There was employed the density functional theory plane-wave pseudopotential method with local density approximation and generalized gradient approximation to investigate the structural, elastic and mechanical properties of the intermetallic compound $Ni_3Ga$. The calculated equilibrium lattice constant and bulk modulus are in good agreement with the experimental values. The elastic constants were determined from a linear fit of the calculated stress-strain function according to Hooke's law. From the elastic constants, the bulk modulus B, anisotropy factor A, shear modulus G, Young's modulus E and Poisson's ratio υ for $Ni_3Ga$ compound are obtained. Our results for the bulk modulus B, anisotropy factor A, shear modulus G, Young's modulus E and Poisson's ratio υ are consistent with the experimental values. The sound velocities and the Debye temperature are also predicted from elastic constants. The dependences of the elastic and mechanical properties of $Ni_3Ga$ compound on pressure were investigated for the first time. It was found that the cubic $Ni_3Ga$ compound is mechanically stable according to the elastic stability criteria and it is not elastically isotropic. By analyzing the ratio B/G, it was concluded that $Ni_3Ga$ compound is ductile in nature.
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