Calibration in a closed system: the case of X-ray diffraction analysis

2007 ◽  
Vol 40 (4) ◽  
pp. 694-701
Author(s):  
Thaung Lwin
Keyword(s):  
Diffraction Analysis ◽  
Least Squares ◽  
Functional Relationship ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
X Ray Diffraction ◽  
Unknown Parameters ◽  
X Ray ◽  
Relationship Model ◽  
Least Squares Approach

Knudsen [X-ray Spectrom.(1981),10, 54–561] proposed and demonstrated a least-squares approach to estimating the unknown parameters of a system of equations required for calibration in X-ray diffraction analysis. The approach is an ordinary least-squares approach which does not incorporate information on the errors of the measured intensities for a set of samples used as standards. The purpose of the present paper is to show that a functional relationship model can be applied to the problem to account for all the variation due to sampling and measurement error in the peak intensities. It is also shown that Knudsen's calibration estimator can be regarded as an approximation to a more general and potentially more efficient weighted least-squares estimator derived from the functional relationship model. The closeness of the approximation depends on the nature of the covariance structure of the intensity measurements.

THE CRYSTAL STRUCTURE OF K2TeBr6

1964 ◽  
Vol 42 (12) ◽  
pp. 2758-2767 ◽  
Author(s):  
I. D. Brown
Keyword(s):  
Crystal Structure ◽  
Diffraction Analysis ◽  
Least Squares ◽  
Three Dimensional ◽  
Monoclinic Space Group ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Cubic Form ◽  
Efficient Packing

Crystals of K2TeBr6 are monoclinic, space group [Formula: see text] with a = 7.521, b = 7.574, and c = 10.730 Å; β = 89° 40′. Atomic positions have been found by three dimensional X-ray diffraction analysis (least squares R = 0.12). The crystals possess a K2PtCl6 structure which is distorted to allow a more efficient packing of the comparatively large anions than is possible with the undistorted cubic form. The stereochemistry of the octahedral TeBr6− ion (Te—Br = 2.71 Å) is discussed.

Revisiting the Rius’ Standardless Method for the Quantitative X-Ray Diffraction Analysis of Mixtures of Inorganic Crystalline Phases

MRS Advances ◽  
2019 ◽  
Vol 4 (57-58) ◽  
pp. 3163-3169
Author(s):  
J. López-Cuevas ◽  
J.C. Rendón-Angeles ◽  
J.L. Rodríguez-Galicia ◽  
C.A. Gutiérrez-Chavarría
Keyword(s):  
Chemical Composition ◽  
Diffraction Analysis ◽  
Least Squares ◽  
General Expression ◽  
X Ray Diffraction ◽  
Crystalline Phases ◽  
X Ray ◽  
Pure Phases ◽  
Integrated Intensities

ABSTRACTAn alternative method for the standardless quantitative x-ray diffraction analysis of mixtures of inorganic crystalline phases proposed in the literature several years ago is presented. Our method requires only previously calculated μ*i values from tabulated data for all phases present in the mixtures. It does not require either the determination of calibration constants or the use of external standards, but it does require that the number of analyzed mixtures is larger than or equal to the number of phases present in them, and that the chemical composition of the mixtures are significantly different from each other. The integrated intensities of the chemically pure phases are estimated by a least-squares procedure from XRD data obtained from the mixtures. The method was tested against data published in the literature, with good results. Finally, a general expression for the “Normalized Height Law” proposed on an empirical basis by other researchers, has been theoretically derived.

scholarly journals Bayesian and Classical Estimation for the One Parameter Double Lindley Model

2020 ◽  
pp. 409-420 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Wahhab Mohammed ◽  
Haitham M. Yousof
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Weighted Least Squares Method ◽  
Von Mises ◽  
New Distribution

The main motivation of this paper is to show how the different frequentist estimators of the new distribution perform for different sample sizes and different parameter values and to raise a guideline in choosing the best estimation method for the new model. The unknown parameters of the new distribution are estimated using the maximum likelihood method, ordinary least squares method, weighted least squares method, Cramer-Von-Mises method and Bayesian method. The obtained estimators are compared using Markov Chain Monte Carlo simulations and we observed that Bayesian estimators are more efficient compared to other the estimators.

scholarly journals AutoCal: A software application for calibrating photometric data

2016 ◽  
Vol Volume 112 (Number 3/4) ◽  
Author(s):  
Daniël J. Wium ◽  
Brian van Soelen ◽  
◽  
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Magellanic Cloud ◽  
Photometric Data ◽  
Field Of View ◽  
Small Magellanic Cloud ◽  
Outlier Removal ◽  
X Ray ◽  
Software Application ◽  
Least Squares Approach

Abstract We present a software application for the calibration of stellar magnitudes in the absence of standard stars. It uses an existing algorithm to match stars in the target’s field of view to catalogue entries and computes the average offset between the two sets of magnitudes using a weighted least-squares approach. This offset is used to calibrate the target’s instrumental magnitude. The software application was used to calibrate magnitudes for six Be/X-ray binary sources in the Small Magellanic Cloud and the results were compared with published results for these sources. Where comparisons were possible, our results agreed with those results within the uncertainties specified. Infrared variability was found for all six of the sources tested. The interactive outlier removal that was made possible by our software allowed for smaller uncertainties to be reported for our results.

Ten-Vertex Polyhedral Monocarbaborane Chemistry. The Novel High-Yield Formation of the Ten-Vertex closo Compound [6-(PMe2Ph)-closo-1-CB9H9] from the Thermolysis of [8,8-(PMe2Ph)2-nido-8,7-PtCB9H11]

1993 ◽  
Vol 58 (12) ◽  
pp. 2924-2935 ◽  
Author(s):  
Jane H. Jones ◽  
Bohumil Štíbr ◽  
John D. Kennedy ◽  
Mark Thornton-Pett
Keyword(s):  
Nmr Spectroscopy ◽  
Diffraction Analysis ◽  
High Yield ◽  
Monoclinic Space Group ◽  
The Novel ◽  
X Ray Diffraction ◽  
Metal Centre ◽  
X Ray ◽  
Yield Formation ◽  
Boiling Toluene

Thermolysis of [8,8-(PMe2Ph)2-nido-8,7-PtCB9H11] in boiling toluene solution results in an elimination of the platinum centre and cluster closure to give the ten-vertex closo species [6-(PMe2Ph)-closo-1-CB9H9] in 85% yield as a colourles air stable solid. The product is characterized by NMR spectroscopy and single-crystal X-ray diffraction analysis. Crystals (from hexane-dichloromethane) are monoclinic, space group P21/c, with a = 903.20(9), b = 1 481.86(11), c = 2 320.0(2) pm, β = 97.860(7)° and Z = 8, and the structure has been refined to R(Rw) = 0.045(0.051) for 3 281 observed reflections with Fo > 2.0σ(Fo). The clean high-yield elimination of a metal centre from a polyhedral metallaborane or metallaheteroborane species is very rare.

Bis(μ-carboxylato)dienerhodium(I) Complexes - Synthesis, Characterization and Catalytic Activity

2008 ◽  
Vol 73 (8-9) ◽  
pp. 1205-1221 ◽  
Author(s):  
Jiří Zedník ◽  
Jan Sedláček ◽  
Jan Svoboda ◽  
Jiří Vohlídal ◽  
Dmitrij Bondarev ◽  
...  
Keyword(s):  
Catalytic Activity ◽  
Diffraction Analysis ◽  
Spectroscopic Methods ◽  
X Ray Diffraction ◽  
X Ray

Dinuclear rhodium(I) η2:η2-cycloocta-1,5-diene (series a) and η2:η2-norborna-2,5-diene (series b) complexes with μ-RCOO- ligands, where R is linear C21H43 (complexes 1a, 1b), CH2CMe3 (2a, 2b), 1-adamantyl (3a, 3b) and benzyl (4a, 4b), have been prepared and characterized by spectroscopic methods. Structures of complexes 2b, 3a and 4a were determined by X-ray diffraction analysis. Complexes prepared show low to moderate catalytic activity in polymerization of phenylacetylene in THF giving high-cis-transoid polymers, but they show only oligomerization activity in dichloromethane.

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