J. Alkemper

Quantitative serial sectioning analysis.

A method for serial sectioning is presented that allows one to take about 20 sections per hour with spacings in the range 1–20 µm between sections. The alignment of the cross‐sections is done with a linear variable differential transformer; it is thus independent of the microstructure of the sample and does not rely upon markers implanted in the sample. The alignment errors as well as tilts and rotation errors between sections associated with the new method are found to be negligible. Once all the sections are captured in a computer a three‐dimensional image can be constructed. This image can be viewed interactively and rotated, thus allowing the direct observation of three‐dimensional shapes. It can further be used to determine a vast array of microstructural parameters including those that cannot be determined from planar sections. The technique is illustrated through the reconstruction of the microstructure of a cast standard aluminium alloy specimen.

Three-dimensional characterization of dendritic microstructures

Abstract The first complete characterization of a dendritic microstructure is presented. The dendrite morphology is obtained via a novel serial-sectioning process that allows the three-dimensional microstructure of opaque materials to be determined in a routine manner. Using the reconstructed dendrite we determine the spatial distribution of the mean and Gaussian curvature as well as the probability density distributions of these curvatures. These measurements yield many insights into the local processes that shape these topologically complex structures that are vital in setting many material properties.

Transient Ostwald ripening and the disagreement between steady-state coarsening theory and experiment

Abstract The coarsening of solid-Sn particles in a Pb–Sn liquid has been studied under microgravity conditions. These experiments permit an unambiguous comparison between theory and experiment to be made. In contrast to steady-state theories, such as those due to Lifshitz and Slyozov and Wagner, the scaled particle size distributions evolve in samples containing 0.1 and 0.2 volume fractions of solid. Steady state was not reached even though the average particle radius increased by a factor of three during the experiment. In addition, the scaled spatial correlation functions were also found to be time dependent in samples containing 0.1, 0.2, and 0.3 volume fractions of solid. The size distributions and correlation functions for all coarsening times at the fractions ≤0.3 agree with the predictions of a theory for transient coarsening. We show that the microstructures have not reached the steady-state regime for all volume fractions, are thus not self-similar, and that given our initial experimental conditions the time required to reach steady-state coarsening increases with increasing volume fraction. In these experiments, and we suspect in others as well, the transients are sufficiently long that steady-state theories cannot adequately describe the evolution of the microstructure.

THE DEVELOPMENT OF SPATIAL CORRELATIONS DURING OSTWALD RIPENING: A TEST OF THEORY

Abstract The coarsening of solid-Sn particles in a Pb–Sn liquid was studied under microgravity conditions. Spatial correlation functions were measured on plane sections in a low-volume fraction system undergoing Ostwald ripening. The correlation functions changed with time in a way that indicated that the microstructure initially consisted of clusters of particles and evolved into one which was more dispersed. The model by Akaiwa and Voorhees (AV) was used to study the effect of spatial correlations on the ripening process. We found that the initially highly correlated structure had no observable effect on the evolution of particle size distributions, but did have an effect on the coarsening rate of the system. Specifically, we determined that a structure consisting of clusters of particles coarsened faster than a system with a random, spatial arrangement of non-overlapping particles. We also found that the approach of the microstructure towards the steady-state regime could be monitored more sensitively using spatial correlations rather than using particle size distributions. The spacial correlations and the particle size distributions measured from the experiment agreed well with those calculated from the AV simulations using the initial experimental correlations and size distribution.

Three-dimensional morphological characterization of coarsened microstructures

Abstract The three-dimensional morphological evolution of a directionally solidified Al-15 wt.% Cu alloy during isothermal coarsening was examined. The microstructure was analyzed using the Interfacial Shape Distribution (ISD), which gives the probability of locating an interfacial patch with a given pair of principle curvatures. By scaling the ISDs by a characteristic length, the inverse of the surface area per unit volume, it was possible to determine if the system reached a scaled time-invariant state. During coarsening, cylindrical interfaces appear in the second coarsened sample and remained for later coarsening times. The appearance of the corresponding peak in the ISD indicated that the microstructure was not evolving in a self-similar manner, despite the linear relationship between the inverse surface area per unit volume and the cube root of coarsening time. Stereographic projections of the interfacial normals indicated that the microstructure of the earliest coarsened sample had a four-fold sym...

Coarsening in solid-liquid mixtures: A summary of results

The coarsening of solid Sn-rich particles in Pb-Sn liquid in a microgravity environment is examined. Volume fractions from 0.1 to 0.8 are analyzed. The low volume fraction samples allow for a direct comparison to coarsening theories with out any adjustable parameters. It was found that the system was not coarsening in a self similar manner, but rather evolved toward the steady-state conditions predicted by theory. The steady-state regime was not reached, even though for volume fractions 0.1 and 0.2, there was a increase of the average particle size by a factor of nearly 3. Also the spatial correlations for volume fractions < 0.3 evolved in time. The evolution of these volume fractions agree with the predictions of a theory describing transient coarsening. We show that the rate at which the coarsening process approaches steady-state decreases as the volume fraction increases.