Calculation methods for fluorescent x-ray spectrometry.  Empirical coefficients versus fundamental parameters

Criss, J. W.; Birks, L. S.

doi:10.1021/ac60263a023

Cited by 452 publications

(113 citation statements)

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“…However, the mass absorption coefficient (m m ) is a function of m divided by the material density, being a more useful value. [28][29][30] Equation 1 shows how FP is applied for a very thin sample excitation by monochromatic radiation, calculated by software DXP-700E (version 1.0).…”

Section: Fundamental Parameter Analysis Of Ash Samples To Determine Tmentioning

confidence: 99%

“…Nevertheless, FP presents a drawback related to the uncertainty in some values employed, such as mass absorption coefficients and fluorescence yields, aspects that can seriously impair the calculations, mainly if the sample under analysis is too complex. 30 Chemometrics or multivariate calibration is considered an important tool for analytical chemistry since it works only with non-correlated spectral variables having relevant information. The combination of XRF and multivariate calibration furnishes excellent solutions, as it can minimize or even eliminate analytical steps, mainly sample preparation.…”

Section: Introductionmentioning

confidence: 99%

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Fast direct determination of titanium dioxide in toothpastes by X-Ray fluorescence and multivariate calibration

Schwab¹,

Da-Col²,

Terra³

et al. 2012

J. Braz. Chem. Soc.

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Recentemente, o dióxido de titânio foi classificado como potencialmente carcinogênico pela International Agency for Research on Cancer (IARC). Dióxido de titânio é um pigmento geralmente utilizado como opacificante em cremes dentais, porém sua concentração não é indicada nos rótulos dos produtos. Neste estudo, 22 amostras de cremes dentais foram calcinadas a 800 ºC e o teor de TiO 2 foi determinado por fluorescência de raios X por energia dispersiva (EDXRF) através do método de parâmetros fundamentais (FP). As mesmas amostras foram irradiadas in natura por 100 s e, através da correlação dos espectros e das concentrações anteriormente determinadas, um modelo multivariado de calibração foi construído. Oito variáveis latentes descreveram o modelo de regressão de mínimos quadrados parciais (PLS) com erros médios de 9,5%, indicando que além do pico referente ao titânio, as informações do espalhamento da radiação também são importantes para minimizar os erros ao usar uma calibração univariada. A rapidez das análises, com mínimo pré-tratamento das amostras, é a grande vantagem do método, que tem frequência analítica de 24 determinações por hora.Recently, the International Agency for Research on Cancer (IARC) has classified titanium dioxide as potentially carcinogenic. Titanium dioxide is a pigment generally used as opacifying agent in toothpastes, but there is no indication of the percentage of this oxide in these products. In this work, 22 distinct toothpaste samples were calcinated at 800 °C and TiO 2 concentration was determined with energy dispersive X-Ray fluorescence (EDXRF) via fundamental parameter (FP) method. The same samples were irradiated in natura for 100 s and through the correlation of spectra and concentrations formerly determined, a multivariate calibration model was constructed. Eight latent variables described the partial least square regression (PLS) model with average errors of 9.5%, indicating that beyond the peak of titanium, the information of the X-Ray scattering irradiation is also important to minimize errors when using an univariate calibration. As a major advantage, the method allows analysis without pretreatment of the samples, with a throughput of 24 determinations per hour.Keywords: toothpaste, titanium dioxide, X-ray fluorescence, partial least square regression, chemometrics IntroductionAmong the common habits used for tooth conservation, the frequent use of dentifrices, mainly in the form of pastes, can be considered the most practiced. Before being presented as pastes, the first dentifrices were commercialized as powders in 1850, in the United States of America. 1 Toothpaste popularization occurred when it was presented in flexible metallic tubes. 2 Nowadays, the chemical composition of toothpastes varies from one brand to another, and even among several presentations of the same brand. They are composed by substances which act as abrasives, pigments, foam inducers, humectants, thickeners, stabilizers, solvents, sweeteners, therapeutic agents, enamel hardeners, etc. Other substances...

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Section: Fundamental Parameter Analysis Of Ash Samples To Determine Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast direct determination of titanium dioxide in toothpastes by X-Ray fluorescence and multivariate calibration

Schwab¹,

Da-Col²,

Terra³

et al. 2012

J. Braz. Chem. Soc.

View full text Add to dashboard Cite

show abstract

“…1967 Claisse and Quintin [7] (CQ): Generalization of the LT method for matrix effect corrections Introduce the weighting factor for each incident wavelength k Influence coefficients vary with concentrations 1968 Gilfrich and Birks [8]: the first measured incident spectrum Criss and Birks [9] The unification of all these XRF methods has led to a new fundamental method called the Fundamental Algorithm. As it stands, the Fundamental Algorithm contains all that is needed to calculate a sample composition from measured Xray intensities and also provides a complete and accurate correction for all matrix effects.…”

Section: (Lt)mentioning

confidence: 99%

The Quest for a Fundamental Algorithm in X-Ray Fluorescence Analysis and Calibration

Rousseau¹

2009

TOSPECJ

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Abstract:The Fundamental Algorithm between concentration (C i ) and intensity (R i ) in X-ray fluorescence analysis is deduced from Sherman's equation without any approximation. Its explicit expression is thus theoretically exact and it corrects completely for all matrix effects on the intensity R i emitted by the analyte i in a given specimen. This powerful algorithm combines the practical flexibility of the influence coefficient concept and the theoretical exactness of the Fundamental-Parameters method. In association with its innovative calibration procedure, the Fundamental Algorithm can be applied to the analysis of any sample type and offers maximum accuracy, limited only by the quality of sample preparation and the standards used.

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“…This analysis was first derived by Hamos (1945), and later discussed by Sherman (1954), Gillam & Heal (1952) and by Shiraiwa & Fujino (1966). However, it was not until Gilfrich & Birks (1968) determined the real spectral intensity distribution for W, Mo and Cr X-ray tubes that it was possible for Criss & Birks (1968) to calculate the exact fluorescence intensity for primary and secondary fluorescence due to polychromatic radiation. Recently, simplifications have been made in this type of analysis (Shen & Russ, 1977).…”

Section: Introductionmentioning

confidence: 98%

“…In this method, the composition, which may be represented as a vector, is related to the fluorescent intensities, which may also be represented as a vector, by a matrix that contains the influence coefficients. The composition of a specimen is then found from its fluorescent intensities after evaluating the influence coefficient matrix from empirical relationships (Beattie & Brissey, 1954;Birks, 1959) or from multiple regression analysis performed on the fluorescence data for standards of similar composition on the specimen (Alley & Myers, 1965;Mitchell & O'Hear, 1966;Criss & Birks, 1968). The time required to prepare standards and the errors associated with the empirical coefficients, however, limits this approach.…”

Section: Introductionmentioning

confidence: 99%

Determination of inter-element effects through Monte Carlo simulation of X-ray fluorescence

Fine¹,

Benitez-Garcia²

1979

J Appl Cryst

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A Monte Carlo model is developed to simulate the Xray fluorescence process within a homogeneous multielement mixture. Validation of the model is obtained through comparison of the model's predictions with experimental data for the iron-nickel-chromium system, for which the inter-element effects are severe. The results indicate that the Monte Carlo model is an excellent simulator and may be used in place of a set of standards to determine the influence coefficients for analysis of fluorescence data.

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Calculation methods for fluorescent x-ray spectrometry. Empirical coefficients versus fundamental parameters

Cited by 452 publications

References 21 publications

Fast direct determination of titanium dioxide in toothpastes by X-Ray fluorescence and multivariate calibration

Fast direct determination of titanium dioxide in toothpastes by X-Ray fluorescence and multivariate calibration

The Quest for a Fundamental Algorithm in X-Ray Fluorescence Analysis and Calibration

Determination of inter-element effects through Monte Carlo simulation of X-ray fluorescence

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