Revealing the Mixed-Mode Precipitation Kinetics of $\Gamma'$ with a Modified Kampmann-Wagner Numerical (Kwn) Model

Abstract

The precipitation kinetics of $\gamma'$ particles in solid-state has long been a topic of scientific and industrial interest due to their significant impact on the mechanical properties of Ni-based superalloys. Although numerous studies over the past decades have sought to understand the coarsening mechanism of $\gamma'$ precipitates, there remains a long-standing debate regarding the dominant mass transport mechanism-whether it is interface-controlled or matrix diffusion-controlled. The challenge is that analytical theories of coarsening are only valid in the long-time regime, which is difficult to achieve experimentally. To address this, we have developed a modified Kampmann-Wagner numerical (KWN) model that incorporates both mass transport mechanisms. Using this precipitation model, we revisited experimental data from a model alloy (Ni-12.5 at.\% Al) to clarify the dominant mass transport mechanisms from nucleation to coarsening. Our study demonstrates that a single mass transport mechanism cannot adequately reproduce the entire set of precipitation data. Specifically, the matrix diffusion mechanism aligns more closely with the early nucleation and growth stages but fails to account for the anomalous effect of increasing volume fraction on the coarsening rate. Conversely, while the interface-controlled mechanism fits the coarsening data better, it does not accurately represent the early nucleation and growth stages. These comparative results highlight the existence of a mixed-mode character throughout the entire precipitation process of $\gamma'$ particles, which is numerically captured by our modified KWN model.

Keywords: Nucleation, Growth, Coarsening, Mixed-mode, Mean-field model