Mechanical properties of Mg-RE (RE = Sc, Y, Gd-Tm) solid solutions: first-principles determination

To understand the effect of rare earth (RE) solute atoms on the mechanical properties of the Mg matrix, the elastic parameters and ideal shear strengths of Mg52RE2 (RE = Sc, Y, Gd-Tm, similar to 3.7 at% RE) binary solid solutions were systematically investigated by first-principles calculations based on density function theory. The independent elastic constants (C-ij) were obtained by quadratic fitting the deformation energy-strain relation, then the bulk modulus (B), shear modulus (G), Young's modulus (Y), Poisson's ratio (v) and anisotropy factor (A) at zero temperature were predicted in the framework of the Voigt-Reuss-Hill approximation. Furthermore, elastic moduli at room temperature were estimated using a semi-empirical formula. It was found that the bulk modulus and hardness of Mg52RE2 strongly depend on the degree of localization of the valence electron orbitals of the solute atoms. Based on the study of ideal shear stress-strain relations, we propose that the addition of RE elements into an Mg lattice increases the shear strength and anisotropy of the mechanical properties, but reduces the deformation-to-failure strain. The results show that Sc is the most effective element for strength while Gd is most effective for ductility in the studied Mg-RE solid solutions.