Tests of MacPherson-Srolovitz Grain Growth in Metallic Polycrystals

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

TECHNICAL: Cellular structures, ranging from soap bubbles or other froths to crystalline grains in polycrystals, tend to coarsen over time. Coarsening refers to the fact that some cells grow while others shrink and disappear. Understanding this process in any cellular structure contributes to controlling it and tailoring it for particular needs and applications. In two dimensions, the famous 1950s von Neumann-Mullins calculation expresses the rate of change of the area of a cell in terms of the number of its triple points (points where the cell has two neighbors). Until 2007, when MacPherson and Srolovitz published a d-dimensional generalization, there was no analogous formula in three dimensions. The MacPherson and Srolovitz calculation gives the rate of change of a cell volume in terms of simple geometrical quantities: the grain size (the mean width) and the total length of triple lines bounding the grain. However, applying this calculation to grain growth in polycrystals is somewhat suspect since it assumes that all boundaries have the same properties. Unfortunately, this is not true for crystal-to-crystal interfaces where properties depend on five mesoscopic parameters. So the question is, does the theoretical result help us understand growth in real materials? Can it be taken as a starting point from which to develop more complex models? These are basic scientific questions with direct implications for real world materials. Making materials with desirable properties requires control over grain size and grain boundary type distributions. Gaining predictive control over these properties requires a detailed, verified model. Contemporaneous with theoretical developments is the development of x-ray diffraction microscopy (XDM), a non-destructive, high energy, synchrotron x-ray technique that measures the location, shape, and orientation of large numbers of crystalline grains inside bulk polycrystals. Being non-destructive means that an ensemble of grains can be mapped, the sample annealed to allow growth, and the same volume of material re-mapped to determine changes. Within micron scale resolution limits, the measurements yield the types of each grain boundary and the geometry of grains. XDM measurements will begin with a high purity aluminum polycrystal that should approximate assumptions of the MacPherson-Srolovitz theory and continue with more complicated (impure and more anisotropic) materials. The objective is to determine whether the theory is applicable and whether it is useful as a starting point even when the assumptions are not well met. NON-TECHNICAL: The ability to perform non-destructive 3D microstructure measurements will have a broad impact in the materials sciences. Grain growth measurements will demonstrate the capabilities of microstructure mapping at the Advanced Photon Source (APS) and will help attract a community of users to the dedicated facility that has been developed over the past five years. The facility will include hardware and the software and computational power necessary to generate microscope output. Results and other measurements using the facility will help to constrain and/or validate theories and computer simulations of materials response to a variety of processing treatments including thermal, mechanical, and chemical. The technique can be used to study any crystal-based materials. Graduate and undergraduate students in Physics and Materials Science and Engineering will work in an interdisciplinary environment that cuts across fundamental materials issues, x-ray science, and applications technology. They will work within a large, active microstructure-community at CMU and at APS.