During grain growth, larger grains tend to grow at the expense of their smaller neighbors, resulting in a steady increase in the average crystallite size. Because the growth rate of any given grain is affected by that of its neighbors, the manner in which growth occurs is determined to a large extent by correlations in the sizes of neighboring grains. Quantitative information concerning these correlations can be extracted only from a truly three-dimensional characterization of the sample microstructure. We have used x-ray microtomography to measure the nearest-neighbor size correlations in a polycrystalline specimen of Al alloyed with 2 at.% Sn. The tin atoms segregate to the grain boundaries, where they impart a strong contrast in x-ray attenuation that can be reconstructed tomographically. From such reconstructions, we measured the size, topology and local connectivity of nearly 5000 contiguous Al grains and subsequently computed the size correlations in this material. The resulting information was incorporated into a non-mean-field theory for grain growth, the accuracy of which could be evaluated by comparing its predictions to the observed microstructure of the Al-Sn samples.
One major goal in x-ray tomography is to increase the resolution in space and time. For the methods with high temporal resolution we will present pink beam imaging and tomography. Experiments were realised at the ESRF undulator beamline ID22 with hard x-rays in the range from 11 keV to 20 keV. For the tomographic scans the exposure time per image was reduced by one to two orders of magnitude to less than 50 ms per image. The obtained image quality was comparable to that done with monochromatic beam. Further time reducing for a tomographic scan is possible with an improved acquiring and control system. The goal in the future is to realise tomographic scans within a minute with micrometer resolution. In order to achieve in the hard x-ray range sub-micrometer resolution we will show first results of x-ray magnified tomography. Different lens systems are available for this purpose. We obtained with aluminium parabolic compound refractive lenses a resolution of 1 micrometers and expect to overcome this limit hand in hand with the improvement of lens technology.
The inadequacies of current analytical models for grain growth are thought to arise in part from their mean-field nature: they ignore the presence of correlations in the sizes of neighboring grains induced by the process of grain growth itself. Although grain-size correlations have been identified in microstructures generated by computer simulations of grain growth, no comparable evidence has been obtained from real samples - primarily because of the experimental difficulties associated with evaluating this inherently three-dimensional property. Using absorption- contrast x-ray microtomography, we have attempted to characterize the network of grain boundaries in polycrystalline samples of Al doped with up to 3 at.% Sn. In principle, since the tin atoms segregate to the grain boundaries, it should be possible to determine the size and relative position of each grain from a three-dimensional reconstruction of the Sn distribution, from which the desired correlation function could be calculated directly. However, the grain boundaries in Al-Sn are not uniformly decorated with tin, which presents a formidable challenge to quantifying the microstructural properties of such samples. Significant progress toward overcoming this problem has been achieved by applying a constrained phase-field grain-growth algorithm to an approximate microstructure gleaned from the tomographic contrast data.