tion to adding more instruments is the amount of available memory. I n terms of hardware data acquisition capabilities, a total of ten instruments in the slow-to-medium speed range (say, less than 500 points/sec each) could easily be accommodated. When (and if) the number of instruments interfaced to the computer increases to the point where their table information begins to saturate memory, one acceptable solution (and one easy to implement) would be to restrict the number of data collection runs that can be made simultaneously. This number will depend on the characteristics (rates, amount of processing, etc.) of the particular instruments being run. Instrument control via the computer presents another area for further development of the system. Monitoring and control of a single variable, such as temperature, could be done relatively simply with the present hardware but there is no immediate need for such control with the instruments now interfaced. The development of such control loops will depend on the particular instruments which will be connected in the future. One complex area to be analyzed involves obtaining better system performance through modification of the instruments. In many instruments the mechanism for producing a chart record restricts the speed of scanning and, in addition, is a limiting part of the control network. In-
creased speed and greater signal resolution, if obtained, could lead to the need for analog to digital conversion at the instrument. Presently, only instruments located within the building can be connected to the computer because of the parallel transmission of signals. It is conceivable that a simple telemetering system could be designed and implemented that would allow the multiplexing of digital control and data signals over a low capacity telephone line or dedicated transmission cable. This would allow expansion of the system beyond the confines of the present location. ACKNOWLEDGMENT
We acknowledge the contributions of a number of coworkers to the design and implementation of the system-in particular the contributions of William Holsinger, who designed the DADS unit; Jay Vinton, who wrote the software system for utilizing the remote consoles; Jeff Buzen, who wrote the programs for improving interrupt response time ; and Mrs. Marie Chang and Dr. Richard Simon who provided much of the system and application software. RECEIVEDfor review September 23, 1970. December 15, 1970.
Accepted
Digital Methods of Photopeak Integration in Activation Analysis Philip A. Baedecker Department of Chemistry and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Cali,f. 90024
A study of the precision attainable by several methods of gamma-ray photopeak integration has been carried out. The “total peak area” method, the methods proposed by Covell, Sterlinski, and Quittner, and some modifications of these methods have been considered. A modification by Wasson of the total peak area method is considered to be the most advantageous because of its simplicity and the relatively high precision obtained. A computer routine for the analysis of spectral data from nondestructive activation analysis experiments employing a Ge(Li) detector-spectrometer system is described. The routine processes the spectral data, applies appropriate corrections for decay, and provides a readout in concentration units.
developing computer programs for reducing activation analysis data, I have evaluated several digital methods for photopeak integration. Methods of Analysis. Seven methods of peak area estimation have been examined in the present study. These methods are illustrated diagrammatically in Figure 1 [with the exception of method (9) described below], and are summarized by the following equations: (a) Total Peak Area method (TPA): i=r
A
ai
= i=Z
THE PRECISION OBTAINABLE in an activation analysis experiment is to a large degree dependent on the precision with which the analyst can determine radionuclide abundance from counting data, most often obtained from gamma-ray spectrometry. Several methods of photopeak integration have been proposed and evaluated in the literature. Some of these treat the digital data directly (1-6), while others fit the data to a function and integrate that function to determine peak area (7-9). I n (1) D. F. Covell, ANAL.CHEM., 31, 1785-90 (1959). (2) S. Sterlinski, ibid., 40, 1995-8 (1968). (3) Ibid., 42, 151-5 (1970). (4) P. Quittner, ibid., 41, 1504-6 (1969). (5) H. P. Yule, ibid., 40. 148Cb6 (1968). (6) P. Quittner, Nucl. I,&um. Merhodx, 76, 115-24 (1969). (7) R. G. Helmer, R. L. Heath, M. Putnam, and D. H. Gipson, ibid., 57, 46-57 (1967). (8) J. T. Routti and S. G. Prussin, ibid., 72, 125-42 (1969). (9) L. Varnell and J. Trischuk, ibid., 76, 109-14 (1969).
-
(a2
+ a,) x (r - I + 1)/2
where ai = number of counts accumulated in channel i I = channel number at left hand limit of photopeak r = channel number at right hand limit of photopeak
(b) A modification by Wasson of the TPA method (10):
where n
=
6,
=
the number of channels on the left and right from channel zero (the centermost channel) the background in channel n as determined from a straight line drawn between channels I and r (the left and right hand limits of the peak)
(10) J. T. Wasson, private communication, ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
405
TOTAL
PEAK A R E A
WASSON
(e) A combination of the Wasson and Sterlinski methods:
i
COVELL
A
+
=
n
(n - j j=l
+ 1) (Q + ai) -
(f) Quittner's method: i=+n
A
I
STERLIkSKI
WASSON-STERLINSKI
QUITTNER
I
=
(ai - Ci)
where Ct = the background in channel i as determined from the following expression provided by Quittner ( 4 , 6)
Ct = P Z
+ qt (X,+ i - XL)+
Figure 1. Six of the seven methods of photopeak integration employed in this study where (c) Covell's method ( I ) :
2k
+
1 channels are fitted to a quadratic on each side of the photopeak X L and X R are the center channels in the left and right quadratics, respectively ( X L = I - k , X R = r k ) X , is the centermost channel p z andp7are the values of the quadratics at X L and X R q Z and q7 are the slopes of the quadratics at X L and X R M = X R - XL
+
(d) Sterlinski's method ( 2 , 3 ) :
6.0
s.oJ
-..-.... .. ...-. .- .-.. . .. . . ~..._.. . . . . .. . .
o . ~ ~ Lo.oo j ~ ~yo.00 7
1
6o.oo
1
Bo.00
1
100.00
1c0.00
1
1440.00
160.00
I
iao.oo
1
zm.00
C H R N N E L NUMBER
rro.oq -10
cu0.m
'z6o.m
Figure 2. Gamma-ray spectrum of the Allende chondrite, two weeks following irradiation 406
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
zao.00
mo.oo
5.0,
1.0-
0.0
(8) A combination of the Sterlinski and Quittner methods:
A
=
nuo
+
(n - j j= 1
+ 1) (a-j +
z=(n-l) aj)
n
/
V(b) =
i = ( n - 1)
c
i = - (7’ - 1)
ai
+
ai i = -(n-l)
+ (a, +
a-n)
+
l \
Methods a, c, d, and f have been previously described and evaluated (1-6). The TPA method of integration (a) achieves the greatest total number of counts for a given peak. Wasson has modified this method (b) to allow for the fact that while the channels in the wings of the photopeak add considerably to the error of a peak integration, they add little to the net number of counts (10). Covell’s method (c) has the theoretical advantage over the total peak area method that only those channels which have the smallest relative standard deviation are used in the analysis, and uncertainties with regard to choosing the best base line are removed. Sterlinski’s method (d) is based on the observation that the calculated relative standard deviation (based on counting statistics) for the calculated intensity of a photopeak will be smaller by giving increasingly greater weight to those channels which have increasingly greater total accumulated counts. However, both Cove11 and Sterlinski have failed to consider the fact that the calculated variances using their techniques are increased by virtue of the fact that the summation is carried out using a relatively high base line, rather than one drawn across the limits of the photopeak. For example, using Covell’s method the variance on the area can be calculated as V(0) =
whereas in Wasson’s method
and if Quittner’s approach employs a nonlinear base-line sub traction technique. Several channels (Quittner recommends using between 15 and 23 channels) are taken on each side of the peak, to the left and right of the peak limits, and the data points fitted to second-order polynomials using the methods described by Savitzky and Golay (11). The calculated values and slopes of the polynomials at the center channels are used to define a cubic equation which describes the base line under the peak. Quittner points out that his technique gives greater precision than Covell’s method. However, this would be expected, since the base line is lower. Whether or not Quiltner’s technique would provide greater precision than methods (a) or (b) is not immediately apparent. If the modified version of Sterlinski’s technique provides greater precision than Was son’s method (as would be expected from purely statistical considerations), the combination of Sterlinski’s and Quittner’s approaches should provide greater precision than either method alone. (11) A. Savitzky, and M. J. E. Golay, ANAL.CHEM., 36, 1627-39
(1964). ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
407
Table I. Relative Standard Deviations for Integrations of 12 Counts of Nine Photopeaks by Seven Methods of Photopeak Integration Full WassonMethod peak Wasson Covell Sterlinski Sterlinski Quittner Peak (*I (a) (b) (c) (dl (e) (f) 4.39 45,06 308 (2312) 5.48 4.51 6.65 6.11 6.32 4.82 5.12 5.88 5.04 5.53 468 (2039) 5.15 4.14 1.77 3.08 810 (3316) 3.80 2.39 889 (8007) 2.49 1.62 3.73 3.80 1.72 1.57 ( 12746) 1.65 1.35 1.49 1.42 3.49 3.86 1099 3.77 1.60 1.16 (5813) 2.18 1.67 3.06 1120 3.80 (32700) 0.73 0.71 2.39 0.77 0.69 1173 (8051) 1.47 0.93 0.82 0.99 1292 2.82 3.77 0.81 0.73 1.92 2.12 (28391) 0.85 0.74 1332 * Peak area as measured by Wasson’s method.
17,
7
t
O9
0.7
A
m
10
0
*
1099 kev
T O T A L P E A K AREA
*
WASSON
A
COVELL
0
STERLINSKI
0
WASSON-STERLINSKI QUiTTNER O U I T T N E R - S T E R L l NSK I
P
AVERAGE OF I
1
2
*,O,+,and
,
3
4
x 1
1
,
5
6
7
8
AREA OF ,333 kev PEAK AREA OF 1333 kev PEAK in Spectrum 1
Figure 4. Variation in measured photopeak intensity for the 811-KeV and 1099-KeV photopeaks, for the seven methods studied, with increasing 6oCoactivity Data points are the measured areas relative to the intensities of the photopeaksin the irradiatedchondrite counted alone EXPERIMENTAL An 0.5-g sample of a chondritic meteorite (Allende) was irradiated for 3 hours at a flux of 2 X 10I2 n/cm2/sec in the UCLA reactor. After the sample was allowed to decay for 2 weeks, it was counted 12 times in succession, using a Ge(Li) detector which has a resolution of 2.4 KeV for the 1333 KeV photopeak of T o , and a n efficiency of 6.4z relative to a 3-inch X 3-inch NaI(T1) detector at 25 cm. The detector was coupled t o a 4096 channel analyzer, and the resulting spectra read out onto punched paper tape for computer processing. A typical spectrum is shown in Figure 2. The principle activities are 45c, j C r , jgFe, ~ C O6oCo, , and I g 2 1 r . The meteorite sample was also counted seven times with increasing amounts of W o . 408
(9)
43.21 4.92 2.51 1.74 1.53 1.27 0.76 0.87 0.81
A computer program was written to process the spectral data by any one of the several methods listed above. The program could first smooth the spectral data by the method of Savitzky and Golay (11, 12), or the smoothing routine could be bypassed. The program then determined the first derivative at each channel, and used the first derivatives to locate photopeaks and determine the peak limits (5, 13). Compton edges were eliminated from consideration by finding the maximum value of the first derivative on the left side of each peak and the minimum value on the right, and requiring that the absolute values be the same within i50x. As each photopeak in the spectrum was located and the peak limits determined, its area was estimated by one of the methods previously described. For methods (b) through (g), n (the number of channels on each side of the centermost channel used in the summation) was set equal to 3. In Quittner’s method, k (the number of channels to the left and right of the boundary channels X L and X R fitted to a quadratic) was set equal to 7. In methods (a), (b), and (e), the number of counts in the background channels 1 and r was taken to be the average of the counts accumulated in three channels on each side of the photopeak (I, 1 - 1,1 - 2) and ( r , r - 1, r - 2). In each case the spectra were smoothed before processing. RESULTS AND DISCUSSION
+
x
I
QuittnerSterlinski
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
In order to measure the precision of each method of analysis, the standard deviation for each photopeak appearing in the spectrum of the irradiated meteorite was calculated from the 12 successive counts of the meteorite sample. The results are summarized in Table I. As anticipated from the considerations above based on counting statistics, for each photopeak (with the exception of the 309 KeV peak of Ig21r)the methods proposed by Covell and Sterlinski showed poorer precision than the other five methods. The total peak area method gave consistently poorer results than methods (b), (e), (f), and (g), which indicates that including the channels in the lower part of the photopeak in the peak area estimation may lead to a loss of precision, The large per cent standard deviations observed for Quittner’s method and the Sterlinski-Quittner method for the 309-KeV photopeak were due to the fact that the right quadratic was fitted to a portion of the 317 KeV Ig21rphotopeak. As Quittner points out, his method is useful only when the photopeaks are separated by greater than about 20 channels. For all other photopeaks the precisions obtained using methods (b), (e), (f), and (8) were comparable although on the average, the Wasson-Sterlinski method was slightly better. (12) H. P. Yule, Nucl. Instrum. Methods, 54, 61-5 (1967). (13) H. P. Yule, ANAL.C H E M38, . , 103-5 (1966).
Table 11. Relative Standard Deviations for Integrations of Seven Photopeaks by Seven Methods of Photopeak Integration, Based on Sepen Counts, with Each Count Having Increasing Activities of 6oCo Full WassonQuittnerMethod peak Wasson Covell Sterlinski Sterlinski Quittner Sterlinski Peak (a) (b) (c) (d) (e) (f) (8) a 23.90 20.62 41.11 56.97 13.19 32.59 30.94 308 b 6.23 4.02 8.09 10.0 4.21 5.65 5.17 468 810 6.12 4.18 14.01 17.16 5.18 3.58 3.65 889 6.44 4.51 6.08 7.02 4.48 4.90 4.88 1099 2.82 3.32 10.72 10.78 4.19 3.67 4.52 1120 8.39 8.46 9.79 10.50 8.63 9.75 9.75 1292 2.19 3.05 8.33 9.28 3.64 2.98 3.53 a Determined from four spectra. Determined from five spectra. Table 111. Observed Standard Deviations of Integrations of 12 Counts of Nine Photopeaks by the Wasson Method Compared with That Expected from Counting Statistics Photopeak, 1292 1120 1173 810 889 1099 308 468 KeV 1.67 0.71 0.93 1.62 1.35 5.04 2.39 Re1 std Obsd 4.51 2.05 0.59 1.19 6.92 5.95 4.11 2.01 1.20 dev, 7Z Calcd
Since the relatively poor precision observed for Covell’s method, and the modification of Covell’s method proposed by Sterlinski, is caused by choosing relatively high base lines, the precision obtainable using either technique could be increased by carrying out the integration over a greater number of channels. Yule (5) has shown that Covell’s method can provide comparable precision to the TPA method if similar boundary channels are chosen. Selecting integration limits which are too narrow or too broad will result in a loss of precision. The effect of using wider boundaries on Sterlinski’s method was investigated by allowing n in Equation (d) above to range from 3 to 14. When the integration was carried out well past the wings of the photopeak, the precision was found to be comparable to that obtained by methods (b), (e), (f), and (g), although on the average the precision was less than that of the Wasson-Sterlinski method. Increasing the number of channels used in the integrations by the Wasson or WassonSterlinski techniques did not systematically affect the observed precision. One would expect that any benefit to be derived from Quittner’s technique would be most apparent where the background varies under the photopeak. This situation arises most markedly in our spectra for the 1120-KeV photopeak of 46Sc(which was plotted in Figure l), which sits on the Compton edge of the 1333-KeV peak of W o . It can be seen from Table I that for this photopeak Quittner’s method does, in fact, show the lowest relative standard deviation on the various methods of photopeak estimation. In order to check the performance of the various methods when the shape of the spectrum was changing, the meteorite sample was counted seven times with increasing amounts of W o . During this part of the experiment, the deadtime of the analyzer increased from 5 to 2 0 z and the integrated area of the 1333-KeV photopeak of increased by a factor of 8.3. The last spectrum is shown in Figure 3. The seven spectra were treated in the same way as the 12 spectra accumulated in the first part of the experiment, and the results are summarized in Table 11. The computer routine employed in reducing the data failed to locate the 308-KeV photopeak in three of the spectra, and the 468-KeV peak in two of the seven spectra. Again, the methods proposed by Covell and Sterlinski (where n was set equal to 3) yielded consistently poorer results than the other methods. The precision obtained using
1332 0.74 0.60
the remaining five methods was comparable. In general, Wasson’s method showed the best precision, although for the higher energy photopeaks at 1099, 1121, and 1293 KeV, the observed relative standard deviations were lowest for the total peak area method. This may be partly due to a loss of resolution at higher deadtimes. The width of the 1099-KeV photopeak of 59Feincreased from 2.3 KeV in the first spectrum to 2.5 KeV in the last. It is of interest to see how the quantity (peak areajpeak area in spectrum 1) varies for the various methods as one increases the activity due to W o . Figure 4 shows a plot of this quantity plotted against (area of 1333 peak of 6oCo/areaof 1333 peak in spectrum 1) for the photopeaks at 811 KeV and 1099 KeV which were the least and most intense photopeaks in the spectrum other than those from W o and lg21r. For the 1099 KeV photopeak, the points for methods (b), (e), (f), and (g) virtually overlap in all spectra except the last, and in these cases, average values for the four methods are plotted, the bars showing the range of values observed. The same behavior was observed in similar plots for the 889, 1121, and 1292 KeV photopeaks (not shown). In general, the quantity (peak area/peak area in spectrum 1) decreases for all methods with increasing activity due to W o . (This decrease is more pronounced for the 889,1121, and 1292 KeV photopeaks than for those plotted in Figure 4.) In all cases the decrease is more rapid for Covell’s and Sterlinski’s methods than for the other techniques studied. For the last three spectra in the series (with the highest amounts of ~OCO), the decrease is least for the TPA method. Therefore, in activation analysis experiments where there are large differences in deadtime between sample and flux monitor, and where changes in resolution may be a problem, the TPA method appears to be the best choice. This observation has previously been made by Yule (5). The fact that the more complex methods proposed by Sterlinski and Quittner did not provide significantly greater precision than the more simple methods leads us to generally favor the Wasson technique for peak area estimation. In general, the observed relative standard deviations for the various photopeaks based on the 12 repeated counts of the meteorite sample, and integrated by the Wasson method, are close to the standard deviations expected based on counting statistics alone, as shown in Table 111. The Wasson method described above is used routinely in ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
409
our laboratory in a computer routine (SPECTRA) for processing activation analysis data. (The TPA method is included as a n option in the program.) The spectral data are recorded on punched paper tape, along with spectra of appropriate gammaray standards. After searching out a photopeak, as described above, the centroid of the peak is determined using the method of Savitzky and Golay ( Z I ) , and the energy of the photopeak determined using the energy calibration provided by the analysis of the gamma-ray standards. Thus, the energy and intensity of the photopeaks in each spectrum are determined. The energies of the photopeaks to be used in the activation analysis experiments are read in on cards, along with the halflives of the corresponding radionuclides and the concentration of the element in the flux monitor. A second set of data cards lists the sample or flux monitor weight, time of day that the count of the sample was started, live time duration, and, when appropriate, clock time duration, for each spectrum on the
tape. The program first analyzes the flux monitor spectra and calculates the “specific counting rates” for each photopeak, The program makes corrections for decay, and, for the rase where very short-lived isotopes are being measured, for the variations in deadtime of the analyzer. When the flux monitor spectra have been processed, the sample spectra are processed and the concentration of each element in each sample is calculated. ACKNOWLEDGMENT
The author wishes to thank Dr. John T. Wasson for helpful discussions during the course of this work.
RECEIVED for review August 10, 1970. Accepted December 21, 1970. This work was supported by the National Aeronautics and Space Administration under contract NAS 9-8096,
Potentiometric Studies with an Ion Permselective Membrane Sudarshan La1 and Gary D. Christian Department of Chemistry, University of Kentucky, Lexington, K y . 40506
A dithizone-containing membrane is described which shows varying degrees of permselectivity to a large number of cations and anions, including mono-, di-, and trivalent ions. It has been used successfully for the potentiometric monitoring of precipitation, chelometric, redox, acid-base, and nonaqueous titrations. Relative selectivities of the membrane toward different ions are used to interpret different shapes of titration curves. Effects of sample concentration, organic solvents, and extraneous salts on the shapes of titration curves are reported. The effect of the membrane plasticizer on permselectivity to different ions and on titration curves has been studied. The membrane is stable for several months, except when used in purely nonaqueous solvents.
A GOOD DEAL OF INTEREST has developed during the past decade in the prospective use of ion selective electrodes for monitoring various ions. Several membranes that have been used as ion sensing devices have recently been summarized by Rechnitz (1). A number of membranes have been used successfully for potentiometric titrations; some exhibit Nernstian response but others d o not. Some recently described membranes include ion exchange membranes (2-6) used for certain acid-base and precipitation titrations, and the barium arsenate impregnated parchment paper membrane of Liteanu et al. ( 7 ) used for limited acid-base titrations. Reviews of ion exchange membrane electrodes have been presented by Gregor (8), Spiegler (9), and Lakshminarayanaiah (10). (1) G. A. Rechnitz, Chem. Eng. News, 43 (25), 146 (1967). (2) F. P. Ijssling and E. van D a h , Anal. Chim. Acta, 36,166 (1966). (3) Zbid., 40, 421 (1968). (4) Zbid., 43, 77 (1968). (5) J. S. Parson, ANAL.CHEM., 30, 1262 (1958). (6) S. K. Sinha, J . Indian Chem. SOC.,32, 36 (1955). (7) C. Liteanu, M. Mioscu, and I. Popescu, Rec. Roum. Chim., 13, 569 (1968). (8) H. P. Gregor, Ann. Rec. Phys. Chem., 8,463 (1957). (9) K. S. Spiegler, “Ion Exchange Technology,” F. C. Nachod and J. Schubert, Ed., Academic Press, New York, N. Y . , 1956, pp 118-1 8 1. (10) N. A. Lakshminarayanaiah, Chem. Reu., 65,491 (1965).
410
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
Bloch, Kedem, Vofsi, and coworkers (11-16) have described membranes in which permeability is made possible by specific solvation or complexation of a particular permeant by the membrane matrix. These are the so-called solvent membranes. They have been used for separation of iron(II1) from aluminum(II1) in high concentrations of hydrochloric acid(I1) and for the separation of uranyl nitrate from a mixture containing iron and aluminum (12). In the former case, the active membrane contains a n alkyl-phosphoric ester such as tributyl phosphate, which selectively “extracts” the uranyl nitrate. The ester also serves as a plasticizer for the polymeric polyvinyl chloride matrix. These membrane separations have been likened to solvent extraction systems, hence the name “solvent membrane.” Recent evidence (17) has indicated that the mechanism of transport involves distribution of the metal ion at the aqueous solutionmembrane interface and the rate (kinetics) of complex formation in the membrane. Solvent membranes have recently received attention a s possible active ion selective membranes in electrodes. Bloch, Shatkay, and Saroff (18) described a calcium selective electrode in which the membrane consisted of polyvinyl chloride, tributyl phosphate as plasticizer, and thenoyltrifluoroacetone as the selective chelating agent. The electrode showed high selectivity for calcium in the presence of sodium, magnesium,
(11) R. Bloch, 0. Kedem, and D. Vofsi, Nature, 199, 802 (1963). (12) R. Bloch, A. Finkelstein, 0. Kedem, and D. Vofsi, Znd. Eng. Chem., Process Des. Decelop., 6, 231 (1967). (13) R. Bloch, A. Katchalsky, 0. Kedem, and D. Vofsi, U. S . Patent 3,450,630, June 1969. (14) Zbid., 3,450,631. (15) R. Bloch. A. Katchalsky, 0. Kedem, and D. Vofsi, Brit. Patent 1,049,041 (1966). (16) Yeda Research and Development Co., Ltd., ibid., 1,090,096 (1967). (17) D. Vofsi, 0. Kedem, R. Bloch, and S. Marian, J . Znorg. Nucl. Chem., 31, 2631 (1969). (18) R. Bloch, A. Shatkay, and H. A. Saroff, Biophys. J., 7, 865 (1967). ~
