Analytical method for observed powder diffraction intensity data based on maximum likelihood estimation

2013 ◽  
Vol 28 (2) ◽  
pp. 124-126 ◽  
Author(s):  
Takashi Ida ◽  
Fujio Izumi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Single Crystal ◽  
Powder Diffraction ◽  
Rietveld Method ◽  
Structure Refinement ◽  
Likelihood Estimation ◽  
New Method ◽  
Structure Parameters ◽  
Crystal Data

A new methodology based on maximum likelihood estimation for structure refinement using powder diffraction data is proposed. The method can not only optimize the parameters adjusted in Rietveld refinement but also parameters to specify errors in a model for statistical properties of the observed intensity. The results of structure refinements with relation to fluorapatite Ca5(PO4)3F, anglesite PbSO4, and barite BaSO4 are demonstrated. The structure parameters of fluorapatite and barite optimized by the new method are closer to single-crystal data than those optimized by the Rietveld method, while the structure parameters of anglesite, whose values optimized by the Rietveld method are already in good agreement with the single-crystal data, are almost unchanged by the application of the new method.

New Testifying Method of Unit Weight Mean Square Error of No-Equal Precision Independent Surveying Values

2012 ◽  
Vol 170-173 ◽  
pp. 2904-2907 ◽  
Author(s):  
Yong He Deng
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
New Method ◽  
Unit Weight ◽  
Mean Square ◽  
Maximum Likelihood Estimation Method

For unit weight mean square error of no-equal precision independent surveying values,this paper summed up several old estifying methods, pointed out their scarcities or mistakes, and advanced a sort of new method- maximum likelihood estimation method which is simple and strict.This is useful for theory of unit weight mean square error of no-equal precision independent surveying values to be perfect and for college surveying textbook to be improved and unified.

scholarly journals A New Online Calibration Method Based on Lord’s Bias-Correction

2017 ◽  
Vol 41 (6) ◽  
pp. 456-471 ◽  
Author(s):  
Yinhong He ◽  
Ping Chen ◽  
Yong Li ◽  
Shumei Zhang
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bias Correction ◽  
Likelihood Estimation ◽  
Calibration Method ◽  
New Method ◽  
Parameter Estimates ◽  
Item Calibration ◽  
Online Calibration ◽  
True Values

Online calibration technique has been widely employed to calibrate new items due to its advantages. Method A is the simplest online calibration method and has attracted many attentions from researchers recently. However, a key assumption of Method A is that it treats person-parameter estimates [Formula: see text] (obtained by maximum likelihood estimation [MLE]) as their true values [Formula: see text], thus the deviation of the estimated [Formula: see text] from their true values might yield inaccurate item calibration when the deviation is nonignorable. To improve the performance of Method A, a new method, MLE-LBCI-Method A, is proposed. This new method combines a modified Lord’s bias-correction method (named as maximum likelihood estimation-Lord’s bias-correction with iteration [MLE-LBCI]) with the original Method A in an effort to correct the deviation of [Formula: see text] which may adversely affect the item calibration precision. Two simulation studies were carried out to explore the performance of both MLE-LBCI and MLE-LBCI-Method A under several scenarios. Simulation results showed that MLE-LBCI could make a significant improvement over the ML ability estimates, and MLE-LBCI-Method A did outperform Method A in almost all experimental conditions.

Solving the Crystal Structure of Cd5(OH)8(NO3)2·2H2O from Powder Diffraction Data. A Comparison with Single Crystal Data

1991 ◽  
Vol 6 (1) ◽  
pp. 10-15 ◽  
Author(s):  
Patricia Bénard ◽  
Michèle Louër ◽  
Daniel Louër
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Method ◽  
Subsequent Treatment ◽  
Crystal Data ◽  
Powder Diffraction Data ◽  
Indexing Method ◽  
Parameter Values

AbstractA comparison between the results of ab initio structure determination from X-ray powder diffraction data of a new cadmium hydroxide nitrate, Cd5(OH)8 (NO3)2·2H2O (SG C2/m), and those obtained from single crystal data is presented. The powder diffraction pattern has been analysed by an indexing method and fitting techniques. A total of 119 unambiguously indexed reflections has been extracted and used in subsequent treatment. The power of powder techniques to index the pattern and to find the structure model by normal Patterson and Fourier methods is clearly shown. The refinement of approximate coordinates has been carried out by the Rietveld method (444 reflections). The comparison of results with those obtained from single crystal data (2218 reflections) shows that the precision of positional parameter values is lower by a factor of 10, on average, in the powder study. These results are discussed in terms of crystallographic parameters (number of reflections used, number of parameters to refine, contrast between atoms) and, also, in terms of sample dependent properties (preferred orientation effect, impurity). Finally, the crystal structure has been derived from powder data with a precision probably sufficient for most purposes.

Application of a theory for particle statistics to structure refinement from powder diffraction data

2011 ◽  
Vol 44 (5) ◽  
pp. 921-927 ◽  
Author(s):  
T. Ida ◽  
F. Izumi
Keyword(s):  
Crystal Structure ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Maximum Likelihood Method ◽  
Rietveld Method ◽  
Structure Refinement ◽  
Likelihood Method ◽  
Structure Parameters ◽  
Powder Diffraction Data ◽  
Particle Statistics

A new methodology is proposed for structure refinement using powder diffraction data, from which models for particle statistics and any other statistical errors can be formally optimized. This method is nothing but a straightforward implementation of the maximum-likelihood method, extended to the error estimation. Structure parameters refined by the method for fluorapatite [Ca5(PO4)3F], anglesite (PbSO4) and barite (BaSO4) become significantly closer to those obtained by single-crystal structure analyses in comparison with the results of the conventional Rietveld method.

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