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 Cij 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.