scholarly journals Crystallographic analysis of the lattice metric (CALM) from single electron backscatter diffraction or transmission Kikuchi diffraction patterns

2021 ◽  
Vol 54 (3) ◽  
Author(s):  
Gert Nolze ◽  
Tomasz Tokarski ◽  
Łukasz Rychłowski ◽  
Grzegorz Cios ◽  
Aimo Winkelmann
Keyword(s):  
Electron Backscatter Diffraction ◽  
Reciprocal Lattice ◽  
Lattice Parameter ◽  
Crystallographic Analysis ◽  
Lattice Parameters ◽  
Bravais Lattice ◽  
Backscatter Coefficient ◽  
Reciprocal Lattice Point ◽  
Diffraction Patterns ◽  
Lattice Planes

A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 × 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.

Properties of the Interference Function for Unbent, Spherically, and Cylindrically Bent Lattices

1974 ◽  
Vol 32 ◽  
pp. 486-487
Author(s):  
Necip Güven
Keyword(s):  
Lattice Point ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Point ◽  
Interference Function ◽  
Cell Parameters ◽  
Real Cell ◽  
Crystalline Films ◽  
Lattice Planes ◽  
Image Position ◽  
Diffraction Effects

Kinematical diffraction effects from thin crystalline films may be readily explained in terms of the interference function (ϕ). For an undeformed and orthogonal lattice:It can be shown that this function is independent of reciprocal and real cell parameters. It is dependent only on the number of lattice planes in a given direction and on the distance from a reciprocal lattice point. Furthermore, this function is symmetrical at each reciprocal lattice point.

scholarly journals Improved crystal orientation and physical properties from single-shot XFEL stills

2014 ◽  
Vol 70 (12) ◽  
pp. 3299-3309 ◽  
Author(s):  
Nicholas K. Sauter ◽  
Johan Hattne ◽  
Aaron S. Brewster ◽  
Nathaniel Echols ◽  
Petrus H. Zwart ◽  
...  
Keyword(s):  
Crystal Orientation ◽  
Degrees Of Freedom ◽  
Reciprocal Lattice ◽  
Single Shot ◽  
X Ray Diffraction ◽  
Reciprocal Lattice Point ◽  
X Ray ◽  
Structure Factors ◽  
Rotational Degrees Of Freedom ◽  
Diffraction Patterns

X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg's law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographicRfactors and sharpening anomalous differences that are near the level of the noise.

Phase Analysis in the Region Brazed with Ni-14Cr-10Co-3.5Al-2.5Ta-2.8B Filler Metal Using Electron Backscatter Diffraction

2008 ◽  
Vol 569 ◽  
pp. 93-96 ◽  
Author(s):  
Yong Hwan Kim ◽  
S.I. Kwun
Keyword(s):  
Solid Solution ◽  
Filler Metal ◽  
Electron Backscatter Diffraction ◽  
Lattice Parameter ◽  
Lattice Parameters ◽  
Metal Powders ◽  
Orthorhombic Structure ◽  
Electron Backscatter ◽  
Wide Gap ◽  
Backscatter Diffraction

The phases formed in the wide-gap region brazed with Ni-14Cr-10Co-3.5Al-2.5Ta-2.8B filler metal powder in IN738 superalloy were investigated by electron backscatter diffraction (EBSD). The wide-gap brazing process was carried out in a vacuum of 2×10-5 torr at 1503 K. The region brazed with filler metal powders had a microstructure consisting of two kinds of eutectic colonies, one is Ni solid solution-CrB eutectic and the other is Ni solid solution-Ni3B eutectic. EBSD pattern analysis revealed that the CrB phase had orthorhombic structure with lattice parameters of a=0.297, b=0.786 and c=0.293 nm, and the Ni3B phase had orthorhombic structure with lattice parameters of a=0.439, b=0.522 and c=0.662 nm. The cuboidal-shaped phase precipitated in the Ni solid solution was found to be the γ' (Ni3Al) phase, which had cubic structure with lattice parameter of a=0.357 nm.

scholarly journals Lattice row distance

2014 ◽  
Vol 70 (a1) ◽  
pp. C1454-C1454
Author(s):  
Hejing Wang ◽  
Ting Li ◽  
Ling Wang ◽  
Zhao Zhou ◽  
Lei Yuan
Keyword(s):  
Reciprocal Lattice ◽  
Early Time ◽  
Basic Feature ◽  
Lattice Points ◽  
Lattice Parameters ◽  
Parallel Lines ◽  
Basic Characteristics ◽  
Diffraction Patterns ◽  
Distance Formulae

Lattice and diffraction are two relating aspects of a crystal. The former reflects the nature of a crystal and the latter describes the basic feature of a crystal. A lattice possesses points and rows two basic characteristics. Great attention has been paid to the points and their distances and directions (angles) they form since the early time of crystallography. Starting from lattice points people have already revealed and found so many regulations in crystals and made great progresses in crystallography. What about the lattice rows? Starting from the geometric relations of reciprocal lattice, we propose six general formulae [1] to describe the relationships between the lattice row distance, the Miller indices h, k, l and the lattice parameters for all crystal systems along any direction. This, like the lattice points, establishes the foundation of the row-indexing, row-refinement of lattice parameters and row-determination of incidence direction theoretically. It is a new method from the lattice row distance to the Miller indices, to the lattice parameters or to the incidence direction. Five steps are optimized for the procedure of "Row-indexing" or "Row-refinement". For example, the procedure of row-indexing is described as 1) measurement of row distance; 2) calculation of row distance; 3) comparison of the measured with the calculated row distances; 4) indexing, and 5) check according to the crystallographic regulations. In respect to diffraction patterns, a series of diffraction spots (points) comprise row(s) and arrange into a series of parallel "lines". When diffraction is strong, diffraction spots are isolated and sharp. However, when diffraction is weak, those spots are obscure or gloomy and often distorted into elongation, asymmetry, deformation, etc. This leads to the outstanding of the rowing "lines" relatively and hence, the row-distance formulae are able to be utilized to structure analysis for those "linear diffraction patterns".

On-line diffraction pattern analysis and phase identification using a JEM 2000FX AEM with a macintosh-based program

1994 ◽  
Vol 52 ◽  
pp. 1006-1007
Author(s):  
C. R. Hills ◽  
G. A. Poulter
Keyword(s):  
Electron Diffraction ◽  
Diffraction Pattern ◽  
Real Time ◽  
Pattern Analysis ◽  
Reciprocal Lattice ◽  
Computer Software ◽  
Crystallographic Analysis ◽  
Lattice Points ◽  
Phase Identification ◽  
Reciprocal Lattice Point

A number of computer programs have been written to aid in the indexing of transmission electron diffraction pattcrns. These programs are useful for determining crystallographic orientation and for phase identification and often simplify the analysis of complex patterns. Over the last few years there has been a trend toward automated electron microscopy. It is natural to extend this automation to real time diffraction pattern analysis and phase identification using A/D data acquisition boards and computer software to interface the modern AEM with an electron diffraction database (EDD). This paper describes a real-time Macintosh-based system (hardware and software) for automated electron diffraction pattern analysis and phase identification developed for the JEM 2000FX AEM. Crystallographic analysis with this system is attractive because of the rapid analysis time, ease of implementation, and it is inexpensive compared to buying a digitizing board and video system.Computer-aided diffraction pattern-indexing programs typically require the user to input reciprocal lattice point spacings (r-spacings) and the interplanar angle measurements for at least three non-colinear lattice points in the pattern. It is also necessary to know the crystal structure and lattice constants of the sample.

scholarly journals Phase Mapping in EBSD Using Convolutional Neural Networks

2020 ◽  
Vol 26 (3) ◽  
pp. 458-468
Author(s):  
Kevin Kaufmann ◽  
Chaoyi Zhu ◽  
Alexander S. Rosengarten ◽  
Daniel Maryanovsky ◽  
Haoren Wang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Learning Algorithm ◽  
Electron Backscatter Diffraction ◽  
Lattice Parameter ◽  
Machine Learning Techniques ◽  
Space Groups ◽  
Learning Techniques ◽  
Phase Mapping ◽  
Diffraction Patterns ◽  
Backscatter Diffraction

AbstractThe emergence of commercial electron backscatter diffraction (EBSD) equipment ushered in an era of information rich maps produced by determining the orientation of user-selected crystal structures. Since then, a technological revolution has occurred in the quality, rate detection, and analysis of these diffractions patterns. The next revolution in EBSD is the ability to directly utilize the information rich diffraction patterns in a high-throughput manner. Aided by machine learning techniques, this new methodology is, as demonstrated herein, capable of accurately separating phases in a material by crystal symmetry, chemistry, and even lattice parameters with fewer human decisions. This work is the first demonstration of such capabilities and addresses many of the major challenges faced in modern EBSD. Diffraction patterns are collected from a variety of samples, and a convolutional neural network, a type of machine learning algorithm, is trained to autonomously recognize the subtle differences in the diffraction patterns and output phase maps of the material. This study offers a path to machine learning coupled phase mapping as databases of EBSD patterns encompass an increasing number of the possible space groups, chemistry changes, and lattice parameter variations.

Blind lattice-parameter determination of cubic and tetragonal phases with high accuracy using a single EBSD pattern

2018 ◽  
Vol 74 (6) ◽  
pp. 630-639 ◽  
Author(s):  
Ming Han ◽  
Chen Chen ◽  
Guangming Zhao ◽  
Lili Li ◽  
Gert Nolze ◽  
...  
Keyword(s):  
Electron Backscatter Diffraction ◽  
Lattice Parameter ◽  
High Accuracy ◽  
Lattice Parameters ◽  
Parameter Determination ◽  
Tetragonal Crystal ◽  
Ebsd Pattern ◽  
Ebsd Technique ◽  
Relative Errors ◽  
Backscatter Diffraction

The Bravais lattices and their lattice parameters are blindly determined using electron backscatter diffraction (EBSD) patterns of materials with cubic or tetragonal crystal structures. Since the geometric relationships in a single EBSD pattern are overdetermined, the relative errors of determining the lattice parameters as well as the axial ratios are confined to about 0.7 ± 0.4% and 0.07 ± 0.03%, respectively, for ideal simulated EBSD patterns. The accuracy of the crystal orientation determination reaches about 0.06 ± 0.03°. With careful manual band detection, the accuracy of determining lattice parameters from experimental patterns can be as good as from simulated patterns, although the results from simulated patterns are often better than expermental patterns, which are lower quality and contain uncertain systematic errors. The reasonably high accuracy is obtained primarily because the detection of the diffracting-plane traces and zone axes is relatively accurate. The results here demonstrate that the developed procedure based on the EBSD technique presents a reliable tool for crystallographic characterization of the Bravais lattices of unknown phases.

An auxiliary method of indexing electron diffraction patterns by means of gnomonic projections

1983 ◽  
Vol 16 (1) ◽  
pp. 70-73
Author(s):  
F. S. Borges
Keyword(s):  
Electron Diffraction ◽  
Diffraction Pattern ◽  
Reciprocal Lattice ◽  
Tangential Component ◽  
Spurious Solutions ◽  
Diffraction Patterns ◽  
Lattice Planes ◽  
The One ◽  
Planar Feature ◽  
Low Symmetry

A method is described which eliminates most – if not all – spurious solutions usually obtained when indexing an electron diffraction pattern from a substance having a structure with low symmetry. The proposed method is applicable when the diffraction pattern includes non-zero Laue zones, or when crystallographic planar features are recognized in the contrast images of the areas from which the diffraction patterns were taken. In the first situation, the tangential component of the stacking vector of reciprocal-lattice planes, normal to each beam direction calculated by the computer for a given diffraction pattern, is determined by means of gnomonic projections, and then compared with the one derived from the observed Laue zones. In the second situation, the trace orientation of a known planar feature observed is compared with those that can be drawn on the gnomonic projections. Alternatively, if a selected-area diffraction pattern has already been indexed, a presumed crystallographic orientation of a planar feature can be checked on a gnomonic projection.

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 : .

High resolution STEM imaging study on high Tc superconductor YBa2CuaO7-x

1988 ◽  
Vol 46 ◽  
pp. 882-883
Author(s):  
H.-J. Ou ◽  
J. M. Cowley
Keyword(s):  
Crystal Structure ◽  
High Resolution ◽  
Grain Boundary ◽  
Strong Field ◽  
Imaging Study ◽  
Structure Defects ◽  
High Tc ◽  
High Tc Superconductor ◽  
Diffraction Patterns ◽  
Lattice Planes

Using the dedicate VG-HB5 STEM microscope, the crystal structure of high Tc superconductor of YBa2Cu3O7-x has been studied via high resolution STEM (HRSTEM) imaging and nanobeam (∽3A) diffraction patterns. Figure 1(a) and 2(a) illustrate the HRSTEM image taken at 10' times magnification along [001] direction and [100] direction, respectively. In figure 1(a), a grain boundary with strong field contrast is seen between two crystal regions A and B. The grain boundary appears to be parallel to a (110) plane, although it is not possible to determine [100] and [001] axes as it is in other regions which contain twin planes [3]. Following the horizontal lattice lines, from left to right across the grain boundary, a lattice bending of ∽4° is noticed. Three extra lattice planes, indicated by arrows, were found to terminate at the grain boundary and form dislocations. It is believed that due to different chemical composition, such structure defects occur during crystal growth. No bending is observed along the vertical lattice lines.

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