Quantitative elemental analysis of individual particles with the use of micro‐beam X‐ray fluorescence method and Monte Carlo simulation

Czyzycki, Mateusz; Bielewski, Marek; Lankosz, M.

doi:10.1002/xrs.1203

Cited by 8 publications

(7 citation statements)

References 20 publications

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“…This then allows calculation of very many resulting X-ray fluorescence spectra by Monte Carlo simulation and statistical conclusions about the obtained spectral population can be made. See an example in Czyzycki et al [72].…”

Section: Fundamental Modelsmentioning

confidence: 97%

Principles of Proper Validation: use and abuse of re‐sampling for validation

Esbensen¹,

Geladi

2010

Journal of Chemometrics

239

176

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Validation in chemometrics is presented using the exemplar context of multivariate calibration/prediction. A phenomenological analysis of common validation practices in data analysis and chemometrics leads to formulation of a set of generic Principles of Proper Validation (PPV), which is based on a set of characterizing distinctions: (i) Validation cannot be understood by focusing on the methods of validation only; validation must be based on full knowledge of the underlying definitions, objectives, methods, effects and consequences-which are all outlined and discussed here. (ii) Analysis of proper validation objectives implies that there is one valid paradigm only: test set validation. (iii) Contrary to much contemporary chemometric practices (and validation myths), cross-validation is shown to be unjustified in the form of monolithic application of a one-for-all procedure (segmented cross-validation) on all data sets. Within its own design and scope, cross-validation is in reality a sub-optimal simulation of test set validation, crippled by a critical sampling variance omission, as it manifestly is based on one data set only (training data set). Other re-sampling validation methods are shown to suffer from the same deficiencies. The PPV are universal and can be applied to all situations in which the assessment of performance is desired: prediction-, classification-, time series forecasting-, modeling validation. The key element of PPV is the Theory of Sampling (TOS), which allow insight into all variance generating factors, especially the so-called incorrect sampling errors, which, if not properly eliminated, are responsible for a fatal inconstant sampling bias, for which no statistical correction is possible. In the light of TOS it is shown how a second data set (test set, validation set) is critically necessary for the inclusion of the sampling errors incurred in all 'future' situations in which the validated model must perform. Logically, therefore, all one data set re-sampling approaches for validation, especially cross-validation and leverage-corrected validation, should be terminated, or at the very least used only with full scientific understanding and disclosure of their detrimental variance omissions and consequences. Regarding PLS-regression, an emphatic call is made for stringent commitment to test set validation based on graphical inspection of pertinent t-u plots for optimal understanding of the X-Y interrelationships and for validation guidance. QSAR/QSAP forms a partial exemption from the present test set imperative with no generalization potential.

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Section: Fundamental Modelsmentioning

confidence: 97%

Principles of Proper Validation: use and abuse of re‐sampling for validation

Esbensen¹,

Geladi

2010

Journal of Chemometrics

239

176

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“…The chemical composition and the thickness of layers can be reconstructed with this code by the deconvolution of depth‐sensitive profiles recorded experimentally. (Previous edition of the MC code was devoted for the quantification of individual particles examined by conventional μXRF.) All tabular data, including, for example, interaction cross sections, radiative transition probabilities and fluorescence yields, necessary to simulate the spectrum of the secondary radiation of an irradiated specimen, were taken from the xraylib library …”

Section: Quantificationmentioning

confidence: 99%

The perspective of new multi‐layer reference materials for confocal 3D micro X‐ray fluorescence spectroscopy

Czyzycki

Wróbel

Szczerbowska-Boruchowska

et al. 2012

X-Ray Spectrometry

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Multi‐layered components are commonly used in hi‐tech branches of modern industry. This fact generates a need for suitable reference materials for experimental examination of such specimens, and it also induces the development of mathematical procedures for quantification. To reveal experimentally the chemical composition of (multi‐)layered specimens in 3D space in a non‐destructive way, a confocal 3D micro X‐ray fluorescence spectroscopy (3D μXRF) can be employed. The scope of this paper covers preparation, preliminary experimental examination and quantification of new, multi‐layer stack systems as the perspective of reference materials to be used in 3D μXRF spectroscopy. The prepared stacks consist of nine individual layers based on a low‐Z organic matrix loaded alternately with Cu2O and ZnO oxides. The stacks are characterized by the homogeneous areal distribution of inorganic fillers and the constant thickness of distinguishable layers to the extent of millimeters. A Monte Carlo (MC) simulation was used to reconstruct the chemical composition, mass density and thickness of individual layers within the stacks. Results of the simulation accurately reflected the nominal mass shares of fillers and the thickness of layers additionally determined by optical microscopy and 2D μXRF scanning. The prepared stack systems seem to be suitable materials for the validation of mathematical procedures for the quantification of multi‐layer specimens examined by depth‐sensitive X‐ray techniques. Copyright © 2012 John Wiley & Sons, Ltd.

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“…1. A variance reduction technique [27] was applied. The simulation starts with the selection of a photon in the incident beam and the position of the interaction point in the sample.…”

Section: Quantificationmentioning

confidence: 99%

“…In this work, a new MC simulation code for the determination of chemical composition and thickness of individual layers in stratified materials with the use of confocal 3D µXRF spectroscopy was developed. Previous edition of the MC simulation code, [27] predicting a complete spectral response of individual particles measured by conventional µXRF spectrometer, was adapted to solve 3D µXRF problem for stratified materials. The investigated samples were scanned in depth to obtain profiles of X-ray fluorescence intensity of elements.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo simulation code for confocal 3D micro‐beam X‐ray fluorescence analysis of stratified materials

et al. 2011

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Stratified materials are of great importance for many branches of modern industry, e.g. electronics or optics and for biomedical applications. Examination of chemical composition of individual layers and determination of their thickness helps to get information on their properties and function. A confocal 3D micro X-ray fluorescence (3D µXRF) spectroscopy is an analytical method giving the possibility to investigate 3D distribution of chemical elements in a sample with spatial resolution in the micrometer regime in a non-destructive way. Thin foils of Ti, Cu and Au, a bulk sample of Cu and a three-layered sandwich sample, made of two thin Fe/Ni alloy foils, separated by polypropylene, were used as test samples. A Monte Carlo (MC) simulation code for the determination of elemental concentrations and thickness of individual layers in stratified materials with the use of confocal 3D µXRF spectroscopy was developed. The X-ray intensity profiles versus the depth below surface, obtained from 3D µXRF experiments, MC simulation and an analytical approach were compared. Correlation coefficients between experimental versus simulated, and experimental versus analytical model X-ray profiles were calculated. The correlation coefficients were comparable for both methods and exceeded 99%. The experimental X-ray intensity profiles were deconvoluted with iterative MC simulation and by using analytical expression. The MC method produced slightly more accurate elemental concentrations and thickness of successive layers as compared to the results of the analytical approach. This MC code is a robust tool for simulation of scanning confocal 3D µXRF experiments on stratified materials and for quantitative interpretation of experimental results.

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Quantitative elemental analysis of individual particles with the use of micro‐beam X‐ray fluorescence method and Monte Carlo simulation

Cited by 8 publications

References 20 publications

Principles of Proper Validation: use and abuse of re‐sampling for validation

Principles of Proper Validation: use and abuse of re‐sampling for validation

The perspective of new multi‐layer reference materials for confocal 3D micro X‐ray fluorescence spectroscopy

Monte Carlo simulation code for confocal 3D micro‐beam X‐ray fluorescence analysis of stratified materials

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