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Dose rate effects in radiation damage to vitrified radioactive waste
480
Nuclear
DOSE RATE EFFECTS
IN RADIATION
DAMAGE
Instruments
and Methods
in Physics Research B32 (1988) 480-486 North-Holland, Amsterdam
TO VITRIFIED RADIOACTIVE
WASTE
J.A.C. MARPLES Hawell ~b~yat~~~
AERE,
Hatwe&
UK
In solidified high level waste, most atom displacements (and hence potential damage) will be caused by the a-decay of incorporated actinides. In order to study the effect of these, several glass compositions were doped with 238Pu so that they received in a few years a dose equivalent to many millenia for the real waste. The densities of the glasses changed by less than 1% over a period of a few years by which time the changes had approached saturation, following the equation:
& 1
[I-exp(-(uR+k)f(uR+k)t)], [ where Ap is the density change, A is a proportionality constant, u is the volume damaged by each a-decay, k is the recovery constant (assuming first order recovery) and t is the time. On annealing, if the recovery is first order, the irradiation induced density change Ap should recover
Ap=A
R IS the rate of damage, exponentially
with time:
Ap = Apa exp( - kt),
(ii) where Ap, is the change in density at the start of the annealing experiment. The recovery constant was found at various temperatures by isochronal annealing and its value at ambient temperatures was then deduced by extrapolation. On this simple theory, it can then be shown that, at the slow dose rates to be expected in real vitrified waste, damage will anneal out as fast as it occurs and there will be little buildup. During actinide doping experiments there may be some partial recovery whilst
at the high dose rates of ion-bombardment techniques there will be almost none. However,subsidiaryexperimentshave shown that this theory is oversimplified.For example, at moderate annealing temperatures exponential recovery (eq. (ii)) was only followed at short times and some damage remained even after annealing for long periods.
1. Inixoduction It has been pointed out by various authors - for example, ref. [l] - that the most likely cause of any radiation damage effects in vitrified waste is the o-decay of the incorporated actinides. The cy-particles displace some atoms from their positions in the glass network while the recoiling actinide nuclei lose virtually all their energy in this way. Assuming a displacement energy of 25 eV, each e-particle will displace - 150 atoms spread along its range of - 20 pm, and each recoiling nucleus - 1500, the latter being concentrated in a “spike”, somewhat akin to a fission spike, with a diameter of a few tens of nanometers. The actual number of u-decays that will occur in a given volume of vitrified waste depends on the fission product (and hence a&ride) content, the fuel burnup, the cooling-time before reprocessing, and, after about 10000 years, the amount of plutonium left in the waste after the solvent extraction process. Some examples of the increase in e-decays with time are shown in fig. 1. The increase in the number of e-decays with bum-up is due to the larger amounts of actinides produced (primarily ~ericium) and the increase with increased cooling time is because the 241Pu in the fuel decays to 24’Am which remains in the highly active waste after the plutonium has been extracted. 0168-583X/88/%03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
lO"FI102
103
IO&
/
/
/
105
106
107
108
TIMElYEARS
Fig. 1. Numbers
of a- and /3- decays for vitrified against time.
waste plotted
Several methods have been used to study the effect of the a-decays on the glass. Among these are: (a) Doping the glass with a short half-life o-emitter such as ‘“Cm 244Cm or 238Pu. This has the advantage that it is real&c in that the same damaging process is operating as will occur in the real waste but at a somewhat higher dose-rate. It has the disadvantages that it takes a few years to build up a dose equivalent to many millenia in the real waste and that o-active glove box facilities are needed. All the other methods simulate the u-decays by some other method of irradiation. This
481
J.A.C. Marples / Dose rate effects in radiation damage
is not entirely satisfactory because the equivalent doses are not always unambiguous and because the distributions of the defects may be different. (b) Neutron irradiation in a reactor. For borosilicate glasses, the B(n, a)Li reaction can be used with slow neutrons, the specimen thus being damaged by aparticles and Li nuclei. There is no equivalent to the recoil nucleus and the dose is concentrated near the surface of the specimen. Alternatively, the specimen can be doped with uranium and the slow neutrons filtered out. The fission fragments from the uranium then produce fission spikes in the glass, but each produces - 300 times more displaced atoms than the recoils from a-decay. Experimentally, the specimens are difficult to handle because of fission product and induced activity but the necessary dose can be acquired in a few days. (c) Irradiation with heavy ions in an accelerator. This method is convenient in that no active facilities are necessary and the simulation of the recoil atoms is quite good although largely monodirectional - i.e. the tracks are mainly normal to the surface. Also, the damage is confined to a layer - 50 nm thick near the surface which makes assessment of any effects of the damage difficult. However, Dran et al. [2] overcame this problem in an ingenious way by irradiating samples with Pb ions through an electron microscope grid and showed that the irradiated areas were more readily leached than those shielded by the grid. (d) Irradiation with high voltage electrons in an electron microscope. This method is equally convenient and enables the damaged areas to be studied during the damage process. However, the dose rates are usually extremely high and the distribution of displaced atoms is largely isotropic in the small volume of the sample that is irradiated i.e. there is no equivalent of the high local concentration of defects caused by the recoiling actinide nucleus. Some studies by this method have shown that “bubbles” are formed in the glass [3,4] but of course there is no possibility of observing any effect of the damage on the leach rate.
2. Effects of irradiation damage on the leach rate As noted above, Dran’s [2] initial experiments showed fifty-fold increases in the leach rate of some glasses irradiated by Pb ions after a critical dose that they estimated to be equivalent to about 2 x 1018 a-decays g -‘. Subsequent work [5] showed that the effect on the leach rate was dependent on the glass composition and method of leaching. However, samples doped with 238Pu or 244Cm have been held until the accumulated dose was well in excess of this value [1,6,7] and the observed changes in the weight-loss leach rates were small (O-5 x ) although they were somewhat dependent on glass composition [5]. One possible reason for this apparent dif-
ference is that it is due to the difference in dose rate in the two experiments. The dose rate in the actinide doped experiments is 104-lo5 times that which will occur in the real waste whereas in the ion bombardment experiments it is about lo9 times. Studies of the annealing of the density changes produced by irradiation suggest that these differences in dose rates may be significant [l].
3. Effect of irradiation on the density Several workers [1,6-lo] have shown that small changes in the density of vitrified waste occur on irradiation. These changes may be positive or negative in direction depending on the glass composition although no completely satisfactory relationship between composition and the sign of the effect has been proposed. As part of a CEC sponsored programme [6,7], some samples of glass with compositions suggested by the collaborating European laboratories and given in table 1 were doped with 2.5 wt.% 238Pu. The samples were stored at ambient temperature (21-25OC) until they had reached a dose of about 2.8 x 1018 a-decays per gram. The densities were measured at intervals and followed the exponentially saturating curves as shown in fig. 2. The change in densities were fitted to the equation: An/pa
=A(1
- exp( -aD)),
(1)
where Ap is the change from the original density p,,, D is the dose and A and a are constants. The values of A and a that give the best fits to the data are given in
Table 1 The compositions of the glasses used in accelerated a-damage experiments (weight s) Oxide
189
209
SON58
B1/3
VG98/3
Fission product oxides SiO, BzO, Na,O Li,O
9.5 41.5 21.9 1.1 3.7
9.8 50.9 11.1 8.3 4.0
22.1 43.6 19.0 9.4
15.5 41.9 10.5 22.3
5.0
5.1
0.1
6.2
6.3
0.4
0.4
2.1
2.7
0.6
14.6 28.0 6.4 3.8 2.4 12.8 1.2 4.0 14.8 3.6 4.6 0.8 1.5
Cr203
0.6
0.6
0.2
0.4
0.2
NiO U308
0.4 0.1
0.4 0.1
0.1 3.6
0.2 0.5
0.2 1.2
A’203
MgO CaO BaO ZnO TiO, ZrO, Fe203
1.2 0.4 2.3
3.5 0.7
IX. NUCLEAR WASTE MATERIALS WORKSHOP
482
J.A.C. Marples / Dose rate effects in radiation damage
If we assume that the density change Ap is proportional to the volume fraction damaged Ap = CF=
Alpho
dlsmtegratlons
per gram
C[l - exp( -uRt)].
(5)
At long times Ap approaches and:
a saturation
exp( - uRt)
C = Ap,,,
= 0.
Therefore
and we have after dividing
value, Ap,,,,
by p0
[21 =[%I,,
[l - exp( -vRt)].
Fig. 2. Changes in density with dose for 238Pu doped samples of simulated vitrified waste.
table 2 and the curves drawn in fig. 2 were obtained from substituting these values in eq. (1). The data follow these curves quite closely although they were obtained using only two adjustable parameters. The radiation damage to the glass caused by the a-decays is almost entirely in the form of heavily damaged zones round the track of the recoil nuclei and the buildup of damage consists essentially of the increase in the number of such zones within the glass. It is assumed that the volume of glass within the damaged zone cannot be further damaged by another event whose zone overlaps the first one. Let R = rate of damage, (a-decays cme3 s-l), o = volume of the damaged zone (cm3) and F = fraction of the sample volume occupied by damaged zones at time t. In the absence of any recovery: = vR(1 -F),
dF/dt
(2)
where 1 - F is the probability that any new damaged zone overlaps a previous one. Integrating we have: F=B-exp(-uRt),
(3)
where B is an integration constant. But F is zero when t = 0 and therefore B = 1 and we have F=
1 - exp(vRt).
(4)
Table 2 Best fit values of the constants Ap/p,=A[l-exp(-aD)]
A and a iu the equation:
Glass
A [%I
cY/lO-*O [cm31
Radius of equiv. sphere (A)
189 209 SON 58.30.20 B1/3 VG 98/3
- 0.40 f 0.01 - 0.75 *0.04 + 0.62 f 0.02 - 0.484 f 0.006 -0.78 kO.02
51 *5 19.5 * 2 21.9k1.5 36.5k1.3 38.9k2.4
50*5 36+4 37+3 44*2 45*3
Thus in eq. (l), A is the saturation change in Ap/p and, since the dose D is equal to Rt, a = v, the volume damaged by each disintegration. The results in table 2 suggest that, (a) if eq. (1) continued to hold, the density changes will saturate at between 0.4 and 0.8% (b) each a-decay fully damages a volume with a radius of 35-50 A.
4. Recovery and the effect of dose-rate
In these experiments, it is possible that some recovery is taking place, simultaneously with the damage. In the simplest case, this will be first order and eq. (2) then becomes: dF/dt=vR(Z-F)-kF.
This can be integrated F=
--&[l-exp[-(vR+k)t]]
(7)
as before
to give: (8)
and again an exponentially saturating function is predicted but with the saturation value of F reduced to vR/(vR + k). This reduction will apply to the density changes and also to the change in any other property that is proportional to F, the fraction damaged. If vR > k then the effect of any recovery can be neglected and, conversely if vR ==z k then the damage will anneal out as fast as it occurs and no effect will be seen. In table 3, the value of vR/(vR + k) is given for various values of k and vR. Values of R were used appropriate for real waste at about 100 and about 10000 years, for the 238Pu doped glasses and for the ion bombardment experiments of Dran et al. [2,5]. A value of lo-l8 cm3 was chosen for v, this being a little larger than those given in table 1 on the basis that some annealing may be taking place in the 238Pu doped glass experiments (see below). In order to determine k as a function of temperature, the glass samples were annealed “isochronally” i.e. they were heated to successively higher temperatures for a constant time (here 15 hours) before being slowly cooled to room temperature and the density remeasured. The results are shown in fig. 3.
J.A.C. Marples / Dose rate effects VI radiation damage Table 3 Calculated
values of vR/(vR
+ k) for ranges R =)
Real waste c1OOyr c 10000 yr Pu-238 doped glass Heavy ion bombardment
of values of vR and k in s-’ vR b’
108 106 3 x 10’0 6~10’~”
483
10-10 lo-‘* 3x10-8 6~10-~
k lo-”
10-‘0
10-s
10-s
lo-’
1o-6
0.91 0.09 1 1
0.5 10-2 0.997 1
0.09 10-s 0.97 1
10-2 10-4 0.75 1
10-s 10-s 0.23 1
1o-4 1o-6 0.03 0.998
a) In e-decays cm-3 s-‘. b, For v = lo-‘s cm3 a-decay-‘. ‘) Assuming 2 X lo’* events per cm3 in 1 hour.
0.006 -
-0.002
-
-0.006
-
Fig. 3. Annealing
of the density changes
produced
bv damane
in the 238Pu doued samules.
IX. NUCLEAR
WASTE
MATERIALS
WORKSHOP
484
L
’
1.4
’
‘,,,...r!. 1.6
1, ’
’ 1.6
2.0 1000/T
In radiation damage studies of metals or cornpounds, this technique sometimes reveals the presence of different types of defect irr the structure when they anneal out at different temperatures_ If this occurs the iso&ronal bang curve will have “steps” in it e.g. {II-lZZ$ There is no sign of this in the present experiments which suggests that there is either a single broad annealing stage or, perhaps more probably given the complex structure of the glasses, the superposition of a large number of overlapping stages. The densities have recovered to their originaI undamaged values at 4X%-530°C except for glass Ig!+ where this temperature is much lower, and it is possible that the signScant temperature is where the density
’ 2.2
’
’
2.4
’
’
2.6
’
’
2.8
(“lC1)
change on annealing reverses direction. When the glasses were first made, they were annealed at 5Oa 9 C for one hour and then cooled in a furnace. This furnace was not availabie for the post damage anneabng 6.5 years later and the same cooling rates may not have been used. At each temperature, if the recovery is first order then the density change should follow the equation: Ap = Ap’ exp( -k,t), where li is the annealing time (15 hours} at temperature T, A$ and bp are the density changes before and after the anneal and k, is the value of k at that temperature. The values of k found for each temperature in fig. 3 are shown on an Arrhenius plot in fig 4. As might be
J.A.C. Marples / Dose rate effects m radiation damage
Table 4 Values of the recovery
constant k at 20 o C deduced
by extrapolation
485
from fig. 4
Glass
189
209
SON58.30.20
B1/3
VG98/3
k (s-l)
1.2x10-7
1.2x10-7
2x10-”
2.6x10@
6x10-*
expected there is some scatter in the data but in general they lie on reasonably straight lines. These lines were extrapolated to 20 o C giving values for k appropriate to the holding temperature as shown in table 4. These values cannot be expected to be very precise but the four glasses that expanded on irradiation yielded values of k between 0.1 and 6 X lo-’ s-‘. From table 3 it can be seen that for values of k in this range, for real waste all the damage will anneal out as fast as it is formed. In the 238F’u doped glasses, significant annealing will take place but almost none will occur when an ion bombardment technique is used. Changes in the intensity of the bombardment would not be expected to alter this situation since all damage rates obtainable by this technique would be too high. This analysis assumes that the recovery processes can be described by a single parameter k. This is unlikely to be true since there will be many types of defect in the glasses. Two experiments in particular showed that the real situation was more complicated. (a) A sample of glass 209 was annealed isothermally,
0
a az” z z
r
20 -
H Y f 5 z z z a I I 100 200 TIME (HOURS)
.;ooJ(
I
300
Fig. 5. Isothermal annealing of a damaged 238Pu doped sample of gk+S 209.
Dose
5
u-Decoys
per gram
10
--------___
x 10"
15
20
25
Observed values' + 2ooc 013ooc
Calculated curve 13ooc
z OOOL: I_ fi D ooosA c z i? 0006-
Fig. 6. Decrease
in density
of a 238Pu doped sample of glass VG 98/3
held at 20 o C and 130 o C.
IX. NUCLEAR
WASTE
MATERIALS
WORKSHOP
486
J.A.C. MarpIes / Dose rate effects in radiation damage
i.e. it was held at a constant elevated temperature for a long period, being returned briefly to room temperature at intervals for density measurements. The results are given in fig. 5 and show that the densities only followed an exponential annealing curve for a short period before becoming almost constant - i.e. there was a proportion of the radiation induced density change that was stable at each temperature. (b) After annealing, the 238Pu doped sample of glass VG 98 was held at 130°C. The density changes found (measured at room temperature) are shown in fig. 6 and are 60% of those found during the earlier room temperature experiment. The density changes expected at 130°C were calculated using eq. (8). The value of k appropriate for 130 o C was taken from the values obtained during the annealing experiment (fig. 4) whilst the proportionality constant between the damaged fraction of the glass (F) and the resulting density change was obtained from the density changes observed at 20 o C (fig. 2). It can be seen in fig. 6 that the agreement between the observed and calculated density changes is poor.
5. Conclusions The formula including a single first order recovery term suggests that there wilI be almost complete recovery of the irradiation damage due to a-recoils over the time scales appropriate to real waste, that some recovery may occur in actinide doped samples but that there will be no recovery over the short time scales necessary in ion (or electron) bombardment experiments. Further examination of this theory has suggested that it is too simplistic and that some of the radiation damage is more stable than the theory predicts. This may occur because of the saturation damage which occurs in the heavily damaged zone round the track of the recoiling actinide nucleus leads to stable associated defects.
Nevertheless, we have shown that some recovery will occur under the low dose-rates that will occur in the real waste and that such recovery is unlikely to occur in ion-bombardment experiments. This article is based on work Jointly funded by the Commission of the European Communities and by the UK Department of the Environment as part of their Radioactive Waste Management Programme. In the Department of the Environment context, the results may be used in the formulation of UK Government policy but at present they do not represent that policy.
References
PI W.G. Bums, A.E. Hughes, J.A.C. Marples,
R.S. Nelson and A.M. Stoneham, J. Nucl. Mater 107 (1982) 245. 121J.C. Dran, M. Maurette and J.C. Petit, Science 209 (1980) 1418. and D.G. Howitt, Ceramic Bulletin 61 131 J.F. DeNatale (1982) 582. 141 M. Antonini, A. Manara and S. Buckley, Radiat. Eff. 65 (1982) 55. PI J.C. Dran, M. Maurette, J.C. Petit and B. Vassent, in: Scientific Basis for Nuclear Waste Management, Vol. 3, ed. J.G. Moore (Plenum Press, New York, 1981) p. 449. and [61 W. Lutze, A. Manara, J.A.C. Marples, P. Offermann P. Van Iseghem, in: Radioactive Waste Management and Disposal, ed. R. Simon (Cambridge Univ. Press, 1986) p. 232. 171 J.A.C. Marples, A.R. Hall, A. Hough and K.A. Boult, in: Solidified High-level Waste Forms, ed. A.R. Hall, European Commission Report EUR 10852 En (1987). Radioactive Waste Management 2 (1981) [81 R.P. Turcotte, 169. 191 R.P. Turcotte, J.W. Wald, F.P. Roberts, J.M. Rusin and W. Lutze, J. Amer. Cer. Sot. 65 (1982) 589. WI W.J. Weber, in: Sixth Int. Symp. on the Scientific Basis for Nuclear Waste Management, D.G. Brookens (1983). Defects and Radiation Damage in IllI M.W. Thompson, Metals (Cambridge Univ. Press, 1969) p. 264 et seq. WI W.J. Weber, J. Nucl. Mater. 114 (1983) 213.
Nuclear
DOSE RATE EFFECTS
IN RADIATION
DAMAGE
Instruments
and Methods
in Physics Research B32 (1988) 480-486 North-Holland, Amsterdam
TO VITRIFIED RADIOACTIVE
WASTE
J.A.C. MARPLES Hawell ~b~yat~~~
AERE,
Hatwe&
UK
In solidified high level waste, most atom displacements (and hence potential damage) will be caused by the a-decay of incorporated actinides. In order to study the effect of these, several glass compositions were doped with 238Pu so that they received in a few years a dose equivalent to many millenia for the real waste. The densities of the glasses changed by less than 1% over a period of a few years by which time the changes had approached saturation, following the equation:
& 1
[I-exp(-(uR+k)f(uR+k)t)], [ where Ap is the density change, A is a proportionality constant, u is the volume damaged by each a-decay, k is the recovery constant (assuming first order recovery) and t is the time. On annealing, if the recovery is first order, the irradiation induced density change Ap should recover
Ap=A
R IS the rate of damage, exponentially
with time:
Ap = Apa exp( - kt),
(ii) where Ap, is the change in density at the start of the annealing experiment. The recovery constant was found at various temperatures by isochronal annealing and its value at ambient temperatures was then deduced by extrapolation. On this simple theory, it can then be shown that, at the slow dose rates to be expected in real vitrified waste, damage will anneal out as fast as it occurs and there will be little buildup. During actinide doping experiments there may be some partial recovery whilst
at the high dose rates of ion-bombardment techniques there will be almost none. However,subsidiaryexperimentshave shown that this theory is oversimplified.For example, at moderate annealing temperatures exponential recovery (eq. (ii)) was only followed at short times and some damage remained even after annealing for long periods.
1. Inixoduction It has been pointed out by various authors - for example, ref. [l] - that the most likely cause of any radiation damage effects in vitrified waste is the o-decay of the incorporated actinides. The cy-particles displace some atoms from their positions in the glass network while the recoiling actinide nuclei lose virtually all their energy in this way. Assuming a displacement energy of 25 eV, each e-particle will displace - 150 atoms spread along its range of - 20 pm, and each recoiling nucleus - 1500, the latter being concentrated in a “spike”, somewhat akin to a fission spike, with a diameter of a few tens of nanometers. The actual number of u-decays that will occur in a given volume of vitrified waste depends on the fission product (and hence a&ride) content, the fuel burnup, the cooling-time before reprocessing, and, after about 10000 years, the amount of plutonium left in the waste after the solvent extraction process. Some examples of the increase in e-decays with time are shown in fig. 1. The increase in the number of e-decays with bum-up is due to the larger amounts of actinides produced (primarily ~ericium) and the increase with increased cooling time is because the 241Pu in the fuel decays to 24’Am which remains in the highly active waste after the plutonium has been extracted. 0168-583X/88/%03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
lO"FI102
103
IO&
/
/
/
105
106
107
108
TIMElYEARS
Fig. 1. Numbers
of a- and /3- decays for vitrified against time.
waste plotted
Several methods have been used to study the effect of the a-decays on the glass. Among these are: (a) Doping the glass with a short half-life o-emitter such as ‘“Cm 244Cm or 238Pu. This has the advantage that it is real&c in that the same damaging process is operating as will occur in the real waste but at a somewhat higher dose-rate. It has the disadvantages that it takes a few years to build up a dose equivalent to many millenia in the real waste and that o-active glove box facilities are needed. All the other methods simulate the u-decays by some other method of irradiation. This
481
J.A.C. Marples / Dose rate effects in radiation damage
is not entirely satisfactory because the equivalent doses are not always unambiguous and because the distributions of the defects may be different. (b) Neutron irradiation in a reactor. For borosilicate glasses, the B(n, a)Li reaction can be used with slow neutrons, the specimen thus being damaged by aparticles and Li nuclei. There is no equivalent to the recoil nucleus and the dose is concentrated near the surface of the specimen. Alternatively, the specimen can be doped with uranium and the slow neutrons filtered out. The fission fragments from the uranium then produce fission spikes in the glass, but each produces - 300 times more displaced atoms than the recoils from a-decay. Experimentally, the specimens are difficult to handle because of fission product and induced activity but the necessary dose can be acquired in a few days. (c) Irradiation with heavy ions in an accelerator. This method is convenient in that no active facilities are necessary and the simulation of the recoil atoms is quite good although largely monodirectional - i.e. the tracks are mainly normal to the surface. Also, the damage is confined to a layer - 50 nm thick near the surface which makes assessment of any effects of the damage difficult. However, Dran et al. [2] overcame this problem in an ingenious way by irradiating samples with Pb ions through an electron microscope grid and showed that the irradiated areas were more readily leached than those shielded by the grid. (d) Irradiation with high voltage electrons in an electron microscope. This method is equally convenient and enables the damaged areas to be studied during the damage process. However, the dose rates are usually extremely high and the distribution of displaced atoms is largely isotropic in the small volume of the sample that is irradiated i.e. there is no equivalent of the high local concentration of defects caused by the recoiling actinide nucleus. Some studies by this method have shown that “bubbles” are formed in the glass [3,4] but of course there is no possibility of observing any effect of the damage on the leach rate.
2. Effects of irradiation damage on the leach rate As noted above, Dran’s [2] initial experiments showed fifty-fold increases in the leach rate of some glasses irradiated by Pb ions after a critical dose that they estimated to be equivalent to about 2 x 1018 a-decays g -‘. Subsequent work [5] showed that the effect on the leach rate was dependent on the glass composition and method of leaching. However, samples doped with 238Pu or 244Cm have been held until the accumulated dose was well in excess of this value [1,6,7] and the observed changes in the weight-loss leach rates were small (O-5 x ) although they were somewhat dependent on glass composition [5]. One possible reason for this apparent dif-
ference is that it is due to the difference in dose rate in the two experiments. The dose rate in the actinide doped experiments is 104-lo5 times that which will occur in the real waste whereas in the ion bombardment experiments it is about lo9 times. Studies of the annealing of the density changes produced by irradiation suggest that these differences in dose rates may be significant [l].
3. Effect of irradiation on the density Several workers [1,6-lo] have shown that small changes in the density of vitrified waste occur on irradiation. These changes may be positive or negative in direction depending on the glass composition although no completely satisfactory relationship between composition and the sign of the effect has been proposed. As part of a CEC sponsored programme [6,7], some samples of glass with compositions suggested by the collaborating European laboratories and given in table 1 were doped with 2.5 wt.% 238Pu. The samples were stored at ambient temperature (21-25OC) until they had reached a dose of about 2.8 x 1018 a-decays per gram. The densities were measured at intervals and followed the exponentially saturating curves as shown in fig. 2. The change in densities were fitted to the equation: An/pa
=A(1
- exp( -aD)),
(1)
where Ap is the change from the original density p,,, D is the dose and A and a are constants. The values of A and a that give the best fits to the data are given in
Table 1 The compositions of the glasses used in accelerated a-damage experiments (weight s) Oxide
189
209
SON58
B1/3
VG98/3
Fission product oxides SiO, BzO, Na,O Li,O
9.5 41.5 21.9 1.1 3.7
9.8 50.9 11.1 8.3 4.0
22.1 43.6 19.0 9.4
15.5 41.9 10.5 22.3
5.0
5.1
0.1
6.2
6.3
0.4
0.4
2.1
2.7
0.6
14.6 28.0 6.4 3.8 2.4 12.8 1.2 4.0 14.8 3.6 4.6 0.8 1.5
Cr203
0.6
0.6
0.2
0.4
0.2
NiO U308
0.4 0.1
0.4 0.1
0.1 3.6
0.2 0.5
0.2 1.2
A’203
MgO CaO BaO ZnO TiO, ZrO, Fe203
1.2 0.4 2.3
3.5 0.7
IX. NUCLEAR WASTE MATERIALS WORKSHOP
482
J.A.C. Marples / Dose rate effects in radiation damage
If we assume that the density change Ap is proportional to the volume fraction damaged Ap = CF=
Alpho
dlsmtegratlons
per gram
C[l - exp( -uRt)].
(5)
At long times Ap approaches and:
a saturation
exp( - uRt)
C = Ap,,,
= 0.
Therefore
and we have after dividing
value, Ap,,,,
by p0
[21 =[%I,,
[l - exp( -vRt)].
Fig. 2. Changes in density with dose for 238Pu doped samples of simulated vitrified waste.
table 2 and the curves drawn in fig. 2 were obtained from substituting these values in eq. (1). The data follow these curves quite closely although they were obtained using only two adjustable parameters. The radiation damage to the glass caused by the a-decays is almost entirely in the form of heavily damaged zones round the track of the recoil nuclei and the buildup of damage consists essentially of the increase in the number of such zones within the glass. It is assumed that the volume of glass within the damaged zone cannot be further damaged by another event whose zone overlaps the first one. Let R = rate of damage, (a-decays cme3 s-l), o = volume of the damaged zone (cm3) and F = fraction of the sample volume occupied by damaged zones at time t. In the absence of any recovery: = vR(1 -F),
dF/dt
(2)
where 1 - F is the probability that any new damaged zone overlaps a previous one. Integrating we have: F=B-exp(-uRt),
(3)
where B is an integration constant. But F is zero when t = 0 and therefore B = 1 and we have F=
1 - exp(vRt).
(4)
Table 2 Best fit values of the constants Ap/p,=A[l-exp(-aD)]
A and a iu the equation:
Glass
A [%I
cY/lO-*O [cm31
Radius of equiv. sphere (A)
189 209 SON 58.30.20 B1/3 VG 98/3
- 0.40 f 0.01 - 0.75 *0.04 + 0.62 f 0.02 - 0.484 f 0.006 -0.78 kO.02
51 *5 19.5 * 2 21.9k1.5 36.5k1.3 38.9k2.4
50*5 36+4 37+3 44*2 45*3
Thus in eq. (l), A is the saturation change in Ap/p and, since the dose D is equal to Rt, a = v, the volume damaged by each disintegration. The results in table 2 suggest that, (a) if eq. (1) continued to hold, the density changes will saturate at between 0.4 and 0.8% (b) each a-decay fully damages a volume with a radius of 35-50 A.
4. Recovery and the effect of dose-rate
In these experiments, it is possible that some recovery is taking place, simultaneously with the damage. In the simplest case, this will be first order and eq. (2) then becomes: dF/dt=vR(Z-F)-kF.
This can be integrated F=
--&[l-exp[-(vR+k)t]]
(7)
as before
to give: (8)
and again an exponentially saturating function is predicted but with the saturation value of F reduced to vR/(vR + k). This reduction will apply to the density changes and also to the change in any other property that is proportional to F, the fraction damaged. If vR > k then the effect of any recovery can be neglected and, conversely if vR ==z k then the damage will anneal out as fast as it occurs and no effect will be seen. In table 3, the value of vR/(vR + k) is given for various values of k and vR. Values of R were used appropriate for real waste at about 100 and about 10000 years, for the 238Pu doped glasses and for the ion bombardment experiments of Dran et al. [2,5]. A value of lo-l8 cm3 was chosen for v, this being a little larger than those given in table 1 on the basis that some annealing may be taking place in the 238Pu doped glass experiments (see below). In order to determine k as a function of temperature, the glass samples were annealed “isochronally” i.e. they were heated to successively higher temperatures for a constant time (here 15 hours) before being slowly cooled to room temperature and the density remeasured. The results are shown in fig. 3.
J.A.C. Marples / Dose rate effects VI radiation damage Table 3 Calculated
values of vR/(vR
+ k) for ranges R =)
Real waste c1OOyr c 10000 yr Pu-238 doped glass Heavy ion bombardment
of values of vR and k in s-’ vR b’
108 106 3 x 10’0 6~10’~”
483
10-10 lo-‘* 3x10-8 6~10-~
k lo-”
10-‘0
10-s
10-s
lo-’
1o-6
0.91 0.09 1 1
0.5 10-2 0.997 1
0.09 10-s 0.97 1
10-2 10-4 0.75 1
10-s 10-s 0.23 1
1o-4 1o-6 0.03 0.998
a) In e-decays cm-3 s-‘. b, For v = lo-‘s cm3 a-decay-‘. ‘) Assuming 2 X lo’* events per cm3 in 1 hour.
0.006 -
-0.002
-
-0.006
-
Fig. 3. Annealing
of the density changes
produced
bv damane
in the 238Pu doued samules.
IX. NUCLEAR
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MATERIALS
WORKSHOP
484
L
’
1.4
’
‘,,,...r!. 1.6
1, ’
’ 1.6
2.0 1000/T
In radiation damage studies of metals or cornpounds, this technique sometimes reveals the presence of different types of defect irr the structure when they anneal out at different temperatures_ If this occurs the iso&ronal bang curve will have “steps” in it e.g. {II-lZZ$ There is no sign of this in the present experiments which suggests that there is either a single broad annealing stage or, perhaps more probably given the complex structure of the glasses, the superposition of a large number of overlapping stages. The densities have recovered to their originaI undamaged values at 4X%-530°C except for glass Ig!+ where this temperature is much lower, and it is possible that the signScant temperature is where the density
’ 2.2
’
’
2.4
’
’
2.6
’
’
2.8
(“lC1)
change on annealing reverses direction. When the glasses were first made, they were annealed at 5Oa 9 C for one hour and then cooled in a furnace. This furnace was not availabie for the post damage anneabng 6.5 years later and the same cooling rates may not have been used. At each temperature, if the recovery is first order then the density change should follow the equation: Ap = Ap’ exp( -k,t), where li is the annealing time (15 hours} at temperature T, A$ and bp are the density changes before and after the anneal and k, is the value of k at that temperature. The values of k found for each temperature in fig. 3 are shown on an Arrhenius plot in fig 4. As might be
J.A.C. Marples / Dose rate effects m radiation damage
Table 4 Values of the recovery
constant k at 20 o C deduced
by extrapolation
485
from fig. 4
Glass
189
209
SON58.30.20
B1/3
VG98/3
k (s-l)
1.2x10-7
1.2x10-7
2x10-”
2.6x10@
6x10-*
expected there is some scatter in the data but in general they lie on reasonably straight lines. These lines were extrapolated to 20 o C giving values for k appropriate to the holding temperature as shown in table 4. These values cannot be expected to be very precise but the four glasses that expanded on irradiation yielded values of k between 0.1 and 6 X lo-’ s-‘. From table 3 it can be seen that for values of k in this range, for real waste all the damage will anneal out as fast as it is formed. In the 238F’u doped glasses, significant annealing will take place but almost none will occur when an ion bombardment technique is used. Changes in the intensity of the bombardment would not be expected to alter this situation since all damage rates obtainable by this technique would be too high. This analysis assumes that the recovery processes can be described by a single parameter k. This is unlikely to be true since there will be many types of defect in the glasses. Two experiments in particular showed that the real situation was more complicated. (a) A sample of glass 209 was annealed isothermally,
0
a az” z z
r
20 -
H Y f 5 z z z a I I 100 200 TIME (HOURS)
.;ooJ(
I
300
Fig. 5. Isothermal annealing of a damaged 238Pu doped sample of gk+S 209.
Dose
5
u-Decoys
per gram
10
--------___
x 10"
15
20
25
Observed values' + 2ooc 013ooc
Calculated curve 13ooc
z OOOL: I_ fi D ooosA c z i? 0006-
Fig. 6. Decrease
in density
of a 238Pu doped sample of glass VG 98/3
held at 20 o C and 130 o C.
IX. NUCLEAR
WASTE
MATERIALS
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486
J.A.C. MarpIes / Dose rate effects in radiation damage
i.e. it was held at a constant elevated temperature for a long period, being returned briefly to room temperature at intervals for density measurements. The results are given in fig. 5 and show that the densities only followed an exponential annealing curve for a short period before becoming almost constant - i.e. there was a proportion of the radiation induced density change that was stable at each temperature. (b) After annealing, the 238Pu doped sample of glass VG 98 was held at 130°C. The density changes found (measured at room temperature) are shown in fig. 6 and are 60% of those found during the earlier room temperature experiment. The density changes expected at 130°C were calculated using eq. (8). The value of k appropriate for 130 o C was taken from the values obtained during the annealing experiment (fig. 4) whilst the proportionality constant between the damaged fraction of the glass (F) and the resulting density change was obtained from the density changes observed at 20 o C (fig. 2). It can be seen in fig. 6 that the agreement between the observed and calculated density changes is poor.
5. Conclusions The formula including a single first order recovery term suggests that there wilI be almost complete recovery of the irradiation damage due to a-recoils over the time scales appropriate to real waste, that some recovery may occur in actinide doped samples but that there will be no recovery over the short time scales necessary in ion (or electron) bombardment experiments. Further examination of this theory has suggested that it is too simplistic and that some of the radiation damage is more stable than the theory predicts. This may occur because of the saturation damage which occurs in the heavily damaged zone round the track of the recoiling actinide nucleus leads to stable associated defects.
Nevertheless, we have shown that some recovery will occur under the low dose-rates that will occur in the real waste and that such recovery is unlikely to occur in ion-bombardment experiments. This article is based on work Jointly funded by the Commission of the European Communities and by the UK Department of the Environment as part of their Radioactive Waste Management Programme. In the Department of the Environment context, the results may be used in the formulation of UK Government policy but at present they do not represent that policy.
References
PI W.G. Bums, A.E. Hughes, J.A.C. Marples,
R.S. Nelson and A.M. Stoneham, J. Nucl. Mater 107 (1982) 245. 121J.C. Dran, M. Maurette and J.C. Petit, Science 209 (1980) 1418. and D.G. Howitt, Ceramic Bulletin 61 131 J.F. DeNatale (1982) 582. 141 M. Antonini, A. Manara and S. Buckley, Radiat. Eff. 65 (1982) 55. PI J.C. Dran, M. Maurette, J.C. Petit and B. Vassent, in: Scientific Basis for Nuclear Waste Management, Vol. 3, ed. J.G. Moore (Plenum Press, New York, 1981) p. 449. and [61 W. Lutze, A. Manara, J.A.C. Marples, P. Offermann P. Van Iseghem, in: Radioactive Waste Management and Disposal, ed. R. Simon (Cambridge Univ. Press, 1986) p. 232. 171 J.A.C. Marples, A.R. Hall, A. Hough and K.A. Boult, in: Solidified High-level Waste Forms, ed. A.R. Hall, European Commission Report EUR 10852 En (1987). Radioactive Waste Management 2 (1981) [81 R.P. Turcotte, 169. 191 R.P. Turcotte, J.W. Wald, F.P. Roberts, J.M. Rusin and W. Lutze, J. Amer. Cer. Sot. 65 (1982) 589. WI W.J. Weber, in: Sixth Int. Symp. on the Scientific Basis for Nuclear Waste Management, D.G. Brookens (1983). Defects and Radiation Damage in IllI M.W. Thompson, Metals (Cambridge Univ. Press, 1969) p. 264 et seq. WI W.J. Weber, J. Nucl. Mater. 114 (1983) 213.