{\em Ab initio} study of Fe-rich Fe-Cu alloys

Cu precipitates are important for strengthening steel. Our {\em ab initio} study aims to model the thermodynamical stability of Cu precipitations in $\alpha$-Fe. As a first step, a density functional theory (DFT) supercell approach is applied to study $Fe_{1-x}Cu_x$ alloys at small concentrations $x$. From the DFT total energies a strongly nonbonding substitutional energy $E_{subs} \approx 0.7eV$ is derived, which is significantly larger than results of a previous DFT study [1]. Based on force constants derived by the same DFT approach the temperature dependent vibrational free energy is determined [2]. In particular at higher temperatures the vibrational entropy significantly reduces the formation energy. Finally, by using the entropy of mixing the dilute Fe-Cu alloy becomes stabilized. The derived phase diagram is in good agreement with experimental data [3]. According to our analysis, the vibrational free energy is very important for a correct modelling of the phase stability of Fe-rich Fe-Cu alloys. [1] C. Domain et al., PRB, 65, 024103 (2001) [2] D. Alf{\`e} et al, PRB, 65, 045123 (2001) [3] B. Predel, Landolt-B{\"o}rnstein - IV, Springer, Volume 5d (1994)