Characterizing the Internal Grain Boundary Network Structure of Polycrystals:
The Current State of the Art and Opportunities for High Energy X-ray Diffraction Microscopy
Gregory S. Rohrer
Carnegie Mellon University; Department of Materials Science and Engineering
It is widely recognized that the grain boundary network structure influences th properties of polycrystalline materials used in engineered systems. Therefore, the ability to comprehensively characterize the distribution of grain boundary types, to understand how the distribution arises during processing, and to understand the relationship between the network structure and the properties of the material is of tremendous practical importance. The principal challenge associated with reaching these goals is to accumulate a sufficient number of observations to characterize the five-dimensional space of grain boundary types and their connectivity.
Recently, the use of automated electron backscattered diffraction (EBSD) measurements in the scanning electron have made it possible to measure the grain boundary character distribution as a function of five macroscopic parameters [1-5]. In this presentation, three of these parameters are used to specify the lattice misorientation and two are used to specify the interface plane orientation. The studies have led to a number of findings that appear to apply quite generally to a wide range of materials. First, grain boundary planes are textured to favor low index planes that correspond to low energy free surfaces. For example, in MgO, {100} planes dominate the population (see Fig. 1a) [1] and in Al, {111} plane are most common [5]. It has also been found that grain boundary configurations in the five parameter space occur with a frequency that is inversely related to their energy and that boundaries formed from low surface energy planes have low energies themselves (see Fig. 1b). Finally, there appears to be a steady state grain boundary character distribution that is predictable based on the rules for curvature driven motion [6]. We propose that the five parameter grain boundary distribution is a new metric for the characterization of a microstructure, that it can be predicted based on measurable interfacial properties, and that it can be used as input to model the macroscopic properties of a material.
Fig. 1. (a) The distribution of grain boundary planes in MgO, plotted in the crystal reference frame on a stereographic projection along [001] in multiples of a random distribution (MRD). (b) Normalized values of the grain boundary population (l) as a function of the reconstructed grain boundary energy (ggb). The average of all normalized values within a range of 0.032 a.u. is represented by the point; the bars indicate one standard deviation above and below the mean [1,4].
While EBSD based methods for measuring the grain boundary character distribution have been successful, there are some restrictions on their uses. For example, the accuracy of stereologically measured grain boundary character distributions depends on the sampling of large numbers of randomly configured bicrystals, and this can be a problem if the material has strong texture, or if the grains have a strong shape anisotropy. If the distribution is measured by serial sectioning, the vertical resolution (normal to the sample surface) is difficult to increase without decreasing the size of the section area. For example, focused ion beam sectioning can be very accurate, but this can only be accomplished over a relatively small area. Much larger areas can be studied using polished sections, but with diminished vertical resolution. Finally, it must be noted that serial sectioning is a destructive technique and it is therefore not possible to conduct true time-lapse studies of grain boundary network evolution during annealing, or the application of external fields.
Several X-ray techniques have emerged recently that show a great deal of potential.Three-dimensional X-ray microtomography uses absorption contrast to map the shapes of large numbers of grains, but does not deliver orientation data [7]. Three Dimensional X-Ray Diffraction Microscopy [8,9] and Differential Aperture X-ray Microscopy [10] have the potential to deliver both geometric and orientation data in a dynamic mode, and it is in this area where their capabilities exceed that of the EBSD based techniques. Studies of (electric, magnetic, or stress) field driven boundary motion, the relative contributions of grain boundary sliding, plastic flow, and grain rotation to deformation, and topological distinctions between growing and shrinking grains are all possible with 3D orientation microscopy using high energy X-rays.
For the X-ray measurements to be competitive with static measurements of the grain boundary character distribution, it will be necessary to characterize more the 1.5x103 contiguous grains with submicron spatial resolution in all three directions. While static EBSD studies require a time interval on the order of days, dynamic X-ray studies will have to proceed at much higher rates. The angular resolution of the X-ray studies is expected to greatly exceed the EBSD-based techniques. In short, X-ray diffraction microscopy is expected to be a powerful characterization technique with the unique ability to study of microstructural dynamics.
References
[1] D.M. Saylor, A. Morawiec, G.S. Rohrer, "Distribution of Grain boundaries in Magnesia as a Function of Five Macroscopic Parameters," Acta Mater., 51 (2003) 3663-74.
[2] D.M. Saylor, B.S. El-Dasher, B.L. Adams, G.S. Rohrer, "Measuring the Five Parameter Grain Boundary Distribution From Observations of Planar Sections," Metall. Mater. Trans., 35A (2004) 1981.
[3] D.M. Saylor, B.S. El-Dasher, Y. Pang, H.M. Miller, P. Wynblatt, A.D. Rollett, G.S. Rohrer, "Habits of Grains in Dense Polycrystalline Solids," J. Amer. Ceram. Soc., 87 (2004) 724-26.
[4] G.S. Rohrer, D.M. Saylor, B.S. El-Dasher, B.L. Adams, A.D. Rollett, and P. Wynblatt, " The Distribution of Internal Interfaces in Polycrystals," Z. Metall., 95 (2004) 197-214.
[5] D.M. Saylor, B.S. El-Dasher, A.D. Rollett, and G.S. Rohrer, "Distribution of Grain Boundaries in Aluminum as a Function of Five Macroscopic Parameters," Acta Mater., 52 (2004) 3649-3655.
[6] J. Gruber, D.C. George, A.P. Kuprat, G.S. Rohrer, A.D. Rollett, "Effect of Anisotropic Interfacial Energy on Grain Boundary Distributions During Grain Growth," 2nd International Conf. on Recrystallization and Grain Growth, Aug. 2004, in press.
[7] K.M. Döbrich, C. Rau, C.E. Krill III, “Quantitative Characterization of the 3D Microstructure of Polycrystalline Al-Sn using X-ray Microtomography,” Metall. Mater. Trans 35A (2004) 1953-61.
[8] H.F. Poulsen, S.F. Nielsen, E.M. Lauridsen, S. Schmidt, R.M. Suter, U. Lienert, L. Margulies, T. Lorentzen, D. Juul Jensen, "Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders," J. Appl. Cryst. 34 (2001) 751–756.
[9] S. Schmidt, S.F. Nielsen, C. Gundlach, L. Margulies, X. Huang, D. Juul Jensen, “Watching the Growth of Bulk Grains During Recrystallization of Deformed Metals,” Science 305 (2004) 229.
[10] B.C. Larson, W. Wang, G.E. Ice, J.D. Budai, J.Z. Tischler, “Three dimensional x-ray structural microscopy with submicrometre resolution,” Nature 415 (2002) 887-90.
