First-principles study on the lattice vibration, anisotropy, tensile strength and electronic properties of CuxHfySiz intermetallics

The stability, lattice vibrations, anisotropy in elasticity and stress-strain behavior of the CuxHfySiz ternary silicide were calculated by first-principles methods. According to the formation enthalpy and lattice vibration frequency, the CuxHfySiz phase is confirmed to be stable. The elastic constants show that these ternary borides are mechanically stable. Based on the B-H/G(H) rule, CuHfSi is 1.788 and more significant than 1.75, which should be ductile. The elastic hardness indicates that CuHfSi2 shows the largest hardness among CuxHfySiz phases, which is 18.9 GPa. It is speculated that CuHfSi2 may be the most muscular hardness in these four types of intermetallics. The size of anisotropy expressed by anisotropy and elastic modulus three-dimensional diagram is Cu4Hf3Si4 > Cu4Hf3Si2 > CuHfSi > CuHfSi2. The structural stability, hardness and chemical bonds were further explained by electronic structures.