A phase-field model for grain growth is briefly described. In this model, a poly-crystalline microstructure is represented by multiple structural order parameter fields whose temporal and spatial evolutions follow the time-dependent Ginzburg-Landau (TDGL) equations. Results from phase-field simulations of two-dimensional (2D) grain growth will be summarized and preliminary results on three-dimensional (3D) grain growth will be presented. The physical interpretation of the structural order parameter fields and the efficient and accurate semi-implicit Fourier spectral method for solving the TDGL equations will be briefly discussed.
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