cm-1 region there are many strong and relatively sharp hydrocarbon bands which can markedly affect the differential spectra of gasolines if there is slight mismatching of sample and reference cells. On the other hand there are no discrete gasoline hydrocarbon bands in the spectra of gasolines near 3600 cm-l although the transmission level varies with frequency. The absorptivities of the OH stretching bands are less than those of the CO stretching bands, but the higher transmission of the gasolines in the 3600 cm-l region makes possible the use of longer pathlength cells which more than compensates for the lower absorptivities. Jenkins and Scruton ( 4 ) state that the 1100 cm-l region method of Powell ( 2 ) is unsatisfactory for additive concentrations of less than 0.5 %, and also that unidentified bands are sometimes superimposed on the additive spectrum and interfere with the determination. The present method is also superior to that of Jenkins and Scruton ( 4 ) which employs infrared examination of the antiicing additive in the 1100 cm-l region after extraction into water. In their method the extraction is also a concentration step, the fuel/water ratio being l O O / l , because strong infrared absorption by water necessitates the use of short pathlength cells (0.024 mm). Because of the high fuel/water ratio the extraction of the anti-icing additive is incomplete and the extraction efficiency is dependent on temperature and gasoline composition. The chemical (6, 7) and the freezing-point-depression methods (5) are reported for the determination of methyl Cellosolve in jet fuel but they can be applied to the other antiicing additives in gasolines. However, the anti-icing additive can not be identified by any of these methods and accurate results can only be obtained if the additive is known or is identified by another technique. The dichromate method ( 6 ) is also relatively lengthy and time-consuming. An 8Ojl fuel/water extraction is involved in the freezing-point-depression method and, as above, the extraction is temperature- and composition-dependent. Also infrared examination of water extracts (to identify the anti-icing additive) often show that materials other than anti-icing additives are present and these
will obviously affect the results obtained by the freezing-pointdepression method. The present analytical method is therefore an essentially simple and rapid procedure which overcomes the disadvantages and difficulties experienced with other methods. It has been used successfully to identify and determine the freezing-point-depressant anti-icing additives in a number of gasolines and jet fuels containing known amounts of antiicing additive and in a number of commercially available gasolines. The analysis can be carried out on most linear wavenumber grating spectrometers, and on linear wavelength prism instruments for the glycol and glycol-ether additives where both appearance and frequency of the bands differ. Difficulty would probably be experienced in distinguishing between isopropanol and methanol on a prism spectrometer. Time required for identification and determination of the anti-icing additives is approximately 30 minutes. The precision of the method is very good; standard deviations, based on the calibration data of Tables I and 11, are 0.0005, 0.0024, 0.0004, 0.022, and 0.016% for hexylene glycol, methoxy glycol, methyl Cellosolve, methanol, and isopropanol, respectively. Under the conditions of the analysis the limit of detection for methoxy glycol is almost 0.01 and somewhat less for hexylene glycol and methyl Cellosolve; the limits of detection for methanol and isopropanol are approximately 0.03 and 0.07 %, respectively. The analytical conditions have been chosen to be suitable for the expected concentrations of the anti-icing additives in the hydrocarbon fuels. Thus the limit of detection for the alcohols could be decreased by a factor of ten by using a five-fold dilution, and there is also some latitude for variations in cell pathlength and dilution for hexylene glycol and the glycol-ethers.
RECEIVED for review March 13,1970. Accepted June 4,1970. Presented in part at the 16th Spectroscopy Symposium of Canada, Montreal, October, 1969.
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Quantitative Analysis of Ternary and Quaternary Semiconducting Alloys with Electron Microprobe Mary C . Finn Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Mass. 02173
QUANTITATIVE ANALYSIS with the electron microprobe depends upon the conversion of measured X-ray intensities to chemical compositions, This paper describes a method which uses theoretical calibration curves in the determination of elements A and B in ternary A1-,B,C alloys which are pseudobinary solid solutions of the semiconducting compounds AC and BC. This method has been used for analyzing the following alloys: CdTel-,Se,, CdS1-,Se,, Znl-,Cd,S, Znl-,Cd,Te, ZnTel-,S,, ZnTel-,Se,, ZnSel-,S,, Hgl-,Cd,Te, Pbl-,Ge,Se, Pbl-,Ge,Te, Pbl-,Sn,S, Pbl-,Sn,Se, Pbl-,Sn,Te, Snl-, Ge,Te,GaAsl-,P,, 1084
Ga,-,In,P, Gal-,In,As, InSbl-,Te,, Pbl-,Cd,S. Except for the systems formed between InSb and InTe and between PbS and CdS, both constituent compounds in each system belong to the same group of semiconductors, either the 11-VI, IV-VI, or 111-V group. In all the systems the atom fraction of element C in the constituents is known to be 0.50 0.01 within experimental error, and is assumed to be '12 in the alloys. An iterative procedure for using theoretical calibration calculations in determining all four elements in the quaternary solid solution Pbl-,Sn,Tel-,Se, is also described.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 9, AUGUST 1970
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ANALYSIS OF TERNARY ALLOYS
Conventional experimental techniques are used to obtain the X-ray intensity data. The alloy sample or samples and the standards for elements A and B are polished flat and then mounted on a cylindrical brass sample holder for insertion into the micoprobe. Samples of ZnSel-,Te, and Hgl-,Cd,Te are coated with an evaporated carbon film to prevent electrostatic charge accumulation. The standards used are the constituent binary compounds AC and BC, except for the determination of Sn in Pbl-,Sn,S. In this case, Sn metal is used, since we do not have SnS available. Some of the other pure elements could also be used as standards, but it would be impractical to use a number of them (for example, Pb, As, and S) because it is difficult to prepare these with polished, flat surfaces. The microprobe has a take-off angle of 15.5" and is equipped with two spectrometers. The excitation voltage is 25 kV. The electron beam is normally focused to a spot size of 2-3 pm. Sample, standard, and background counts are taken. The sample measurements are made at a number of different locations, usually at least 10. In making these measurements, simultaneous readings are taken with both spectrometers, one aligned for each element being determined. To reduce the data, background corrections are made, and the ratio k of sample counts to standard counts is then determined for each element. The weight fraction of the element in the alloy is then obtained by using a theoretical calibration curve, which gives the counts ratio k as a function of the ratio of the weight fraction of the element in the alloy to its weight fraction in the standard. The calibration calculations employ the atomic number correction of Duncumb and Shields ( I ) with the Nelms electron range values ( 2 ) ; the absorption correction of Philibert (3) modified by Duncumb and Shields (4) with the mass absorption coefficients of Heinrich (5); and the characteristic fluorescence correction of Reed (6). (Interpolated values of k as a function of weight fraction ratio, which can be used to construct the calibration curves for each element in each alloy system, are available from the author.) The final step in the determination is to convert the weight fraction of the element to the mole fraction of the corresponding compound, either (1 - x ) or x in A,-,B,C. Table I lists the results of analyses on five different samples of Znl-,Cd,Te. The first column gives the mole fraction of ZnTe, (1 -x), obtained from the analytical data for Zn, and the second gives the mole fraction of CdTe, x , found by the independent determination of Cd. The total of (1 - x ) and x is listed in the third column. In each case this total differs from 1 by less than 1%. Similar consistency between the independent determinations of the two elements has been obtained for all the other ternary alloys analyzed, except for a few samples which appear to be extremely inhomogeneous. (1) P. Duncumb and P. K. Shields, Brir. J. Appl. Phys. 14, 617 (1963). (Numerical values of R used are those tabulated by
T. 0. Ziebold in The Electron Microanalyzer and its Application, Lecture notes for summer program at the Massachusetts Institute of Technology, 1965.) (2) A. T. Nelms, NBS Circular 577 (1956) and Supplement (1958). (Numerical values of S used are those tabulated by T. 0. Ziebold, Ibid.) (3) J. Philibert, in X-Ray Optics and X-Ray Microanalysis, H. H. Pattee, V. E. Cosslett, and A. Ergstrom, Eds. Academic Press, New York, N. Y . , 1963, p 379. (4) P. Duncumb and P. K. Shields, in The Electron Microprobe, T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Eds. John Wiley & Sons, New York, N. Y., 1966, p 284. (5) K. F. J. Heinrich, ibid., p 296. (6) S . J. B. Reed, Brit. J . Appl. Phys. 16,913 (1965).
Table I. Analysis of Znl-,CdzTe Alloys X Total
1-x
0.647 0.502 0.388 0.284 0.169
0.350 0.490 0.617 0.710 0.839
0.997 0.992 1.005 0.994 1.008
2
0.351 0.494 0.614 0.714 0.832
Table 11. Comparison of Microprobe and Wet Chemical Analyses Microprobe analysis, mole fraction
Wet chemical analysis, mole fraction
PbTe
SnTe
Pbl-,Sn,Te Total PbTe
SnTe
Total
0.968 0.943 0.799 0.620
0.031 0.062 0.207 0.378
0.999 1.005 1.006 0.998
0.986 0.940 0.797 0.608
0.017 0.057 0.206 0,385
1.003 0.997 1.003 1.003
PbSe
SnSe
Pbl-,Sn,Se Total PbSe
SnSe
Total
0.927 0.833
0.060 0.140
0.987 0.973
0.060 0.137
0.994 1,003
0.934 0.866
The last column in Table I gives the values of I,the quantity found by dividing the value of x in the second column by the total given in the third column. This quantity is the average mole fraction of CdTe obtained by weighting the independent results of the Zn and Cd determinations on the assumption that the relative error of measurement is the same for each determination. We have adopted 3 (or the corresponding quantity l-x = 1-E) as the most significant analytical result to be reported. For two of the alloys analyzed, Pbl-,Sn,Te and Pbl-,Sn,Se, enough sample material was available for the microprobe analysis to be checked by wet chemical methods which could be standardized experimentally. In the wet chemical analyses, Pb and Sn were determined independently, by using potentiometric titration techniques for the telluride samples and X-ray fluorescence techniques for the selenide samples. The results are shown in Table 11. There is good agreement between the microprobe and wet chemical methods, except for the two Pbl-,Sn,Te samples with lowest Sn content, where the error in both analyses is large. This agreement further supports the validity of the calculated calibration curves for the microprobe analysis. ANALYSIS OF Pbl-,Sn,Tel-,Se,
ALLOYS
In these quaternary alloys, none of the elements has a fixed atom fraction, as C does in the A1-,B,C ternary alloys. However within the error of the microprobe, the sum of the atom fractions of Pb and Sn must equal l / 2 , as must the sum of the Te and Se atom fractions. This restriction is used in an iterative method of calculating the chemical compositions from the measured X-ray intensities. The experimental technique is the same as used in analyzing the ternary alloys, except that intensity measurements are made for all four elements. The standards used are PbTe for Pb and Te, SnTe for Sn, and PbSe for Se. The first step, lA, is to determine an initial value of (1 -x) from the measured k for Pb, by using the calculated curve of (1-x) us. kpb for
ANALYTICAL CHEMISTRY, VOL. 42, NO. 9, AUGUST 1970
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Sample 1
2 2 2 3
2
4 2
1
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Table 111. Analysis of Representative Pbl-SnzTel-$3e, Alloys Pb Sn Te Wt. frac. 0.540 0.068 0.384 X At. frac. 0.180 0.974 0.820 Wt. frac. 0.535 0.082 0.360 X At. frac. 0.789 0.211 0.893 Wt. frac. 0.533 0.060 0.326 X At. frac. 0.837 0.163 0.754 Wt. frac. 0.072 0.291 0.573 X At. frac. 0.820 0.180 0.640
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Figure 1. X-ray counts ratio k as a function of the mole fraction of Pb (1 - x), in Pbl-,Sn,Te and Pbl-,Sn,Se alloys, for take-off angle of 15.5’ and E, = 25 kV Pbl-,Sn,Te plotted in Figure 1 . A reasonably accurate estimate of (1-x) can be obtained in this way because the value of (1 - x ) corresponding to a given k is found to be almost independent of the Te/Se ratio. This is seen in Figure 1, which shows that the variation of (1-x) with k is almost the same even for the two extreme cases, Pbl-,Sn,Te and Pbl-,Sn,Se. We use the curve for Pbl-,Sn,Te merely because our samples are richer in Te than Se. The next step, lB, is to calculate for each of the four elements a correction factor, k/C, where C is the ratio of the weight fraction in the sample to the weight fraction in the standard. The value of k/C for each element is found by averaging values of this factor calculated for the initial (1 -x) and various values of y between 0 and 0.4, the range of y in our samples. The k calculations employ the atomic number and absorption corrections mentioned previously. No characteristic fluorescence corrections are needed. In step 1C the
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Se
Total
0.007 0.026
0,999 (2) 1.004 (2) 0.985 (2) 1.037 (2)
0.027 0.107 0.066 0.246 0.101 0.360
measured k for each element is divided by the calculated value of k/C to obtain C and then the weight fraction for that element. The weight fractions obtained in Step 1C are only approximate, and because they are determined independently their sum is not equal to 1. In Step 2A they are normalized to total 1, and in Step 2B the new weight fractions are used to calculate a new k/C factor for each element. In Step 2C these new factors are used with the measured k’s to obtain new values for the weight fractions. In Step 3 the procedure of Step 2 is repeated until there is no longer a significant change in the calculated weight fractions. In all the analyses which we have performed, the first repetition has given the same weight fractions as obtained in Step 2. The final step, 4, is to convert the weight fractions to atom fractions, normalize so that the atom fractions of Pb and Sn total 0.5 and those of Te and Se total 0.5, and calculate the values of (1-x), x , (1-y), and y . Since the total of these four quantities is 2, each one is found by doubling the corresponding atom fraction. The analytical results for four representative quaternary alloys, obtained by the procedure described, are given in Table 111. The values of (1 -x), x, (1 - y ) , and y calculated from the corresponding weight fractions are designated by “2 x at. frac.” Even in the worst case (Sample 4), the sum of the weight fractions obtained from independent measurements of X-ray intensity for the 4 elements differs from 1 by only 3.7%. ACKNOWLEDGMENT
The author thanks R. M. Morandi for the sample preparation, Mrs. M. J. Button for the data processing, J. C. Cornwell and E. B. Owens for the wet chemical analysis, and A. J. Strauss for many helpful discussions.
RECEIVED for review January 13, 1970. Accepted May 20, 1970. This work was sponsored by the Department of the Air Force.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 9,AUGUST 1970
