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In the present work, the elastic constants and derived properties oftetragonal and cubic Heusler compounds were calculated using the high accuracyof the full-potential linearized augmented plane wave (FPLAPW). To find thecriteria required for an accurate calculation, the consequences of increasingthe numbers of $k$-points and plane waves on the convergence of the calculatedelastic constants were explored. Once accurate elastic constants werecalculated, elastic anisotropies, sound velocities, Debye temperatures,malleability, and other measurable physical properties were determined for thestudied systems. The elastic properties suggested metallic bonding withintermediate malleability, between brittle and ductile, for the studied Heuslercompounds. To address the effect of off-stoichiometry on the mechanicalproperties, the virtual crystal approximation (VCA) was used to calculate theelastic constants. The results indicated that an extreme correlation existsbetween the anisotropy ratio and the stoichiometry of the Heusler compounds,especially in the case of Ni$_{2}$MnGa.

A critical study of the elastic properties and stability of Heusler compounds: Phase change and tetragonal $X_{2}YZ$ compounds