Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T09:50:24.611Z Has data issue: false hasContentIssue false
  • English
  • Français

Pattern Center and Distortion Determined from Faint, Diffuse Electron Diffraction Rings from Amorphous Materials

Published online by Cambridge University Press:  24 April 2017

János L. Lábár Open the ORCID record for János L. Lábár [Opens in a new window]  and
Partha P. Das
János L. Lábár*
Affiliation:
Centre for Energy Research, Institute of Technical Physics and Materials Science, Hungarian Academy of Sciences, H-1121 Budapest, Konkoly-Thege M. u. 29-33, Hungary
Partha P. Das
Affiliation:
Electron Crystallography Solutions, Orense 8, 28032 Madrid, Spain
*
*Corresponding author.[email protected]
Get access

Abstract

Diffuse rings from amorphous materials sit on a steep background resulting in a monotonically decreasing intensity over scattering vector length, frequently with no clear local maximum that could be used to determine the center of the ring. The novelty of the method reported here is that it successful processes such weak patterns. It is based on separating the angular dependence of the positions of the maxima on the azimuthal angle in the measured two-dimensional pattern for a manually preselected peak. Both pattern center and elliptical distortion are simultaneously refined from this angular dependence. Both steps are based on nonlinear least square fitting, using the Levenberg–Marquardt method. It can be successfully applied to any amorphous patterns provided they were recorded with experimental conditions that facilitate dividing them into sectors with acceptable statistics. Patterns with the center shifted to the camera corner (recording a quadrant of a ring) can also be reliably evaluated, keeping precalibrated values of the elliptical distortion fixed during the fit. Finally, the limited number of counts in any pattern is overcome by cumulating many patterns (from equivalent areas) into a single pattern. Eliminating false effects is facilitated by masking out unwanted parts of any recorded pattern from processing.

Keywords

TEMthin filmscomputer programpartial patternsamorphous materials
Type
Instrumentation and Software
Information
Microscopy and Microanalysis , Volume 23 , Issue 3 , June 2017 , pp. 647 - 660
Copyright
© Microscopy Society of America 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Belletti, D., Calestani, G., Gemmi, M. & Migliori, A. (2000). QED V1.1: A software package for quantitative electron diffraction data treatment. Ultramicroscopy 81, 57–65.CrossRefGoogle Scholar
Capitani, G.C., Oleynikov, P., Hovmöller, S. & Mellini, M. (2006). A practical method to detect and correct for lens distortion in the TEM S. Ultramicroscopy 106, 66–74.CrossRefGoogle Scholar
Carvalho, D. & Morales, F.M. (2012). High-resolution electron diffraction: Accounting for radially and angularly invariant distortions. Microsc Microanal 18, 638–644.CrossRefGoogle ScholarPubMed
Hou, V.D.-H. (2008). A DigitalMicrographTM script to characterize elliptical distortion of electron diffraction patterns in TEM. Microsc Microanal 14(Suppl 2), 1124–1125.CrossRefGoogle Scholar
Hou, V.D.-H. & Li, D. (2008). A method to correct elliptical distortion of diffraction patterns in TEM. Microsc Microanal 14(Suppl 2), 1126–1127.CrossRefGoogle Scholar
Jansen, J. (2006). Structure refinement by taking dynamical diffraction into account. In Electron Crystallography, Weirich, Th.E., Lábár, J.L. & Zou, X.D. (Eds.), NATO Science Series II: Mathematics, Physics and Chemistry, vol. 211, pp. 355–372. Dordrecht: Springer.CrossRefGoogle Scholar
Klinger, M. & Jager, A. (2015). Crystallographic Tool Box (CrysTBox): Automated tools for transmission electron microscopists and crystallographers. J Appl Crystallogr 48, 2012–2018.CrossRefGoogle ScholarPubMed
Klinger, M., Nemec, M., Polivka, L., Gartnerova, V. & Jager, A. (2015). Automated CBED processing: Sample thickness estimation based on analysis of zone-axis CBED pattern. Ultramicroscopy 150, 88–95.CrossRefGoogle ScholarPubMed
Lábár, J.L. (2000). “ProcessDiffraction”: A computer program to process electron diffraction patterns from polycrystalline or amorphous samples. In Proceedings of the 12th European Congress on Electron Microscopy, Frank, L. & Ciampor, F. (Eds.), pp. I379–I380. Brno: Czechoslovak Society for Electron Microscopy.Google Scholar
Lábár, J.L. (2002). A tool to help phase identification from electron diffraction powder patterns. Eur Microsc Anal 75, 9–11.Google Scholar
Lábár, J.L. (2005). Consistent indexing of a (set of) single crystal SAED pattern(s) with the ProcessDiffraction program. Ultramicroscopy 103, 237–249.CrossRefGoogle ScholarPubMed
Lábár, J.L. (2008). Electron diffraction based analysis of phase fractions and texture in nanocrystalline thin films, Part I: Principles. Microsc Microanal 14, 287–295.CrossRefGoogle Scholar
Lábár, J.L. (2009). Electron diffraction based analysis of phase fractions and texture in nanocrystalline thin films, Part II: Implementation. Microsc Microanal 15, 20–29.CrossRefGoogle ScholarPubMed
Lábár, J.L. & Adamik, M. (2001). ProcessDiffraction V1.2: New possibilities in manipulating electron diffraction ring patterns. Microsc Microanal 7(Suppl 2), 372–373.CrossRefGoogle Scholar
Li, X. (2007). Quantitative analysis of polycrystalline electron diffraction patterns. Microsc Microanal 13(Suppl 2), 966–967.CrossRefGoogle Scholar
Mitchell, D.R.G. (2008a). Circular Hough transform diffraction analysis: A software tool for automated measurement of selected area electron diffraction patterns within Digital Micrograph. Ultramicroscopy 108, 367–374.CrossRefGoogle ScholarPubMed
Mitchell, D.R.G. (2008b). DiffTools: Electron diffraction software tools for DigitalMicrographTM . Microsc Res Tech 71, 588–593.CrossRefGoogle Scholar
Mitchell, D.R.G. & Petersen, T.C. (2012). RDFTools: A software tool for quantifying short-range ordering in amorphous materials. Microsc Res Tech 75, 153–163.CrossRefGoogle ScholarPubMed
Mitchell, D.R.G. & Van den Berg, J.A. (2016). Development of an ellipse fitting method with which to analyse selected area electron diffraction patterns. Ultramicroscopy 160, 140–145.CrossRefGoogle ScholarPubMed
Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. (1996). Numerical Recipes in FORTRAN 77. Cambridge: Cambridge University Press.Google Scholar
Székely, L., Sáfrán, G., Kis, V., Horváth, Z.E., Mayrhofer, P.H., Moser, M., Radnóczi, G., Misják, F. & Barna, P.B. (2014). Crossover of texture and morphology in (Ti1−xAlx)1−yYyN alloy films and the pathway of structure evolution. Surf Coat Technol 257, 3–14.CrossRefGoogle Scholar
Wu, C.H., Reynolds, W.T. Jr. & Murayama, M. (2012). A software tool for automatic analysis of selected area diffraction patterns within Digital Micrograph™. Ultramicroscopy 112, 10–14.CrossRefGoogle ScholarPubMed