912
ANALYTICAL CHEMISTRY
done hj- the comparative method ( 6 ) with aluminum as the standard. Typical results are given in Figure 3, in which a maximum corresponds t o a minimum in Figure 1 owing to the difference in ordinates. It is clear immediately that deviations from linearity do occur, for a maximum was obtained under some conditions with a sample of each of the volumes listed. The magnitude of the deviations is, of course, reduced by the appreciable absorption of x-rays by the nonmetallic elements in thesamples.
alumiiium foil therein (4). The resulting values are given in Figure 3 alongside most experimental points. Effective wave lengths obtained as just described often serve for the estimation of absorbance (Equation 2) when polychromatic beams are used and Equation 1 is valid-e.g., in the case of the nitrate solutions of Figure 1. When the deviations under discussion occur, however, Figure 3 shows that absorbances may pass through maxima while effective wave lengths vary in one direction. Circumstances such as this tend to reduce the usefulness of the concept of effective wave length. For a given volume of sample Figure 3 shows that the tendency to produce a maximum is greater as the voltage on the x-ray tube is increased. This effect is no doubt due to the concomitant change in the energy distribution in the beam incident on the sample, but the authors have not attempted to prove this quantitatively, partly because all the requisite data are not available. I n the case of curves I11 and V, however, such proof is scarcely required. For curve 111, the short wave-length limit (0.43 A. at 28.5 kv.) is almost coincident with the absorption edge (that of silver near 0.48 A.) responsible for the maximum. Accordingly, the beam will contain very little energy in the neighborhood of the absorption edge, and no appreciable deviation from linearity traceable to this absorption edge is to be expected (contrast with Figure 1). There is no such close coincidence for curve T’. CONCLUSIOri
VEASURED EFFECTIVE WAVE L E N G T H G I V E N AT E A C H POINT
1
j
20 80
0 100
Figure 3.
I11
v
I
I
60 40
80
60
20
100 %Aq NO, SOLUTION 0 %Cu(NO,),SOLUTION
Deviation from Linearity for Copper and Silver Yitrate Volume of Solution, MI.
Curve
I I1 IV
I
40
.
50 25 10 10 25
Solutions of
Peak Voltage, Kv.
34.5 34.5 34.5 42.0
It appears to be established that the presence of absorption edges can lead to deviations from the linear mass absorption coefficient relatiowhip when a polychromatic x-ray beam is incident upon a sample containing more than one element. It is certain that this article does not describe all the systems in which such deviations are possible, and it is probable that these may take forms different from those shown in Figures 1 and 3. Although the occurrence of these deviations restricts the usefulness of polychromatic b e a m for purposes of chemical analysis, this restriction should not prove generally serious, provided the investigator is forewarned. When such deviations occur, it will often be possible to carry out the analysis by x-ray methods under other experimental conditions.
28.5
Under the simplest conditions, the ordinates (mils of aluminum equivalent to 1 ml. of solution) should be identical for all solutions of copper nitrate alone. That they are not is probably due t o another type of deviation commonly encountered with polychromatic beams-namely, the well-known variation of p m with wave length for monochromatic beams. As a consequence of this variation, the mass absorption coefficient of a sample for a polychromatic beam decreases with the thickness of the sample because the effective wave length decreases continuously as the beam progresses through the sample. This deviation is more pronounced for aluminum (owing to its lower mass absorption coefficient) than for copper, and the equivalent thickness of aluminum per milliliter of copper nitrate consequently increases with the thickness of the copper nitrate sample. The same argument applies t o solutions of silver nitrate (in this connection, see 1 , Table XIII, and 4 , Figure 3). When polychromatic x-ray beams are used in absorptiometry, it is ordinarily useful to consider their “effective r a v e lengths,” these being the wave lengths of the corresponding monochromatic beams toward which the sample exhibits the same absorption coefficient. The true effective wave lengths of the beams operating on the solutions of Figure 3 are unknown. In default of these, effective wave lengths of the beams emerging from the solutions were measured by determining the absorbances of thin
ACKNOWLEDGMENT
The authors wish to thank Kurt Berman for doing the calculations on hypothetical elements A and C, and Grace Poellmitz for carrying out the measurements on the copper-silver nitrate solutions. LITERATURE CITED
(1) Calingaert, G., Lamb, F. W.,Miller, H. L., and Soakes, G. E., *4N.4L. CHEM., 22, 1238 (1960). (2) Compton, A. H., and Allison, S. K., “X-Rays in Theory and Experiment,” Xew York, D. Van Nostrand Co., 1935. (3) Liebhafsky, H. A., ANAL.CHEM.,21, 17 (1949). (4) Liebhafsky, H. A., Smith, H. M., Tanis, H. E., and Winslow, E. H., Ibid., 19, 861 (1947). (5) Treloar, L. R. G., Phil. M a g . , 6, 1008 (1928). (6) Zemany, P. D., Winslow, E. H., Poellmitz, G. S., and Liebhafsky, H. A., -4XAL. CHEM.,21, 493 (1949). RECEIVED December 20, 1960.
CORRECTION. I n the article on “Design and Operational Characteristics of Cartesian hfanostats” [AXAL. CHEM.,23, 157 (1951)] the model referred to as the Ritzer manostat should have been the Holzschuh-Long manostat. ROGERGILMONT
