Fundamental parameters method

The methodical elaboration is included for estimation of random and systematic errors by using of single factor dispersion analysis. For this aim the set of reference samples is used. X-ray analyses of reference samples are performed with followed calculation of mass parts of components and comparison of results with real chemical compositions. Metrological characteristics of x-ray fluorescence silicate analysis are established both for a-correction method and simplified fundamental parameter method. It is established, that systematic error of simplified FPM is less than a-correction method, if the correction of zero approximation for simplified FPM is used by preliminary established correlation between theoretical and experimental set data. 

Alternatively, fundamental parameter methods (FPM) may be used to simulate analytical calibrations for homogeneous materials. From a theoretical point of view, there is a wide choice of equivalent fundamental algorithms for converting intensities to concentrations in quantitative XRF analysis. The fundamental parameters approach was originally proposed by Criss and Birks [239]. A number of assumptions underlie the application of theoretical methods, namely that the specimens be thick, flat and homogeneous, and that, for calibration purposes, the concentrations of all the elements in the reference material be known (having been determined by alternative methods). The classical formalism proposed by Criss and Birks [239] is equivalent to the fundamental influence coefficient formalisms (see ref. [232]). In contrast to empirical influence coefficient methods, in which the experimental intensities from reference materials are used to compute the values of the coefficients, the fundamental influence coefficient approach calculates... 

There are two possible ways of XRF analysis used in fundamental parameter methods, namely analysis with and without standards. The intensity of the measured characteristic radiation 7 is related to the calculated intensity of radiation /icai... 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

The fundamental parameters method, using complex algorithms, based on the basic equations of the fluorescence of each element... 

In this case, the matrix effects are modelled from the qualitative spectrum using the fundamental parameters method developed in 1983 by Broil and Tertian. 

For a modern XRF equipped with a powerful computer system, the fundamental parameter method (FP method) is most widely used for quantitative analysis. The method determines the concentration of an element when its theoretical intensity matches its measured intensity. The fluorescence X-ray intensity of a given composition can be calculated using theoretical formulas with given specimen physical and instrumental parameters. The physical parameters include specimen density, thickness, X-ray absorption coefficients and fluorescence yield. The instrumental parameters include excitation voltage of the X-ray tube, optical geometry and detector characteristics. 

The ZAF method relies extensively on a computer, similar to the fundamental parameter method. First, the weight fraction of elements in the specimen is estimated from their relative intensities (kl/ fflkl). Then, the (ZiAiFi) factor for each element is estimated and is used for calculating kt. The calculated kt will compare with the measured kt. The iteration of computation continues until the two values converge. 

Chemical analysis by x-ray spectrometry Fundamental-Parameter method... 

The advantage of the fundamental-parameter method is that only pure element standards are required. The disadvantage is that a large computer is needed, because the intensity calculations must be integrated over all the wavelengths in the primary beam in addition, p/p and (o values are not known very exactly, especially for the lighter elements. 

Fundamental-parameter method. The physics of x-ray production by electron impact is more complex than x-ray fluorescence. The calculation from first principles of line intensity vs. concentration is therefore more difficult. 

Omote j, Kohno H and Toda K (1995) X-Ray fluorescence analysis utilizing the fundamental parameter method for the determination of the elemental composition in plant samples. Anal Chim Acta 307 117-126. 

Bos M, Vrielink JAM (1998) Constraints, iteration schemes and convergence criteria for concentration calculations in X-ray florescence spectrometry with the use of fundamental parameter methods. Anal Chim Acta 373 298-302... 

To determine major and minor elements in complex samples, more elaborate matrix correction algorithms need to be appHed. They can be roughly divided into two categories the influence coefficient methods and the fundamental parameter method. 

Fundamental parameter method The fundamental parameter method is based on the physical theory of X-ray production rather than on empirical rdations between observed X-ray count rates and concentrations of standard samples. In general, the observed XRF count rate Rj of (the K line of) an element i, obtained by polychromatic exdtation of a sample with thickness d and density p, can be written as ... 

The above fundamental parameter equation relates the intensity of one element to the concentration of all elements present in the sample. A set of such equations can be written, one for each element to be determined. This set of equations can only be solved in an iterative way, making the method computationally complex. Moreover, an accurate knowledge of the shape of the excitation spectrum Io E)dE, of the detector efficiency e and of the fundamental parameters //, r, w and p is required. The fundamental parameter method is of interest because it allows for semi-quantitative (5—10% deviation) analysis of completely unknown samples and is therefore of use in explorative phases of investigations. Several computer programs are available that allow one to perform the necessary calculations at various levels of sophistication. As an example, in Tab. 11.9, the relative standard deviation between certified and calculated concentration of the constituents of a series of tool steels are listed. 

Calibrations in surface and thin layer analysis have to be performed differently by measuring external standards of pure elements, analyzing dried residues of a standard element, or after spin coating of a support or wafer with a spiked solution. Internal standardization is not suitable for quantification as angle variation of the glancing incident beam does alter the fluorescence intensity. Peak fitting and quantification has to be carried out by using the fundamental parameter method as known for conventional XRF spectrometry. 

Anilkumar, S., Krishnan, N. and Abani, M.C. (1999). Application of fundamental parameter method for investigation of the branching intensity of 1001 keV gamma energy of ""Pa, Appl. Radiat. Isotopes, 51, 725-728. 

Alternatively, standardless fundamental parameter (FP) techniques are based on built-in mathematical algorithms that describe the physics of the detector response to pure elements. In this case, the typical composition of a sample must be known, while the calibration model may be verified and optimized by one single standard sample. The techniques include the fundamental parameter method,the influence coefficient method, and the empirical coefficient method. 

---