A phase field model is developed to study the discontinuous (cellular) precipitation (DP) reaction in a hypothetical A-B miscibility gap system. Unlike previous treatments, the model employs an interaction energy term which couples the composition and the phase field variable to enable the necessary grain boundary movement. The influence of factors such as interaction energy, interfacial mobility and grain boundary diffusivity on the transformation rate and overall microstructure evolution are discussed.

A recently developed phase-field model for simulating diffusion-induced grain boundary migration (DIGM) is applied to binary Fe-Zn. The driving force for the boundary migration is assumed to come from the coherency strain energy mechanism suggested by Sulonen. The effect of the angle of the grain boundary with the surface on the velocity of the boundary migration is studied in detail. The simulation results compare favorably with experimental observations, such as the oscillatory motion of the grain boundary, velocity of the moving grain boundary during DIGM, and the maximum value of mole fraction of Zn at the surface after 20 h of heat treatment.

Simulations of spinodal decomposition in an Fe-36 wt%Cr alloy at 773 K are performed by solving the non -linear Cahn-Hilliard equation, and the results are compared with atom probe tomography measurements. The influence of gradient energy coefficient, atomic mobilities and initial structure on the kinetics of spinodal decomposition is studied. It is shown that a proper initial structure, accounting for the thermal history above the miscibility gap, is crucial and enables predictive simulations of spinodal decomposition in Fe-Cr alloys.

The Phase field method has been used to study Diffusion Induced Grain boundary Migration (DIGM) in binary alloys. Simulations are performed for a simple hypothetical binary substitutional solid solution. The model is developed by taking into account the elastic interactions arising due to changes in concentration across a grain boundary when solutes are diffusing along the grain boundary. This gives a coupling term in the Gibbs energy functional that acts as a driving force for grain boundary migration. Two different kinds of coupling terms are studied: one acting on both the abutting grains and the other acting on only one grain. The former gives a freedom of choice as to in which direction the grain boundary will move, and is considered more general, whereas the latter only moves in one direction, regardless of the shape of the grain boundary. The results from the model are in qualitative agreement with previous experimental studies.

Discontinuous precipitation at high temperatures in (Ti,Zr)C was modeled using the phase field method. The modelling was based on previous treatments of diffusion induced grain boundary migration and spinodal decomposition. A fair agreement with experimental observations was obtained. However, a more refined treatment of the effect of strain energy is left for future work.

A phase field model is developed to study the discontinuous (cellular) precipitation(DP) in a hypothetical A-B miscibility gap system. The model employs an interaction energy term which couples the mole fraction (x_A) and the phase field variable (Φ) to study the mechanism behind the precipitation process. The term was used recently to model diffusion induced grain boundary migration in a hypothetical binary system Ref. Mukherjee et al. 2020. The interaction term suggests that strain energy develops after nucleation of DP strands at grain boundaries. The strands are observed to grow behind a moving grain boundary which favours one of the grains, thereby, taking the same orientation of the grain behind the growth front. The factors such as gradient energy coefficient (κ), the prefactor (K) from Hillert's expression for strain energy Ref. Hillert 1983, interfacial mobility (M_Φ) and interface diffusion (F) are altered to study their influence on lamellar spacing.

A recently developed phase-field model for simulating diffusion-induced grain boundary migration (DIGM) is applied to binary Fe--Zn. The driving force for the boundary migration is assumed to come from the coherency strain energy mechanism suggested by Sulonen. The effect of the angle of the grain boundary with the surface on the velocity of the boundary migration is studied in detail. The simulation results compare favorably with experimental observations, such as the oscillatory motion of the grain boundary, velocity of the moving grain boundary during DIGM, and the maximum value of mole fraction of Zn at the surface after 20~h of heat treatment.