Intensity parameters method

SELECTION AND USE OF INTENSIVE PARAMETERS OF ANALYTICAL SIGNAL ON MULTICOMPONENT ANALYSIS BY NON-SELECTIVE METHODS... 

Multicomponent analysis by non-selective methods is based on the measurement of total analytical signal (AS) of mixture of components at several intensive parameters and on the constmction of combined equations and the solving of it. The difference of partial sensitivity of components determined in common defines uncertainty. 

In addition to qualitative identification of the elements present, XRF can be used to determine quantitative elemental compositions and layer thicknesses of thin films. In quantitative analysis the observed intensities must be corrected for various factors, including the spectral intensity distribution of the incident X rays, fluorescent yields, matrix enhancements and absorptions, etc. Two general methods used for making these corrections are the empirical parameters method and the fimdamen-tal parameters methods. 

The empirical parameters method uses simple mathematical approximation equations, whose coefficients (empirical parameters) are predetermined from the experimental intensities and known compositions and thicknesses of thin-film standards. A large number of standards are needed for the predetermination of the empirical parameters before actual analysis of an unknown is possible. Because of the difficulty in obtaining properly calibrated thin-film standards with either the same composition or thickness as the unknown, the use of the empirical parameters method for the routine XRF analysis of thin films is very limited. 

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... 

Calibration method. The measured fluorescence parameter should be independent of indicator concentration, geometry of sample, and sensitivity of detection system. Thus, an intensity-based method requires wavelength-ratiometric probes. Lifetime and anisotropy methods do not require wavelength-ratiometric probes, but the lifetime or anisotropy must be sensitive to analyte. 

This study demonstrates that the nonlinear optimization approach to parameter estimation is a flexible and effective method. Although computationally intensive, this method lends itself to a wide variety of process model formulations and can provide an assessment of the uncertainty of the parameter estimates. Other factors, such as measurement error distributions and instrumentation reliability can also be integrated into the estimation procedure if they are known. The methods presented in the crystallization literature do not have this flexibility in model formulation and typically do not address the parameter reliability issue. 

The eight-coordinate tetrakis(diethyldithiocarbamate) lanthanide complexes are isomor-phous and the lanthanum complex has a quasi-tetrahedral configuration of the four CS2 chelate groups. The transition frequencies and dipole strengths of these complexes available over the accessible f-f manifold allowed the extraction of the Judd-Ofelt intensity parameters Qx for k = 2, 4, 6 by standard least squares methods [112,113]. The values of observed Qx and calculated Q, values are given in Table 8.10. The three components of f2() are... 

The purpose of classical methods is to obtain transferable molecular intensity parameters, to calculate reliable intensities within reasonable computation times, and to investigate large interesting molecules. 

The ratio of the polarized light intensity scattered from two different coaxial beams illuminating a particle can be used to determine particle size. Azzizy and Hess [191] used two coaxial beams of different wavelengths at 30° from the forward axis polarized in different directions. The ratio of these two parameters gives a unique curve that is a function only of particle size. They found errors of a similar magnitude to those found with intensity ratio methods. 

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. 

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. 

In the present study, a FLIM measurement system was constructed and applied to Halobacterium salinarum (Hb. salinarum) loaded with 2, 7 -bis-(carboxyethyl)-5(6)-carboxyfluorescein (BCECF) to obtain information on the intracellular environment as well as the intracellular pH in each ofthe cells [9-12]. Hb. salinarum belongs to the family of extreme halophilic archaebacteria, and considerable attention has been paid to this bacterium in relation to proton transport, phototaxis or the adaptation of an organism to extreme environments [13-15]. Intracellular pH is an essential parameter for Hb. salinarum in the regulation of intracellular processes [14, 16, 17], and fluorescence intensity ratio methods have been used to measure the intracellular pH [18,19]. The... 

This property is absent in the parent non-chiral spectroscopies. Chiroptical methods sometimes provide enhanced resolution, because of the simple fact that di-chroic bands can be positive and negative. Chiral spectroscopies give also a new dimension to the intensity parameter. The information about structure is also encoded in the sign, the absolute value and the width of spectral bands. Not only the positions of bands, but also the entire shape of the spectral pattern carries structural information on the sample. While parent spectroscopies are more oriented toward the positions of the spectral bands, chiroptical spectroscopies are primarily intensity oriented, although band positions are just as important as in the parent methods. Chiroptical spectroscopies can draw on substantial knowledge on electronic and vibrational molecular transitions that has been collected throughout the years of analytical use of the parent spectroscopies. 

Sometimes, the distribution of the statistic must be derived under asymptotic or best case conditions, which assume an infinite number of observations, like the sampling distribution for a regression parameter which assumes a normal distribution. However, the asymptotic assumption of normality is not always valid. Further, sometimes the distribution of the statistic may not be known at all. For example, what is the sampling distribution for the ratio of the largest to smallest value in some distribution Parametric theory is not entirely forthcoming with an answer. The bootstrap and jackknife, which are two types of computer intensive analysis methods, could be used to assess the precision of a sample-derived statistic when its sampling distribution is unknown or when asymptotic theory may not be appropriate. 

The third parameter comes into play when considering film-covered surfaces. The reason for calling it a "forgotten parameter is that it cannot be measured directly by intensity-reflection methods and so it is too often ignored completely. 

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. 

In this study, we evaluate the oscillator strength of hypersensitive transitions in LnX3 (X = Cl, Br, I) molecules with the multi-reference spin-orbit (MRSO) Cl method and discuss the origin of hypersensitive transition intensities, especially focusing on the Ln dependence, halogen dependence, and also the effect of LMCT. To compare our ab initio results and the semi-empirical concepts, such as the JO theory and the DC model, we evaluate the oscillator strengths and two kinds of JO intensity parameters T Cdc) and rxC b) in Sect. 4.1. These two parameters T Cdc) T Cab), the details of which are defined in Sect. 3 and Ref. [5], represent the contributions only from the DC theory and those from all the effects considered in the ab initio calculations, respectively. If the origin of hypersensitive transition intensities can be explained by the DC model alone, these two JO intensity parameters T Cdc) and TAC b) are expected to show similar... 

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. 

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