Elastic and phonon properties of quaternary Heusler alloys CoFeCrZ (Z = Al,Si, Ga and Ge) from density functional theory

The structural, elastic and phonon properties of the quaternary CoFeCrZ (Z = Al, Si, Ga and Ge) Heusler alloys have been investigated using the generalized gradient approximation method within density functional theory. The ground-state properties, including, lattice constant and bulk modulus are in good agreement with the available theoretical and experimental data. The elastic constants C_ij are computed using the stress–strain technique. The calculated results indicate that CoFeCrZ (Z = Al, Si, Ga and Ge) alloys are ductile materials. Debye temperatures are predicted from calculated elastic constants. The phonon dispersion relations of CoFeCrZ (Z = Al, Si, Ga and Ge) alloys are calculated for the first time using the density functional theory and the direct method with 2 × 2 × 2 supercell.