3D INTERACTIVE DATA LANGUAGE POLE FIGURE VISUALIZATION

Transcription

1 111 3D INTERACTIVE DATA LANGUAGE POLE FIGURE VISUALIZATION ABSTRACT Colleen S. Frazer, Mark A. Rodriguez, and Ralph G. Tissot Sandia National Laboratories, Albuquerque, NM The Interactive Data Language has been used to produce a software program capable of advanced 3D visualizations of pole figure and!-2! data. The data can also be used to calculate quantitative properties such as strain level and to minimize the peak-height texture effects in individual!-2! scans. The collection of the large data sets necessary for the analyses is facilitated by use of a PSD or area detector. INTRODUCTION The Interactive Data Language (IDL), ideally suited for visualizations and analysis of 3D structures, is already widely used in medical applications such as tracking heart irregularities and imaging brain scans [1-3]. In x-ray applications, complex visualizations that require dynamic contrast and background level changes can be created using IDL. These 3D IDL visualizations supply qualitative information on various levels and allow for real-time association of 3D texture with the more traditional 2D pole figure representations. Of the three categories of texture in solid materials, random, somewhat-textured, and single crystal, the majority of materials fall into the somewhat-textured type. A 3D structure in IDL can encapsulate data corresponding to any texture level, in particular that of partially textured materials that are otherwise difficult to analyze, and allow for quantitative comparisons of texture levels between samples in addition to the qualitative comparisons. The full data sets required for the visualizations are large and would be prohibitively time consuming if it weren't for the advent of faster data-collection schemes. New Position Sensitive Detectors (PSD) and area detectors allow for rapid collection of data sets that map diffraction intensity as a function of 2!, ", and #, either as pole figures or!-2! scans, thereby facilitating the collection of complete data sets in a single working day. The vital combination of IDL visualization and PSD measurement capabilities enables the creation of full 3D textured data sets ready for immediate visual analysis. METHODOLOGY A complete pole figure column can be created from either a data set of pole figures (figure 1(a) below) taken at incremental 2! values or a set of!-2! patterns (figure 1(b)) taken at various combinations of " and #. In the case of a data set comprised of pole figures, a typical 2! range would run from 20º to 60º at a step size of 0.05º, and # would run to at least 70º with a 5º increment. The resulting data set would be made up of 801 pole figures. The same data set could be made up of!-2! scans where 2! would run from 20º to 60º at a step size of 0.05º. The!-2! scans would be taken at every positional combination of " and # that would make up a typical pole figure, resulting in a total of 1080 scans (72 " positions with 15 # positions each). The type

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3 112 of detector used for the experiment determines which collection scheme is less time consuming. In our case, the PSD detector employed in this experiment (figure 2) was able to collect rapid!- 2! scans, so that was our chosen data format. (a) (b) Figure 1. Typical (a) pole figure and (b)!-2! scan. #,! cradle w/xyz translation Pinhole Collimator Alignment Laser Alignment Microscope Vantec PSD Figure 2. Bruker D8 Discover diffractometer with VANTEC$ PSD. The IDL program written to handle such data is then employed to turn the set of!-2! scans into pole figures for visualization. The pole figures are sorted according to 2! value, added to a single image array, and plotted in 3D using imbedded IDL visualization tools. The final pole figure column structure, shown in figure 3, contains the complete data for a given sample over the measured 2! range.

4 113 Figure 3. Pole figure column formed either by a set of pole figures or!-2! scans. Once the 3D pole figure column is created, pole figures and/or!-2! patterns may be generated from any position and real-time visualizations may be used to visibly analyze the texture. RESULTS Immediate visual analysis of volumetric data can be achieved, including use of through-volume 2D image planes to slice the column at any 2! position via motion of the mouse, as shown in figure 4. This is especially useful in cases where the maximum reflection intensity is not known and needs to be determined quickly before further analysis is done. The 3D and 2D visualizations include further manipulation techniques to control contrast, background level, color tables used, and ", # positions for!-2! scan extractions. (a) (b) Figure 4. Section of textured Mo pole figure column (a) with image plane (b).

5 114 Visualizations aren't the only analysis that can be achieved with the IDL program. It is also possible to perform stress quantification using the same data set. Since macrostrain present in a material will show up in the form of shifted peak positions as a function of #, the strain data as a function of these variables is automatically included in the basic data set collection. Plus, due to the plethora of information on peak position as a function of # contained in a single columnar data set, the measured strain and calculated stress can be obtained for any level of texture. The second primary quantitative analysis technique that the IDL program can perform is that of texture minimization. The presence of texture will change the relative intensities of peaks measured in a!-2! scan [4-5], complicating phase identification and making further refinement difficult. Integrated intensities from pole figures taken at these peak positions can be used to minimized texture-induced relative intensity distortion, as shown in figure 5. The data shown in the figure is uncorrected for defocusing and background, and as such the peaks in the texture minimized scan do not exactly follow the same relative intensities listed in the JCPDS file for the material [6]. Corrections for defocusing, background and similar typical x-ray phenomenon are included in the IDL program. JCPDS Int.: 40% 60% 100% (a) (b) Figure 5. Images of (a) a highly textured!-2! scan with the pole figures taken at each peak shown and (b) the texture minimized!-2! scan with the JCPDS (random) relative integrated peak intensities. CONCLUSIONS IDL has been used to produce advanced 3D visualization software for large x-ray diffraction data sets collected with the use of PSD's or area detectors. Interactive qualitative texture analysis, strain quantification, and texture minimization techniques have been included in the program. ACKNOWLEDGEMENTS Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.

6 115 REFERENCES [1] IDL Online Help, Interactive Data Language version 6.2, RSI, [2] IDL Speeds Assessment of Myocardial Perfusion, Creaso, [3] IDL-based KRONOS application also aiding research in Paget's disease and osteoporosis, Creaso, [4] Matthies, S.; Lutterotti, L.; Wenk, H.R., Advances in texture analysis from diffraction spectra Journal of Applied Crystallography, 1997 [30] pp [5] Jones, J.L.; Vogel, S.C.; Slamovich, E.B.; Bowman, K.J., Quantifying texture in ferroelectric bismuth titanate ceramics Scripta Materialia, 2004 [51] pp [6] Klemm, W.; Bommer, H., "The rare earth metals" Z. Anorg. Chem., 1937, pp