and c(2 x 2) reconstruction on the W (100) surface. The relaxation energy is primarily due to two-body terms, while the reconstruction requires the angular terms. Agreement with ab-initio results is obtained for reasonable values of the parameters in the model. However, the energy difference between the reconstructed surface and the optimally relaxed surface is quite sensitive to the details of the implementation of the method. INTRODUCTION The accuracy of atomistic simulations for transition metals has been greatly enhanced by the introduction of formats such as the "embedded-atom" [1] and the "N-body" [2] methods, which improve on pair-potential descriptions by giving the bonding energy for a particular atom as a nonlinear function of its local environment. These have led to a much improved description of broken-bond energies in various geometries [3]. However, these methods cannot describe structural-energy differences in transition metals. The problems are particularly severe in bee transition metals, because most radial interaction methods will have a preference for more closely packed structures, unless special precautions are taken. Several methods have attempted to resolve these problems by developing angular terms in the energy from various approximations in treating the electronic structure. At present, the most viable approaches are the free-electron approach [4], in which various couplings involving the d-shells and a background electron gas are treated perturbatively, and the tight-binding approach [5], in which an approximate electronic density of states (DOS) based on its low-order moments is utilized. Free-electron methods have given excellent results for bulk properties; they have been generalized to treat surfaces, but do not obtain reconstruction properties correctly [6]. Tight-binding analyses have been shown to give correct chemical trends in several types of structural properties [5,7,8], and can in fact be interpreted [5] via approximate four-body potentials which are similar in shape to those obtained by the free-electron analysis. It is our aim here to explore the extent to which the basic physics contained in the tight-binding analysis can be combined with some experimental inputs to obtain a reliable, accurate angular-force scheme. FUNCTIONAL FORM The method described here is essentially an application of a method pr
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