Theoretical investigation of the bonding and solubility in Nb _2-xW_xAlC

We have performed theoretical studies of the solubility within Nb _2-xW_xAlC by means of ab initio total energy calculations. If x is increased from 0 to 2 the bulk modulus can be increased by as much as 31%. The bulk modulus deviates from Vegard's rule, which may be understood based on substitution-induced changes in the CNb_2-xW_x bond angle resulting in flattening of the Nb_2-x W_xC layers upon solid solution formation. This rather extensive increase in the bulk modulus can be understood by considering the changes caused by the substitution of Nb through W for the equilibrium volume and chemical bonding. Based on the energy of formation analysis we suggest that the investigated system shows complete solubility. The bond length calculations suggest that both the Nb-C bond length as well as the W-C bond length are not significantly affected by variations in x. Based on a comparison to other solid solutions we suggest that this anomaly may be specific to the family of nanolaminates investigated here.