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High-Resolution Electron Diffraction: Accounting for Radially and Angularly Invariant Distortions

Published online by Cambridge University Press:  08 May 2012

Daniel Carvalho
Affiliation:
Department of Materials Science and Metallurgical Engineering and Inorganic Chemistry, Materials Science and Engineering Group, Faculty of Sciences, University of Cádiz, 11510, Puerto Real, Cádiz, Spain
Francisco M. Morales*
Affiliation:
Department of Materials Science and Metallurgical Engineering and Inorganic Chemistry, Materials Science and Engineering Group, Faculty of Sciences, University of Cádiz, 11510, Puerto Real, Cádiz, Spain
*
Corresponding author. E-mail: [email protected]
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Abstract

The distortions present in an electron diffraction pattern can be classified into two categories: one is radially invariant and the other is angularly invariant. We report a method to compensate these displacements undergone by diffraction features promoted by any kind of artifacts generated in parallel beam electron diffraction conditions. This approach is not aimed at quantifying these distortions but only intends to aid in the measurement of lattice parameters of crystals with a significant increase of accuracy and precision as compared to previous approaches. It is based on statistical estimations of the relative positions between diffraction rings and/or spots after performing a transformation of the digitalized patterns to polar coordinates. The analytical method is based on fitting a Gaussian type profile to intensity distributions. This makes it possible to determine the lattice parameters of a polycrystal or single crystal with relative errors smaller than 0.1% for diffractograms acquired in photographic films and below 0.01% for those collected in imaging plates.

Type
Techniques Development
Copyright
Copyright © Microscopy Society of America 2012

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References

Belletti, D., Calestani, G., Gemmi, M. & Migliori, A. (2000). QED V 1.0: A software package for quantitative electron diffraction data treatment. Ultramicroscopy 81(2), 5765.CrossRefGoogle ScholarPubMed
Boswell, F.W.C. (1951). Precise determination of lattice constants by electron diffraction and variations in the lattice constants of very small crystallites. Proc Phys Soc A 64(5), 465.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. Ultramicroscopy 106(2), 6674.CrossRefGoogle ScholarPubMed
Cohen, H.A., Schmid, M.F. & Chiu, W. (1984). Estimates of validity of projection approximation for three-dimensional reconstructions at high resolution. Ultramicroscopy 14(3), 219226.Google Scholar
Coleman, T.F. & Li, Y. (1994). On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Math Program 67(1), 189224.CrossRefGoogle Scholar
Cowley, J.M. (1984). Diffraction Physics. Amsterdam, The Netherlands: North-Holland Physics Publishing.Google Scholar
David, W. (1986). Powder diffraction peak shapes. Parameterization of the pseudo-Voigt as a Voigt function. J Appl Crystallogr 19(1), 6364.CrossRefGoogle Scholar
Hirsch, P., Howie, A., Nicholson, R.B., Pashley, D.W. & Whelan, M.J. (1977). Electron Microscopy of Thin Crystals. Malabar, FL: Krieger Publishing Company.Google Scholar
Hou, V.D.H. & Li, D. (2008). A method to correct elliptical distortion of diffraction patterns in TEM. Microsc Microanal 14(Suppl 2), 11261127.Google Scholar
Lábár, J.L. (2005). Consistent indexing of a (set of) single crystal SAED pattern(s) with the ProcessDiffraction program. Ultramicroscopy 103(3), 237249.CrossRefGoogle ScholarPubMed
Mitchell, D.R.G. (2008). DiffTools: Electron diffraction software tools for DigitalMicrograph™. Microsc Res Techniq 71(8), 588593.Google Scholar
Morales, F.M., González, D., Lozano, J.G., García, R., Hauguth-Frank, S., Lebedev, V., Cimalla, V. & Ambacher, O. (2009). Determination of the composition of InxGa1−xN from strain measurements. Acta Mater 57(19), 56815692.CrossRefGoogle Scholar
Mugnaioli, E., Capitani, G., Nieto, F. & Mellini, M. (2009). Accurate and precise lattice parameters by selected-area electron diffraction in the transmission electron microscope. Am Mineral 94(5-6), 793800.Google Scholar
Nicula, R., Jianu, A., Ponkratz, U. & Burkel, E. (2000). High-pressure stability of Ti-Zr-Ni quasicrystals. Phys Rev B 62(13), 88448848.Google Scholar
Schamp, C.T. & Jesser, W.A. (2005). On the measurement of lattice parameters in a collection of nanoparticles by transmission electron diffraction. Ultramicroscopy 103(2), 165172.Google Scholar
Shapiro, S.S. & Wilk, M.B. (1965). An analysis of variance test for normality (complete samples). Biometrika 52(3-4), 591611.Google Scholar
Többens, D.M., Stüßer, N., Knorr, K., Mayer, H.M. & Lampert, G. (2001). The new high-resolution neutron powder diffractometer at the Berlin Neutron Scattering Center. Mater Sci Forum 378, 288293.CrossRefGoogle Scholar
Wang, C.Y., Kirste, L., Morales, F.M., Manuel, J.M., Röhlig, C.C., Köhler, K., Cimalla, V., Garcia, R. & Ambacher, O. (2011). Growth mechanism and electronic properties of epitaxial In2O3 films on sapphire. J Appl Phys 110(9), 093712093717.CrossRefGoogle Scholar
Williams, D.B. & Carter, C.B. (2009). Transmission Electron Microscopy. New York: Springer.Google Scholar
Zuo, J.M. (1993). New method of Bravais lattice determination. Ultramicroscopy 52(3-4), 459464.CrossRefGoogle Scholar