Quantitative Analysis of Complex Three-Dimensional MicrostructuresPublic Deposited
The morphological evolution due to coarsening is analyzed for two distinctive types of microstructure. First, the feasibility of characterizing spatial correlations of interfacial curvature in topologically complex structures is demonstrated with the analysis of bicontinuous two-phase mixtures produced using phase field modeling. For structures produced with both conserved and nonconserved dynamics, new characteristic length scales are identified. In the nonconserved case, despite the local evolution law governing interfacial motion, long-range correlations develop that lead to a characteristic length scale associated with the distance between high curvature tunnels. In the conserved case the diffusional dynamics leads to a length scale that is related to correlations and anticorrelations between regions of curvature of opposite sign. Positive correlations due to this length scale can be measured out to seven times the characteristic length of the system. Spatial correlations are also compared for symmetric and asymmetric mixtures produced with conserved dynamics. In addition, the microstructure of directionally solidified and isothermally coarsened Pb-Sn samples are examined at various coarsening times. The samples, composed of Pb-69.1$wt\%$Sn, have an overall volume fraction of 22\% solid which is not uniformly distributed through the sample but clustered into regions of approximately 37\% solid separated by empty eutectic regions. The morphology of the dendrites, both in the dense regions and at the edge of the eutectic spaces is analyzed using three-dimensional reconstructions, Interface Shape Distributions and Interface Normal Distributions. These methods are used to track the evolution of the structures from being dominated by secondary and tertiary arms in the plane perpendicular to the solidification direction to predominance of the primary stalks running in the solidification direction. Finally, the method of characterizing spatial correlations introduced above is applied to the experimentally obtained dendritic structures. For these samples, changes to the correlations are found due to increased coarsening time, changes in volume fraction, and whether the sample comes from a dense or non-dense region. This technique proves to be a method of broad applicability that has the potential to unlock valuable details about a variety of different systems and phenomena.