Determination of lattice parameters from 3D electron diffraction (3D ED) data measured in a transmission electron microscope is hampered by a number of effects that seriously limit the achievable accuracy. The distortion of the diffraction patterns by the optical elements of the microscope is often the most severe problem. A thorough analysis of a number of experimental datasets shows that, in addition to the well known distortions, namely barrel-pincushion, spiral and elliptical, an additional distortion, dubbed parabolic, may be observed in the data. In precession electron diffraction data, the parabolic distortion leads to excitation-error-dependent shift and splitting of reflections. All distortions except for the elliptical distortion can be determined together with lattice parameters from a single 3D ED data set. However, the parameters of the elliptical distortion cannot be determined uniquely due to correlations with the lattice parameters. They can be determined and corrected either by making use of the known Laue class of the crystal or by combining data from two or more crystals. The 3D ED data can yield lattice parameter ratios with an accuracy of about 0.1% and angles with an accuracy better than 0.03°.

Department of Structure Analysis Institute of Physics of the Czech Academy of Sciences Na Slovance 1999 2 Prague 8 18221 Czech Republic

Institute of Inorganic Chemistry Leibniz University of Hannover Callinstraße 9 Hannover 30167 Germany

Zobrazit více v PubMed

Ångström, J., Chen, H. & Wan, W. (2018). J. Appl. Cryst. 51, 982–989.

Brázda, P. & Palatinus, L. (2023a). Manuscript in preparation.

Brázda, P. & Palatinus, L. (2023b). Manuscript in preparation.

Brázda, P., Palatinus, L. & Babor, M. (2019). Science, 364, 667–669. PubMed

Bücker, R., Hogan-Lamarre, P. & Miller, R. J. D. (2021). Front. Mol. Biosci. 8, 624264. PubMed PMC

Capitani, G. C., Oleynikov, P., Hovmöller, S. & Mellini, M. (2006). Ultramicroscopy, 106, 66–74. PubMed

Clabbers, M. T. B., Gruene, T., Parkhurst, J. M., Abrahams, J. P. & Waterman, D. G. (2018). Acta Cryst. D74, 506–518. PubMed PMC

Gemmi, M., Mugnaioli, E., Gorelik, T. E., Kolb, U., Palatinus, L., Boullay, P., Hovmöller, S. & Abrahams, J. P. (2019). ACS Central Sci. 5, 1315–1329. PubMed PMC

Hall, C. E. (1966). Introduction to Electron Microscopy, 2nd ed. Boston, Massachusetts, USA: McGraw-Hill.

Hawkes, P. W. (2015). Ultramicroscopy, 156, A1–A64. PubMed

Hüe, F., Johnson, C. L., Lartigue-Korinek, S., Wang, G., Buseck, P. R. & Hÿtch, M. J. (2005). J. Electron Microsc. 54, 181–190. PubMed

Kolb, U., Gorelik, T., Kübel, C., Otten, M. T. & Hubert, D. (2007). Ultramicroscopy, 107, 507–513. PubMed

Kolb, U., Gorelik, T. & Otten, M. T. (2008). Ultramicroscopy, 108, 763–772. PubMed

Krivanek, O. L., Dellby, N. & Lupini, A. R. (1999). Ultramicroscopy, 78, 1–11.

Mahr, C., Müller-Caspary, K., Ritz, R., Simson, M., Grieb, T., Schowalter, M., Krause, F. F., Lackmann, A., Soltau, H., Wittstock, A. & Rosenauer, A. (2019). Ultramicroscopy, 196, 74–82. PubMed

Mitchell, D. R. G. & Van den Berg, J. A. (2016). Ultramicroscopy, 160, 140–145. PubMed

Mugnaioli, E., Capitani, G. C., Nieto, F. & Mellini, M. (2009). Am. Mineral. 94, 793–800.

Nannenga, B. L., Shi, D., Leslie, A. G. W. & Gonen, T. (2014). Nat. Methods, 11, 927–930. PubMed PMC

Nederlof, I., van Genderen, E., Li, Y.-W. & Abrahams, J. P. (2013). Acta Cryst. D69, 1223–1230. PubMed PMC

Ophus, C. (2019). Microsc. Microanal. 25, 563–582. PubMed

Palatinus, L., Brázda, P., Boullay, P., Perez, O., Klementová, M., Petit, S., Eigner, V., Zaarour, M. & Mintova, S. (2017). Science, 355, 166–169. PubMed

Palatinus, L., Brázda, P., Jelínek, M., Hrdá, J., Steciuk, G. & Klementová, M. (2019). Acta Cryst. B75, 512–522. PubMed

Plana-Ruiz, S., Krysiak, Y., Portillo, J., Alig, E., Estradé, S., Peiró, F. & Kolb, U. (2020). Ultramicroscopy, 211, 112951. PubMed

Plana-Ruiz, S., Portillo, J., Estradé, S., Peiró, F., Kolb, U. & Nicolopoulos, S. (2018). Ultramicroscopy, 193, 39–51. PubMed

Rauch, E. F., Harrison, P. & Véron, M. (2021). Symmetry, 13, 1675.

Rauch, E. F., Portillo, J., Nicolopoulos, S., Bultreys, D., Rouvimov, S. & Moeck, P. (2010). Z. Kristallogr. 225, 103–109.

Rose, H. H. (2008). Sci. Technol. Adv. Mater. 9, 014107. PubMed PMC

Smeets, S., Zou, X. & Wan, W. (2018). J. Appl. Cryst. 51, 1262–1273. PubMed PMC

Smith, W. J. (2007). Modern Optical Engineering, 4th ed. Boston, Massachusetts, USA: McGraw-Hill.

Vincent, R. & Midgley, P. A. (1994). Ultramicroscopy, 53, 271–282.

Wang, B., Zou, X. & Smeets, S. (2019). IUCrJ, 6, 854–867. PubMed PMC

Williams, D. B. & Carter, C. B. (2009). Transmission Electron Microscopy, 2nd ed. Heidelberg: Springer.

Zhang, D., Oleynikov, P., Hovmöller, S. & Zou, X. (2010). Z. Kristallogr. 225, 94–102.

Crystal Structure of Nd10.67Pt4O24, a New Neodymium Platinate

Ionisation of atoms determined by kappa refinement against 3D electron diffraction data

Reactive Noble-Gas Compounds Explored by 3D Electron Diffraction: XeF2-MnF4 Adducts and a Facile Sample Handling Procedure

Dynamical refinement with multipolar electron scattering factors

ROY Crystallization on Poly(ethylene) Fibers, a Model for Bed Net Crystallography

Chlorfenapyr Crystal Polymorphism and Insecticidal Activity

Unveiling the topology of partially disordered micro-crystalline nitro-perylenediimide with X-aggregate stacking: an integrated approach