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High Energy X-ray Diffraction Microscopy (HEDM): Observing microstructure evolution inside of bulk materials Grain growth in high purity aluminum measured with HEDM at the Advanced Photon Source (S.F. Li, C.M. Hefferan, U. Lienert, R.M. Suter, unpublished):  Colors are mapped from three crystallographic misorientation parameters calculated on a voxel-to-voxel basis between an initial measured state and an annealed state. Only misorientations greater than 5 degrees are plotted so as to show the motion of large angle grain boundaries under annealing. Hexagon indicates simulated region used in reconstruction.

Table of Contents (modified October 2009)

1. Recent publications
2. Examples of reconstructions
   
3. Overview
4. Technique summary and schematic
5. Apparatus at the APS
6. The July 2004 crew

Related Publications

1. Microstructural Characterization and Evolution in 3D, S.R. Wilson, C.M. Hefferen, S.F. Li, J. Lind, R.M. Suter and A.D. Rollett, Risoe 2010 Symposium proceedings, accepted.
   
   
2. 3DXRD at the Advanced Photon Source: Orientation Mapping and Deformation Studies, U. Lienert, M.C. Brandes, J.V. Bernier, M.J. Mills, M.P. Miller, S.F. Li, C.M. Hefferan, J. Lind, R.M. Suter, Risoe 2010 Symposium proceedings, accepted.
   
   
3. Statistics of High Purity Nickel Microstructure From High Energy X-ray Diffraction Microscopy, C.M. Hefferan, S.F. Li, J. Lind, U. Lienert, A.D. Rollett, P. Wynblatt, R.M. Suter, Computers, Materials and Continua, 14, 209-219 (2009).
   


4. Tests of Microstructure Reconstruction by Forward Modeling of HEDM Data, C.M. Hefferan, S.F. Li, J. Lind, and R.M. Suter, Journal of Powder Diffraction, 25, 132-137 (2010).
   
   

5. Probing Microstructure Dynamics With X-ray Diffraction Microscopy, R.M. Suter, C.M. Hefferan, S.F. Li, D. Hennessy, C. Xiao, U. Lienert, B. Tieman, J. Eng. Mater. Technol., 130, 021007 (2008); proceedings of the Materials Processing Defects-5 conference, Cornell University, July 2007).
   

6. 3-Dimensional Characterization of Polycrystalline Bulk Materials Using High-Energy Synchrotron Radiation, U. Lienert, J. Almer, B. Jakobsen, W. Pantleon, H.F. Poulsen, D. Hennessy, C. Xiao, and R.M. Suter, Materials Science Forum 539-543, 2353-2358 (2007).

7. Forward Modeling Method for Microstructure Reconstruction Using X-ray Diffraction Microscopy: Single Crystal Verification, R.M. Suter, D. Hennessy, C. Xiao, U. Lienert.  Reviews of Scientific Instruments, 77, 123905 (2006).

8. Tracking: a method for structural characterization of grains in powders or polycrystals, E.M. Laurdisen, S. Schmidt, R.M. Suter, and H.F. Poulsen, J. Appl. Cryst., 34, 744-750 (2001).

9. Three-dimensional maps of grain boundaries and the stess state of individual grains in polycrystals and powders, H.F. Poulsen, S.F. Nielsen, E.M. Laurdisen, S. Schmidt, R.M. Suter, U. Lienert, L. Margulies, T. Lorentzen, and D. Juul Jensen, J. Appl. Cryst., 34, 751-756 (2001).

10. Future Trends: Texture Analysis for Structure-Sensitive Properties, B.L. Adams, D. Juul Jensen, H.F. Poulsen, and R. Suter, Materials Science Forum, 273-275, 29-40 (1998).

Some examples of microstructure measurements using x-ray diffraction microscopy

All data shown here were collected at the Advanced Photon Source, beamline 1-ID at Argonne National Laboratory. Participants include Chris Hefferan, Frankie Li, Robert Suter (CMU) and Ulrich Lienert (APS). Important computational assistance was provided by Brian Tieman of the APS; analysis was performed using custom software developed at CMU running on a 68 node cluster at the APS.

Questions or comments? e-mail: suter@andrew.cmu.edu

1. A section through the middle of a NIST certified 152 micron diameter single crystal ruby sphere.  a) The color map on the left shows misorientations from the average orientation.  Red-green-blue color contributions are proportional to the Rodrigues vector describing the misorientation.  The maximum rotation angle is 0.3 degrees. The green circle shows the nominal 152 micron sample cross-section while the hexagon shows the entire region included in the analysis. The maximum radial deviations are roughly 8 microns. b) The map on the right shows the 'confidence' fitting paramter indicating maximal overlap of the simulation with the experimental data in the central region and reduced overlap near the edges. This reduction is due to background subtraction removing weak edges of the imaged diffraction spots. This fit is based on simulation of 1118 ruby Bragg peaks about 115 of which could be observed at more than one detector distance in the experimental data set. A confidence of 0.79 means that over 90 simulated peaks overlap experimentally observed peaks; 0.33 confidence implies 38 overlaps.

Ruby sphere orientation map (expanded scale)	Relative confidence map for image at left

2. Near surface sections through an aluminum 1050 alloy polycrystal sample. Colors indicate grain orientations, again coded by Rodrigues vector components. The blue circle indicates the 1 mm nominal sample diameter while the hexagon is the analysis box. Black lines in the maps are draw between elements with more than 5 degree misorientation.

• Evidently, the sample surface is not parallel to the x-ray beam nor is it planar -- in the image at right, 10 microns deeper into the material, the fitted region has expanded on both the lower left and upper right sides.
• The appearance of regions of apparently uniform color is the result of many triangular area elements being independently found to have similar crystallographic orientation. That is to say, the grain structure emerges from the analysis -- sharp Bragg scattering is assume to emerge from each element, but no neighbor correlations are assumed. On expanded color scales or through quantitative analysis, one sees that some grains contain orientation gradients corresponding to defect content. Note that some five degree boundary lines separate regions of almost the same color -- these are low angle grain boundaries.
• The third image below shows a map of the misorientation between the two layer shown here. With 10 micron separation between layers, most of the area is occupied by the same grains and has low misorientation (blue). Since the grain boundaries are in general tilted relative to the translation axis, there is significant misorientation near the grain boundaries (boundaries from the z=0 layer are superimposed).
  
• After measuring many such layers, a three dimensional digital representation of the sample microstructure can be created. Since the measurement is non-destructive, one can treat the sample in some way (annealing, straining,...) and re-measure to see how the structure responds.
  

z = 0
z = -10um
Point-to-point crystallographic misorientation between the above two layer measurements. Black lines show boundaries in the z = 0 layer.

Overview of relevance of HEDM microstructure mapping techniuqe

Polycrystals are aggregates of single crystals joined together by a network of internal interfaces called grain boundaries. Polycrystalline materials, in both single and multi-phase forms, are ubiquitous in engineered systems: integrated circuits, aircraft and automotive components, communications devices, machine tools, and many others. The three dimensional geometry, arrangement, and relative orientation of the grains and the consequent grain boundary network (i.e., the microstructure) are crucial determinants of mechanical, chemical, thermal, and electrical properties. While there has been dramatic progress made in gaining three dimensional information about microstructure from two dimensional measurements made at surfaces (CMU MRSEC), it remains a great challenge to be able to watch microstructural evolution in response to external stimuli. With such observations made deep inside bulk materials, we should be able to deepen our understanding of phenomena and develop accurate constitutive relations governing the evolution and thereby learn how to do predictive calculations and to tailor microstructures to specific applications.

Three Dimensional X-ray Diffraction Microscopy (see articles listed above and the monograph by H.F. Poulsen, "Three Dimensional X-ray Diffraction Microscopy," Springer, 2004) is the only method available that can non-destructively image macroscopic volumes of internal microstructures. Based simply on Bragg diffraction, it is as versatile as, for example, electron backscatter diffraction analysis of surface microstructures. But by using high energy x-rays, it looks through millimeters of  material without the need for destructive serial sectioning. Similar to serial sectioning work, measurements are done layer-by-layer. After the measurement, the sample still exists and can be re-measured after processing. Real-time dynamics can be monitored. The x-rays can penetrate sample chambers, making in-situ measurements possible. In sum, high energy x-ray diffraction microscopy (HEDM) promises to open the world of microstructure dynamics and response to a new light. In combination with powerful new computational tools, one can look forward to a new level of understanding and a new level of "dynamic three dimensional command over materials structure," (ONR BAA 04-024) processing, and properties.

Schematic and Outline of the Technique

1.  Monochromatic high energy x-rays (energies 50 - 100 keV) are focused in the vertical direction to form a line-focused beam roughly 1 -2 microns high and about 1.3mm wide (red).
   
2. This beam illuminates a thin planar section of the sample (green).
   
3. Bragg spots (black) from individual grains are imaged on a CCD detector (gray); spots have the shape of the illuminated grain cross section projected onto the detector plane at the scattering angles 2q and f.
   
4. Measuring a set of spots at multiple sample-to-detector distances yields the path of the diffracted beam and, by inversion, the position of the diffracting grain.
   
5. Step-wise measurements over a range of sample orientations, w, yield multiple spots from each grain; this implies complete crystallographic orientation information and projected images of each grain from multiple points of view

7. After image processing, our analysis code performs a simulation of the entire measurement and microstructure. The sample space is gridded (above right) and the crystallographic orientation in each grid element (or voxel) is adjusted to optimize the overlap of simulated Bragg scattering with the experimental data. The search algorithm works on each voxel independently making parallelization of the code straightforward.
   

Apparatus at APS beamline XOR-1

The following images were taken during our January 2008 beam time:  various updates (such as new CCD cameras) have occurred since then.

	Sample stage at 1-IDB. CCD camera lens collects scintillation light off a 45 degree mirror. Ce/YAG scintillator and 45 degree mirror holder Beam block (black) Sample (vertical cylinder) XYZ translations stage Precitech air-bearing rotation stage
	Frankie and Chris at 1-ID command central