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We study the accuracy and convergence of the real space cluster expansion (RSCE) for the total energies of the Pd-rich PdX (X=Ru, Rh) alloys, which are used to study the phase stability and phase equilibria of the Pd-rich PdX alloys. In the present RSCE, the X atoms of minor element are treated as impurities in Pd. Then-body interaction energies (IEs) among X impurities in Pd, being used in the expansion of the total energies of the Pd-rich PdX alloys, are determined uniquely and successively from the low body to high body, by the full-potential Korringa-Kohn-Rostoker (FPKKR) Green's function method (FPKKR) for the perfect and impurity systems (Pd-host and Xnin Pd,n=1~4), combined with the generalized gradient approximation in the density functional theory. In the previous paper, we showed that the RSCE, in which the perturbed potentials due to the insertion of Xnimpurities in Pd were redetermined self-consistently up to the first-nearest neighboring (nn) host atoms around Xnimpurities, reproduce fairly well (the error of ~ 0.2mRy per atom) the FPKKR-band-calculation result of the ordered Pd3Rh alloy in L12structure, but a little wrongly (the error of ~ 0.7mRy per atom) for the ordered Pd3Ru alloy in L12structure. In the present paper, we show that this small RSCE error for the Pd3Ru alloy is corrected very well (from ~ 0.7mRy to ~ 0.1mRy per atom) by enlarging the self-consistent region for the perturbed potentials up to the 2nd-nn host atoms around Run impurities in Pd. We also clarify the correction for each value of the n-body (n=1~ 4) IEs.

We give systematic ab initio calculations for the interaction energies (from first to eighth neighbors) of impurity pairs X–X (X = Sc–Zn, Y–Cd) in Al and discuss the micromechanism of the structural stability of Al-rich AlX alloys. The calculations are based on the generalized gradient approximation in the density-functional theory and employ the all-electron full-potential Korringa–Kohn–Rostoker Green's function method for point defects, which guarantees the correct embedding of the cluster of impurities and vacancies in an otherwise perfect crystal. We show: (1) the fundamental features of phase diagrams of these alloys, such as ordering and segregation, are understood by the sign of first-neighboring X–X interaction energies; (2) the structural stability of Al-rich AlX alloys such as L1 2 (Al 3 Sc and Al 3 Y), DO 22 (Al 3 V and Al 3 Nb), and Mackay icosahedron in AlMn quasicrystal, are understood qualitatively by using the medium-ranged and oscillating X–X interactions, due to the strong sp-d (Al–X) hybridization; (3) the strength and oscillating behavior of the medium-ranged X–X interaction energies are specified very well by the d-electron numbers of X impurities.

The present and subsequent papers give ab initio data for the study of the stability of the atomic structures of Al-rich AlX (X–ScZn) alloys, including the AlMn quasicrystal. We consider the minority elements of alloys as impurities and divide the cohesive energies of AlX alloys into four components :(i) cohesive energies of Al and X; (ii) solution energies of X in Al; (iii) X–X interaction energies (IEs) in Al; (iv) many-body IEs of X-agglomerates in Al. In the present paper, we show the calculated results for (i), (ii), 1st-neighbor X–X IEs (one part of (iii)) and X–Vacancy IEs in Al and discuss quantitatively the fundamental features of the interatomic interactions characteristic to the Al-rich AlX alloys: (1) the sp–d interaction of X(=Sc–Ni) with neighboring Al atoms is stronger than the d-d interaction of the 1st-neighbor X–X; (2) Al atoms in the Al-rich AlX alloys may be rearranged easily on the condition that electron density does not change very much because of the strong free-electron character of Al sp-electrons. Both results suggest that the atomic structures of Al-rich AlX (X=Sc–Ni) are mainly determined by the medium-ranged and oscillating X–X interactions, due to the sp–d interaction of Al–X.

The AlMn quasicrystal (QC) is a metastable phase with quasiperiodic arrangement of Mackay icosahedrons (MIs) (Al42Mn12, a vacancy at the center) and is stabilized by the the addition of Si. We give qualitative discussions for the micromechanism of the stability of the atomic structures of MI in AlMn QC, as well as the Al-rich AlX (X=Sc, V, Cu, Zn) alloys, by using the ab initio calculations for point defects in Al(fcc), where the minority elements in the AlX alloys are considered as impurities. We show: (1) the atomic structure of MI may be stabilized by the medium-ranged interaction of Mn pairs, which is strongly attractive around the interatomic distance of 4.9 A, which is close to the observed interatomic distance for the first-neighbor Mn–Mn pairs in MI. (2) Magnetism plays an important role around the interatomic distance 7.5 A, which is close to the interatomic distance of second-neighbor Mn–Mn pairs in MI. We also discuss the effect of a vacancy and Si impurities in MI.

We give ab initio calculations for vacancies in Al. The calculations are based on the generalized-gradient approximation in the density-functional theory and employ the all-electron full-potential Korringa-Kohn-Rostoker Green's function method for point defects, which guarantees the correct embedding of the cluster of point defects in an otherwise perfect crystal. First, we confirm the recent calculated results of Carling [Phys. Rev. Lett. 85, 3862 (2000)], i.e., repulsion of the first-nearest-neighbor (1NN) divacancy in Al, and elucidate quantitatively the micromechanism of repulsion. Using the calculated results for vacancy formation energies and divacancy binding energies in Na, Mg, Al, and Si of face-centered-cubic, we show that the single vacancy in nearly free-electron systems becomes very stable with increasing free-electron density, due to the screening effect, and that the formation of divacancy destroys the stable electron distribution around the single vacancy, resulting in a repulsion of two vacancies on 1NN sites, so that the 1NN divacancy is unstable. Second, we show that the cluster expansion converges rapidly for the binding energies of vacancy agglomerates in Al. The binding energy of 13 vacancies consisting of a central vacancy and its 12 nearest neighbors, is reproduced within the error of 0.002 eV per vacancy, if many-body interaction energies up to the four-body terms are taken into account in the cluster expansion, being compared with the average error (>0.1 eV) of the glue models which are very often used to provide interatomic potentials for computer simulations. For the cluster expansion of the binding energies of impurities, we get the same convergence as that obtained for vacancies. Thus, the present cluster-expansion approach for the binding energies of agglomerates of vacancies and impurities in Al may provide accurate data to construct the interaction-parameter model for computer simulations which are strongly requested to study the dynamical process in the initial stage of the formation of the so-called Guinier-Preston zones of low-concentrated Al-based alloys such as Al1-cXc (X=Cu, Zn; c

The magnetic properties of Fe 4 N are studied by the screened full-potential Korringa–Kohn–Rostoker (SFPKKR) band-structure calculation method combined with the generalized-gradient approximation of density-functional theory. The present calculations reproduce very well the experimental equilibrium lattice parameter ( a ) and magnetic moments (MMs); the Fe–N bonding drastically changes its character from a strong bonding one (of small MMs) to a weak bonding one (of large MMs) around the lattice parameter (∼6.96 a.u. ) being a little bit shorter than a .

The screened full-potential Korringa–Kohn–Rostoker (SFPKKR) band-structure calculation method, developed by the Julich group, may be one of the most efficient methods for the study of structural, electronic, and magnetic properties of large systems. We show the accuracy of the SFPKKR method combined with the generalized-gradient approximation of density-functional theory. The present calculations reproduce the ground-state structure of Fe as well as the sequence of crystal structures through the 4d transition metal series (HCP–BCC–HCP–FCC).