Current development in quantitative phase-field modeling of solidification

The quantitative phase-field simulations were reviewed on the processes of solidification of pure metals and alloys.The quantitative phase-field equations were treated in a diffuse thin-interface limit, which enabled the quantitative links between interface dynamics and model parameters in the quasi-equilibrium simula-tions.As a result, the quantitative modeling is more effective in dealing with microstructural pattern for-mation in the large scale simulations without any spurious kinetic effects.The development of the quanti-tative phase-field models in modeling the formation of microstructures such as dendritic structures, eutec-tic lamellas, seaweed morphologies, and grain boundaries in different solidified conditions was also re-viewed with the purpose of guiding to find the new prospect of applications in the quantitative phase-field simulations.