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

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