Substitution–dilution method to correct the matrix effect in multi-element quantitative analysis by X-ray fluorescence

A mathematical model based on the dilution–addition method (DAM) for multi-elemental analysis using an X-ray fluorescence technique is proposed. The conditions for sample preparation do not require both the unknown and standard samples to be similar in composition and mineralogy, and the unknown sample is replaced quantitatively by the standard sample, hence the denomination substitution–dilution method (SDM). This method makes it possible to correct the matrix effect in multi-elemental quantitative analysis by X-ray fluorescence for each analyte. The proposed model presents hyperbolic behaviour of the experimental data when the X-ray fluorescence intensities are represented versus the substitution factor (h) for each analyte. After calculating the A/B parameter relations, which depend on the X-ray fluorescence intensity of each analyte (I_i^ns) and the substitution factor (h) and determining the analyte concentration in the multi-element standard sample (C_i^p), it is possible to calculate the analyte concentration in the multi-element unknown using an algorithm suggested for this purpose. This work studies the substitution–dilution phase proposed in the method, and the factors arising from incorporation of the standard and diluent are established according to the nature of the samples and the modifications. These factors make it possible to establish the experimental interval of analyte concentration, generally narrow, which corresponds to a section of the hyperbolic function which is so short that it can be accepted as linear. This linear model can be accepted for a wide variety of samples with a diluent/sample ratio greater than 10. The proposed linear method provides satisfactory results which are comparable to those calculated by applying the hyperbolic method. The proposed method (SDM) has been applied to two different types of matrices, a binary alloy (without diluent, using the hyperbolic model) and a geological sample (with diluent, using both hyperbolic and linear models). In all cases the results were satisfactory.     

Determination of the Ta and Nb ratio in LiNb1−xTaxO3 by total reflection X-ray fluorescence spectrometry

A procedure for evaluation of the mass ratio between Ta and Nb in LiNb_1−xTa_xO₃ single crystals by total reflection X-ray fluorescence spectrometry (TXRF) is described. The developed procedure does not require chemical preparation of the samples and it proves to be fast (30 min for sample preparation and 10 min for analysis), precise (down 1% RSD) and easy to perform. To check the methodology, the lattice parameter of each LiNb_1−xTa_xO₃ sample was determined by powder X-ray diffraction. While the a hexagonal lattice parameter remains constant, a strong and linear dependence of the c hexagonal lattice parameter with Ta content in molar percentage has been observed for the first time.     

Influence of the distance between a spectrometer and sample on the intensity of X-ray fluorescence

Expressions for calculating the extreme point coordinates of focal spots of X-ray tubes and a detector’s sensitive area are found. These coordinates are used in calculations of the sample area. The dependence of the X-ray fluorescence intensity on the distance between a spectrometer and an analyzed sample is studied experimentally. The intensities of the FeK _α spectral lines in iron-containing materials are calculated at different geometric parameters of a spectrometer. It is found that the distance between a sample and detector at which the maximum of the measured intensity is observed depends on the size and position of the detector and X-ray tube collimators, as well as on the relative position of the X-ray tube and detector. Recommendations on how to achieve the maximum intensity of X-ray fluorescence are proposed. The results of the present work can be used for the development of X-ray fluorescence analysis techniques applicable for free-flowing materials directly in technological processes.     

A mathematical model based on the limit dilution method to obtain linear calibration curves which eliminate the matrix effect in quantitative analysis by X-ray fluorescence

We propose a mathematical model from an analytical application viewpoint inspired in the limit dilution method. The theoretical development of the model and its results are given. The model shows that there is a linear relation between the inverse of fluorescence intensity and the inverse of the dilution factor; each analytic system (sample, diluent and analyte) is characterised by a general linear function which is easily obtained. The analytical applications arising from this linearity are of great importance in X-ray fluorescence analysis. The following immediate applications are proposed: direct procurement of the total correction factor Y/H, rapid calculation of the fluorescence intensity of the analyte in a sample (I_i^s) and direct calculation of the corrected fluorescence intensity (I_i^sF). The suggested model makes it possible to deduce a linear function between the fluorescence intensity of the analyte and the analyte concentration in successive dilutions of a standard; this straight line behaves as a calibration curve with direct application in X-ray fluorescence analysis. The proposed model may be applied to complex samples of geological origin, with elimination of the matrix effect. The results obtained in the determination of Ca, K, Fe and Ti in a standard soil show complete agreement with the certified reference values with a relative error about 0.5%, even using a standard shale with very different chemical composition as reference sample.     

An alternative version of X-ray fluorescence analysis

Publications on a version of X-ray fluorescence analysis (XFA) based on new principles are considered. Limitations on the sample sizes, shapes, and the quality of surfaces are excluded. The sample preparation of emitters is performed on polishing papers. The thin layers of materials are analyzed. The ratio between the spectral line intensities of the pairs of components is an analytical signal. A formula and a procedure for calculating the composition from the measured intensity ratios and the relative intensity coefficients of the pairs of components, which are independent of the sample composition, are given. The dependence of spectral line intensities on the atomic rather than weight concentrations of components is shown. The developed version of XFA excludes the need for the knowledge of a primary spectrum and the application of corrections for matrix effects. The examples of the analyses of multicomponent nonferrous alloys, steels, and powders are considered. The analytical characteristics of standard XFA and alternative XFA (AXFA) are compared.     

Energy dispersive X-Ray fluorescence determination of thorium in phosphoric acid solutions

Energy dispersive X-ray fluorescence studies on determination of thorium (in the range of 7 to 137 mg/mL) in phosphoric acid solutions obtained by dissolution of thoria in autoclave were made. Fixed amounts of Y internal standard solutions, after dilution with equal amount of phosphoric acid, were added to the calibration as well as sample solutions. Solution aliquots of approximately 2–5 µL were deposited on thick absorbent sheets to absorb the solutions and the sheets were presented for energy dispersive X-ray fluorescence measurements. A calibration plot was made between intensity ratios (Th Lα/Y Kα) against respective amounts of thorium in the calibration solutions. Thorium amounts in phosphoric acid samples were determined using their energy dispersive X-ray fluorescence spectra and the above calibration plot. The energy dispersive X-ray fluorescence results, thus obtained, were compared with the corresponding gamma ray spectrometry results and were found to be within average deviation of 2.6% from the respective gamma ray spectrometry values. The average precision obtained in energy dispersive X-ray fluorescence determinations was found to be 4% (1σ). The energy dispersive X-ray fluorescence method has an advantage over gamma ray spectrometry for thorium determination as the amount of sample required and measurement time is far less compared to that required in gamma ray spectrometry.     

X-ray fluorescence imaging with polycapillary X-ray optics

X-ray fluorescence spectrometry imaging is a powerful tool to provide information about the chemical composition and elemental distribution of a specimen. X-ray fluorescence spectrometry images were conventionally obtained by using a μ-X-ray fluorescence spectrometry spectrometer, which requires scanning a sample. Faster X-ray fluorescence spectrometry imaging would be achieved by eliminating the process of sample scanning. Thus, we developed an X-ray fluorescence spectrometry imaging instrument without sample scanning by using polycapillary X-ray optics, which had energy filter characteristics caused by the energy dependence of the total reflection phenomenon. In the present paper, we show that two independent straight polycapillary X-ray optics could be used as an energy filter of X-rays for X-ray fluorescence. Only low energy X-rays were detected when the angle between the two optical axes was increased slightly. Energy-selective X-ray fluorescence spectrometry images with projection mode were taken by using an X-ray CCD camera equipped with two polycapillary optics. It was shown that Fe Kα (6.40 keV) and Cu Kα (8.04 keV) could be discriminated for Fe and Cu foils.     

粉末压片-X-射线荧光光谱法分析砂岩型铀矿制样中粘结剂用量的探讨

由于砂岩型铀矿的成矿特性,样品粉末的内聚力小,采用直接压片法有时难以成型,样片表面常见裂纹,上机测量易碎裂。混合压片法适应性强,制样成功率高,但常见的问题是样品经粘结剂稀释会影响元素的检出限及结果的准确性。本文对粉末压片-X射线荧光光谱法测定砂岩型铀矿地质样品时,前期制样中添加粘结剂的比例进行了研究。试验按照不同比例在铀矿石标准物质GBW04101、GBW04102中添加粘结剂,在扫描电镜下观察到随着粘结剂用量的增加样片表面的光滑度及致密度都呈上升趋势,在X-射线荧光光谱仪上对主量元素进行测定后发现X射线强度在粘结剂添加量大于0.2 g时明显下降,经与GBW04101、GBW04102标准值进行对比后优选出粘结剂与样品的最佳比例为1：20,在此比例下制成的样片光滑平整,不易碎裂,用粉末压片-X射线荧光光谱法进行测定,标准物质测定结果的相对误差为0.56%～6.76 %,相对标准偏差(RSD,n=12)为0.013 %～7.68 %,均达到了《地质矿产实验室测试质量管理规范》DZ/T 0130-2006的要求。本文为粉末压片-X射线荧光光谱法分析砂岩型铀矿地质样品提供了可靠的实验参考依据。     

The use of the ratios of intensities of spectral lines for X-ray fluorescence analysis of metal alloys and oxide materials

An X-ray fluorescence analysis technique is proposed, which is based on using ratios of intensities of spectral lines. The technique includes performing calculations for evaluation of calibration equations, which allows using few reference samples or carrying out standardless analysis, if necessary. That parameters of the calibration equations depend linearly on concentrations of disturbing elements allows one to simplify taking their influence into account. To apply the developed technique to analysis of samples containing a significant amount of undetectable light elements, a use of a dependence of intensity ratio of the characteristic radiation of the X-ray tube’s anode, coherently and incoherently scattered by a sample, on a total content of undetectable elements is proposed. The technique’s adequacy is demonstrated by analysis of standard steel samples, metal cuttings and iron-ore materials.     

Method for improving the accuracy of continuous X-ray fluorescence analysis of iron ore mixtures

The dependence of the intensity of X-ray fluorescence on the distance between the spectrometer and the test sample is studied. Changes in the intensity of primary X-radiation, absorption of X-rays by the air, and surface area of the analyzed material are calculated. An efficient method is proposed for improving the accuracy of continuous X-ray fluorescence analysis of iron ore mixtures on the conveyor belt through the exclusion of incorrect results by the dead time of the detection unit. The proposed method is universal and can be used for various loose materials.     

Analysis of nuclear materials by energy dispersive X-ray fluorescence and spectral effects of alpha decay

Energy dispersive X-ray fluorescence (EDXRF) spectra collected from alpha emitters are complicated by artifacts inherent to the alpha decay process, particularly when using portable instruments. For example, ²³⁹Pu EDXRF spectra exhibit a prominent uranium L X-ray emission peak series due to sample alpha decay rather than source-induced X-ray fluorescence. A portable EDXRF instrument was used to collect qualitative spectra from plutonium and americium, and metal alloy identification was performed on a Pu-contaminated steel sample. Significant alpha decay-induced X-ray fluorescence peaks were observed in spectra obtained from the plutonium and americium samples due to the ²³⁵U and ²³⁷Np daughters, respectively. The plutonium sample was also analyzed by wavelength dispersive XRF (WDXRF) to demonstrate that alpha decay-induced X-ray emission has a negligible effect on WDXRF spectra.     

X-ray fluorescence analysis of soft materials using needle-type collimators enabling greater tolerance in analysis depth

A simple micro-X-ray fluorescence (XRF) method was proposed by using commercially available injection needles. Two needles were arranged in confocal configuration inside the sample. One injection needle, which was connected directly to an X-ray tube, was used as an X-ray guide to irradiate X-rays into the sample. Another needle, which was also inserted into the sample, was used to detect the X-ray fluorescence excited inside the sample. From the beam size, the analyzing volume was evaluated to be 0.24 mm³. Therefore, the X-ray fluorescence emitted from a micro region inside the sample could be detected, although this method can only be applied for soft samples. It was demonstrated that the X-ray fluorescence of Zn in a gelatin sample could be measured, and a good linear relationship was obtained for this element. X-ray fluorescence from an oyster sample was also successfully measured by using the injection needles collimator system.     

INTENSITY DEPENDENCE OF FLUOROPHORE PHOTOBLEACHING BY A STEPPED-INTENSITY SLOW-BLEACH EXPERIMENT

Abstract— We describe a simple method for determination of the dependence of fluorophore photo-bleaching on the intensity of the incident light. A sample of fluorophore is illuminated uniformly with an intensity which is sufficient only to bleach a small fraction of the fluorophore during a fluorescence lifetime period. The long-term decay of fluorescence due to photobleaching is monitored before and after a stepped increase in the incident intensity. The order of the photobleaching reaction is determined by taking the ratio of the logarithms of the limiting values of the slope of the fluorescence bleaching curve and the absolute fluorescence change. The method is applied to fluorescein, bound to dextran or ovalbumin, in aqueous solution, and the order of the reaction in both cases is shown to be unity.     

Characterization of a confocal three-dimensional micro X-ray fluorescence facility based on polycapillary X-ray optics and Kirkpatrick–Baez mirrors

A new confocal three-dimensional micro X-ray fluorescence (3D micro-XRF) facility based on polycapillary X-ray optics in the detection channel and Kirkpatrick–Baez (KB) mirrors in the excitation channel is designed. The lateral resolution (l_x, l_y) of this confocal three-dimensional micro-X-ray fluorescence facility is 76.3(l_x) and 53.4(l_y) µm respectively, and its depth resolution d_z is 77.1 μm at θ = 90°. A plant sample (twig of B. microphylla) and airborne particles are analyzed.     

Effect of the Al/Si atomic ratio on surface and structural properties of sol-gel prepared aluminosilicates

A series of aluminosilicates with an Al/Si ratio ranging from 0 to ∞ (0 for pure silica and ∞ for pure alumina) was prepared by sol-gel process and characterized by surface and structure techniques. Aluminum trisecbutoxide and tetramethylorthosilicate were used as precursors for the sol-gel synthesis. The acidic properties of the oxides were studied by determination of the zero point charges, through mass titration method, and, for selected samples, by FT-IR spectroscopy of adsorbed pyridine used as a probe for both Brønsted and Lewis acidity. A dependence of the acidity on the Al/Si atomic ratio was found. According to the X-ray diffraction patterns, all the oxides have an amorphous structure except pure alumina exhibiting a γ-alumina pattern. The surface areas of the mixed oxides increase with increasing amount of alumina and are higher as compared to the individual oxides. The surface elemental distribution and electronic properties were investigated by X-ray photoelectron spectroscopy. According to the results, good agreement between the surface Al/Si atomic ratio and the analytical ratio is obtained.     

Effect of ZSM-5 zeolite morphology on the catalytic performance of the alkylation of toluene with methanol

A series of ZSM-5 zeolites, with the morphologies of sphere, sphere with cubic particles on the surface, and cubic particles, were synthesized by hydrothermal method using n-butylamine as the template, assisted by the addition of NaCl and crystal seed. X-ray diffraction(XRD),scanning electron microscope(SEM), X-ray fluorescence(XRF) and temperature-programmed desorption of ammonia(NH3-TPD) were used to characterize these samples. The samples were tested with toluene methylation reaction. The modified sample composed of spherical particles with 3 μm crystal particles on the surface had a para-xylene selectivity of 95% and maintained 79% of the initial conversion after running the reaction for 50 h. This modified sample showed the best stability among the tested three modified samples.     

X-ray fluorescence spectrometric analysis of erbium oxide for rare earth impurities

An X-ray fluorescence spectrometric method has been developed for the analysis of high purity erbium oxide for the determination of yttrium, terbium, dysprosium, holmium, thulium, ytterbium and lutetium oxide impurities in the concentration range 0.005–0.1%. The sample is taken in oxalate form, mixed with a binder (boric acid) in the weight ratio 31 and made into a double layer pellet. The analysis is done on a Philips PW 1220 X-ray fluorescence spectrometer using a LiF (200) analyzing crystal. The precision at each concentration of the standards and theoretical minimum detection limit for each element has been calculated.     

X-ray fluorescence determination of the molar ratio of metals in heterobimetallic complexes

A method was developed for the X-ray fluorescence determination of the molar ratio of metals in heterobimetallic complexes. The procedure includes simple rapid sample preparation and a novel algorithm of measurements and data processing. It was demonstrated that the procedure can be also used for the determination of the metal ratio in films of complexes applied to oxide supports.     

Atomic-fluorescence spectroscopy of magnesium with a high-intensity hollow-cathode lamp as line source

Atomic fluorescence of magnesium is possible in air-propane or air-acetylene flames at 285.21 nm, using a high-intensity hollow-cathode magnesium lamp for excitation. The technique permits determinations of magnesium in the range 0.01–5 p.p.m., i.e. with more than 10 times the sensitivity of the atomic absorption method even for this most sensitive element. The detection limit in either flame is 1 ng/ml (signal: noise ratio 1 : 0.75). In a nitrous oxide-acetylene flame, atomic fluorescence may be carried out with linear signal/concentration dependence up to 100 p.p.m. without interference even from metals such as aluminium, titanium, etc. at a 1000-fold excess ratio to magnesium. A brief comparison is made with atomic absorption using the same source and equipment.     

The dependence of persistent phosphorescence on annealing temperatures in CaTiO3:Pr nanoparticles prepared by a coprecipitation technique

Red emitting phosphors of CaTiO₃:Pr³⁺ nanoparticles with size ranging from 6 to 95 nm have been prepared by a coprecipitation technique and structurally characterized by X-ray diffraction, energy dispersive spectroscopy and scanning electron microscopy. The fluorescence and phosphorescence of CaTiO₃:Pr³⁺ nanoparticles as a function of annealing temperature are investigated. It is found that fluorescence intensities monotonously increase with increasing temperature. However, a maximum in phosphorescence with the increase of annealing temperature occurs for the sample prepared at 700 °C. Based on the measurement of fluorescence emission, fluorescence excitation and reflectance spectra as well as time decay patterns of fluorescence and phosphorescence, it is demonstrated that the dependence of fluorescence and phosphorescence on annealing temperature originates from the decrease of surface defects with the increase of temperature.