A Method to Characterize and Correct Elliptical Distortion in Electron Diffraction Patterns

Hou, Vincent; Li, Du

doi:10.1017/s1551929500059253

Cited by 8 publications

(10 citation statements)

References 2 publications

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Strictly speaking, the determined unit cell in this example is not a cubic phase but a triclinic structure. A similar case is often encountered during electron diffraction analysis because of the large measurement uncertainties of the pattern, which often suffers from image distortions and the unreliable camera length (Mugnaioli et al, 2009;Hou & Li, 2008). Hence, in this work the user-defined parameters " 1-3 are introduced to accommodate the measurement uncertainties of the observed cell (or the input cell).…”

Section: Determination Of the Reduced Cell And The Unit Cell Of A High-symmetry Lattice (Large Errors)mentioning

confidence: 99%

“…Electron diffraction is a powerful technique to determine crystal structure at the nanoscale (Zheng et al, 2014;Wen et al, 2018;Sheng et al, 2016), and the 3D reciprocal cell can be determined directly from electron diffraction patterns (Shi & Li, 2021;Jiang et al, 2011;Li, 2019;Zhao et al, 2008;Zou et al, 2004). However, the primitive cell measured from an electron diffraction pattern suffers from a poor measurement precision because the measured d spacings exhibit around 1% error, resulting from the diffraction distortions of the electromagnetic lens and the uncertainty of the camera length of the transmission electron microscope (Mitchell & Van den Berg, 2016;Hou & Li, 2008). Moreover, the measurement error of interzonal angles of a tilt series can be up to a few degrees.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Niggli reduction and Bravais lattice determination

Shi¹,

Li²

2022

J Appl Cryst

View full text Add to dashboard Cite

A new algorithm has been developed and coded in DigitalMicrograph (DM) to reduce a three-dimensional primitive cell to the Niggli cell and further convert to the Bravais-lattice unit cell. The core of this algorithm is the calculation of the three shortest non-coplanar vectors to compose the reduced cell. The reduced cell is converted into the real-space reduced cell and then to the Bravais-lattice unit cell. The symmetry-constrained unit cell is, in turn, converted back into the real-space reduced cell, the reciprocal reduced cell and the reciprocal primitive cell. The DM package demonstrates superior numerical stability and can tolerate large uncertainties in the experimentally measured input primitive cell, making it especially suitable for electron diffraction analysis. Additionally, the DM package can be used to calculate various crystallographic parameters including Bravais-lattice plane indices, zone-axis indices, tilt angles and the radius of the high-order Laue zone ring, thus facilitating the correct determination of the Niggli cell and the Bravais lattice.

show abstract

Section: Determination Of the Reduced Cell And The Unit Cell Of A High-symmetry Lattice (Large Errors)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Niggli reduction and Bravais lattice determination

Shi¹,

Li²

2022

J Appl Cryst

View full text Add to dashboard Cite

show abstract

“…8,17 Numerous corrective procedures have been proposed for elliptical distortions but are generally time-consuming compared to tilting the incident beam. 37,38 After multiple diffraction patterns are acquired over a range of tilting angles or offset directions, they may be spliced together prior to producing a PDF. The process from diffraction collection to data splicing is shown in Figure 5.…”

Section: Advancements and Considerations In Epdf Acquisition And Anal...mentioning

confidence: 99%

“…While this approach accomplishes the same goal as tilting, it is less preferred because offsetting beam shifts have been shown to introduce elliptical distortions in the diffraction pattern. This distortion results in errors to the PDF. , Numerous corrective procedures have been proposed for elliptical distortions but are generally time-consuming compared to tilting the incident beam. , …”

Section: Advancements and Considerations In Epdf Acquisition And Anal...mentioning

confidence: 99%

Quantifying the Local Structure of Nanocrystals, Glasses, and Interfaces Using TEM-Based Diffraction

2021

View full text Add to dashboard Cite

Although order is a defining characteristic of crystals, disordered structuresespecially near interfacesoften govern a material’s performance. For example, the interfaces in batteries, coatings, or catalysts exemplify systems in which disorder plays a critical role. Despite this importance, characterization of local structure in disordered materials remains a challenge. To solve this challenge, the electron pair distribution function (ePDF) method has given insight into the local structure of many complex samples because the technique can be applied to disordered materials containing as few as tens or hundreds of atoms. The ePDF method takes a transmission electron microscope (TEM) diffraction pattern and transforms this into information about the bond lengths present in a material. This information can then be used to create a 3D, atomic-scale model of local chemical structure. In this review, we introduce the theory behind ePDF, describe common methods for data acquisition, and highlight recent advances in the ePDF technique, including its combination with cryo-electron microscopy, ultrafast TEM, and precession electron diffraction. We also show how ePDF has been applied to important classes of materials, including 2D heterostructures, nanoscale interfaces, and materials fabricated by atomic layer deposition. Finally, we review how ePDF can be combined with other techniques to provide a comprehensive understanding of a material. Because ePDF can be performed on most TEMs, it is beginning to emerge as a routine method for the analysis of complex, disordered structures in technologically important materials.

show abstract

“…To obtain the required precision, the pattern from the standard is acquired after that of the unknown using the same lens currents, corrected for hysteresis by a normalization procedure in both the imaging and di raction mode of the microscope. The analyst uses a DigitalMicrograph plug-in, EDP, derived from VHou's plug-in [2] and extended to correct the distortion as outlined by Capitani et al [1], perform the radial average, and output the pro le as a comma-delimited le. All the postprocessing uses the Open Source R language.…”

mentioning

confidence: 99%

An Improved Workflow for Reproducible Processing and Analysis of Polycrystalline Electron Diffraction Patterns

Minter¹

2013

Microsc Microanal

View full text Add to dashboard Cite

Successful quantitative analysis of electron di raction patterns from thin, polycrystalline samples requires careful attention todetail at each stage. First, one must record patterns from the unknown and standard under equivalent electron optical conditions (equivalent lens currents corrected for hysteresis.) Next, one must locate the center of each pattern and measure and correct for the elliptical distortion [1, 2, 3] and compute a radial average. The continuous scattering(background) must be subtracted. Peak positions from the standard are then used to determine the camera constant and calibrate the unknown pattern. The peaks in the unknown may then be compared to those expected from candidate structures. Until recently analysts in our laboratory have used a pair of programs with graphical user interfaces to locate the center and compute the elliptical distortion [2] and to correct the distortion, calibrate the pattern, and compare [3] to the ICDD di raction database. This analysis required a lot of "point-click-copy-paste" by the analyst and was di cult to automate. This report summarizes the development of a more e cient and reproducible work ow. Our tool chain permits more automated report generation as outlined by Vandewalle et al.[4].To obtain the required precision, the pattern from the standard is acquired after that of the unknown using the same lens currents, corrected for hysteresis by a normalization procedure in both the imaging and di raction mode of the microscope. The analyst uses a DigitalMicrograph plug-in, EDP, derived from VHou's plug-in [2] and extended to correct the distortion as outlined by Capitani et al. [1], perform the radial average, and output the pro le as a comma-delimited le. All the postprocessing uses the Open Source R language. The core functions (unit operations) to tune the background subtraction of the radially-averaged intensity, measure the camera constant from the standard, plot a calibrated background-subtracted pro le from an unknown pattern, and overlay lines from known phases were encapsulated in a custom R package, edp, which permits an analyst to tune and script an analysis of a new material with a minimum amount of coding. Background subtraction and peak location functions were used from the R package, Peaks [5]. This approach is consistent with the "do not repeat yourself" (DRY) coding practice to minimize inconsistencies. The edp package contains data and examples (unit tests) that are run each time the package is built and checked. The source code for both our DigitalMicrograph plug-in and the R package are maintained under version control using the distributed version control program, git. We intend to release both packages under the Gnu Public License. A typical work ow is to tune the background subtraction for a new unknown pattern, measure the camera constant for the standard, display the pattern and compare to candidate phases using a script using the Open Source RStudio integrated development environment. The Sweave package in R permits the analyst to em...

show abstract

A Method to Characterize and Correct Elliptical Distortion in Electron Diffraction Patterns

Cited by 8 publications

References 2 publications

Niggli reduction and Bravais lattice determination

Niggli reduction and Bravais lattice determination

Quantifying the Local Structure of Nanocrystals, Glasses, and Interfaces Using TEM-Based Diffraction

An Improved Workflow for Reproducible Processing and Analysis of Polycrystalline Electron Diffraction Patterns

Contact Info

Product

Resources

About