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We present the ab-initio calculations for the lattice distortion effect of substitutional single impurities, I (= Sc ³ Ge, Sn), and substitutional two impurities, II and ISn, in bcc-Fe. Sn is a perturbed-angular-correlation (PAC) probe. The calculations are based on the generalizedgradient-approximation in the density-functional formalism and the full-potential Korringa-Kohn-Rostoker (FPKKR) Green's function method. For single impurities, we show that the available experimental results, such as lattice distortion around the impurities and the atomic volume changes per impurity, are reproduced very well by the present calculations. For two impurities, we clarify the lattice distortion effect on 1st-nearest neighbor (NN) interaction energies of II and ISn pairs in Fe, being a difference between the distortion energies with two impurities located on the infinitely separated sites and on the neighboring sites. We initially show that the lattice distortion effect is very low for the interaction energies between two impurities with a small size-misfit, compared with the host atom, although it becomes high for the interaction energies of two impurities with a large size-misfit. The lattice distortion effect on the II (I = Cr ³ Zn) interaction energies is less than 0.02 eV, while the lattice distortion effect on the ISn (I = Sc, Ge) interaction energies is greater than 0.2 eV. Secondly, we show that we can improve the agreement with the experimental results for the interaction energies of ISn pairs in bcc-Fe, by taking into account the lattice distortion. Finally, we show that the magnetic interaction is important for the lattice distortion of the ISn (I = Cr, Mn) pairs. The high lattice distortion for ISn pairs (I = Cr, Mn) is partly caused by the antiferromagnetic interaction of impurities I with the 1st-NN host atom on the opposite site of the Sn impurity, resulting in the high energy gain (0.13 eV, 0.06 eV) of ISn interaction.

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We calculate systematically the atomic volume changes caused by Sc-Ge impurities in Al, using the formalism given by the Kanzaki model. All the parameters in the Kanzaki model, such as the Hellmann-Feynman (HF) forces and the lattice distortion, are calculated by the ab-initio calculations based on the generalized-gradient approximation in density functional formalism and the full-potential Korringa-Kohn-Rostoker (FPKKR) Green's function method for point defects. Most of the calculated results agree very well (within the error of 5%) with the available experimental results. We found that the calculated results for the HF forces on the 1st-nearest neighboring host atoms around impurities are strongly correlated with the volume changes per impurity in Al. The magnetism of 3d transition-metal impurities (Cr, Mn, Fe) is also discussed.