V. J. WHEELER UKAEA,
tritium tracer measurements. the equation D=O.O37 The
The data are fitted by
O,4 pug Hz/g defauts
exp - (14300 & 900 calories/RT)cm2/s. of hydrogen
Les donnees obtenues satisfont a l’equation:
D = 0,037 exp - (14300 *
The diffusion of hydrogen has been measured in UOz single crystals in the temperature range 500-1000 (i) vacuum-extraction, using two techniques:
900 calories/RT)cm2/s. varie entre
de la structure
wurde zwischen 500 und 1000 “C nach zwei Methoden,
0.4 ,ug Hz/g UOZ, depending upon the defect structure
of the UOz crystal.
und durch Tracermessungen Aus
die Gleichung La diffusion de l’hydrogene monocristaux
de temperatures 500-1000 1) l’extraction
a ete mesuree dans des d’UOz,
Die Loslichkeit von Wasserstoff
0,03 und 0,4 pg Hz/g UO2 und hiingt von der Defekt-
“C, en utilisant 2 techniques:
sous vide, 2) des mesures par le traceur
0,037 exp - (14300 f
The present paper describes an experimental study to remedy this gap in our knowledge of an increasingly important nuclear fuel.
A considerable volume of work has now been published on diffusion phenomena in uranium dioxide. Both cation and anion self-diffusion have been studied in great detail, and work
on oxygen diffusion in temperature, electrical and chemical potential gradients has also been described. Fission product migration has been the subject of a number of investigations. A somewhat surprising omission is the absence of any investigation of the solubility and diffusion of hydrogen in UOs. The final stage in the preparation of UOs fuel pellets often involves sintering in hydrogen at - 1650 “C, yet despite some evidence for hydrogen solubility reported by Roberts I), no attempt has previously been made to measure the solubility, nor the rate of diffusion through UOs, although hydrogen solubility and diffusion in a number of other oxides (for example SiOs, TiOs and ZnO) have been reported.
2.1. MATERIALS UOs crystals were obtained as grown from the vapour phase at Mol, Belgium 7, the impurities determined spectrographically being Cr < 50, TiZn< 20, FeCo < 10, Ni 5, all others < 5 ,ug/g. Experiments were carried out on four separate crystals ground to the form of spheres (about 1 mm radius) in order to simplify the mathematical treatment. It was found that the crystals were undamaged during the experiments, and so could be used for a number of separate runs. The gas used for the vacuum extraction experiments was British Oxygen Company “high purity” (99.99%) cylinder hydrogen. For the tritium tracer experiments, B.O.C. 189
V. J. WHEELER
with 1 curie of tritium
the Radiochemical Centre, to each 1 litre flask. 2.2. 2.2.1.
determination carried out. The sequence of operations
fig. 1. Analysis of the gas evolved from the UOs crystal by means of adsorption by a
UOZ crystal could be calculated. Finally, this gas was pumped off and a final “blank”
The selected crystal was prepared by heating in a stream of hydrogen at the required temperature (670-1000 “C) for several hours, and then rapidly cooled by tilting the furnace tube so that the crystal fell into a collector at room temperature. It was then transferred to the analytical apparatus, which consisted of a silica or mullite tube connected to a vacuum system, and incorporated a McLeod gauge (for accurate pressure measurements) and a Pirani gauge, the signal of which was recorded continuously on a Honeywell recorder. The furnace tube was outgassed at the temperature of the experiment, until a constant “blank” leak rate was obtained when the pumps were switched off. The UOs crystal was then dropped into the furnace tube and the hydrogen evolution followed until the recorder trace showed that the “blank” leak rate had again been reached. The pressure in the system was then measured with the McLeod gauge, from which the total quantity of hydrogen in the
palladium wire and by mass spectrometry showed that it consisted entirely of hydrogen. 2.2.2.
The selected crystal was heated in hydrogen/ tritium at the required pressure (0.1-0.9 x 105 N em-s) and temperature (500-750 “C) in a, vacuum system for several hours and then rapidly cooled as before. It was then transferred to the side-arm of a furnace tube, the furnace being maintained at the required temperature (again, 500-750 “C), and the tube swept with flowing argon (99.995% purity). The exit gas was mixed with a stream of carbon dioxide (99.5% purity) to give a mixture A : COs = 95 : 5, with a total flow rate of 100 ml/min, and passed F. 0111 gas-flow proportional into a “Panax” counter, which has a counting efficiency of about 65% for sHs. After measuring the background count rate (usually 3-4 counts per minute), the UOs crystal was tipped from the side-arm into the furnace tube, and the count rate measured.
TIME(S) Fig. 1.
Typical recorder chart plot
for vacuum extraction of hydrogen from UOz single crystal (radius 1.30 mm) at 1000 “C.
The rate of diffusion of tritium from the crystal was thus determined, and the total number of counts obtained in each experiment gave a measure of the hydrogen content of the crystal, which could be compared with the pressure and
stirred fluid of infinite volume:
,“z>y -$exp -
temperature of treatment. The absolute correlation of gas count rate with total quantity of hydrogen was determined by counting a measured
pleted at time t(s) D = diffusion coefficient
(cm2 . s-1)
a = radius of sphere (cm).
Experimental values of 01 (fraction of the diffusion process completed) as a function of time, for various crystals at various temperatures, are shown in fig. 2. These curves have, of course, all been corrected for the “blank” or background corresponding to each run. There are no individual experimental points for the vacuum extraction curves, since these have been derived from continuous recorder chart plots. The experimental data were analysed by the mathematical treatment described by Crank s), assuming diffusion from the crystal into a well-
A calibration plot of 01 against Dt/a2 may be constructed from this equation (see ref. 3, figure 6.4), leading to a plot of Dt/a2 against time, the required values of Dt/a2 being taken from the corresponding values of oc at the appropriate experimental time t. Figure 3 shows some plots of Dt/a2 against time. If eq. (1) is obeyed, these should be straight lines through the origin, of slope Dla2, from which D can be calculated. Figure 3 shows that the equation is, in fact, fairly closely followed - deviations may be due to (i) imperfect roundness of the spheres (ii) the difficulty of determining t = 0 exactly, since the crystals take a finite time to reach the temperature of the furnace, and- in the case of the tritium experiments-the sweep gas takes tracer N 10 set to pass from the furnace to the counter. In practice, errors introduced by these effects must be very small. (iii) A larger error in the 1rlacuum extraction experiments is
Fraction of diffusion process completed (a) function of time, for various crystds and temperetures.
Dt/az as &function
of time, derived from fig. 2.
by the response of the Pirani gauge
and the comparatively high “blank”. In the tritium tracer experiments the recording of N lo4 counts in a typical experimental run, and the very low background obtained with the counter, gives reliable values for LY, and correspondingly more accurate values for D. Within experimental error, the diffusion coefficient was found to be independent of the temperature and pressure of saturation of the
widely between limits of about 0.03-0.4 ,ug Hz/g UOs, with no simple correlation with the temperature and pressure of treatment. No systematic measurement of temperature or pressure-dependence was possible therefore, the reasons for which are suggested below. The surface area of the crystals used was N 2 x 10-4 m2.g-l, so that surface adsorption of hydrogen
crystal, and to depend only upon the temperature of hydrogen/tritium removal. Figure 4 shows values of D as a function of temperature, where it is seen that agreement between the two experimental techniques, and from crystal to crystal, is extremely good. From least squares analysis of the data the diffusion coefficient is given by:
must have contributed only a Trerysmall amount to the total. When at the completion of a diffusion experiment, the crystal was heated to a higher temperature, a further release of hydrogen was sometimes observed. This too did not appear to depend in any regular manner on the preparative conditions, but was usually N 5-15o/o of the “normal” hydrogen release.
D = 0.037 exp
- (14300 & 900 calories)/M’
!+-I) Fig. 4. Diffusion of hydrogen in UOz single crystals. Open symbols : vacuum extraction. Closed symbols : tlitium
represent different crystals.
The results show a pattern of very rapid diffusion of hydrogen through the UOs structure, but very low - and irreproducible - solubility. The explanation of these facts lies in a detailed consideration of the crystal structure. UOs has the face-centred cubic (fluorite type) lattice, with a=O.547 nm. It has a wide range of composition over the single phase region (UOs+%) in which oxygen dissolves interstitially, up to a limit ICN 0.2 at 1000 “C. At higher temperatures (> 1500 “C) oxygen may be lost from the structure (to give U02_z), while maintaining the single phase. Neutron diffraction measurements have shown that nearly stoichiometric UOs contains a balance between vacancies on normal anion sites and interstitial anions, the two types of defect ordering into “clusters” in different regions of the crystal 4). The interstitial oxygen is not accommodated in the 8 i + position in the unit cell, but at two sites slightly displaced from it. The thermodynamic properties of UC2 change very rapidly near to the stoichiometric composition, and discrepancies between different sets of measurements have been ascribed to differences in the balance between anion vacancies and interstitials from sample to
using a galvanic cell technique have shown that
specimens etc. 5). Now the radius of the hydrogen molecule (0.12 nm) is slightly smaller than that of an oxygen ion (0.14 nm), and it is reasonable to
even with such small differences in composition there are detectable differences in the thermodynamic properties 12). This factor is probably the cause of the variable hydrogen solubility
suppose that the hydrogen molecule ean enter a vacant or unoccupied interstitial anion site,
results : small, undetectable variations O/U ratio and the vacancy/interstitial
without altering the uranium valency, and diffuse through the structure by a vacancy/ interstitial mechanism. An analogous mechanism has been proposed to explain the diffusion of hydrogen through zirconia 6). ESR examination of UOs crystals, heated in hydrogen and then irradiated by y-rays at 78 K, shows no signal due to hydrogen atoms 7), suggesting that the hydrogen is present as molecules (hy~ogen atoms have been detected by this technique in CaFa 8) and MgO9)). The additional release of hydrogen on further heating of the crystal is evidence for more than one type of site, which may he related to the choice between vacancies and interstitials. It is conceivable that - OH groups may be formed, under circumstances involving a valency change of the uranium, but unfortunately it is not possible to test this directly by infrared s~etroscopy due to the high absorption of UOa, although this technique has been successfully applied to SiOa 10) and TiO:! ii) at this level of hydrogen content, and in these cases the -OH group is usually associated with a lower valency cation imp~ity, such as Ala-t or Fea+. In the present experiments, the low
balance, arising from the preparative conditions, will influence the number of sites available in the structure. The very low saturation concentration of hydrogen suggests that only a few sites are available in any ease, but the mobility of the hydrogen molecule is sufficiently high that its diffusion is not significantly hindered. It is somewhat surprising that hydrogen can move so readily from site to site, yet more hydrogen apparently cannot dissolve in the structure. This behaviour is also observed for SiOs and TiOs. Further evidence for this explanation is that the hydrogen content of UOZ crystals heated at 1000 “C in dry hydrogen is always greater than that of crystals heated in hydrogen which has first been bubbled through water at room temperature, a phenomenon which has also been observed for zirconia”). Evidently the slightly higher oxygen potential of the watersaturated hydrogen facilitates an increase in the interstitial oxygen ion concentration of the UOa, although this is not detectable by the
activation energy for diffusion, and the variable hydrogen content from experiment to experiment, suggest that impurities are not significantly involved in the case of UOa. It should be noted that even the upper limit for hydrogen solubility (0.4 pg/g UOa) only corresponds to 1.4 x lOr*Ha molecules/cma, or about 1 hydrogen molecule in every 5000 UOa unit cells. If this number of interstitial oxygen ions were added to stoichiometric UOz, the O/U ratio would only be increased to 2.00006: this is beyond the limits of control or detection by present preparative or analytical techniques (i 0.0005), but careful coulometric titrations
in hydrogen gas may contain up to 2-3 ,ugHaj g UOz ; some of this will be present as “dissolved” hydrogen, but most will be trapped in closed pores or at grain boundaries. For a pellet with 5% closed porosity, if these pores are filled with hydrogen this will correspond to N 0.4 pg/g UOZ -a level about the same as the upper limit for the “lattice” solubility already discussed. It is diRicult to estimate the quantity trapped at grain boundaries, and one can only speculate as to the mechanism here, but the high defect concentration may allow comparatively high hydrogen solubility : the present results suggest l-2 E*lg/g.
on the thermal treatment
in the anion
available techniques. These results have some significance for the commercial production of UOz. Pellets sintered
is such that most
this gas will be released on heating to “C in vacuum or in an inert gas stream, 20% may be retained, and is likely to but be released subsequently during irradiation. Our N 500
experiments suggest that if O/U> 2.00 the hydrogen content will be reduced; on the other hand, if O/U < 2.00, uranium metal will probably be precipitated on cooling, leading to much higher hydrogen contents, owing to its high solubilitv in uranium or. conceivablv. to the formation of uranium hydride. Yl
J. Crank, The Mathematics University
of Diffusion (Oxford
Press, 1956) p. 86
B. T. M. Willis,
6) C. E. Holley (ed.), Thermodynamic and Transport Properties
6, T. Smith, J. Nucl. Mater. 18 (1966) 323 7)
A. J. Tenth (Harwell)
and J. F. J. Kibblewhite,
8) J. L. Hall and R. T. Schumacher, Phys. Rev. 127 (1962) 9)
Chem. Solids 26 (1965)
and J. M. Stevels, Phys. Chem. Glasses 3 (1962) 69
The author would like to thank Mr. A. Parker and Mr. T. J. Webber for help with the vacuum extraction experiments.
11) G. J. Hill, British J. Applied 1151;
J. Chem. Sot.
P. I. Kingsbury, 1s)
T. L. Markin and R. J. Bones, UKAEA AERE-R.
L. E. J. Roberts,
10) A. Kats, Thesis, Delft, 1961; A. Kats, Y. Haven