Analytical Study of Raw Materials of Zinc Oxide Used for Enamels on Industrial Ceramics: Quantitative Analysis of Zinc,Lead, and Sulfur in These Samples by X‐ray Fluorescence and Flame Atomic Absorption Spectrometry

An analytical study is carried out to optimize X‐ray fluorescence (XRF) and flame atomic absorption spectrometry (FAAS) quantitative analysis of Zn, Pb, and S in ZnO samples commonly used to obtain industrial ceramic enamels. Pb and S in the raw materials often contaminate ZnO and are very detrimental in industrial applications. Thus, very accurate analytical determination of these elements in ceramic samples is extremely important. First of all, a mineralogical study by X‐ray diffraction (XRD) on the different components in these raw materials and the materials produced during the firing process is performed in order to establish the mineral forms in a reference sample for analysis by XRF spectrometry. The working conditions are optimized for XRF multielemental analysis, using the sample in the form of pellets, due to high loss on ignition (LOI) values. The preparation of suitable standards and working conditions for FAAS analysis have also been optimized. The content of these elements was determined by FAAS for the reference sample and several samples for industrial use, and the results were compared with those obtained by XRF. Comparison of the results obtained from XRF and FAAS analysis of Pb and Zn show more accurate values for FAAS. For ZnO, an accuracy of 0.11% with ±0.1% precision by FAAS and 0.46% accuracy with ±0.2% precision by XRF are found. For PbO, 1.06% accuracy and ±0.06% precision using FAAS and 5.6% accuracy and ±0.35% precision by XRF were found. For SO₃ determined only by XRF, accuracy was 4.76% with ±0.25% precision. These values are highly satisfactory given that these two elements are only found in small proportions.     

Direct chemical characterisation of clay suspensions by WD‐XRF

This study was performed to develop a method for directly controlling the chemical composition of clay slurries used in preparing ceramic floor and wall tile bodies by wavelength‐dispersive X‐ray fluorescence (WD‐XRF) spectrometry, without the prior need to dry and prepare the samples as fused beads or pellets for WD‐XRF measurement, owing to the importance of knowing the suspension chemical composition in real time for appropriate control of the industrial process. The study was conducted on a wide range of ceramic floor and wall tile bodies, which are used to prepare different suspensions. The influence of suspension viscosity (from 300 to 7000 cp), of suspension solids content (between 66 and 69%), and of the type of body composition (floor or wall tile) on the WD‐XRF measurement was determined. In these viscosity and solid content ranges, no appreciable differences were observed in the WD‐XRF measurement results, indicating that the possibly arising variations in viscosity and solids content in such clay suspensions in industrial practice do not influence the WD‐XRF measurement. In contrast, the type of body composition did influence the WD‐XRF measurement. The developed method is rapid, reproducible, and accurate, which was verified by analysis of the materials using the customary method of WD‐XRF measurement on fused beads. In addition, this method is cheaper and more harmless to the environment; it minimises waste generation, since no sample preparation is required and the plastic sample holders can be reused, thanks to the reusable sample holder system designed at the Instituto de Tecnología Cerámica laboratories. Copyright © 2011 John Wiley & Sons, Ltd.     

Multi‐technique study of archaeological cord‐marked wares decorated with red coatings from Taiwan

Archaeological finds of Neolithic to Iron Age pottery show clay potsherds characterized by red cord‐markings. The items date back from 5500 to 1500 B.P. To better understand temporal changes in the provenance of raw‐material sources, and the nature of materials used in the red colorant and ceramic bodies, micro‐Raman spectroscopy, X‐ray diffraction analysis (XRD), and micro X‐ray florescence spectroscopy (μXRF) were applied to 29 red‐coated potsherd samples found at twelve archaeological sites across Taiwan. The techniques identified the chemical and mineralogical composition of the red coatings and ceramic bodies as well as the production methods of ancient potters. Eighteen mineral phases were identified from the Raman spectra, including hematite, α‐quartz, and anatase. Feldspar, rutile, pyroxenes, calcite, gypsum, amorphous carbon, and graphite were also detected. XRD measurements, and μXRF analyses were used as complementary techniques to obtain mineral and chemical compositions. Hematite, anatase, calcite, plagioclase feldspar, and illite were present in potsherds, suggesting pottery produced from illitic clays fired at less than 850 °C under oxidizing conditions. Results further suggest that raw materials were sourced from or near local volcanic rock areas, and more broadly from metamorphic or sedimentary rocks and clays. Chemically, raw materials used for red coatings are different to those of the ceramic bodies. Objects from most sites used the same raw material sources; however, some sites contain objects made from changing sources over time. Pot coatings exhibit polygonal cracks, and loosened cementation strongly suggesting that finely processed moist clays were fired to a biscuit form with no second stage firing process. The non‐destructive Raman experiments identified and characterized mineral phases, which helped understand manufacturing techniques. Overall the multi‐technique approach gave extensive information on the finds, helping to differentiate raw material sources and production technologies. This approach is an important and effective method for investigating archaeological finds. Copyright © 2014 John Wiley & Sons, Ltd.     

XRF analysis without sampling of Etruscan depurata pottery for provenance classification

In order to settle the provenance of a set of ancient ceramic shards, the elemental composition data acquired are usually treated by multivariate analysis techniques. The quantitative X‐ray fluorescence (XRF) analysis is an appropriate tool if it is possible to grind ceramics and analyze a sample that is representative of the object. If we deal particularly with well‐preserved objects, we are often not allowed to sample them. Moreover, moving these objects from museum could be unfeasible as well. The aim of this work is to evaluate if spot XRF analysis on integral objects is adequate to classify row clay provenance even if ceramics is not an intrinsically homogeneous material. So, we performed measurements on a set of Etruscan fine ware already classified according to the archaeological, chemical and mineralogical examination. For each sample, several measurement points in polished areas were considered for XRF analyses, allowing a correct provenance classification. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterization of chromium‐containing ceramic pigments by XRF and XRD

As no methodology was found in the literature for characterizing ceramic pigments chemically and mineralogically, the present study was undertaken to establish a methodology for the chemical and phase characterization of ceramic pigments by x‐ray fluorescence (XRF) spectrometry and x‐ray diffraction (XRD). In view of the large number of pigments described in the literature (around 44), the present study was limited to characterizing pigments that contained chromium, which is the most versatile chromophore used in ceramics. Copyright © 2004 John Wiley & Sons, Ltd.     

Preparation of sulfur reference materials that reproduce atmospheric particulate matter sample characteristics for XRF calibration

Energy‐dispersive X‐ray fluorescence (XRF) is an important tool used in routine elemental analysis of atmospheric particulate matter (PM) samples collected on polytetrafluoroethylene (PTFE) membrane filters. The method requires calibration against thin‐film standards of known elemental masses commonly obtained from commercial suppliers. These standards serve as a convenient and widely accepted interlaboratory reference but can differ significantly from samples in their chemical composition, substrate, and geometry. These differences can introduce uncertainties regarding the absolute accuracy of the calibration for atmospheric samples. Continuous elemental records of the US Interagency Monitoring of Protected Visual Environments (IMPROVE) PM monitoring network extend back to 1988. Evaluation of long‐term concentration trends and comparison with other networks demand a calibration that is accurate and precise compared with the uncertainty of the XRF measurement itself. We describe a method to prepare sulfur reference materials that are optimized for calibration of XRF instruments used to analyze IMPROVE PM samples. The reference materials are prepared by using the atmospheric form of the element, by reproducing the sample geometry, and by using the same substrate as in samples. Our results show that stable, pure, anhydrous, and stoichiometric deposits are collected onto the filter substrates, and furthermore, that the reference material masses are accurate and have acceptable uncertainty in the measurement range. The XRF response of the sulfur reference materials is similar to other commercial standards and is linear in the measurement range, and the slope of the multipoint calibration curve has very low uncertainty. These reference materials are valid for the calibration of XRF systems, and they bring improved transparency and credibility to the IMPROVE calibration. Copyright © 2013 John Wiley & Sons, Ltd.     

Chemical characterisation by WD‐XRF and XRD of silicon carbide‐based grinding tools

This paper addresses the chemical characterisation of silicon carbide‐based grinding tools. These are among the most widely used grinding tools in the ceramic sector, and instruments are required that enable the grinding tool quality to be controlled, despite the considerable complexity involved in determining grinding tool chemical composition. They contain components of quite different nature, ranging from the silicon carbide abrasive to the resin binder. To develop the analysis method, grinding tools containing silicon carbide with different grain sizes were selected from different tile polishing stages. To develop the grinding tool characterisation method, the different measurement process steps were studied, from sample preparation, in which different milling methods (each appropriate for the relevant type of test) were used, to the optimisation of the determination of grinding tool components by spectroscopic and elemental analyses. For each technique, different particle sizes were used according to their needs. For elemental analysis, a sample below 150 µm was used, while for the rest of the determinations a sample below 60 µm was used. After milling, the crystalline phases were characterised by X‐ray powder diffraction and quantified using the Rietvel method. The different forms of carbon (organic carbon from the resin, inorganic carbon from the carbonates and carbon from the silicon carbide) were analysed using a series of elemental analyses. The other elements (Si, Al, Fe, Ca, Mg, Na, K, Ti, Mn, P and Cl) were determined by wavelength‐dispersive X‐ray fluorescence spectrometry, preparing the sample in the form of pressed pellets and fused beads. The chemical characterisation method developed was validated with mixtures of reference materials, as there are no reference materials of grinding tools available. This method can be used for quality control of silicon carbide‐based grinding tools. Copyright © 2010 John Wiley & Sons, Ltd.     

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

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. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of multivariate statistical methods to classify archaeological pottery from Tel‐Alramad site,Syria, based on x‐ray fluorescence analysis

Radioisotope x‐ray fluorescence (XRF) analysis has been utilized to determine the elemental composition of 55 archaeological pottery samples by the determination of 17 chemical elements. Fifty‐four of them came from the Tel‐Alramad site in Katana town, near Damascus city, Syria, and one sample came from Brazil. The XRF results have been processed using two multivariate statistical methods, cluster and factor analysis, in order to determine similarities and correlation between the selected samples based on their elemental composition. The methodology successfully separates the samples where four distinct chemical groups were identified. Copyright © 2006 John Wiley & Sons, Ltd.     

X‐ray spectrometry applied for characterization of bricks of Brazilian historical sites

This paper presents the results of X‐ray fluorescence (XRF) analysis of bricks sampled from historical places in Pernambuco, a state in the northeastern region of Brazil. In this study, twenty bricks found in historical sites were analyzed. Two bricks made in the 17th century, presumably used as ballast in ships coming from Holland, five locally manufactured bricks: one from 18th century, three from 19th century, and one from 20th century, and thirteen bricks collected from a recent Archeological investigation of Alto da Sé, in the town of Olinda. Qualitative determination of the chemical elements present in the samples was undertaken using a self‐assembled portable XRF system based on a compact X‐ray tube and a thermoelectrically cooled Si‐PIN photodiode system, both commercially available. X‐ray diffraction analysis was also carried out to assess the crystalline mineral phases present in the bricks. The results showed that quartz (SiO₂) is the major mineral content in all bricks. Although less expressive in the XRD patterns, mineral phases of illite, kaolinite, anorthite, and rutile are also identified. The trace element distribution patterns of the bricks, determined by the XRF technique, is dominated by Fe and, in decreasing order, by K, Ti, Ca, Mn, Zr, Rb, Sr, Cr, and Y with slight differences among them. Analyses of the chemical compositional features of the bricks, evaluated by principal component analysis of the XRF datasets, allowed the samples to be grouped into five clusters with similar chemical composition. These cluster groups were able to identify both age and manufacturing sites. Dutch bricks prepared with different geological clays compositions were defined.     

X‐ray absorption and x‐ray fluorescence for the characterization of titanium oxide‐modified HPLC silicas

Titanium oxide grafted on to the surfaces of chromatographic silica was investigated by x‐ray fluorescence (XRF) and x‐ray absorption (XAS) spectroscopy and the latter used before and after the extensive use of this material as a support for reversed‐phase high‐performance liquid chromatography (RP‐HPLC). XRF indicated the formation of a complete 2:1 monolayer whereas XAS suggested the presence of more than one titanium oxide structure. These structures show some slight modification after immobilization of PMOS and use in HPLC. Copyright © 2005 John Wiley & Sons, Ltd.     

Chemical analysis of very small‐sized samples by wavelength‐dispersive X‐ray fluorescence

The chemical characterisation of very small‐sized samples is often of major interest in forensic analysis, studies of artworks, particulate matter on filters, raw materials impurities, and so on, although it generally poses considerable problems owing to the difficulty of obtaining precise and accurate results. This study was undertaken to develop a set of methods for the chemical characterisation of very small‐sized samples by wavelength‐dispersive X‐ray fluorescence. To conduct the study, sample preparation (as beads and pellets) and measurement conditions were optimised to reach the necessary detection and quantification limits and to obtain the appropriate measurement uncertainty for characterising the types of materials involved. The measurements were validated by using reference materials. Three test methods were developed. In two methods, the samples were prepared in the form of beads (one method being for geological materials and the other for the analysis of nongeological materials such as particulate matter on filters, glasses, frits, and ceramic glazes and pigments). In the third method, the samples were prepared in the form of pellets for the analysis of volatile elements in geological materials. In the three methods, detection limits, quantification limits and measurement uncertainties were obtained similar to those found when a bead or pellet is prepared by the usual methods from 0.5 g sample. However, in this study, sample size was between 30 and 40 times smaller in the case of beads and 100 times smaller in the case of pellets, thus broadening the range of possible wavelength‐dispersive X‐ray fluorescence applications in the chemical characterisation of materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Confocal macro X‐ray fluorescence spectrometer on commercial 3D printer

Novel confocal X‐ray fluorescence (XRF) spectrometer was designed and constructed for 3D analysis of elementary composition in the surface layer of spatially extended objects having unlimited chemical composition and geometrical shape. The main elements of the XRF device were mounted on a moving frame of a commercial 3D printer. The XRF unit consists of a silicon drift detector and a low‐power transmission‐type X‐ray tube. Both the excitation and secondary X‐ray beams were formed and regulated by simple collimator systems in order to create a macro confocal measuring setup. The spatial accuracy of the mechanical stages of the 3D printer achieved was less than 5 μm at 100‐μm step‐size. The diameter of the focal spot of the confocal measuring arrangement was between 1.5 and 2.0 mm. The alignment of the excitation and secondary X‐ray beams and the selection of the measuring spot on the sample surface were ensured by two laser beams and a digital microscope for visualization of the irradiated spot. The elements of the optical system together with the XRF spectrometer were mounted on the horizontal arm of the 3D printer, which mechanical design is capable of synchronized moving the full spectroscopic device within vertical directions. Analytical capability and the 3D spatial resolution of the confocal spectrometer were determined. Copyright © 2017 John Wiley & Sons, Ltd.     

Surface modification and characterization of Jordanian kaolinite: Application for lead removal from aqueous solutions

Kaolinite clay was tested for removal of lead ions from aqueous solution. This clay was washed with sulfuric acid solution followed by chemical surface modification using 3-chloropropyltriethoxysilane and sodium hydroxide. XRF results showed that silica to alumina ratio was 2.8:1 for the treated sample compared to 1.6:1 for the raw one.XRD analysis displayed different distinct kaolinite and quartz peaks before treatment while kaolinite peaks were diminished after the treatment. SEM morphology indicated that the raw kaolinite appears as plate structure with no local pores on the plates. However, after treatment the surface was found to have micropores.Different adsorption isotherm models were applied to the experimental data and found that Shawabkeh-Tutunji equation best fit these data adequately. It was also found that chemisorption took place at the surface of the modified kaolinite with maximum adsorption capacity of 54.35 mg/g.     

Methodology for the determination of minor and trace elements in petroleum cokes by wavelength‐dispersive X‐ray fluorescence (WD‐XRF)

This article describes a methodology for the analysis of minor and trace elements in petroleum cokes by wavelength‐dispersive X‐ray fluorescence (WD‐XRF) spectrometry. The methodology was developed in order to have a rapid and reliable control method of these elements, because they determine coke end uses. There are a number of standard methods of chemical analysis by WD‐XRF or inductively coupled plasma atomic emission spectrometry (ICP‐OES) techniques. However, the standards that use WD‐XRF measurement give detection limits (L_D) above 10 mg·kg^?1 and only analyse a few elements of interest, whereas the ICP‐OES method requires extensive sample handling and long sample preparation times, with the ensuing errors. In order to improve the method described in the standard ASTM D6376 and reach the L_D and quantification limits (L_Q) required, the different stages of the process, ranging from sample preparation to measurement conditions: analytical line, detector, crystal, tube power, use of primary beam filters, and measurement time, were optimised. The samples were prepared in the form of pressed pellets, under conditions of high cleanliness of the mills, crushers, presses, and dies, and of the laboratory itself. The following reference materials were used in measurement calibration and validation: SRM 1632c, SRM 2718, SRM 2719, SRM 2685b, AR 2771, AR 2772, SARM 18, SARM 19, and CLB‐1. In addition, a series of materials were analysed by WD‐XRF and ICP‐OES, and the results were compared. The developed methodology, which uses WD‐XRF, is rapid and accurate, and very low L_D and measurement uncertainties were obtained for the following elements: Al, Ba, Ca, Cr, Cu, Fe, Ge, K, Mg, Mn, Mo, Na, Ni, P, Pb, S, Sb, Se, Si, Sn, Sr, Ti, V, and Zn. Copyright © 2010 John Wiley & Sons, Ltd.     

Bead‐releasing agents used in the preparation of solid samples as beads for WD‐XRF measurement

This paper carries the results of an evaluation of various materials, which may be used to aid in the release of a fused bead from its mould during a wavelength‐dispersive x‐ray fluorescence (WD‐XRF) measurement. The following bead‐releasing agents were studied: NaI, LiBr, NH₄I, and LiI. Each was incorporated in different quantities, as a solid and/or in an aqueous solution, together with a flux, into samples of ceramic raw materials. Release agent interference in the WD‐XRF measurement was analysed, and the optimum quantity of release agent needed to obtain suitable beads for WD‐XRF measurement was determined. The best results were obtained for LiI, which yielded reproducible beads without significant interference in the WD‐XRF measurement when a relatively small quantity (0.11 LiI g/bead) was used. Copyright © 2008 John Wiley & Sons, Ltd.     

Microfluidic sample preparation for elemental analysis in liquid samples using micro X‐ray fluorescence spectrometry

The integration of microfluidic devices with micro X‐ray fluorescence (micro‐XRF) spectrometry offers a new approach for the direct characterization of liquid materials. A sample presentation method based on use of small volumes (<5 µl) of liquid contained in an XRF‐compatible device has been developed. In this feasibility study, a prototype chip was constructed, and its suitability for XRF analysis of liquids was evaluated, along with that of a commercially produced microfluidic device. Each of the chips had an analytical chamber which contained approximately 1 µl of sample when the device was filled using a pipette. The performance of the chips was assessed using micro‐XRF and high resolution monochromatic wavelength dispersive X‐ray fluorescence, a method that provides highly selective and sensitive detection of actinides. The intended application of the device developed in this study is for measurement of Pu in spent nuclear fuel. Aqueous solutions and a synthetic spent fuel matrix were used to evaluate the devices. Sr, which has its Kα line energy close to the Pu Lα line at 14.2 keV, was utilized as a surrogate for Pu because of reduced handling risks. Between and within chip repeatability were studied, along with linearity of response and accuracy. The limit of detection for Sr determination in the chip is estimated at 5 ng/µl (ppm). This work demonstrates the applicability of microfluidic sample preparation to liquid characterization by XRF, and provides a basis for further development of this approach for elemental analysis within a range of sample types. Copyright © 2014 John Wiley & Sons, Ltd.     

Sample thickness considerations for quantitative X‐ray fluorescence analysis of the soft and skeletal tissues of the human body – theoretical evaluation and experimental validation

A good estimation of the matrix composition and the areal mass of the sample is critical for quantitative X‐ray fluorescence (XRF) analysis. Integrated aspects of the XRF quantitative analysis of various human body organs are presented. Special emphasis is placed on the determination of the sample thicknesses at which the specimen can be regarded as thin, thick, or intermediate thickness depending on the element under consideration. Moreover, a method for a fully quantitative analysis allowing the determination of the masses per unit area of chemical elements in thin, thick, and intermediate thickness samples is discussed. It was found that for an incident beam of 17 keV energy, a 15 µm thick sample is of intermediate thickness for all elements between P and Ca and becomes thin from Fe for most human body tissues in a natural form. Dried samples of soft tissues excluding these of low water content can be regarded as thin for all elements from phosphorus to strontium. The use of thin sample approach in quantification of intermediate thickness specimen may result in about 30–45% discrepancy in areal mass (weight fraction) of phosphorus, 20–35% of sulfur, 15–25% of chlorine, 8–15% of potassium, and 5–10% of calcium. Theoretical evaluations presented in the work are verified experimentally. The analysis of human brain samples (white and gray matter) and bovine liver (National Institute of Standards and Technology standard reference materials 1577b) confirms high accuracy of the XRF quantification on the basis of the described procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

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

The aim of the work was to develop a Monte Carlo (MC) method and combine it with micro‐beam X‐ray fluorescence (XRF) technique for determination of chemical composition of individual particles. A collection of glass micro‐spheres, made of NIST (National Institute of Standards and Technoly) K3089 material of known chemical composition, with diameters in the range of 25–45 µm was investigated. The micro‐spheres were measured in a scanning micro‐beam XRF spectrometer utilising X‐ray tube as a source of primary radiation. Results obtained for low Z elements showed high dependence on particle size. It was found that the root mean square of concentration uncertainty, for the all elements present in the particle, increases with growing sample size. More accurate results were obtained for high Z elements such as Fe–Pb, as compared to others. The elemental percentage uncertainty did not exceed 14% for any particular sample and 6% for the whole group of the measured micro‐spheres as an average. Results obtained by the Monte Carlo method were compared with other analytical approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Approaches to solid sample preparation based on analytical depth for reliable X‐ray fluorescence analysis

In this paper, we discuss approaches to prepare solid samples for X‐ray fluorescence spectrometry (XRF). Although XRF can be used to analyze major and minor elements in various solid samples including powders and grains without dissolution techniques, to obtain reliable XRF results, the prepared sample must meet certain criteria related to homogeneity, particle size, flatness, and thickness. The conditions are defined by the analytical depth of fluorescent X‐rays from analytes, and the analytical depth can be estimated from the X‐ray absorption related to the energy of each X‐ray and the composition and density of the sample. For example, when the sample flatness and particle size are less than the analytical depth and the sample possesses homogeneity within a depth less than the analytical depth, the XRF results are representative of the entire sample. Furthermore, an appropriate sample thickness that is larger than the analytical depth or constant can prevent changes in fluorescent X‐ray intensity with variations in sample thickness. To obtain accurate and reproducible measurements, inhomogeneous solid samples must be pulverized, homogenized, and prepared as loose powder, powder pellets, or glass beads. This paper explains the approaches used to prepare solid samples for XRF analysis based on the analytical depths of fluorescent X‐rays. Copyright © 2016 John Wiley & Sons, Ltd.