Gamma spectrometric assessment of nuclear fuel

Nuclear Instruments and Methods in Physics Research A297 (1990) 507-513 North-Holland

507

G a m m a spectrometric assessment of nuclear fuel * Edvard Kri~tof and Gvido Pregl ~ Institut Jo~.ef Stefan, Jamooa 39, Ljubljana, Yugoslavia o Unioerza v Mariboru, Smetanova ! 7, Maribor, Yugoslavia

Received 29 December 1989 and in revised form 21 August 1990

A description is given of a gamma spectrometric technique which has been developed with the aim of determining the amount of a certain radioactive fission product taking into consideration local variar~ons of the linear attenuation coefficient of gamma rays. Also, an experiment using a fuel element of the TRIGA Mark II reactor in Ljubljana is presented.

I. Introduction A considerable quantity of information on the behaviour of the reactor fuel can be obtained from mezsuring the amount and the distribution of its radioactive isotopes. Data obtained from such measurements ~,erve for studying the migration of fission products, for characterization of the performance of the fuel eiements during irradiation, and for other purposes in safeguarding the nuclear fuel. For example, from fl',e ratios of masses of specific isotopes it is possible to calculate the burnup and cooling time of the individu~,l fuel element. Chemical analysis of spent fuel is difficult and time consuming. Even when performed, the results are not complete. So, emphasis is being pl;,ced on nondestructive techniques, such as passive and active neutron counting, calometric measurements, and several gamma spectroscopy assays. G a m m a scanning is especially useful, as it is the only nor, destructive technique for quantitative measurement ~.ffgamma-emitting fission or activation products in sp,:nt fuel. On account of the attenuation of gamma rays in matter, reliable gam~la spectrometric determination of the desired amount can only be obtained from a measurement of the relevant isotopic density in fuel. With methods resembling those used in medical tomography, these problems have been worked on in the field of nuclear technology (see for example ref. [1] or ref. [2]). However, the neglect of local variation of the linear attenuation coefficient of gamma rays in the= irradiated

* This research work was sponsored by the International Atomic Energy Agency during the period from 1983 to 1988, under Agency Research Contract No. 2997/RB.

fuel remains the main source of systematic error. To eliminate it, we combine the (single) emission gamma ray scanning technique with a transmission measurement. The present paper represents an extension and improvement of the preliminary studies [3-6]. A mathematical procedure combined with experiment is particularly convenient for fuel elements of circular cross section by employing circular pixel analysis. In such a manner good results are obtainable even for a relatively small number of measuring data. Accomplished routines enable us to estimate the finite width of the collimation slit and its influence on the results. Owing to the great number of gamma ray spectra measurements, the experiment was partially automated. Trial measurements were carried out, and the measured data were successfully processed.

2. The experimental setup For measurements of gamma ray spectra a high resolution Ge(Li) detector is employed. It views two shielded fuel elements through a narrow collimator (fig. 1). One of them serves as an additional gamma ray source used in the transmission part of the experiment. The examined fuel element may be rotated and moved normally to the axis connecting the detector and the additional fixed source (fig. 2). It hangs on a torsion wire fastened to the vertical axis of the rotator, which is a part of the moving device. The lower end of the examined fuel element dips into a vessel filled witl:, water. In such a way small oscillations appearing when the object is moved are damped out.

0168-9002/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

E. Krigtof, G. Pregi / Gamma spectrometric assessment of nuclear fuel

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3. Efficiency of the experimental setup

- -

FI R

.

Due to the high activity of spent fuel, the efficiency of an apparatus such as ours must be very low ( - 10- 8). Therefore standard gamma ray sources are not suitable for calibration purposes. For that reason we activated a rectangular silver plate with dimensions 1.12 cm × 2.18 cm in a homogeneous beam of thermal neutrons. The activity of the thus obtained source was determined by gamma spectrometry. Because the activity was too high to be measured directly, we weakened the radiation during data acquisition. The silver plate was positioned at a point where the efficiency e o of the detector is well known for the standard g a m m a line with energy E 0 = 1332 keV. Three measurements using iron slabs z = a, b, and a + b with thicknesses of 6.0, 5.2, and 11.2 c m respectively, were performed. Each time the activated

1

Fig. 2. Vertical section through the experimental setup. Here M denotes the moving device with rotator R, W the torsional wire, G the collimation gap, S the scraper, E the examined fuel element element, PB lead bricks, and V a vessel filled with water.

t,

silver plate, together with the slab, was treated as a source with the virtual activity Qz = Q e x p [ - / x , ( E o ) z ] , where /t:(E0) represents the finear attenuation coefficient of a g a m m a ray of energy E o in slab z. if we denote by v ( E ) the quantum yield for a line of energy E, and by ¢ ( E ) the absolute peak efficiency, thi:; activ.. ity causes the counting rate °

n:(E) = v ( E ) c ( E )

exp[-:,:(E)z]Q.

(I)

By introducing .,

1

1-1:(E)=e( e')exp[(tt=(eo)-la.(E))z]

I

we rewrite eq. (1) as

~;

n . . ( E ) = v ( E ) H z ( E ) Q :.

r,c

, ,] IS

i., ,,

.T

-~

DETECTOR

_i.

© t

Fig. I. Horizontal section through the expeEmental setup. Shielding is of lead and heavy concrete. The effective width of the gap on the detector side of the collimator C for the 662 keV line is 0.08 cm. Rotation of the lead shutter by ,n/2 screens the additional fuel element A. The iron slab, IS, between precollimator PC and the detector serves for suppression of the continuous background and for attenuation of the direct beam. E denotes the examined fuel element.

(2)

(3)

In such a way we can make use of standard routines for the analysis of the measured g a m m a spectra. The following connections are evident:

Q = QoQh/qa+b

(4)

and

¢( E) = Ha( E)Hb( E)/Ha+b( E).

(5)

The activities Q, were calculated numerically considering the condition c0---/-/.(Eo)-~E(Eo) for each z in accordance with relation (2). The required disintegration data for the isotope tl°~Ag were selected from ref. [7]. The result, given as superficial activity, on the 18th of June 1986, was Qs = 5.44 x 106 c m - 2 s - 1. In the final step the flat silver source was placed behind the collimator slit. In the absence of attenuation plates, acquisition of nearly 13 integrated live-time days of spectral data was performed over an extended period of time. F r o m the results of these measurements we

E. Krigtof,, G. Pregl / G a m m a spectrometric assessment o f nuclear fu, i

-. f:,;

obtain the efficiency BR(E), which must be multiplied by the attenuation factor. Expressions

1

HhQh

a

Ha + I,Q a + b

-log

(6) Y

and

1 log

H,,Qa Ha+bQa+t'

(7) -I

are equal within experimental error. So we do not distinguish between bt,~ and #b. As the counting statistics is approximately equal in both cases, we formally set l~= ( a#a + bPb)/ ( a + b) and finally obtain

[ QaQh Ha( E)Hb( E) ] -z/(a+b' Qa+b Ha+b

(8) where ~z(E) is the efficiency of the device [cm2]. Its numerical value equals the counting rate in the photopeak belonging to energy E, if the superficial activity of this line equals unity (I gamma decay cm-2 s-l). z is thickness of the iron plate used during the measurement with fuel.

Q.Qh 2

- 91.87,

Qa+h

log H,, = - 4 8 . 2 6 9 2 + 10.3002y - 0.708539y 2, log H b = - 3 6 . 6 3 6 9 + 7.11506y - 0 . 4 9 0 5 3 0 y 2,

x'-

Fig. 3. The line of integration in the laboratory system x', y'.

In our case the fuel element is moved in the horizontal plane during the measurement. As the broadening of the slice in the vertical direction is negligible, we have in essence a two-dimensional image reconstruction. We treat the field of examination as a circle of unit radius in which the points are given by the polar coordinates p and @ belonging to the body system of the object under examination (fig. 4). The origins of the coordinate systems x, y and p, @ coincide. Tile abscissa x represents the distance between the centre and the fixed axis y ' connecting the detector with the additional source, and the angle ot represents the rotation o.r the system p, ~, with reg,. rd to the system x, y. An array of pixels is formed by dividing the unit circle into K concentric rings with same width 1/K (fig. 5). These rings are composed of particular area elements (pixels). The areas of all pixels are equal. Inside the

log H,,+h = - 6 7 . 7 6 2 5 + 14.6545 v - 0.935882y 2, log r/R = - 0 . 1 5 8 8 1 5 - 3.60863y + 0.216113y 2, y=logE

ADDITIONAL SOURCE

(E inkeV).

The root mean square of the uncertainty in the energy range from 600 to 1600 keV is 0.4%. If we use the iron plate b (z = 5.2 cm), the efficiency for the 662-keV line belonging to the isotope 137Cs is 2.65 × 10 -~ cm 2.

4. Field of examination

The reconstruction of an object from its projections can be described as an inverse transformation. If Z(r) represents the value of a physical property, the measured projections are in the simplest case values of the line integral [ Z ( l - n t ) d t (fig. 3). The mathematician Radon was th., first to solve the basis mathematics of the problem [g]. He proved that the object can be uniquely reconstructed from an infinite set of projections. In practice, the number of data measured is limited and their value is of finite accuracy. Consequently there does not exist a sir, gle way which could satisfy all the geometrical and precision requirements.

/ ,/ / , .

T

~

+0\

1

x=p ly"

fly

DETECTOR Fig. 4. F;eld of examination.

E. KrHtof, G. Pregi / Gammaspectrometricassessmentof nuclearfuel

510

is the attenuation of gamma rays on the the straight line between points p/cos(~-a), ~ and p/cos(~-a), 4. ~t( p, a, 71) is the linear attenuation coefficient at the point p / c o s ( r l - a), 7/ and ( O y / a ¢ ) d o is the element of length on the y' axis. Subsequently we use the abbreviation

L ( p , a , ~ , t 2 ) = S ( p , a , ~ , ~ ) ~ - y l pa~' '~-a)

(11)

In the case of a sufficiently fine division of the field of examination, the simplification of a thin slice breaks down. For this reason we have developed a model which takes into account a real counting response u(p, parameters). This counting response function is proportional to the counting rate when a point source is positioned at p in the body system while the parameters are kept constant. Because the broadening of the slice in our field of examination is negiigible in comparison with its width, we treat the counting response function as a function of only one variable x and parameter p (fig. 6). So in the absence of the additional source, the counting rate is given by the convolution

¥

Fig. 5. Array of pixels. single area element the linear attenuation coefficient of gamma rays and the activity are treated as constants.

r(p,

=

a, O)

f "x'a-S(,) u (" x - p ) A ( x ,

xL(x,a,O,a+O(x))dqdx. 5. Counting rate and activity on the observed cross section

During the measurement, counting rates are determined for chosen distances p as a function of the rotation a. In the absence of the additional source, the only contribution comes from the slice I, II in the field of examination, as it is viewed from the detector. In the following we simply set ',he efficiency of the detectorcollimator system as 1. Temporarily we assume that the thickness of the slice is negligible in comparison with the size of a pixel. Thus we take it as a straight line connecting points l and II. An arbitrary point on this line is determined with p, a, 0: -O(p) ~ O <- O(p). In these circumstances the counting rate is given by:

From this equation we extract the contributions of the ring with the lowest index k. These lie in the interval 0 ~ ( a - O(x), a + ~9(x)). Considering the equality S(x, a, ~ , ~ ) = S ( x , a , ~ , w) S(x,a, oo,~) it follows that

Lf

,,+,,(x, (

"~-ooo u x -p)A(x,

a,

O)

XL(x, ,,, O, ~ +0(x)) dx d0 L~a+O(x)

,~, o, . + O ( x ) ) dO

xL(x,

xA(x,

f ( p , a) = f_°+°A(p, a, O)S(p, ~, O, ~+O)

dx. l/

a--O

(13)

x ay(p,a0O - a ) dO

(9)

where A( p, a, O) is the activity density of the observed gamma line at the point p/cos(O - a), O,

s( p,

(12)

ku(x-p} ,fu(x-p) ¢x--1

,,, ~, ~)

=exp[-f~ ' t L ( p ' a ' n ) a y ( p ' an ~-a)

d ~ ,]

~" ~2

II-

13

X x=p

(10)

F!g. b. Counting response function

u(x- p).

E. KriJtof G. Pregl / Gamma spectrometric assessment of nuclear fuel

In the presence of the additional source, the counting rate increases by the amount transmitted. Denoting by Po the counting rate for the unscreened additional source while the examined one is being shifted away, we have the counting rate

g( p, or)=f(p,

or)+

: i"

IIu h pixel in kth ring

E, aY'

PofxU( X - p )

x s ( x , ., . - 0 ( x ) . . + O ( x ) )

dx.

(14)

I I

n

I I

We write out this relation as

I

I

I I

i

I

I I

I

h(p, a)= f x [ u ( x - p ) S ( x , a, et-O(x), a - O ( x ) )

Xm

Pk

x s ( , , , . . ,, + o ( x ) . .

I I

+ O(x))

×S(x,a,a-#(x),a+O(x))]dx.

(15)

I i I

Here, the measuring data are the values g, f , and P0 in the quotient h = (g-f)/Po. Unknowns belonging to the ring with the lowest index k are hidden in the last function S.

I

I

.Jl_ 123

• .

rn

~indices

Fig. 7. Illustration of the terms u,,, and

Rt,,,(k).

if ! = 10: 6. D i s e r e t i z a t i o n 1 - exp(-p,+,o.tRtom(k

The number of measured projections is determined in such a way that to each position Pk belongs a certain number Nk of spectra measured with the additional source both screened and unscreened. The i th measurement is done at oti = ( i - 1)21r/N k, where only a few neighbouring pixels i + i, - !o < ! < !0 from the k th ring contribute to the counting rate. We here omit a derivation and only give the result of the discretization: k

o,,,., + ,o( k ) =

#, + ,o.k Rio,,, ( k )

)) '

(20)

a,j(k)=S(xj, a,,a,+Oj, et, I-0,),

(21)

C , j ( k ) = S ( x k , o,, a i - Oj, a i + 0j),

(22)

O,j(k) = S( xj, a,, a,-Oj, a,-O,),

(23)

Fj,(k)=

,,+o, A ( x , , , ~ , , , ) L ( x , , a , , , , , ~ , + O , ) d , , f,,+o, (24)

+ i.k

I

=f~.k-Euj[(BijC,,Hj,)(k)+~,(k)]

(16)

J

Hji(k) =

fa'-°JA(x,, a,,

q~)L(xj, a,, q~, a, + 0 j ) dq).

~,,,-sj

(25)

and

hik= Eu, aij(k)Ou(k)I-le-~,+,.,R,,(k) , ) t

(17)

where

q,,(k)=Y'.uma, m(k)R,..(k)o,..,+,(k).

(18)

m

Rt,,,(k)

is the length of prime (I, II) at x = x m within the (i + l)th pixel in the kth ring (fig. 7). ajk [cm s -z] is an unknown value of the function A inside the pixel

j,k. If 1 < 10: ( °m.i+l(k)=S

Xm"

x

ai'

ai+

~t 2 1 + 1 3 2k-l'

ai+O"

1 -exp(-lt,+t.~,Rt,,,(k)) P,+t,kRo.( k )

) (19)

Matrix elements Ri,. are wholly geometrical quantities, and values uj are obtainable by a separate measurement or numerically. From the nonlinear systems of eqs. (17) we estimate the linear attenuation coefficient of the observed line in the area elements of the ring k. The next step is the determination of the matrices q, , , and S. After that follows the computation of the activity from the linear system of equations (16). The computation begins in the outer ring, since we know the conditions outside the measuring field: there all ajk and /~nk are equal to zero. If we denote by r0 [cm] the actual radius of the field examined, then the real volumetric source density sjk [cm-3 s-~] of the line E is given by 1

sjk - ,7:(e)rg ajk"

(26)

512

E. Kri.~tof, G. Pregl / Gamma spectrometric assessment of nuclear fuel

7. Statistical error of the measurement

An average value ~ of the activity of the observed line in the field of examination can be considered as the final result of the measurement. A short derivation shows that the variance on of the average activity is given by variances o! and o~ of the independent measurements f and g as

4=

af.,

Po ah.,

¥.

~-~.,

, "

(27) where m = i, k. The number of numerical operations corresponding to this formula increases approximately as the number of rings to the power 7. For that reason we make an approximation in such a way that we compute for each k only one chosen pair of partial derivatives:

o~---7

.

a~

•

~'oa~

The diameter of the field of examination is 4.5 cm. It is divided into 300 pixels. The observed cross section of the fuel element lies almost concentrically within this field. The eighth ring (R = 1.80 cm) slightly overlaps the circular fuel border (R = 1.76 cm). The number of measured spectra for the additional source, screened and unscreened, was determined so that in both cases it equals the number of pixels. F r o m the evaluated gamma-ray spectra the dominant lines were separated. In fig. 8 we present an activity distribution of the 662 keV line belonging to the isotope 137Cs. The average value of the specific activity in the observed cross section of the fuel was 4.67 (1 + (0.004 + 0.0037)) × 10 o8 cm -3 s -1. This corresponds to 7.53 (1 4-0.008)× 1017 atoms cm -3. The analogous result for 796-keV line belonging to the isotope 134Cs is 1.50 (1 + 0.025) × 10 ~s atoms cm -3 (fig. 9).

(/'* +2~'')

t

In this equation, t means the live time of a particular measurement, t, and w are counting rates of background for both screened and unscreened measurcmcnt~, respectively.

8. Computer routines

We worked out a group of congruent routines, which starts and stops the partial measurements, transfers the measured data into files, and governs the moving device [9]. The spectral data processing is based on Ortec's analysis package [10]. The counting rates of the chosen g a m m a lines are deposited into direct access files. So we retain the data for another group of routines which enables us to compute the activity. All these routines are realized for A/k = 3 ( 2 k - 1). Thu~, the total number of pixels equals 3K 2.

9. Measurement and results

in recent years while the method was being developed, some test measurements were performed. We describe the latest of them. In this case the fuel element used has been cooled for more than four years prior to measurement.

..-/" Fig. 8. The distribution of the isotope 137Cs in arbitrary unit:

E. Kri~tof, G. Pregl / Gamma spectrometric assessment of nuclear fuel

10. Conclusion

I

The nondestructive technique for the d e t e r m i n a t i o n of the amount of an active fission product, as described above, was applied to some fuel elements of the T R I G A M a r k II reactor in Ljubljana. Trial m e a s u r e m e n t s were carried out, and the m e a s u r e d data were successfully processed. We did not carry out any destructive analysis to confirm the results given above. However, we believe that the solution to this p r o b l e m has been proved to be feasible in the m a n n e r conceived.

References [1] [2] [3] [4]

Fig. 9. fhe distribution of the isotope 134Cs in arbitrary units.

The above results include the error of the calibration measurement of 0.4%. The accuracy of the calibration point sources was not taken into account.

J.R. Phillips, Nucl. Technol. 28 (1976) 282. S.T. Hsue, Atom. Eng. Rev. 16 (1978) 1. E. Kri!Rof and G. Pregl, Fizika 11, Suppl. 1 (1979) 117. E. Kri~tof and G. Pregl, Preiskava gorivnega elementa s presevanjem, IJS-DP-219] (1980) internal report. [5] E. Kri~tof and G. Pregl, Nondestructive Method for Assessment of Nuclear Fuel, Fizika 17 (2) (1985) 179. [6] E. Kri~tof and G. Pregl, Gamma spectrometric examination of irradiated fuel, contribution to the 10th TRIGA Users Conf., Vienna, 1988. [7] W.L. Zijp and ,i.H. Baard, Nuclear data guide for reactor neutron metrology, ECN (1981). [8] J. Radon, Ueber die Bestimmung yon Funktionen durch ihre Integralwerte laengs gewisser Mannigfaltigkeiten, Bet. Verb. Saech. Akad. Wiss. Leipzig, Math. Phys. KI. 69 (1917). [9] I. Jen~i~ and B. Zefran, Softwa:e package GORIVO Podgorica (1987) unpublishea. [101 EG&G Ortec, Geligam - Analytical Software for Germanium detectors (1980).