Unexpected Young's modulus dependence of refractory solute diffusion in NiCoFeCr-based high entropy alloys

Abstract

Diffusion of solutes significantly affects the coarsening rate of ${\gamma }^{\prime }$${\gamma }^{\prime }$ precipitates in precipitation-hardened high entropy alloys (PH-HEAs). In this work, we systematically study the refractory solutes M (Hf, Nb, Ta, Mo, W, Re, Ru) diffusion in face-centered-cubic (FCC) NiCoFeCr lattice through a combination of first-principles calculations, diffusion couples, and coarsening of ${\gamma }^{\prime }$${\gamma }^{\prime }$ precipitates experiments. Our calculations reveal that there exists a stronger negative correlation between solute diffusivity and Young's modulus than between solute diffusivity and atomic size; i.e., the higher the Young's modulus, the more difficult solute diffusion is. Based on the electronic structure analysis, the underlying origins for such a relationship could be ascribed to the fact that solutes with high Young's modulus have stronger bonds with neighboring host atoms, less compressibility, and thus poor diffusivity. Afterwards, the main interdiffusion coefficients of three refractory elements with similar atomic sizes and increasing Young's modulus, Mo, W, and Re, at 1150°C in (NiCoFeCr)₉₂Al₃Ti₃M₂ are, in order of magnitude, ${\tilde{D}}_{\text{MoMo}}^{\text{Ni}}>{\tilde{D}}_{\text{WW}}^{\text{Ni}}>{\tilde{D}}_{\text{ReRe}}^{\text{Ni}}$${\tilde{D}}_{\text{MoMo}}^{\text{Ni}}>{\tilde{D}}_{\text{WW}}^{\text{Ni}}>{\tilde{D}}_{\text{ReRe}}^{\text{Ni}}$, as determined by the diffusion-couple experiments. Further investigations on the coarsening kinetics of precipitates confirmed the additions of refractory elements improve the coarsening resistance of ${\gamma }^{\prime }$${\gamma }^{\prime }$ precipitates in the order of Re > W > Mo. The trends in the diffusivity determined by experiment and simulation are in excellent agreement. More importantly, the Young's modulus effect for the diffusion of refractory solutes in HEAs is also carefully analyzed and discussed. Our present findings will give new insights into future design of ${\gamma }^{\prime }$${\gamma }^{\prime }$-strengthened HEAs for high-temperature structural applications.