Structure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementation

Accurate structure refinement from electron-diffraction data is not possible without taking the dynamical-diffraction effects into account. A complete three-dimensional model of the structure can be obtained only from a sufficiently complete three-dimensional data set. In this work a method is presented for crystal structure refinement from the data obtained by electron diffraction tomography, possibly combined with precession electron diffraction. The principle of the method is identical to that used in X-ray crystallography: data are collected in a series of small tilt steps around a rotation axis, then intensities are integrated and the structure is optimized by least-squares refinement against the integrated intensities. In the dynamical theory of diffraction, the reflection intensities exhibit a complicated relationship to the orientation and thickness of the crystal as well as to structure factors of other reflections. This complication requires the introduction of several special parameters in the procedure. The method was implemented in the freely available crystallographic computing systemJana2006.

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Structure refinement using precession electron diffraction tomography and dynamical diffraction theory

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s205327331609851x ◽

2016 ◽

Vol 72 (a1) ◽

pp. s101-s101

Author(s):

Lukas Palatinus

Keyword(s):

Electron Diffraction ◽

Structure Refinement ◽

Diffraction Theory ◽

Diffraction Tomography ◽

Dynamical Diffraction ◽

Precession Electron Diffraction

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Accurate structure refinement from 3D electron diffraction data

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314096259 ◽

2014 ◽

Vol 70 (a1) ◽

pp. C374-C374

Author(s):

Lukáš Palatinus ◽

Cinthia Corrêa ◽

Gwladys Mouillard ◽

Philippe Boullay ◽

Damien Jacob

Keyword(s):

Electron Diffraction ◽

Diffraction Data ◽

Structure Refinement ◽

Three Dimensional ◽

Diffraction Theory ◽

Electron Diffraction Data ◽

Dynamical Structure ◽

Present Contribution ◽

Figures Of Merit ◽

Precession Electron Diffraction

Structure determination from electron diffraction data has seen an enormous progress over the past few years. At present, complex structures with hundreds of atoms in the unit cell can be solved from electron diffraction using the concept of electron diffraction tomography (EDT), possibly combined with precession electron diffraction (PED) [1]. Unfortunately, the initial model is typically optimized using the kinematical approximation to calculate model diffracted intensities. This approximation is quite inaccurate for electron diffraction and leads to high figures of merit and inaccurate results with unrealistically low standard uncertainties. The obvious remedy to the problem is the use of dynamical diffraction theory to calculate the model intensities in structure refinement. This technique has been known and used before, but it has not become very popular, because good fits could be obtained only for sufficiently perfect and sufficiently thin crystals. It has been shown recently on several zone-axis patterns [2] that the quality of the refinement can be improved by using precession electron diffraction. In the present contribution we demonstrate that the same approach can be successfully used to refine crystal structures against non-oriented patterns acquired by EDT combined with PED (PEDT in short). Because the PEDT technique provides three-dimensional diffraction information, it can be used for a complete structure refinement. Several test examples demonstrate that the dynamical structure refinement yields better figures of merit and more accurate results than the refinement using kinematical approximation.

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Structure refinement using precession electron diffraction tomography and dynamical diffraction: tests on experimental data

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520615017023 ◽

2015 ◽

Vol 71 (6) ◽

pp. 740-751 ◽

Cited By ~ 58

Author(s):

Lukáš Palatinus ◽

Cinthia Antunes Corrêa ◽

Gwladys Steciuk ◽

Damien Jacob ◽

Pascal Roussel ◽

...

Keyword(s):

Experimental Data ◽

Electron Diffraction ◽

Structure Refinement ◽

Electron Diffraction Data ◽

Average Error ◽

Reference Structure ◽

Reliable Determination ◽

Dynamical Diffraction ◽

Precession Electron Diffraction

The recently published method for the structure refinement from three-dimensional precession electron diffraction data using dynamical diffraction theory [Palatinus et al. (2015). Acta Cryst. A71, 235–244] has been applied to a set of experimental data sets from five different samples – Ni2Si, PrVO3, kaolinite, orthopyroxene and mayenite. The data were measured on different instruments and with variable precession angles. For each sample a reliable reference structure was available. A large series of tests revealed that the method provides structure models with an average error in atomic positions typically between 0.01 and 0.02 Å. The obtained structure models are significantly more accurate than models obtained by refinement using kinematical approximation for the calculation of model intensities. The method also allows a reliable determination of site occupancies and determination of absolute structure. Based on the extensive tests, an optimal set of the parameters for the method is proposed.

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Structural insights intoM2O–Al2O3–WO3(M= Na, K) system by electron diffraction tomography

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520615007994 ◽

2015 ◽

Vol 71 (3) ◽

pp. 349-357 ◽

Cited By ~ 6

Author(s):

Iryna Andrusenko ◽

Yaşar Krysiak ◽

Enrico Mugnaioli ◽

Tatiana E. Gorelik ◽

Diana Nihtianova ◽

...

Keyword(s):

Electron Diffraction ◽

Three Dimensional ◽

Large Cell ◽

Systematic Investigation ◽

Electron Diffraction Data ◽

Diffraction Tomography ◽

Structure Investigation ◽

X Ray ◽

Cell Parameters ◽

Wide Range

TheM2O–Al2O3–WO3(M= alkaline metals) system has attracted the attention of the scientific community because some of its members showed potential applications as single crystalline media for tunable solid-state lasers. These materials behave as promising laser host materials due to their high and continuous transparency in the wide range of the near-IR region. A systematic investigation of these phases is nonetheless hampered because it is impossible to produce large crystals and only in a few cases a pure synthetic product can be achieved. Despite substantial advances in X-ray powder diffraction methods, structure investigation on nanoscale is still challenging, especially when the sample is polycrystalline and the structures are affected by pseudo-symmetry. Electron diffraction has the advantage of collecting data from single nanoscopic crystals, but it is frequently limited by incompleteness and dynamical effects. Automated diffraction tomography (ADT) recently emerged as an alternative approach able to collect more complete three-dimensional electron diffraction data and at the same time to significantly reduce dynamical scattering. ADT data have been shown to be suitable forabinitiostructure solution of phases with large cell parameters, and for detecting pseudo-symmetry that was undetected in X-ray powder data. In this work we present the structure investigation of two hitherto undetermined compounds, K5Al(W3O11)2and NaAl(WO4)2, by a combination of electron diffraction tomography and precession electron diffraction. We also stress how electron diffraction tomography can be used to obtain direct information about symmetry and pseudo-symmetry for nanocrystalline phases, even when available only in polyphasic mixtures.

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Ab initiostructure determination and quantitative disorder analysis on nanoparticles by electron diffraction tomography

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273317018277 ◽

2018 ◽

Vol 74 (2) ◽

pp. 93-101 ◽

Cited By ~ 7

Author(s):

Yaşar Krysiak ◽

Bastian Barton ◽

Bernd Marler ◽

Reinhard B. Neder ◽

Ute Kolb

Keyword(s):

Electron Diffraction ◽

Direct Methods ◽

Functional Materials ◽

Structural Features ◽

Zeolite Beta ◽

Electron Diffraction Data ◽

Diffraction Tomography ◽

Separation Processes ◽

Data Set

Nanoscaled porous materials such as zeolites have attracted substantial attention in industry due to their catalytic activity, and their performance in sorption and separation processes. In order to understand the properties of such materials, current research focuses increasingly on the determination of structural features beyond the averaged crystal structure. Small particle sizes, various types of disorder and intergrown structures render the description of structures at atomic level by standard crystallographic methods difficult. This paper reports the characterization of a strongly disordered zeolite structure, using a combination of electron exit-wave reconstruction, automated diffraction tomography (ADT), crystal disorder modelling and electron diffraction simulations. Zeolite beta was chosen for a proof-of-principle study of the techniques, because it consists of two different intergrown polymorphs that are built from identical layer types but with different stacking sequences. Imaging of the projected inner Coulomb potential of zeolite beta crystals shows the intergrowth of the polymorphs BEA and BEB. The structures of BEA as well as BEB could be extracted from one single ADT data set using direct methods. A ratio for BEA/BEB = 48:52 was determined by comparison of the reconstructed reciprocal space based on ADT data with simulated electron diffraction data for virtual nanocrystals, built with different ratios of BEA/BEB. In this way, it is demonstrated that this smart interplay of the above-mentioned techniques allows the elaboration of the real structures of functional materials in detail – even if they possess a severely disordered structure.

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Accurate lattice-parameter determination from electron diffraction tomography data using two-dimensional diffraction vectors

Journal of Applied Crystallography ◽

10.1107/s1600576718006635 ◽

2018 ◽

Vol 51 (4) ◽

pp. 982-989 ◽

Cited By ~ 3

Author(s):

Jonas Ångström ◽

Hong Chen ◽

Wei Wan

Keyword(s):

Electron Diffraction ◽

Rotation Axis ◽

Three Dimensional ◽

Lattice Parameter ◽

Parameter Determination ◽

Data Sets ◽

Diffraction Tomography ◽

Two Dimensional ◽

Lower Accuracy ◽

Diffraction Patterns

Electron diffraction tomography (EDT) has emerged as a successful tool for ab initio atomic structure determination of nanometre-sized crystals. However, lattice parameters obtained from EDT data are often of lower accuracy than those from powder X-ray data, owing to experimental errors and data-processing methods. This work describes a lattice-parameter refinement method for EDT data using two-dimensional diffraction vectors and shows that the accuracy of lattice-parameter determination can be improved significantly. It is also shown that the method is tolerant to sample displacement during data collection and to geometric distortions in the electron diffraction patterns due to lens imperfections. For the data sets tested, the method reduces the 95% confidence interval of the worst errors in angles from ±1.98 to ±0.82° and the worst relative errors of the unit-cell lengths from ±1.8% to ±1.3%, compared with the conventional method using clustering of three-dimensional diffraction vectors. The improvement is attributed to the fact that the new method makes use of the positions of two-dimensional diffraction spots, which can be determined with high accuracy, and disregards the position of the central beam, the orientation of the rotation axis and the angles of the diffraction frames, whose errors all contribute to the errors for lattice-parameter determination using the three-dimensional method.

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Specifics of the data processing of precession electron diffraction tomography data and their implementation in the program PETS2.0

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520619007534 ◽

2019 ◽

Vol 75 (4) ◽

pp. 512-522 ◽

Cited By ~ 19

Author(s):

Lukáš Palatinus ◽

Petr Brázda ◽

Martin Jelínek ◽

Jaromíra Hrdá ◽

Gwladys Steciuk ◽

...

Keyword(s):

Electron Diffraction ◽

Data Processing ◽

Diffraction Data ◽

Crystal Orientation ◽

Diffraction Method ◽

Specific Aspect ◽

Electron Diffraction Data ◽

Diffraction Tomography ◽

Profile Fitting ◽

Precession Electron Diffraction

Electron diffraction tomography (EDT) data are in many ways similar to X-ray diffraction data. However, they also present certain specifics. One of the most noteworthy is the specific rocking curve observed for EDT data collected using the precession electron diffraction method. This double-peaked curve (dubbed `the camel') may be described with an approximation based on a circular integral of a pseudo-Voigt function and used for intensity extraction by profile fitting. Another specific aspect of electron diffraction data is the high likelihood of errors in the estimation of the crystal orientation, which may arise from the inaccuracies of the goniometer reading, crystal deformations or crystal movement during the data collection. A method for the refinement of crystal orientation for each frame individually is proposed based on the least-squares optimization of simulated diffraction patterns. This method provides typical angular accuracy of the frame orientations of less than 0.05°. These features were implemented in the computer program PETS 2.0. The implementation of the complete data processing workflow in the program PETS and the incorporation of the features specific for electron diffraction data is also described.

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Precession electron diffraction tomography on twinned crystals: application to CaTiO3 thin films

Journal of Applied Crystallography ◽

10.1107/s1600576719005569 ◽

2019 ◽

Vol 52 (3) ◽

pp. 626-636 ◽

Cited By ~ 2

Author(s):

Gwladys Steciuk ◽

Adrian David ◽

Václav Petříček ◽

Lukáš Palatinus ◽

Bernard Mercey ◽

...

Keyword(s):

Thin Films ◽

Electron Diffraction ◽

Structural Changes ◽

Structural Information ◽

Structure Refinement ◽

Diffraction Theory ◽

Strain Engineering ◽

Diffraction Tomography ◽

Epitaxial Thin Films ◽

Precession Electron Diffraction

Strain engineering via epitaxial thin-film synthesis is an efficient way to modify the crystal structure of a material in order to induce new features or improve existing properties. One of the challenges in this approach is to quantify structural changes occurring in these films. While X-ray diffraction is the most widely used technique for obtaining accurate structural information from bulk materials, severe limitations appear in the case of epitaxial thin films. This past decade, precession electron diffraction tomography has emerged as a relevant technique for the structural characterization of nano-sized materials. While its usefulness has already been demonstrated for solving the unknown structure of materials deposited in the form of thin films, the frequent existence of orientation variants within the film introduces a severe bias in the structure refinement, even when using the dynamical diffraction theory to calculate diffracted intensities. This is illustrated here using CaTiO3 films deposited on SrTiO3 substrates as a case study. By taking into account twinning in the structural analysis, it is shown that the structure of the CaTiO3 films can be refined with an accuracy comparable to that obtained by dynamical refinement from non-twinned data. The introduction of the possibility to handle twin data sets is undoubtedly a valuable add-on and, notably, paves the way for a successful use of precession electron diffraction tomography for accurate structural analyses of thin films.

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Automated diffraction tomography combined with electron precession: a new tool for ab initio nanostructure analysis

MRS Proceedings ◽

10.1557/proc-1184-gg01-05 ◽

2009 ◽

Vol 1184 ◽

Cited By ~ 11

Author(s):

Ute Kolb ◽

Tatiana Gorelik ◽

Enrico Mugnaioli

Keyword(s):

Electron Diffraction ◽

Ab Initio ◽

Crystal Structures ◽

Diffraction Data ◽

Three Dimensional ◽

Direct Methods ◽

Electron Diffraction Data ◽

Diffraction Tomography ◽

Diffraction Mode ◽

Structure Solution

AbstractThree-dimensional electron diffraction data was collected with our recently developed module for automated diffraction tomography and used to solve inorganic as well as organic crystal structures ab initio. The diffraction data, which covers nearly the full relevant reciprocal space, was collected in the standard nano electron diffraction mode as well as in combination with the precession technique and was subsequently processed with a newly developed automated diffraction analysis and processing software package. Non-precessed data turned out to be sufficient for ab initio structure solution by direct methods for simple crystal structures only, while precessed data allowed structure solution and refinement in all of the studied cases.

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