Nuclear Instruments and Methods in Physics Research A330 (1993) 158-164North-Holland

Direct measurement of gaseous activitiesby diffusion-in long proportional counter method

M. YoshidaJapan Atomic Energy Research Institute, Tokaz 319-11, Japan

T. Yamamoto, Y. Wu, T. Aratani, A. Uritani and C. MoriSchool of Engineering Nagoya University, Nagoya 464-01, Japan

Received 14 September 1992 and m revised form 11 January 1993

Direct measurement of gaseous activities by the diffusion-in long proportional counter method (DLPC method) was studied .The measuring time without end effect was estimated by observing the behavior of 37Ar in the counter and was long enough tocarry out the accurate activity measurement . The correction for wall effect was also examined on the basis of the measured andcalculated correction factors . Among the tested gases of methane, P10 gas and propane, P10 gas was made clear to be a suitablecounting gas for the DLPC method because of good diffusion properties and small wall effect . This method is quite effective forstandardization of gaseous activities used for tracer experiments and calibration works of radioactive gas monitoring instruments .

1. Introduction

Radioactive standard gases are utilized in variousworks such as tracer experiments and calibration of theinstruments for measuring or monitoring gaseous activ-ities . For the quality assurance in such works, it isimportant to supply the reliable standard gases ofwhich activities are accurately determined by directmeasurements .

Standardization of gaseous activity is, in general,based on internal gas counting [1] . This method isessentially the same as 47rj3-counting . However, thereare two specific corrections required for end effect andwall effect because gaseous samples distribute through-out the whole volume of counter.

Mann et al . have developed the length compensa-tion method to correct the end effect [2]. The methodneeds plural counters with the same cathode diameterand the same shape of end supports for the anode wirebut with different length . Those counters must beoperated in the same conditions to measure the differ-ence in count rates among them .

Mori et al . have eliminated the effects by anothertechnique using a long position sensitive proportionalcounter (defined volume method or DV method) [3,41.The method requires position analysis to determine theeffective volume. That makes the electrical circuitrysomewhat sophisticated and position calibration impor-tant . The observation of gas behavior in a long counter

2. Experimental apparatus

016&9002/93/$06.00 © 1993 - Elsevier Science Publishers B.V . All rights reserved

NUCLEARINSTRUMENTS& METHODSIN PHYSICSRESEARCH

Section A

by the position analysis has brought about the otherdirect measurement method which is based on thenatural diffusion of sample gases (diffusion-in longproportional counter method or DLPC method) [5].This method entirely depends on the physical proper-ties of gas diffusion. The system is very simple withoutposition analysis . However, it is necessary to seize thebehavior of radioactive gas in counting gases and tomake sure of the complete elimination of end effect .

In this paper, the optimum conditions studied forthe DLPC method concerning measuring time andcounting gas are described. In addition ; the correctionfor wall effect is discussed .

The experimental system consists of a long internalgas counter and its gas circulating loop as illustrated infig . l a. The counter has a cylindrical cathode 40 mm ininner diameter and 900 mm long and made of stainlesssteel. On the cathode wall, there are a central portwhere radioactive gas sample is infected through rub-ber packing and two blind flanges which are used toattach sources for axial position calibration . ANichrome anode wire 15 win in diameter is stretchedbetween Kovar-glass hermetic terminals at both endplates of the counter. The whole resistance of wire isabout 5 kf2 which provides the information about the

(a)Exhaust

Gas inlet

Pressure gouge

cuitry .

Pre-amplifier

Linear amplifier

Logarithmic amplifier

2 parameter dataaquisition system

Fig . 1 . Experimental system . (a) Overview.

M. Yoshida et al. / Direct measurement by DLPC method

(b) Electric cir-

position where the electric charge due to electronavalanche is deposited . Since the counter is containedin a lead shield with large heat capacity and the ambi-ent temperature is controlled at 23°C (t 1°C), thetemperature equilibrium in the counter is maintainedenough . The circulating loop includes a mixing pump, apressure gauge and some valves for filling and exhaust-ing counting gases. The mixing pump is used only forthe DV method which is applied to the measurementof wall effect mentioned in section 3.2 .3 . The wholesystem has been designed to maintain enough integrityand negligible leakage of internal gases in the pressurerange from vacuum to 1 MPa.

The block diagram of electrical circuitry for theexperimental system is shown in fig . lb. The counter isoperated in the proportional region . The signals fromboth ends of the resistive anode wire, after throughamplifiers and an analog to digital converter, lead to atwo-parameter analyzing unit which provides the posi-tion spectrum of deposited charge . By using a logarith-mic amplifier following a linear amplifier, this setup isapplicable to the activity determination even for highenergy ß-ray emitters by the DV method [6] . Since theposition analysis is not needed in the activity determi-nation by the DLPC method,the signals are then col-lected through only one preamplifier detaching theother one .

3. Evaluation methods

3.1 . Determination of diffusion time

The amount of activity in internal gas counting isgenerally limited in order to prevent pileup of pulses .Under the limitation, the measuring time is preferableto be long enough to minimize the counting statisticalerrors . In the DLPC method, the accumulation ofcounts has to be finished before sample gas reaches theinsensitive region near both ends of counter. However,this manner results in the restriction of the measuringtime. The measuring time should be selected as long aspossible within the restricted time interval .The gaseous activity concentration C(x, t) at the

point x and at the instance t is given by the followingequation when the distribution, as is mentioned later,is uniform over the counter cross section vertical to theaxis .

zC x, t =

ex ((

)2 DT

pl

4Dt )'

where D is a mutual diffusion coefficient betweensample gas and counting gas and A is a normalizingfactor. The theoretical diffusion coefficients are knownto show good agreement with experimental ones in lowand moderate pressures (< 0.5 MPa) [7] and can becalculated in table 1. They are determined by thecombination of two sorts of gases and to be propor-tional to the reciprocal of partial pressure of eachconstituent gas. The measurement conditions in theDLPC method should be selected concerning the sortand pressure of counting gases to compare experimen-tal and theoretical position spectrum .

After the injection of radioactive gases, the elapsedtime allowed for counting without end effect was ex-perimentally evaluated using a radioactive gas of ;7Ar .The measured position of each electron emitted from3'Ar depicts only the average position where the chargedue to gas-multiplication is deposited, but it does notnecessarily correspond to the actual position of j'Ar ifthe path of the electron is long in counting gas. TheK-Auger electron emitted after the electron capturedecay of 33~Ar has the energy of 2.6 keV and its range inmethane is less than 1 mm at the natural temperatureand pressure . This short range makes it possible to

159

Table 1

Countinggas

Sample gasMethane Argon Krypton Xenon

Methane 0.217 0.208 0.166 0 .139P10 gas 0.209 0.181 0 .138 0 .112Propane 0.118 0.101 0 .074 0 .060

160

TO

O

NC0v

obtain the real distribution of sample gas. Also,the halflife of "Ar is long enough not to require decay correc-tion during the measurement. This nuclide is bite suit-able to the observation of gas behavior in the counter .

The sample gas of 3~Ar was produced with 99.9%enriched 36Ar gas by the (n, y) reaction in a researchreactor in Japan Atomic Energy Research Institute. Noimpurities were detected in it by Ge -y-ray spectrome-try . The sample gas of 0.05-0.2 cm3 for each measure-ment was injected through the central port by a micro-syringe. Three different counting gases of methane,P10 gas (90% Ar + 10% methane) and propane weretested . The internal gas pressure was changed from 0.1to 0.4 MPa. Fig. 2 shows the pulse height spectra for"Ar measured with the logarithmic amplifier and con-verted into linear pulse height by digital calculation .

3.2. Corrections for threshold and wall effects

Although the DLPC method theoretically enablesthe complete elimination of end effects, it needs suchcommon corrections in the internal gas counting as thecount losses due to the threshold energy and walleffects. Those corrections were classified into the fol-lowing factors and evaluated in experiments and calcu-lations . Those loss factors are proportions of countlosses and called correction factors in this paper.

3.2.1 . The proportion of (3-rays whose energies are belowthreshold energy; Fdc

It was calculated with the theoretical R-ray energyspectra according to the Fermi's theory [8,9] and thethreshold energy defined in the present experiments.Defining the ß-ray energy E and the shape of ß-rayspectra N(E)dE as shown in Appendix Al, Fdc isexpressed by the following equation

fEdN(E) dE0

Fdc -

,fE'N(E) dE0

2000

4000Pulse

height

( channel number 1Fig. 2. Pulse height spectra for "Ar.

M. Yoshida et al. / Direct measurement by DLPC method

where Ed is the threshold energy and Em is the maxi-mum ß-ray energy .

3.2.2. The calculated count loss due to wall effect; F.,In an internal gas counter, the counter wall restricts

the path of ß-rays to the shorter than their range. Theenergy transferred from ß-rays to counting gas is deter-mined by the integration of stopping power over itspath . If it is smaller than the threshold energy, thep-ray is missed without counting . When the missingprobability of ß-rays with energy E is fwo, the correc-tion factor Fwc is given by the following equation

Fwc - fEmN(E)fwc dE,Ed

where suffixes w and c mean wall effect and calcula-tion . The derivation of fwc is given in Appendix A2[10,11] .

3.2.3. The measured count loss due to wall effect; FW�,In a proportional counter, the count loss due to wall

effect decreases as the increase of internal gas pressureor counter diameter. At the infinitely high pressure,there exists no influence of wall effect .

In measurement of the correction factor Fwm, therelationship between count rate and internal gas pres-sure was obtained by the following procedures . Thecount rate from the defined volume of the counter wasmeasured after injecting sample gas and mixing it withcounting gases uniformly. Then, it was repeatedly mea-sured at the various internal pressures which werechanged by introducing the additional counting gas. Byextrapolating to zero-reciprocal pressure with the mea-sured data, Fwn, at the pressure of 0.1 MPa was deter-mined.

As the optimum voltage applied to the counterincreased with the increase of internal gas pressure,the discrimination level was always adjusted at thepeak channel of the L-Auger electrons from 37 Cl asseen in fig . 2. This discrimination level corresponds tothe threshold energy mentioned in section 3.2 .1 .

3.2.4. The measured total count loss due to both thresh-old and wall effect; Fm

The whole pulse height spectrum from the counterincludes the contribution of the ß-rays losing smallenergy due to the wall effect as well as that of lowerenergy ß-rays than threshold energy . The analysis ofthe low pulse height part below the discrimination levelgives the total count loss for the ß-rays . The correctionfactor (F �,) was obtained by the linear extrapolationwith the lower part of pulse height spectrum measuredthrough a logarithmic amplifier.

4. Results and discussion

The diffusion behavior of "Àr in the counting gas ofmethane after the injection is shown in fig . 3 . It wasobserved at the internal pressure of 0.1 MPa and theambient temperature of 23°C . The accumulation ofposition signals during elapsed time from t1 to t2 givesthe spectrum expressed by the following equation ac-cording to eq. (1)

C(x) = fi2C(x, t) dt .

The solid lines in fig . 3 show the spectrum derivedfrom the above equation with the diffusion coefficientlisted in table 1. The real elapsed time was differentfrom the time used for the calculation because thesample gas had already spread over to some extenteven just after the injection . As shown in fig . 3a, thespread corresponded to the calculated distribution ofthe sample gas at the elapsed time of 50 s. Althoughthe observed diffusion is a little more rapid than theexpected one, it can be explained by the calculationwith the theoretical diffusion coefficient .

The relation between count rates and elapsed timewas measured with "Ar for the counting gases ofmethane, P10 gas and propane. The results are shownin fig . 4 with the calculated ones. For all the tested

`~ 102

N

N0

1104

102

nN 10 4

U

102

M. Yoshida et al. / Direct measurement by DLPC method

Fig. 3 . Diffusion behaviour of 37Ar in the counting gas ofmethane for three different times after injection .

100

098

0960

1000

2000

0100

098

096L

0

Elapsed time (s)

Fig . 4. Relation between count rates and elapsed time measured with 37Ar for the counting gases (a) methane, (b) P10,

and (e) propane.

0

1000

2000 3000

gases, the count rates do not decrease beyond thestatistical errors until a definite elapsed time . Then therates gradually decrease as the sample gas diffuses intothe insensitive region near both ends of the counter.The measured results for methane and P10 gas at 0.1MPa show good agreement with the calculated ones .Especially for P10 gas, the elapsed time without changein count rate at 0.3 MPa is nearly twice of that at 0.1MPa as explained theoretically using the mutual diffu-sion coefficient . The diffusion coefficient betweenpropane and argon must be smaller than the others. Inspite of that,the measured data did not show as slowdiffusion as expected . The asymmetrical diffusion wasalso observed in some of the repeated measurements .This tendency was much more notable at 0.3 MPa. Thephenomenon is likely to depend on the way of fillingthe counting gas and considered to be due to the smallviscosity of propane.

Most of radioactive gases used for the calibrationwork of gaseous effluent monitors and the tracer ex-periments are noble gases such as argon, krypton andxenon, and the organic compound gases labeled with3H and 14 C. These mutual diffusion coefficients areexpected to be much smaller than or as small as thosebetween argon and the tested counting gases. Whenmethane or P10 gas is used at 0.1 MPa in a counter ofthe same size as the present one, the elapsed timeinterval of more than 500 seconds can be allowed tomeasure the gaseous sample activities without endeffect . Since the DLPC method does not need theposition analysis, the measurement in the count rate ofseveral thousand counts per second is possible . Thiscondition makes it easy to reduce the statistical errorsless than 0.1% for each measurement.

The radial distribution of sample gas was observedwith the multielement position sensitive proportionalcounter [12] . The counter has a cylindrical cathode

16 2

UJIONÔCOUOO-O

0.5 1.0 1 .5 2 .0Reciprocal

pressure

(10-5 Pal )Fig. 5 . Comparison of the count rates obtained by the DV and

the DLPC method .

with 40 mm inner diameter and provides the detectionsignals from seven independent anode wires. The countrates at the seven regions divided with the anodes werecompared after corrections of the cross-sectional areasof the regions. They showed the same count rates evenin only 7 s after injection . This result means that thesample gas has uniformly enough spread over in theradial direction in a short time interval less than 10 s.

The count rates obtained by the DV method andthe DLPC method are compared in fig. 5 . In themeasurements was selected the combination of "Krand methane which was expected to give notable walleffect . The ratios of count rates agree within experi-mental errors in the pressure range from 0.05 to 0.4MPa.

These results conclude that the same correctionfactors for wall effect can be applied to the two meth-ods.

The calculated correction factors for wall effect(FWc ) are given in fig . 6 for methane, P10 gas andpropane. FWD increases almost linearly with the recip-rocal pressure of counting gases. It is expected to bereduced by selecting such counting gases as P10 gasand propane rather than methane. There is notabledifference between the factors for 3H and "Kr becausetheir maximum ß-ray energies are exceedingly differ-ent. The calculated data for 4'Ar with much highermaximum ß-ray energy are as large as those for 85Kr,although they are not shown in fig . 6.

M Yoshida et al. / Direct measurement by DLPC method

05

10Reciprocal

pressure (10_5 Pa-' )

Fig. 6 . Calculated correction factors for wall effect (F_).

Fig. 7 . Count rates for (a) 3H, (b) 14 C, and (c) s5Kr and by theDV methods as a function of the reciprocal pressure of

methane and P10.

0 0

0.5

1.0Reciprocal

pressure

(105Pâ1 )

P10 gas3H 14c 85 Kr(18.6) (156) (687)

1 .81 0.21 0.030 .09 0.38 1 .080.0(+0.2) 0.4 (±0 .5) 1.4(+0.3)0 .7 0 .9 0 .91 .9 0.6 1 11 .8 0 .6 1 .4

Table 2

Counting gas MethaneRadionuclide 3H 14C 85K

Epmax [keV1 (18.6) (156) (687)

Fd c 1 .81 0.21 0 .03F� 0 .13 0.79 2 .59Fw. 0.3(+0.4) 1.9(+0.3) 3.9(+0.2)Fm 2 .3 1.9 3 .4Fd ~ +F, 1 .9 1 .0 2 .6Fdc + Fwn, 2 .1 2.1 3 .9

In fig . 7, the count rates measured for the same gassample and by the DV method are shown as a functionof the reciprocal pressure of methane and PIO. Theplotted data for both gases fitted well to a line by theleast square fitting . In the case of propane, the datashowed large scatter so that they could not fit to astraight line .

The correction factors determined from the countrate at the zero reciprocal pressure (Fwm) are given intable 2, accompanying the calculated ones (Fwc ) . Thetable also lists the calculated proportion of (3-raysbelow threshold energy (Fd,) and the calculated andmeasured correction factors for the total count lossdue to threshold energy (Fm , Fdc + Fwc and Fd, + FWm) .

Fdc is a correction factor of interest for 3H with lowmaximum ß-ray energy, while wall effect is dominantfor s-5Kr . It is quite reasonable that Fwc and Fwmbecome large with the increase of ß-ray energy, be-cause the stopping power decreases in reverse. Thecorrection factors for P10 gas are about twice smallerthan for methane, which is due to the difference oflinear stopping power.

In the calculation of Fdc and Fw, the thresholdenergy was supposed to be 220 eV on the basis of thebinding energy of L-shells (200-260 eV) [13,14] . Thisenergy, the theoretical ß-ray energy spectrum and thedata of stopping power can cause some uncertaintieson the calculations of Fdc and F, The uncertainty forFm depends on the way of extrapolating the low pulseheight tail in the spectrum . In spite of the existence ofthese uncertainties, Fm, Fdc + Fw, and Fdc + Fwmshowed relatively good agreement except for a fewdata . As a result, it is considered that there is no largedifference among the three estimation methods.

When PIO gas is used for counting gas, the totalcorrection for wall effect is about 1% for 85 Kr . Theuncertainty of the correction is less than 0.5% in finalactivity determination . Because wall effect reduces inproportion to the reciprocal pressure of counting gas,itis several times smaller at the internal pressure ofseveral MPa. The uncertainty of 0.5% is small enoughto supply qualified gaseous standard sources.

P10 gas is rather suitable for the counting gas in theDLPC method . Propane showed poor reproducibilityin the observation of sample gas diffusion and in theevaluation of wall effects . Propane is not preferable toP10 gas in spite of its large linear stopping power forelectrons and small diffusion coefficient . The use ofpropane for the DLPC method requests further studieson its behavior .

5. Summary

The behavior of sample gases in a long cylindricalproportional counter was experimentally studied. The

M. Yoshida et al. / Direct measurement by DLPC method 163

diffusion of 37Ar in counting gases was observed withposition analyzing techniques . The diffusion time mea-sured for the counting gases of methane and P10approximately agreed with the time calculated usingtheoretical mutual diffusion coefficients . The measur-ing time interval allowed for the DLPC method is morethan 500 s at the internal pressure of 0.1 MPa and forthe present counter dimension. It is long enough tocarry out the accurate activity measurements with smallstatistical errors . It becomes much longer with theinternal pressure as theoretically expected . Among thetested counting gases, propane was found out to beunsuitable for this method because of the asymmetricaldiffusion of sample gas and poor reproducibility in therepeated measurements.

The sample gas distribution in radial direction wasobserved with a multielement position sensitive pro-portional counter. It became uniform enough less than10 s after injection . This was supported by the fact thatthere were no discrepancy between the results of theDLPC and the DV methods before correcting walleffect .

The count loss due to wall effect was experimentallyestimated as a function of internal gas pressure . Theresults showed relatively good agreement with the cal-culated ones .

P10 gas was turned out to be a suitable counting gasfor the present purpose because of enough measuringtime and small wall effects . In the measurement fors5 Kr, the uncertainty for the correction of wall effectwas less than 0.5% in final activity determination. Bypressurizing the counting gas, the influences of bothend effect and wall effect can be reduced easily .

The DLPC method is simple in the system and themethod of measurement. It also can provide accuratedetermination of gaseous activities.

Acknowledgements

The authors would like to thank Dr . K. Minami forhis encouragement to this work. They are also gratefulto Mr . K. Yanagida for his technical assistance .

Appendix

Al . ß-ray energy spectrum

Because the distortion of ß-ray energy spectrum isnegligibly small in the internal gas counting, the pro-portion of low energy part below threshold energy canbe calculated on the basis of the theoretical ß-rayenergy spectrum .

164

XFig. 8 . Geometrical measures and angles .

According to Fermi's theory, the theoretical spectraN(E) dE is given in the following

N(E) dE(xC(E) F(Z, E)(Em -E) 2

where F(Z, E) is the Fermi function, and C(E) is acorrection factor given by C(E) = 1 for the allowedtransition and C(E) a 1 - 2E(E� , + E)/(Eo2 - 1) forthe unique first forbidden transition .

A2 . Deriuation off.,

X(E+1)(E 2 +2E) 1/2 dE,

(AI)

Provided that the ß-rays penetrate straightforwardin counting gas, the proportion of missing ß-rays incounting with a cylindrical counter of inner diameter Rcan be calculated in the same manner by Yamane [10].Defining a ß-ray source point P and ß-ray path length1 as shown in fig . 8, fw, is expressed by the followingequation

1 R

4fwc(E) -zI

2, rrr 2 dr--rrR

R-s(E)

41T

Xj02 fo°(1 - r1(a)) sin 0 dB do,

(A2)

where 9 is an angle between the path and OY, 0 is anangle between OX and the projection of the path onthe plane XOZ, a is an angle between the path andthe perpendicular axis to the wall surface, s(E) is theminimum path length which is needed to count theß-ray, and v1(a) is the backscattering coefficient for thewall material .

M. Yoshida et al. / Direct measurement by DLPC method

The relation among r, 1, 8 and 0 is given by

- r +(r 2 cos2 (b +RZ sin20 -1 2 sin20 COS 2 0)r/2cos B =1 sin2,b

do is obtained by replacing s(E) into 1 in eq . (A3) .71(a) is given as functions of a and atomic number

Zaccording to the empirical formula derived by Verdieret al . [11] .

1

9 .4~(a)

(1+ cos a)°'where p(Z) = Zos .

The relation of a, r, 1 and 0 is given by the followingequation

R' -r(r+1 cos 0)cos a =

R1

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[4]

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(A4)

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