Absorption Effects

We are explicitly excluding absorption effects Light-absorbing pollutants modify this description. 

Entrainment Entrainment in a plate column is that liquid which is carried with the vapor from a plate to the plate above. It is detrimental in that the effective plate efficiency is lowered because hquid from a plate of lower volatility is carried to a plate of higher volatility, thereby diluting distillation or absorption effects. Entrainment is also detrimental when nonvolatile impurities are carried upward to contaminate the overhead product from the column. 

This effect, which can also be produced if fluorescent substances are applied to the chromatogram by spraying or dipping after development, is an absorption effect and not a quenching process in the true sense of the word. It is correct to refer to fluorescence or phosphorescence diminishing. The more absorbant sample molecules there are present in the zone the darker this will appear (Fig. 4B). 

There has been much discussion of the relative contributions of the no-bond and dative structures to the strength of the CT complex. For most CT complexes, even those exhibiting intense CT absorption bands, the dative contribution to the complex stability appears to be minor, and the interaction forces are predominantly the noncovalent ones. However, the readily observed absorption effect is an indication of the CT phenomenon. It should be noted, however, that electronic absorption shifts are possible, even likely, consequences of intermolecular interaetions of any type, and their characterization as CT bands must be based on the nature of the spectrum and the structures of the interaetants. This subject is dealt with in books on CT complexes. ... 

Figure 9-81. CO2 absorption effect of carbonate on Koa. Reproduced by permission of the American Institute of Chemical Engineers, Leva, M., AI.Ch.E. Jour., V. 1 (1955) p. 224 all rights reserved.

The preceding oversimplified mathematical treatment really amounts to an evaluation of the absorption effect (6.1). The exponential term in Equation 6-4 is obviously a product of two exponential terms, each deriving from Beerks Law. One term governs the attenuation of the beam incident upon the volume element in question, and the other governs the attenuation of the characteristic line emerging frcJm this element. The films are so thin that the use of one value each for 6 and for 02 over the entire film thickness is justified. Finally, one must assume that the intensity measured by the detector remains proportional to the intensity of the source. An exact treatment of the problem would be so complicated that one is justified in seeing what can be done with the simple relationships obtained above. 

The information given above should make it possible in general to predict the usefulness of x-ray methods in problems involving films. In principle, these methods should be useful occasionally when more than one film is present. The problems in such cases are complex rather than complicated. If these methods are applicable to a duplex film, for example, there will be three characteristic lines to be counted, and absorption effects in three regions to be considered. The three counts should, however, contain enough information in many cases to permit the drawing of valid conclusions. 

To conclude Chapter 6, let us connect it with Chapter 4 through a simple calculation involving the intensity of cobalt Ka as measured by counting 1 square centimeter over a 1-second interval. The measured intensity for massive cobalt corresponds to about 500,000 counts. By means of Equations 6-7 and 6-9, we calculate from this number a value of 23 counts for AI (Equation 6-9) for a monolayer of cobalt atoms. The measured value from Table 4-4 is 15 counts. The good agreement shows that absorption effects may be calculated with confidence. 

The n t effect of the presence of other elements is conveniently assessed by comparing the intensity of the analytical line in their presence with the intensity calculated from Equation 7-1. The net effect may be to increase the intensity over that calculated (positive), or to decrease it (negative). Individual effects may result from the following causes (1) Presence of an element with absorption coefficient smaller than that of E positive absorption effect). (2) The reverse of this situation negative absorption effect). (3) Presence of an element a characteristic line... 

B Fe-Al > rFeS/FeFe Positive absorption effect Mai less than Fe... 

Fig. 7—2. Spectral data to illustrate absorption and enhancement effects for three transition elements. (To avoid crowding, only part of the cobalt absorption curve is shown.) See Table 7-1. Case B. Substitution of A1 for Fe decreases absorption of incident beam and has little effect on analytical line. Net positive absorption effect. Case C. Substitution of Pb for Fe decreases absorption of primary beam but greatly increases absorption of analytical line. Net negative absorption effect. Case D. Note wavelength relationship indicated in figure. Enhancement impossible. Case E. Note wavelength relationship in figure. Enhancement occurs.

Equation 7-6 is thus reasonable as the basic equation for x-ray emission spectrography when only absorption effects are present. 

The change in the absorption effect with chemical composition can be calculated in simple cases by properly adjusting a (Equation 7-5) to allow for the change in mass absorption coefficient. The mass absorption coefficient of the sample for a given wavelength is given by... 

Estimation of Absorption Effects in Sodium Tungstate Solutions... 

Sodium tungstate solutions have provided data for the testing of Equation 7-6. These data, obtained in the authors laboratory, show that absorption effects can be calculated for a series of solutions in which the calculated critical thickness (Equation 6-8) decreases from 0.4 cm for water, the solvent, to only 0.1 cm for the most concentrated solution tested. In order not to confuse the issue here, the details of the cor-... 

In the testing of Equation" 7-6, it is important to remember that the presence of a constant absorption effect would not distort analytical results. It is the change in absorption effect from one sample to another that leads to deviations, and the test of the equation is to determine whether a as calculated from Equation 6-6 satisfactorily reflects this change. 

The constancy of the quotient in the last line of Table 7-2 is greatly improved over that in the line above the last, proving that Equation 7-5 holds. So far as we know, this is the first case in which the absorption effects for a series of solutions have been obtained so precisely. Examples of this kind place on a firmer basis the calculation of semiquantitative analytical results from measured intensities when the composition of the matrix (all of S but E, the element sought) in a sample is approximately known. For example, tungsten contents could be estimated from measurements of L7I intensity for sodium tungstate solutions even when other salts are present in the absence of such salts, tungsten contents... 

As indicated above, absorption effects can generally be predicted and satisfactorily estimated when only monochromatic x-rays are involved. When a polychromatic beam is used for excitation, the filtering of the beam by the sample complicates the situation and modifies the absorption effects. Even then, fairly reliable estimates of the effects can be made. 

Excitation by Ao is the kind of excitation to which Equation 6-4 and its sequels apply this excitation leads to the absorption effects of the previous section. It can be treated successfully (as indicated above) by narrow, parallel beam geometry, which is certainly applicable to the well-collimated beam of a good spectrograph with a detector of small... 

The deviations of Class I, here called absorption and enhancement effects, are known in the literature also as matrix effects, as self-absorption, and as interelement effects. The authors consider the most important objection to each of the last three names to be as. follows. To matrix effect the element sought (ncrt included in the matrix) contributes to the absorption effect for the sample in the same kind of way as any element (free or combined) in the matrix. To self-absorption the name makes no provision for enhancement effects. To interelement effects it fails to recognize that an absorption effect occurs even when only one element is present (Equation 7-4). The term matrix is useful but requires precise definition. What is the matrix when an internal standard is added, or when a powdered sample is dissolved ... 

The first extensive1 study of x-ray excitation (1.17) as a method of producing x-ray spectra for analytical purposes was carried out by Glocker and Schreiber,17 who not only treated absorption effects very thoroughly and introduced the concept of critical thickness, but who... 

The earlier discussion (7.3) leads one to expect absorption and enhancement effects in these high-temperature alloys. For example, the results for nickel will be very sensitive to the iron content. Nickel Ka has a wavelength about 0.1 A shorter than that of the iron K edge (Figure 7-2), and a slight increase in the iron content consequently means an increased absorption of nickel Ka, which tends to reduce the apparent nickel content (negative absorption effect). Furthermore, this increased absorption of nickel Ka will enhance iron Ka, whence an... 

Table 7-4 shows the precision attainable when no part of the observed error can be attributed to inadequacy of the standard. The greater the precision attainable under such conditions, the more desirable it is to restrict the composition range over which a standard is used in order that differences in composition between standard and unknown do not reduce the reliability of the results, owing to a difference (between standard and unknown) in the enhancement and absorption effects of the preceding paragraph. 

Inspection of the table shows that the quotient a/Wj e is in fact nearly constant that I changes much less rapidly than W e] and that the critical depth has doubled when the highest oxide is reached. All three conditions are reflections of the (positive) absorption effect that occurs in this binary system when iron is replaced by oxygen, which has a lower mass absorption coefficient. 

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