Korringa-Kohn-Rostoker

Theoretical calculations were performed with the linear muffin tin orbital (LMTO) method and the local density approximation for exchange and correlation. This method was used in combination with supercell models containing up to 16 atoms to calculate the DOS. The LMTO calculations are run self consistently and the DOS obtained are combined with the matrix elements for the transitions from initial to final states as described in detail elsewhere (Botton et al., 1996a) according to the method described by Vvedensky (1992). A comparison is also made between spectra calculated for some of the B2 compounds using the Korringa-Kohn-Rostoker (KKR) method. 

The LSDA approach requires simultaneous self-consistent solutions of the Schrbdinger and Poisson equations. This was accomplished using the Layer Korringa-Kohn-Rostoker technique which has many useful features for calculations of properties of layered systems. It is, for example, one of only a few electronic structure techniques that can treat non-periodic infinite systems. It also has the virtue that the computational time required for a calculation scales linearly with the number of different layers, not as the third power as most other techniques. 

Ffom a theoretical point of view, stacking fault energies in metals have been reliably calculated from first-principles with different electronic structure methods [4, 5, 6]. For random alloys, the Layer Korringa Kohn Rostoker method in combination with the coherent potential approximation [7] (LKKR-CPA), was shown to be reliable in the prediction of SFE in fcc-based solid solution [8, 9]. 

The techniques for calculating the electronic states of an impurity in a metal from first principles are well understood and have already been implemented. An approximate method that leads to much simpler calculations has been proposed recently. We investigate this method within the framework of the quadratic Korringa-Kohn-Rostoker formalism, and show that it produces surprisingly good predictions for the charge on the impurity. 

R. Zeller and P.H. Dederichs, Phys. Rev. Letters, Electronic structure of impurities in Cu, calculated self-consistently by Korringa-Kohn-Rostoker Green s function method , 42 1713 (1979) ... 

A.N. Andriotis, J.S. Faulkner and Yang Wang, Single impurity calculations using the quadratic Korringa-Kohn-Rostoker method , Solid State Commun. 84 267 (1992). 

D.M.Nicholson and J.S.Faulkner, Apphcations of the quadratic Korringa-Kohn-Rostoker band-theory method , Phys.Rev. B39 8187 (1989). 

The CPA has proved to be an enormously successful tool in the study of alloys, and has been implemented within various frameworks, such as the TB, linear muffin-tin orbital and Korringa-Kohn-Rostoker (Kumar et al 1992, Turek et al 1996), and is still considered to be the most satisfactory single-site approximation. Efforts to do better than the single-site CPA have focused on multi-site (or cluster) CPA s (see, e.g., Gonis et al 1984, Turek et al 1996), in which a central site and its set of nearest neighbours are embedded in an effective medium. Still, for present purposes, the single-site version of the CPA suffices, and we derive the necessary equations here, within the framework of the TB model. 

Stepanyuk et al. [471] have applied local approximation of the density-functional theory and the Korringa-Kohn-Rostoker (KKR) Green s function method to determine the energy of Co adatoms located at the ideal Au(lOO) surface. Total-energy calculations have shown that Co atoms and small Co clusters are preferably embedded inside the substrate. 

APW, self-consistent energy-band calculation by the augmented plane-wave method KKR, Korringa-Kohn-Rostoker method for electronic band calculations in solids. 

TABLE 8.6. Stoner Parameters for Several Elements in Rydbergs (1 Ry = 13.6 eV). Obtained by the Korringa-Kohn-Rostoker (Green Function) Nonspin Polarized Density-Functional Calculations in the Local-Spin Density Approximation... 

Eckelt, P. (1967). Energy band structures of cubic ZnS, ZnSe, ZnTe and CdTe (Korringa-Kohn-Rostoker method). Phys. Status Solidi 23, 307-12. Edwards, A. H., and W. B. Fowler (1985). Semiempirical molecular orbital techniques applied to silicon dioxide MIND03. J. Phys. Chem. Solids 46, 841-57. 

We now discuss the most important theoretical methods developed thus far the augmented plane wave (APW) and the Korringa-Kohn-Rostoker (KKR) methods, as well as the linear methods (linear APW (LAPW), the linear muffin-tin orbital [LMTO] and the projector-augmented wave [PAW]) methods. 

We have recently succeeded in calculating the d< fect energies in metals, such as I-I (I=iinpiirily), P-1 (P=probe), V-I (V=vacancy) in.fraction energies(IE s). The calculations apply the Korringa-Kohn-Rostoker (KKR) Gieen s function method for impurities and are based on the local-spin-density approximation (LSDA) for density-functional (heory. The nice agreement of calculated results foi P-I IE s with available accurate measured values seems to demonstrate the accuracy of our calculations. It was also shown that the Monte Carlo simulations based on the calculated I-I IE s reproduce very well the measured values of temperature-concentration dependence for the solid solubility limit of impurities in metals. 

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