The Elastic Effect of Evolving Precipitate Shapes on the Ripening Kinetics of Tetragonal Phases

Coherent tetragonal precipitates, such as the Ni 3 Nb phase γ ″ found in Ni-base superalloys, appear as plate-shaped particles. These shapes are the result of anisotropic elastic misfit strains. We present 3D sharp phase-field simulations that capture this circumstance well due to the inclusion of the elastic effects from the misfit. These simulations reveal that the ripening behavior of γ ″ precipitates deviates significantly from the classical LSW theory of Ostwald ripening. A ripening exponent of 2 rather than 3 describes the simulated γ ″ size evolution at temperatures between 700 °C and 760 °C best. Employing a quantitative distinction argument, we show that 60 pct of this deviation is attributed to the elastically induced size dependence of the precipitate shapes. With increasing precipitate size, the minimization of elastic energy leads to steadily increasing plate aspect ratios. The precipitate ripening kinetics accelerate with increasing aspect ratio. Fitting the newly received square root time dependence to experimental data yields a physically conclusive activation energy of ripening close to the activation energy of Nb diffusion in the alloy.