liquid scintillator, or are quenching agents. These problems can be resolved, however, if the substance can be burned r>ntirely to coinrnon combustion products that can then be dissolved in liquid scintillators of suitable composition and counted with a reproducible counting efficiency. This enables the activity of compounds of different chernical composition to be compared directly, removing the need for a separate calibration for each substance. Use of a coincidence liquid scintillation system enables relatively low backgrounds to be obtained with very weak p emitters-Le., tritium-thereby permitting an accurate assay of relatively small amounts of the isotope. The use of 2-phenylethylamine, instead of the more widely used Hyamine lox, reduces the cost of assaying carbon-14 and sulfur-35 without adversely affecting the counting efficiency. The flask combustion method can be used for the assay of biological samples (6, 7 ) , or for the determination of the distribution of activities on chromatograms, which can be cut into strips and burned. Larger samples that do not burn readily, or burn with a sooty flame, can be mixed with cellulose
powder, prior to ignition, to assist the combustion. The linearity of the calibration curves (Figures 5 and 6) indicates that the iiiethod described is reproducible for different weights of the same substance. The results for ~1 range of different cheiiiicd compounds (Table IV) also show reasonable agreement nith the expected value, with the exception of the azobenzenes which gave low count rates. Because the azo compounds burned vigorously without a trace of ash, and the aliquots of liquid phosphor showed no discoloration, one can exclude the possibility that the low count rates were due to unburned starting materials. A plausible explanation is that the combustion of this class of compounds produces a unique product with very strong quenching properties. These results indicate it is necessary to determine the counting efficiency after the combustion of different classes of compounds, to ascertain if any pronounced quenching agents are produced. This can be achieved by spiking the aliquot after it has been counted, with a small known volume of a nonquenching standard, and recounting. The reproducibility of the method, however, elimi-
nates the need for repeated efficiency measurements when similar weight. of the same clnsi of compoiinrl m’ to hr asisyed. LITERATURE CITED
( I ) Dobbs, H. ,E., Atoriiic Energy Research Establisliiiirnt (Gt. Brit.), R e p t . M1075 (1962). ( 2 ) Eastham, J. F., Westbrook, H. L., Gonzales, D., Proc. I.A.E.A. Sym-
posium on Detection and Use of Tritium in the Physical and Biological Sciences, Vienna, 1961, Vol. 1, p. 203. (3) Glendenin, L. E., Solomon, 4 . K.,
Phys. Rev. 74, 700 (1948). (4) Gotte, H., Kretz, R., Baddenhausen, H., Angeu. Chem. 69, 651 (1957). (5) Habersbergerovfi-JeniEkovB, h.,Cffka, J., Collection Czechoslov. Chem. Commzcn. 24, 3777 (1959). (6) Kalberer F., Rutschmann, J., Helv. Chim. Acta 44, 1956 (1961). ( 7 ) Kelly, R. G., Peets, E . A , , Gordon, S.,Buyske, A , , Anal. Biochenz. 2, 267 (1961). (8) Kinard, F. E., Rev. Sei. Instr. 28, 293 (1957). (9) , , Macdonald. A . M. G.. Analust 86. 3 (1961). (10) Oliverio, V. T., Denham, C., Davidson, J. D., Anal. Biochem. 4 , 188 (1962). (11) Woeller, F. H., f b i d . , 2, 508 (1961).
RECEIVEDfor review October 15, 1962. Accepted February 21, 1963.
Statistical Aspects of Liquid Scintillation Counting by Internal Standard Technique Single Isotope R. J. HERBERG ,!illy Research laboratories, lndianapolis 6, Ind. Equations are given by which the percentage error in a calculated rate, corrected for counting efficiency, can b e determined. These equations are evaluated for a range of counting efficiencies, activities of internal standard, and counting times before and after internal standard addition. For routine counting the addition of 50,000 d.p.m. of carbon-14 and 150,000 d.p.m. of tritium as internal standard activity, and a 1-minute counting time after addition of internal standard, are adequate.
T
HE ease of sample preparation and the relatively high counting efficiencies attainable have made liquid scintillation counting a common technique. In general, samples prepared for this method of counting are quenched
786
e
ANALYTICAL CHEMISTRY
to various degrees by a solvent component of the counting solution, by color produced by the sample in the counting solution, by a colorless sample itself, or by a combination of these three. For determining the counting efficiency of such quenched solutions, the internal standard method is much used. In this procedure one counts a sample, adds a known amount of activity of the same or other appropriate isotope, and recounts the sample. The increase in count rate resulting from addition of the internal standard is a measure of the counting efficiency of the solution. I n the counting procedure as outlined, seven quantities must be determined for each sample to permit calculation of its absolute disintegration rate: (1) gross count of the sample, (2) sample counting time, (3) gross count of the sample after addition of the internal standard]
(4) counting time of the sample after internal standard addition, (5) background count, (6) background count time, and (7) activity of the added internal standard. The optimum values, or even good values, of some of these quantities are not immediately obvious. The simple case of a sample and its background is discussed for counting systems in general in any book dealing with radioactive counting procedures. Whisman, Eccleston, and Armstrong (9) discuss errors relating to liquid scintillation counting. However, for the situation as a whole-Le., considering the seven quantities mentioned-no complete analysis is available. One merely has available such qualitative information as that as counting time for a sample is increased, the fractional error of a rate decreases, or that the
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the measurements are statistically independent, the variance of a measurement is the measurement itself-Le., the counting instrument is counting stati~ticallya t the time the measurement was made-and the initial rate equation (Equation 1) holds. The rate equation is true as long as quenching is not too severe. Dividing Eyiiation 4 by Equation 1, one obtains an expression for thc fractional error in the rat?, SR/R:
I 00000 53000
Figure 1. Relative contributions to total variance of sample count, background count, count after internal standard addition, and internal standard
greater the degree clf quenching the more activity should he added as internal standard. This article presents and discusses quantitE tive relationships between the different variables and presents, for some common counting conditions, useful values of these variables. Optimum, or good, values for the variables can be determined in several ways. One can make up solutions representing systemat c variation of the variables, count them repeatedly, and from an analysis of the experimental data determine the ef'ect on the variation of the calculated rate. An alternative way, used in this article, involves assumption of certain reasonable values of background, counting efficiency, counting times, etc., and calculation by an appropriate equalion of the fractional error in the final disintegration rate. The combinaticn of the variables can be found that minimizes the fractional error in the rate. RATE AND ERROR EQUATIONS
The formula for the disintegration rate, R, corrected for counting efficiency 1s
This is the basic equation used throughout this article to determine the percentage error in the calculated rate for various combinations of the variables. Before searching for optimum values *' Herberg (1) has shown that the total of the variables, one can profitably see error in the rate, arising from the unthe relative contributions of the four certainty in the individual measuremeasurements to the total variance. ments that comprise the rate equation, I n Figure 1 the fractional contribution can be expressed by a particular propto the variance is plotted against net agation of error equation for a variety count rate, N o , for background BO, of counting modes for a range of values initial sample count, Uo, sample count of both carbon-14 and tritium activities. after internal standard addition, U1, According to Herberg, if R can be and internal standard activity, A. expressed as R = f (zl, z2 . . . Q . . . z~), The following d u e s are assumed; the variance of R, S 2 ~is, given by background rate, B o / ~ B 60 ~ , c.p.m.; sample counting time, tuo, and background counting time, tBI, 10 minutes; counting time after internal standard addition, tc7,,1 minute; internal standIn the present case, from Equation 1 ard activity, A, 50,000 d.p.m.; and error in A , h'd/a4, 1.00%. (The error R = f(Uo, T,7iJ Bo, A , fro,tu,, tau) in A may be considered in two ways: By assuming that the times are errorthe uncertainty in the activity per unit free-Le., that all errors are attributable volume of the internal standard soluto U0, Ul, BO,and A-one can use the tion and the error of addition of the simpler expression R = f ( U O , VI, internal standard volume. It is in the Bo,A ) . While this is not strictly true, latter sense that the error in A is used it reduces the number of variables and is throughout, A value of l . O O ~ o was a reasonable assumption for ordinary chosen as a convenient and limiting work. The variance equation is given value. The relative error can easily be symbolically by The relative contrikept below l%.) bution of the different components varies in a complex way. For different values of the variables other than those assumed, the curves differ somewhat from those shown, but the relative contributions still vary with net count For a radioactive count z,the standard rate in a complex fashion. This shows the need for a systematic analysis of the derivation, S,= so that quantitative interrelationships between variables.
6
The terms in parentheses are not separable. The net count rate, No, not the , separate terms Uo/tco and B o / ~ B ,is adjusted for counting efficiency by the factor A / M . I n general, a background is not quenched in the same fashion as a sample, so that it is improper to apply AIM to sample count rate and bacliground count rate separately and then subtract the two. Equation 1 assumes that the background rate before internal standard addition, Bo'tB,, is the vtme as thnt nftcr addition, Bl/tRI.
ACTIVITY
where T is the numerator of Equation 1 and B is its denominator. The four terms represent the contribution to the total variance of the original count, the count of the sample after the addition of internal standard, the background count, and the internal standard. ICclrintion 3 can IF considered true when
OF INTERNAL STANDARD
The way in which the percentage error in the calculated rate (Equation l), as determined from Equation 5, varies is shown in Figures 2, 3, and 4 for a range of values of internal standard activity. sample activities, and counting efficiencies of 70, 20, and 10%. Counting times for sample, bo,and backgroiind, ts, were taken as 10 minutes, VOL. 35, NO. 7, JUNE 1963
787
ERROR I N ADDiTlON
INTERNAL STANDARD ACTIVITY [A) W
c U
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x
1,000 O P M 5,000 io,ooo
A
25,000
70'9'
EFFICIENCY 1 % E R R O R IN A Ra,=Ru = IOMlN tu I = I M I N
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B c=6OOCOUNTS
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Figure 2.
833 S A M P L E / B A C K G R O U N D
5 1 0
Error in calculated rate vs. net count rate 70% counting efficiency
counting time after internal standard addition, tu,, as 1 minute, and the error in A , Sa/A , as 1.OO%. All three families of curves have the same general shape, and for the lower values of the internal standard activity, all show a minimum, which is due to the changing contributions a t different sample activities of the four elements of the rate equation. For a given sample activity, the fractional error in the rate decreases as the internal standard activity increases. These curves show clearly the internal standard activity needed to attain any particular fractional error for a given net count rate under the conditions assumed. I n this laboratory, where large numbers of samples of varying count rate and counting efficiency are handled, it has been desirable as a routine procedure to use as an internal standard for each isotope counted, a single stock solution of that isotope and a fixed volume of this solution. Curves such as those shown in Figures 2 , 3, and 4 are very useful in determining what the activity of this stock solution should be. The 70% efficiency curve applies to carbon-14 (or sulfur-35) in only slightly INTERNAL STANDARD A C T I V I T Y
quenched solution. Little is gained by exceeding an activity value for internal standard of 50,000 d.p.m. for sample net count rates of 10,000 c.p.m. or less. For the 20% efficiency curve, which would correspond to strongly quenched carbon-14, an internal standard activity of 50,000 d.p.m. still gives a percentage error in the rate less than 2% for net rates of 10,000 c.p.m. or less. For a weak emitter such as tritium, the 20% efficiency curve represents a somewhat quenched situation and the 10% curve a more strongly quenched condition. At these efficiencies an internal standard activity of 100,000 d.p.m. or more is desirable. Data for curves such as those shoa-n in Figures 2, 3, and 4 have been calculated and the curves drawn for counting times of 3 and 30 minutes for efficiencies of 70, 20, and 10%. For all six groups of curves, the curves show a minimum for the lower values of internal standard activity. For the 70 and 20% efficiency curves an internal standard activity of 50,000 d.p.m. gives an error less than 2%. For the 10% efficiency curve internal standard activity should be 100,000d.p.m. or more.
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167
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833
NET CPM
ANALYTICAL CHEMISTRY
(No)
SAMPLE/BACKGROUND
Error in calculated rate vs. net count rate 20% counting efficiency
788
COUNTING TIMES
After Internal Standard Addition. Equation 5 shows t h a t for fixed values of sample count rate, background count rate, count rate after internal standard addition, and internal standard activity, the contribution of any one of the first three elements is inversely proportional to its counting time. The way in which the percentage error in the rate varies with counting time after addition of internal standard is shown in Figure 5 for three values of the counting time a t two efficiencies. At the 70% efficiency value there is very little difference between the curves. =1 1-minute counting time is adequate. At 20% efficiency, the difference between the curves is more pronounced. However, a t the highest net count rate shown, 25,000 c.p.m., the fractional error in the rate is 1.58% for the 10-minute counting time and 2.89% for the 1-minute counting time. The difference, 1,31%, is hardly significant
(A)
W
E 0 U d
INTERNAL STANDARD
The uncertainty in the efficiency determination caused by an error in addition of internal standard has been mentioned frequently as a drair back of the internal standard method of quench correction. It is important to knon how the error in the measurement of the internal standard contributes to the over-all error. Equation 5 shows tliat as the contributions to the total fractional error of the sample count, background count, and count after internal standard addition are decreased by an increase in times tc0, tao, and ti,, the error contribution of the internal standard activity, (SA/A)*, becomes the limiting factor. In the calculations the results of which appear in Figures 2 , 3, and 4, S 4 / A was taken as 1.00%. The curves show that this is the relative error value approached as the internal standard activity becomes larger a t high net count rates.
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Figure 4.
Error in calculated rate vs. net count rate 10% counting efficiency
24 22 -
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COUNTING
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100,000
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Figure 5. Error in ccilculated rate vs. net rate for counting times after internal standard addition of 1 , 3, and 10 minutes
(No)
1
,
167 IO000
-
a33 50000
S A M P L E / BACKGROUND
Figure 6. Error in calculated rate vs. net rate for sample and background counting times of 1, 5, 10, and 50 minutes 70% counting efficiency
70 and 20% counting efficiencies
ordinarily, so that even a t this low efficiency a 1-minute count after internal standard addition is reasonable for routine counting. Sample and Background. Figure shows the fracticnal error in the calculated rate (from Equation 5) us. net count rate, N O ,for several counting times of sample and background. The d a t a were calculated with assumed values as follows: 70% counting efficiency, internal standard activity of 50,000 d.p.m., 1-minute counting time after internal standard addition, and 1.00% error in the internal standard addition. 4 t low net count rates the combined contributions of sample and background constitute a large part of the who e percentage error in the rate, so that an increase in their rounting times diminishes the error appreciahly. As the nct rate increases, there is less and les: advantage to be gained by increasing sample and background counting times. For the conditioiis assumed the contribution of the internal standard itself is 1%. Past 10,000 c.p.m. there s very little gain in increasing the counting time past 1 minute. At 10,000 c.p.m. the fractional error for 1-minute counting time is 1.6%; a t 50 minutes the error is 1.1%, a very slight improvement ordinarily. SIMPLER COUN llNG MODE
Khen the solvent system and other characteristics of a set of samples are essentially identical, it is feasible to determine the counting efficiency of one of a set of samples and apply this value to the others. For this situation R can be expressed as :
E can be expressed as :
The fractional error in R is given by :
The fractional error in E is given by:
(9)
Equations 6 and 7 are a two-stage expression of Equation 1; 8 and 9 are two-stage expressions of 5. The limiting value of S R / R in Equation 8 is S E / E , the error in the counting efficiency. In turn, the limiting value of SE/E is the fractional error in A , so that, as was seen previously from Equation 5 , the limiting value of Sn/R is the fractional error in A. In the singlestage treatment of Equation 5 , one does not know explicitly the error in the efficiency. The magnitude of the relative errors in efficiency determination is shown in Figure 7 as a function of net count rate, No, for efficiencies of 70 and 20% and the following assumed values: internal standard activity, 50,000 d.p.m.; background, Bo, for 70y0 efficiency, 60 c.p m.; background for 207, efficiency, 30 c.p.m.; counting times of sample and background, 10 minutes; counting time after internal standard addition, 1 minute; error in A , S A / A , 1.00%. For 70% counting efficiency, the error in efficiency a t 50,000 d.p.m. is 1.3%, only 0.3% above the limiting value of 1.0%. At 207, efficiency, the error curve rises sooner and more steeply. At 25,000 d.p.m. the error is 2.27&, O.80/0 above the limiting value,
1.4%. At this lower efficiency an internal standard activity of 100,000 d.p.m. or more is preferable In general, the error in the efficiency value can be made to fall in the range 1 to 2%. This means in turn that the limiting value of the percentage error in the rate from Equation 8 is 1 to 2%. The way in which the percentage error in the rate varies with relative error in counting efficiency determination is shown in Figure 8 for relative errors of 1, 2, and 3%. For the values assumed ( A = 50;OOO d.p.m., tuo = 10 minutes, tr-, = 1minute), the percentage error in the rate becomes equal to the relative error in the efficiency for net rates of 2000 c.p.m. or greater. DRIFT CORRECTION
Counting instruments are not perfect. Their efficiency may change with time. Commonly, standards are interspersed throughout a group of samples as a means of correcting for efficiency changes. Since the count of a standard itself is subject to an uncertainty, the mathematical operations with the standard count rate introduce uncertainty into the corrected driftrfree rate. It is well to know whether the added uncertainty can exceed the eliminated drift and how best to minimize the uncertainty from the standards. The observed gross counts from a group of standards, S , samples, U , and background, B, may be designated Si, Go,, U",, U o Z . . . Uoi. . .Bo. . . Uo,. . . Sz with counting times designated by the properly subscripted t . The second subscript on the U indicates sample number-Le., UOiis the gross count in the original counting of sample i. The gross count of the set after internal standard addition may be designated 8 3 , VI,, UI,, U1,* * . Uli. . .Ell. . * vi,. . .s,. VOL. 35, NO. 7, JUNE 1963
789
is statistically significant a t the 10% level and correction is required. (The chi squared value for the four is 24.62; the allowable value a t the lOyolevel is 6.25.) The results of the evaluation of the complete equation are shown in Table I. At low count rates the standards contribute only a small part of the whole variance. At a net rate of 60,000 c.p.m. the standards make up nearly half of the entire variance. By neglecting the error added by the standards at high count rates, for conditions as shown, one considerably underestimates the total percentage error in the calculated rate. This is in a sense offset by the fact that at high count rates, for conditions as shown, the percentage error in the rate is small.
Table I. Variance Contributions of Standards to Total Variance of Calculated Rate
Net samplebackground ratio
Corrected disinte-
1 10 100 1000
86 866 8,674 88.106
gration rate
70
yo error
7.27 1.92 1.41 1.10
1.48 0.03 20.95 48.58
error due to in rate standards
Again the second subscript indicates sample number-Le., U1,is the gross count of sample 3 after internal standard addition. The times are the properly subscripted t ’ p . The rate equation for the ith sample, corrected for drift and for counting efficiency, is given by:
Here the T ’ S are functions of the standards’ rates and permit the correction of an observed count rate for drift. (In this expression a separate background, B1, has been used for the set after internal standard addition.) The functional relationship between the r’s and the standards’ count will depend on what kind of drift is assumed between standards. The simplest assumption is that the drift is linear; another possibility is a sinusoidal drift. At best any form assumed is but an approximation. Since it is the simplest mathematically, a linear drift is used here. It is convenient and simplifies the drift correction equations if the same standard solution is used at the head and end of both the original set and the set after addition of internal standard. If the initial count rate is taken as the reference rate, the linear drift correction factors for Equation 10 are:
- kl
TI
= 1
T*
= 1-
k2
(1
- ”)’
(11)
(1
- Szlts
(12)
SlltS, -2)
SlltS,
Here the k’s are the time locations of solutions in a set The constant k , for the ith sample consists of elapsed time from midpoint of counting time of standard 1 to midpoint of counting time of sample i divided by the elapsed time from the midpoint time of standard 1 to midpoint time of standard 2. If, as before, time is disregarded as a variable, the corrected rate, R, is a function of the nine quantities, L-0, BO, VI, B1, A , SI, Si, S3, and Sd. The variance equation will consist of nine terms representing the variance contribution of each of the nine variables. The variance equation is lengthy and is hardly suitable for routine use if computer calculation is not available.
NOMENCLATURE
activity (d.p.m.) of added internal standard = denominator of Equation l = gross background count after addition of internal standard = gross background count = absolute counting efficiency = M / A = functional relationship = subscript used to designate ith iarnple = constant indicating time location of a sample in a series = net c.p.m. = CO’I~L~ Bo/tso = increase in count rate after internal standard addition = U1/trl - r0/tv0 = correction factor for instrument drift = corrected disintegration rate of a sample = partial derivative of R with respect to any quantity x =
The variance contribution of a standard to the percentage error of the rate is found to be inversely proportional to its count rate. Standards should thus have the highest possible count rate consistent with other requirements. The complete variance equation was evaluated for net sample to background ratios of 1, 10, 100, and 1000 for the following assumed values: activity of internal standard, 50,000 d.p.m.; counting efficiency 70%, fractional error in A , 1.00%; background rates ( B o / ~and B~ Bl/tB;), 60 and 70 c.p.m., respectively; 10 minutes or lo5 counts the cut-off factor for sample and background counting time; and I-minute counting time after internal standard addition. The values used for the observed rates of the standard were Sl/ts,, 50,000 c.p.m.; Sl/ts,, 49,020 c.p.m.; &/t.~,, 49,505 c.p.m.; and S4/ts4, 50,505 c.p.m. These four values were chosen so that the variation between them
ERROR
IN
LFFICIENCY
100% 20046
A 300%
-10
100 NET
1.000 RATE (NO)
!
1
10,000
100,000
10
100
10,000
1,000
NET
RATE
--
A
100,000
(NO)
Figure 7. Error in determination of counting efficiency vs. net rate
Figure 8. Error in calculated rate vs. net rate for efficiency errors of 1,2, and 3%
70 and 20% counting efficiencies
70% counting efficiency
790
ANALYTICAL CHEMISTRY
s
variance of any quantity x S, = standard deviation of any quantity x S,/X = fractional error in any quantity 1: SI, Sz,S,,S4 = gross counts from first, second, third, and fourth countings of a standard ts , h$2, ts,, ts, = counting times for standards SI,8 2 , S3, and S4 Itlo = counting time for backgrosnd Bo tnl = counting time for background B1 =
ZZ
tu, too
T
uo U1
UQ, Uli
counting time after internal standard addition = counting time for sample = numerator of Equation 1 = initial gross count of sampie = gross count of sample after internal standard addition = gross initial count of sample i = gross count of sample i after internal standard addition
=
ACKNOWLEDGMENT
C. S.Rice and R. E. Shultz of this laboratory were the originators of a n IBM program by which many of the calculations presented here were made. LITERATURE CITED
(1) Herberg, R. J., ANAL. CHEM. 33, 1308 (1961). ( 2 ) Whisman, M. L., Eccleston, B. H., Armstrong, F. E., Ibid., 32, 484 (1960).
RECEIVEDfor review July 13, 1962. Accepted March 21, 1063.
Determination of Oxygen in Gallium Arsenide by Neutron Activation Analysis R. F. BAILEY and D. A . ROSS RCA Laboratories, Pririceton, N. J.
b Neutron activation of oxygen in gallium arsenide has been carried out using the 0 l 6 ( T , nIF'8 reaction with the tritons being produced by the Li6(n, T)He4 reaction. The maximum sensitivity of the method is about 7 X gram of oxygen in gallium arsenide, representins1 5 atomic parts per million in the samples used. The actual bulk concentraiion in the GaAs 18 atomic samples used was 72 parts per million.
S
METHODS for the determination of 0xyge.n are satisfactory when there is a large amount of material with a high oxygen Concentration. With small samples and an oxygen concentration in the submicrogram range, the standard methods arc no longer adequate. For these low concentrations where most instrumental methods fail, analysts have been turiiing to activation analysis using both accelerators and nuclear reactors (1-3, 6, 18). Direct activation of the oxygen by neutrons gives rise tc short-lived isotopes which can be used to measure the total concentratior in the bulk and physically or chemically sorbed on the surface and in the surrounding atmosphere (12, 17, 19). To study penetmtion profiles or bulk cor.centrations only, it is necessary for the rdioactive isotope to have :t long enough life for radioc1icmir:d procedures ;such as etching arid chernical separations. Activation hy charged particles froni nn rlccelerator 1t:i.s I ~ c t ~Icported n (IC). One rnetliod is to use the 0l6(T,n)FiSrcaction (4, 7 , IS, 16). The F18 appears to be the TANDARD
most suitable isotope resulting from oxygen bombardment. It has a half life of 1.87 hours, which is long enough to carry out radiochemical separations and to etch the sample to eliminate the surface oxygen which might mask that in the bulk. It decays by positron emission and the resulting annihilation radiation is easy to count with a gammaray spectrometer (11). To carry out this type of activation with a nuclear reactor, it is necessary to produce the tritons through a secondary reaction. This can be done by bombarding lithium, resulting in the reaction Li6(n, T)He4. The reaction is exoergic with a Q value of 4.78 m.e.v. (8). The tritons are emitted with an energy of slightly over 2 m.e.v., which is sufficient to penetrate about 0.002 inch of density-5 material. By placing a layer of lithium on each side of a wafer of the material under investigation, a relatively-uniform flux of tritons is produced throughout the sample, and the resulting F18 can be used to obtain the bulk oxygen concentration. EXPERIMENTAL
The technique to be described was developed to determine the oxygen concentration in materials. GaAs n-as used in this experiment. Electrical measurements showed the presence of c,arrier traps at concentrations of the order of 1017 cm.-3 (9, 14). Analysis of rhc.iuica1impurities other than oxygen with conventional techniques showed tha>t, none n w c ~ ~ r c s c ni nt these coricciitratioiis. Of tlic methods for thc: tletcrmination of oxygen, activation appeared to be the only one that would
eliminate surface oxides and permit measurement of the bulk oxygen concentration. The technique used was to irradiate thin wafers of GaAs wrapped in lithium metal. The tritons produced by the neutrons in the lithium had enough energy to penetrate the GaAs wafer, producing FIE. If the neutron flux and the effective cross section for the reaction is known, it is possible to calculate the oxygen concentration. While the cross section for both the LiG(n, T)He4 and the 016(T, n)F@ reactions are known, the triton flux in the sample is difficult to calculate because of neutron-flux depression in the lithium and the variation in lithium thickness. The effective activation cross section was therefore determined experimentally. To do this, intimately mixed powder samples of lithium-oxygen compounds were irradiated. The effective activation cross section was determined from the amount of Fl8 present. I n addition, lithium-wrapped powdered oxides were irradiated. The values obtained were internally consistent and agreed with a value obtained by Osmond and Smales (15) using powdered B e 0 mixed with LiF. The measured activation cross section was 5 X 10-28 The only possible competing reaction which might also produce F18 was F19(n, 2n)F18. The yields of the GaGg((n, 2n)Ga68 and ~ too low to the AS^^(^, 2 n ) A ~ 7 were determine in the present experiment. This n-as checked by GaAs blanks put t>liroughthe separation procedure. To tleterniiiie whether the fluorine conceiitlratioii could be a serious sourcc of error, it was necessary to measure the cross section for the reaction in a modified fission sliectrum which wits not list,cd iri thc literature. This was doiie by irradiating various fluoride samples, such as Teflon and ammonium fluoride, VOL. 35, NO. 7, JUNE 1963
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