Two different phases of Ga 3 Zr with tetragonal (D0 22) and cubic (Ll 2) structures under high pressure are investigated by using density functional theory (DFT) calculations. The elastic constants (C ij) and mechanical moduli, including bulk modulus (B) and shear modulus (G), are calculated under various pressures. When pressure goes up, the increasing tendency of C ij , B and G are confirmed. On the basis of Pugh's criterion, Ll 2-Ga 3 Zr has better ductility comparing with D0 22-Ga 3 Zr under various pressures in the range of 0~60 GPa. The brittleness of D0 22-Ga 3 Zr depends on the pressure, it will become ductile when the pressure rise up higher than ~35 GPa. For the both phases, Debye temperature (Θ D) is also calculated under high pressures. For the both phases, Debye temperature increases with pressure rising up. Under pressures ranging from 0 GPa to 60 GPa, the Θ D values of Ll 2-Ga 3 Zr are lower than the ones of D0 22-Ga 3 Zr.
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