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DIFFUSION D’ESPÈCES ATOMIQUES ET IONIQUESRARE GAS ATOMS IN IONIC
CRYSTALS : METHODS, RESULTS AND APPLICATION TO THE STUDY OF LATTICE
DEFECTS
F. Felix
To cite this version:
F. Felix. DIFFUSION D’ESPÈCES ATOMIQUES ET IONIQUESRARE GAS ATOMS IN IONIC CRYSTALS : METHODS, RESULTS AND APPLICATION TO THE STUDY OF LATTICE DE- FECTS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-149-C9-158. �10.1051/jphyscol:1973929�.
�jpa-00215404�
RARE GAS ATOMS IN IONIC CRYSTALS : METHODS, RESULTS AND APPLICATION TO THE STUDY OF LATTICE DEFECTS
F. W. FELIX
H a h n - M e i t n e r Institute f o r Nuclear Research Berlin G m b H . D 1 Berlin (West)
Rksumk. - Depuis la preliiiere preparation de I'lielium par degazage des lnineraux d'uraniurn en 1895, les systemes gazisolide ont rencontri: un grand interkt en science et en technologic (par exemple la metliode d'emanation selon Hahn, la determination de 1'5ge geologique des rninkraux d e potassium, le coniportement des gaz de fission dans les combustibles nucleaires). Dans les dix dernieres annees, le transport atomique de Ar, Kr et Xe dans les cristaux ioniques de structure cubique (des types NaCI, CsCl et C a F 2 ) a ete intensivement etudie. Ce rapport resume la litterature publiee jusqu'a aujourd'liui, relative i I'introduction d'atomes de gaz rares par reaction nucleaire des composants des cristaux. Les d e ~ ~ x resultats les plus importants sont que les gaz rares sont mobiles dans la plupart des systemes conime interstitiels et qu'ils peuvent reagir avec des defauts cristallins tels que les lacuncs cationiques (introduites soit par action thermique, soit chirnique- rnent) ou les defauts introduits par irradiation.
Les lnethodes pour la dCterniination de la mobiliti. des gaz avec !'aide des traceurs radioactifs sont brievement decrites ; les rksultats significatifs sont presentes en sonimaire et comparCs avec les rksultats theoriques de Norgett et Lidiard.
Abstract. - Ever since the preparation of the first terrestrial helium by degassing uraniurn- minerals in the year 1895 rare gas/solid systen~s have been of interest in science and technology (e. g. the Hahn emanation nietliod, the determination of the geological age of potassium minerals, the behaviour of fission gases in reactor fuels).
I n the last ten years a fundamental aspect, namely tlie atomic transport of Ar, Kr and Xe in simple cubic ionic crystals (alkali halides of NaCI- and CsCI-structure, and alkaline earth fluorides of CaF2-structure) has been studied tlioro~~glily. This paper gives a survey of the hitherto published literature, however, witli emphasis on the work based on tlie introduction of rare gas atoms by transfornlation of lattice components with r i ~ ~ c l e a r reactions.
The two main features of these investigations are that tlie gas atoms are mobile in most cases a s interstitials and that they react with lattice defects. Such defects may be e. g. thermally o r chemi- cally introduced cation vacancies and radiation induced defects.
The experimental technique to determine tlie gas mobility with tlie help of radioactive tracers is briefly described. Tlie main experimental results are summarized and compared witli the calcu- lations of Norgett and Lidiard.
0. Introduction. - T h i s paper gives a survey o n the literature published o n t r a n s p o r t measurenients of gas a t o m s i n simple cubic ionic crystals. Tlie emphasis is o n t h e w o r k based o n introduction of radioactive gas a t o m s by nilclear reactions \vith reactor neutrons.
Section 1 gives a n historical account o f tlie devclop- ment of this field a n d its connections t o technological and cosmologicnl investigations. Section 2 describes the fundamental expcriment:~l techniques for gas production a n d mcnsurcrnent o f gas release together with a c o r n p a r i s o n with o t h e r gas introducing methods.
as ion b o m b a r d m e n t . recoil irijection. etc. Section 3 outlines the evaluation of' gas release n i e a s ~ ~ r e ~ n e n t s . Section 4 sumniurizes thc r c s i ~ l t s 01' g a s transport in alkalihalides a n d i ~ l k a l i n e e:~rth fluorides both :~l.ter low irradiation doses in pure crystals a n d in crystals with high defect conccntrations. In section 5 conclu- sions a r e d r a w n by cornparin: the euperimental rcsults with t h e model : ~ n d the calculated v:tlues of' Norgctt and Lidiard.
I. Historical development and motivation. - T h e fundamental studies o n gas transport in ionic crystals described in this paper a r e part o f a large c o m p l e x o f investig;~tions o n gas containing solids (Table I). T h e historical starting point may be set t o the year 1895
\\,hen R a m s a y a n d Raleigh isolated t h e first terrestrial helium by 1ie:iting uranium miner;~ls. In 1900, R u t h e r - ford observed that R ~ I samples continuously e m i t a
~ x i i o a c t i v e gas namely R n . Latcr, H a h n a n d Miiller could establish a relationship between t h e so-called e m a n a t i o n power of n solid a n d its specific surface.
This l-fnhn e m a n a t i o n method could be a n d still is used t o cl~nractcri/.c solids :~l'tcr :I theoretical base had heen given by Fliigge a n d Zinicn [I]. These a u t h o r s showed. that tlic Rn-releasc is partly d u e t o recoil o f I'reshly l~ormcd g a s :itoms a n d partly t o d i f u s i o n t o the surface. With thc beyinning of t h e nuclear age, reactors bccamc the i n s t ~ . ~ ~ m c n t s . which not only m a d e a w r i c t g of new gas riuclitlcs casily avail:tble, but also h1.0~1g11 t L I ~ scvcrc tccIi~ioIogic;~I problems d u e t o
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973929
C9-150 F. W. FELIX formation of large amounts of the fission gases K r and Xe in solid reactor fuels and He production in structural materials. Without going into detail, topics like atomic transport, interaction of gas atoms with radiation induced defects, formation of gas bubbles at high gas concentrations have had to be studied. The motivation to study the same phenomena with ionic crystals lies in the fact that these systems are experi- mentally much easier to handle and also theoretically easier to characterize than the technological materials are up to date.
Also another method, the determination of the geo- logical age of minerals can be traced back to the classical times of nuclear science : Already Rutherford explained that the He content in natural U and Th minerals is of radiogenic origin and thus a measure for the time of existence that the mineral spent in solid state. Since 1927 many other systems have been inves- tigated, also with non-gaseous radiogenic partners.
But obviously have radiogenic gases the great advan- tage to be most easily separable from the solid material. This advantage, however, turns into the most important drawback, as any release before the age determination may pervert the result. This is another motivation to study the transport behaviour of gases.
2. Experimental techniques. - 2 . 1 NUCLEAR CHE- MISTRY OF THE INVESTIGATED SYSTEMS. - 2.1 . 1 GUS producing reactions. - Figure 1 summarizes the possi- bilities for gas producing neutron reactions in the relevant part of the periodic system of the elements.
He, Ne and Rn are not available for the method of radioactive gas release measurements, being non- radioactive, of too short a half-live or product of an artificial element resp. As only some general remarks
FIG. 1. - Neutron reactions leading t o radioactive rare gas nuclides with t l , ~ > 1 h.
containing material the gas concentration. During irradiation this concentration increases continuously, often to such amounts that a second neutron activation produces detectable amounts of a radioactive gas nuclide.
- By the fission reaction several Kr and Xe isotopes are formed amongst a large variety of other nuclides.
However, any fissile material does not contain after a decay period of about five days after neutron-irradia- tion any radioactive gas but Xe-133. An unambiguous assay of fission K r is possible with Kr-88, the only Kr-isotope with a radioactive daughter product.
are given here, the reader is referred for details to [2] : 2 . 1 . 2 Gas ~??ixtures. - Different combinations of
- (n, p)- and (n, u)-reactions on alkali and alkaline the gas producing reactions are possible and offer an earth elements need fast neutron irradiation. important opportunity to gain information on gas
- The (n, 7)-reaction on halogen elements works transport mechanism :
with thermal neutrons. Every activated halogen is - pure alkali halides : reaction (1) and (3) always transformed by j--decay into a stable rare gas nuclide occur simultaneously, however, KI and RbI are most and it is this reaction which determines in any halogen suited to form Ar/Xe and Kr/Xe mixtures ;
Classical and n?odertz aspects of m e gaslsolid systenzs 1895 Ramsey and Raleigh Isolation of He from Cleveite
1900 Rutherford Solid Ra compounds emit Rn
1927 Rutherford Radiogenic He as geological clock
1932 Hahn and Miiller Hahn emanation method
1939 Fliigge and Zimen Theory of Hahn's emanation method
1942 Zimen Artificial nuclides in emanation studies
> 1942 Nuclear age Xe-135 as reactor poison
Reactor fuel swelling due to fission K r and Xe Void formation
He embrittlement of structural materials due to (n, a)-reactions in high flux reactors
Solar wind experiments in the Apollo program
> 1969 Space age
- mixed alkali halides : usually any gas mixture from reactions ( I ) in mixed halides is easily separated by analysing the radioactive decay curve of a gas sample. Only in the case of a mixture of the long- living Ar-39 and Kr-85 a chromatographic separation becomes necessary ;
- U-doped alkaline earth fluorides : these crystals take sufficiently enough U4' into the lattice, so that fission K r and Xe can be introduced besides tlie (n, cr)-gases.
2. 1 . 3 Nuclenr r l o l ~ i i i g \r9itli ulioiwlctlt e/et?lci1t,v. -
Up to date n o el-Tect of tlie formation of non-gaseous impurities on the defect structure of irradiated ionic crystals has been studied. This is certainly due to tlie fact that the concentration is usually much smaller than the natural concentration of impurities (e. g.
transformation of K after neutron-activation into Sr by 1-decay).
3 . 2 OTHER GAS INTRODUCING METHODS. -
2 . 2 . 1 Honrogri~eotts gris c/i.strihutiotl. - Besides the already mentioned production of fission gases in situ of U-containing materials, one also may isolate fission iodine from tlie bulk of fission products, add it in a suitable form to an iodine containing material and let it decay to Xe. This method has a n important advan- tage, as the gas production is acconlpanied by a negligible radiation damage. This method has been used already in 1942 by Z i n ~ e n to investigate AgJ after precipitation from a fission iodine containing solution [3]. Recently, Mears and Elleman [4] made an exten- sive study of Xe-133 mobility in crystals of tlie alkali- iodides, which were grown from a melt containing the fission product I- 133.
2 . 2 . 2 Et?intlntioti i~letllorl ntirl i17-pile e,~/~eritnetrts. -
These methods belong in a way to the homogeneous distribution case, they are, however, characterized by a continuous gas production in the solid.
The measured gas release rate is in this case the result of an equilibration of production rate vs radio- active decay and dil'fusion to the surface. Very few expriments have been perfornied by the emanation technique on ionic crystals. e. g. the study of sintering and melting behaviour of KBr by Zaborenko et nl. [5].
Any attempt to transfer the emanation technique to an in-pile experiment with ionic crystals has not yet been made. Such a n experiment should be planned as valuable infornintion is to be expected.
2 . 2 . 3 Suyn:/iciril lrrt~rllitlg. - A large amount of results have been published d c ~ ~ l i n g with gas release from superficially labelled ionic crystals. This labelling may be performed either by injection of suitable recoil atoms from a nuclear reaction or by esposing the solid to a bean1 of accelerated radioactive gas ions.
- Recoil rlopitig : in this technique, ihe to be labelled solid is in intimate contact with a nuclear source. For Rn-labels this is done by impregnating
the solid with e. g. a Th-228 solution, cf. [6], [7]. For Xe-133 the solid is wrapped in a U-foil enriched in
U-235 and reactor irradiated, cf. [8].
-- 1011 boinbarcli?ieiit : the great methodical varia- bility of ion bombardment technique has been demons- trated by numerous papers of Jech, Kelly and Matzke, cf. their summarizing paper [9] and [lo] by Matzke.
Obviously, these techniques have a n unlimited appli- cation to any solid material. However, when compared with the nuclear chemical gas doping, certain disad- vantages have to be mentioned : Depending on the kinetic energy the injected gas ions penetrate from some atomic layers up to ccm into the solid. In order to be above the limit of detection in the following gas release experiment, this rather small surface layer has to be loaded with very high gas concentrations ( I O'"I 0'' c m - 3 which compares to about 10" c r f 3 for nuclear doping a t its limit of detection) which is unavoidably combined with high damaging of the lattice. T o exclude disturbance of any surface effects, Pronko and Kelly [ I l l refined the ion bombardment technique considerably by stripping the damaged surface layer and then by measuring but the release of those gas atoms which penetrated by channeling deeply into the undisturbed lattice.
2 . 3 APPARATUS FOR MEASURING GAS RELEASE KINE-
Trcs. - The equipment for studying gas release mea-
FIG. 2. - Measurement of gas release after neutron irradiation.
A Discontiniious method with direct sample taking ; B Dis- continuoi~s method with gas collection by adsorption ; C Conti- nuous method ; F Furnace, LS Lead shield, P C Proportional
counter, CT Charcoal trap in liquid air.
C9-152 F. W. FELIX surements is rather simple, minor complications arise only if rather high temperatures have t o be reached (alkaline earth fluorides) o r if a controlled atmosphere (e. g. the hygroscopic alkali fluorides) becomes neces- sary. Figures 2 a n d 3 give some principal features of the technique, for more details see [2]. As already mentioned in section 2 . 1 the assay of the radio- active gases does not pose problems and may be performed with standard equipment.
p-; I F I - - -;2; I
--
PVC Y
A '\
\
* ,
G P M
FIG. 3. - Heating arrangement for alkali halide crystals (above), CS Czacko type stopcock ; PVC Rubber seal ; A Asbestos thermal insulation ; Q Quartz rod to reduce free gas volume ; M Metal block ; C Crystal probe ; TC Thernlocouple.
Container for gas sampling and radiometric assay (below), G glas ; P picein seal ; M brass chamber ; H organic foil ;
E epoxy resin seal.
3, Evaluation of gas release experiments. -
3 . 1 INTERPRETATION OF RELEASE KINETICS. - AS rare gases are practically insoluble in solid materials, one expects a gas concentration gradient between the bulk a n d the surface of the sample as long as the sample is not completely exhausted. The decrease of this gra- dient has been described by lnthoff and Zimen [I21 by solving Fick's 2nd law for the appropriate boun- dary conditions, shown in figure 4. For many different shapes similar solutions are tabulated as F vs.
const. x Dt, cf. Lagerwall and Zimen [13].
A large number of gas release experiments did in fact follow this ideal difrusion pattern. However.
perhaps the larger part of the experimental work did show deviations, which were very early ascribed to trapping of gas atoms by lattice defects, cf. Schme- ling 1141.
Mathematically such a trapping effect has been introduced in Fick's law by adding absorption and desorption terms on the basis of a quasicl~en~ical reaction between mobile gas atoms and ;L stable distribution of traps (Fig. 5).
Solutions of this problem have been published by Hurst [I51 in numerical and by Gaus [I61 in analytical form. The number of parameters (D, the reaction rates, ii and h and the initial fraction of mobile and trapped gas, po and q, resp.) is sufficiently large now
FIG. 4. - Boundary conditions for gas release from a homo- geneously doped sphere (above) and theoretical gas release curve with approximative solutions (below) according to
Lagerwall, Zimen [ I 31.
to describe almost any shape of a release curve. Caution is therefore recommended, when the physical signifi- cance of this mathematical model has to be checked.
A detailed discussion of non-ideal kinetic behavious of gases in highly irradiated ionic crystals will be given in reference [17].
A n important special case of the Hurst-Gaus rnodei is given when the trapping reaction has reached its ther- mal equilibriurli : the differential equation reduces to the simple Fick type, but with D,,,,, which is smaller than D for undisturbed dilrusion. So whatever the initial conditions are, if the equilibrium is reached during the experiment, reliable diffusion coefficients can be evaluated.
This is illustrated in figure 6 with three examples for diffusion with trapping behaviour. The curve KC1 : Sr represents trapping into cation vacancies with rapid equilibration, thus a curve of apparent ideal beliaviour results. The other two curves start from an initial non-equilibri~lm. due to radiation induced traps. In one case all atoms are trapped initially.
17, = 0, in the other freely mobile, p, = I. However,
both curves reach asymptotically the ideal one.
Ideal diffusion : Fick's 2nd law
Trapping reaction ...
[ E ] = c , at t = O c = p ,
[ET] = m , at t = 0 m = q, with p , + go = 1.
... with rapid equilibration
1 with I
FIG. 5. - Differential equations for gas release with interaction of traps, according to Hurst [15], and Gaus [16].
FIG. 6. - Typical experimental release curves with trapping behaviour.
3 . 2 OTHER I N I T I A L PROFILES. - For the superficially labelled solid similar solutions have been published for both ideal diffusion and for trapping behaviour : for a linearly decreasing profile cf. DiCola, Matzke [18], and Mears, Elleman [19] and for a exponentially decreasing profile cf. Kelly, Matzke [20].
4. Results. - The aim of this section is t o demons- trate by a selection of Arrhenius-diagrams the most typical facts of gas mobility and trapping behaviour.
4.1 GAS DIFFUSION I N NOMINAL PURE CRYSTALS AFTER LOW DOSE NEUTRON IRRADIATION. - Figure 7 summarizes all results on diffusion of gases produced by (n, p) reaction on the alkali in all alkali halides
FIG. 7. - Comparison of gas release behaviour in alkali halide crystals with NaCI- and CsCI-structure after low irradiation dose,
from Felix [2].
available to the method of nuclear doping. The 1/T-scale is normalized with respect to the absolute melting point. Three groups are to distinguish :
- Non-fluorides of NaC1-structure : The very high D-value at the melting point (comparable to diffusion in liquid state) and the low activation energy at high temperatures indicate an interstitial diffusion mecha- nism. The increased activation enthalpy below about 5
of the absolute mel~ing point means, that the trapping equilibrium, mentioned in section 3.1, is moved in favour of the formrttion of gas!trap associates.
- The alkalifluorides do not show but a single and very high activation enthalpy. The diffusion coefficients differ much for KF, R b F and CsF. A trapping mecha- nism is assumed for the whole temperature region by analogy to the low-temperature branch of the other alkali halides.
- The CsCI-type alkali halides again show a single activation energy with very similar D-values for the different halides.
Very similar D-values were also observed for diffe-
rent rare gases, when crystals slightly doped with K
C9-154 F. W. FELIX and R b could be investigated. By this interesting
observation the assumption of an interstitial mecha-
nism for the CsC1-structure became doubtful. -5 The difference of gas diffusion with respect to the
NaCI- and CsCl-lattice is very instructively shown in figure 8 for CsCl with its phase transformation at 469 OC [21]. In the low-temperature CsC1-phase all gases have practically the same mobility, but in the
NaC1-phase a tremendeous separation of Ar, Kr 1
and Xe takes place, for the former e. g. by a 200 fold higher D. As the interstitial space is extremely small "
in the CsC1-structure, the gas has to move by another 5
4- -10
mechanism. The calculations of Muller and Nor- - m
gett [22], [23 1 showed that mobile gas-divacancy associates quantitatively fit the experimental results.
-T I°Cl
-
-
- K r
Kr
-
BaF2
-
CaF,
Figure 9 finally shows the results with alkaline earth -Tl"cl
fluorides. In principle the behaviour is the same as in 800 700 600 500 400 300
I
MP'
the nonfluorides of NaC1-structure, i. e. again very + -
-5 - K Br
high D-values at the melting point, however, with greater activation enthalpies. The diffusion mechanism should therefore be an interstitial one again, as first discussed by Lagerwall [25] and later theoretically supported by Norgett [26]. The higher enthalpies with respect to the NaC1-structure reflect the much denser structure of the CaF,-lattice.
4 . 2 EFFECT OF HIGHER DEFECT CONCENTRATIONS. - - Until now no specification has been given on the ;
dnature of the traps. The first step in this direction is to investigate in the traditional way the influence of doping with divalent cations.
400 I C S C ~ 1 0 I I TMP/T I - I 1.5 Ar I I Xe
FIG. 9. - Rare gas release from alkaline earth fluorides, from
1 -6: Felix, Lagerwall [24].
c;=.
7
'ul
Figure 10 clearly shows the double nature of cation
x 0 -7-
- vacancies, acting as diffusion carriers for self diffusion
- m and as traps to decrease the gas mobility in KBr.
-8 - Figure 11 gives the intersting case of KI, where
the gas atoms are obviously unaffected by an increase of cation vacancies. The trapping behaviour is in this
-9 I I 1 I I case due to other defects, as pre-existing or radiation-
11 12 13 11 15
induced ones.
loL [ O K - ~ I -
- T Figure 12 shows then, that in the NaC1-lattice, here Ko,,Rbo.,C1, a reduction ofthe gas mobility isachieved FIG. 8. - Rare gas release from CsCI, from Felix, Meier [21]
The resulting increase in the concentration of \. .-.
cation vacancies was determined by measuring the -15. I , , , , I , , , ,
10 15 20
ionic conductivity. (These values are transformed in @ ~ o K - ~ ] -
figures I0 and I I by the Nernst-Einstein relation into T
D-values LO enable direct comparison wit11 the gas- F,,. 10, - Influence of Sr'+-doping in KBr on Ar-release
diffusion.) from KBr, from Felix, Miiller [27].
FIG. 11. - Influence of Sr2+-doping on Ar-release from KI, from Felix, Miiller [27].
- T P C I
700 600 500 LOO 300
I 1
KO, Rb,, CI /As, Kr
\
FIG. 12. - Influence of Sr2+-doping and high neutron dose On gas-release from Ko.3Rbo.7CI, from Felix [28].
through introduction of defects as well clieniically as by high irradiation doses. Second, in accordance with the interstitial mechanism, different gases diffuse and also react independently with tlie dominating defects.
The fact that at a given temperature, the same decrease in gas mobility can be produced either chemi- cally or by irradiation resolved earlier contradictions about the influence of divalent dopants, see Felix.
Miiller [27].
Figure 13 gives the similar behaviour Sol- Xe-difTusion in both CsCI-modifications. I t is interestinz that ~11so
FIG. 13. - Influence of Ba2+-doping and high neutron dose on Xe-release in CsCI, from Felix, Meier [29].
4 . 3 COMPARISON WITH THE THEORETICAL CALCULA- TIONS. - The information about transport mechanism a n d trapping behaviour was confirmed a n d refined by the theoretical calculations of Lidiard and Norgett [30].
Starting from tlie same trapping equation from sec- tion 3.1 interpreted in terms of the mass action law tlie authors gave a complete description of the tempe- rature dependence of gas diffusion with interaction of point defects in the extrinsic and intrinsic region and radiation induced defects. As an example shows figure 14 two typical equations which describe diffu- sion with trapping into point defects, corresponding to the experimental case of trapping into cation vacancies. In the extrinsic region (constant trap concentration) D,,, is in fact inversely proportional to the trap concentration. I n the intrinsic region (traps in thermal equilibrium) a simple Arrlienius type equation is valid, however, with activation entllalpy slightly larger than tlie value for pure undis- turbed mobility, namely corrected by the difference between the binding energy of tlie gas atom into the trap and tlie formation energy of the trap itself.
The importance of this work is, that every contribu- tion to tlie apparent activation enthalpy could be quant~tatively calculated on the basis of a Born- model. Table I 1 gives n summary of the results, from [XI, [23] arid [3 I].
G
