Correction parameters in X-ray fluorescence analysis applying the limit dilution method (LDM)

Summary Some corrective parameters: H, M, Y and Y/H are defined from the mathematical development justifying the Limit Dilution Method (LDM) in XRF analysis. These corrective parameters, for a given diluent and dilution, are characteristic of the analyte in each sample. The influence of these parameters on important phenomena such as the diluent effect is evaluated by a theoretical model. Using parameters Y, an algorithm is proposed which corrects the diluent effect and establishes linear functions of fluorescence intensity vs. analyte concentration. This paper also proposes a selection procedure for the optimum standard for a given problem using the Y/H parameter. The method is applied to the XRF analysis of mixtures of iron and zirconium oxides and these results show the corrective action of the suggested parameters and the appropriateness of the selection of the standards.     

A new method of radioactivation analysis based on the quantitative isotope dilution principle

The simple quantitative isotope dilution method proposed, allows the errors due to flux fluctuation and self-shielding, normal to ordinary radioactivation analysis, to be avoided. Three different methods are discussed. The most satisfactory method from a theoretical viewpoint involves division of the irradiated sample into two parts; in one part, an amount m is extracted and the radioactivity a is measured. An amount of carrier M is added to the other part, an amount m is again extracted and its radioactivity a' is measured. The unknown amount M_x is then calculated from (a/a') I = M/Mx. A method for the determination of traces of copper and silver in metallic tin and zinc based on this principle is described.     

Evaluation of matrix effect in isotope dilution mass spectrometry based on quantitative analysis of chloramphenicol residues in milk powder

In the present study, we developed a comprehensive strategy to evaluate matrix effect (ME) and its impact on the results of isotope dilution mass spectrometry (IDMS) in analysis of chloramphenicol (CAP) residues in milk powder. Stable isotope-labeled internal standards do not always compensate ME, which brings the variation of the ratio (the peak area of analyte/the peak area of isotope). In our investigation, impact factors of this variation were studied in the extraction solution of milk powder using three mass spectrometers coupled with different ion source designs, and deuterium-labeled chloramphenicol (D5-CAP) was used as the internal standard. ME from mobile phases, sample solvents, pre-treatment methods, sample origins and instruments was evaluated, and its impact on the results of IDMS was assessed using the IDMS correction factor (θ). Our data showed that the impact of ME of mobile phase on the correction factor was significantly greater than that of sample solvent. Significant ion suppression and enhancement effects were observed in different pre-treated sample solutions. The IDMS correction factor in liquid–liquid extraction (LLE) and molecular imprinted polymer (MIP) extract with different instruments was greater or less 1.0, and the IDMS correction factor in hydrophilic lipophilic balance (HLB) and mix-mode cation exchange (MCX) extract with different instruments was all close to 1.0. To the instrument coupled with different ion source design, the impact of ME on IDMS quantitative results was significantly different, exhibiting a large deviation of 11.5%. Taken together, appropriate chromatographic conditions, pre-treatment methods and instruments were crucial to overcome ME and obtain reliable results, when IDMS methods were used in the quantitative analysis of trace target in complex sample matrix.     

Evaluation of the interelemental effect in X-ray fluorescence analysis by the total addition method

Summary An algorithm for quantifying interelemental effects in X-ray fluorescence techniques is developed. By applying an addition process, the ratio between the mass absorption coefficients of the analyte and the unknown sample ( _i ^* / _s ^* ) is calculated to correct the fluorescence intensity of the element to be determined and linearize the I-c calibration plot. This coefficient can be calculated graphically and numerically. The method is applied to the determination of tin in lead alloys with good results over wide concentration ranges.Notation used Q Constant of proportionality in Eq. (4) X-ray fluorescence intensity of the I _i ^o standard - I _i ^s unknown sample - I _i ^ns dilute unknown sample - I _i ^ms unknown sample after addition of i analyte Corrected fluorescence intensity of the I _i ^cs unknown sample - I _i ^msc unknown sample after addition of i analyte Relationship of fluorescence intensity between R_i sample and standard - R _i dilute sample and standard Factor of f_m addition - f_x addition equivalent to the mass fraction of the i analyte in the unknown sample Mass absorption coefficient of _i ^* analyte - _s ^* unknown sample - _ms ^* unknown sample after addition Mass fraction of c _i ^s analyte - c _i ^ms unknown sample after addition     

A rapid fluorescence based method for the quantitative analysis of cell culture media photo-degradation

Cell culture media are very complex chemical mixtures that are one of the most important aspects in biopharmaceutical manufacturing. The complex composition of many media leads to materials that are inherently unstable and of particular concern, is media photo-damage which can adversely affect cell culture performance. This can be significant particularly with small scale transparent bioreactors and media containers are used for process development or research. Chromatographic and/or mass spectrometry based analyses are often time-consuming and expensive for routine high-throughput media analysis particularly during scale up or development processes.     

A method for correction of matrix effects in activation analysis based on characteristic X-ray measurements

The empirical coefficient method represents the absorption and enhancement effect of each element on each other by parameters independent of mass concentrations. This method is used together with the internal standard method for the determination of cadmium, bromine and selenium by 14 MeV neutron activation followed by X-ray spectrometry. The results of analysis show a relative error not more than ±5%.     

Effect of the sample matrix on measurement uncertainty in X-ray fluorescence analysis

The estimation of measurement uncertainty, with reference to univariate calibration functions, is discussed in detail in the Eurachem Guide “Quantifying Uncertainty in Analytical Measurement”. The adoption of these recommendations to quantitative X-ray fluorescence analysis (XRF) involves basic problems which are above all due to the strong influence of the sample matrix on the analytical response. In XRF-analysis, the proposed recommendations are consequently applicable only to the matrix corrected response. The application is also restricted with regard to both the matrices and analyte concentrations.In this context the present studies are aimed at the problems to predict measurement uncertainty also with reference to more variable sample compositions. The corresponding investigations are focused on the use of the intensity of the Compton scattered tube line as an internal standard to assess the effect of the individual sample matrix on the analytical response relatively to a reference matrix. Based on this concept the estimation of the measurement uncertainty of an analyte presented in an unknown specimen can be predicted in consideration of the data obtained under defined matrix conditions.     

A novel algorithm for linear multivariate calibration based on the mixed model of samples

We present a novel algorithm for linear multivariate calibration that can generate good prediction results. This is accomplished by the idea of that testing samples are mixed by the calibration samples in proper proportion. The algorithm is based on the mixed model of samples and is therefore called MMS algorithm. With both theoretical support and analysis of two data sets, it is demonstrated that MMS algorithm produces lower prediction errors than partial least squares (PLS2) model, has similar prediction performance to PLS1. In the anti-interference test of background, MMS algorithm performs better than PLS2. At the condition of the lack of some component information, MMS algorithm shows better robustness than PLS2.     

Application of the powder dilution method to the analysis of various kinds of minerals and ores by energy-dispersive X-ray analysis

Summary It is shown that the powder dilution may be applied to the multielement analysis of any kind of silicatic and non-silicatic minerals and ores. The agreement of the results with those obtained by other methods is within ±2% for major constituents and up to ±10% for minor constituents in the concentration range >0.1%. The deviations may be higher for elements in the concentration range <0.1%. Advantages and disadvantages of the powder dilution method are discussed.

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Anwendung der Pulververdünnungsmethode für die Analyse verschiedenartiger Minerale und Erze durch energie-dispersive Röntgenanalyse

Zusammenfassung Es wird gezeigt, daß die Pulververdünnungsmethode für die Multielementanalyse aller Arten von silicatischen und nicht-silicatischen Mineralien und Erzen verwendet werden kann. Die Übereinstimmung der Ergebnisse mit solchen, die durch andere Methoden erhalten werden, liegt innerhalb von ±2% für Hauptbestandteile und bis zu ±10% für Nebenbestandteile im Konzentrationsbereich >0,1%. Die Abweichungen können größer sein für Elemente im Konzentrationsbereich <0,1%. Die Vorteile und Nachteile der Pulververdünnungsmethode werden diskutiert.

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We thank the Institute of Mineralogy of the Technische Hochschule Darmstadt for supplying the silicatic samples and the Bundesministerium für Forschung und Technologie for financial support.     

The error in absorption measurements caused by the use of non-monochromatic light-III Application to linear calibration curves

When in spectrophotometry the absorption is measured with non-monochromatic light, a curved calibration curve is often obtained. Some errors are introduced if a linear calibration curve is still used. The magnitude of these errors has been calculated.     

A correction method of matrix,density and thickness effects in thin samples analysed by X-ray fluorescence spectrometry

This paper deals with X-ray fluorescence spectrometry of powdered materials deposited on collection filters. The general applicability of this method is limited because the spectral response is affected by sample density and thickness and interelement effects may occur due to the specimen composition.The present work is aimed at contributing to the solution of the above mentioned problems, and reports a mathematical correction method which changes fluorescence intensity measurement data into fluorescence intensity values free from density and thickness effects. The correction of the thickness effect was obtained by overlapping the powder sample with a standard pellet containing some reference elements.The method allows the evaluation of the thickness of the unknown samples by measuring the intensity decrease of the X-ray fluorescence radiation coming from the reference pellet and passing through the unknown sample. These data are used to correct the intensity fluorescence values of the unknown samples.A computer program to elaborate spectral data by means of different and selected mathematical algorithms was set up.     

Matrix effect on the detection limit and accuracy in total reflection X-ray fluorescence analysis of trace elements in environmental and biological samples

The effect of matrix contents on the detection limit of total reflection X-ray fluorescence analysis was experimentally investigated using a set of multielement standard solutions (500 ng/mL of each element) in variable concentrations of NH₄NO₃. It was found that high matrix concentration, i.e. 0.1–10% NH₄NO₃, had a strong effect on the detection limits for all investigated elements, whereas no effect was observed at lower matrix concentration, i.e. 0–0.1% NH₄NO₃.     

A taylor series model to evaluate the interelemental effects in X-ray fluorescence analysis, applied to the iron-zirconium-diluent system

A semi-empirical model has been developed to quantify the interelemental effects in X-ray fluorescence analysis. The measured X-ray fluorescence intensity has been expressed as a function of the different fluorescence elements composing the sample. this complex function has become an operative function via a Taylor series development. An explication has been given for the significance of the different terms of the series. These terms respond to mathematical functions known as characteristic functions for each chemical system. A parameter (B) has been defined which makes it possible to quantify the influence of the interelemental effect as a function of the analyte concentration (C) and that of the concomitant elements. The proposed model has been applied to the Fe-Zr-diluent chemical system. Simple relationships between B vs C have been obtained independently considering iron or zirconium as analyte.     

The maintenance of the second-order advantage: second-order calibration of excitation-emission matrix fluorescence for quantitative analysis of herbicide napropamide in various environmental samples

A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L⁻¹ sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL⁻¹, respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices.     

Application of a method for matrix correction using compton-scattering for the quantitative determination of metals in silica by wavelength dispersive X-ray fluorescence spectroscopy (WDXRF)

Summary A correction method to diminish errors caused by different mass absorption coefficients of the samples is described. Also errors caused by differing device parameters are diminished. The method is used for the determination of Fe, Cr, Ni, Co, Mn, Zn, Cd, Cu, Hg and Pb on chemically modified silica in the g/g-range.

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Anwendung einer Methode zur Matrixkorrektur durch Compton-Streupeaks für die quantitative Bestimmung von Metallen in Kieselgelen mit Hilfe der wellenlängendispersiven Röntgenfluorescenzanalyse (WDXRF)

Zusammenfassung Ein Korrekturverfahren zur Verminderung von Meßfehlern, die durch unterschiedliche Massenabsorptionskoeffizienten der Proben verursacht werden, wird beschrieben. Ebenso werden Fehler durch Schwankungen von Geräteparametern verringert. Die Methode wird benutzt zur Bestimmung von Fe, Cr, Ni, Cd, Co, Mn, Zn, Cu, Hg und Pb auf chemisch modifizierten Kieselgelen im g/g-Bereich.

     

Application of a crystallization kinetics model to simulate the effect of operation conditions on Crystaf profiles and calibration curves

Crystallization analysis fractionation (Crystaf) is a polymer characterization technique used to estimate chemical composition distributions (CCDs) of semicrystalline copolymers. The Crystaf profile can be transformed into a CCD using a calibration curve that relates average comonomer content to peak crystallization temperature. The calibration curve depends on copolymer molecular properties and Crystaf operation conditions. In this investigation, we applied a crystallization kinetics model to simulate Crystaf calibration curves and to quantify how Crystaf calibration curves depend on these factors. We applied the model to estimate the CCDs of three ethylene/1‐hexene copolymers from Crystaf profiles measured at different cooling rates and showed that our predictions agree well with the CCDs described by Stockmayer's distribution. We have also used this new methodology to investigate the effects of cooling rate, molecular weight, and comonomer type on Crystaf profiles and calibration curves. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 866–876, 2009     

Multivariate analysis to separate the signal given by cross-reactants in immunoassay with sample matrix dilution

This paper describes a new approach to achieve selectivity in an immunoassay by separating the signals given by two cross-reactive compounds present simultaneously in a complex sample matrix. The method is based on the sequential dilution of the sample containing a mixture of the two analytes, spiking each diluted sample with a reference compound, and the detection by enzyme-linked immunosorbent assay (ELISA). The obtained multivariate response was used for the individual calibrations of the assay for each of the two cross-reactants simultaneously by using principal component analysis (PCA) and partial least squares regression (PLSR) data modeling. The calibration models showed that the signal separation due the analytes 2,4-dinitrophenol (2,4-DNP) and 4-nitrophenol (4-NP) was possible with a prediction concentration error of 1.4 M and 72 M, respectively.     

A novel method for the determination of iodide in table salt by X-ray fluorescence

A novel HI generation technique was developed and evaluated for the determination of iodide in table salt. HI was generated from the samples by the addition of concentrated sulfuric acid and adsorbed onto an ion-exchange resin loaded paper disk. The disk was then measured by X-ray fluorescence. The method compared favorably to the cellulose pellet technique, being more sensitive and reproducible and requiring less time per analysis. The method was applied to six samples of table salt and one of sea salt.     

The method of concentration-dependent distribution in the quantitative use of radioisotopes : Theoretical calibration curves and comparison to the “substoichiometric principle”

The method is based on the utilization of a calibration curve which shows the dependence of the distribution ratio in a two-phase system containing the substance to be determined or a substance reacting with it, on the total concentration of the substance to be determined. The relationship of the proposed method to radiometric titration and to the “substoichiometric principle” in isotopic dilution is discussed. Formulae for the theoretical calibration curves in 4 systems are derived: sorption conforming to the Langmuir isotherm or to the Freundlich isotherm, extraction with a constant quantity of an extracting agent, and sorption or extraction in the presence of a constant quantity of a chelating agent. Theoretical sensitivities are given.     

Determination of nickel,gold and silver in gallium arsenide by radioactivation analysis based on the quantitative isotope dilution principle

A method of radioactivation analysis has been developed for the determination of Ni, Au and Ag impurities in gallium arsenide. The separation and substoichiometric extraction of these elements were studied and analytical procedures are suggested for their determination. All components are separated by suitable procedures and determined by substoichiometric methods. Ni is extracted as diethyldithiocarbamate into toluene, Au as a complex of rhodamine-B in chloroform, and Ag as dithizonate in carbon tetrachloride. The contents of Ni, Au and Ag in a gallium arsenide crystal with a carrier concentration of 1.8·10¹⁶/cm³ were 0.05–0.08, 0.006–0.008 and 0.002–0.005 ppm, respectively.