The processes of absorption and enhancement in x-ray fluorescence spectrometry preclude the direct conversion of measured intensities to concentrations unless the specimens being analyzed are practically identical to the reference materials that were used as standards for calibration. While well known techniques of spectrometry such as the use of internal standards or techniques specific to x-ray fluorescence such as Compton scatter may be used in some instances, the analysis of alloys for example is not amenable to these techniques. The goal of mathematical correction procedures is to compensate adequately for matrix effects and therefore to extend the concentration range within which analysis may be accomplished. The evolution of the concepts and expressions that have been proposed for this purpose spans some 50 years, is somewhat fascinating and examined in outline after a brief nostalgic look at where it all began.

In the last decade, the Fundamental Parameter (FT) method has been increasingly used in quantitative XRF analysis as an effective means for interelement effect corrections. Many authors have contributed to its continuous development both in theory and practice [1 - 26]. Among various implementations, the FP-alpha method has been used widely in bulk-sample analysis because of its unique advantage of speed [1 - 6]. In recent years, however, with the advent of faster computers, a rigorous full FP approach has become feasible and practical. This is especially true in the field of multilayer thin-film, analysis, where the FP-alpha approach has not yet been applied.

Qualitative inorganic analysis is required for the identification of unknowns, the classification of type, and sometimes to decide what subsequent quantitative analysis is needed. The traditional way of performing qualitative XRF analysis on unknown materials is by subjecting the sample to a full spectral scan. This takes time and an experienced operator to interpret the spectra. Classifying the elements detected as major, minor or trace can also be person dependent. Round robin tests have confirmed this by showing considerable variation in results between laboratories.

A fundamental parameter algorithm for quantitative XFA with characteristic Kα- and Lα-radiations of the specimens is presented. This allows an application to programmable pocket calculators or a fast evaluation of measured countrates for the unknown composition of the specimen by means of PCs. For the practical utilization we need the incidence angle and the takeoff angle of the x-rays in the instrument, the high voltage V in kV which is supplied to the x-ray tube (E0) and reference measurements on either pure elements or a single reference specimen. The quality of the analytical results depends on the concentration differences of the unknown specimen and the reference specimen.

Kramers described the cross section of electron interaction with target atoms of atomic number Z by

where Eo is the kinetic energy of impinging electrons, and E o S) the energy of x-ray photons of the continuum, Smith et al modified this equation, introducing an exponent x, so that

We applied the cross-section σS, E to the evaluation of experimental results. The evaluation of the measured spectral responses of the x-ray signals nE was performed by

where f(deff) describes the absorption of x-rays of energy E in the target, RE accounts for backscattering of electrons, DE quantifies the efficiency of x-ray detection within the solid angle Ω.

EDXRF analysis is conveniently split into two parts: (1) the determination of X-ray intensities and (2) the determination of elemental amounts from X-ray intensities. For the first, most EDXRF analysis has been done by some method of integrating the essentially Gaussian distribution of observed full energy pulse heights. This might be done, for example, by least-square fitting of Gaussian distributions superimposed on a straight line or a quadratic background. Recently more elaborate shapes of the energy peaks also have been considered (Kennedy, 1990). After the X-ray intensities have been determined, interelement effects between the analyte element and other elements must be corrected for in order to obtain the elemental amounts from X-ray intensities. This correction can be done either by an empirical correction procedure as in the influence coefficient method which requires measurements on a number of standard samples to determine the required coefficients, or by theoretical calculation as in the fundamental parameters method which does not require standard samples.

Some x-ray fluorescence - concentration relationships in the framework of XRF were researched. Fundamental calculation approaches for primary fluorescence and incoherent scattering were realized for evaluation of matrix influence. A new binary approach was produced for the cases considered, and its unification was related to the empirical and regression types of the “standard background” technique, widely used in the analytical practice of XRF. It is confirmed that application of the calculations by fundamental parameters (FP) in combination with the empirical approach allows the reduction of the set of standards (to as few as one) in the analysis procedure with wide variations in matrices and concentrations, without loss of accuracy.

It is well-known that in EDXRF, using high-resolution semiconductor detectors, evaluation of x-ray fluorescence radiation line intensities from multiplex spectrometric information represents definite difficulties, especially in automation of measurement-calculation procedures.

A common spectrum decomposition problem is to get the following parameters: a number of spectral lines and their centroids, intensities from measured experimental data and their errors.

We have developed special software for solving this problem using personal computers and high-level programming language C. It uses profiles of real-form lines of pure chemical elements produced by semiconductor detector spectrometers and these techniques: digital filters with parameters for suppression of background, multiplex structure analysis, and stable linear least-squares fit to get peak intensities. Also it established special criteria for reliability of the results.

We compared our investigation with software “EDXRF” (ver.1.32) arid spectrum decomposition with Gaussian peaks.

The fundamental parameters method (FPM) enables one to determine with high accuracy the chemical composition of homogeneous samples, having only one reference sample. However, the reference sample composition should be similar to that of the samples analyzed.

The x-ray fluorescence analysis of multicomponent heterogeneous materials (ores, minerals, their mixtures, welding electrode coating mixtures, fluxes, etc.) is made by the Δμ-correction method based on the combined use of the fundamental and empirical correlations maintaining all the advantages of the FPM. Sample composition is calculated on the basis of the element intensities measured in the sample and in the reference specimen and is corrected for the disturbing effect of excitation conditions and heterogeneity as well as the calculated values of one of the fundamental parameters (μ1). At the preliminary stage of calibration, the coefficients are determined using regression and the absolute fundamental expression for the element fluorescence intensity.

The Kulenkampff-Kramers formula giving the spectral distribution of the continuum as a function of wavelength allows a correct calculation of background under the peak. It is only necessary to measure two backgrounds, one on each side of the peak, The true background under the peak is given by multiplying them by adequate coefficients and adding them up. This method has been applied to the determination of low amounts of Ce, La, Ba and Cs in geological samples.

The recently developed code SHAPE allows the build-up of EDXRF spectra for collimated and monochromatic excitation. In this work the code is applied to investigate the Importance of the scattering corrections to the more intense XRF characteristic lines from low and medium Z elements. Results are given graphically for pure elements from Z=11 (Na) to Z=42 (Mo). Heavier element lines from a multi-component geological sample, where light matrix amplifies the influence of scattering, are studied.

A review is given of the main gas-discharge sources and auxiliary equipments which were used in soft and ultra-soft X-ray emission spectrometry. Special attention is paid to the basic principles and instrumentation of low-energy electron-induced X-ray spectrometry (LEEIXS) whose excitation source is an electron beam generated in a glow-discharge system. Capabilities of LEEIXS in surface and thin film analysis and characterization are illustrated by examples dealing with control and optimization of surface treatment and thin film deposition processes. Sensitivity of the technique down to the submonolayer range and influence of backscattering phenomena are shown.

Sherman described the excitation of characteristic radiations by primary x-rays and by secondary excitation. The derivation has been made assuming a homogeneous sample. Criss and Birks inverted the problem from the calculation of fluorescent countrates to the quantitative XFA by means of fundamental parameters. Theoretical and instrumental developments enabled a reduction of the sample area and led to small area XFA and imaging XFA sytems. Depth profiling by means of XFA is a further development. We continue the original concept of variable take-off angle technique for the determination of film thicknesses without reference samples and apply the variation of the incidence angle to depth profiling.

The X-ray fluorescence analysis of a trace element under a grazing incidence condition has been developed using synchrotron radiation. The interference effect plays an important role for determining the depth distribution of the elemental concentration. The elemental distribution above, on or below the material surface has been studied. The glancing angle dependence of the X-ray fluorescence signal around the critical angle strongly reflects the elemental distribution, and can be used to determine the position of the element of interest.

Reflection and fluorescence intensity profile curves for thin films were measured under the grazing incidence conditions using synchrotron radiation. A titanium layer and a carbon / titanium bilayer sputtered on a silicon wafer were subjected to heat treatment. The analysis of the reflection and fluorescence profile curves shows that the sample without the heat treatment has another high-density layer on the surface or interface, and that the heat treatment results in the removal of the high-density layer and the formation of a thick homogeneous layer.

A novel method using Fourier transform algorithm is proposed to determine each layer thickness of multi-layered thin films from interference oscillation observed in X-ray specular reflection. The peak position in Fourier space gives each layer thickness of the film. The principle of the present technique as well as its applications are described.

Chromium nitride hard coatings have been prepared by a plasma process by varying nitrogen partial pressure. The crystallographic structure of these samples has been investigated by XRD and their chemical composition and stoichiometry by Low Energy Electron Induced x-ray Spectrometry (LEEIXS).

An analytical framework for calculation of multiple scattering intensities emitted by a multi-layer sample are obtained with transport theory. The n-th order Flux solution of the Boltzsiann transport equation renders the iterative solution for multi-layers samples of thin or infinite thickness.

The first-order intensity is written for a generic sample with I layers and for the predominating interactions in the X-ray regime: the photoelectric effect, and the Compton and the Rayleigh scattering. As an example, the case of a thin deposit on an infinite thickness substrate is discussed.

The multiple scattering contributions to the emitted intensity of a thin homogeneous sample under X-Ray excitation are studied with recourse to the Boltzmann transport theory. The corrective terms to the XRF characteristic line due to a second collision of either the photoelectric effect (secondary XRF), or the Compton, or the Rayleigh scattering, are deduced for reflection geometry. Analytical expressions for the intensities are given that allow their computation for variable incidence and take-off beam directions and source wavelength.

Variable sample exit angle x-ray fluorescence spectroscopy (VEA-XRF) employing the Lβ/Lα intensity ratio for transition metals and their oxides has been shown to be useful for non-destructively studying transition metal surfaces and oxidation, as well as, superconductors. Thus the theoretical formulation of the Lβ/Lα intensity ratio dependence on the sample exit angle, θe, is of some interest and we develop it here. We also present methods of obtaining parameters needed in the formulation, such as Lβ absorption coefficients, which are not available in the literature, for wavelengths greater than about 12Å.