Effect of magnetism on the solution energy of 3p (Al, Si) and 4p (Ga, Ge) elements in iron

The method based on the density-functional theory has been used to study the solubility of 3p (Al, Si) and 4p (Ga, Ge) elements in ferromagnetic and paramagnetic states of bcc iron. To simulate the paramagnetic state, two different approaches have been employed, which were implemented using the SIESTA and LSGF packages. It has been established that the solution energy of all these impurities decreases upon the transition into the paramagnetic state. The solution energies obtained by averaging over the ensemble of unpolarized magnetic configurations agree well with the values obtained in the coherentpotential approximation. At the same time, the allowance for the magnetic polarization in the vicinity of an impurity leads to a decrease in the solution energy, which is most clearly pronounced at temperatures close to T (C). The temperature dependence of the solution energies of the impurities in the paramagnetic state is discussed.