Full-Potential KKR Calculations for Lattice Distortion of Impurities in Fe-Based Dilute Alloys, Based on the Generalized-Gradient Approximation

The presence of a point defect in a crystal, such as a vacancy or an impurity atom, generally cause a displacement of the neighboring host atoms from their ideal lattice positions. For examples, the experimental results are shown in Refs.1–3. From the theoretical point of view the treatment of structural relaxation due to defects in crystals is a difficult task. The problem of the lattice distortion has been mostly dealt with on a phenomenological basis, e.g., by applying models of lattice statics or continuum theory. A reliable microscopic description of lattice relaxation effects based on first-principles electronic structure calculations requires very accurate total energies or forces and has mostly been attempted so far for simple metals and semiconductors on the basis of pseudopotential treatments. The difficulty arises mainly from the fact that energy differences due to local atomic displacements are quite small, of the order of 0.1 ev, compared with, e.g., the cohesive energy (~5eV) of the solid. At present we can calculate accurately the atomic volumes of impurities in transition metals, by using ab-initio all-electron calculations of the electronic structure of solids, based on the FPKKR Green’s function method and the density functional theory. Papanikolaou et al succeeded in calculating the atomic volumes of 3d, 4sp, 4d, and 5sp impurities in Cu [4]. We also succeeded in calculating the lattice relaxation energies of vacancies in Cu and Al [5].The aim of the present paper is to examine systematically the lattice relaxation due to the 3d and 4sp impurities (Sc-Ge) in Fe. In sec 2, we describe the calculational method. In sec 3 we show the calculated results. The present calculations reproduce very well the available experimental results for the lattice expansion or compression due to impurities in Fe [1,3].