Qr‘ASTITXTIYE X-RAY ASXLYSIY Copper-Silver and Copper-Zinc Alloys BY HENRP TERREY AND E n I c GEORGE VICTORY BARRETT
Introduction The application of X-ray spectroscopy to chemical analysis may be said to have commenced with the work of Moseleyl on the relationship between the atomic number of an element and the frequency of its characteristic radiation. In the realm of qualitative analysis, X-ray spectroscopy has demonstrated its use in a wide field, especially in the det,ection of “missing elements” in the periodic system. Attempts to make the analyses quantitative however have not so far been so successful owing to the complex nature of the phenomena involved. The general method employed in the quantitative analysis of a substance is the determination of the intensities of corresponding lines of the elements present in the emission spectrum of a sample of the substance, which is made to function as the anticathode in an X-ray tube. In order to determine the relative amounts of the different elements present from the intensity data obtained it is necessary to assume the following: that under equal exciting conditions corresponding lines in the same series of different, atomic spectra appear in an intensity ratio i:orrespmding to the atomic concentrations of the sample on the aiiticathc ie. Th chief sources of error encountered in this emission method are set, out in a paper by Glocker and Frohnmayer.? Some previous w o r k e d have obtained anomalous values for the intensities of the characteristic radiation measured. These results cannot be explained satisfactorily either by supposing vaporisation of one or more constituents from the anticathode, or by errors arising from the methods employed in the determination of the line intensities. These anomalous intensity ratios would appear to be due to the absorption of the characteristic radiation of one element by another on the anticathode. This absorption effect will occur whenever there are present on the anticathode two elements such that the characteristic radiation of one falls within the absorption region of the other. Theoretical I t may be assumed that the energy of an X-ray line is proportional to the number of atoms of the corresponding element on the anticathode. This may be written as follows:E, = m.c, ’Phil. Mag., 26, 1024 (1913); 27, 703 (19x4). Ann. Physik, 76, 369 (1925 ) . J H . Stintzing: 2. physik. Chem., 108, 51 (1923); Coster and Nishina: Chem. Sews, 130, 179 (1925); Gunter and Stranski: 2. physik. Chem., 118, 257 (1925); Gunter and Wilke: 119, 219 (1926).
QrAXTITATIVE X-RAY AXALTSIB
IIj7
The proportionality between energy and concentration would hold for all kinds of atoms and is a general expression. I n the particular case of two atoms adjacent t.o one another in the periodic system it is possible to carry this relationship a step further. Such atoms would have very similar inner electron systems and consequently the energy relationship for the same lines in their respective spectra, under equal exciting conditions, will be given by:-
El _ E?
Xo. of atoms of I . No. of atoms of Y .
The intensity of a line is a measure of the energy of the line. Thus the intensity of a given spectral line is proportional to the atomic concentration of the element emitting the line. In the special case of two elements adjacent in the periodic system the relationship given above will, under equal exciting conditions, hold for the ratio of the intensities. There remains to be considered the effect of the applied voltage upon the line intensity. Kebster and Clark’ found that the intensity of a given line was proportional to the 3 2 power of the difference between the applied voltage and the critical exciting tension of the series of the element under consideration.
I
=
Constant (V-V,,,,J3!*
Whether this relationship is general or only applies to the elements investigated by Kebster and Clark is open to question.2 From the above work however it may be assumed that the intensity is proportional to some function of the difference between the applied voltage and the critical exciting voltage.
1 0:
f [(V-vrnin.)l
Taking the case of two elements radiating under constant exciting conditions, it is seen that the intensity relationship of t,hc spectral lines in t’he characteristic radiation of these elements will be constant.
Ki(Y - I7,in,)” Kz(V-V,i,,)” XI1 the expressions in the right hand side of the equation are constant so that 11- K1.f.(V- Ymin) or I? K?.f.(V-irmin,)
=
The applied voltage then does not alter the relationship between inten-itv and concentration, provided that it is kept constant Thuq it ib powihle to write for anv two elements
Phys. Rev.,
(2)
9,
571 (191j).
* Cf. Eddy and Laby: Proc. Roy. SOC., 127A,2 2 (1930)where reference to other relation-
ships is given.
1158
HENRY TERREY AND ERIC GEORGE VICTORY BARRETT
where Il and Ip are the intensities of the same line in the same series of the characteristic spectra of the two elements. The above is only true when neither of the elements absorbs the characteristic radiation of the other. Whether absorption occurs or not, the most general equation connecting intensity and atomic concentration is the following
I,
=
MI.
c1
In the special case of two elements adjacent to one another in the periodic system, the minimum critical exciting voltages of the two are almost equal. If a sufficiently high voltage be applied to the tube so that the difference between the applied voltage and the critical exciting voltage of either element is large in comparison to the difference between the critical exciting voltages of the elements, then we have
Considering these two elements together on the anticathode, the following intensity concentration relationship would hold for similar lines of their emission spectrum.
Of all possible methods of carrying out quantitative analysis by means of X-ray spectra the simplest is the Emission method. This is by a direct measurement of the intensities of the lines of the characteristic radiations of the elements on the anticathode. As has been seen the intensity of a given line in the emission spectrum is proportional to the number of atoms emitting that line. So that if the proportionality factor be known it is possible to determine the number of atoms present. In the emission method the question of absorption arises. Where there are present on the anticathode two elements, such that the lines in the emission spectrum of one falls within the absorption region of the other then absorption will occur. Also a strengthening of the radiation of the absorbing element will take place owing to the emission of secondary or "fluorescent" radiation. In the present work alloys of copper and silver and copper and zinc are used, and measurements of the intensities of the K a radiations made. Taking a mean value for the wavelengths we have the following values KCY2.1
Silver Zinc Copper The absorption limits are as follows: Zinc Copper
0. j60
A"
1.445 A" 1.539 A"
1.296 A' 1.379 A"
QCANTITATIVE X-RAY KVALYSIS
1159
From these figures it is seen that the Kcr,,, line of silver falls within the absorption region of copper, as also does the weaker KB silver radiation. This silver radiation will be partially absorbed and its intensity suffer diminution. The intensit'y of the copper radiation however will be strengthened by the addition of the secondary Cu radiation set up by the absorbed Ag radiation. Copper and silver therefore afford a very good example of this absorption effect. In the case of the copper-zinc alloys no absorption of the Kcx,,,zinc line occurs, and hence the mixture approximates to the conditions where two elements adjacent to one another in the periodic system are excited to emit radiation. Thus the copper-zinc concentrations can be directly deduced from the intensity ratios, the line intensities being in the same ratio as the atomic concentrations of the respective elements. Vaporisation yet remains to be considered. This is the most serious difficulty that is to be met with in the emission method. Previous workers have attempted to eliminate this source of error by keeping the current passing through the tube as small as possible, in order to minimise heat effects, and by embedding the analysed substance in a non-volatile medium. By the use of alloys however the trouble of volatilisation is almost entirely eliminated. K i t h long exposures however in the case of the copper-zinc alloys, the well known zinc volatilisation occurs. A11 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. In the present work this source of error is eliminated by measuring the intensities of the lines by means of the ionisation produced by their passage through a gas. The method however suffers from the drawback that it is not as sensitive as the photographic method, and that it requires a relatively intense beam to produce any marked ionisation effect. For this reason it was found t o be impossible to make any measurements, using the ionisation method, on a mixture of oxides or on a mineral. Another method of measuring the intensities WXP tlcvised by the authors. It is a photographic method: hut it docs not dcprntl on the estimation of the blackening of a photographic film .I \rcdgc-shapcd pirw of aluminium is placed in front of the photopxphic film in t h e c:iriwr:i, I.incs will be obtained on the film whose height w i l l tl(,pcxntl o n thr thickness i l f aluminium that each particular beam has bcrn :ihlo t o pcxnc>tr;it(i. 13y ;I iiir:isurrnirnt of the height of thi. tliiiii.ri.;ion> of the \rc~lgc%, the thicknesses of these lines and a knowl(~tlgc~ of aluminium that the v*irioti- lint,. ti:iv
