A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits

Downward, L.; Booth, C. H.; Lukens, Wayne W.; Bridges, F.

doi:10.1063/1.2644450

Cited by 121 publications

(136 citation statements)

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“…3 for Zn Li must decrease by the fraction on the Nb site. The fit does not want a peak at the expected position for Zn Nb and rapidly becomes poor if a significant fraction of the Zn is on the Nb site; fits can be achieved with up to 6-7 % of the Zn on Nb, by varying σ and allowing a rather large increase in r. However the goodness-of-fit parameter only increases slightly; although there are more parameters, by using the Hamilton F-test, 16 this peak is not significant. Thus 6-7 % of the Zn is much too large an estimate for a Nb site occupation.…”

Section: (Ms) Peaks (Zn-o-nb and Zn-o-o)mentioning

confidence: 99%

No difference in local structure about a Zn dopant for congruent and stoichiometricLiNbO3

2016

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We compare EXAFS (extended x-ray absorption fine structure) data at the Zn K edge for a low concentration of Zn (0.7 mol%) in a stoichiometric crystal with that for higher Zn concentrations (nominally 5 and 9 mol%) in congruent LiNbO3 (LNO). Note that stoichiometric and congruent LNO have significantly different optical properties. We find no significant difference in the local structure about Zn out to 4Å for the two types of crystals and different dopant levels. Although some earlier theoretical models suggest a self compensation model with 75 % of Zn on a Li site and 25 % Zn on Nb, we find no clear evidence for a significant fraction of Zn on the Nb site, and estimate at most 2-3 % of Zn might be Zn Nb .

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Section: (Ms) Peaks (Zn-o-nb and Zn-o-o)mentioning

confidence: 99%

No difference in local structure about a Zn dopant for congruent and stoichiometricLiNbO3

2016

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“…For each model system an R-factor is calculated by RSFIT. Finally, a confidence level, α, that the fit including the manganese scattering path is statistically better than the fit without it, is obtained using a modified F-Test [5,6,13]. The α values are calculated 1000 times for each combination of simulated files and k max .…”

Section: Simulation Methods and Resultsmentioning

confidence: 99%

“…In this way, all significant systematic error sources are eliminated in the simulated data. The structural model is then fit to the simulated data, decreasing the noise and increasing the k-range of the fit until the veracity of the model passes an F-test [5,6].…”

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Predetermining acceptable noise limits of EXAFS spectra in the limit of stochastic noise

Booth

2009

J. Phys.: Conf. Ser.

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Abstract.The effect of stochastic noise on Extended X-ray Absorption Fine Structure (EXAFS) data measurement, analysis, and fitting is discussed. Stochastic noise reduces the ability to uniquely fit a calculated model to measured EXAFS data. Such noise can be reduced by common methods that increase the signal-to-noise ratio; however, these methods are not always practical. Therefore, predetermined, quantitative knowledge of the level of acceptable stochastic noise when fitting for a particular model system is essential in maximizing the chances of a successful EXAFS experiment and minimizing wasted beamtime. This paper outlines a method to estimate, through simulation, the acceptable level of stochastic noise in EXAFS spectra that still allows a successful test of a proposed model compound.1. Introduction EXAFS measurements are used to probe a variety of experimental systems, but excel at elucidating local structure in samples which have slight disorder or no long-range crystalline order. Of special interest to the authors is the use of EXAFS in understanding the molecularlevel binding structure and characteristics of actinides on the surface of environmental minerals and model mineral analogs [1]. In environmental systems the element of interest can be on the order of 10 −7 % by weight of the total sample. Obviously such samples would be impossible to measure using EXAFS techniques. It is therefore essential to increase the concentration of the element of interest while still preserving a sample's ability to represent environmental conditions. Under such low concentration limits it is expected that the collected data is countrate, or stochastically limited. This condition occurs as we approach the signal-to-noise (S/N) limit of the technique where the random noise of the measurement process dominates over possible systematic errors [2,3]. When stochastic error is expected to dominate systematic error, it is possible to predict, with the use of simulations, the ability of model fits to tolerate a certain level of stochastic noise. Elsewhere in these proceedings, we discuss how to tell when systematic errors dominate in measured EXAFS spectrum [4].Here, we outline a technique for determining the number of EXAFS scans necessary to test the relevance of a given structural model. Appropriate stochastic noise levels are determined for each point in r-space by collecting data on a real system. These noise levels are then applied to EXAFS simulations using a test model. In this way, all significant systematic error sources

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“…This distance, however, is consistent with the presence of TcO 2 ·2H 2 O, and is attributed to the presence of residual Tc(IV) not incorporated into the goethite lattice in Sample 2. Downward et al (2006). (a) Goethite from Szytulstroka et al (1968).…”

Section: Xafs Analysis Of Tc In Tc-goethitementioning

confidence: 99%

Immobilization and Limited Reoxidation of Technetium-99 by Fe(II)-Goethite

Um¹,

Chang²,

Icenhower³

et al. 2010

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A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits

Cited by 121 publications

References 15 publications

No difference in local structure about a Zn dopant for congruent and stoichiometricLiNbO3

No difference in local structure about a Zn dopant for congruent and stoichiometricLiNbO3

Predetermining acceptable noise limits of EXAFS spectra in the limit of stochastic noise

Immobilization and Limited Reoxidation of Technetium-99 by Fe(II)-Goethite

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