Thermodynamic stability of Mg-based laves phases

To investigate the stability of various Mg-based Laves phases, the formation enthalpy and phonon dispersion were obtained by firstprinciples calculation. The calculated formation enthalpy and phonon dispersion indicate that MgX₂ (X = Al, Co, Ni, Cu, Zn) and Mg₂X (X = Ca, Sr, Y, Ba, La) are stable both statically and dynamically. These results are consistent with the experimental results except for MgAl₂ and Mg₂La. These compounds are considered to be in a metastable state in each binary system. We also used the cluster expansion method to examine the possibility of adding a third element to MgZn₂. Our theoretical investigations suggest attractive interaction between Zn and a third element such as Ag, Ca, and Zr in the MgZn₂ lattice. However, Ca and Zr replace a small amount of Zn in MgZn₂ owing to the instability of MgCa₂ and MgZr₂, in agreement with the experimental result. Furthermore, it is suggested that Zr becomes stable at the Mg site in the MgZn₂ lattice owing to the stability of ZrZn2.