Correcting for the Absorption of Weak Beta-Particles in Thick Samples General Method f o r Use in Tracer Work PETER E. YANKWICH, THORIAS H. NORRIS,
ASD
JOHN HUSTOw
Department of Chemistry and Radiation Laboratory, Cniversity of California, Berkeley, Culif.
Tracer work using isotopes such as C14and S3jis often hindered because the betaparticles which these materials emit are sc weak that a large fraction of them are absorbed in the materials of the samples themselves. I n this paper, a general method is presented, by the use of which accurate corrections can be made for this “self-absorption.” Data are presented far samples of RaC.l4O3,typical applications are shown, and the effect of geometric efficiency is discussed.
T
HE use in chemical and biological resexch of radioactive isot,opes which decay by the emission of beta-particles of low cnc.rgy, such as CI4, E,,,. = 0.145 m.e.v. ( 6 ) ; S35,E,,,,,. = 0.120 ni.e.v. (4); and -1s7*~7~, E,,,,. = 0.050 m.e.v. ( I ) , has made it nereasary to develop a method n.hereby the errors due to the ahsorption of the radiations in the material of the sample itself (selfahsorption) niay be eliminated. A large part of such development is the achievement of reproducible sample manipulation.
II, 0‘
-
dTdX
PREVIOUS N-ORIi
.bong thil procedures Tvhich have hcen used heretofore to all o k for thc sc,lf-absorption of weak radiations in sample materials are the follon-ing: 1. Samples have been mounted in very thin layers, so that the error which results when the ahsorption is neglected is small wheii compared with other experimental errors. Though widely used in the counting of alpha-particles, the application to betaactive samples is limited by the frequency with vihich samples of low specific activity (activity per unit weight) are exountered. 2. A1ttemptshave been made to reproduce accurately one of a number of sample thicknesses chosen as standard. Though this is a more flexible procedure than that mentioned above, there is usually considerable difticultp attached to getting a given weight of sample onto a mount in a perfectly homogeneous layer of predetermined area.
I Tm
I
Xm
Figure 1. Activity Observed E S . Thickness of Absorber
Ideally such& method would enable one to calculate the actual activity of a sample of any thickness or radioactive strength. Such “actual” activities need only be corrected for sample-counter geometry, window and air-path absorption, and beta-particle path obliquit,y to yield absolute disintegration rate data. I n a n earlier publication (9) two of t,he aut,hors presented data obtained by the method esplained below, using CI4. I n this paper is presented a general experimental method for obtaining curves by the use of which observed activities can be corrected for selfabsorption in the sample material, with data illustrating the application of the method t o BaCIQa.
Figure 2. Fraction of RIaximum Activity w. Sample Thickness
3. Occasionally samples have been mounted in very thick and massive layers, an attempt being made to approach the condition of the so-called “infinitely thick’’ layer, which is of such a thickness that the radiation from the bottom of the sample is completely stopped in the sample itself. The activity of such a layer is dependent upon the specific activity of the sample material. This method fails only when the sample is weak and the amount available is small.
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Present address, Department of Chemistry, University of llinnesota, Minneapolis, Irlinn. 2 Present address, Department of Chemistry, Oregon State College, Corvallis, Ore.
439
VOLUME
440 PHENOMENA DUE TO SELF-ABSORPTION
If the observed activities of a series of successively thicker layof constant, area of material containing a n isotope which decays hy the emission of a heta-particle of low energy are plotted against the thickness of tht. sample layer, it \Till be noted that the activity observahle approaches a inmimum (Figure 3). All samples of thickness greater than that corresponding to this niaximum or saturation valut. have the same activity. It is himediately ohvious that the apparent specific activity of the sample substance drcwases as one increases the thickness of the measurrld layer. If the extent, of this decrease is accurately known, samples of any thickness may be used and their “actual” activitirs cttlculatrd f r o m thoscs ohs;t~rvcd.
(AI’S
19, N O . 7
Calculation of Function G ( X ) . Consider a sample layer 01 unit area and specific activity having a thickness X. Let T be the total absorber thickness, and t , the equivalent thickness 01 the counter window and air path. X = T - tw. K h e n thii sample is counted through a window of thickness t,, the activity of the top layer will appear to bef(t,), while that of the bottom X ) . T h e total activity of the sample layer layer will be f(t. is :
+
The activity of the infinitely thick layer is the area under the curve out from the window, or
CALCULATION OF SELF-ABSORPTI0.Y CORRECTION CURVES
Three functions of saniplv thickness are used in I nutint. srlfabsorption calculations. Let X be the thickness of the layer whose activity is t o be measured, and let T be the total thickness of absorber-i.e., sample plus counter window plus air path between sample and window. (Counter-windoTY and air-path thicknesses must be expressed in terms of an equivalent thickness of the sample material.) 1. The function F ( X or T),when plotted against X or T,is the absorption curve of the radiation in the sample materjal (Figure 1). 2. G(X) represents the variation with sample thickness of the fraction of the maximum observable act’ivity. It is, for a particular sample, the observed activity divided by the activity of the “infinitely thick” layer (Figure 3). 3. The function J ( X ) represents the variation with sample layer thickness of the apparent specific activity. It is defined as the observable fraction of the true maximum specific activity (Fpecific activity of an “infinitesimally thick” layer) (Figure 4).
The activity of a sample of thickness X divided by the activity of the infinitely thick sample is equal t o G(X).
I-aluw of G(X) ha\.(%I)c.c.n obtained for precipitates of BaS3604 ( 2 ) and HaC140, (91. Calculation of Function J ( X ) . I n routine tracer work with thick samples, the value of the function J ( X ) for each sample thickness is used to calculate the actual activity from that observed. In Figure 2, the line drawn tangent to G( X ) at X = 0 is represented by the equation
--
h
=
[SI[ G ’ ( O ) ]
(4)
where h is the value of the ordinate and G ’ ( 0 ) is the slope of G(X) a t X = 0. It represents the activities of sampleswhich suffer no loss in strength due to self-absorption; it is the line of maximum specific activity. J ( X ) has been defined as the observable fraction of the true maximum specific activity. G ’ ( 0 ) is the true specific activity of the sample material and G ( X ) / X ic the observable specific activity. Thus
J(X) SAMPLE
Figure 3.
=
G(X) ‘X.G’(O)
(5.’
THICKNESS, M6JSP. CM.
Fraction of RIaximum Xctiiity z’s. Sample Thickness Experimental points
Expressions for G(X) and J ( X ) are easily computed if one assumes exponential absorption of the beta-particles (S), and for many beta-active isotopes, such is actually observed. If an accurate curve is known for the absorption in the sample material, or in some substance having the same scattering power for the beta-particles of the particular isotope being used, these functions are easily obtained by graphical means.
Values for J ( X ) h a w been published for BaC,“03 ( 9 ) , obtained by computation, and for BaS3j04(2, S ) , obtained by dilution experiments. Unpublished data have recently been obtained in these laboratories (?) for thick samples of certain phosphates = 1.71 m.e.v. (8). containing P3*,E,,,. It is difficult to obtain directly values for the function F(X7, when sample substances such as carbonates, sulfat,es, and phosphates are being used. However, G(X) is easily obtained rxperimentally and from a difference table of its point to point value& one can const,ruct the absorption curve, F ( X ) , in whatever material makes up the samples whose radioactivities are t o be detrrmined. Once this curve is known, the values of J ( X ) can be calculated for any combination of sample and moderate \~indv\\thicknesses.
JULY
441
1947
and air-path ab;.orptions equivalent to 2.8, 3.1, and 4.1 mg. per rq. cm. and sample-counttlr grometry of 16.4Yc. I n each case t hr calculatd and observrd plots of G ( X ) \\-ere idcntical within thti counting (lrror, 0.5c;.
Y
ROUTI%E USE OF G ( X ) 4 K D J(.Y)
SAMPLE
Figure I..
THICKNESS, MQ/W. CM,
Fraction of >\laximum Specific .Acti>ity M . Sample Thickness EXPERIMENTAL
Aiswies of twenty-st’ven aamplt. plates of greatly varying thickwas prepared from a large quantity of BaC”O:i. These
IIIW
plates were niade and thtbir radioactivities determined with the apparatus described in a n earlirr paper. The equivalent t,hi(:kn ~ s of s the count’er window and air path was 3.6 my. per sq. m i . The result,s are ~ h o n . nin Figure 3. The protmlde error in thtb (letc~i~minations of the activities w’au 0.3$.
Tahle I. X,SIg. per Sq. Cni.
G(W
0
0,000
1
0 245
2
0.431
EFFECT OF GEOMETRY
F(9
+
1/2)
0.245
J (S) 1.000 0.866
0.186 0.560
4
0.663
5
0 .i 4 5
10
0 934
11
U 94i
1d
0 Y78
16
0 983
20
0 YYS
21
0 Y96
24
0 9YY
25
1 000
Examples. A sariiplc weighing 23.04 mg. having a thickness of 2.00 mg. per sq. em. is found to have an observable activity of 1000 counts per minute. .\t this thickness, G( X ) = 0.431 and J ( X ) = 0.761. Using G(X), the activity of the infinitely thick layer is 100,’ 0.431 or 2320 counts per minute. The specific activity of t h e sample material is proportional t o 2320. The constant of proportionality must be evaluated by a separate experiment. If J ( X ) is used, the activity of the sample which would have heen observed if there had been no self-absorption is 1000/0.761 or 1314 counts per minute. The specific activity of the sample materinl is 1314/23.01 = 57.04 counts per minute per mg.
Experimental Points
0.761 0.129
3
I n oidiriary ti.ac.c.r \\.(irk one may USC’ eitlier of the functions G ( X ) anti ./(*Y) in c o i ~ c ~ * t ifol ng If thtl ohst~rvtdactivity of a ssmple whose thicknrss is ltiss than that which cirresponds to G ( X ) = 1, about 25 nig. per sq. cni., is tlividrd 1)y the proper valuc. of G ( X ) ,thc quotient is that activity ivhicli would have been obscrved if the sample had been infinitely thick. Thi.- figure is proportional t,o the actuitl ohsc~rvablespecific, activity of the sample material. If ,/[XI is usrd in thc saint: niannc’r, the figurc. obtaintd is equal to that activity which \\oultl have been observcd if the sample had t)c~,nof m’ro thicknc~ss-i.c~., if thtlre had twcn no self-ahsorptiou. \\-htln this numher is divitlrd h y tht. \wight, of saniplt, material spcicific activity of countcd, tht. quotient is t h e wtual ohsc~wal)lt~ the h:tmplt~matr~i.ia1.
0,660
0.103
0 586
0 . 082 0.527
0.013
0 330 0.304
0.230 0.005 0 21T
0 001
0 li6 0 168
0 001
0 147
0 141
Thct n i ~ ~ adrhviation n of tht. points from the smooth curve is 1 . 7 7 . It is iritt~rc~stiiig to note that the curve obtained for F ( X ) lies .xithin 15; of a plot, based on exponential absorption. I n Tablc I are twllected a number of values of G(X) taken from the sniooth curve in Figure 3, their differences, n-ith which F(X)may ht, plotted, and values of J ( X ) for tu, = 3.6 my. per aq. cm. A value of 0.283 for t h r slope, G’(O), of the maximum activity line was obtained by successive approximations. B value of G ’ ( 0 ) smaller than 0.283 results in a J ( X ) curve which has negative second derivatives in t h r region near S = 0. J ( X ) is plottcld in Figure 4. T o test calculations niade using the curve for F ( X ) o1)taind in Tahle I, a series of samples whose observed radioactivities lay ~ i g h ton tht. G(X) curve, Figure 3, \va$ recounted with window
Tht. paths of thtb emitted beta-particlw through the sample and various absorptive layers are all essentially oblique. The effective absorber thicknessw are thcrefore greater t,han those measurtd. The magnitude of this difference is dependent upon the gcuiicstric arrangement of the sample and sensitive.volume of the countrr tube. T h e paths of beta-particles actually counted using a n arrangtsment resulting in low gcometric efficicncy are more nearly perpendicular to thcl plane of the sample plate than these counted x i t h high gcomcxtric efficic1n(:y. Reid ha-: r(m,ntly published a treatment of this phrnonit.non (i). This effect is troubl(w)mc only if it is larger than the niounting error ( * 1 . 5 7 ) for the rangt. of gwmetric efficiencies usually encountprcd. In order t o dctc,rniine thc relative importancc of this obliquity effrct, several of thc, sample plat,es used in dvtcrniining G(X)were recounted under counters having geometric efficiencies of 7.6, 10.7, 16.4, and 20.5(;. Reid gives obliquit,y correction factors of 1.08, 1.12, 1.21. and 1.28 for these efficiencies. I n cach c a w the relative, actiritic- of thcb several plates were thr. same within the mounting and counting error (*2cl,), and thtrtLfore the, curves for G(X) construc.tcd from these activities w ’ r e itlentic:il within thcs s:tme error. LITERATURE CITED
(1) I.;lliot and Deutscli. Phys. Rec., 63, 457 (1943).
(2) Hendricks, Bryner, Thomas, and Ivie, J . Phys. Chem., 47, 469 (1943).
Henriquen, Kistiakowsky, Margnetti, and Schneider, ISD. ENG. CHEM.,ANAL.ED.,18, 349 (1946). (4) Eiayen, Phys. Rezl., 60, 537 (1941). ( 5 ) Reid, A. F., et al., “Preparation and Measurement of Isotopic Tracers,” Ann Arbor, Mich., Edwards Bros.. 1946. (ti) Ruben and Kamen, Phys. Rec., 57, 549 (1940); 59, 349 (1941). (7) Scott, K., private communication. ( 8 ) Sieghahn, S u t u r e , 153, 221 (1944). (9) Yankwich, Rollefson. mid Xorris. J . Chem. Phys., 14, 131 (1946). (3)
,.1
H E experimental p n r t of this paper u-ab performed under the auspicea of t h e .\Ianhartan District, Contract W-7405-Eng-48.
