Mass attenuation coefficient

The evaluation of the various XRF measurements will be discussed for different effects in EDXRS the spectra evaluation is perfonned by different programs with varying assumptions, partially different mass attenuation coefficients are used, the calibration procedures are principally different (e.g., thin foils with given thickness, or, infinitely thick samples), measurement under atmospheric pressure or in vacuum, secondary excitation (enhancement) mainly of Al by Si radiation. 

In X-ray spectrometry, attenuation, deflection and interference must be considered. Attenuation is described by the well-known Lambert-Beer law and the mass attenuation coefficient as given for conventional XRF. 

The value of p, the linear attenuation coefficient, depends on the substance, its density, and on the wavelength of the x-rays [2]. The mass attenuation coefficient, p., is obtained by dividing p, by the density of the substance. Although a powder mixture may be composed of several components, it can be regarded as being composed of just two components component J (which is the unknown), and the sum of the other components (which is designated as the matrix). The intensity of line i of component J in a powder mixture is given as... 

It is possible to calculate the mass attenuation coefficient value of a compound from its elemental composition. If wh w2,. . wn are the weight fractions of elements 1, 2,. . ., n in the compound and x 1, p.2, .. ., x are their respective mass attenuation coefficients (for radiation of a particular wavelength), then the mass attenuation coefficient of the compound, x, is [2]... 

The mass attenuation coefficient values of the elements are available in the literature [46]. Therefore, the mass attenuation coefficient of a compound can be calculated. Thus and (in Eq. 15) can be calculated provided the molecular formulas of components 1 and 2 are known. It is then possible to calculate the intensity ratio, /u/(/ii)o> as a function of xx. This ratio can also be experimentally obtained. The intensity of peak i of a sample consisting of only 1 is determined [(/ii )o] This is followed by the determination of the intensity of the same peak in mixtures containing different weight fractions of 1 and 2. This enables the experimental intensity ratio, /n/(/n)o, to be obtained as a function of xx. The principles discussed above formed the basis for the successful analyses of quartz-beryllium oxide and quartz-potassium chloride binary mixtures [45]. 

In this series, fi and /x are respectively the mass attenuation coefficients of anhydrous carbamazepine and carbamazepine dihydrate. The calculated values were fi = 5.21 cm2 g-1 and /x = 5.87 cm2 gThe theoretical line in Fig. 5 is based on these values. 

Note that the order in which the series of materials occurs is immaterial the contribution of each is weighted according to its areal density and mass attenuation coefficient. 

Figure 5 X-ray mass attenuation coefficients for aluminum as a function of photon energy. At low energies, photoelectric absorption predominates. At higher energy, incoherent (Compton) scatter becomes almost the exclusive contributing mode. Eventually, pair production dominates at very high energies (above 10 MeV).

Figure 6 The atomic number dependence of the total mass attenuation coefficient in different energy domains (50, 500, and 5000 keV).The strongest Zdependenceis seen for X-ray energies in the low-energy range.

Figure 7 The atomic number dependence of attenuation in different energy domains. This is illustrated by how the mass attenuation coefficient of the predominating mode (photoelectric (PE) at 50 keV, incoherent (Inc) at 500 keVand pair production (PP) at 5 MeV) varies with Z.

Figure 8 X-ray mass attenuation coefficient as a function of atomic number for monoenergetic X-rays of 50 and 100 keV. Sharp declines occur when the energy for k-edge absorptionjust exceeds the X-ray energy.

The mass attenuation coefficient am, defined as the extinction cross section per unit particle mass, is related to the volume attenuation coefficient by... 

Measurements of extinction by small particles are easier to interpret and to compare with theory if the particles are segregated somehow into a population with sufficiently small sizes. The reason for this will become clear, we hope, from inspection of Fig. 12.12, where normalized cross sections using Mie theory and bulk optical constants of MgO, Si02, and SiC are shown as functions of radius the normahzation factor is the cross section in the Rayleigh limit. It is the maximum infrared cross section, the position of which can shift appreciably with radius, that is shown. The most important conclusion to be drawn from these curves is that the mass attenuation coefficient (cross section per unit particle mass) is independent of size below a radius that depends on the material (between about 0.5 and 1.0 fim for the materials considered here). This provides a strong incentive for deahng only with small particles provided that the total particle mass is accurately measured, comparison between theory and experiment can be made without worrying about size distributions or arbitrary normalization. 

If a piece of nickel is suspended at a depth of 1 cm in an aqueous solution, what fraction of the intensity of the transition Ka, emitted when metal atoms are excited, will reach the surface Mass attenuation coefficients for hydrogen and oxygen are H 0.4 cm2/g O 13.8 cm2/g. 

The table of mass attenuation coefficients indicates that for aluminium and the Ka of copper, fim — 264cm2/g. Knowing the density of this metal leads us to the linear coefficient ... 

Figure 17.10 Mass attenuation coefficient for energetic photons in lead. (From Evans, 1955.)...

This approach was used to determine the weight fractions of anhydrous carbamazepine and carbamaze-pine dihydrate when they occurred as mixtures. Based on the mass attenuation coefficients of the anhy-drate and the dihydrate, the intensity ratios [/ii/(fii)o] were calculated as a function of the anhydrate content in the mixture (the line in Fig. 10). These were in good agreement with the experimentally obtained values of [fil/CfiOo]-... 

It is possible to calculate the mass attenuation coefficients of the analyte and the matrix based on their chemical compositions. This enables the calculation of the relative intensity [Ii / In)o as a function of the weight fraction of the analyte in the mixture and thus generate a theoretical curve. This eliminates the need for the preparation of experimental standard curves. An added advantage of this approach is that there is no requirement of an internal standard. 

Position of the emitting atom Resonance-absorption cross section Mass attenuation coefficients Line width Isotope abundance... 

Table 1 Weight Fraction of Minor Phases and Mass Attenuation Coefficient of Aluminium Titanate/Zirconia-Alumina Composites as a Function of Sample...

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