Mass absorption coefficients of the elements

The region of greater practical importance, the region of 4 infinite thickness, is characterized by a horizontal line in Figure 6-4. This line is the upper limit of a curve the form of which is determined in part by the mass absorption coefficients of the element for the incident, and for the emergent x-ray beam. If the sample contains elements other than E, the mass absorption coefficients of these other elements will similarly help determine the intensity I s of the analytical line at infinite thickness of sample. 

Values of the Mass Absorption Coefficients of the Elements in the Region from 0.1 A to 10 A... 

For a given material of known composition, //, can be calculated using a table that gives the mass absorption coefficients of the elements that constitute that material. After calculating the weighted mass coefficient pM (cm2/g) of the material, it is possible to obtain p = pM p where p is expressed in g/cm3. 

There is convincing experimental evidence for the following important statement. To a degree of approximation satisfactory for most analytical work, the mass absorption coefficient of an element is independent of chemical or physical state. This means, for example, that an atom of bromine has the same chance of absorbing an x-ray quantum incident upon it in bromine vapor, completely or partially dissociated in potassium bromide or sodium bromate in liquid or solid bromine. X-ray absorption is predominantly an atomic property. This simplicity is without parallel in absorptiometry. 

Even if c (Equation 5-12) is fairly large, an element cannot be precisely determined—or may even escape detection—if it is present in too small amount relative to the matrix. What amount is too small depends not only upon the relative mass (or weight-fraction) of element sought but also upon the mass absorption coefficient of the matrix, as Equations 5-8 and 5-9 imply. 

Inasmuch as the thickness measurement depends on the absorption of x-rays by iron, the results of Figure 6-2 ought to be in accord with the known mass absorption coefficients of that element. Whether such accord exists can be determined by using the exponential absorption law in the form... 

In the earlier discussion of critical depth (6.5), it was pointed out that this depth is determined by the density, and by the mass absorption coefficients of the sample for the incident beam and for the analytical line. With light elements, the coefficient for the analytical line can be so large that the coefficient of the incident beam may be neglected in... 

The correction for the pyrolytic production of elemental carbon is accomplished by measuring the amount of elemental carbon oxidation necessary to return the filter reflectance to its initial value. This is facilitated by the three-step elemental carbon oxidation which produces a relatively slow initial rise in the reflectance. A typical output is shown in Figure 3. The pyrolysis correction corresponds to the shaded area which is added to peaks 1 and 2 to give the corrected value for organic carbon. This procedure assumes that the mass absorption coefficient of the pyrolytically produced elemental carbon is the same as that of the original elemental carbon. Research to test this assumption is continuing. 

Table 2.3. Mass absorption coefficients (in cm /g) of selected chemical elements for the commonly used anode materials. The mass absorption coefficients of the best P-filter...

It is occasionally necessary to know the mass absorption coefficient of a substance containing more than one element. Whether the substance is a mechanical mixture, a solution, or a chemical compound, and whether it is in the solid, liquid, or gaseous state, its mass absorption coefficient is simply the weighted average of the mass absorption coefficients of its constituent elements. If Wi, W2, etc., are the weight fractions of elements 1, 2, etc., in the substance and pjp)i, (jiIp)2, etc., their mass absorption coefficients, then the mass absorption coefficient of the substance is given by... 

It is important to rcali/c that the X-rays produced in the fluorescence process are generated not only from atoms at the surface of a sample bui also from atoms well below ihc surface. Thus, a part of both the incideiU radiation and the resuliiiigfluorescence iraverse a significani thickness of sample within which absorption and scattering can occur. T he extent either beam is attenuated depends on the mass absorption coefficient of the medium. which in turn i.s determined by the absorption coefficients of all of the elements in the sample. T here-... 

For elemental analysis. X-ray absorption is not particularly useful. As we saw in Eq. (8.10), the mass absorption coefficient needed for the Beer s Law calculation [Eq. (8.19)] must be calculated from the weight fractions of elements present in the sample. The weight fractions are usually unknown. Quantitative analysis by X-ray absorption is usually only used for the determination of a high atomic number element in a matrix of lower atomic number elements. Examples include the determination of lead or sulfur in hydrocarbon fuels, and the determination of Pt catalyst in polymers, where the difference in mass absorption coefficients between analyte and matrix is large. One approach to quantitative analysis using X-ray absorption is based on the measurement of the intensities of two or more monochromatic X-rays passed through the sample. This is called X-ray preferential absorption analysis or dual-energy transmission analysis. The analysis depends on the selective absorption of the transmitted X-rays by the analyte compared with absorption by the rest of the sample (the matrix). The sensitivity of the analysis also depends on the difference in mass absorption coefficients of the analyte and sample matrix for the transmitted X-rays a big difference results in a more sensitive analysis. The analyte... 

Relationships among the mass absorption coefficients for different elements and for different wavelengths, to be discussed later, further emphasize the simplicity of x-ray absorption. 

In this expression, n/p] pec is the mass absorption coefficient of X-rays from element A in the specimen, a is the detector take-off angle, p is the density of the specimen... 

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