Effect of chemical composition, defect structure, and stress state on the elastic properties of (V 1− x Al x ) 1− y N y

For (V 1− x Al x ) 1− y N y an extensive and theoretically unexplained spread in experimentally obtained elastic moduli ranging from 254 to 599 GPa is reported in literature. To identify its origin, the effect of chemical composition (0 ⩽ x ⩽ 0.75), non-metal to metal ratio (N/M-ratio: 0.48 ⩽ y ⩽ 0.52), and stress state (−6 ⩽ σ ⩽ 2 GPa) on the elastic modulus at room temperature is studied sytematically by density functional theory employing the Debye–Grüneisen model. As the Al concentration is increased from x = 0 to x = 0.75, strong Al–N sp 3 d 2 hybridization causes an increase in elastic modulus of 26%. The effect of the N/M-ratio on the elastic properties is also Al content dependent. As y is increased from y = 0.50 to y = 0.52, decreasing bond distance upon vacancy formation causes an anomalous increase in the elastic modulus of 6% for V 1− y N y , while a decrease in elastic modulus of up to 5% occurs for (V 1− x Al x ) 1− y N y . A stress state variation from +2 to −6 GPa increases the elastic modulus e.g. for (V 0.5 Al 0.5 ) 0.5 N 0.5 by 70 GPa and hence 13% due to shifts in density of states towards lower energies implying bond strengthening. Thus, it is suggested that the extensive spread of 58% in reported elastic moduli for (V 1− x Al x ) 1− y N y can at least in part be rationalized based on variations in chemical composition, off-stoichiometry induced point defects, and stress state.