QUANTITATIVE ANALYSIS OF ALLOYS BY X-RAY SPECTROSCOPY BY C. E. EDDY A S D T. H. LABY
In a recent paper Terrey and Barrett' have given an account of quantitative analysis carried out by the method of X-ray emission spectra. It is our experience that correct analyses can be made with this method provided certain conditions are fulfilled, and we wish therefore to offer some comments regarding their experiments as we think that their conclusions may prejudice the X-ray emission method of quantitative analysis. The X-ray tube.-The target of their X-ray tube was inadequately cooled owing to the high thermal resistance of the path between the focal spot and the cooling water. This resulted in the vaporisation of zinc from a brass target and no doubt was the source of many of their difficulties, including the change in atomic concentration of their target. The overheating of the target would further contribute to the very long exposures they found necessary. With a path of low thermal resistance, alloy targets with melting points as low as 160°C. have been used without volatilisation even with tube energies of one kilowatt.* Amalgams can be used in hot-filament type X-ray tubes if the cooling system is properly d e ~ i g n e d . ~It is true that substances volatile a t room temperatures and non-metallic substances (i.e., substances with low thermal conductivities) have so far proved difficult or impossible to use as the target of an X-ray tube, but no difficulty should be experienced with alloys of high melting point. The measurement of exposures.-In quantitative analysis it is necessary to measure the exposures (which are proportional to (voltage)" X tube current X exposure time) with the accuracy desired in the analysis. In practice the voltage should be kept constant throughout, and it is preferable to keep the current constant in order to avoid the serious difficulties of measuring the average value of a varying current. The authors used an induction coil to excite their X-ray tube. Of high tension generators the induction coil is the least suitable for quantitative X-ray work both on account of the wave-form of the potential which it generates and of its irregularity of operation. The applied voltage was measured with a spark gap, which has the the defect that it only indicates when the voltage exceeds the value fixed by the length of the gap, and the mean R.M.S. value for the whole exposure cannot be inferred with certainty. An electrostatic kilovoltmeter is much to be preferred t o a spark gap as it gives a continuous record of the R.M.S. value throughout the exposure. TT'ith the poor regulation given by an inducTerrey and Barrett: J. Phys. Chem., 35, 1 1 5 6 (1931). ? E d d y and Laby: Proc. Roy. SOC.,127, 32 (1930);(afterwards referred to aa I). ?Eddy and Turner: R o c . Roy. Soc., 111, 119 (1926).
3636
C. E . EDDY AND T. H. LABY
tion coil, changes in the tube current due to the evolution of gas from a hot target would be accompanied by large changes in the applied voltage, and the condition of constant voltage could not be maintained. The photographzc method of measurang lzne intensitzes.-Terrey and Barrett state that “all photographic methods used in the determination of the intensities of X-ray spectral lines are, on account of the shape of the blackening curve, liable to introduce error.” I t should be pointed out that this statement ignores the development in recent years of an accurate technique for the photographic measurement of spectral line intensities. It is possibly of value to recall the history of this. With the development of quantum theories, intensity relationships in optical spectra became predictable, and photographic methods of measurement were developed to confirm these predictions. The Physical Laboratory of the University of Utrecht has made notable contributions1 to this subject and the results obtained are accepted universally and are in agreement with theory. The photographic action of X-rays was investigated here in 1 9 1 9and ~ photographic methods have been applied in this and other laboratories3 to the measurement of X-ray line intensities; the method yields results reproducible to about 1% and in agreement with those obtained by both the ionisation and counting methods and with the0ry.l There can be no doubt now as to the accuracy and convenience of the photographic method, in which the shape of the blackening curve can be readily determined. Terrey and Barrett found by the wedge method, which they used in many of their experiments, that the ratio of the intensity of the K al line to that of the N 012 line had a value of one or less. It is well known that the value of this ratio is z for the doublets they measured. I t is evident that the intensities they obtained using the wedge method are unreliable and to an extent which vitiates their conclusions based on this method of measurement. The accuracy of the measurements made with the ionisation chamber cannot be checked in this way, as the azand allines were not measured separately. A possible explanation of the incorrect values which they found for the intensities of the lines is that the spectrometer crystal was not rocked uniformly and symmetrically in a wide sweep about the mean position of the two lines whose intensities were to be compared. If this essential condition is not satisfied, serious errors will occur in the measurement of the ratio.d The e f e d 01 absorptzon.-Terrey and Barrett in their treatment of the effect of absorption of radiation in the target state: “This absorption effect will occur whenever there are present on the anticathode two elements such that the characteristic radiation of one falls mithin the absorption region of the other.” “From these figures (see p. 1158) it is seen that the K a2.1line of silver falls within the absorption region of copper.” “Copper and silver See Dorgelo: Physik. Z., 26, 756 (1925). Miss Allen and Laby: Proc. Roy. SOC.Vict., 31,4 2 1 (1919); Glocker and Trauhe: Physik. Z., 22, 345 (1921);Bouwers: Z. Physik, 14, 374 (1923); Dissertation, Utrecht (1924). 3Rogers: Proc. Phys. Soc., 43, 59 (1931); Webster: 41, 181 (1929); I, p. 26. See the papers of Duane and co-workers, Siegbahn and co-workers, Allison and Armstrong, H. C. Webster, and others; or Siegbahn: “Spectroscopy of X-rays,” p. 97. I, p. 31. 1 2
ANALYSES O F ALLOTS BY X-RAY SPECTROSCOPY
3637
therefore afford a very good example of this absorption effect.” “In the . ~ of zinc occurs.” case of the copper-zinc alloys no absorption of the K ( ~ 2 line As will be seen from the table of absorption coefficients given below, the last of these statements is incorrect and the first three are inexact in their quantitative implications.’ To illustrate the effect of absorption, the authors take a silver-copper alloy as a “very good example” of a target for which the K lines of silver would be absorbed in the copper, and they take brass as an example in which there is “no absorption” of the zinc K a doublet. Actually the zinc lines would be more strongly absorbed than the silver lines. Although the absorbed silver radiation would give rise to fluorescent copper radiation, the effect of this would be more than offset by the very great absorption of the copper rays in silver. It is true that the effect of absorption in the target material is all-important in quantitative analysis by X-ray spectroscopy, and this has been investigated and discussed by several workers.z Radiation
Silver K a Zinc K a Copper a
Wave length
0.5
w
4
1.4 1.5
-4
Absorber
Copper Copper Silver
.4bsorption coe5cient 27
gm-l cm2
43 gm-l cmz 160 gm-l cm2
The abrupt discontinuity in Graph I shown by Terrey and Barrett cannot be explained by “assuming that the number of copper atoms present are insufficient to absorb the optimum quantity of emitted silver radiation” as the absorption is proportional to the number of copper atoms present. Theorelzcal dzscussion. The fourth equation on p. I I 5 7 and the second on page I 158 of the theoretical discussion are incorrect (probably as a result of printers’ errors), but it is not clear why a value of 4.3 j should be substituted for the constant K to obtain the results given in the last column of Table IT’. From these results it would appear that the authors obtained values from the photographic method in closer agreement with those of chemical analysis than from the ionisation method. There seems to be no reason why the expression
for elements of
nearly equal atomic number should become 2 I a (’I- for elements of widely I2 Cl C? different atomic number. Results of preizous workers. Several workers? have shown that, with alloys of elements of nearly equal atomic number, the quantity of an element can be determined from a direct comparison of line intensities. Recently* we have investigated a number of alloys of elements of nearly equal atomic number, with widely varying concentrations, and the results obtained by X-ray and other methods are given below.
+
For a treatment of X-ray absorption see Siegbahn: “Spectroscopy of X-rays,” p. 6, or Compton: “X-rays and Electrons,” p. 6. ZHevesy, Bohm, and Faessler: 2. Physik, 63, 74 (1930); Glocker and Schrieber: Ann. Physik, 85, 1089 (1928); Schneber: Z. Physik, 58, 619 (1929). See I, p. 24.
’ I, 0.3j.
3638 Alloy
C. E. EDDY AND T. H. LABY
X-ray analysis Mean
Chemical analysis or synthesis
Cu in Zn
cu.
73 .oo c'c
Cu in Zn
12c;
cu.
0 112y
cu.
I
Cu in Zn
0.114 0.113
0.124
I
1?
0.116)
Sn in Cd
j1.I 71.2
0.11;
I
>
~
70.9 71.3 J ~
P b in Bi
60.1 60.6 60.1 60,1
Zn in ZnCuSn
12.1 12.1
12.2 12.2
71.1
7 0 . 8 ~ ; Sn.
60.2
60
12.2
12.217~
' 1
1
1 '
45';
Pb.
I
1 j
Zn.
I t will be seen that the agreement is particularly good when it is remembered that the discrepancies include the errors arising in the photographic measurements of intensity as well as in the determination of the amount of the element by chemical methods or by synthesis. Methods of quantitative analysis have also been developed for mixtures of elements of widely different atomic number. Coster, Hevesy, Nishina and others' have carried out determinations of the hafnium content of a large number of zirconium minerals, and we have analysed a number of lead-zinc alloys with a lead content varying from 0.1 to o.ooj',v~.2 'Vatural Philosophy Laboratory, Cniuersily of Melbourne, August 15, 1931. 1 Coster and Nishina: Chem. News, 30, 149 f1g25j; Hevesy: "Recherches sur les propri6ti.s du Hafnium." 1, P. 39.
