Application of the level-set method to the analysis of an evolving microstructure

Examination of three-dimensional microstructures and their evolution requires accurate quantification of morphologies. We developed a smoothing algorithm, termed “level-set smoothing,” that smoothes a discontinuous or nearly discontinuous function that describes interfaces. The proposed method can be applied to any voxel-based data describing a two-phase structure. The level-set smoothing method is a set of sequential data-processing schemes that consists of first generating the signed distance function for the given microstructure using the level-set method, followed by smoothing via diffusion. This algorithm is designed to substantially reduce the artificial shift in the interfacial positions, as compared to simple smoothing methods, so that interfacial properties, including their rate of change, are accurately calculated. The accuracy of the proposed method is demonstrated by comparisons of the numerically calculated interfacial properties from data sets smoothed by the proposed method with their analytical solutions and of the interfacial locations of a complex microstructure from unsmoothed and smoothed data sets. Higher accuracy in calculating time derivatives of curvatures is achieved by using the advective method and choosing the time difference such that interfacial displacement is about two to three Cartesian grid points.