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The release of fission-recoiled xenon from Zr-2.5 wt% Nb alloy
166
Journal
THE RELEASE
OF FISSION-RECOILED
A.R. PAUL, K.N.G. KAIMAL,
of Nuclear
Materials 160 (1988) 166-171 North-Holland, Amsterdam
XENON FROM Zr-2.5 wt% Nb ALLOY
M.C. NAIK and K.S. VENKATESWARLU
Water Chemistry Division, Bahbha Atomic Research Centre, Trombay, Bombay 400 085, India Received
18 April 1988; accepted
30 June 1988
The release of fission-recoiled 133Xe from Zr-2.5 wt% Nb alloy was measured range 640-880 K, where purely OLphase exists, a linear relationship between represented by the equation:
in the temperature range 640-1080 K. In the log D versus l/T is observed and can be
142.7 kJ/mol D(640-880
K) = 6.24~
10m9 exp
m*/s. dT
The release has been attributed to the non-volume diffusion process. In the temperature range 930-1080 K where both n and p phases coexist, the linearity in the plots of log D versus l/T is violated. The present values of the release parameters have been compared with the corresponding values for the release of fission-recoiled ‘33Xe from Zircaloy-2. Alloying elements seem to have very small effect on the release kinetics. The results have been presented and discussed
1. Introduction In an earlier work [l] the authors had studied the release behaviour of 13’Xe from Zircaloy-2 by using the fission-recoil technique for doping the material with the inert gas. In this method of doping, the specimen surface is put in contact with an uranium foil and irradiated in a nuclear reactor. The fission product atoms have high energies (in the range of MeV) and so they penetrate deep into the solid. As a result of this, the effects of surface proximity to the overall release process become negligible and consequently, the release behaviour of the fission gases from the bulk of the material could be studied. The present investigation is an extension of this earlier work and deals with the study of the release behaviour of fission recoiled 133Xe from Zr-2.5 wt% Nb alloy. In the present study the concentration of fission gas atoms were kept very low (,( lo-’ at%). Even at this concentration there is some effect of gas-gas and/or gas-damage interaction on the release of xenon from Zr-2.5 wt% Nb alloy. Under this circumstances the effective value of diffusion coefficients have been evaluated from release experiments. The fractional release as a function of the time for isothermal heating at various temperatures in the range 640-1080 K is presented in the paper. Results of a few experiments with
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‘foil’ specimens, where the release takes place through both the ‘front’ and the ‘back’ surfaces are also presented.
2. Experimental procedure The Zr-2.5 wt% Nb alloy specimens of mainly two thicknesses, namely - 2 x 10e3 m and - 2 x lo-’ m (‘foil’), were used in the present investigation. The 2 x 10m3 m thick specimens were in the form of circular discs of - 1 x lo-* m diameter punched out of a sheet of the material. The thinner specimens were cut from a foil into rectangular shapes of - 1.2 X lo-* m length and - 1 X lo-* m breadth. These original samples were found to have average grain sizes of - 60 pm. These specimens, after thorough cleaning, were wrapped in tantalum foils and then annealed at - 1350 K for about 50 h under high vacuum. After removing from the vacuum system, the two flat parallel faces of each thick specimen were polished on Carborundum papers of different grades and then with alumina pastes on microcloths which were attached to the polishing wheels. This gave mirror finish to the polished surfaces. The foil specimens in the as-received condition had an apB.V.
A. R. Paul et al. / Release of fission-recoiled
pearance of good surface finish and did not require any mechanical polishing. The cold worked material from the specimen surfaces were removed by lightly etching in a solution containing glycerol, nitric acid and hydrofluoric acid (mixed in the volumetric ratio of 4 : 2 : 1) [2]. The specimens were then observed under the microscope and the average grain size was measured to be - 600 pm. The loading of the specimens with 133Xe was carried out by the fission recoil process from a natural uranium metal foil, about 20 pm thick, which was sandwiched between two specimens and irradiated in the APSARA reactor at a thermal flux of - 1016 n mm2 s-l for several hours. In this way two specimens were loaded for each irradiation. The total number of samples doped was 18. Care was taken to keep the temperature rise of each specimen during irradiation to a minimum value. For this purpose, the material was sealed in a quartz ampoule filled with ultra-high purity helium gas at atmospheric pressure. Use of such high-purity helium gas in the quartz capsule also helped in avoiding oxidation of the sample surface during irradiation. It was estimated that during the irradiation process the temperature in any of the samples did not exceed - 400 K. The sample surfaces were examined after the irradiation _ they were visibly shining as before irradiation and no traces of oxide formation on any of the sample surfaces could be detected. The irradiated specimens were ‘cooled’ for several days to allow the precursors to decay into xenon; also the level of activity of the specimens came down appreciably thereby facilitating handling. Slight contamination of the specimen surface by uranium was detected this was removed by giving light etching to the contaminated surfaces in the etchant mentioned earlier. There however, was no detectable loss of weight of the sample due to such light etching ( < 10m6 gm). This also implies that the presence of contaminating uranium had been superficial only. The release experiments were carried out using the conventional flow type of furnace [3-51 in which the specimen was heated in a long quartz tube. The high temperature part of the tube was internally lined with a tantalum foil which was heated at the experimental temperature for several hours in the flow of ultra-purified helium before introducing the sample into the constant temperature hot zone of the furnace. Temperature was controlled to within f 1 K and measured with a calibrated chromel-alumel thermocouple. Time taken by the specimen to reach the experimental temperature was less than one minute and could be neglected compared to the total time of the release experiment. In a
Xe from Zr-2.5
wt % Nb alloy
167
few experiments the release rate was much less than expected values - results of such experiments were discarded. The released xenon was collected over a liquid N,cooled charcoal trap which was placed directly over a 2a geometry NaI(Tl) scintillation counter of the y-ray spectrometer. During the annealing time there is considerable decay of 133Xe (half life 5.29 days). The correction has been applied for the decay. The sweep gas used was helium. The helium gas normally available contained a few ppm of other impurity gases. Use of such helium for sweeping the released gas contaminated the sample surface and the release from such specimen was much reduced. For this reason, the sweep gas was ultra-purified by passing through a helium diffusion furnace. The amount of xenon collected into the charcoal trap was determined by counting the 0.081 MeV y-ray from 133Xe by using a pulse height analyser. In order to calculate the value of fractional release, the amount of the gas remaining in the solid at the end of the release experiment was determined by dissolving the specimen in a solution of glycerol, nitric acid and hydrofluoric acid. 133Xe gas thus freed was collected into the charcoal trap by passing helium through the solution. The total amount of xenon introduced into the sample was also calculated theoretically: this value was within - 2% of the experimentally determined value. In the case of the foil specimens, the total gas content was determined by heating the sample to a high temperature (- 1300 K). It was found that complete release (within 1% of the theoretically calculated value) was obtained within - 2 h of heating.
3. Analytical procedure In order to be able to analyse the gas release data, the initial concentration distribution of the gas atoms inside the sample must be known. The implantation profiles in the samples coupled to a fissioning source has been considered by several authors [6,7]. It has been shown that in the case of fission recoil doping of a slab from an infinitely thick source, the initial concentration distribution inside the sample is given by [7-91: for
O
for
R
(1)
where R and R’ are the recoil ranges of the fission fragment in the specimen and the source materials respectively; L is the thickness of the slab (specimen). This shape of the initial distribution of the recoil atoms
168
A.R. Paul et al. / Release of fission-recoiled
has been verified by many workers. In the present investigations, the thickness of the fissionable source was - 20 pm and the initial distribution is, therefore, given by eq. (1). The solution of the diffusion equation for this specific shape of the initial concentration profile into the slab was worked out by Di Cola and Matzke. The complete solution applicable for any value of the fractional release has the following form [7,9]:
F(t)
“5
= l-
Table 1
Summary of the results of the release experiments Phase
a
l
p _ sin[(2i + 1)7$] (2i+
I
1)7r
Xexp I - (2i + 1)2a2r2],
(2)
where F(t) is the cumulative fractional release of the gas atoms (xenon) for isothermal heating for time 1; p = R/L and r2 = Dt/L2 are the two dimensionless quantities. The series in eq. (2) converge for large values of 72 only and is applicable for ‘thick’ as well as for ‘thin’ specimens (where the release takes place through the ‘front’ as well as the‘back’ surfaces). The short time solution of the diffusion equation was also given by Di Cola and Matzke [7,9] in the form:
Temperature (K)
(V/3)’ i=O (2i + 1)2
X
Xe from Zr-2.15 wt W Nb alloy
e+B
640 610 670 700 730 760 800 840 880 880 930 980 980 1030 1080 1080
b, a) a) a)
a)
Duration of heating
Total gas released
Diffusion coefficient
(h)
(%)
(m2/s)
150 150 150 150 150 150 150 150 150 150 150 60 60 4 4 4
2.5 4.5 5.0 1.5 13.0 21.0 32.0 48.5 65.0 60.5 84.5 99.5 91.0 86.5 92.0 98.5
1.26x10-” 4.38x10-*’ 4.73 x 10-2s 1.31 x lo-‘9 3.87 x lo-l9 l.o9xlo-‘s 2.95 x lo-l8 8.55 x 10-r’ 2.02 x 10 - r7 1.89x10-t’ 8.35x10-” 9.51 x lo-‘6 1.06x10-t5 8.13 x lo-r5 2.40x10~‘4 2.31 x 1O-‘4
a) Thickness of these four specimens was 20 pm. b, Thickness of this specimen was reduced from 20 pm to 19 pm by careful etching of the irradiated surface (R = 6.5 Cm, see text). Thickness of rest of the specimens was 2 x lop3 m.
zqt)=l-(l+y)erf(&)
+2(
&$)[2-ew(-&)].
(3)
For low values of fractional release (d O.l), the release values could be represented quite adequately by the following equation [9]: F(t)
= { 16Dt/(
nR2)}‘?
(4)
The value of R was taken to be 7.5 pm [lo].
4. Results and discussions Results of the release experiments carried out on the fission recoil doped Zr-2.5 wt!% Nb alloy specimens are presented in table 1. As already mentioned, the specimens were isothermally heated at the temperature of the release experiments, i.e. in the temperature range 640-1080 K. A few characteristic plots of F versus I’/~ are shown in fig. 1. For the samples heated at the three lowest temperatures, namely 640, 670 and 700 K, the cumulative fractional release during the entire period of heating (150 h) did not exceed - 10% and the experimental points could be fitted within the limit of experi-
ItrIM”)
M -
Fig. 1. Fractional release of fission-recoiled ‘33Xe from Zr-2.5 wt% Nb alloy. Comparison between experimental and theoretical results.
A.R. Paul ei al. / Release of fission-recoiled
mental error by straight lines. The D values in these cases were calculated by using eq. (4). For higher temperatures the total release was much higher and the release plots showed considerable deviation from the initial straight lines. In these cases, depending upon the thickness of the specimen, either eq. (2) (for the foil specimens, i.e. where the release was estimated to have taken place through the ‘front’ as well as the ‘back surfaces) or eq. (3) (for the ‘thick’ specimens) was used. The D values were calculated by comparing the experimental points with the F(t) versus Dt curves generated from these equations by using an ND-500 computer. The average values of D obtained in this way are presented in the last column of table 1. These values of D were used to generate the F(t) versus t’j2 curves (shown by a continuous line in fig. 1). It is observed that the fit between the experimental points (dots l) and the curve calculated from the average value of D is very good. As mentioned earlier, the release was studied at several temperatures (namely, 880, 930, 980 and 1080 K) from foil specimens. The long time release values from such specimens were to some extent higher than that expected from a thick sample. This is illustrated in fig. 1 for two specimens (foils heated at 930 and 980 K) where the dashed lines represent the calculated curves for ‘front’ surface release only. The higher values of release at longer time of anneal from the foil specimens is due to the fact that after some time of heating some of the diffusing gas atoms reach the opposite surface of the foil and start getting released. The time at which the gas atoms start getting released through the back surface could be found out by comparing the experimental release curve for the thin foil with the one expected for a thick sample where the release is through the front surface only. It was observed that this time for the start of the release through the ‘back’ surface was governed by diffusion. Also, it was observed that there is good agreement between results obtained from both types of specimens (cf. D values in table 1 for four samples heated at 980 and 1080 K). After recoil doping, one foil specimen was cut into two halves: one half was then carefully etched to remove about 1 pm of material from the irradiated surface. Experiments carried out on this etched specimen showed an apparent enhancement of release compared to that from the unetched half. For the sake of comparison, these two release curves (880 K heatings) for the etched and unetched foil specimens are shown in fig. 1. Faster release from the etched specimen gives one the impression that surface conditions might be responsible for causing the release to occur at different rates from the two ‘half specimens, but on calcula-
Xe from Zr-2.5
wt % Nb alloy
169
tion it was found that both the release curves yield more or less the same value of the diffusion coefficient. The enhanced release from the etched specimen would result from the fact that by the process of etching to remove - 1 pm from the irradiated surface, the value of R is reduced and although the shape of initial distribution profile of the recoiled atoms remains unchanged, it is ‘shifted’ towards the surface and hence there is faster release from the etched specimen. The release through the sides of the sample was calculated and found to be negligibly small. As already mentioned, the irradiation of the specimen (in contact with uranium foil) was carried out for several hours at a thermal neutron flux of - 1016 n mm2 s- I. The amount of fission gases introduced into the sample was calculated and found to be 5 10m7 at%. Even at such low concentration of gas it is expected that there would be some gas-gas, gas-fission products impurities and/or gas-damage interactions in the irradiated specimen. It is difficult to evaluate exactly these interactions and thus the evaluated values of diffusion coefficient represent effective diffusivity. The Arrhenius plot of log D versus l/T is shown in fig. 2. In the temperature range 640-880 K where only pure (Y phase exists, the log D versus l/T plots were linear within the limit of experimental error (*12X). The values could be expressed in the following form: D(640-880
K) 142.7 kJ/mol RT
m2/s
for release of 133Xe from a-Zr-2.5 wt% Nb alloy. The frequency factor (D,, in m2/s) and the activation energy (Q in kJ/mol) in the above relation has been calculated by the least square method. The value of D,, usually observed for system in which interstitial or vacancy mechanism of mass transport is operative, is 10m7 m2 s-l [ll]. As compared to this, the DO value obtained from the study of the release behaviour of xenon from the cY-Zr-2.5 wt’% Nb alloy specimens in the present investigation is very low (6.24 X 10e9 m2 s-l) and when substituted in the relation D,, = ya’vf exp(AS/R) (where y is a constant whose value depends, for a given mechanism of diffusion, on the type of crystal lattice; 01 is the jump distance, Y is the frequency of lattice vibration; f is the correlation factor for diffusion and AS is the entropy of activation), yields a negative value for the entropy of activation. Although the entropy of activation is found to be negative, it is not possible to predict the exact mechanism of diffusion. The results of the diffusion parameters such as D, D,, and Q obtained in the present study of release
170
A. R. Paul et al. / Release of fission-recoiled
211 0.8
0.9
' l.0
1'1
12
3
1.3
1'1
l-5
1.6
1.7
I 1.8
GT--
Fig. 2. Diffusivity of 133Xe in Zr-2.5 wt% Nb alloy as a function of temperature. 8 and + represent the results for 19 and 20 pm thick specimensand dots (0) represent the same for the 2 x 10A3 m thick specimens.
of ‘33Xe for Zr-2.5 wt% Nb alloy are comparable with the corresponding values for 133Xe release from Zircaloy-2 studied earlier [l]. Thus, the D values for xenon in Zircaloy-2 at 640 and 880 K (extrapolated), are 3.27 x lo-” and 7.73 x lo-‘* m’/s, respectively, compared to 1.26 X 10-20 and - 2 x lo-i7 m2/s for Zr-2.5 wt% Nb alloy. Similarly, the Do and Q values are found to be 7.66 X lop9 m’/s and 151.4 kJ/mol for xenon diffusion in Zircaloy-2, which are quite close to the values of 6.24 X 10e9 m*/s and 142.7 kJ/mol for ‘33Xe release from Zr-2.5 wt% Nb alloy. These values (of both Do and Q) are also similar to those obtained for self diffusion and for the diffusion of various impurity atoms in polycrystalline specimens of cu-Zr [12-191, indicating thereby a similar of mode of transport of xenon in Zr-2.5 wt% Nb. It can be seen from fig. 2 that at higher temperatures, beyond the a-phase, the plots of log D versus l/T is non-linear. It can be mentioned here that like many other alloys of zirconium (e.g., Zircaloy-2) the e//3 phase transformation in the Zr-Nb alloy system also takes place over a wide range of temperatures. For the Zr-2.5 wt%Nb alloy the lower limit of this range is - 885 K and the upper limit - 1120 K [20]. In between these limits of temperatures, i.e. between 885 and 1120 K, the alloy would consist of various proportions of the a and the /3 phases. While several workers have treated the mass transport process in such complicated multiphase regions as taking place through the volumes of both the (Y and /i phases [2,21-231, others have consid-
Xe
fromZr-2.5 WI % Nb alloy
ered the diffusion as taking place through mainly the boundaries [24]. In either case, however, a precise knowledge of the values of Da, Da and C,, Cs (where Da, Ds and C,, Cs are the diffusion coefficients and the concentrations of the two phases present at the temperature of the release experiment) is required in order to be able to establish the functional relationship between the effective diffusion coefficient D,,, andD,, Do and C,, Cs. The highest temperature of study in the present investigation was 1080 K which is well within the e/P phase transformation range. It can be seen from column 3 of table 1 that at the highest temperature of the release experiment, i.e. 1080 K, although the duration of heating was comparatively short (only 4 h), - 92% of the fission gas atoms recoiled into the specimen was released. Attempts were made to carry out experiments at still higher temperatures in the j3 and e/p phase regions, but the rate of release was so fast that the release curves could not be established with any accuracy and so the D values could not be calculated. Consequently, the mechanism of diffusion in the p and a/p phase transition region could not be ascertained.
References
111A.R. Paul, M.C. Naik and K.S. Venkateswarlu, J. Nucl. Mater. 119 (1983) 333.
121 R.P. Agarwala and A.R. Paul, J. Nucl. Mater. 58 (1975)
25. Kaimal and M.D. 131 M.C. Naik, A.R. Paul, K.N.G. Karkhanavala, Radiat. Eff. 25 (1975) 73. 141 M.C. Naik, A.R. Paul and K.N.G. Kaimal, J. Nucl. Mater. 96 (1981) 57. Kaimal and M.D. 151 M.C. Naik, A.R. Paul, K.N.G. Karkhanavala, J. Nucl. Mater. 71 (1977) 105. [61 T.S. Elleman, L.D. Mears and R.P. Christman, J. Am. Ceram. Sot. 51 (1968) 560. 171 G. Di Cola and Hj. Matrke, Tech. Rep. EUR-2157e (1964). 181 G. Di Cola and Hj. Matzke, Tech. Rep. EUR-3488e ((1967). [91 G. Di Cola and Hj. Matzke, Nucl. Instr. and Meth. 57 (1967) 341. WI J. Mory, D. Guillebon and G. Delsarte, Radiat. Eff. 5 (1970) 37. illI C. Zener, J. Appl. Phys. 22 (1951) 372. WI J. Askill, Tracer Diffusion Data for Metals, Alloys and Simple Oxides (IFI/Plenum, New York, 1970) p. 54. 1131 P.L Gruzin, V.S. Emelyanov, G.G. Ryabova and G.B. Fedorov, in: Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy, Geneva, Vol. 19 (1958) p. 187. P41 J.I. Federer and T.S. Lundy, Trans. Met. Sot. AIME 227 (1963) 592.
A.R. Paul et al. / Release of fission -recoiled Xe from Zr-2.5
wt % Nb alloy
171
[15] M.C. Naik and R.P. AganvaIa, in: Proc. Symp. on Nuclear Radiation Chemistry, WaItair (Department of Atomic Energy, India, 1966) p. 282. [16] R.P. AgatwaIa, S.P. Murarka and MS. Anand, Acta Metal. 16 (1968) 61. [17] G.B. Fedorov and F.I. Zhomov, Met. Metalloved Chistykh Metal Sb Nauchn Robot 3 (1961) 193. [18] M.C. Naik and R.P. AgarwaIa, Acta MetaIl. 15 (1967) 1521.
[20] C.E. Lunden and R.H. Cox, USAEC Report GEAP 4089, Vol. 1 (1962) p. 9. (211 SD. Gertsriken, I.Ya. Dekbtyar, L.M. Kumok and E.G. Madatova, Vaprosi Fisiki Metallovi Metahovedeniya No. 8 (Kiev, 1957) 108. [22] B.M. Pande, M.C. Naik and R.P. Agarwala, J. Nucl. Mater. 28 (1968) 324. [23] B.M. Pande and R.P. Agarwala, J. Nucl. Mater. 42 (1972) 43.
[19] A.R. Paul and R.P. Agatwala, in: Proc. Symp. on Thermodynamics of Nuclear Materials, Vol. I (IAEA, Vienna, 1975) p. 109.
[24] R. Piotrkowski and F. Dyment, J. Nucl. Mater. 137 (1986) 94.
Journal
THE RELEASE
OF FISSION-RECOILED
A.R. PAUL, K.N.G. KAIMAL,
of Nuclear
Materials 160 (1988) 166-171 North-Holland, Amsterdam
XENON FROM Zr-2.5 wt% Nb ALLOY
M.C. NAIK and K.S. VENKATESWARLU
Water Chemistry Division, Bahbha Atomic Research Centre, Trombay, Bombay 400 085, India Received
18 April 1988; accepted
30 June 1988
The release of fission-recoiled 133Xe from Zr-2.5 wt% Nb alloy was measured range 640-880 K, where purely OLphase exists, a linear relationship between represented by the equation:
in the temperature range 640-1080 K. In the log D versus l/T is observed and can be
142.7 kJ/mol D(640-880
K) = 6.24~
10m9 exp
m*/s. dT
The release has been attributed to the non-volume diffusion process. In the temperature range 930-1080 K where both n and p phases coexist, the linearity in the plots of log D versus l/T is violated. The present values of the release parameters have been compared with the corresponding values for the release of fission-recoiled ‘33Xe from Zircaloy-2. Alloying elements seem to have very small effect on the release kinetics. The results have been presented and discussed
1. Introduction In an earlier work [l] the authors had studied the release behaviour of 13’Xe from Zircaloy-2 by using the fission-recoil technique for doping the material with the inert gas. In this method of doping, the specimen surface is put in contact with an uranium foil and irradiated in a nuclear reactor. The fission product atoms have high energies (in the range of MeV) and so they penetrate deep into the solid. As a result of this, the effects of surface proximity to the overall release process become negligible and consequently, the release behaviour of the fission gases from the bulk of the material could be studied. The present investigation is an extension of this earlier work and deals with the study of the release behaviour of fission recoiled 133Xe from Zr-2.5 wt% Nb alloy. In the present study the concentration of fission gas atoms were kept very low (,( lo-’ at%). Even at this concentration there is some effect of gas-gas and/or gas-damage interaction on the release of xenon from Zr-2.5 wt% Nb alloy. Under this circumstances the effective value of diffusion coefficients have been evaluated from release experiments. The fractional release as a function of the time for isothermal heating at various temperatures in the range 640-1080 K is presented in the paper. Results of a few experiments with
0022-3115/88/$03.50 (North-Holland
0 Elsevier
Physics
Publishing
Science
Publishers
Division)
‘foil’ specimens, where the release takes place through both the ‘front’ and the ‘back’ surfaces are also presented.
2. Experimental procedure The Zr-2.5 wt% Nb alloy specimens of mainly two thicknesses, namely - 2 x 10e3 m and - 2 x lo-’ m (‘foil’), were used in the present investigation. The 2 x 10m3 m thick specimens were in the form of circular discs of - 1 x lo-* m diameter punched out of a sheet of the material. The thinner specimens were cut from a foil into rectangular shapes of - 1.2 X lo-* m length and - 1 X lo-* m breadth. These original samples were found to have average grain sizes of - 60 pm. These specimens, after thorough cleaning, were wrapped in tantalum foils and then annealed at - 1350 K for about 50 h under high vacuum. After removing from the vacuum system, the two flat parallel faces of each thick specimen were polished on Carborundum papers of different grades and then with alumina pastes on microcloths which were attached to the polishing wheels. This gave mirror finish to the polished surfaces. The foil specimens in the as-received condition had an apB.V.
A. R. Paul et al. / Release of fission-recoiled
pearance of good surface finish and did not require any mechanical polishing. The cold worked material from the specimen surfaces were removed by lightly etching in a solution containing glycerol, nitric acid and hydrofluoric acid (mixed in the volumetric ratio of 4 : 2 : 1) [2]. The specimens were then observed under the microscope and the average grain size was measured to be - 600 pm. The loading of the specimens with 133Xe was carried out by the fission recoil process from a natural uranium metal foil, about 20 pm thick, which was sandwiched between two specimens and irradiated in the APSARA reactor at a thermal flux of - 1016 n mm2 s-l for several hours. In this way two specimens were loaded for each irradiation. The total number of samples doped was 18. Care was taken to keep the temperature rise of each specimen during irradiation to a minimum value. For this purpose, the material was sealed in a quartz ampoule filled with ultra-high purity helium gas at atmospheric pressure. Use of such high-purity helium gas in the quartz capsule also helped in avoiding oxidation of the sample surface during irradiation. It was estimated that during the irradiation process the temperature in any of the samples did not exceed - 400 K. The sample surfaces were examined after the irradiation _ they were visibly shining as before irradiation and no traces of oxide formation on any of the sample surfaces could be detected. The irradiated specimens were ‘cooled’ for several days to allow the precursors to decay into xenon; also the level of activity of the specimens came down appreciably thereby facilitating handling. Slight contamination of the specimen surface by uranium was detected this was removed by giving light etching to the contaminated surfaces in the etchant mentioned earlier. There however, was no detectable loss of weight of the sample due to such light etching ( < 10m6 gm). This also implies that the presence of contaminating uranium had been superficial only. The release experiments were carried out using the conventional flow type of furnace [3-51 in which the specimen was heated in a long quartz tube. The high temperature part of the tube was internally lined with a tantalum foil which was heated at the experimental temperature for several hours in the flow of ultra-purified helium before introducing the sample into the constant temperature hot zone of the furnace. Temperature was controlled to within f 1 K and measured with a calibrated chromel-alumel thermocouple. Time taken by the specimen to reach the experimental temperature was less than one minute and could be neglected compared to the total time of the release experiment. In a
Xe from Zr-2.5
wt % Nb alloy
167
few experiments the release rate was much less than expected values - results of such experiments were discarded. The released xenon was collected over a liquid N,cooled charcoal trap which was placed directly over a 2a geometry NaI(Tl) scintillation counter of the y-ray spectrometer. During the annealing time there is considerable decay of 133Xe (half life 5.29 days). The correction has been applied for the decay. The sweep gas used was helium. The helium gas normally available contained a few ppm of other impurity gases. Use of such helium for sweeping the released gas contaminated the sample surface and the release from such specimen was much reduced. For this reason, the sweep gas was ultra-purified by passing through a helium diffusion furnace. The amount of xenon collected into the charcoal trap was determined by counting the 0.081 MeV y-ray from 133Xe by using a pulse height analyser. In order to calculate the value of fractional release, the amount of the gas remaining in the solid at the end of the release experiment was determined by dissolving the specimen in a solution of glycerol, nitric acid and hydrofluoric acid. 133Xe gas thus freed was collected into the charcoal trap by passing helium through the solution. The total amount of xenon introduced into the sample was also calculated theoretically: this value was within - 2% of the experimentally determined value. In the case of the foil specimens, the total gas content was determined by heating the sample to a high temperature (- 1300 K). It was found that complete release (within 1% of the theoretically calculated value) was obtained within - 2 h of heating.
3. Analytical procedure In order to be able to analyse the gas release data, the initial concentration distribution of the gas atoms inside the sample must be known. The implantation profiles in the samples coupled to a fissioning source has been considered by several authors [6,7]. It has been shown that in the case of fission recoil doping of a slab from an infinitely thick source, the initial concentration distribution inside the sample is given by [7-91: for
O
for
R
(1)
where R and R’ are the recoil ranges of the fission fragment in the specimen and the source materials respectively; L is the thickness of the slab (specimen). This shape of the initial distribution of the recoil atoms
168
A.R. Paul et al. / Release of fission-recoiled
has been verified by many workers. In the present investigations, the thickness of the fissionable source was - 20 pm and the initial distribution is, therefore, given by eq. (1). The solution of the diffusion equation for this specific shape of the initial concentration profile into the slab was worked out by Di Cola and Matzke. The complete solution applicable for any value of the fractional release has the following form [7,9]:
F(t)
“5
= l-
Table 1
Summary of the results of the release experiments Phase
a
l
p _ sin[(2i + 1)7$] (2i+
I
1)7r
Xexp I - (2i + 1)2a2r2],
(2)
where F(t) is the cumulative fractional release of the gas atoms (xenon) for isothermal heating for time 1; p = R/L and r2 = Dt/L2 are the two dimensionless quantities. The series in eq. (2) converge for large values of 72 only and is applicable for ‘thick’ as well as for ‘thin’ specimens (where the release takes place through the ‘front’ as well as the‘back’ surfaces). The short time solution of the diffusion equation was also given by Di Cola and Matzke [7,9] in the form:
Temperature (K)
(V/3)’ i=O (2i + 1)2
X
Xe from Zr-2.15 wt W Nb alloy
e+B
640 610 670 700 730 760 800 840 880 880 930 980 980 1030 1080 1080
b, a) a) a)
a)
Duration of heating
Total gas released
Diffusion coefficient
(h)
(%)
(m2/s)
150 150 150 150 150 150 150 150 150 150 150 60 60 4 4 4
2.5 4.5 5.0 1.5 13.0 21.0 32.0 48.5 65.0 60.5 84.5 99.5 91.0 86.5 92.0 98.5
1.26x10-” 4.38x10-*’ 4.73 x 10-2s 1.31 x lo-‘9 3.87 x lo-l9 l.o9xlo-‘s 2.95 x lo-l8 8.55 x 10-r’ 2.02 x 10 - r7 1.89x10-t’ 8.35x10-” 9.51 x lo-‘6 1.06x10-t5 8.13 x lo-r5 2.40x10~‘4 2.31 x 1O-‘4
a) Thickness of these four specimens was 20 pm. b, Thickness of this specimen was reduced from 20 pm to 19 pm by careful etching of the irradiated surface (R = 6.5 Cm, see text). Thickness of rest of the specimens was 2 x lop3 m.
zqt)=l-(l+y)erf(&)
+2(
&$)[2-ew(-&)].
(3)
For low values of fractional release (d O.l), the release values could be represented quite adequately by the following equation [9]: F(t)
= { 16Dt/(
nR2)}‘?
(4)
The value of R was taken to be 7.5 pm [lo].
4. Results and discussions Results of the release experiments carried out on the fission recoil doped Zr-2.5 wt!% Nb alloy specimens are presented in table 1. As already mentioned, the specimens were isothermally heated at the temperature of the release experiments, i.e. in the temperature range 640-1080 K. A few characteristic plots of F versus I’/~ are shown in fig. 1. For the samples heated at the three lowest temperatures, namely 640, 670 and 700 K, the cumulative fractional release during the entire period of heating (150 h) did not exceed - 10% and the experimental points could be fitted within the limit of experi-
ItrIM”)
M -
Fig. 1. Fractional release of fission-recoiled ‘33Xe from Zr-2.5 wt% Nb alloy. Comparison between experimental and theoretical results.
A.R. Paul ei al. / Release of fission-recoiled
mental error by straight lines. The D values in these cases were calculated by using eq. (4). For higher temperatures the total release was much higher and the release plots showed considerable deviation from the initial straight lines. In these cases, depending upon the thickness of the specimen, either eq. (2) (for the foil specimens, i.e. where the release was estimated to have taken place through the ‘front’ as well as the ‘back surfaces) or eq. (3) (for the ‘thick’ specimens) was used. The D values were calculated by comparing the experimental points with the F(t) versus Dt curves generated from these equations by using an ND-500 computer. The average values of D obtained in this way are presented in the last column of table 1. These values of D were used to generate the F(t) versus t’j2 curves (shown by a continuous line in fig. 1). It is observed that the fit between the experimental points (dots l) and the curve calculated from the average value of D is very good. As mentioned earlier, the release was studied at several temperatures (namely, 880, 930, 980 and 1080 K) from foil specimens. The long time release values from such specimens were to some extent higher than that expected from a thick sample. This is illustrated in fig. 1 for two specimens (foils heated at 930 and 980 K) where the dashed lines represent the calculated curves for ‘front’ surface release only. The higher values of release at longer time of anneal from the foil specimens is due to the fact that after some time of heating some of the diffusing gas atoms reach the opposite surface of the foil and start getting released. The time at which the gas atoms start getting released through the back surface could be found out by comparing the experimental release curve for the thin foil with the one expected for a thick sample where the release is through the front surface only. It was observed that this time for the start of the release through the ‘back’ surface was governed by diffusion. Also, it was observed that there is good agreement between results obtained from both types of specimens (cf. D values in table 1 for four samples heated at 980 and 1080 K). After recoil doping, one foil specimen was cut into two halves: one half was then carefully etched to remove about 1 pm of material from the irradiated surface. Experiments carried out on this etched specimen showed an apparent enhancement of release compared to that from the unetched half. For the sake of comparison, these two release curves (880 K heatings) for the etched and unetched foil specimens are shown in fig. 1. Faster release from the etched specimen gives one the impression that surface conditions might be responsible for causing the release to occur at different rates from the two ‘half specimens, but on calcula-
Xe from Zr-2.5
wt % Nb alloy
169
tion it was found that both the release curves yield more or less the same value of the diffusion coefficient. The enhanced release from the etched specimen would result from the fact that by the process of etching to remove - 1 pm from the irradiated surface, the value of R is reduced and although the shape of initial distribution profile of the recoiled atoms remains unchanged, it is ‘shifted’ towards the surface and hence there is faster release from the etched specimen. The release through the sides of the sample was calculated and found to be negligibly small. As already mentioned, the irradiation of the specimen (in contact with uranium foil) was carried out for several hours at a thermal neutron flux of - 1016 n mm2 s- I. The amount of fission gases introduced into the sample was calculated and found to be 5 10m7 at%. Even at such low concentration of gas it is expected that there would be some gas-gas, gas-fission products impurities and/or gas-damage interactions in the irradiated specimen. It is difficult to evaluate exactly these interactions and thus the evaluated values of diffusion coefficient represent effective diffusivity. The Arrhenius plot of log D versus l/T is shown in fig. 2. In the temperature range 640-880 K where only pure (Y phase exists, the log D versus l/T plots were linear within the limit of experimental error (*12X). The values could be expressed in the following form: D(640-880
K) 142.7 kJ/mol RT
m2/s
for release of 133Xe from a-Zr-2.5 wt% Nb alloy. The frequency factor (D,, in m2/s) and the activation energy (Q in kJ/mol) in the above relation has been calculated by the least square method. The value of D,, usually observed for system in which interstitial or vacancy mechanism of mass transport is operative, is 10m7 m2 s-l [ll]. As compared to this, the DO value obtained from the study of the release behaviour of xenon from the cY-Zr-2.5 wt’% Nb alloy specimens in the present investigation is very low (6.24 X 10e9 m2 s-l) and when substituted in the relation D,, = ya’vf exp(AS/R) (where y is a constant whose value depends, for a given mechanism of diffusion, on the type of crystal lattice; 01 is the jump distance, Y is the frequency of lattice vibration; f is the correlation factor for diffusion and AS is the entropy of activation), yields a negative value for the entropy of activation. Although the entropy of activation is found to be negative, it is not possible to predict the exact mechanism of diffusion. The results of the diffusion parameters such as D, D,, and Q obtained in the present study of release
170
A. R. Paul et al. / Release of fission-recoiled
211 0.8
0.9
' l.0
1'1
12
3
1.3
1'1
l-5
1.6
1.7
I 1.8
GT--
Fig. 2. Diffusivity of 133Xe in Zr-2.5 wt% Nb alloy as a function of temperature. 8 and + represent the results for 19 and 20 pm thick specimensand dots (0) represent the same for the 2 x 10A3 m thick specimens.
of ‘33Xe for Zr-2.5 wt% Nb alloy are comparable with the corresponding values for 133Xe release from Zircaloy-2 studied earlier [l]. Thus, the D values for xenon in Zircaloy-2 at 640 and 880 K (extrapolated), are 3.27 x lo-” and 7.73 x lo-‘* m’/s, respectively, compared to 1.26 X 10-20 and - 2 x lo-i7 m2/s for Zr-2.5 wt% Nb alloy. Similarly, the Do and Q values are found to be 7.66 X lop9 m’/s and 151.4 kJ/mol for xenon diffusion in Zircaloy-2, which are quite close to the values of 6.24 X 10e9 m*/s and 142.7 kJ/mol for ‘33Xe release from Zr-2.5 wt% Nb alloy. These values (of both Do and Q) are also similar to those obtained for self diffusion and for the diffusion of various impurity atoms in polycrystalline specimens of cu-Zr [12-191, indicating thereby a similar of mode of transport of xenon in Zr-2.5 wt% Nb. It can be seen from fig. 2 that at higher temperatures, beyond the a-phase, the plots of log D versus l/T is non-linear. It can be mentioned here that like many other alloys of zirconium (e.g., Zircaloy-2) the e//3 phase transformation in the Zr-Nb alloy system also takes place over a wide range of temperatures. For the Zr-2.5 wt%Nb alloy the lower limit of this range is - 885 K and the upper limit - 1120 K [20]. In between these limits of temperatures, i.e. between 885 and 1120 K, the alloy would consist of various proportions of the a and the /3 phases. While several workers have treated the mass transport process in such complicated multiphase regions as taking place through the volumes of both the (Y and /i phases [2,21-231, others have consid-
Xe
fromZr-2.5 WI % Nb alloy
ered the diffusion as taking place through mainly the boundaries [24]. In either case, however, a precise knowledge of the values of Da, Da and C,, Cs (where Da, Ds and C,, Cs are the diffusion coefficients and the concentrations of the two phases present at the temperature of the release experiment) is required in order to be able to establish the functional relationship between the effective diffusion coefficient D,,, andD,, Do and C,, Cs. The highest temperature of study in the present investigation was 1080 K which is well within the e/P phase transformation range. It can be seen from column 3 of table 1 that at the highest temperature of the release experiment, i.e. 1080 K, although the duration of heating was comparatively short (only 4 h), - 92% of the fission gas atoms recoiled into the specimen was released. Attempts were made to carry out experiments at still higher temperatures in the j3 and e/p phase regions, but the rate of release was so fast that the release curves could not be established with any accuracy and so the D values could not be calculated. Consequently, the mechanism of diffusion in the p and a/p phase transition region could not be ascertained.
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wt % Nb alloy
171
[15] M.C. Naik and R.P. AganvaIa, in: Proc. Symp. on Nuclear Radiation Chemistry, WaItair (Department of Atomic Energy, India, 1966) p. 282. [16] R.P. AgatwaIa, S.P. Murarka and MS. Anand, Acta Metal. 16 (1968) 61. [17] G.B. Fedorov and F.I. Zhomov, Met. Metalloved Chistykh Metal Sb Nauchn Robot 3 (1961) 193. [18] M.C. Naik and R.P. AgarwaIa, Acta MetaIl. 15 (1967) 1521.
[20] C.E. Lunden and R.H. Cox, USAEC Report GEAP 4089, Vol. 1 (1962) p. 9. (211 SD. Gertsriken, I.Ya. Dekbtyar, L.M. Kumok and E.G. Madatova, Vaprosi Fisiki Metallovi Metahovedeniya No. 8 (Kiev, 1957) 108. [22] B.M. Pande, M.C. Naik and R.P. Agarwala, J. Nucl. Mater. 28 (1968) 324. [23] B.M. Pande and R.P. Agarwala, J. Nucl. Mater. 42 (1972) 43.
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