Effect of carbon concentration on shear modulus of (W1/2Al1/2)CZ

Using density functional theory (DFT), we have studied the effect of carbon concentration Z on the shear modulus G, elastic constant cij, and Poisson ratio ν of carbides (W1/2Al1/2)CZ while the most stable structures are determined by calculating the lowest formation energy. It is found that the maximal G value and the lowest Poisson ratio ν value are reached at Z = 3/4 due to atomic configuration changes, additionally, G values of (W1/2Al1/2)CZ should be lower than that of WC due to lower cij values. The results of electronic analysis show that the increased covalent bonding of C-2p and W-5d contributes to anisotropic cij and G positively and results in a lower ν value because the excess negative charge induced by the substitution of Al³⁺ for W⁴⁺ is balanced by decreasing C atoms.