Problems in Using Mossbauer Spectrometry for Quantitative Analysis: Application to Tin P. A. Pella, J. R. DeVoe, and D. K. Snediker‘ National Bureau of Standards, Washington, D.C.
Leopold May Catholic University of America, Washington, D.C.
Initial studies for the application of Mossbauer spectrometry to the quantitative analysis of tin compounds are described. The effect of variables such as drift in detector response, sample thickness, and sample concentration on the spectral parameters was studied using P d P m S nas a source and synthetic samples of SnOz in an AL02 matrix as absorbers. Under controlled conditions, the reproducibility of the spectral parameters was studied for sample sizes from 3 to 122 mg of SnOz with a relative standard deviation (of a single measurement) for three replicates of 0.5 to 5% over this range of sample size. The data were well approximated by an exponential absorption law. Such factors as source-sample-detector geometry, use of filters, and a high resolution detector were considered in an effort to optimize the ratio of the resonant absorption intensity to the total transmitted intensity.
MOSSBAUER SPECTROMETRY is a spectrophotometric technique which uses gamma photons from a source to populate lowlying nuclear energy levels in the sample under study. This radiation is sufficiently monochromatic that changes in the nuclear energy levels caused by the immediate electronic environment surrounding the nucleus can be measured. As a result, hyperfine interactions such as chemical shift, electric quadrupole, and magnetic dipole interactions reveal structural information about the material in which the resonant nucleus is incorporated. Many reviews have appeared which discuss various applications of this technique (1-6). In addition to structural information, the application of this spectrometry to the quantitative measurements of a specific compound or entity present in a solid material would result in a more complete physicochemical characterization of that material. The spectrometric method involves a source of gamma photons of a particular radioisotope having a fraction, f s , of photons that have been emitted without recoil (e.g., that exhibit the Mossbauer effect). A fraction, fa, of these will resonantly absorb without recoil in the absorber. The difference in the nuclear energy transitions resulting from differences in chemical environment between the source and absorber is provided by Doppler shifting the energy of the gamma-rays emanating from the source. The energy width of the gamma ray is so small that no nuclei other than those of the Mossbauer radioisotope for that particular element in the sample are 1
Present address, General Electric Corp., Valley Forge, Pa.
(1) V. I. Gol’danskii, At. Energy Rev., 1, 3 (1963). (2) . , E. Fluck. W. Kerler, and W. Neuwirth, Angew. Chem., Intern. Ed., 2, 277 (1963). (3) G. K. Wertheim, Science, 144, 253 (1964). (4j H. Frauenfelder; “The Mossbauer Eff‘ect,” W. A. Benjamin, Inc., New York, N. Y. 1962. (5) J. R. DeVoe and J. J. Spijkerman, ANAL.CHEM.,38, 382R (1966). (6) N. N. Greenwood, Chem. Brit., 3, 56 (1967).
46
ANALYTICAL CHEMISTRY
likely to be resonantly excited by the incident gamma photons and in this respect the method would be completely specific. Of course, it is possible to analyze only for the specific Mossbauer isotope whose excited state is in the source. Therefore, this technique will analyze for only one element in the absorber and its direct quantitation is limited by the accuracy of the element’s isotopic abundance in the sample. However, the use of standards will help to eliminate this difficulty (see below). An expression derived by Margulies and Ehrman (7)related the magnitude of the resonant absorption to the concentration of the absorbing nuclei for a single energy transition using a non-self-absorbing source.
e is called the Mossbauer fraction of resonant radiation absorbed, Z( m ) and Z(0) refer to the transmitted intensities for nonresonant and resonant absorption, respectively. The effective absorber thickness is given by the expression TA = fAaoffAnAtAwhere fs and fA are the Debye-Waller factors for the source and absorber, respectively, uois the cross section for nuclear resonance, and CY^ is the isotopic abundance for nA atoms per unit volume with a sample of thickness, tam Jo is the zero-order Bessel function with an imaginary argument. Because fA depends on the lattice dynamic characteristics of the sample, an absolute determination of nA based on Equation l would be difficult even if the remaining parameters-i.e., fs, ao, aA and tA-COUld be measured with high accuracy. Therefore, in a manner analogoustoanalytical spectrophotometry, quantitative analysis for a specific element could be performed by dissolution of the sample and incorporating the analate in a reproducible matrix. A series of standards in an identical matrix would then serve as the basis for a calibration curve. If the element to be determined is present in the solid sample as two or more different chemical compounds, it may be possible to measure the ratio of these compounds provided the spectral resolution is adequate. This has been demonstrated in the determination of the ratio of Fe(I1) and Fe(II1) in silicate minerals (8) and more recently in iron phosphate glasses (9). Before the general quantitative approach can prove fruitful, it is necessary to establish the effect of certain variables on the Mossbauer spectral parameters. One of the variables considered was the time stability of the single channel analyzer (SCA). The function of the SCA is to permit detection of
(7) S. Margulies and J. R. Ehrman, Nucl. Instr. Methods, 12, 131 (1961). ( 8 ) T. C. Gibb and N. N. Greenwood, Int. Atomic Energy Agency, Vienna, 1955, Tech. Report Series No. 50, p 143. (9) T. Yoshioka, Y. Gohshi, and H. Kohno, ANAL.CHEM.,401 603 (1968).
100 98
>
5
96
r ( HALFWIDTH
W
I-
z
94
W
>
H
92
= I (a)- I
(0)
1
W
90
I ( 0 ) +I’
1. 0
I
I
I
I
1
I
I
I
A
Mossbauer Experiments. PROCEDURE A. Two values of sample thickness (0.5 and 2.5 mm), 5 values of sample composition from 7 to 86% of Sn02, and 5 SCA widths were tested. The lower level discriminator of the SCA was set at about 20 keV and the upper level was varied in five steps from 30 to 60 keV. This permitted an energy range from 10 to 40 keV to be detected. A weighed sample of the mixture was placed in the cell and mounted. The spectra were accumulated until a total of approximately 9 X lo5 counts/ channel appeared in the base line. This required from 2 to 6 hours per spectrum. All spectra were fitted as a singlet. PROCEDURE B. A 300-mg sample of mixture was placed in the 0.5-mm cell and mounted. The source-to-sample distance was 4.6 cm. This geometry was convenient because the sample could be mounted and removed without moving the detector, hence constant geometry is ensured. The single channel was set to pass radiation from 20 to 30 keV. The spectra were accumulated until a base line of 8 X lo6 counts/ channel appeared and required from 1.5 to 2 hours per spectrum. The uncertainty in the computer-estimated height of the Lorentzian function varied from 0.8 to 3% (relative standard deviation) whereas the uncertainty in the area varied from 2 to 7%. RESULTS AND DISCUSSION
photons within a certain energy range by pulse height discrimination. Other factors to be considered are the effects of sample thickness and sample concentration on the Mossbauer spectral parameters. A series of synthetic stannic oxidealuminum oxide samples were used to evaluate the method and to measure the effect of critical spectrometric parameters. EXPERIMENTAL
Apparatus. The NBS drift-free Mossbauer spectrometer was used in these experiments (IO). The aluminum sample absorber holder was especially constructed for mounting powdered samples of varying thickness from 0.5 to 2.5 mm (ZZ). The area of the cell was 2.84 cm2. The single line source containing 2.5 mCi 1191nSn was made as the alloy Pd3Sn (12). The pulse height spectrum of Pds ll9mSn taken with a NaI(T1) crystal consists of a broad single peak from approximately 18 to 35 keV. The energy of the gamma photons exhibiting the Mossbauer resonance effect is 23.8 keV. The moving absorber geometry was used throughout this work. The detector consisted of a NaI(T1) crystal (2.5 cm in diameter x 0.2 cm thick). Reagents and Preparation of Sn02-A1~03Mixtures. Stock solutions of tin and aluminum were prepared by dissolving reagent grade tin metal in concentrated HCl and A1(N03)3 9H20 in distilled water. The aluminum solution was standardized by complexometric titration with the disodium salt of EDTA. The hydrous oxides were coprecipitated according to Kolthoff and Sandell (Z3), placed in Pt crucibles, and heated in an electric furnace to about 1200 “C for complete conversion to the nonhygroscopic oxides. The SnOz content of these mixtures varied from 1 to 86%. In constructing the calibration curves, the tin contents of three of the mixtures were verified by controlled potential coulometry to an accuracy of better than 1%. (10) F. C. Ruegg, J. J. Spijkerman, and J. R. DeVoe, Reu. Sci. Instr., 36, 356 (1965). (11) L. May and D. K. Snediker, Nucl. Instr. Methods, 55, 183 (1967). (12) D. K. Snediker, “Mossbauer Effect Methodology,” Vol. 2, Plenum Press, New York, N. Y., 1966, pp 161-70. (13) I. M. Kolthoff and E. B. Sandell, “Textbook of Quantitative
Inorganic Analysis,” The Macmillan Company, New York, N. Y., 3rd ed., 1952, p 318.
In Figure 1 is a typical spectrum of SnOa in A1203. The height (H) and the full-width at half-height (r) are computed from the fitting’ of a Lorentzian function for the absorption peak and a parabola for the base line to the experimental points by an iterative least-squares procedure (14). For the Lorentzian, the peak area (A)is then related to the peak height by the equation A = 1/2 nm-
(2)
Experimentally, the transmission of nonresonant radiation [Z( m )] through the sample is accompanied by background radiation (Z’) from the source which appears in the window of the SCA. Therefore, the total transmitted intensity [Z( a) Z’]represents the base line (B)of the Mossbauer spectrum. The background radiation is comprised of other sources of radiation even though pulse-height discrimination is used. A number of X-rays are produced in the Pd8119”Sn source, the most important being the 21, 25, and 28 keV X-rays. These cannot be resolved with the detector, and therefore contribute to Z‘. In addition, photons of higher energy (180 to 1170 keV) have been identified in this source. The gamma rays are degraded in energy by Compton scattering so that they are accepted by the SCA and contribute to I’ (see below). In addition to the attenuation of the incident photons due to resonant absorption, there is an attenuation of the incident photons by the sample due primarily to the photoelectric absorption process. Because photoelectric absorption should affect the resonant and nonresonant portions of the incident radiation in the same way, the absolute magnitude of the ratio of peak area or peak height to the base line would not be affected. For this reason the ratios of AIB and HIB are used in these experiments. Stannic oxide was selected for this study because of our experience with this compound (IS) and the availability of a good single-line tin source, Le., Pd3119”Sn. An matrix was chosen because the photoelectric absorption of the 23.8keV Mossbauer gamma photons is small, and homogeneous samples are easily prepared.
+
(14) J. R. DeVoe, Ed., NBS Technical Note 404 (1966), pp 108-15. (15) R. H. Herber and J. J. Spijkerman, J . Chem. Phys., 42, 4312 (1965). VOL. 41, NO. 1 , JANUARY 1969
47
1
sn 02,mg
Figure 2. H / B us. mg SnO2 An experiment using a modified Youden square was designed to test the effect of varying the window width, the amount of SnO,, and the sample thickness on A / B and H / B (Procedure A). An analysis of variance did not give any evidence of an effect with variation in SCA over the indicated range. In addition, when either the amount of SnOz or thickness was increased, no effect on the portion of the pulse-height spectrum passed by the SCA was detected, other than a decrease in height because of the attenuation of the incident radiation. The increase in sample thickness from 0.5 to 2.5 mm resulted in a large increase in self-absorption by SnOz. A significant broadening of the spectral line was also observed. Line broadening as a function of sample thickness has been discussed (see above) (7). The results from this study showed that the reproducibility (standard deviation of a single measurement) at the larger sample thickness was much less than anticipated. This suggested that a more rigid control over the source-sampledetector geometry was necessary. Additional measurements were made (Procedure B) under carefully fixed geometry conditions. Figures 2 and 3 show the variation of H / B and AIB, respectively, with increasing amount of SnO,. The results are tabulated in Table I. As seen from Figure 2 , H / B has nearly reached a maximum value at 50 mg of SnO,. Above this value the peak continues to broaden, hence A / B increases as shown in Figure 3 over a much larger range of concentration. ~~~~~~~
SnOz, mg
HIB
(Mean)a (AIL?) sb (Mean)a ( H / B ) sb 0.0116 O.ooo6 3.50 0.1994 0.0105 0.0016 9.04 0.4298 0.0082 0.0314 0.0015 0.0496 16.28 0.6937 0.0015 0.0015 0.0726 1.064 0.017 28.82 0.0017 0.0831 38.22 1.286 0,028 0.0016 0.053 0.0943 52.84 1.534 0.0012 0.032 0.1004 56.85 1.648 0,0006 0.1086 76.35 1.961 0.040 0.0006 0.034 0.1165 97.11 2.249 121.9 2.422 0.086 0.1181 0.0005 Average of 3 replicates. * Computed standard deviation of single measurement based on 2 degrees of freedom. 0
48
ANALYTICAL CHEMISTRY
The “sensitivity” criterion of Mandel (16) was selected to determine if either A / B or H / B was a statistically superior spectral parameter for measuring the concentration of Sn02. The “sensitivity” of a curve at a given concentration is defined as the ratio of the slope to the standard deviation of a single measurement at that Concentration. The sensitivity of H / B appeared to remain relatively constant with increasing concentration since the standard deviation decreased at about the same rate as the slope of the curve. The sensitivity of A / B decreased with increasing concentration since the slope decreased while the standard deviation increased. Because of the uncertainties in the data, however, the confidence intervals for the estimated sensitivities of H / B and AIB overlapped in most of the regions of interest. These results suggest that the use of either parameter would be comparable from a statistical standpoint in the range from 3 to 76 mg of SnOz. Of the variables studied, the critical one is the source-sample-detector geometry. A least-squares fit of the experimental data to Equation 1 was performed. If I’ is assumed constant, Equation 1 can be rewritten in the form
~~~~
Table I. Variation of Spectral Parameters with Amount of SnOz Sample thickness, 0.5 m m AIB
Figure 3. A / B us. mg SnO,
where f =
I(m)
+ I”
K includes the constants V (volume),
f a , ro,CYA, t A , and rn is the mg of SnO, (nAV ) . The Bessel func-
tion Jo(iKrn/2) = Zo(Krn/2) see (17). At low concentrations (e.g., low E A ) , the assumption can be made that the function, Zo(Km/2),is approximately one; therefore, Equation 4 can be written as the familiar exponential relationship (similar to Beer’s law) H/B
= ,f’(l
-
(5)
where f’ and K ‘ are empirical constants that approach the theoretical constantsfand K , respectively, as m approaches 0. (16) J. Mandel, “The Statistical Analysis of Experimental Data,” Interscience Publishers, New York, N. Y.,1964, p 366. (17) M. Abraimowitz and I. A. Stegun, Eds., “Handbook of Mathematical Functions,” AMS 55, U. S. Government Printing Office, Washington, D. C . , 1966, p 378.
IOK
I
1
I
1
Table 11. Comparison of Calculated Values with Observed Values of H/B SnOz,mg
Observed
Calcd 10
Zo(Km/2)
Calcd 2b
3.50 9.04 16.28 28,82 38.22 52.84 56.84 76.35 97.11 121.9
0.0116 0.0314 0.0496 0.0726 0.0831 0.0943 0.1004 0.1086 0.1165 0.1181
0.0133 0.0311 0.0495 0.0719 0.0835 0.0961 0.0987 0.1083 0.1148 0.1199
1.002 1.014 1.045 1.146 1.263 1.532 1 ,628 2.260 3.363 5.627
0.0125
0.0297 0.0481 0.0716 0.0840 0.0974 0.1001 0.1094 0.1146 0.1177
Based upon least squares fit to a H/B = f[l - e - K m / 2 lo (Km/2)]; f = 0.158, K = 0.026. Residual standard deviation = 1.67 x 10-3. a H/B = f’(1 - e - K ’ m / 2 ) ; f’ = 0.120, K’ = 0.031. Residual standard deviation = 1.85 X 10-3. Standard deviation was estimated from the last iteration of a nonlinear fitting procedure based on a Taylor series expansion about the estimated values. 0 13
0
Although the exact form given in Equation 4 is preferable, it can be seen from Table I1 that both Equations 4 and 5 fit the experimental data. This indicates that the presence of the Bessel function does not change the exponential form of Equation 5 appreciably. Therefore, over the concentration range studied, Equation 5 can be used but Equation 4 is preferable on the basis of its greater generality and theoretical validity. In order to maximize the ratios of H/B and A/B, it is necessary to reduce Z’. The source-sample-detector geometry was investigated for one sample concentration. Table I11 shows an increase in HIB and A / B as the source-to-detector distance was increased while keeping the source-to-sample distance constant. The decrease in I’ is believed to be due to a reduction in the detected X-rays produced by fluorescence in the samples. Of course, this improvement was realized at the expense of a reduction in transmitted intensity, necessitating a much longer time to reach the same statistical precision in the base line. Another way of decreasing I’ is to reduce the 25 keV Sn X-rays by using a palladium foil which has a K-absorption
21
20
kev Figure 4. Pulse-height spectrum of PdallgmSn Taken with Li-drifted silicon detector edge at 24.3 keV (18). There is some reduction in the intensity of these X-rays due to the presence of palladium in the source itself. However, as shown in Table IV, there is a 25 increase in H / E when a 1.5-mil Pd foil was placed between the sample and detector. This increase is independent of the sample thickness over the range investigated. The same results were obtained when the foil was placed between the source and the sample. Increasing the resolution of the detector also reduces I ’ . In Figure 4 is a pulse-height spectrum of Pdg119mSntaken with a Li-drifted silicon detector (sensitive area 80 mm2; sensitive depth 2 mm) which has a resolution between 1.2 and 1 . 3 keV (18) H. A. Stockler and H. Sano, Nucl. Instr. Methods, 44, 103 (1966).
Table 111. Effect of Geometry on Spectral Parameters Source-to-Detector Base line Dist., cm AIB HIB Time, min counts X los 0.0743 57.0 8.751 2.0 1.182 97.4 7.897 4.6 1.286 0.0831 345.8 7.852 9.1 1.445 0.0947 Sample content, 38.2 mg SnOz. Sample thickness, 0.5 mm. Source-to-sample distance, 1.0 cm.
Transmission rate, cpm 1.54 x 104 0.81 x 104 0.23 x 104
Table IV. Effect of P d Filter on Spectral Parameters No Pd foil
1.5-mil Pd foil
Sample
SnOz, mg AIB 0.5 38.2 1.286 1.5 97.7 2.265 2.5 154.7 2.917 2.5 154.7 1.5 mil Pd foil placed between source and sample.
thickness, mm
a
HIB 0.0831 0.1166 0.1294
AIB
1.654 2.795 3.566 3. 616a
HIB 0.1065 0.1454 0.1614 0. 1611a
VOL. 41, NO. 1, JANUARY 1969
49
FWHM for photon energies between 8 and 45 keV (19). With this detector, the single channel can be set t o pass only 23.8 and 25 keV photons. In conjunction with a Pd foil filter, the 25-keV Sn X-ray can virtually be eliminated and therefore permit only 23.8 gamma photons t o be detected. Again because the sensitive area is only 80 mm2, the counting efficiency is such that long counting times are required for the Mossbauer experiments. The tin source used has high energy gamma emitters as contaminants which produce Comptonscattering in materials adjacent to the detector which has the proper energy t o be accepted by the SCA and therefore t o contribute to I’. Of course, this can be reduced by the production of a tin source with a minimum of contaminants. All of these factors mentioned should be considered for the possible application of this technique to the nondestructive analysis of a sample in which tin is a minor constituent. It seems reasonable that if standards are to be prepared in matrices which are chemically different from the sample matrix, then it is necessary for all scattering processes which appear in the term I’ be as similar as possible for both the sample and standard. If this were not possible, it would be (19) M. G . Hollstein and J. R. DeVoe, “Proceedings of the Second Symposium on Low Energy X- and Gamma-Ray Sources and Applications,” ORNL-IIC-IO, Vol. 1, pp 483-502.
necessary to evaluate I’ for each sample in order to make an appropriate correction. The differences in photoelectric absorption between the matrices of the sample and standard should present no difficulties because the ratio of H / B and AIB are the measured quantities. However, the magnitude of photoelectric absorption should not be so large as t o make the length of time impractical for obtaining data. The sample thickness can be adjusted by means of the special sample holder so that photoelectric absorption will be minimized. We are presently investigating problems of interferences in the destructive analysis of tin using the above method. In addition, factors such as the effect of matrix on the base line and on spectral shape are also being investigated for the possibility of the nondestructive analysis of a series of tin-containing ores. ACKNOWLEDGMENT
The authors thank David Hogben and Brian Joiner for their aid in the statistical evaluation of the data, and John Travis and Jon Spijkerman for their helpful suggestions.
RECEIVED for review April 3, 1968. Accepted October 9,1968. Presented in part at the 156th National Meeting, ACS, Atlantic City, N.J., September 1968.
Analysis of Rare Earth Materials by Cathodoluminlescence Spectra Excited in an Electron Microprobe R. N. Kniseley, Francis C. Laabs, and Velmer A. Fassel Institute f o r Atomic Research and Department of Chemistry, Iowa State University, Ames, Iowa 50010
The o ptica I f I uorescence (cathod ol uminescence) (2-5) have utilized broad band cathodoluminescence spectra emitted by some materials when they are irradiated by excited in a microprobe for estimating the number of excess a sharply focused beam of electrons provides an excarriers in semi-conductors. Greer and White studied the ceptionally powerful means of detecting and determinbroad band cathodoluminescence of several meteorites also ing impurities at very low absolute concentration levels. excited in a microprobe (6). While the present investigation The focused beam provided by electron microprobe instruments is ideally suited for these applications, was in progress, Larach (7) identified the spectral lines in the because the beam size may be reduced to areas less cathodoluminescent emission of several rare earths when they than 1 p 2 . Thus, spectroscopic analysis of the emitted occurred as impurities in appropriate hosts, and Wickersheim, radiation can provide information on the spatial disBuchanan, and Sobon (8) described the quantitative detertribution of impurities as well as the overall composition of the sample. Detection limits as low as 50 ppb mination of dysprosium in yttria. Both Larach (7) and have been obtained for rare earth elements in ideal Wickersheim et al. employed unfocused electron beams. host materials such as La203and Y203. Considering The electron microprobe is an ideal instrument for exciting the volume sampled by the electron beam, this corcathodoluminescence spectra because the wide variation in responds to an absolute detection limit of ~ 1 0 - I ~ beam size allows the examination of areas of less than 1 p z gram, a level seldom obtained by other analytical techniques. Several problems involved in quantitato over 300 p 2 . Thus the analysis can provide information tive analysis are considered and methods for circumon the spatial distribution of impurities as well as the overall venting these are discussed. composition of the sample. In addition, the scanning capaELECTRON EXCITEDoptical fluorescence (cathodoluminescence) offers considerable promise as a spectroscopic technique for the detection and determination of impurities at the very low concentration levels required for research on high purity materials. Although the analytical potentials of cathodoluminescence were suggested about 60 years ago ( I ) , there have been few quantitative applications. Wittry and coworkers (1) G . Urbain, Ann. Chem. Phys., 8E Series, 18 (1909).
50
0
ANALYTICAL CHEMISTRY
(2) D. B. Wittry and D. F. Kyser, USCEE Report 233 (Available
from Defense Documentation Center as AD-663242). (3) D. B. Wittry, Appl. Phys. Leffers,8 , 142 (1966). (4) D. B. Wittry and D. F. Kyser, J . Pl7ys. SOC.Japan, 21 (Supplement), 312 (1966). (5) D. B. Wittry and D. F. Kyser, J . Appl. Phys., 38, 375 (1967). (6) R. T. Greer and E. W. White, Paper No. 51 presented at the
Second National Conference on Electron Microprobe Analysis, Boston, Mass., 1967. (7) S. Larach, Anal. Chim. Acfa, 41, 189 (1968). (8) K. A. Wickersheim, R. A. Buchanan, and L. E. Sobon, ANAL CHEM., 40, 807 (1968).
