Ab initio calculations on the third-order elastic constants for selected B2–MgRE (RE = Y, Tb, Dy, Nd) intermetallics

We present the third-order elastic constants for the magnesium-rare-earth alloys MgY, MgTb, MgDy, and MgNd with CsCl-type B2 structure. Density functional theory (DFT) within generalized-gradient-approximation (GGA) combining with the method of homogeneous deformation is employed. The predictions for the elastic constants are obtained from the nonlinear least-squares polynomial fit to the calculated strain–energy relation from first-principles total-energy calculations. To judge that our computational accuracy is reasonable, we compare the ab initio calculated results for the third elastic constants with experimental data and previous theoretical results for Si. Our calculated second-order elastic constants for the selected magnesium-rare-earth alloys agree well the previous calculations and the experiments. The third-order effects really matter when the finite strains are larger than approximately 2.5%.