Rapid Calculation of Sensitivities, Interferences, and Optimum Bombarding Energies in " e Activation Analysis Enzo Ricci and R . L. Hahn' Analytical Chemisfry Dirision, Oak Ridge National Laboratory, Oak Ridge, Tenn. To facilitate calculations of sensitivities and interferences in terms of bombarding energies, €, in 3He activation analysis, an approximate method has been developed for the rapid computation of the average cross section, e. This energy-dependent parameter is otherwise difficult to obtain by rigorous mathematics and, yet, it is vital in those calculations because: the analytical sensitivity is directly proportional to e; and the interference is shown here to depend on the ratio, a,/eal for the interfering and the sought reactions, respectively. The method is based on the straight-line fitting of excitation functions, which leads
2 3
to the final Simple formula e = -mE
-
+ b/p.
The
constants m, a, b, and other important parameters are given for the 12 most significant nuclear reactions of 3He ions with the elements which display the highest sensitivities in 3He activation: Be, B, C, N, 0 , and F. Detailed typical examples are given to illustrate the wide usefulness of the proposed method, even under quite unfavorable analytical conditions; a number of calculations of average cross sections, sensitivities, and ratios, e,[e8, a r e included. The variation of the latter with E IS used to find optimum experimental 3He bombarding energies for particular analyses. The average error of the method is found to be no larger, and in most cases much less, than 13.5%.
CONSIDERABLE EFFORT has been devoted in recent years to the method of 3He activation analysis (1-5) which appears quite promising because of its characteristic high sensitivity for light elements. For example, a few parts per billion of beryllium, boron, carbon, nitrogen, oxygen, and fluorine could potentially be detected with a 100 pA beam of 18-MeV 3He-particles ( I ) ; in fact, the sensitivity for oxygen is also quite high at 10 MeV (2). The very sensitivity of 3He activation, however, added to the diversity of products formed by 3He reactions, leads to interference. In fact, most of the 3He reaction products from light elements are positron emitters, and can be determined with high counting efficiency, either by measuring their common 0.511 MeV annihilation radiation, or by gross betacounting. Fortunately, computer least-squares decay-curve analysis can be applied successfully (2) to separate mathematically the desired radioactivities by taking advantage of differences in half-life. Where computer techniques fail, there is still the alternative of radiochemical separation. However, a more difficult interference problem occurs when an undesired nuclear reaction produces a nuclide identical to that sought in the activation analysis. For example, in the analysis for beryllium by the reaction 9Be( 3He,n)11C,boron can produce llC by the processes 1oB(3He,pn)11C, 1oB(3He,d)11C, 11B(3He,Chemistry Division. (1) E. Ricci and R. L. Hahn, ANAL.CHEM., 39, 794 (1967). (2) Ibid.,37, 742 (1965). (3) S. S. Markowitz and J. D. Mahony, Ibid.,34, 329 (1962). (4) J. D. Mahony, University of California Rept., UCRL-11780
(1965). (5) E. L. Steele, General Atomic Rept., GA-6568 (1965).
54
0
ANALYTICAL CHEMISTRY
p2n)11C, 11B(3He,dn)11C,and 11B(3He,t)11C. This type of interference cannot be avoided by using adequate counting techniques or chemical separations. However, differences in radioactivation rates between the sought element and the interference can be used to minimize the contribution of the latter to the measured radioactivity. In general, interference depends on the type of sample subjected to analysis, and it is always advantageous for the analyst to be able to appraise the relative importance of the interference, before he plans an analytical procedure. In 3He activation analysis, this aim can be achieved if activation rates can be predicted; these rates are proportional to reaction cross sections which, in turn depend on the bombarding energy of the 3He ions. Figures 1 and 2 show the excitation functions (6, 7) for the most important reactions induced by 3He particles in light elements, from beryllium to fluorine. These curves were obtained by irradiation of targets containing natural elements; thus, each curve represents all the reactions induced in an element that result in a given product, despite the fact that the curve is labeled after the most probable nuclear reaction or reactions. For example, curve c of Figure 1 represents the 5 reactions, mentioned above, by which llC may be formed during 3He bombardment of boron. The effective threshold energies E, (see below), are given at the bottom of the figures, where each letter corresponds to a curve; e.g., the value for B -+ l*Cis 1.66 MeV (c in Figure 1). With the problems of counting, and identical-product interference in mind, two interesting conclusions may be drawn from Figures 1 and 2. First, with only one exception, the effective thresholds of these reactions are too close together to allow any useful energy discrimination; it is not easy to find a 3He bombarding energy below the threshold of the interfering reaction but so far above the threshold of the desired reaction as to result in good analytical sensitivity. Second, the shapes and magnitudes of the curves are so different that they strongly suggest the possibility of finding an optimum bombarding energy for each analysis, at which the ratio of interfering to sought radioactivities, D,/Ds, is minimum. We will use this ratio as an adequate expression for the relative importance of the interference. Most 3He activation analyses involve thick samples-Le., samples whose thicknesses are greater than the ranges of 3He particles in them; thus, not the excitation functions of Figures 1 and 2, but rather the average cross sections ( I ) , obtained by integration of these curves, must be used in the calculation of the ratios D,/D,9. Though several authors have determined 3He activation analysis sensitivities and reaction yields at a few bombarding energies (I-5), their data are not sufficient to establish the continuous variation of the thick-target ratio D j / D scs. 3Heenergy f q r any given particular analysis. The purpose of this paper is to present a simple, general method, which makes use of excitation function data to predict the dependence between average cross section and 3He kinetic energy. This relation~~
-. .
~
(6) R . L. Hahn and E. Ricci, Phys. Rec., 146, No. 3, 650 (1966). (7) Ihid.,Niiclear Phys.. A101, 353 (1967).
-'9
0
3
5
8
4
12
20
0
Figure 1. Excitation functions and effective thresholds (E,,) for 3He reactions which produce I T , 13N, and 1 4 0 from Be, B, C, and N
THEORY
The charged-particle activation equation for thick targets may be written: =
InBR (1 - e-A')
4
8
12 MeV E3He'
(6
20
Figure 2. Excitation functions and effective thresholds ( E o ) of reactions which produce W, 17F, and I*F from N, 0, and F.
ship leads immediately to the one between 3He induced radioactivity and particle energy which, in turn, results in the rapid determination of two important energy-dependent parameters : the analytical sensitivity, and the interference ratio Di/D,. From the latter, the optimum 3He bombarding energy may be easily obtained.
D
-
5-
I
V
0
-
(1)
where D is the disintegration rate (in dpm) of the radioactive product whose decay constant is A; I is the beam intensity, in particles per minute; n, the number of target atoms per mg of irradiated sample; R,the range in mg/cm*, Le., the total depth penetrated by the particles in the sample; t , the irradiation time; and a, the average cross section. The definition of this parameter at bombarding energy, E, is: ( I , 2)
where u is the value of the excitation function at energy E , and E, is the effective threshold energy of the reaction (see below). The sensitivity, S, expressed in dpm/ppb in charged particle activation analysis (2) is
for an irradiation lasting one half-life of the product; No is Avogadro's number; cy, the fractional natural abundance of the target isotope; and W , the gram atomic weight of the corresponding element, expressed in mg. The relative amount of counting interference is given by the ratio, D l / D s , corresponding to the bombardment of a given matrix. By Equation 1 we have:
where the C's represent experimentally measured radioactivities expressed in cpm. Equation 4 is justified by the fact that irradiation times and beam intensities, as well as ranges and counting efficiencies (for /3+ or 0.51 1 MeV?), are the same for both the interfering and the sought radioactivities. The same situation holds for interference by identical product. Moreover, here X i = A,; thus, during bombardment, or at any time after it, we have: VOL. 40, NO. I , JANUARY 1968
55
DclD,
CtjCs = (ntins) (Ct/as)
=
(5)
The fraction, f,of the interfering radioactivity is, then: f =
Di ~
Dt
+ D,
DiIDs - ____-
1
ct/c,
+ (Dt/Ds) - 1 + (Ci/C,) -
(6)
Evidently, all these equations and, particularly, Equations 3-5 depend o n the bombarding energy, E, because the 8's are energy dependent, according to Equation 2 . However, none of the other parameters involved in the calculations of S and D t / D s vary with E; in fact, they can be easily obtained from tables and from the conditions of the analysis involved. Effective Threshold Energy, E,. The value E, of Equation 2 is defined as the lowest particle kinetic energy at which the nuclear reaction can take place. If the reaction is exoergic, E, is equal to the corresponding Coulomb barrier. Because of quantum mechanical tunneling, however, a n exoergic nuclear reaction may proceed a t energies below the classical Coulomb barrier. In fact, the variation of charged-particle capture cross section, uc with bombarding energy, E, may be approximated (8) by uC =
K(l
- kV'/E)
(7)
where V' is the classical Coulomb barrier, K and k are constants, and k < 1; clearly, uChas a non-zero value when E = V ' ; conversely, the reaction no longer proceeds (uc = 0) if E = kV'. This value V = kV' is called the corrected Coulomb barrier of the reaction. By using the well known definition for the classical Coulomb barrier (9), we find that V , and therefore E,, for exoergic nuclear reactions is: E,(MeV)
=
V(MeV)
=
0.959 k
2122
All'
A2"3
3
+
E , MeV
Figure 3. Straight-line fitting (--) of the excitation function (- - -) for the reaction 160(3He,~)150. Experimental (6) points
+
where the 2 ' s and the A's are atomic and mass numbers, respectively, corresponding to the bombarding particle (1) and the target nucleus ( 2 ) . In 3Hebombardment of light elements, k = 0.62 (8), Zl = 2 , and A1 = 3 ; thus, for exoergic 3He reactions, Equation 8 becomes : E,(MeV)
=
+ Az1'9
1.19 Z2/(1.44
(9)
The threshold energy, E T for a 3He-induced endoergic reaction is given ( 9 ) by the equation ET = - Q ( A z ~)/Az, where Q is the energy released (negative in this case) during one nuclear interaction. For endoergic reactions, then, the effective threshold energy, E,, is equal either to ET or to V , whichever is larger. Table I lists values of V ' , V , ET, and E, calculated by the above equations for the most important reactions induced by 3He bombardment of light elements, as well as the corresponding Q values. Average Cross Section, a, it1 Terms of Bombarding Energy, E. Calculation of a values by Equation 2 is tedious and time consuming, because it requires graphical integration of excitation functions. However, this equation becomes integrable if a simple expression of u rs. e can be found. To achieve this purpose, the excitation functions (6, 7) for 3He reactions in light elements (Figures 1 and 2 ) were approximately fitted by straight lines, as is illustrated in Figure 3 for the reaction l60(3He,a)ljO. For a given excitation curve, the linear equations and their intervals of validity are:
+
(8) I. Dostrovsky, 2. Fraenkel, and G. Friedlander, Phys. Rel;., 116, No. 3, 683 (1959). (9) G. Friedlander, J. M. Kennedy, and J. M. Miller, "Nuclear and Radiochemistry," 2nd Ed., Wiley, New York, 1964.
56
ANALYTICAL CHEMISTRY
The symbols are all graphically defined in Figure 3. Substituting Equations loa-d in Equation 2, we can easily integrate to obtain expression of 8 us. E. Clearly, if the bombarding energy is within the interval 0 6 E 6 E,, Equation 2 gives 8 = 0 (see Equation loa). For the interval E, 6 E 6 E,, by Equations 2 and 10b we have:
2 m 1 (E3 3 - E,E' + 9 ) (11) 2 6 ~
E2
and defining the constants a1 = mlE,, and bl = m1Eo3/3
(12)
we have :
a
=
2 m1E - a1 3
-
+ bl/E2
(13)
Finally if the bombarding energy is within the interval E m E 6 E,, the value of acorresponding to the whole excitation function, up to energy E, is:
6
Table I. Energy Parameters for 3He Reactions on Light Elements4
Group
Reactionb Most important
Coulomb barrier Classical ( V ' ) Corrected ( V ) 2.18 2.67 2.61 3.08 3.08 3.08 3.49 3.49 3.87 3.87 4.20 4.20
1.35 1.66 1.62 1.91 1.91 1.91 2.16 2.16 2.40 2.40 2.60 2.60
Energy releasedb
Threshold energy
Effective threshold
7.56 3.20 10.2 1.86 -3.55 -1.15 1.80
...
1.35 1.66 1.62 1.91 4.44 1.91 2.16 2.16 2.40 2.40 2.60 2.60
...
...
...
4.44 1.44
... ... ... ...
1 .oo
4.91 2.02 9.94 10.14
...
...
All values in MeV. * Each process in the first column represents the group of reactions which yield the same radioactive product from a given element. The V-values of all the reactions in one group are approximately the same, but their Q values differ; only the largest Q-value and the corresponding reaction are listed in columns 5 and 2, respectively. a
Substituting Equations 10b and c in this equation:
obtain: al = 96.58 mb, bl = 185.4 mb MeVZ, a2 = -361.3 mb, and bz = 40.24 [2 X (6.60)3/3 - 2.40 X (6.60)2 (2.40)3/3] -
+
3 By comparison with Equation 11 the above integrals give:
Defining now the constants: a2 = mZE,
- urn,and bz =
X 29.13 X (6.60)3 - 169 X (6.60)2 = -6462 mb MeV2.
Table I1 lists values of these constants for all the curves of Figures 1 and 2, as well as other parameters necessary for the calculation of average cross sections by Equations 13 and 18. Taking into account the approximations involved in the calculations of the parameters given in Tables I and 11, it is clear that most of these values could be rounded off. However, in order not to introduce additional approximations, it is advisable to drop nonsignificant figures only once, by rounding off the final 8 values. ERRORS
we arrive at an expression similar t o Equation 13; we have b =
b =
2 - mlE 3
- a1
+ b1/E2,
E,
6
E
6
E,
(13)
L
- a2 + bz/E2,
E,
6
E
6
El
(18)
-
3
mzE
Thus, once the constants involved are computed, these simple equations lead easily to values of 8 , in terms of bombarding energy, E. Note that, though Equation 18 can only be used within the interval E , 6 E 6 E f , its result is the total 8, integrated from E, to E (see Equation 14). CALCULATION OF CONSTANTS
The constants m1, mZ,at, a2,bl, and b2 of Equations 13 and 18 were calculated for all the excitation functions shown in Figures 1 and 2, by using Equations 12 and 17. Each excitation curve was replotted on linear scale, as shown in Figure 3 and the parameters which appear in Equations 12 and 17 were read or calculated (Equations 10d) from the graphs. For example, for the reactions 160(3He,a)150,in Figure 3 we read: urn = 169 mb, u / = 102 mb, E, = 6.60 MeV, E/ = 8.90 MeV, E, = 2.40 MeV (Table I). Then, by Equations 10d: ml = 40.24 mb/MeV, and m2 = -29.13 mb/MeV. When we substitute these values in Equations 12 and 17, we
To appraise the accuracy of this method, a number of calculated disintegration rates were compared with corresponding values accepted as accurate. The calculated rates were obtained by substituting in Equation 1 values of 5 computed by Equations 1 3 and 18 (see Examples below). The accurate rates resulted either from experiment (1) or from careful graphical integration of excitation functions (6, 7). Table I11 shows results of this comparison for each one of the reactions of interest. Most errors are seen to be smaller than 7%; in fact, even the largest deviation (13.5%) is not unreasonable. Because of the characteristics of the fitting procedure, the error corresponding to each reaction varies with bombarding energy. Though a strict error evaluation should take this fact into account, it was indicated previously that accurate systematic data are not available for all currently employed bombarding energies. As an alternative, Table I11 covers a number of different situations and, therefore, can give an overall appraisal of the reliability of the method. EXAMPLES
Applications of the present method are illustrated below by a few examples. It should be emphasized that these are simple examples of calculations, which d o not attempt to draw conclusions about experimental characteristics of 3He activation analysis. For example, when we discuss fluorine interference by 18F in analysis of uranium for oxygen, we do VOL. 40, NO. 1 , JANUARY 1968
57
Table 11. Parameters Required for Calculation of Average Cross Sections Em Em, E/, ml , bi, mz, bz, Reaction u,,mb uf,rnb MeV MeV MeV mb/MeV a l , m b mbMeV2 mb/MeV az, mb mbMeV* QBe(3He,n)1lC 119. 0 1.35 3.60 18.0 52.7 71.1 43.2 -8.25 -148. -905 10B(3He,d)1*C 74.7 49.9 1.66 9.10 18.0 10.0 16.7 15.3 -2.79 -100. -3,208 11B(3He,n)13N 5.35 2.15 1.62 8.90 16.5 0.735 1.19 1.04 -0.421 -9.10 -271 12C(3He,a)11C 378. 317. 1.91 8.07 9.50 61.4 117. 143. -42.7 - 722. - 18,080 12C(3He,d)13N 98.9 -a 4.44 9.50 ... 19.6 86.8 570. ... ... ... 1*C(3He,n)140 16.5 7.72 1.91 6.30 9.30 3.76 7.18 8.73 -2.93 -34.9 - 549 14N(3He,d)150 285. 285. 2.16 15.4 18.0 21.5 46.5 72.3 0 -285. -26,133 14N(3He,a)13N 26.7 88.0 2.16 13.3 18.0 2.40 5.18 8.05 +13.0* +147. +8,357 '60(3~e,~)150 169 102. 2.40 6.60 8.90 40.2 96.6 185. -29.1 - 361. -6,462 - 773. -15,963 160(3He,p)18F 414. 261, 3.19 6.73 9.60 116. 364. 1,204 -53.3 1gF(3He,an)1iF 50.0 45.2 2.60 8.30 9.30 8.77 22.8 51.4 -4.80 -89.8 -2,535 19F(3He,a)18F 24.4 15.8 2.60 6.60 9.30 6.10 15.9 35.7 -3.19 -45.4 - 854 This excitation function has no descending portion. (See Figure 1.) Thus, only parameters for the interval E, 6 E 6 E,,, are available. * This curve has no descending portion, but it was fitted by two straight lines of different positive slopes (see Figure l), which meet at the point (E,,,, u,,,); this point does not correspond to the curve maximum in this case, but all the parameters for this reaction can be used in the usual manner in Equations 13 and 18. The excitation function for this reaction could not be fitted properly if the calculated value E, = 2.40 MeV (Table I) was used. The value 3.15 MeV was obtained by graphical extrapolation of the cross-section curve.
Table 111. Comparison of Correct Disintegration Rates with Values Calculated by the Present Method Disintegration rate" Bombarding Present method Range, Accurate, energy, Reaction E , MeV Target R,mg/cm2 5, mb D, 10'0 dpmb Do, 1Olo dpmc Deviation, %d 18.0 Be 46.04 46.4 13.4 OBe -+ llC 13.3 +0.68 B - llC 18.0 45.27 B 12.9 +2.8 56.7 13.3 1 1 -. ~, 1 3 ~ B -3.1 3.47 0.561 0.579 16.5 38.89 14.4 243. 14.5 9.0 12.69 c -L " C C +O. 76 2.05 9.0 12.69 C 37.5 2.24 C + 13N +9.3 0.633 12.69 10.6 0.633 c-. "0 9.0 0 C 44.90 N -+ 1 5 0 18.0 204. 15.4 13.5 +13.5 Be3N2 35.6 2.68 2.72 44.90 18.0 -1.3 N-., 13N Be3N2 107. 2.21 2.22 31.66 -0.14 CeOn 9.0 o 150 CeOn 9.0 256. 5.31 5.68 31.66 -6.6 0 -c I6F 19F -P 17F CaFz 29.7 0.735 0.728 +O .96 17.12 9.0 I?IF 18F CaF2 17.12 15.8 0.390 0.398 -1.9 9.0 a Irradiation for one product half-life, with a 10 p A 3He beam current. Obtained by substituting in Equation 1, 5 values calculated by Equations 13 and 18 (column 5). The values for E = 9.0 MeV resulted from using in Equation 1, 5 values calculated by careful graphical integration of excitation functions (Figures 1, 2, and Refs. 6, 7); the values for higher energies are experimental ( I ) . Deviation % = 10qD - D,)/D,. -+
-
not wish to imply that this interference will be necessarily present in all samples; nor d o we overlook the possibility of using the reaction ~ ~ O ( ~ H ~ , Cwhose Y ) ~ product ~O, cannot be formed by 3He on fluorine. On the other hand, we neither pause to appraise the difficulties of counting 1 5 0 (T1,z = 124 sec), if a radiochemical separation is required, nor to consider the complications introduced in the analysis by the oxygen layer that normally covers uranium samples. What is important in all practical cases is the rapid calculation of yields and of the ratio D I / D , , and the following examples illustrate how the present method facilitates those computations. Evaluation of Optimum Bombarding Energy. Assume that carbon is being analyzed by the reaction 1ZC(3He,~)11C in aluminum which also contains boron. Figure 1 shows that though the cross section for this reaction is, at all energies, higher than that for the reactions B -+ I1C, the latter is quite significant and interference from boron may be expected. The figure suggests also that, according to Equation 5, the minimum value of D J D , (or &IDc here) might occur at 8-9 MeV. Subscripts B and C stand for boron (interference, i) and carbon (sought element, s), respectively. We now proceed to calculate aBand U C at E = 8 MeV, t o obtain DBIDc 58
ANALYTICAL CHEMISTRY
-
by Equation 5. As E, = 9.10 MeV > 8 MeV, for B llC (Table 11),Equation 13 should be used to calculate 8 ~ .Using the values given in Table I1 for ml,al, and bl for this reaction, we have simply: 8g =
2 x' 10.0 X 8 - 16.7 3
+ 158 3 = 37.0 m b
We compute irC in an analogous manner, since also for C -., llCwe have E, = 8.07 MeV > 8 MeV:
Then, if in Equation 5 we assume n~ = nc, for simplicity, we have DMIDC= b B / i r C = 37.01210 = 0.18. The fraction, f,of the interfering radioactivity is, by Equation 6 , f = 0.18/(1 -I0.18) = 0.15-i.e., the radioactivity due to boron interference is 15% of the total 11C radioactivity, both during bombardment or at any time after it. The sensitivity for analysis of carbon in aluminum with 8MeV 3He particles can be immediately calculated by substituting ac = 2.1 X cm2 and other known parameters
Table IV. Calculated Sensitivities for 3He Activation Analysis of Carbon in Aluminum, and Ratios for Boron Interference, in Terms of Bombarding Energy Average cross sections Range in Sensitivity, c -L "C, AI. R. ~~
Enerm.
22.0 3.2 3.18 5.0 56.0 12.0 4.75 11 .o 29.0 93.0 17.0 6.59 54.0 24.0 I30 8.70 170 88.0 30.0 11.06 140 37.0 210 13.68 190 9 45.0 240 16.54 26OC 230 49.0 19.64 10 a At end of bombardment for one half-life of 'IC, with 10 pA beam current. b For i f H = i f C (Equations 5 and 6). c This value implies a short extrapolation of straight line u2 (Equation 1Oc) beyond 15,. 3 4 5 6 7 8
0.23
19.0
0.20 0.18 0.18 0.18 0.18 0.19 0.19
17.0 15.0 15.0 15.0 15.0
Table V. Calculated Sensitivities for 3He Activation Analysis of Oxygen in Uranium, and Ratios for Fluorine Interference, in Terms of Bombarding Energy Range in Energy, U,R, Average cross sections Sensitivity, E , MeV mg/cm2 'jf --- lrF, 81, mb 0 '%F,Bot-, mb Sol, dpm'ppb" Ratio, 51/ B O F 1.8 0.14 3 11.03 0.27 0.68 21 .o 15.87 2.6 12.0 0.12 4 71 . O 5 53.0 0.083 5.9 21.26 130 0.073 6 27.15 9.5 130 7 13.0 240 0.065 200 33.52 0.063 240 8 40.35 15.0 340 260 Y 47.60 16.0 430 0,062 10 2 m 55,29 16.OC 5 IO 0.062 At end of bombardment for one half-life of lSF with 10 pA beam current. b For i i ~= /70F (Equations 5 and 6). c These values imply extrapolations of the corresponding curves u2 (Equation 1Oc) beyond E,.
-
~
Interference, loof, %*
16.0
16.0
Interference loof, %b 12.0 11.0 7.7 6.6 6.1 5.9 5.8 5.8
Q
in Equation 3. We have No = 6.023 X l o z 3and, for l?C, CY = 0.9889 and W = 12,011 mg. The beam intensity, I , should be expressed in 3He+2ions/minute; if we assume a beam curcoul sec-l PA-' rent of 10 pA, we have: l = 10 p A X x 60 sec min-l/(2 X 1.602 X coul ion-') = 1.873 X 10l5 3He+2 ions/min. Finally, the range, R,of 8-MeV 3He particles in aluminum is (10) 13.68 mg/cm2. Thus, Equation 3 yields SC = 140 dpm/ppb. In conclusion, for ne = nc our results indicate that with 8-MeV 3He ions, we could analyze carbon in aluminum with good sensitivity, and with an error of 1 5 % due t o boron interference. The analyst should always be certain that he is using conditions of strict minimum interference in his work. One way t o find these conditions is t o apply simple calculations, analogous to the ones just described, to several bombarding energies near the region of expected minimum interference. Clearly, once Equations 3, 13, and 18 have been applied to one bombarding energy, the same parameters can be rapidly and easily used to calculate values at other energies. Table 1V lists results of this procedure for our example and shows that, indeed, bombardment at 7 or 8 MeV ensures the best sensitivity obtainable with minimum interference error. Though the energy of minimum interference is independent of the concentration of interference (see column 6) the relative importance of n e and ne determines whether the interference can or cannot be neglected. I t is clear, for example, that large error may be introduced by neglecting it, if ne > nc in this example. Our third example will illustrate a solution for a problem of this kind. ( I O ) C. F. Williamson and J. P. Boujot, French Rept., CEA-R3042 (1966).
With regard to the results given in Table IV, it should be mentioned that Equation 13 was used to obtain Cn for E from 3 through 9 MeV, and 8~ from 3 through 8 MeV. The rest of the values were obtained by Equation 18. Assume now that oxygen is being analyzed by the reaction 160(3He,p)1bF in the presence of fluorine in a n otherwise pure uranium matrix. Figure 2 shows that we may expect some, but not much, interference from the reaction 19F(3He,a)18F. Calculations similar to those performed for the first example result in the data listed in Table V (which has the same format as Table IV); subscripts F and OF correspond now to the reactions lQF+ l*F and 0 + 18F, respectively. Within the range of our excitation functions we d o not find a bombarding energy for which the interference is minimum. The ratio, C ~ / C , > ~is, generally small and decreases very slowly above 7 MeV. It may appear at first that high bombarding energies would give the best results, because of the higher sensitivities. However, above 7 MeV there is neither a significant improvement of the interference ratio, nor a drastic increase in sensitivity (only a factor of 2). In addition, activation of other interfering elements of the matrix may become severe at higher energies; thus, 7-8 MeV should be optimum in this particular case. If n p = ~ O F the , expected interference error is small (-6%) and could be safely neglected in many analyses. Subtraction of Interference. Assume that oxygen has to be analyzed in germanium by the reaction 1 6 0 ( 3 H e , ~ ) 1 in 50 the presence of nitrogen, which interferes by the process 14N(3He,d)150. Figure 2 suggests that interference may be significant in this case, and that the most convenient bombarding energy should be near 6 MeV, which corresponds to the maximum of the 0 + ' 5 0 excitation function. Using Equation 13 and Table I1 for 6 MeV, we obtain ?rx = 41.0 mb, 80 = VOL. 40, NO. 1 , JANUARY 1968
e
59
69.0 mb, and 8 s / h = 0.59, where subscripts N and 0 correspond to the reactions N --c I5Oand 0 + 1 5 0 , respectively. For n N = no we would havef = 0.37-i.e., the interference error could not be neglected in this particular analysis. Our method has thus helped to appraise quickly the analytical situation and, furthermore, it can be used to solve this unfavorable case if the concentration of interference is known. Suppose then that the nitrogen concentration is independently determined in the germanium sample, for example by the reaction 14N(3He,a)13N,t o be 20 ppb; assume also that a total 1 5 0 activity, D = 800 dpm, is measured at the end of an irradiation, during one half-life of l50,with a 10-pA beam of 6MeV 3He particles. We assign a 5 % error to this measurement; thus D = 800 + 40 dpm. To obtain the oxygen concentration we should first subtract from D the activity, Dx, caused by the 20 ppb of nitrogen interference. Our method provides a simple way to calculate D,; we simply compute the sensitivity, Ss,for the reaction 14N(:$He,d)150,caused by 6MeV 3He ions in a germanium sample. By substituting h, R = 14.03 mg/cm2 (IO), and other known values in Equation 3 we obtain Ss = 23.0 dpm/ppb. Thus 20 ppb of nitrogen produce Dh.= 460 dpm of IjO. Since Table I11 indicates an error of 13.5 (the largest in the table) for the method when applied to this reaction, we have D N = 460 f 62 dpm. Finally, the activity of l60due to oxygen is D O = D - D N =
800 - 460 = 340 dpm; this value can now be directly used for comparison with the 150activity measured in the standard and the activation analysis would thus be completed. However, it is very important to know what is the error of DO; it may be obtained by propagation: 1/402+622= 74 dpmLe., 22% of Do. This error is quite reasonable considering the unfavorable conditions chosen for our example : the present method can quickly show that the sought oxygen concentration is 10 ppb-Le., half that of the interference. Tables IV and V illustrate an interesting and unique characteristic of charged particle activation analysis: the influence of the range on the sensitivity, quantitatively expressed by Equation 3. The tables show that the sensitivities (column 5 ) grow faster than the average cross sections (column 4), as energy increases, instead of being directly proportional to the cross section as in neutron and photon activation analysis. Indeed, the influence of the matrix may be quite drastic; for example, the increase in yield or sensitivity due to the large range of particles in a heavy matrix like uranium (Table V) is about twice that observed in aluminum (Table IV).
RECEIVED for review September 5,1967. Accepted November 8, 1967. Research sponsored by the U S . Atomic Energy Commission under contract with the Union Carbide Corp.
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Zone Refinilng for the Separation of Radioactive Trace Contaminants from Organic Compounds Bodo Diehn,' F. S. Rowland,2 and A. P. Wolf Departments of Chemistry, Unicersity of Kansas, Lawrence, Kans., and Brookhacen National Laboratory, Upton, N . Y The purification by zone refining of propionamide containing traces of radioactive acetamide as impurity was studied because of the particular difficulties involved in the separation of homologous solid compounds if conventional methods are used. The separation efficiency has been determined quantitatively as a function of travel speed of the liquid zone, number of zone passes, and impurity concentration. With the automatic zone refining apparatus described in this paper, the concentration of acetamide in propionamide was readily reduced by lo4 from its original concentration of 0.02% with a minimum of handling of the sample. The technique offers particular advantages in studies of nuclear recoil reactions in solid substances, and in other situations in which traces of very high specific activity contaminants are encountered.
THE PURIFICATION of organic compounds from radioactive contaminants to the level at which the melting point, infrared spectrum, etc., correspond to those of an authentic pure sample usually presents n o special problems caused by the radioactivity. However, purification t o radiochemical purity,Le., negligible contamination by radioactive impurities-can present major difficulties if the contaminant is present in trace, high-specific-activity quantities. Special cases of this kind are not uncommon, and occur frequently in the study of chemical Present address Department of Chemistry, The University of Toledo, Toledo, Ohio 43606 Present address Department of Chemistry, University of California Irvine, Calif. 92664
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ANALYTICAL CHEMISTRY
reactions, especially noteworthy among which are those accompanying nuclear transformations. Two purification techniques currently known which effect consistently good separation from trace contaminants are derivatization and gas chromatography. The former, often involving complete chemical cycles, can frequently provide good purification (1). However, the preparation of derivatives can be very time consuming, and can also be accompanied by low chemical yields, such that recycling must be very limited in scope. Furthermore, the separation of members of homologous series may be quite difficult, Gas-liquid chromatography (2), which usually gives excellent separations, can be conveniently carried out on gases and liquids, but the handling of solid samples is in most cases unsatisfactory. A study was therefore undertaken to determine the applicability of zone refining as a means for achieving radiochemical purity. If applicable to a particular compound, the process can be completely automated, and has the additional convenience that it can be used for 1-100 gram samples per batch. Since its introduction by Pfann (3), this technique has been widely used for the purification of metallic elements, particularly in the semiconductor industry. Applications to organic (1) A. P. Wolf and R. C. Anderson, J . Am. Cliem. Soc., 77, 1608 (1955).
(2) R. J. Kokes, H. Tobin, Jr., and P. H. Emmett, Ibid.,77, 5860 ( 1955).
(3) W. G. Pfann, J. Metals, (New York,) 4, 747 (1952).
