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Diffusion of tritium in single crystal Li2O
Journal of Nuclear Materials 1IS (1983) IOO-108 North-Holland Publishing Company
100
DIFFUSION OF TRITIUM IN SINGLE CRYSTAL Li,O D. GUGGI,
H.R. IHLE,
Ke~nfors~~~gsa~~a~e EURATOM-KFA
D. BRijNING,
U. KURZ
Jiilich GmbH, fnstitut fiir Chemie, P. 0. Box 1913, 51713 Ji&h,
Federal Republic of Germany, As~~c~ati~n
and S. NASU
*, K. NODA,
T. TANIFUJI
Japan Atomic Energy Research institute,
Tokai - mura, ~~rak~ - ken, 319 - Ii Japan
Received 28 January 1983; accepted 21 March 1983
The release of tritium from neutron irradiated spherical samples of single crystal Li,O was measured by isothermal annealing experiments. The release is shown to be controlled by diffusion of tritium in the solid under appropriate experimental conditions. Deviations from solely diffusion controlled release were observed when traces of water were present in the He-purge gas used in the experiments. The diffusivity of tritium in single crystal Li,O is given by ln(D/cm*s-‘)=
-(5.93&0.48)-(81.73*4.24)103J/RT
for850K~T
1. Introduction Lithium oxide is regarded as a prime candidate among the solid blanket materials for fusion reactors on account of its favourable tritium breeding properties. A substantiai amount of experimental work has been done
on the release of tritium from Li,O in several laboratories. However, most results from these works do not permit the deduction of diffusivities and the calculation of the mean concentration of tritium in a blanket. Mainly, the un~rt~nties arise from a lack of knowledge as to whether diffusion [ 1,2] within the solid, or chemical reactions at the solid-gas phase boundary, control the release of tritium from Li,O; observed overall rate coefficients are spread over several orders of magnitudes [3]. For the proposed use of ceramic lithium solids [4], it is assumed that the diffusivity of tritium in the solid, which is inversely proportional to the mean residence
* Present adress: USHIO Inc, Harima Himeji-shi, Hyogo-ken, 671-02 Japan. 0022-3 115/83/$03.00
Plant, Eessho-cho,
0 1983 Elsevier Science Publishers
time of a tritium atom at steady state in a blanket, controls the tritium inventory. In earlier work it was experimentally shown that the tritium release from /?Li, A 10, can be described by a diffusion mode1 [5]. Results obtained in earlier work on the release of tritium from finely powdered samples of Li,O, irradiated with thermal neutrons, in our laboratory yielded an exponential decrease of the release rate with time for the “late” release [6]. The values obtained in this work have mistakenly been cited as data for the diffusivity of tritium from Li,O [2,3], because diffusion was not shown to control the tritium release. The samples used up to that time consisted of agglomerations of fine particles of unknown shape and size distribution. In view of the findings from the present investigation, the great discrepancy between the above mentioned earlier results and those obtained in this work is not surprising. Tritium release from neutron irradiated Li,O has been assumed to be controlled by first order kinetics instead of diffusion by several authors [7,8]. The former mechanism has been reported to be frequently observed, if reactions at the surface are controlling the rate of release of gases from solids [9). B.V.
D. Guggi et al. / Diffusionof tritiumin single crystal Li,O
101
2. Experimental
d
2.1. Preparation of single crystals of lithium oxide
Owing to the chemical interaction of molten lithium oxide with all materials in which it could be contained, a crucible free preparation method by floating zonegrowth was used to prepare cylindrical single crystals of Li,O. Apparatus and preparation technique have been described elsewhere [ 10,111.
-b
2.2. Preparation of spherical samples A cylindrical rod (- 8 mm in diameter, - 80 mm in length) of Li,O-single crystal was cut into discs by means of abrasive cut-off blades coated with diamond dust, rotating at - 60 000 rpm. These discs were subsequently cut into cubes, which were thereupon ground into spheres of different diameters by the use of a rotating corundum disc [121. The range of diameters of the spherical single crystals was between 1.77 and 3.15 mm. Mean radii were calculated from the mass and density, assuming ideal spherical geometry. Small deviations from the ideal shape were observed (on the average - 1% difference between the smallest and the greatest diameter measured on a sphere). The samples were first outgassed in open plantinum crucibles in a vacuum of - 4 X 10e4 Pa at a temperature of - 880 K. After this thermal pretreatment, the samples were enclosed in vacuum in platinum cells, together with fragments of single crystals to avoid excessive vaporization, and hermetically sealed. The samples were then heated to - 1280 K over a period of - 8 h; by this procedure a very smooth surface was obtained. For neutron irradiation and subsequent isothermal annealing, the samples were transferred to platinum cells as shown in fig. 1. The lid (a) was fitted with a closed-end pipe (c), extended into the interior of the cylindrical cell (b), for insertion of a thermocouple. These cells, each containing one sample, were hermetically sealed under vacuum. An open capillary (d) attached to the lid was used to evacuate the cell. It was closed finally by electron beam melting. All sample handling was carried out in a dry atmosphere. The sealed samples were then neutron irradiated to yield an atom-ratio T/Li - 5 X lo-’ (fluence: - 6 x lOI cme2, thermal neutron flux: - 6 X 10” cm-2s-‘, epithermal contribution < 250 ppm, fast contribution d 150 ppm).
I
,
10 mm
PLATINUM
- CELL
Fig. 1. Platinum cell, used to contain Li 2O samples,
2.3. Isothermal release experiments The time dependence of the isothermal release of tritium from the neutron irradiated spherical samples was observed by measuring the concentration of the desorbed tritiated species in a flow of helium (at atmospheric pressure) with a proportional counter. Shortly after its contact with the sample, the sweep-gas passed a Zn-reductor in order to reduce tritiated water, which is the predominant molecular species desorbed from the surface of Li,O by thermal annealing. A constant flow of the sweep-gas (5 cm3 helium/mm) was used; methane was admixed in a ratio of 4: 1 after passage of the helium through the reductor. The sample was heated by a RF-generator, the platinum cell serving as susceptor. The cell temperature-attained in approx. 1 minutewas regulated to a constancy of within f2 K. The thermocouple was calibrated by measuring the melting points of lead, aluminium and silver, using cells of similar geometry as the platinum cells. Fig. 2 shows the experimental arrangement, which was described earlier [ 12,131, minor modifications having been made. After pre-purification, the helium sweep gas is led through a liquid-nitrogen trap immediately before it enters the “tritium release unit” (detail “a”, fig. 2). This last purification step proved to be necessary, because an inleakage of traces of water into the helium stream during its passage from the pre-purification unit to the release unit could not be excluded for technical reasons.
t). Guggi et al. / Difjwon
of tritium in single crystal Li,O
-.._____ HEATING
PREPURIFICATION 1
OX I SO&
IMESSER
2
TI-SPONGE
lSm*Cl
3
CHARCOAL-TRAP
GRlESHElM
_
W ii RESISTANCE
I
WH TC
i77Kl
I RAWFREQUENCY :l~~~~~
> HEAT’NG -,
i
FM= FLOW
_.._._~.~ RESULTS
RECORDER
j
/I
METER II
J-----.
‘\
GAS SUPPLY AND PURIFICATION
I
T RELEASE UNIT
-TC
t-
._____ i
ELECTRONICS
_LI_NEAA-MOTIONFEEDTHROUGH
/
’
DETAIL “A” Fig. 2. Ewperimental arrangement for post irradiation annealing experiments using inert gas transpiration method.
The tritium release unit is composed of a system of ~n~nt~caliy mounted quartz and copper tubes (fig. 2, detail “A”). Helium flows first through the interspace between the quartz tubes. After reversal of flow direction, the helium is led over the sample, where tritium species desorbed from the sample surface are taken up. The tritium containing helium then enters the bulge of the “inner quartz tube”, filled with zinc granules, kept at (650 f l)K, and held in position by a wad of quartz wool on both sides. After passage of the sweep gas through the reductor, methane as counting gas is added at a point close to the zinc-reductor to obtain small transit times and to minimize wall-contamination. The
gas mixture is then led through copper tubes held at - 450 K to the proportional counter (volume 10 cm3) kept at the same temperature. At the beginning of an experiment, the loaded platinum cell (fig. 1) was mounted at the top of a linear motion fen-trout (see fig. 2). The tritium release unit was then evacuated to a vacuum of - 4 X lOA Pa for a period of - 6 h, and finally filled with helium. The plantinum cell was then opened by pushing it towards a tungsten tip. The opened cell was subsequently drawn back to a position in the center of the RF-heater coil. The units used for data acquisition are also shown in fig. 2.
103
D. Guggi et al. / Diffusion of tritium in single crystal Liz0 3. Evaluation of data 3.1. Corrections applied to experimental
signal was normally attained after 5-7 min in the “ test-mode”, whereupon the gas flow was switched back to the “measuring-mode”. The corrected data were obtained by subtracting the counter background from the observed signal.
results
3.1.1. Correction for counter-contamination Although most of the T,O(HTO) is reduced to T2(HT) by the zinc reductor, a certain degree of counter-contamination cannot be avoided. To correct the experimental data for this effect, a gas-bypass system was used, which allowed the measurement of the background signal of the proportional counter at any time without impairing the isothermal release experiments. This was realized by diverting the helium-methane gas mixture, before it was led into the counter tube, through a bypass to the exhaust; further, a second gas flow with the same flow rate and mixing ratio was fed into the counter tube. This “test-mode” was used several times during a release experiment. Constancy of background
fraction
3.1.2. Corrections for effects due to the zinc reductor During the passage of the sweep gas through the reductor, chemical reactions between the heated zinc granules and the tritiated species occur. Retention of tritium by the zinc is observed during the initial stage of an experiment; whereas during the “late” release, the retained tritium is partially liberated from the zinc bed to the helium sweep gas. To correct for errors arising from the zinc reductor, each experiment was interrupted when the fractional release (ratio of tritium atoms released to tritium atoms initially contained in the sample) had attained a suffi-
x 100 1) observed
h
#\
10‘ c
\
tritium
corrected
release
curve
2-2a)
curve
for counter
contamination
2-3)
curve corrected for counter zinc reductor effects
contamination
and
‘1 \ i
5 ol
2
I.
lo3 -
lo2 i
I
I
I
I
1
1
2
3
4
5
Fig. 3. Experimental tritium release curve and corrections.
1
time
01)~
I
1
I
I
1
1
1
e
9
10
11
12
D. Guggi ef al. / Diffusion
104
ciently large value by turning off the RF-power. This caused the sample to cool down quickly. All tritium registered after the sample had attained a sufficiently low temperature was assumed to originate from the reductor, which was maintained at a constant temperature. When the reductor temperature is lowered to room temperature, the signal approaches background level. From the observed reduction of the signal by the thermal quenching of the sample, the ratio of the flows of tritium originating from the sample and from the reductor was determined for the time at which the release was interrupted. In this way, one point on the “true” tritium release curve corrected for both counter-contamination and zinc reductor effects was obtained. From there a tangent was graphicafly drawn to the “counter-corrected” logarithm of the release rate versus time curve. The time at which the tangent touches the release curve corresponds to a fractional release of > 0.70. Above this fraction, simple exponential decay of the signal from diffusional tritium release should occur. The relative amount of tritium released from the zinc reductor between time t, and t, (see fig. 3) was found on the average to be - 4% of the tritium initially contained in the sample. After time t,, the amount of tritium released from the zinc reductor was on the average - 8% of the total tritium. In the calculation of fractional release versus time from experimental results, corrected as outlined above, the contribution of fractions of tritium retained by the zinc reductor were taken into account. The use of a zinc reductor, although its disturbing effects can be corrected for, imposes a limitation on the accuracy of the transpiration method used in this work. 3.2. Rate law analysis 3.2.1. Time dependence of fractional release The rate of tritium release is directly proportional to the corrected counting rate during an isothermal postirradiation annealing experiment at constant counting efficiency. The sum of corrected accumulated counts at any time, t, divided by the corrected sum of all counts obtained during the experiment and during a subsequent annealing at - 1280 K for a period of - 6 h, is identical with the fractional release F(t), where F(t)=
l-i
P(t)-c, ccl-
Cf
( !
with c, = initial concentration of tritium in the sample, cr = final concentration; T(t) = average concentration at time t.
of tritium
tn single crystal Li,O
Table 1 Diffusion data obtained by annealing a sphere of R = 0. i 13 at T=1005
ln( t/s) Run 6.98 7.09 7.19 7.27 7.35 7.43 7.50 7.65
em
K.
F(f)%
b(f)
D x 10’
(cm2/s)
(D-5)x10’ (cm2/s)
1.11 1.11 1.11 1.13 1.13 1.16 1.16 1.18 1.18 1.18 1.20 1.13 1.16 1.16 1.16 1.16 1.16 1.13 1.13 1.13 1.13 I.11 1.11 I .09
- 0.03 - 0.03 -0.03 -0.01 -0.01 0.02 0.02 0.04 0.04 0.04 0.06 -0.01 0.02 0.02 0.02 0.02 0.02 - 0.01 -0.01 -0.01 -0.01 -0.03 -0.03 -0.05
1
7.78 7.90
8.01 8.10 8.41 8.59 8.75 8.88 9.00 9.10 9.29 9.44 9.51 9.69 9.80 9.89 Average:
29.8 31.3 32.8 34.2 35.5 36.8 38.1 41.0 43.6 46.0 48.1 50.1 55.1 60.0 63.7 66.8 69.5 71.9 76.1 79.1 82.6 85.0 87.1 88.7 o=
- 1.12 - 1.06 - 1.01 - 0.97 - 0.92 - 0.88 - 0.84 - 0.76 - 0.69 - 0.63 - 0.57 - 0.52 -0.39 - 0.29 -0.21 -0.15 - 0.09 -0.04 0.05 0.12 0.19 0.25 0.29 0.34
1.14kO.03
(cm’/s).
Minute amounts of tritium retained in the samples after completion of an experiment were determined by liquid scintillation counting of the tritium content of the outgassed samples. The residual amount of tritium was found to be smaller than 40 ppm of the initial content in all experiments. The release of tritium from neutron irradiated Li,O may be considered to consist of at least two processes: the transport through the bulk of the solid and subsequent desorption from the surface of the sample. Which of these two consecutive steps controls the overall process of the tritium release will depend on the magnitudes of the rate constants of the individual processes and on the volume to surface ratio of the samples. The experimental conditions were chosen so that the tritium release is likely controlled by diffusion. To this aim, the following suppositions were verified: careful degassing of the samples in vacua to remove traces of water, cryogenic removal of minute amounts of moisture from the helium sweep gas and choice of a reasonably long
D. Guggiet al. / Diffusionof tritiumin diffusion path by using a proper volume to surface ratio of the samples. Using samples of relatively large radii also enables one to carry out the experiments in a temperature range where annealing times for radiation damage effects can be assumed to be small. Since the chemical form in which tritium is desorbed from the single crystal surface is not related to the diffusion process within the bulk of the material, no attempt was made to distinguish between T,(HT) and T,O(HTO). 3.2.2. Nomographic description of diffusional release A proof of whether diffusion is the rate determining step can conveniently be obtained by use of a nomogram which is constructed in the following way [5]: The time dependence of the fraction removed, F(r), for spherical sample geometry and diffusivities independent of concentration, is expressed by:
with X = D/R2. Boundary conditions are: homogeneous distribution of tritium within the sample for t = 0, and concentration at the sample surface is assumed to be zero for t > 0. Experimentally obtained F( r)-values are transformed to cp(r)-values by the use of eq. (2): P(t)=l--$
E
lexp
o-l o2
-
i
u2Tr3’p2( t)
.
36
i
(4
Eq. (2) originates from a combination of eq. (1) with eq. (3) which can be used approximately instead of eq. (1) in the range of low fractions (F(r) < 0.25), where F(t)
-ln[l
Experimental data from three runs out of a total of range from 8, which were made in the temperature 850 K to - 1200 K, are shown in fig. 4, where calculated data for diffusion controlled release (solid lines) are compared with experimental results (dotted least square lines). Also indicated are calculated data for a first order law controlled release mechanism
= kt,
-I]
(4)
k is the rate constant. It is seen that the slopes of the regression lines from the data of the three runs, shown in fig. 4, are close to + l/2 over a range of 0.30 5 F(t) 5 0.90. Data for release fractions outside this range are not used for the evaluation because of disturbing effects at the beginning and in the late phase of an experiment. Numerical values for the data shown in fig. 4 are given in table 1. Here, F(t), In t and the resulting diffusion coefficient for each point of the release curve for run 1 are given as example. The deviations of the diffusivities from their average value are also given in this table; they are small and do not exhibit any significant systematic trend, which proves the presence of a diffusion controlled process. The resulting slopes for all 8 runs are given in table 2. From these results, we conclude that diffusion is the rate determining step for the tritium release under our experimental conditions. The temperature dependence of the diffusion coefficient of tritium in Li,O single crystals obtained in this work is given by eq. (5) and shown in fig. 5; numerical values are given in table 2. A 3 u-error is quoted in eq. (5) to take into account the uncertainties arising from the various corrections (see section 3.1) applied to the experimental data: ln( D/cm2 s-
’)
= - (5.93 5 0.48) - (81.73 f 4.24)103J/RT,
(5)
for850K~T~1200K(R=8.314JK-‘mol-‘).
Table 2 Diffusivity temperature
4. Experimental results
105
(hatched lines). The magnitudes of the rate coefficients for this latter mechanism were chosen so as to fit in the range of the release rates observed by experiment. The time dependence of the fraction removed, F(t), for a first order law controlled reaction is expressed by
- cp(t) 1141.
A plot of lncp( t) versus lnt yields a straight line with the slope + l/2 for a diffusion controlled process.
single crystal Li,O
of tritium
in single
crystal
Li,O
as function
Run
T(K)
D(cm’/s)
R (cm)
Slope
la 2 3 4 5 6 I 8
1005 1103 1200 901 1054 956 858 1151
(1.14*0.03)x 10-7 (2.91+0.25)x lo-’ (7.84*0.70)x 10-7 (5.19*0.52)x10-* (2.65~0.4O)XlO-’ (1.12~0.05)XlO-’ (2.77+0.17)X lo-’ (5.68f0.62)XlO-’
0.113 0.127 0.156 0.112 0.116 0.114 0.089 0.149
0.494 f 0.002 0.455 f 0.001 0.436 f 0.002 0.569 f 0.002 0.603 f 0.002 0.519*0.001 0.502 f 0.003 0.563 f 0.002
’ See table 1.
of
D. Guggi et al. / Diffusion
106
120 min 4
60
30
15
10
of tritium in single crystal Li,O
I
I
I
In(t/set) Fig. 4. Nomographic
presentation
950
x)00
1
1o-8 l
Fig. 5. Diffusion
I
of fractional
900
I
I
008
coefficient
850
I
release of tritium
800
I
Y 750
700
1
I
single crystals
650
I
1
IO
11
single crystals
)
as function
550
I
I
in Liz0
(3 runs).
600
I
09 lo3 K T of tritium
from Li,O
of temperature.
I
I
1.2
D. Guggi et al. / Diffusion of tritium in single crystal Liz0 10
I
15
30
60
1
120 min -b
I
In (t/set) Fig. 6. Nomographic
presentation
of fractional
release of tritium
from Li,O
single crystals
using helium containing
traces of water (3
runs).
5. The influence of traces of moisture on the kinetics of the tritium release from Li,O single crystals Some preliminary experiments were performed at the beginning of this study to investigate the influence on the temporal behaviour of the tritium release of traces of water in the sweep gas using tank helium with a water content of - 1 vpm without any drying. Three typical results from experiments performed under these conditions are shown in fig. 6. It is seen from the resulting slopes that neither diffusion nor first order law controlled behaviour can be deduced from these data. Obviously, under these conditions the overall release process is not solely controlled by diffusion within the solid, but chemical processes at the surface also play a role. A pronounced effect of water on the release kinetics of tritium using powdered Li,O-samples, contaminated by water, was earlier found in our laboratory. (see fig. 3 in ref. 6).
fects, which can influence the kinetics of the release of tritium from Li,O, a small neutron dose was chosen to keep the tritium concentration just sufficiently high to carry out reliable measurements. Optical absorption and ESR-studies on electronic lattice defects in neutron irradiated Li,O single crystals have recently been carried out [ l&16,17]. From these studies, annealing times can be estimated which are short compared with the time interval of the initial phase of our experiments. The tritium release during the initial phase of the experiments was not used for detailed data evaluation. If we assume that other irradiation induced lattice defects are annealed at a rate similar to that observed for electronic defects, the diffusivities of tritium in Li,O single crystals obtained in this work can be regarded as being practically unaffected by radiation damage effects. This assumption is also supported by the observation that the diffusivity data obtained during an isothermal release experiment do not show any significant trend with annealing time.
6. Considerations on radiation damage effects
7. Conclusion
During reactor irradiation, lattice defects are generated due to radiation damage. To minimize these ef-
Obviously, details of the transport mechanism of tritium in Li,O cannot be deduced from thermal release
108
D. Guggi et al. / Diffusion of trrtium in single crystal Li,O
measurements. In a different metal oxide-tritium system, namely for tritium in rutile (TiO,) single crystals, a conception of the mechanism pertaining to the diffusional motion of tritium in an oxide host lattice was worked out, which is based on findings from a number of different experimental approaches [ 18,191. From these investigations it is concluded that tritium migrates as the T+ ion, where as the OT- ion is thought to be a rest state of tritium in the lattice. In addition, a second, slow mechanism of tritium diffusion in the form of T,-molecules is believed to play a role. The nature of the state and motion of tritium in Li,O may have some similarities with that suggested for the system rutile-hydrogen isotopes; however, experimental evidence does not yet exist on which a diffusion mechanism can be proposed. Our findings that traces of water change the rate controlling process of the tritium release from the Li,O-surface is in accord with results from a theoretical study of the H,O-Li,O reaction. In this work it is found that the reaction of gaseous H,O with solid Li,O proceeds without activation 1201. From more recent work on the thermal release of tritium from Li,O-powders (commercial products), diffusion coefficients for lower temperature ranges were obtained. If these data are extrapolated to higher temperature e.g. 923 K, the results are D = (1-5) X lo-” cm2s-’ [l] and D = 2.4 x 10e8 cm2s-’ [2] which are compared with the value from the present work D = 6.2 x lo-* cm*s-I. The differences in the data are mainly due to the different types of samples used, and also to some dissimilarities in the methods applied.
Acknowledgement The authors wish to thank A.F. Blair for carrying out the tritium analyses of the Li,O samples and W. Reimer for assistance in the design of the apparatus.
References
[ 1] R. Wiswall, E. Wirsing, BNL 50748 (Oct. 1977). [2] H. Kudo, K. Okuno, J. Nucl. Mater. 101 (1981) 38-43. (31 K. Okula, D.K. Sze, American Nuclear Society National Topical Meeting, Dayton, Ohio, Apr. 29th-May lst, 1980, on: Tritium Technology in Fission, Fusion and Isotopic Applications, Proc. pp 286-292. [4] J.R. Powell, Internat. Conf. on Radiation Effects and Tritium Technology for Fusion Reactors, Gatlinburg/ Term. (USA), Oct. l-3rd, 1975, Proc. Vol. III, pp. 197-231 (CONF-750989). [5] D. Guggi, H.R. Ihle, U. Kurz, D. Brtining, 11th Symp. on Fusion Technol., Oxford (UK), Sept. 15-19th, 1980, Proc. pp 553-558. [6] D. Guggi, H.R. Ihle, U. Kurz, 9th Symp. on Fusion Technol., Garmisch-Partenkirchen (FRG), June 14-18th, 1976, Proc. pp 337-344. [7] H. Kudo, K. Tanaka, H. Amano, J. Inorg. Nucl. Chem. 40 (1978) 363-367. [8] T. Tanifuji, K. Noda, S. Nasu, K. Uchida, J. Nucl. Mater. 95 (1980) 108-118. [9] H. Diinwald, C. Wagner, 2. Phys. Chemie B 24 (1934) 53-58. [lo] T. Akashi, K. Matumi, T. Okada, T. Mitzutani, IEEE Transactions on Magnetics, Vol. MA 6-5, No. 3, (1969) pp 285-289. [ 11) I. Shindo, S. Kimura, K. Noda, T. Kurasawa, S. Nasu, J. Nucl. Mater. 79 (1979) 418-419. [12] D. Guggi, H.R. Ihle, U. Kurz, 10th Symp. on Fusion Technology, Padova (Italy), Sept. 4-9th, 1978, Proc. pp 645-650. [13] D. Guggi, H.R. Ihle, A. Neubert, R. Walfle, Intemat. Conf. on Radiation Effects and Tritium Technology for Fusion Reactors, Gatlinburg/Tenn. (USA), Oct. l-3rd, 1975, Proc. Vol. III, pp 416-432 (CONF-750989). [14] F.T. Miles, R.J. Heus, R.H. Wiswall Jr., BNL 482.91.54 (1954). [15] K. Uchida, K. Noda, T. Tanifuji, S. Nasu, T. Kirihara, A. Kikuchi, Phys. stat. sol. (a) 58 (1980) 557-566. [16] K. Noda, K. Uchida, T. Tanifuji, S. Nasu, J. Nut. Mater. 91 (1980) 234-236. (171 K. Noda, K. U&da, T. Tanifuji, S. Nasu, Physical Review B 24 (1981) 3736-3742. [18] J.B. Bates, R.A. Perkins, Physical Review B 16 (1977) 3713-3722. [ 191 J.V. Cathcart, R.A. Perkins, J.B. Bates, L.C. Manley, J. Appl. Phys. 50 (1979) 41 lo-41 19. [20] K. Raghavachari, J. Chem. Phys. 76 (1982), 5421-5426.
100
DIFFUSION OF TRITIUM IN SINGLE CRYSTAL Li,O D. GUGGI,
H.R. IHLE,
Ke~nfors~~~gsa~~a~e EURATOM-KFA
D. BRijNING,
U. KURZ
Jiilich GmbH, fnstitut fiir Chemie, P. 0. Box 1913, 51713 Ji&h,
Federal Republic of Germany, As~~c~ati~n
and S. NASU
*, K. NODA,
T. TANIFUJI
Japan Atomic Energy Research institute,
Tokai - mura, ~~rak~ - ken, 319 - Ii Japan
Received 28 January 1983; accepted 21 March 1983
The release of tritium from neutron irradiated spherical samples of single crystal Li,O was measured by isothermal annealing experiments. The release is shown to be controlled by diffusion of tritium in the solid under appropriate experimental conditions. Deviations from solely diffusion controlled release were observed when traces of water were present in the He-purge gas used in the experiments. The diffusivity of tritium in single crystal Li,O is given by ln(D/cm*s-‘)=
-(5.93&0.48)-(81.73*4.24)103J/RT
for850K~T
1. Introduction Lithium oxide is regarded as a prime candidate among the solid blanket materials for fusion reactors on account of its favourable tritium breeding properties. A substantiai amount of experimental work has been done
on the release of tritium from Li,O in several laboratories. However, most results from these works do not permit the deduction of diffusivities and the calculation of the mean concentration of tritium in a blanket. Mainly, the un~rt~nties arise from a lack of knowledge as to whether diffusion [ 1,2] within the solid, or chemical reactions at the solid-gas phase boundary, control the release of tritium from Li,O; observed overall rate coefficients are spread over several orders of magnitudes [3]. For the proposed use of ceramic lithium solids [4], it is assumed that the diffusivity of tritium in the solid, which is inversely proportional to the mean residence
* Present adress: USHIO Inc, Harima Himeji-shi, Hyogo-ken, 671-02 Japan. 0022-3 115/83/$03.00
Plant, Eessho-cho,
0 1983 Elsevier Science Publishers
time of a tritium atom at steady state in a blanket, controls the tritium inventory. In earlier work it was experimentally shown that the tritium release from /?Li, A 10, can be described by a diffusion mode1 [5]. Results obtained in earlier work on the release of tritium from finely powdered samples of Li,O, irradiated with thermal neutrons, in our laboratory yielded an exponential decrease of the release rate with time for the “late” release [6]. The values obtained in this work have mistakenly been cited as data for the diffusivity of tritium from Li,O [2,3], because diffusion was not shown to control the tritium release. The samples used up to that time consisted of agglomerations of fine particles of unknown shape and size distribution. In view of the findings from the present investigation, the great discrepancy between the above mentioned earlier results and those obtained in this work is not surprising. Tritium release from neutron irradiated Li,O has been assumed to be controlled by first order kinetics instead of diffusion by several authors [7,8]. The former mechanism has been reported to be frequently observed, if reactions at the surface are controlling the rate of release of gases from solids [9). B.V.
D. Guggi et al. / Diffusionof tritiumin single crystal Li,O
101
2. Experimental
d
2.1. Preparation of single crystals of lithium oxide
Owing to the chemical interaction of molten lithium oxide with all materials in which it could be contained, a crucible free preparation method by floating zonegrowth was used to prepare cylindrical single crystals of Li,O. Apparatus and preparation technique have been described elsewhere [ 10,111.
-b
2.2. Preparation of spherical samples A cylindrical rod (- 8 mm in diameter, - 80 mm in length) of Li,O-single crystal was cut into discs by means of abrasive cut-off blades coated with diamond dust, rotating at - 60 000 rpm. These discs were subsequently cut into cubes, which were thereupon ground into spheres of different diameters by the use of a rotating corundum disc [121. The range of diameters of the spherical single crystals was between 1.77 and 3.15 mm. Mean radii were calculated from the mass and density, assuming ideal spherical geometry. Small deviations from the ideal shape were observed (on the average - 1% difference between the smallest and the greatest diameter measured on a sphere). The samples were first outgassed in open plantinum crucibles in a vacuum of - 4 X 10e4 Pa at a temperature of - 880 K. After this thermal pretreatment, the samples were enclosed in vacuum in platinum cells, together with fragments of single crystals to avoid excessive vaporization, and hermetically sealed. The samples were then heated to - 1280 K over a period of - 8 h; by this procedure a very smooth surface was obtained. For neutron irradiation and subsequent isothermal annealing, the samples were transferred to platinum cells as shown in fig. 1. The lid (a) was fitted with a closed-end pipe (c), extended into the interior of the cylindrical cell (b), for insertion of a thermocouple. These cells, each containing one sample, were hermetically sealed under vacuum. An open capillary (d) attached to the lid was used to evacuate the cell. It was closed finally by electron beam melting. All sample handling was carried out in a dry atmosphere. The sealed samples were then neutron irradiated to yield an atom-ratio T/Li - 5 X lo-’ (fluence: - 6 x lOI cme2, thermal neutron flux: - 6 X 10” cm-2s-‘, epithermal contribution < 250 ppm, fast contribution d 150 ppm).
I
,
10 mm
PLATINUM
- CELL
Fig. 1. Platinum cell, used to contain Li 2O samples,
2.3. Isothermal release experiments The time dependence of the isothermal release of tritium from the neutron irradiated spherical samples was observed by measuring the concentration of the desorbed tritiated species in a flow of helium (at atmospheric pressure) with a proportional counter. Shortly after its contact with the sample, the sweep-gas passed a Zn-reductor in order to reduce tritiated water, which is the predominant molecular species desorbed from the surface of Li,O by thermal annealing. A constant flow of the sweep-gas (5 cm3 helium/mm) was used; methane was admixed in a ratio of 4: 1 after passage of the helium through the reductor. The sample was heated by a RF-generator, the platinum cell serving as susceptor. The cell temperature-attained in approx. 1 minutewas regulated to a constancy of within f2 K. The thermocouple was calibrated by measuring the melting points of lead, aluminium and silver, using cells of similar geometry as the platinum cells. Fig. 2 shows the experimental arrangement, which was described earlier [ 12,131, minor modifications having been made. After pre-purification, the helium sweep gas is led through a liquid-nitrogen trap immediately before it enters the “tritium release unit” (detail “a”, fig. 2). This last purification step proved to be necessary, because an inleakage of traces of water into the helium stream during its passage from the pre-purification unit to the release unit could not be excluded for technical reasons.
t). Guggi et al. / Difjwon
of tritium in single crystal Li,O
-.._____ HEATING
PREPURIFICATION 1
OX I SO&
IMESSER
2
TI-SPONGE
lSm*Cl
3
CHARCOAL-TRAP
GRlESHElM
_
W ii RESISTANCE
I
WH TC
i77Kl
I RAWFREQUENCY :l~~~~~
> HEAT’NG -,
i
FM= FLOW
_.._._~.~ RESULTS
RECORDER
j
/I
METER II
J-----.
‘\
GAS SUPPLY AND PURIFICATION
I
T RELEASE UNIT
-TC
t-
._____ i
ELECTRONICS
_LI_NEAA-MOTIONFEEDTHROUGH
/
’
DETAIL “A” Fig. 2. Ewperimental arrangement for post irradiation annealing experiments using inert gas transpiration method.
The tritium release unit is composed of a system of ~n~nt~caliy mounted quartz and copper tubes (fig. 2, detail “A”). Helium flows first through the interspace between the quartz tubes. After reversal of flow direction, the helium is led over the sample, where tritium species desorbed from the sample surface are taken up. The tritium containing helium then enters the bulge of the “inner quartz tube”, filled with zinc granules, kept at (650 f l)K, and held in position by a wad of quartz wool on both sides. After passage of the sweep gas through the reductor, methane as counting gas is added at a point close to the zinc-reductor to obtain small transit times and to minimize wall-contamination. The
gas mixture is then led through copper tubes held at - 450 K to the proportional counter (volume 10 cm3) kept at the same temperature. At the beginning of an experiment, the loaded platinum cell (fig. 1) was mounted at the top of a linear motion fen-trout (see fig. 2). The tritium release unit was then evacuated to a vacuum of - 4 X lOA Pa for a period of - 6 h, and finally filled with helium. The plantinum cell was then opened by pushing it towards a tungsten tip. The opened cell was subsequently drawn back to a position in the center of the RF-heater coil. The units used for data acquisition are also shown in fig. 2.
103
D. Guggi et al. / Diffusion of tritium in single crystal Liz0 3. Evaluation of data 3.1. Corrections applied to experimental
signal was normally attained after 5-7 min in the “ test-mode”, whereupon the gas flow was switched back to the “measuring-mode”. The corrected data were obtained by subtracting the counter background from the observed signal.
results
3.1.1. Correction for counter-contamination Although most of the T,O(HTO) is reduced to T2(HT) by the zinc reductor, a certain degree of counter-contamination cannot be avoided. To correct the experimental data for this effect, a gas-bypass system was used, which allowed the measurement of the background signal of the proportional counter at any time without impairing the isothermal release experiments. This was realized by diverting the helium-methane gas mixture, before it was led into the counter tube, through a bypass to the exhaust; further, a second gas flow with the same flow rate and mixing ratio was fed into the counter tube. This “test-mode” was used several times during a release experiment. Constancy of background
fraction
3.1.2. Corrections for effects due to the zinc reductor During the passage of the sweep gas through the reductor, chemical reactions between the heated zinc granules and the tritiated species occur. Retention of tritium by the zinc is observed during the initial stage of an experiment; whereas during the “late” release, the retained tritium is partially liberated from the zinc bed to the helium sweep gas. To correct for errors arising from the zinc reductor, each experiment was interrupted when the fractional release (ratio of tritium atoms released to tritium atoms initially contained in the sample) had attained a suffi-
x 100 1) observed
h
#\
10‘ c
\
tritium
corrected
release
curve
2-2a)
curve
for counter
contamination
2-3)
curve corrected for counter zinc reductor effects
contamination
and
‘1 \ i
5 ol
2
I.
lo3 -
lo2 i
I
I
I
I
1
1
2
3
4
5
Fig. 3. Experimental tritium release curve and corrections.
1
time
01)~
I
1
I
I
1
1
1
e
9
10
11
12
D. Guggi ef al. / Diffusion
104
ciently large value by turning off the RF-power. This caused the sample to cool down quickly. All tritium registered after the sample had attained a sufficiently low temperature was assumed to originate from the reductor, which was maintained at a constant temperature. When the reductor temperature is lowered to room temperature, the signal approaches background level. From the observed reduction of the signal by the thermal quenching of the sample, the ratio of the flows of tritium originating from the sample and from the reductor was determined for the time at which the release was interrupted. In this way, one point on the “true” tritium release curve corrected for both counter-contamination and zinc reductor effects was obtained. From there a tangent was graphicafly drawn to the “counter-corrected” logarithm of the release rate versus time curve. The time at which the tangent touches the release curve corresponds to a fractional release of > 0.70. Above this fraction, simple exponential decay of the signal from diffusional tritium release should occur. The relative amount of tritium released from the zinc reductor between time t, and t, (see fig. 3) was found on the average to be - 4% of the tritium initially contained in the sample. After time t,, the amount of tritium released from the zinc reductor was on the average - 8% of the total tritium. In the calculation of fractional release versus time from experimental results, corrected as outlined above, the contribution of fractions of tritium retained by the zinc reductor were taken into account. The use of a zinc reductor, although its disturbing effects can be corrected for, imposes a limitation on the accuracy of the transpiration method used in this work. 3.2. Rate law analysis 3.2.1. Time dependence of fractional release The rate of tritium release is directly proportional to the corrected counting rate during an isothermal postirradiation annealing experiment at constant counting efficiency. The sum of corrected accumulated counts at any time, t, divided by the corrected sum of all counts obtained during the experiment and during a subsequent annealing at - 1280 K for a period of - 6 h, is identical with the fractional release F(t), where F(t)=
l-i
P(t)-c, ccl-
Cf
( !
with c, = initial concentration of tritium in the sample, cr = final concentration; T(t) = average concentration at time t.
of tritium
tn single crystal Li,O
Table 1 Diffusion data obtained by annealing a sphere of R = 0. i 13 at T=1005
ln( t/s) Run 6.98 7.09 7.19 7.27 7.35 7.43 7.50 7.65
em
K.
F(f)%
b(f)
D x 10’
(cm2/s)
(D-5)x10’ (cm2/s)
1.11 1.11 1.11 1.13 1.13 1.16 1.16 1.18 1.18 1.18 1.20 1.13 1.16 1.16 1.16 1.16 1.16 1.13 1.13 1.13 1.13 I.11 1.11 I .09
- 0.03 - 0.03 -0.03 -0.01 -0.01 0.02 0.02 0.04 0.04 0.04 0.06 -0.01 0.02 0.02 0.02 0.02 0.02 - 0.01 -0.01 -0.01 -0.01 -0.03 -0.03 -0.05
1
7.78 7.90
8.01 8.10 8.41 8.59 8.75 8.88 9.00 9.10 9.29 9.44 9.51 9.69 9.80 9.89 Average:
29.8 31.3 32.8 34.2 35.5 36.8 38.1 41.0 43.6 46.0 48.1 50.1 55.1 60.0 63.7 66.8 69.5 71.9 76.1 79.1 82.6 85.0 87.1 88.7 o=
- 1.12 - 1.06 - 1.01 - 0.97 - 0.92 - 0.88 - 0.84 - 0.76 - 0.69 - 0.63 - 0.57 - 0.52 -0.39 - 0.29 -0.21 -0.15 - 0.09 -0.04 0.05 0.12 0.19 0.25 0.29 0.34
1.14kO.03
(cm’/s).
Minute amounts of tritium retained in the samples after completion of an experiment were determined by liquid scintillation counting of the tritium content of the outgassed samples. The residual amount of tritium was found to be smaller than 40 ppm of the initial content in all experiments. The release of tritium from neutron irradiated Li,O may be considered to consist of at least two processes: the transport through the bulk of the solid and subsequent desorption from the surface of the sample. Which of these two consecutive steps controls the overall process of the tritium release will depend on the magnitudes of the rate constants of the individual processes and on the volume to surface ratio of the samples. The experimental conditions were chosen so that the tritium release is likely controlled by diffusion. To this aim, the following suppositions were verified: careful degassing of the samples in vacua to remove traces of water, cryogenic removal of minute amounts of moisture from the helium sweep gas and choice of a reasonably long
D. Guggiet al. / Diffusionof tritiumin diffusion path by using a proper volume to surface ratio of the samples. Using samples of relatively large radii also enables one to carry out the experiments in a temperature range where annealing times for radiation damage effects can be assumed to be small. Since the chemical form in which tritium is desorbed from the single crystal surface is not related to the diffusion process within the bulk of the material, no attempt was made to distinguish between T,(HT) and T,O(HTO). 3.2.2. Nomographic description of diffusional release A proof of whether diffusion is the rate determining step can conveniently be obtained by use of a nomogram which is constructed in the following way [5]: The time dependence of the fraction removed, F(r), for spherical sample geometry and diffusivities independent of concentration, is expressed by:
with X = D/R2. Boundary conditions are: homogeneous distribution of tritium within the sample for t = 0, and concentration at the sample surface is assumed to be zero for t > 0. Experimentally obtained F( r)-values are transformed to cp(r)-values by the use of eq. (2): P(t)=l--$
E
lexp
o-l o2
-
i
u2Tr3’p2( t)
.
36
i
(4
Eq. (2) originates from a combination of eq. (1) with eq. (3) which can be used approximately instead of eq. (1) in the range of low fractions (F(r) < 0.25), where F(t)
-ln[l
Experimental data from three runs out of a total of range from 8, which were made in the temperature 850 K to - 1200 K, are shown in fig. 4, where calculated data for diffusion controlled release (solid lines) are compared with experimental results (dotted least square lines). Also indicated are calculated data for a first order law controlled release mechanism
= kt,
-I]
(4)
k is the rate constant. It is seen that the slopes of the regression lines from the data of the three runs, shown in fig. 4, are close to + l/2 over a range of 0.30 5 F(t) 5 0.90. Data for release fractions outside this range are not used for the evaluation because of disturbing effects at the beginning and in the late phase of an experiment. Numerical values for the data shown in fig. 4 are given in table 1. Here, F(t), In t and the resulting diffusion coefficient for each point of the release curve for run 1 are given as example. The deviations of the diffusivities from their average value are also given in this table; they are small and do not exhibit any significant systematic trend, which proves the presence of a diffusion controlled process. The resulting slopes for all 8 runs are given in table 2. From these results, we conclude that diffusion is the rate determining step for the tritium release under our experimental conditions. The temperature dependence of the diffusion coefficient of tritium in Li,O single crystals obtained in this work is given by eq. (5) and shown in fig. 5; numerical values are given in table 2. A 3 u-error is quoted in eq. (5) to take into account the uncertainties arising from the various corrections (see section 3.1) applied to the experimental data: ln( D/cm2 s-
’)
= - (5.93 5 0.48) - (81.73 f 4.24)103J/RT,
(5)
for850K~T~1200K(R=8.314JK-‘mol-‘).
Table 2 Diffusivity temperature
4. Experimental results
105
(hatched lines). The magnitudes of the rate coefficients for this latter mechanism were chosen so as to fit in the range of the release rates observed by experiment. The time dependence of the fraction removed, F(t), for a first order law controlled reaction is expressed by
- cp(t) 1141.
A plot of lncp( t) versus lnt yields a straight line with the slope + l/2 for a diffusion controlled process.
single crystal Li,O
of tritium
in single
crystal
Li,O
as function
Run
T(K)
D(cm’/s)
R (cm)
Slope
la 2 3 4 5 6 I 8
1005 1103 1200 901 1054 956 858 1151
(1.14*0.03)x 10-7 (2.91+0.25)x lo-’ (7.84*0.70)x 10-7 (5.19*0.52)x10-* (2.65~0.4O)XlO-’ (1.12~0.05)XlO-’ (2.77+0.17)X lo-’ (5.68f0.62)XlO-’
0.113 0.127 0.156 0.112 0.116 0.114 0.089 0.149
0.494 f 0.002 0.455 f 0.001 0.436 f 0.002 0.569 f 0.002 0.603 f 0.002 0.519*0.001 0.502 f 0.003 0.563 f 0.002
’ See table 1.
of
D. Guggi et al. / Diffusion
106
120 min 4
60
30
15
10
of tritium in single crystal Li,O
I
I
I
In(t/set) Fig. 4. Nomographic
presentation
950
x)00
1
1o-8 l
Fig. 5. Diffusion
I
of fractional
900
I
I
008
coefficient
850
I
release of tritium
800
I
Y 750
700
1
I
single crystals
650
I
1
IO
11
single crystals
)
as function
550
I
I
in Liz0
(3 runs).
600
I
09 lo3 K T of tritium
from Li,O
of temperature.
I
I
1.2
D. Guggi et al. / Diffusion of tritium in single crystal Liz0 10
I
15
30
60
1
120 min -b
I
In (t/set) Fig. 6. Nomographic
presentation
of fractional
release of tritium
from Li,O
single crystals
using helium containing
traces of water (3
runs).
5. The influence of traces of moisture on the kinetics of the tritium release from Li,O single crystals Some preliminary experiments were performed at the beginning of this study to investigate the influence on the temporal behaviour of the tritium release of traces of water in the sweep gas using tank helium with a water content of - 1 vpm without any drying. Three typical results from experiments performed under these conditions are shown in fig. 6. It is seen from the resulting slopes that neither diffusion nor first order law controlled behaviour can be deduced from these data. Obviously, under these conditions the overall release process is not solely controlled by diffusion within the solid, but chemical processes at the surface also play a role. A pronounced effect of water on the release kinetics of tritium using powdered Li,O-samples, contaminated by water, was earlier found in our laboratory. (see fig. 3 in ref. 6).
fects, which can influence the kinetics of the release of tritium from Li,O, a small neutron dose was chosen to keep the tritium concentration just sufficiently high to carry out reliable measurements. Optical absorption and ESR-studies on electronic lattice defects in neutron irradiated Li,O single crystals have recently been carried out [ l&16,17]. From these studies, annealing times can be estimated which are short compared with the time interval of the initial phase of our experiments. The tritium release during the initial phase of the experiments was not used for detailed data evaluation. If we assume that other irradiation induced lattice defects are annealed at a rate similar to that observed for electronic defects, the diffusivities of tritium in Li,O single crystals obtained in this work can be regarded as being practically unaffected by radiation damage effects. This assumption is also supported by the observation that the diffusivity data obtained during an isothermal release experiment do not show any significant trend with annealing time.
6. Considerations on radiation damage effects
7. Conclusion
During reactor irradiation, lattice defects are generated due to radiation damage. To minimize these ef-
Obviously, details of the transport mechanism of tritium in Li,O cannot be deduced from thermal release
108
D. Guggi et al. / Diffusion of trrtium in single crystal Li,O
measurements. In a different metal oxide-tritium system, namely for tritium in rutile (TiO,) single crystals, a conception of the mechanism pertaining to the diffusional motion of tritium in an oxide host lattice was worked out, which is based on findings from a number of different experimental approaches [ 18,191. From these investigations it is concluded that tritium migrates as the T+ ion, where as the OT- ion is thought to be a rest state of tritium in the lattice. In addition, a second, slow mechanism of tritium diffusion in the form of T,-molecules is believed to play a role. The nature of the state and motion of tritium in Li,O may have some similarities with that suggested for the system rutile-hydrogen isotopes; however, experimental evidence does not yet exist on which a diffusion mechanism can be proposed. Our findings that traces of water change the rate controlling process of the tritium release from the Li,O-surface is in accord with results from a theoretical study of the H,O-Li,O reaction. In this work it is found that the reaction of gaseous H,O with solid Li,O proceeds without activation 1201. From more recent work on the thermal release of tritium from Li,O-powders (commercial products), diffusion coefficients for lower temperature ranges were obtained. If these data are extrapolated to higher temperature e.g. 923 K, the results are D = (1-5) X lo-” cm2s-’ [l] and D = 2.4 x 10e8 cm2s-’ [2] which are compared with the value from the present work D = 6.2 x lo-* cm*s-I. The differences in the data are mainly due to the different types of samples used, and also to some dissimilarities in the methods applied.
Acknowledgement The authors wish to thank A.F. Blair for carrying out the tritium analyses of the Li,O samples and W. Reimer for assistance in the design of the apparatus.
References
[ 1] R. Wiswall, E. Wirsing, BNL 50748 (Oct. 1977). [2] H. Kudo, K. Okuno, J. Nucl. Mater. 101 (1981) 38-43. (31 K. Okula, D.K. Sze, American Nuclear Society National Topical Meeting, Dayton, Ohio, Apr. 29th-May lst, 1980, on: Tritium Technology in Fission, Fusion and Isotopic Applications, Proc. pp 286-292. [4] J.R. Powell, Internat. Conf. on Radiation Effects and Tritium Technology for Fusion Reactors, Gatlinburg/ Term. (USA), Oct. l-3rd, 1975, Proc. Vol. III, pp. 197-231 (CONF-750989). [5] D. Guggi, H.R. Ihle, U. Kurz, D. Brtining, 11th Symp. on Fusion Technol., Oxford (UK), Sept. 15-19th, 1980, Proc. pp 553-558. [6] D. Guggi, H.R. Ihle, U. Kurz, 9th Symp. on Fusion Technol., Garmisch-Partenkirchen (FRG), June 14-18th, 1976, Proc. pp 337-344. [7] H. Kudo, K. Tanaka, H. Amano, J. Inorg. Nucl. Chem. 40 (1978) 363-367. [8] T. Tanifuji, K. Noda, S. Nasu, K. Uchida, J. Nucl. Mater. 95 (1980) 108-118. [9] H. Diinwald, C. Wagner, 2. Phys. Chemie B 24 (1934) 53-58. [lo] T. Akashi, K. Matumi, T. Okada, T. Mitzutani, IEEE Transactions on Magnetics, Vol. MA 6-5, No. 3, (1969) pp 285-289. [ 11) I. Shindo, S. Kimura, K. Noda, T. Kurasawa, S. Nasu, J. Nucl. Mater. 79 (1979) 418-419. [12] D. Guggi, H.R. Ihle, U. Kurz, 10th Symp. on Fusion Technology, Padova (Italy), Sept. 4-9th, 1978, Proc. pp 645-650. [13] D. Guggi, H.R. Ihle, A. Neubert, R. Walfle, Intemat. Conf. on Radiation Effects and Tritium Technology for Fusion Reactors, Gatlinburg/Tenn. (USA), Oct. l-3rd, 1975, Proc. Vol. III, pp 416-432 (CONF-750989). [14] F.T. Miles, R.J. Heus, R.H. Wiswall Jr., BNL 482.91.54 (1954). [15] K. Uchida, K. Noda, T. Tanifuji, S. Nasu, T. Kirihara, A. Kikuchi, Phys. stat. sol. (a) 58 (1980) 557-566. [16] K. Noda, K. Uchida, T. Tanifuji, S. Nasu, J. Nut. Mater. 91 (1980) 234-236. (171 K. Noda, K. U&da, T. Tanifuji, S. Nasu, Physical Review B 24 (1981) 3736-3742. [18] J.B. Bates, R.A. Perkins, Physical Review B 16 (1977) 3713-3722. [ 191 J.V. Cathcart, R.A. Perkins, J.B. Bates, L.C. Manley, J. Appl. Phys. 50 (1979) 41 lo-41 19. [20] K. Raghavachari, J. Chem. Phys. 76 (1982), 5421-5426.