Profile agreement indices in Rietveld and pattern-fitting analysis

1990 ◽  
Vol 23 (6) ◽  
pp. 462-468 ◽  
Author(s):  
R. J. Hill ◽  
R. X. Fischer
Keyword(s):  
Crystal Structure ◽  
Signal To Noise Ratio ◽  
Structure Refinement ◽  
Data Sets ◽  
Structure Model ◽  
Signal To Noise ◽  
Neutron Data ◽  
Reduction Stage ◽  
X Ray ◽  
Diffraction Patterns

Two definitions of profile agreement indices are now in common use for estimating the degree of fit in Rietveld refinement and in structure-independent pattern-fitting methods of powder diffraction analysis. In the original program written by Rietveld, the background was subtracted and the `non-peak' regions of the pattern were removed from further consideration in a preliminary data-reduction stage prior to Structure refinement. However, the agreement indices used in many of the more recent programs retain the background counts in the observed step intensities and include all portions of the pattern in the sums. These latter definitions are strongly dependent on the signal-to-noise ratio and on the relative amount of `background-only' regions and do not, therefore, provide a sound basis for comparing the degree of fit of peak profile and crystal structure model refinements in the general case. The extent of this dependence is illustrated quantitatively using conventional and synchrotron X-ray and constant-wavelength and time-of-flight neutron data sets with different inherent background levels and peak densities. The unweighted background-corrected peak-only profile agreement index R′ p = Σ i |Y io − Y ic|/Σ i |Y io −Y ib | (and, to a lesser extent, its weighted equivalent) is recommended as the most appropriate criterion of fit for comparative work between diffraction patterns of all kinds.

scholarly journals New processing tools for weak and/or spatially overlapped macromolecular diffraction patterns

1999 ◽  
Vol 55 (10) ◽  
pp. 1733-1741 ◽  
Author(s):  
Dominique Bourgeois
Keyword(s):  
Signal To Noise Ratio ◽  
Data Sets ◽  
Signal To Noise ◽  
Weighting Method ◽  
Time Resolved ◽  
Accurate Evaluation ◽  
Profile Fitting ◽  
Integration Program ◽  
Diffraction Patterns ◽  
New Processing

Tools originally developed for the treatment of weak and/or spatially overlapped time-resolved Laue patterns were extended to improve the processing of difficult monochromatic data sets. The integration programPrOWallows deconvolution of spatially overlapped spots which are usually rejected by standard packages. By using dynamically adjusted profile-fitting areas, a carefully built library of reference spots and interpolation of reference profiles, this program also provides a more accurate evaluation of weak spots. In addition, by using Wilson statistics, it allows rejection of non-redundant strong outliers such as zingers, which otherwise may badly corrupt the data. A weighting method for optimizing structure-factor amplitude differences, based on Bayesian statistics and originally applied to low signal-to-noise ratio time-resolved Laue data, is also shown to significantly improve other types of subtle amplitude differences, such as anomalous differences.

scholarly journals FELIX: an algorithm for indexing multiple crystallites in X-ray free-electron laser snapshot diffraction images

2017 ◽  
Vol 50 (4) ◽  
pp. 1075-1083 ◽  
Author(s):  
Kenneth R. Beyerlein ◽  
Thomas A. White ◽  
Oleksandr Yefanov ◽  
Cornelius Gati ◽  
Ivan G. Kazantsev ◽  
...  
Keyword(s):  
Free Electron Laser ◽  
Signal To Noise Ratio ◽  
X Ray Diffraction ◽  
Signal To Noise ◽  
Monoclinic Crystal ◽  
Slight Tendency ◽  
X Ray ◽  
Serial Crystallography ◽  
Diffraction Patterns ◽  
Novel Algorithm

A novel algorithm for indexing multiple crystals in snapshot X-ray diffraction images, especially suited for serial crystallography data, is presented. The algorithm, FELIX, utilizes a generalized parametrization of the Rodrigues–Frank space, in which all crystal systems can be represented without singularities. The new algorithm is shown to be capable of indexing more than ten crystals per image in simulations of cubic, tetragonal and monoclinic crystal diffraction patterns. It is also used to index an experimental serial crystallography dataset from lysozyme microcrystals. The increased number of indexed crystals is shown to result in a better signal-to-noise ratio, and fewer images are needed to achieve the same data quality as when indexing one crystal per image. The relative orientations between the multiple crystals indexed in an image show a slight tendency of the lysozme microcrystals to adhere on (\overline 110) facets.

Communication between cation environments in aluminosilicate frameworks: incommensurately modulated crystal structure of ane-plagioclase

2016 ◽  
Vol 72 (5) ◽  
pp. 787-801 ◽  
Author(s):  
Rie T. Fredrickson ◽  
Daniel C. Fredrickson
Keyword(s):  
Crystal Structure ◽  
Low Temperature ◽  
Structure Model ◽  
X Ray Diffraction ◽  
Modulated Structure ◽  
X Ray ◽  
Space Groups ◽  
Structural Details ◽  
Diffraction Patterns ◽  
Centrosymmetric Structure

Despite being one of the most common minerals in the earth's crust the crystal structure of intermediatee-plagioclase remains only partially understood, due in a large part to its complex diffraction patterns including satellite reflections. In this article we present a detailed analysis of the structure ofe-plagioclase (An44) using single-crystal X-ray diffraction measured at ambient and low temperature (T= 100 K), in which the full modulated structure is successfully refined. As in earlier studies, the diffraction pattern exhibits strong maina-reflections and weake-satellite reflections. The average structure could be solved in terms of an albite-like basic cell with the triclinic centrosymmetric and non-centrosymmetric space groups P \bar 1 andP1 (treated in its C \bar 1 andC1 setting, respectively, to follow conventions in the literature), while the incommensurately modulated structure was modeled in (3 + 1)D superspace, employing both the centro- and non-centrosymmetric superspace groups X \bar 1(αβγ)0 andX1(αβγ)0, whereXrefers to a special (3 + 1)D lattice centering with centering vectors (0 0 ½ ½), (½ ½ 0 ½), and (½ ½ ½ 0). Individual positional and occupational modulations for Ca/Na were refined with deeper insights being revealed in the non-centrosymmetric structure model. Through the structural details emerging from this model, the origin of the modulation can be traced to the communication between Ca/Na site positions through their bridging aluminosilicate (Si/Al)O4tetrahedra.

scholarly journals Deep learning for visualization and novelty detection in large X-ray diffraction datasets

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Lars Banko ◽  
Phillip M. Maffettone ◽  
Dennis Naujoks ◽  
Daniel Olds ◽  
Alfred Ludwig
Keyword(s):  
Thin Film ◽  
Crystal Structure ◽  
Artificial Intelligence ◽  
Deep Learning ◽  
Novelty Detection ◽  
Structural Similarity ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Patterns ◽  
Post Hoc

AbstractWe apply variational autoencoders (VAE) to X-ray diffraction (XRD) data analysis on both simulated and experimental thin-film data. We show that crystal structure representations learned by a VAE reveal latent information, such as the structural similarity of textured diffraction patterns. While other artificial intelligence (AI) agents are effective at classifying XRD data into known phases, a similarly conditioned VAE is uniquely effective at knowing what it doesn’t know: it can rapidly identify data outside the distribution it was trained on, such as novel phases and mixtures. These capabilities demonstrate that a VAE is a valuable AI agent for aiding materials discovery and understanding XRD measurements both ‘on-the-fly’ and during post hoc analysis.

scholarly journals Lower resolution Laue neutron data yield correct nanocluster formulations

2014 ◽  
Vol 70 (a1) ◽  
pp. C187-C187
Author(s):  
Alison Edwards
Keyword(s):  
Neutron Diffraction ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Precise Determination ◽  
Data Sets ◽  
X Rays ◽  
Low Resolution ◽  
Neutron Data ◽  
X Ray ◽  
Product Formulation

"The renaissance in Laue studies - at neutron sources - provides us with access to single crystal neutron diffraction data for synthetic compounds without requiring synthesis of prohibitively large amounts of compound or improbably large crystals. Such neutron diffraction studies provide vital data where proof of the presence or absence of hydrogen in particular locations is required and which cannot validly be proved by X-ray studies. Since the commissioning of KOALA at OPAL in 2009[1] we have obtained numerous data sets which demonstrate the vital importance of measuring data even where the extent of the diffraction pattern is at relatively low resolution - especially when compared to that obtainable for the same compound with X-rays. In the Laue experiment performed with a fixed radius detector, data reduction is only feasible for crystals in the ""goldilocks"" zone – where the unit cell is relatively large for the detector, a correspondingly low resolution diffraction pattern in which adjacent spots are less affected by overlap will yield more data against which a structure can be refined than a pattern of higher resolution – one where neighbouring spots overlap rendering both unusable (in our current methodology). Analogous application of powder neutron diffraction in such determinations is also considered. Single crystal neutron diffraction studies of several important compounds (up to 5KDa see figure below)[2] in which precise determination of hydride content by neutron diffraction was pivotal to the final formulation will be presented. The neutron data sets typically possess 20% or fewer unique data at substantially "lower resolution" than the corresponding X-ray data sets. Careful refinement clearly reveals chemical detail which is typically unexplored in related X-ray diffraction studies reporting high profile chemistry despite the synthetic route being one which hydride ought to be considered/excluded in product formulation."

Cancellation method to improve signal to noise ratio of an electrodeless microwave-biased ZnO single crystal x-ray detector

2022 ◽  
Vol 93 (1) ◽  
pp. 015006
Author(s):  
Xiaolong Zhao ◽  
Ming Ye ◽  
Zhi Cao ◽  
Danyang Huang ◽  
Tingting Fan ◽  
...  
Keyword(s):  
Single Crystal ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
X Ray ◽  
Noise Ratio ◽  
Zno Single Crystal

scholarly journals Erratum: “Signal-to-noise ratio in x-ray dark-field imaging using a grating interferometer” [J. Appl. Phys. 110, 053105 (2011)]

2011 ◽  
Vol 110 (10) ◽  
pp. 109902 ◽  
Author(s):  
Michael Chabior ◽  
Tilman Donath ◽  
Christian David ◽  
Manfred Schuster ◽  
Christian Schroer ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Dark Field ◽  
Signal To Noise ◽  
X Ray ◽  
Dark Field Imaging ◽  
Grating Interferometer ◽  
Noise Ratio ◽  
Field Imaging

CRYSTAL STRUCTURE OF ZIRCONIUM TRICHLORIDE

1964 ◽  
Vol 42 (10) ◽  
pp. 1886-1889 ◽  
Author(s):  
B. Swaroop ◽  
S. N. Flengas
Keyword(s):  
Crystal Structure ◽  
Room Temperature ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Main Cell ◽  
Diffraction Patterns

The crystal structure of zirconium trichloride was determined from X-ray diffraction patterns. Zirconium trichloride belongs to the [Formula: see text]space group. The dimensions of the main cell at room temperature are: a = 5.961 ± 0.005 Å and c = 9.669 ± 0.005 Å.The density of zirconium trichloride was measured and gave the value of 2.281 ± 0.075 g/cm3 while, from the X-ray calculations, the value was found to be 2.205 g/cm3.

Sign in / Sign up

Export Citation Format

Share Document