Mass absorption coefficient, X-ray

X-ray mass absorption coefficient vs. atomic number at (a) 8.34 A (aluminum Ka,3 line) and (b—facing page) 13.34 A (copper Let,a line)... 

Figure 2.13 Variation with wavelength of the x-ray mass absorption coefficient of nickel. The K absorption edge is at k = 1.488 A.

R. D. Dewey, R. S. Mapes, and T. W. Reynolds, A Study of X-Ray Mass Absorption Coefficients with Tables ofCoefficients, Reynolds Metals Co., Metallurgical Research Div., Richmond, Va., 1967. 

N. V. Philips Gloeilampenfabrieken, Application Lab., Table of x-ray mass absorption coefficients, Norelco Reporter, 9(3) (1962). 

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).

HubbeD, J.H. and Seltzer, S.M. (1996) Tables of X-Ray mass attenuation coefficients and mass energy-absorption coefficients. NISTIR, 5632. Available at ... 

X-rays are absorbed depending on the X-ray mass absorption (mass attenuation) coefficients of the material. The absorption is given by... 

Table 7.8 contains values of p,/p for the common target elements employed in X-ray work. A more extensive set of mass absorption coefficients for K, L, and M emission lines within the wavelength range from 0.7 to 12 A is contained in Heinrich s paper in T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry (eds.). The Electron Microprobe, Wiley, New York, 1966, pp. 351-377. This article should be consulted to ascertain the probable accuracy of the values and for a compilation of coefficients and exponents employed in the computations. 

AT the path length, and P (A) the mass absorption coefficient at wavelength A. Between absorption edges, P (A) is proportional to Z A and is nearly independent of physical or chemical state. An absorption measurement on each side of an absorption edge is required for each element analyzed. X-ray absorption is especially useful in determining heavy elements in mixed materials of lower Z, such as lead in gasoline and uranium in aqueous solution. 

Flere C is the volume concentration of j-phase particles is the mass concentration of the analyte in the j-phase particles w is the x-ray fluorescence radiation yield t. is the mass absorption coefficient of the analyte for the primar y radiation d. is the j-phase particle effective size r fs... 

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. 

Equation 1-5 was written for a sample containing a single element upon which monochromatic x-rays are incident. In so far as x-ray absorption is an atomic property, the mass absorption coefficients for other samples are additive functions of the weight-fractions of the elements, free or combined, that are present that is,... 

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. 

Fig. 3-3. Attenuation and filtering of polychromatic x-rays by aluminum. Variation of effective wavelength with thickness. The effective wavelengths shown in tin figure correspond to the measured mass absorption coefficients. The change ir effective wavelength accounts for the deviations from the (dashed) straight lines The x-ray intensities used gave 210 /xamp through 0.0127-cm aluminum (curve A) 3200 /xamp through 0.381-cm aluminum (curve B). (Liebhafsky, Smith, Tanis, anc Winslow, Anal. Chem., 19, 861.)...

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... 

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. 

An interesting variant of Group I is the determination of thorium in monazite concentrates.73 Here the variations that may occur in the chemical composition of the matrix leave its x-ray absorbance virtually unaltered. This simplicity is possible because the principal individual rare-earth elements present in the samples lie in the range of atomic numbers from 57 to 60, a range so small as to preclude marked variations in the over-all mass absorption coefficient. 

Manganese, determination by x-ray emission spectrography, 328 in domestic ores, 200, 202, 203 trace analysis by x-ray emission spectrography, 228, 229, 231, 232 Manipulative errors, standard counting error comparable with, 285-287 Mass absorption coefficient, additivity, 15... 

Both WDXRF and EDXRF lend themselves admirably to quantitative analysis, since there is a relationship between the wavelength or energy of a characteristic X-ray photon and the atomic number of the element from which the characteristic emission line occurs. The fluorescence intensity of a given element is proportional to the weight fraction. Emitted fluorescence radiation is partly absorbed by the matrix, depending on the total mass absorption coefficient ... 

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... 

For all chemical elements, mass absorption coefficients p/p arc tabulated [13, 85] as a function of the X-ray wavelength. Chemical composition, mass density p, and thickness t of the sample are known. 

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