Self-Consistent-Field KKR-CPA Calculations in the Atomic-Sphere Approximations
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SELF-CONSISTENT-FIELD KKR-CPA CALCULATIONS IN THE ATOMIC-SPHERE APPROXIMATIONS PRIABHAKAIt P. SINGH*, A. GONIS* and DIDIER DE FONTAINE" *Department of Chemistry and Materials Sciences, Lawrence Livermore National Laboratory, Livermore, CA 94550 of Materials Science & Mineral Engineering, University of California, Berkeley, California 9,4720 and Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
"*Department
ABSTRACT We present a formulation of the Korringa-Kohn-Rostoker coherent potential approximation (KKPt-CPA) for the treatment of substitutionally disordered alloys within the KKR atomic-sphere approximation (ASA). This KKR-ASA-CPA represents the first step toward the implementation of a full cell potential CPA, and combines the accuracy of the KKR-CPA method with the flexibility of treating complex crystal structures. The accuracy of this approach has been tested by comparing the self-consistent-field (SCF) KKR-ASA-CPA calculations of Cu-Pd alloys with experimental results and previous SCF-KKR-CPA calculations.
I. INTRODUCTION Multiple-scattering theory has been very successfully used for describing the electronic structure of ordered as well as disordered systems. In particular, the Korringa-Kohn-Rostoker method in the coherent potential approximation (KKR-CPA) provides an accurate description of the electronic properties of substitutionally disordered alloys. Using KKR-CPA, but with varying degree of self-consistency, several substitutionally disordered systems have been studied with results that are very often in good agreement with the experiments [1-6]. The computational usefulness of the KKR-CPA is somewhat compromised, however, because of the need to calculate energy dependent structure constants. Thus all calculations that have been reported thus far were carried out on a nionatomic basis and for face-centered cubic or body-centered cubic lattices. On the ohter hand, the energy independent structure constants introduced by Andersen [7-8] and widely used in calculations based on the method of linear muffin- tin orbitals (LMTO) are much more flexible and catn be used in conjunction with lattice structures of very low symmetry. It was the desire to take a. first-principles CPA approach to the study of phase stability of alloys based on complex structures that motivated the present development.
II. FORMALISM As pointed out in Ref. [9], our formulation differs from that of Temmerman, Gydrffy and Stocks [10] in four significant ways: (i) we linearize the partial waves using the LMTO approach, which improves somewhat the efficiency of the SCF-KKR-CPA calculations, (ii) we parametrize the potential functions which makes it easier to carry out non-charge-self-consistent calculations, (iii) we calculate the energy independent structure constants once for each structure type, and (iv) due to the exact transformation of tlse long-ranged structure constants into localized structure constants, it is possible to speed up the CPA self-consistency loop itself by doing a cluster calc
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