TY - JOUR

T1 - Accurate lattice parameters from 3D electron diffraction data. I. Optical distortions

AU - Brázda, Petr

AU - Klementová, Mariana

AU - Krysiak, Yaşar

AU - Palatinus, Lukáš

N1 - Funding Information: The following funding is acknowledged: Czech Science Foundation (grant No. 19-08032S); European Structural and Investment Funds and Czech Ministry of Education, Youth and Sports (grant No. SOLID21 CZ.02.1.01/0.0/0.0/16_019/ 0000760); Czech Ministry of Education, Youth and Sports (grant No. LM2018110).

PY - 2022/11

Y1 - 2022/11

N2 - 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°.

AB - 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°.

KW - 3D electron diffraction

KW - distortions

KW - lattice parameters

KW - parabolic distortion

KW - precession electron diffraction

UR - http://www.scopus.com/inward/record.url?scp=85158907880&partnerID=8YFLogxK

U2 - 10.1107/s2052252522007904

DO - 10.1107/s2052252522007904

M3 - Article

VL - 9

SP - 735

EP - 755

JO - IUCRJ

JF - IUCRJ

SN - 2052-2525

IS - 6

ER -