Crystallometric and projective properties of Kikuchi diffraction patterns

2017 ◽  
Vol 50 (1) ◽  
pp. 102-119 ◽  
Author(s):  
Gert Nolze ◽  
Aimo Winkelmann
Keyword(s):  
Lattice Parameter ◽  
Parameter Determination ◽  
Lattice Plane ◽  
Kikuchi Pattern ◽  
Mathematical Properties ◽  
Fundamental Information ◽  
Precision And Accuracy ◽  
Diffraction Patterns ◽  
Definition Of ◽  
Basis Vectors

Kikuchi diffraction patterns can provide fundamental information about the lattice metric of a crystalline phase. In order to improve the possible precision and accuracy of lattice parameter determination from the features observed in Kikuchi patterns, some useful fundamental relationships of geometric crystallography are reviewed, which hold true independently of the actual crystal symmetry. The Kikuchi band positions and intersections and the Kikuchi band widths are highly interrelated, which is illustrated by the fact that all lattice plane trace positions of the crystal are predetermined by the definition of only four traces. If, additionally, the projection centre of the gnomonic projection is known, the lattice parameter ratios and the angles between the basis vectors are fixed. A further definition of one specific Kikuchi band width is sufficient to set the absolute sizes of all lattice parameters and to predict the widths of all Kikuchi bands. The mathematical properties of the gnomonic projection turn out to be central to an improved interpretation of Kikuchi pattern data, emphasizing the importance of the exact knowledge of the projection centre.

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

2018 ◽  
Vol 51 (4) ◽  
pp. 982-989 ◽  
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.

scholarly journals Algorithms for target transformations of lattice basis vectors

2020 ◽  
Vol 76 (6) ◽  
pp. 713-718
Author(s):  
Semën Gorfman
Keyword(s):  
Electron Diffraction ◽  
Lattice Plane ◽  
Energy Calculations ◽  
Specific Target ◽  
First Case ◽  
Dimensional Version ◽  
Cleavage Energy ◽  
Diffraction Patterns ◽  
Supporting Materials ◽  
Basis Vectors

Simple algorithms are proposed for the transformation of lattice basis vectors to a specific target. In the first case, one of the new basis vectors is aligned to a predefined lattice direction, while in the second case, two of the new basis vectors are brought to a lattice plane with predefined Miller indices. The multi-dimensional generalization of the algorithm is available in the supporting materials. The algorithms are useful for such crystallographic operations as simulation of zone planes (i.e. geometry of electron diffraction patterns) or transformation of a unit cell for surface or cleavage energy calculations. The most general multi-dimensional version of the algorithm may be useful for the analysis of quasiperiodic crystals or as an alternative method of calculating Bézout coefficients. The algorithms are demonstrated both graphically and numerically.

Application of diffraction instrumental monitoring to the analysis of diffraction patterns from a Round Robin project on KCl

2001 ◽  
Vol 16 (1) ◽  
pp. 6-15 ◽  
Author(s):  
Giovanni Berti
Keyword(s):  
Cell Parameter ◽  
Direct Consequence ◽  
Lattice Parameter ◽  
Round Robin ◽  
X Ray Diffraction ◽  
X Ray ◽  
Standard Values ◽  
Instrumental Monitoring ◽  
Diffraction Patterns ◽  
Definition Of

The outcome of the analysis of data from a Round Robin on a KCl sample is reported. The research project has led to a definition of a working protocol for the treatment of X-ray diffraction data from powders (XRPD). The protocol is based on the method of “Diffraction Instrumental Monitoring” (DIM), whose main characteristics are briefly illustrated. When experimental data are referred to the expected standard values of the lattice parameter, the method enables comparison with data obtained from differing instrumentation found in different laboratories. Application of DIM to the KCl Round Robin demonstrates the ability of DIM to effectively evaluate systematic contribution. Accuracy on the cell parameter is obtained as a direct consequence; in this application, where the knowledge of the KCl d-spacing was not a problem, the accuracy of lattice parameter is a feedback for constraining the evaluation of the effective values of the experiment-related parameters.

Review of X-ray powder diffraction data of rhombohedral bismuth tri-iodide

1996 ◽  
Vol 11 (2) ◽  
pp. 91-96 ◽  
Author(s):  
L. Keller ◽  
D. Nason
Keyword(s):  
Rietveld Refinement ◽  
Room Temperature ◽  
Internal Standard ◽  
Standard Technique ◽  
Rietveld Analysis ◽  
Lattice Parameter ◽  
Parameter Determination ◽  
Data Set ◽  
X Ray ◽  
Diffraction Patterns

Single crystals of rhombohedral bismuth tri-iodide grown by physical vapor transport are possible candidates for room-temperature detectors. Previously reported, low angle reflections in X-ray diffraction patterns of various BiI3 starting powders are attributed to the BiI3 structure from Rietveld analysis. Accordingly, the lattice parameters of stoichiometric BiI3 are determined as a0=7.5192±0.0003 Å and c0=20.721±0.004 Å at room temperature. It also appears that lattice parameter determination using Rietveld refinement can lead to significant errors if experimental aberrations are present and their nature and magnitude are unknown. A modified internal standard technique is applied to the data set prior to Rietveld refinement for more reliable lattice parameter determination.

An indexing algorithm independent of peak position extraction for X-ray powder diffraction patterns

2017 ◽  
Vol 50 (5) ◽  
pp. 1323-1330 ◽  
Author(s):  
Alan A. Coelho
Keyword(s):  
Monte Carlo ◽  
Parameter Space ◽  
Powder Diffraction ◽  
Merit Function ◽  
Limited Range ◽  
Lattice Parameter ◽  
Peak Position ◽  
Parameter Determination ◽  
X Ray ◽  
Diffraction Patterns

Lattice parameter determination from X-ray powder diffraction patterns, called indexing, invariably requires the extraction of peak positions which are then used by indexing algorithms that are peak position dependent. The success of these algorithms depends on the accuracy of the extracted peak positions. Peak positions that do not overlap significantly with nearby peaks can be readily determined with great accuracy. However, in heavily overlapped regions it is difficult to determine the number of peaks and even more difficult to determine the peak positions accurately. This paper describes a new indexing algorithm,Lp-Search, that is implemented in the computer programTOPAS Version 7(Bruker AXS, Karlsruhe, Germany).Lp-Searchdoes not require peak position extraction nor does it require knowledge of the number of peaks present.Lp-Searchcombines Monte Carlo searches of lattice parameter space with a Pawley refinement used at the end of each search. Critical to the success of the Monte Carlo search is a new figure of merit function which allows the parameter space to be searched efficiently.Lp-Searchhas proved to be effective for patterns with heavily overlapped peaks; monoclinic to cubic lattices are successfully indexed in a matter of seconds and triclinic lattices within a minute or two. Diffraction patterns spanning a limited range, such that 30–40 peaks of the highestdspacing peaks are omitted, can be successfully indexed; this demonstrates the robust nature ofLp-Search.

Problems Associated with Kα Doublet in Residual Stress Measurements

1979 ◽  
Vol 23 ◽  
pp. 333-339
Author(s):  
S. K. Gupta ◽  
B. D. Cullity
Keyword(s):  
Residual Stress ◽  
Silicon Powder ◽  
Lattice Parameter ◽  
Diffraction Peak ◽  
Parameter Determination ◽  
X Ray Diffraction ◽  
X Ray ◽  
Analysis Techniques ◽  
The Difference ◽  
Similar Accuracy

Since the measurement of residual stress by X-ray diffraction techniques is dependent on the difference in angle of a diffraction peak maximum when the sample is examined consecutively with its surface at two different angles to the diffracting planes, it is important that these diffraction angles be obtained precisely, preferably with an accuracy of ± 0.01 deg. 2θ. Similar accuracy is desired in precise lattice parameter determination. In such measurements, it is imperative that the diffractometer be well-aligned. It is in the context of diffractometer alignment with the aid of a silicon powder standard free of residual stress that the diffraction peak analysis techniques described here have been developed, preparatory to residual stress determinations.

EFFECTS OF A PARTIAL SUBSTITUTION OF Cu ELEMENTS BY Nb ELEMENTS IN YBaCuO SYSTEM

1990 ◽  
Vol 04 (12) ◽  
pp. 823-830 ◽  
Author(s):  
S. HIGO ◽  
Y. HAKURAKU ◽  
T. OGUSHI ◽  
I. KAWANO ◽  
Y. ISHIKAWA
Keyword(s):  
Solid State Reaction Method ◽  
Lattice Parameter ◽  
Partial Substitution ◽  
Maximum Temperature ◽  
X Ray ◽  
Cubic Lattice ◽  
Nb Content ◽  
Molecular Ratios ◽  
Diffraction Patterns ◽  
Two Phases

Samples of the YBaCuNbO system with different molecular ratios of YBa 2 NbO y to YBa 2 Cu 3 O 7−d, were prepared in air by the solid-state reaction method. The X-ray powder diffraction patterns showed that the sample was composed of two phases, one corresponding to the YBa 2 Cu 3 O 7−d phase and the other to the YBa 2 NbO y phase with a cubic lattice parameter of 8.425 Å to 8.436 Å depending on the Nb content. The superconducting zero resistivity temperature, T c 0, of the YBaCuNbO system increased with the increase of the molecular ratios, from 91.2 K up to a maximum temperature of 92.8 K, and then, by a further increase in the molecular ratio, the T c 0 was drastically reduced with a gradient of −1.94 K /%x.

scholarly journals Diffuse multiple scattering

2015 ◽  
Vol 71 (1) ◽  
pp. 20-25 ◽  
Author(s):  
A. G. A. Nisbet ◽  
G. Beutier ◽  
F. Fabrizi ◽  
B. Moser ◽  
S. P. Collins
Keyword(s):  
Multiple Scattering ◽  
Lattice Parameter ◽  
Parameter Determination ◽  
Line Method ◽  
New Form

A new form of diffraction lines has been identified, similar to Rutherford, Kikuchi and Kossel lines. This paper highlights some of the properties of these lines and shows how they can be used to eliminate the need for sample/source matching in Lonsdale's triple convergent line method in lattice-parameter determination.

Microstructure and Precipitates in Mg-Zn-Y Alloys

2007 ◽  
Vol 546-549 ◽  
pp. 203-206
Author(s):  
M. Zhang ◽  
Wen Zheng Zhang ◽  
Guang Yin Yuan ◽  
Q.L. Zhao
Keyword(s):  
Grain Boundaries ◽  
Energy Dispersive Spectrometer ◽  
Lattice Parameter ◽  
Energy Dispersive ◽  
Experimental Result ◽  
Icosahedral Quasicrystals ◽  
Diffraction Patterns ◽  
New Phase ◽  
Zr Alloys

The present work studied the precipitate microstructures in as-cast Mg-Zn-Y-Zr alloys. The experimental result showed that there is significant number of small precipitates within the grains besides the icosahedral quasicrystals along the grain boundaries. Among these precipitates, a new phase has been identified. The new phase displays square morphologies with the size in the range of 200 nm to 2 μm. According to the energy dispersive spectrometer (EDS), this phase could be a metallic Y-riched compound. The diffraction patterns can be indexed with an f.c.c. structure with the lattice parameter a = 0.52±0.1 nm. The structure does not agree with any precipitate structures that have been reported from the previous studies of Mg-Zn-Y alloys.

Synchrotron X-ray studies of metal-organic framework M2(2,5-dihydroxyterephthalate), M = (Mn, Co, Ni, Zn) (MOF74)

2012 ◽  
Vol 27 (4) ◽  
pp. 256-262 ◽  
Author(s):  
W. Wong-Ng ◽  
J. A. Kaduk ◽  
H. Wu ◽  
M. Suchomel
Keyword(s):  
Powder Diffraction ◽  
Metal Organic Framework ◽  
National Laboratory ◽  
Argonne National Laboratory ◽  
Lattice Parameter ◽  
X Ray ◽  
Metal Organic ◽  
Sorbent Materials ◽  
Diffraction Patterns ◽  
Unsaturated Metal Sites

M2(dhtp)·nH2O (M = Mn, Co, Ni, Zn; dhtp = 2,5-dihydroxyterephthalate), known as MOF74, is a family of excellent sorbent materials for CO2 that contains coordinatively unsaturated metal sites and a honeycomb-like structure featuring a broad one-dimensional channel. This paper describes the structural feature and provides reference X-ray powder diffraction patterns of these four isostructural compounds. The structures were determined using synchrotron diffraction data obtained at beam line 11-BM at the Advanced Photon Source (APS) in the Argonne National Laboratory. The samples were confirmed to be hexagonal R 3 (No. 148). From M = Mn, Co, Ni, to Zn, the lattice parameter a of MOF74 ranges from 26.131 73(4) Å to 26.5738(2) Å, c from 6.651 97(5) to 6.808 83(8) Å, and V ranges from 3948.08 Å3 to 4163.99 Å3, respectively. The four reference X-ray powder diffraction patterns have been submitted for inclusion in the Powder Diffraction File (PDF).

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