By means of first-principles calculations, we have investigated the effects of rare earth elements (REEs) on the structures and mechanical properties of magnesium. The lattice parameters, elastic constants, bulk moduli, shear moduli, Young's moduli and anisotropic parameter of these solid solutions have been calculated and analyzed. The nearest-neighbor distance between Mg and the REEs is also analyzed to explore the correlation with the bulk moduli. The results show that the 4f-electrons and atomic radii play an important role in the strengthening process. The anomalies of the lattice parameters and mechanical properties at Eu and Yb are due to the half-filled and full-filled 4f-electron orbital states. Finally, the increase of directional bonding character near the alloying elements may account for the anisotropy and brittleness of these magnesium alloys.
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