Mass absorption coefficient

Table 7.8 Mass Absorption Coefficients for Ka., Lines and WLa-, Line...

Mass Absorption Coefficients. Radiation traversing a layer of substance is diminished in intensity by a constant fraction per centimeter thickness x of material. The emergent radiant power P, in terms of incident radiant power Pq, 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. 

TABLE 7.8 Mass Absorption Coefficients for Kai Lines and W Lai Line (Continued)... 

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... 

For good spectra to be obtained, the difference between the ln(I /lQ) before and after the absorption edge, the edge jump, should be between 0.1 and 1. This may be calculated from the mass absorption coefficient of a sample ... 

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,... 

The mass absorption coefficient is sometimes denoted with a subscript e.g., Hm, which will be omitted in this book. Subscripts will be used to identify ni (linear) and fj.a (atomic), m = m/p and pa — pM/N, when p = the density (in grams per cubic centimeter) of the absorbing material, M is its atomic weight, and N is Avo-gadro s number. 

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. 1-10. Log-log plot showing mass absorption coefficient as a function of wavelength for three common metals. Note that the discontinuities locate the absorption edges, (K) and (L). (Liebhafsky, Ann. N.Y. Acad. Sci., 53, 997.)...

The values of r and a in Table 4-2 show that photoelectric absorption generally makes the greater contribution to the mass absorption coefficient. Absorption leading to scattering, which will be discussed in the next section, gains in relative importance as atomic number Z and wavelength X decrease. 

Between absorption edges, the photoelectric (true) mass absorption coefficient r can be expressed as the following approximate empirical function of Z and X ... 

Inasmuch as mass absorption coefficients vary with wavelength (Equa-7 The elementary composition of a substance is called its ultimate composition. 

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.)...

It is obvious that Figure 3-6 serves as a calibration curve with the help of which the chlorine content of unknown, similar materials could be readily determined. It will now be shown that the solid line agrees closely with kf values calculated from the mass absorption coefficients of benzene, hydrogen, and chlorine small variations in effective wavelength will be disregarded. 

Since the mass absorption coefficient of hydrogen changes very little with wavelength, its value (0.435) may be taken from the literature. For carbon, 0.567, which was obtained from the measured kf for benzene by allowing for the absorption due to hydrogen, will serve. For chlorine, the rounded value na = 12 was chosen on the basis of the literature, which gives 11.6 at 0.71 A.13 With the numerical values inserted, Equation 3-8 becomes... 

Effective wavelengths have been included in Table 3-1 to show the changes that occur in this important variable when one gas is substituted for another. These wavelengths correspond to mass absorption coefficients calculated from Equation 3-14 and were obtained by interpolation from tabulated values of absorption coefficients for different wavelengths.15... 

At the wavelength (0.71 A) of molybdenum Ka, the three mass absorption coefficients of Equation 5-6 have the values given (0.381) ... 

It is gratifying that no empirical calibrating factor was needed with the Fe-55 source, which means that the results were predictable from Equation 5-6 by insertion of accepted values for the mass absorption coefficients. The deviation corrected by the introduction of this empirical factor (Equation 5-7) was of the kind produced by the filtering of polychromatic beams. About all that can be said about such empirical factors and about background corrections is this Always unwelcome, not to be introduced unless necessary, the need for them does not in itself make a method less desirable, but it does usually indicate that something is incompletely understood. 

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