Density functional study of elastic and vibrational properties of the Heusler-type alloys Fe$_2$VAl and Fe$_2$VGa

The structural and elastic properties as well as phonon-dispersion relations of the Heusler-type alloys Fe$_2$VAl and Fe$_2$VGa are computed using density-functional and density-functional perturbation theory within the generalized-gradient approximation. The calculated equilibrium lattice constants agree well with the experimental values. The elastic constants of Fe$_2$VAl and Fe$_2$VGa are predicted for the first time. From the elastic constants the shear modulus, Young's modulus, Poisson's ratio, sound velocities and Debye temperatures are obtained. By analyzing the ratio between the bulk and shear modulii, we conclude that both Fe$_2$VAl and Fe$_2$VGa are brittle in nature. The computed phonon-dispersion relation shows that both compounds are dynamically stable in the L1$_2$ structure without any imaginary phonon frequencies. The isomer shifts of Fe in the two compounds are discussed in terms of the Fe s partial density of states, which reveal larger ionicity/less hybridization in Fe$_2$VGa than in Fe$_2$VAl. For the same reason the Cauchy pressure is negative in Fe$_2$VAl but positive in Fe$_2$VGa