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Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

Published online by Cambridge University Press:  13 April 2016

Ákos K. Kiss  and
János L. Lábár
Ákos K. Kiss
Affiliation:
Hungarian Academy of Sciences, Research Center for Energy Research, Institute for Technical Physics and Materials Science (MTA EK MFA), Konkoly Thege M. út 29-33, H-1121 Budapest, Hungary Doctoral School of Molecular- and Nanotechnologies, Faculty of Information Technology, University of Pannonia, Egyetem u. 10, H-8200 Veszprém, Hungary
János L. Lábár*
Affiliation:
Hungarian Academy of Sciences, Research Center for Energy Research, Institute for Technical Physics and Materials Science (MTA EK MFA), Konkoly Thege M. út 29-33, H-1121 Budapest, Hungary
*
*Corresponding author. [email protected]
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Abstract

Grain boundaries (GB) are characterized by disorientation of the neighboring grains and the direction of the boundary plane between them. A new approach presented here determines the projection of GB that can be used to determine the latter one. The novelty is that an additional parameter of GB is quantified in addition to the ones provided by the orientation maps, namely the width of the projection of the GB is measured from the same set of diffraction patterns that were recorded for the orientation map, without the need to take any additional images. The diffraction patterns are collected in nanobeam diffraction mode in a transmission electron microscope, pixel-by-pixel, from an area containing two neighboring grains and the boundary between them. In our case, the diffraction patterns were recorded using the beam scanning function of a commercially available system (ASTAR). Our method is based on non-negative matrix factorization applied to the mentioned set of diffraction patterns. The method is encoded in a MATLAB environment, making the results easy to interpret and visualize. The measured GB-projection width is used to determine the orientation of the GB-plane, as given in the study by Kiss et al.

Keywords

grain boundary planenon-negative matrix factorizationelectron diffractioncomputer programpolycrystalline thin films
Type
Technique and Instrumentation Development
Information
Microscopy and Microanalysis , Volume 22 , Issue 3 , June 2016 , pp. 551 - 564
Copyright
Copyright © Microscopy Society of America 2016

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References

Berry, M.W., Browne, M., Langville, A.N., Pauca, V.P. & Plemmons, R.J. (2007). Algorithms and applications for approximate nonnegative matrix factorization. Comput Stat Data Anal 52, 155–173.Google Scholar
Brunet, J.-P., Tamayo, P., Golub, T.R. & Mesirov, J.P. (2004). Metagenes and molecular pattern discovery using matrix factorization. Proc Natl Acad Sci U S A 101(12), 4164–4169.Google Scholar
Buciu, I. & Pitas, I. (2004). Application of non-negative and local non negative matrix factorization to facial expression recognition. Proceedings of the 17th International Conference on Pattern Recognition, 23–26 August 2004; Cambridge, UK; pp. 288–291.Google Scholar
Devarajan, K. (2008). Nonnegative matrix factorization: An analytical and interpretive tool in computational biology. PLoS Comput Biol 4(7), e1000029.Google Scholar
Egerton, R.F. (2011). Electron Energy-Loss Spectroscopy in the Electron Microscope, 3rd ed.New York, Dordrecht, Heidelberg and London: Springer Science+Business Media.Google Scholar
Eggeman, A.S., Krakow, R. & Midgley, P.A. (2015). Scanning precession electron tomography for three dimensional nanoscale orientation imaging and crystallographic analysis. Nat Commun 6, doi: 10.1038/ncomms8267.Google Scholar
Forwood, C.T. & Clarebrough, L.M. (1991). Electron Microscopy of Interfaces in Metals and Alloys. Bristol and New York: IOP Publishing. (Figure 4.8), p. 113.Google Scholar
Grimmer, H., Bollmann, W. & Warrington, D.H. (1974). Coincidence-site lattices and complete pattern-shift in cubic crystals. Acta Crystallogr A30, 197–207.Google Scholar
Kelly, P.M., Jostsons, A., Blake, R.G. & Napier, J.G. (1975). The determination of foil thickness by scanning transmission electron microscopy. Phys Status Solidi 31(2), 771–780.Google Scholar
Kiss, Á.K. & Lábár, J.L. (2013). A method for complete characterization of the macroscopic geometry of grain boundaries. Mater Sci Forum 729, 97–102.10.4028/www.scientific.net/MSF.729.97Google Scholar
Kiss, Á.K., Rauch, E.F., Pécz, B., Szívós, J. & Lábár, J.L. (2015). A tool for local thickness determination and grain boundary characterization by CTEM and HRTEM techniques. Microsc Microanal 21, 422–435.Google Scholar
Lábár, J.L., Kiss, Á.K., Christiansen, S. & Falk, F. (2012). Characterization of grain boundary geometry in the TEM, exemplified in Si thin films. Solid State Phenom 186, 7–12.10.4028/www.scientific.net/SSP.186.7Google Scholar
Lee, D.D. & Seung, H.S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791.10.1038/44565Google Scholar
Lee, D.D. & Seung, H.S. (2001). Algorithms for non-negative matrix factorization. In Advances in Neural Information Processing Systems 13, Leen, T.K., Dietterich, T.G. & Tresp, V. (Eds.), pp. 556–562. Available at http://papers.nips.cc/book/advances-in-neural-information-processing-systems-13-2000.Google Scholar
Lin, C.-J. (2007). Projected gradient methods for non-negative matrix factorization. Neural Comput 19, 2756–2779.Google Scholar
Lloyd, G.E., Farmer, A.B. & Mainprice, D. (2012). Misorientation analysis and the formation and orientation of subgrain and grain boundaries. Tecnophysics 279, 55–78.Google Scholar
Midgley, P.A. & Dunin-borkowski, R.E. (2009). Electron tomography and holography in materials science. Nat Mater 8, 271–280.Google Scholar
Paatero, P. & Tapper, U. (1994). Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5, 111–126.Google Scholar
Pozsgai, I. (1997). The determination of foil thickness by scanning transmission electron microscopy. Ultramicroscopy 68(1), 69–75.Google Scholar
Randle, V. (1993). The Measurement of Grain Boundary Geometry. London: The Institute of Physics Publishing.Google Scholar
Randle, V. (2001). A methodology for grain boundary plane assessment by single-section trace analysis. Scr Mater 44, 2789–2794.Google Scholar
Rauch, E.F., Véron, M., Portillo, J., Bultreys, D., Maniette, Y. & Nicolopoulos, S. (2008). Automatic crystal orientation and phase mapping in TEM by precession diffraction. Microsc Anal 22(6), S5–S8.Google Scholar
Saylor, D.M., El-Dasher, B.S., Adams, B.L. & Rohrer, G.S. (2004). Measuring the five-parameter grain-boundary distribution from observations of planar sections. Metall Mater Trans A 35A, 1981–1989.Google Scholar
Saylor, D.M., Morawiec, A. & Rohrer, G.S. (2003). Distribution of grain boundaries in magnesia as a function of five macroscopic parameters. Acta Mater 51, 3663–3674.Google Scholar
Smaragdis, P. & Brown, J.C. (2003). Non-negative matrix factorization for polyphonic music transcription. In Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 177–180. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics; 19–22 October 2001; New Paltz, New York.Google Scholar
Sotiras, A., Resnick, S.M. & Davatzikos, C. (2015). Finding imaging patterns of structural covariance via non-negative matrix factorization. Neuroimage 108, 1–16.Google Scholar
Stadelmann, P.A. (1987). EMS—A software package for electron diffraction analysis and HREM image simulation in materials science. Ultramicroscopy 21, 131–146.Google Scholar
Zaefferer, S., Wright, S.I. & Raabe, D. (2008). Three-dimensional orientation microscopy in a focused ion beam–scanning electron microscope: A new dimension of microstructure characterization. Metall Mater Trans A 39A, 374–389.Google Scholar
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