Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-07T08:34:19.021Z Has data issue: false hasContentIssue false
  • English
  • Français

Electron Diffraction Based Analysis of Phase Fractions and Texture in Nanocrystalline Thin Films, Part I: Principles

Published online by Cambridge University Press:  04 July 2008

János L. Lábár
János L. Lábár*
Affiliation:
Research Institute for Technical Physics and Materials Science, Thin Film Physics Laboratory, H-1121 Budapest, Konkoly-Thege M. út 29-33, Hungary
*
Corresponding author. E-mail: [email protected]
Get access

Abstract

A method for phase analysis, similar to the Rietveld method in X-ray diffraction, was not developed for electron diffraction (ED) in the transmission electron microscope (TEM), mainly due to the dynamic nature of ED. Nowadays, TEM laboratories encounter many thin samples with grain size in the 1–30 nm range, not too far from the kinematic ED conditions. This article describes a method that performs (semi)quantitative phase analysis for nanocrystalline samples from selected area electron diffraction (SAED) patterns. Fractions of the different nanocrystalline components are determined from rotationally symmetric ring patters. Both randomly oriented nanopowders and textured nanopowders, observed from the direction of the texture axis produce such SAED patterns. The textured fraction is determined as a separate component by fitting the spectral components, calculated for the previously identified phases with a priori known structures, to the measured distribution. The Blackman correction is applied to the set of kinematic diffraction lines to take into account dynamic effects for medium grain size. Parameters of the peak shapes and the other experimental parameters are refined by exploring the parameter space with the help of the Downhill-SIMPLEX. Part I presents the principles, while future publication of Parts II and III will elaborate on current implementation and will demonstrate its usage by examples, respectively.

Keywords

electron diffractionSAEDring patternsnanocrystalsthin filmsphase fractionstexturequantitative analysisTEM
Type
Microanalysis
Information
Microscopy and Microanalysis , Volume 14 , Issue 4 , August 2008 , pp. 287 - 295
Copyright
Copyright © Microscopy Society of America 2008

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

REFERENCES

Avilov, A., Kuligin, K., Nicolopoulos, S., Nickolskiy, M., Boulahya, K., Portillo, J., Lepeshov, G., Sobolev, B., Collette, J.P., Martin, N., Robins, A.C. & Fischione, P. (2007). Precession technique and electron diffractometry as new tools for crystal structure analysis and chemical bonding determination. Ultramicroscopy 107, 431–444.CrossRefGoogle ScholarPubMed
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.Google Scholar
Berg, B.S., Hansen, V., Midgley, P.A. & Gjonnes, J. (1998). Measurement of three-dimensional intensity data in electron diffraction by the precession technique. Ultramicroscopy 74, 147–157.Google Scholar
Bethe, H.A. (1928). Theorie der Beugung von Elektronen an Kristallen. Ann Physik 87, 55–129.CrossRefGoogle Scholar
Blackman, M. (1939). On the intensities of the electron diffraction ring. Proc Roy Soc London A173, 68–82.Google Scholar
Cordier, P., Ungár, T., Zsoldos, L. & Tichy, G. (2004). Dislocation creep in MgSiO3 perovskite at conditions of the Earth's uppermost lower mantle. Nature 428, 837–840.CrossRefGoogle ScholarPubMed
David, W.I.F., Shankland, K., McCusker, L.B. & Baerlocher, Ch. (Eds.) (2002). Structure Determination from Powder Diffraction Data, IUCr Monographs on Crystallography, No. 13. Oxford: Oxford University Press.Google Scholar
Delhez, R., de Keijser, Th.H., Landford, J.I., Louer, D., Mittemeier, E.J. & Sonneveld, E.J. (1993). Crystal imperfection broadening and peak shape in the Rietveld method. In The Rietveld Method, Young, R.A. (Ed.), IUCr Monographs on Crystallography, No. 5, pp. 132–166. Oxford: Oxford University Press.Google Scholar
Dimmeler, E. & Schröder, R.S. (2000). Global least-squares determination of Eulerian angles from single electron diffraction patterns of tilted crystals. J Appl Crystallogr 22, 1088–1101.Google Scholar
Fujimoto, F. (1959). Dynamical theory of electron diffraction in Laue-case, I. General theory. J Phys Soc Japan 14, 1158–1568.CrossRefGoogle Scholar
Hart, H.V. (2002). ZONES: A search/match database for single-crystal electron diffraction. J Appl Crystallogr 35, 552–555.Google Scholar
Hovmöller, S. (1992). CRISP: Crystallographic image processing on a personal computer. Ultramicroscopy 41, 121–135.Google Scholar
Humphreys, C.J. (1979). The scattering of fast electrons by crystals. Rep Prog Phys 42, 1825–1887.Google 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.Google Scholar
Lábár, J.L. (2000). ProcessDiffraction: A computer program to process electron diffraction patterns from polycrystalline or amorphous samples. In Proc. EUREM 12, Brno, Czech Republic, Frank, L. & Ciampor, F. (Eds.), Vol. III, pp. I379–380. Brno, Czech Republic: Czechslovak Society for Electron Microscopy.Google Scholar
Lábár, J.L. (2002). A tool to help phase identification from electron diffraction powder patterns. Microsc Anal 75, 9–11.Google Scholar
Lábár, J.L. (2005). Consistent indexing of a (set of) SAED pattern(s) with the ProcessDiffraction program. Ultramicroscopy 103, 237–249.Google Scholar
Lábár, J.L. & Adamik, M. (2001). ProcessDiffraction V1.2: New possibilities in manipulating electron diffraction ring patterns. Microsc Microanal 7(Suppl. 2), 372–373.Google Scholar
Lábár, J.L., Kovács, A., Barna, B.P., Hanada, T., Ishimaru, M., Hirotsu, Y. & Bae, I.T. (2003). Variation of the short range order with the composition in an amorphous Al-Pt alloy, existing in a wide compositional range. Proc. 6th Multinational Congress on Electron MicroscopyPula, pp. 469–470. Zagreb, Croatia: Croatian Society for Electron Microscopy.Google Scholar
Li, X.Z. (2004). JECP/PCED—A computer program for simulation of polycrystalline electron diffraction pattern and phase identification. Ultramicroscopy 99, 257–261.CrossRefGoogle ScholarPubMed
Megaw, H.D. (1973). Crystal Structures: A Working Approach. Philadelphia, London, Toronto: W.B. Saunders Company.Google Scholar
Midgley, P.A., Saunders, M., Vincent, R. & Steeds, J.W. (1995). Energy-filtered convergent-beam diffraction: Examples and future prospects. Ultramicroscopy 59, 1–13.CrossRefGoogle Scholar
Narayan, C. (1986). A sorting and searching computer program to index electron diffraction patterns from crystals of low symmetry. J Electron Microsc Tech 3, 151–158.CrossRefGoogle Scholar
Nelder, J.A. & Mead, R. (1965). A simplex method for function minimization. Comp J 7, 308–313.Google Scholar
Nicolopoulos, S., Kuligin, A., Kuligin, K., Khalid, B., Lepeshov, G., DelPlancke, J.L., Avilov, A., Nickolsky, M. & Ponce, A. (2006). New instrumentation for TEM electron diffraction structure analysis: Electron diffractometry combined with beam precession. In Electron Crystallography, Weirich, Th.E., Lábár, J.L. & Zou, X.D. (Eds.), NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 211, pp. 169–184. Dordrecht: Springer.Google Scholar
Oleynikov, P., Hovmöller, S. & Zou, X.D. (2006). Quantification of texture patterns. In Electron Crystallography, Weirich, Th.E., Lábár, J.L. & Zou, X.D. (Eds.), NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 211, pp. 121–142. Dordrecht: Springer.CrossRefGoogle Scholar
Oleynikov, P., Hovmöller, S. & Zou, X.D. (2007). Precession electron diffraction: Observed and calculated intensities. Ultramicroscopy 107, 523–533.Google Scholar
Richardson, J.W. (1993). Background modeling in Rietveld analysis. In The Rietveld Method, Young, R.A. (Ed.), IUCr Monographs on Crystallography, No. 5, pp. 102–110. Oxford: Oxford University Press.CrossRefGoogle Scholar
Rietveld, H.M. (1969). A profile refinement method for nuclear and magnetic structures. J Appl Crystallogr 2, 65–71.CrossRefGoogle Scholar
Rodriguez-Carvajal, J. (2000). FULLPROF—A Program for Rietveld, Profile Matching and Integrated Intensities Refinement of X-ray and/or Neutron Data. Laboratoire Léon Brillouin, CEA-Saclay, France.Google Scholar
Saunders, M., Bird, D.M., Zaluzec, N.J., Burgess, W.G., Preston, A.R. & Humphreys, C.J. (1995). Measurement of low-order structure factors for silicon from zone-axis CBED patterns. Ultramicroscopy 60, 311–323.Google Scholar
Shankland, K. & David, W.I. (2002). Global optimization strategies. In Structure Determination from Powder Diffraction Data, David, W.I.F., Shankland, K., McCusker, L.B. & Baerlocher, Ch. (Eds.), IUCr Monographs on Crystallography, No. 13, pp. 252–285. Oxford: Oxford University Press.Google Scholar
Snyder, R.L. (1993). Analytical profile fitting of X-ray powder diffraction profiles in Rietveld analysis. In The Rietveld Method, Young, R.A. (Ed.), IUCr Monographs on Crystallography, No. 5, pp. 111–131. Oxford: Oxford University Press.CrossRefGoogle Scholar
Spence, J.C.H. (1993). On the accurate measurement of structure-factor amplitudes and phases by electron diffraction. Acta Cryst A49, 231–260.CrossRefGoogle Scholar
Tonejc, A.M., Djerdj, I. & Tonejc, A. (2002). An analysis of evolution of grain size-lattice parameters dependence in nanocrystalline TiO anatase. Mater Sci Eng C19, 85–89.CrossRefGoogle Scholar
Vainshtein, B.K. (1964). Structure Analysis by Electron Diffraction. Oxford: Pergamon Press.Google Scholar
Vainshtein, B.K., Zvyagin, B.B. & Avilov, A.S. (1992). Electron diffraction structure analysis. In Electron Diffraction Techniques, Cowley, J.M. (Ed.), IUCr Monographs on Crystallography, No. 3, Vol. 1, pp. 216–312. Oxford: Oxford University Press.CrossRefGoogle Scholar
Walck, S.D. & Ruzakowski-Athey, P. (1998). Analysis of selected area diffraction patterns with WINJADE. Proc Microsc Microanal 4.Google Scholar
Walryck, M. & Andruszkiewicz, M. (1997). WINREKS—A computer program for the reciprocal lattice reconstruction from a set of electron diffractograms. In Electron Crystallography, Dorset, D.L., et al. (Eds.), pp. 427–430. Dordrecht: Kluwer Academic Publisher.Google Scholar
Warren, B.E. (1959). X-ray studies of deformed metals. Prog Metal Phys 8, 147–201.Google Scholar
Warren, B.E. & Averbach, B.L. (1950). The effect of cold-work distortion on X-ray patterns. J Appl Phys 21, 595–599.Google Scholar
Warren, B.E. & Averbach, B.L. (1952). The separation of cold work distortion and particle size broadening in X-ray patterns. J Appl Phys 23, 497–498.Google Scholar
Weirich, Th.E., Winterer, M., Seifried, S., Hahn, H. & Fuess, H. (2000). Rietveld analysis of electron powder diffraction data from nanocrystalline anatase, TiO2. Ultramicroscopy 81, 263–270.CrossRefGoogle ScholarPubMed
Weirich, Th.E., Winterer, M., Seifried, S. & Mayer, J. (2002). Structure of nanocrystalline anatase solved and refined from electron powder data. Acta Crystallogr A58, 308–315.Google Scholar
Williams, D.B. & Carter, C.B. (1996). Transmission Electron Microscopy; A Textbook for Materials Science, p. 285. New York and London: Plenum Press.Google Scholar
Williamson, G.K. & Hall, W.H. (1953). X-ray broadening from filed aluminium and wolfram. Acta Metallurgica 1, 22–31.CrossRefGoogle Scholar
Wilson, A.J.C. (1942). Determination of absolute from relative X-ray intensity data. Nature 150, 151–152.CrossRefGoogle Scholar
Young, R.A., (Ed.) (1993). The Rietveld Method, IUCr Monographs on Crystallography, No. 5. Oxford: Oxford University Press.CrossRefGoogle Scholar
Zuo, J.M. (1993). Automated structure-factor refinement from convergent-beam electron diffraction patterns. Acta Cryst A49, 429–435.Google Scholar
Zuo, J.M & Spence, J.C.H. (1991). Automated structure factor refinement from convergent-beam patterns. Ultramicroscopy 35, 185–196.Google Scholar
Zuo, J.M., Weickenmeier, A.L., Holmstead, R. & Spence, J.C.H. (1993). Are HOLZ lines kinematic in off-zone-axis orientations? In Proc. 51st Annual Meeting of the Microscopy Society of America, Bailey, G.W. & Rieder, C.L. (Eds.), pp. 692–693. San Francisco: San Francisco Press.Google Scholar
Zuo, J.M & Weickenmeier, A.L. (1995). On the beam selection and convergence in the Bloch-wave method. Ultramicroscopy 57, 375–383.Google Scholar
Zou, X., Hovmöller, A. & Hovmöller, S. (2004). TRICE—A program for reconstructing 3D reciprocal space and determining unit-cell parameters. Ultramicroscopy 98, 187–193.Google Scholar
Zou, X.D. & Hovmöller, S. (2006). 3D reconstruction of inorganic crystals. In Electron Crystallography, Weirich, Th.E., Lábár, J.L. & Zou, X.D. (Eds.), NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 211, pp. 301–320. Dordrecht: Springer.Google Scholar