scholarly journals Pattern-matching indexing of Laue and monochromatic serial crystallography data for applications in materials science

2020 ◽  
Vol 53 (3) ◽  
pp. 824-836
Author(s):  
Catherine Dejoie ◽  
Nobumichi Tamura
Keyword(s):  
Pattern Matching ◽  
Materials Science ◽  
Reciprocal Lattice ◽  
Unit Cell ◽  
Crystallographic Structure ◽  
Experimental Conditions ◽  
Lattice Vector ◽  
Small Unit ◽  
Orientation Matrix ◽  
Serial Crystallography

Serial crystallography data can be challenging to index, as each frame is processed individually, rather than being processed as a whole like in conventional X-ray single-crystal crystallography. An algorithm has been developed to index still diffraction patterns arising from small-unit-cell samples. The algorithm is based on the matching of reciprocal-lattice vector pairs, as developed for Laue microdiffraction data indexing, combined with three-dimensional pattern matching using a nearest-neighbors approach. As a result, large-bandpass data (e.g. 5–24 keV energy range) and monochromatic data can be processed, the main requirement being prior knowledge of the unit cell. Angles calculated in the vicinity of a few theoretical and experimental reciprocal-lattice vectors are compared, and only vectors with the highest number of common angles are selected as candidates to obtain the orientation matrix. Global matching on the entire pattern is then checked. Four indexing options are available, two for the ranking of the theoretical reciprocal-lattice vectors and two for reducing the number of possible candidates. The algorithm has been used to index several data sets collected under different experimental conditions on a series of model samples. Knowing the crystallographic structure of the sample and using this information to rank the theoretical reflections based on the structure factors helps the indexing of large-bandpass data for the largest-unit-cell samples. For small-bandpass data, shortening the candidate list to determine the orientation matrix should be based on matching pairs of reciprocal-lattice vectors instead of triplet matching.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 540-541
Author(s):  
I.N. Yadhikov ◽  
S.K. Maksimov
Keyword(s):  
Reciprocal Lattice ◽  
Unit Cell ◽  
Reciprocal Lattice Vector ◽  
Unit Cell Parameters ◽  
Lattice Vector ◽  
Cell Parameters ◽  
Accuracy Of Measurements ◽  
The Difference ◽  
Image Position ◽  
Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

scholarly journals Small-angle scattering simulations for suspensions of nanocrystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C597-C597
Author(s):  
Martin Schmiele ◽  
Simone Gehrer ◽  
Tobias Unruh
Keyword(s):  
Small Angle ◽  
Dispersion Medium ◽  
Scattering Length ◽  
Thickness Distribution ◽  
Reciprocal Lattice ◽  
Small Angle Scattering ◽  
Crystallographic Structure ◽  
Lattice Vector ◽  
Reliable Determination ◽  
Angle Scattering

Suspensions of nanocrystals which possess large lattice spacings d(hkl) and only a small number of unit cells along the direction of the reciprocal lattice vector G(hkl) can feature broadened Bragg peaks in small-angle scattering (SAS) patterns. The scattering from molecules located at the interface between the nanocrystals and the dispersion medium which stabilize and functionalize the nanocrystals can interfere with the scattering of the nanocrystals and affect the shape and position of their Bragg peaks. This allows to study how these molecules arrange on the surface of the nanocyrstals. As an example we study suspensions of lecithin stabilized β-tripalmitin nanocrystals which adopt a platelet-like shape. Their SAS patterns exhibit a broadened 001 Bragg peak (cf. SAXS curves in the graphical abstract). With the x-ray and neutron powder pattern simulation analysis (XNPPSA) we have demonstrated that the SAXS and SANS patterns of dilute tripalmitin (3 wt%) suspensions can be simultaneously reproduced on an absolute scale [1,2]. Thereby, powder averaged SAS diffractograms are computed for an ensemble of nanocrystals which are embedded in a dispersion medium. The crystallographic structure of the nanocrystals (CIF-file) and their geometry are taken into account and the amphiphilic lecithin molecules which cover the nanocrystals are modelled with two shells (cf. model in the right inset). From the analysis of the fitted shell thicknesses and scattering length densities it turns out that the lecithin molecules arrange rather flatly and densely packed on the surface of the nanocyrstals. Moreover, the XNPPSA method allows a reliable determination of the thickness distribution of the nanocrystals with molecular resolution [1,2]. With rising tripalmitin concentration the platelets form self-assembled stack-like structures [1,3] and finally nematic liquid-crystalline domains. The XNPPSA allows to investigate the structure and amount of such stacks in the suspensions.

scholarly journals TheLaueUtiltoolkit for Laue photocrystallography. I. Rapid orientation matrix determination for intermediate-size-unit-cell Laue data

2011 ◽  
Vol 44 (6) ◽  
pp. 1182-1189 ◽  
Author(s):  
Jarosław A. Kalinowski ◽  
Anna Makal ◽  
Philip Coppens
Keyword(s):  
Open Source ◽  
Unit Sphere ◽  
Reciprocal Lattice ◽  
Unit Cell ◽  
Data Sets ◽  
Data Set ◽  
X Ray ◽  
Orientation Matrix ◽  
Intermediate Size

A new method for determination of the orientation matrix of Laue X-ray data is presented. The method is based on matching of the experimental patterns of central reciprocal lattice rows projected on a unit sphere centered on the origin of the reciprocal lattice with the corresponding pattern of a monochromatic data set on the same material. This technique is applied to the complete data set and thus eliminates problems often encountered when single frames with a limited number of peaks are to be used for orientation matrix determination. Application of the method to a series of Laue data sets on organometallic crystals is described. The corresponding program is available under a Mozilla Public License-like open-source license.

Dynamical Scattering in Crystalline Biological Specimens. I. Criteria of Validity for Scattering Approximations

1975 ◽  
Vol 33 ◽  
pp. 192-193
Author(s):  
Robert M. Glaeser ◽  
Bing K. Jap
Keyword(s):  
Biological Sciences ◽  
Electron Microscopy ◽  
Electron Microscope ◽  
Electron Diffraction ◽  
Born Approximation ◽  
Materials Science ◽  
Image Data ◽  
Dynamical Effect ◽  
Crystallographic Structure ◽  
Electron Microscope Image

The dynamical scattering effect, which can be described as the failure of the first Born approximation, is perhaps the most important factor that has prevented the widespread use of electron diffraction intensities for crystallographic structure determination. It would seem to be quite certain that dynamical effects will also interfere with structure analysis based upon electron microscope image data, whenever the dynamical effect seriously perturbs the diffracted wave. While it is normally taken for granted that the dynamical effect must be taken into consideration in materials science applications of electron microscopy, very little attention has been given to this problem in the biological sciences.

A new method of complex structure analysis by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 628-629
Author(s):  
V.V. Rybin ◽  
E.V. Voronina
Keyword(s):  
Complex Structure ◽  
Reciprocal Lattice ◽  
Stacking Faults ◽  
Plastic Strains ◽  
Base Position ◽  
Structural Regularity ◽  
Orientation Matrix ◽  
Computerized Processing ◽  
Fully Automatic ◽  
Diffraction Patterns

Recently, it has become essential to develop a helpful method of the complete crystallographic identification of fine fragmented crystals. This was maainly due to the investigation into structural regularity of large plastic strains. The method should be practicable for determining crystallographic orientation (CO) of elastically stressed micro areas of the order of several micron fractions in size and filled with λ>1010 cm-2 density dislocations or stacking faults. The method must provide the misorientation vectors of the adjacent fragments when the angle ω changes from 0 to 180° with the accuracy of 0,3°. The problem is that the actual electron diffraction patterns obtained from fine fragmented crystals are the superpositions of reflections from various fragments, though more than one or two reflections from a fragment are hardly possible. Finally, the method should afford fully automatic computerized processing of the experimental results.The proposed method meets all the above requirements. It implies the construction for a certain base position of the crystal the orientation matrix (0M) A, which gives a single intercorrelation between the coordinates of the unity vector in the reference coordinate system (RCS) and those of the same vector in the crystal reciprocal lattice base : .

Observation of faint contrast at planar faults in alloys

1978 ◽  
Vol 36 (1) ◽  
pp. 340-341
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Kumano ◽  
T. Eguchi
Keyword(s):  
Reciprocal Lattice ◽  
Beam Theory ◽  
Al Alloys ◽  
Small Displacement ◽  
Electron Microscopic ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Planar Fault ◽  
Lattice Displacement ◽  
The Many

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.

Structure Information From Electron Diffraction Intensities

1990 ◽  
Vol 48 (2) ◽  
pp. 516-517
Author(s):  
J. Gjønnes ◽  
N. Bøe ◽  
K. Gjønnes
Keyword(s):  
Computational Effort ◽  
Unit Cell ◽  
Small Unit ◽  
Structure Information ◽  
Dispersion Surface ◽  
Integrated Intensity ◽  
The One ◽  
Image Position ◽  
Convergent Beam ◽  
Beam Patterns

Structure information of high precision can be extracted from intentsity details in convergent beam patterns like the one reproduced in Fig 1. From low order reflections for small unit cell crystals,bonding charges, ionicities and atomic parameters can be derived, (Zuo, Spence and O’Keefe, 1988; Zuo, Spence and Høier 1989; Gjønnes, Matsuhata and Taftø, 1989) , but extension to larger unit cell ma seem difficult. The disks must then be reduced in order to avoid overlap calculations will become more complex and intensity features often less distinct Several avenues may be then explored: increased computational effort in order to handle the necessary many-parameter dynamical calculations; use of zone axis intensities at symmetry positions within the CBED disks, as in Figure 2 measurement of integrated intensity across K-line segments. In the last case measurable quantities which are well defined also from a theoretical viewpoint can be related to a two-beam like expression for the intensity profile:With as an effective Fourier potential equated to a gap at the dispersion surface, this intensity can be integrated across the line, with kinematical and dynamical limits proportional to and at low and high thickness respctively (Blackman, 1939).

Toward quantitative defect analysis using HREM

1994 ◽  
Vol 52 ◽  
pp. 714-715
Author(s):  
David J. Smith
Keyword(s):  
Electron Microscope ◽  
Unit Cell ◽  
Defect Analysis ◽  
Significant Progress ◽  
Detailed Characterization ◽  
Small Unit ◽  
Resolution Electron ◽  
High Resolution Electron Microscope ◽  
Large Unit Cell ◽  
Made In

The electron microscope has evolved to the level where it is now straightforward to record highresolution images from thin samples (t∼10 to 20nm) that are directly interpretable in terms of atomic arrangements. Whilst recorded images necessarily represent two-dimensional projections of the structure, many defects such as dislocations and interfaces may be linear or planar in nature and thus might be expected to be amenable to detailed characterization. In this review, we briefly consider the recent significant progress that has been made in quantitative defect analysis using the high-resolution electron microscope and then discuss some drawbacks to the technique as well as potential scope for further improvements. Surveys of defect modelling for some small-unit-cell materials and interfaces have recently been published, and reference should be made to other papers in this symposium for further examples.The technique of structure imaging originated in the early '70s with observations of large-unit-cell block oxides.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

Angle calculations for a three-circle goniostat

2006 ◽  
Vol 39 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen ◽  
Jon Are Beukes
Keyword(s):  
General Procedure ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Laboratory System ◽  
Lattice Vector ◽  
New Approach ◽  
Rotation Matrices ◽  
Rotation Axes ◽  
Vector Description

A general procedure for angle calculations for a three-circle goniostat has been developed. This new approach is based on a vector description of the transformation of a reciprocal-lattice vector under the action of a rotation shaft. It does not invoke the use of rotation matrices and applies equally well to cases where the directions of the rotation axes do not conform with coordinate axes of the laboratory system adopted for the analysis.

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