It will be shown that the Lachance-Traill XRF matrix correction equations can be derived from the statistical multiple linear regression model. By selecting and properly transforming the independent variables and then applying the statistical multiple linear regression model, the following form of the matrix correction equation is obtained:

Furthermore, it will be shown that the Lachance-Traill influence coefficients have a deeper mathematical meaning. They can be related to the multiple regression coefficients of the transformed system:

Finally, it will be proposed that the Lachance-Traill model is equivalent to the statistical multiple linear regression model with the transformed independent variables. Knowing these facts will simplify correction subroutines in Quantitative/Empirical XRF Analysis programs. These mathematical facts have already been implemented and presented in a paper: “Automated Quantitative XRF Analysis Software in Quality Control Applications” (Pacific-International Congress on X-ray Analytical Methods, Hawaii, 1991).

This demonstrates that the Lachance-Traill model has a strong mathematical foundation and is naturally justified mathematically.

In a previous publication, we compared measurements of the x-ray microfluorescence of calcium and iron from homogeneous spherical glass particles with the results of Monte Carlo simulation. That work was performed to verify a Monte Carlo model developed for the characterization of particle size effects using a polished flat sample of the same composition as a reference standard. The present work extends our comparison to synthetic glass particles containing elements of higher atomic number. We also modified our Monte Carlo model to include simulation of x-ray fluorescence from elements in irregular shaped synthetic particles. In addition, the Compton scattering from spherical and irregular shaped particles was simulated using Monte Carlo and compared with experimental measurements.

SUPERXAP (Super X-ray Analysis Program) enables IBM-compatible personal computers to analyze energy-dispersive spectra using least-squares spectral deconvolution. The program corrects for instrument drift, background, peak overlap, and matrix effects. Pull down menus provide 24 subroutines and functions, that allow spectra to be transferred, stored, viewed, manipulated, and analyzed. Spectral peaks can be identified manually or automatically with color-coded K, L or M lines. Working curves are developed using an interactive routine that creates standard files by least-squares fitting of peak intensities to known elemental abundances. Elemental abundances in unknowns may be determined in a variety of ways including on-line analysis of spectra as they are generated by an energy-dispersive detector and by batch analyses of spectra stored on disk. Standard deviation, based on counting statistics, is reported for each element in each analysis. Written in QuickBASIC 4.5 for interface with a KEVEX 7000 radioactive-source x-ray fluorescence analyzer, SUPERXAP could be adapted, with minor modification, to accept and analyze data from other instruments that produce energy-dispersive spectra.

Analysis of light elements, such as C, B, and Be, differs from analysis of heavier elements by the low fluorescent yields as well as by the wide gap between their absorption edge energies and the low energy limit of the available tube-photons. Because of the fact that the (relatively large) difference between these energies is transferred to the photoelectron after an ionization event, additional excitations of light elements are very likely to occur. Other possibilities of unusual secondary excitation effects include excitation by Auger electrons and by Lα-photons after K-shell ionization. The order of magnitude of these effects has been computed for the system Fe/Fe3C. The mathematical models are based on the methods of Green and Cosslett, and Scott and Love. Results show that the C-Kα counts of pure carbon are increased by a factor 2.5-3, and count rate ratios in Fe-C binary systems increase by a factor 5-10, depending upon the experimental conditions. Fit coefficients for mass absorption coefficients of Fe and C have been calculated from experimental data collected by Saloman and Hubbel for energies between 100eV and 1keV.

For carbon analysis in an iron-matrix the C-Kα intensity is not only a function of the amount of graphite. but also of the diameter of the spherolites and, for a given total carbon content, of the graphite/cementite ratio. In order to verify this, steel and caststeel sample surfaces were photographed before and after etching and the images digitized. The arcal fractions covered by graphite, cementite, and iron were used to compute the corresponding individual weight fractions and total carbon contents. Count rates were drawn to the scale of these as well as of the nominal carbon concentrations.

A set of standard samples consisting of low alloy steels, tool steels and a graphite standard was prepared carefully for measurements by polishing (down to 0.3μm alumina powder) and cleaning of the surfaces. Photographs from optical and scanning electron microscopical images were taken in order to provide information about the microstructure. The measured carbon fluorescent intensities are interpreted in view of this information as well as compared to calculated data based on fundamental parameter models. Thereby excitation by iron and carbon photoelectrons as well as secondary enhancement effects by iron K and L lines and other matrix elements were taken into account.

Results suggest that the count rates are not only a function of the total carbon content, but also of graphite segregations and to some extent of the specimen preparation procedure. Graphite particles are easily washed out and the little remaining holes may remain partially covered with carbon or filled with polishing residuals, which leads to reduced count rates.

The fundamental parameter (FP) method has been applied to many elemental analysis fields because of the advantage that it does not require standards of the same matrix as the unknown. In most FP software packages only primary and secondary excitations are included in the mathematical models, and hardly any software for routine applications has ever been reported involving the secondary enhancement by scattered radiation (SESR) as well as the scattered primary fluorescent radiation (SPFR). This can lead to errors in the analyses of compounds rich in light elements, like oxides, nitrides, carbides, borides, etc.

The development of X-ray fluorescence analysis of light elements (e.g. O, C, B and Be) has been carried out for many applications. Recently, the revolutional expansion of semiconductor electronic and memory devices has roused the needs of analysis and identification of the surface and the single- and multi-layered film structure in devices, using the fundamental parameter method for the soft and ultrasoft X-ray region. From the view point of the extensive studies of soft and ultrasoft X-ray measurements.

Oxygen K-V (Kα) X-ray fluorescence spectra of MgO, Cu2O, CuO, La2CuO4, La2-xSrxCuO4, YBa2Cu3O7-x , and GdBa2Cu3O7-x are measured. The local (oxygen) and partial (2p) electron density of states (DOS) of these compounds are calculated by the cluster approximation with the discrete variational (DV) Hartree-Fock-Slater (Xα) method. The calculated O 2p DOS are compared with the measured X-ray fluorescence spectra. It is found that the measured 0 K-V X-ray fluorescence line shapes are well reproduced by the O 2p DOS calculated by a cluster including the second nearest neighbor atoms (oxygen atoms) in the solids. This indicates that the oxygen K-V X-ray emission spectra reflect the oxygen-oxygen orbital hybridization in the solid as well as the oxygen-metal orbital hybridization.

Accurate analysis of the light elements has been, from the early applications of X-ray fluorescence spectrometry a struggle compared to the determination of heavy elements in the same matrices. In contrast, there has been virtually no upper limit to the atomic number of the element that could be determined. The lower limit, however, has been continuously adjusted downward through the years. Clearly, the sensitivity as well as the lower limit of detection for the heavy elements have also been improved, but the effect is Jess striking than the advances made in the region of tight element performance. This paper deals specifically with wavelength dispersive sequential x-ray fluorescence spectrometry, although some of the observations made are equally applicable to energy dispersive spectrometry.

The approach for the description of the emission of white and characteristic x-rays from standard x-ray tubes is modified for an application to transmission anodes. This modification is based on the assumption of a negligible penetration depth of the electrons in comparison to the thickness of the anode. The results of our considerations are presented for Cu, Mo and W anodes with two different thicknesses. For comparison, the spectra of standard anodes which have been operated with identically high voltages and anode currents are given. A typical feature of transmission anodes is their spectral hardening of the energy distribution of emitted photons. A further interesting detail is the development of narrow band excitation anodes as can be seen from the results for Mo. With anode thicknesses of approximately 200 μm and a high voltage of 30 kv the spectral distribution is restricted to an energy ranging from 15 to 20 keV.

Diffraction peaks can occur as unidentifiable peaks in the energy spectrum of an x-ray spectrometric analysis. Recently, there has been increased interest in oriented thin polycrystalline films and epitaxial films on single crystal substrates for electronic applications. Since these materials diffract x-rays more efficiently than randomly oriented polycrystalline materials, diffraction peaks are being observed more frequently in x-ray fluorescent spectra In addition, micro x-ray spectrometric analysis utilizes a small, intense, collimated x-ray beam that can yield well defined diffraction peaks. In some cases these diffraction peaks can occur at the same position as elemental peaks. These diffraction peaks, although a possible problem in qualitative and quantitative elemental analysis, can give very useful information about the crystallographic structure and orientation of the material being analyzed. The observed diffraction peaks are dependent on the geometry of the x-ray spectrometer, the degree of collimation and the distribution of wavelengths (energies) originating from the x-ray tube and striking the sample.

This paper describes the imaging of fossils using elemental x-ray area mapping (EXAM). The technique utilizes a commercially available instrument originally designed for the silicon chip industry. The EXAM data are processed digitally with imaging software to remove surface irregularities and enhance specimen details. Applications of this technique to specimens with irregular surfaces are described.

On-line analysis is a valuable tool for many industrial manufacturing processes. Real-time analytical results allow immediate control of a manufacturing process, giving significant improvements in product quality, and reductions in product wastage and labor.

Coating weight measurements by X-ray fluorescence analysis have been well established technology in industrial applications. The coating film measurements such as tin-plated steel and galvanized steel are carried out with an on-line gauge which is based on laboratory experiments. The approximate sample speed is 200m/min for a tin plate gauge, 150m/min for galvanized steel and 100m/min for electrolytic zinc coating steel.

X-ray fluorescence analysis has been used in the aluminum industry since the beginning of the 1950's. Initial applications involved predominantly raw materials such as bauxite. During the last decades its use expanded to every stage of aluminum production and today, XRF analysis is a recognized analyticaI technique, applied routinely in exploration, reduction and fabrication processes. Typical XRF applications in the aluminum industry at present are listed in Table 1. The number of determinations given represents usual industrial requirements, and may vary between laboratories. The sample preparation techniques are again the most commonly used for the applications.

The sources of raw materials used in the manufacture of Portland cement include pure to argillaceous limestones, shale and clay, plus minor quantities of sand, iron ore, fly ash, coal ash and suitable industrial wastes. To ensure a high quality product, rapid - precise - reproducible and practical analytical techniques are required. Quantitative XRF analysis techniques meet those demands.

For this comparative technique, the instrument used is a wavelength dispersive sequential spectrometer. The advantages and the drawbacks of the technique are discussed, along with the procedure of the specimen fused bead preparation. The importance of calibration standards and unknown samples being prepared in an identical manner, and being presented to the instrument under similar conditions, is stressed. International and synthetic standards, concentration ranges for the five major elements, mathematically generated coefficients to correct absorption and enhancement effects, and a summary of the standard error of estimates are examined and discussed.

The accuracy of the method is verified by the analysis of known standard reference materials such as obsidian rock, coal fly ash, argillaceous limestone and blastfurnace slag. The values are compared with the known certified values.