Abstract:The solubility curves of Er in Al-Er alloys were investigated by means of first principles calculations based on the density functional theory. The solution energies of Er atoms in these Al-Er alloys were calculated by using the “Frozen core” approximation and “Standard potential” approximation for the 4f electrons, respectively. The calculated results showed that the solution energies of hR20, cP4 and hP8-Al3Er were -1.003 and -0.767 eV/Er atom, -0.989 and -0.787 eV/Er atom, -0.967 and -0.713 eV/Er atom, respectively, obtained from the two approximations. The lattice dynamics calculation showed that the excess enthalpies of hR20, cP4 and hP8-Al3Er were 3.301, 3.226 and 3.309 kB/Er atom. The simulated solubility curves were obtained by combining the lattice dynamics values and the weighted average of the solution energy values. The calculated solubility curves of cP4-Al3Er were consistent with the experimental values, which indicates that the 4f electrons play a very important role. In addition, the solubility curve of cP4-Al3Er was very close to that of the hR20-Al3Er, but lower than that of hP8-Al3Er at the same temperature. The chemical driving forces corresponding to the solubility curves of hR20 and cP4-Al3Er were also close to each other, but larger than that of the hP8-Al3Er. Due to the smaller interfacial energy in Al matrix of cP4-Al3Er than that of hR20-Al3Er, it could be deduced that the cP4-Al3Er precipitation was the first in priority order, which was consistent with the experimental observations.