Mechanical properties and anisotropy of thermal conductivity of Fe_3-xCr_XO₄ (x = 0-3)

The ground state properties of Fe_3-xCr_XO₄ (x = 0-3) compounds were studied using first principles calculation. Stress-strain methods were used to evaluate elastic constants of these compounds. These compounds are mechanically stable structures, because they satisfy the mechanical stability criteria. The mechanical moduli were estimated using the Voigt-Reuss-Hill approximation. The calculated bulk moduli of Fe₃O₄, Fe₂CrO₄, FeCr₂O₄, and Cr₃O₄ are 190.9 GPa, 135.5 GPa, 180.1 GPa, and 235.6 GPa, respectively. Both of anisotropic indexes and 3-D surface contour were used to illustrate the elastic anisotropy. Debye temperature and anisotropy of acoustic velocity of Fe_3-xCr_XO₄ compounds were also investigated. The maximum Debye temperature is attributing to Cr₃O₄ with 507.6 K among Fe_3-xCr_XO₄ compounds. The minimum thermal conductivity of Fe_3-xCr_xO₄ compounds was estimated by both Clarke's model and Cahill's model. Moreover, 3-D surface contour of the anisotropic thermal conductivity of Fe_3-xCr_XO₄ compounds was obtained based on the Clarke's model and anisotropic Young's modulus.