Quantitative nondiagonal phase field modeling of pearlite growth involving multi-diffusion paths

Despite extensive research on pearlite formation, the rate-controlling mechanisms of pearlite growth remain under debate. Phase field modeling has become a key tool for investigating such transformations; however, in solid-state systems where diffusion occurs both within individual phases and along their interfaces, the commonly assumed local-equilibrium boundary conditions are rarely satisfied, leading to artificial interface effects in conventional diagonal formulations. Here, we present a thermodynamically consistent nondiagonal three-phase field model formulated within the grand-potential framework to investigate pearlite growth. By introducing an Onsager-symmetric cross-coupling term between conserved and nonconserved order parameters, the model inherently recovers the correct equilibrium boundary conditions regardless of the active diffusion pathways, including bulk diffusion and interfacial diffusion. We systematically analyze four diffusion scenarios: (i) diffusion in austenite; (ii) diffusion in austenite, ferrite, and cementite; (iii) diffusion in austenite and ferrite; and (iv) diffusion in austenite combined with interfacial diffusion along austenite/ferrite and austenite/cementite boundaries. The model's quantitative performance is benchmarked against available analytical solutions for each case. Overall, the proposed framework provides a robust and thermodynamically sound approach for elucidating how different diffusion pathways control pearlite growth kinetics.