Analytic embedded atom method model for bcc metals
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I. INTRODUCTION The embedded-atom-method of computer modeling (EAM) has been used extensively for face-centered cubic metals1"4 but has seen little application to body-centered cubic metals. The terminology "embedded-atom-method" was introduced by Daw and Baskes5'6 for their approach based on density functional theory, but is used here to cover all models with the same analytic format, such as the Finnis and Sinclair formulation7 based on tight-binding theory. Finnis and Sinclair did develop their model for bcc metals and some bcc calculations have been performed,8'9 but there has been little discussion or comparison of bcc and fee models. A general form for the embedding function is presented in the present report as well as a general analytic EAM model for all crystal structures. This model is used to compare fee and bcc perfect crystal properties.
II. BACKGROUND The embedded atom method6 involves the calculation of the total energy of a set of atoms as a sum of the energy from two-body interactions and an energy from inserting each atom in the electron density arising from all the other atoms. The embedded atom method is based on the concept that the embedding energy for a particular species of atom is a unique function of electron density independent of the source of that electron density. The electron density at any site normally is taken as a linear superposition of spherically symmetric electron densities from contributing atoms. Using the notation of Johnson3 for a monatomic model, the two-body potential is 4>{r), the atom electron density is f{r), the electron density from superposition is p(f), and the embedding function is F(p). The concept of an effective two-body potential has been discussed in the literature.3'6'7'10'11 An EAM model is invariant to a transformation in which a term linear in the electron density is added to or subtracted from the embedJ. Mater. Res., Vol. 4, No. 5, Sep/Oct 1989
ding function and an appropriate adjustment is made to the two-body potential. The two-body potential becomes the effective two-body potential when this transformation is made such that the slope of the embedding function is zero when evaluated at the equilibrium electron density for the perfect crystal. The change from the perfect crystal energy is then dominated by the effective two-body potential for any atomic configuration in which the electron density at atom sites is not significantly altered. Since the electron density at an atom site is a superposition of the contribution from all neighboring atoms, its change is commonly small in defect configurations in tight-packed metals. Thus, the effective two-body potential yields a good approximation for the calculation of defect energies, which explains why early two-body models12'13 in which the potential was similar in form to that found for the EAM effective two-body potential, were surprisingly successful. In summary, if an EAM model is adjusted so that the twobody potential is the effective two-body potential, the embedding function, while contributing a
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