Ab initio investigations of electronic structure, mechanical properties, phonon stability, and thermodynamics of the Mg-Er system

We report the results of a first principles study of electronic structure, elastic properties, ideal strengths, phonon stability and thermodynamic properties of the Mg-Er system. The calculations have been carried out within density-functional theory (DFT) and density-functional perturbation theory (DFPT) frameworks. The calculated lattice constants, cell volumes, bulk moduli and their pressure derivations, as well as formation enthalpies are in good agreement with the existing experimental and theoretical data. The single-crystal elastic constants and polycrystalline moduli were derived from the energy-strain relationships and Hill model, we show that Pm-3m-MgEr, I-43m-Mg24Er5, and I4/mmm-MgEr2 systems are all thermodynamically and mechanically stability. The ideal tensile and shear strengths of three phases have been evaluated from first-principles method. Especially, the phonon dispersion relations and densities of states of Pm-3m-MgEr, I-43m-Mg24Er5, and I4/mmm-MgEr2 alloys are investigated systematically from the linear response method of DFPT. Furthermore, the Raman-active and Infrared-active phonon modes at the center of Brillouin Zone (BZ) have been assigned combining with the factor group theory. Our calculated results indicate that three magnesium-erbium phases are also all dynamically stable. Accordingly, within the calculated phonon vibrations and quasi-harmonic Debye model, the vibration entropy and the lattice heat capacity of three phases have also been predicted.