First principles calculation of composition dependence tracer and interdiffusion with phase change in γ/γ′ superalloy: A case study of Ir/Ir3Nb

In this work, the composition dependent tracer and interdiffusion coefficient with phase change in γ/γ′ Ir/Ir₃Nb superalloy are studied by means of first-principles calculation together with nudged elastic band, and quasi−harmonic thermodynamics. The formulae scattered in the literature for composition dependence tracer diffusion coefficient are summarized and executed using first principles calculation. Each term in the newly derived formulae, such as energy barrier, jump frequency, defect concentration, correlation, solvent enhancement factor, effective escape frequency, etc. is meticulously calculated. We find the composition dependent tracer diffusion coefficient of Nb in L1₂ γ′-Ir₃Nb phase is contributed mainly from the antisite bridge rather than five-frequency model proposed in FCC γ-Ir dilute solid solution. The faster diffuser is Nb in γ-Ir, while Ir in γ′-Ir₃Nb. Based on the tracer diffusion coefficient, the interdiffusion coefficient is obtained using Darken-Manning equation. The composition profile and phase boundary movement of γ/γ′ Ir/Ir₃Nb superalloy are evaluated through an analytical solution of Matano-Boltzmann equations. The calculated diffusion coefficients and composition profile are in good agreement with experiments. Our findings not only serve as a successful example for the quantitative calculation of composition dependent tracer diffusion coefficient, but also shed lights on the physics behind the diffusion in intermetallics.