<i>R</i>_1−xFe_x (<i>R</i> = Y, Ce, Nd, Sm, and Dy) compounds: Entropy-induced phase stabilization at finite temperature

Up to now, phase stability problems of permanent magnets are still not yet entirely eliminated. Motivated by this, we report the dynamical and thermodynamic stability of the binary R_1−xFe_x (0< x <1) compounds (R= Y, Ce, Nd, Sm, and Dy) at finite temperature predicted by first-principles calculation based on density functional theory (DFT). We first demonstrate that thermodynamic stability problems cannot be elucidated when using the static DFT energy at T = 0 K. By considering the entropy contribution, including electronic and vibrational free energies, we obtained convex hull plots at finite temperatures, which successfully explain the phase stability of known compounds. Our results show a trend of stabilizing many R_1−xFe_x compounds studied here with increasing temperature. This entropy-induced stabilization mainly comes from the vibrational free energy, which decreases dramatically with temperature. We will discuss the origin of the stabilization and its rare-earth dependence.