Bannasch, W.

Schmeling, P.

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~<.~P. SchmelingDezember 1965Institut für RadiochemieDiffusion of Krypton in Rubidium Chlorideand its Dependence on Radiation DamagecJ"~\j....'->W. Bannasch,Forschungszentrum Karls-..he Gmin der Helmholtz-Ge1T1elnsc'la~KFK 391J. Phys. ehern. Bolids Pergamon Press 1965. Vol. 26, pp. 1999-2005. Printed in Great Britain.DIFFUSION OF KRYPTON IN RUBIDIUM CHLORIDEAND ITS DEPENDENCE ON RADIATION DAMAGEW. BANNASCH and P. SCHMELINGInstitut für Radiochemie, Gesellschaft für Kernforschung, Karlsruhe, Germany(Received 12 March 1965)Abstract-The diffusion of krypton in neutron irradiated rubidium chloride was determinedby measuring the release of Kr-S5m. After negligible irradiation the gas release mechanism cor-responded to ideal diffusion. Above 360°C the process was characterized by an activation energyof 10 ± 2 kcal,'mole and diffusion by an interstitial mechanism seems probable. IrradiatIOn to highneutron doses resulted in a marked decrease of the measured diffusion coefficient. The healingout of damaged lattice regions was demonstrated as a rapidly increasing krypton release duringan isothermal anneal. Possible diffusion mechanisms in the damaged lattice are discussed.w/o Ca2... , < 10-4 w/o St2-, andfast neutrons produces isotopes ofto the reactionsCJ35 (n,p) S35, halflife 8idRb85 (n,p) Kr85m, half life 4·4hRb87 (n,p) Kr87, half life iSmw/o K+, 2 X 10-46 X 10-4 w/o BaZ,.Irradiation withkrypton accordingThe naturally abundant rubidium isotopes Rb85 andRb87 are present with i2 per cent and 28 per cent respec-tively, and irradiation in the FR-2 reactor for 10 min ata thermal ftux of 3 x 1013 cm-2 sec1 (integrated fast ftuxabout 1015 cm-2) produces both Kr85m and Kr87 inquantities. Agas sampie measured one hr after irradia-tion with the equipment described below gives 1·0 x 104ipm of Kr85m and 1·4 x 103 ipm of Kr87 per gram RbCI;some hours later only Kr85m is measured. Kr85 does notseem to be produced directly but only by decay ofKrS5m. In order to avoid strangly radioactive specimensthe irradiations were performed in O' 1 cm cadmium,thereby suppressing the production of Rb86 • Howe,-er,the creation of S35 could not be eliminated in this wayas it is produced by fast neutrons:and1. INTRODUCTIONINVESTIGATIONS of rare-gas diffusion in solidshave for the most part been limited to the releaseof the fission gases krypton and xenon from nuclearfuels such as U02 and DC. The resulting data areof immediate interest for nuclear reactor tech-nology but have hitherto yielded litde informationfor the understanding of diffusion processes. Onereason for this may be the complicity of theinvestigated materials and the difficulties in inter-preting the gas release data, (1) and it seemsnecessary to study less complicated systems inorder to obtain basic knowledge of the transportmechanism.Reports on argotJ. diffusion in potassium andcalcium salts show that considerable basic informa-tion on the diffusion process may be obtained fromneutron-irradiated materials, (2-8) and the presentstudy of krypton diffusion in single crystal RbClis part of a program initiated with the purpose oflearning more about the movement of rare-gas2toms in solids.After irradiation the specimens were transferred to theannealing apparatus. Briefty, this consisted of a quartztube containing the single crystal and a thermoelectriccouple; the tube was connected to vacuum via an acti,-a-ted charcoal trap. After evacuation of the apparatus the2. EXPERIMENTAL PROCEDURE quartz tube was heated with a furnace and the releasedSingle crystal rubidium chloride of optical quality krypton gas was collected in the trap which was cooledwas delivered by Firma Korth in the form of parallele- with liquid nitrogen. After a time the charcoal trap waspipedic pieces with approximate dimensions O· 5 x 1 x 1 closed and a parallel trap was connected to the system.cm. The material contained small amounts of impurities, In this way gas sampIes Were taken with appropriatemainly ions of the alkali and alkaline-earth metals ; an time intervals, and the krypton content of each trap.analysis showed the presence of 0'01 w/o Na+, 0'01 was transferred into a standard gas container fitted with19992000 W. BANNA8CH and P. 8CHMELINGFIG. 1. Release curve from a typical multi-temperatureexperiment with a specimen irradiated to an integratedfast flux of 9 x 1014 cm-2•The straight-line relationship above 360°C wascalculated whereby all points shown in Figs. 2 and3 were taken into account:D = 8 X 10-4 exp( -9,0 x 103 jRT)Considering the fact that most of the multi-temperature experiments shown in Fig. 2 exhibitactivation energies of about 11 kcaljmole, valuesoflogDo = -3'1±0'4andQ = 1O±2kcaljmolemay be adopted as good estimations.Figure 4 shows a multi-temperature annealwith a slightly irradiated crystal; the temperaturewas first held at 415°C and then raised to 582°C.The crystal was then cooled whereupon thetemperature was again kept at 415°C. As is seenfrom the slope of the 0/2 curve of Fig. 4, the diffu-sion coefficient at 415°C was practically the samethough a temperature break at 582°C had beenundertaken which indicates an ideal diffusionbehaviour. From this experiment an activationenergy of 10 kcaljmole was calculated.50 100 150 200 250 300 350 400 450o"5-10-05-20-u~- /'0 500 - r---~. 400~'---------"f- 3.0t-----------------1----lI//i,/,//4>2,,/'" .........-/ •.-,0'./'l. ........./( ......~.1.......... •........-' .'/r. •.e/,lI,.""..........,I.~;,."i~T I I I I 1 I I Ia 14 mgfcm2 aluminum window allowing the measure-ment of Kr85m with a proportional counter in a fixedgeometric position. Each container was periodicallymeasured giving the typical4'4h decay after subtractionof the background which was determined after two daysand caused by 8 35 and Kr85• At the end of each run thecrystal was melted and vaporized in order to release allremaining gas. The activity of each gas sampIe wascompared at a fixed time and the fractional gas releasecould be calculated as a function of diffusion time.3. EVALUATION METHODThe theoretically valid relationship between thefractional gas release F, the diffusion time t, and thediffusion coefficient D has been given by INTHoFF andZIMEN,(10) and tables of the relevant functions havebeen published by LAGERWALL and ZIMEN.(ll) Theideal relationship may be approximated by the tangentthrough the originq,2 = 4/7r(S/V)2 Dt (1)where SfV is the surface-to-volume ratio of the speci-men. The function q, is reasonably equal to F for valuesF< 0·25. At higher values one can introduce a correc-tion factor for Fand thereby transform the experi-mentally determined value of F into q,. (3,4) It is thuspossible to use equation (1) for all values of Fand thediffusion coefficient is easily calculated from the slope ofa q,2 versus time plot:D = 1Tf4-1f(S/V)2 drp/dt (2)Figure 1 shows a typical release curve from a multi-temperature experiment. F2 as weil as q,2 is plottedagainst time, and the possible variation of the slope ofq,2 is taken as probable error for the diffusion coefficient.The variation in temperature is also taken into accountand the deviations are shown for each point in theArrhenius diagram, cf. Fig. 2.4. RE8ULTSMulti-temperature anneals were performed withspecimens irradiated to an integrated fast flux of9 x 1014 cm-2 (cf. Fig. 1) and Fig. 2 shows theresulting diffusion coefficients in an Arrheniusdiagram. Above 360°C a straight-line relationshipis valid:D = Doexp( - QjRT) (3)The region below 360°C seems to be governed bya process with an activation energy of the order of60 kcaljmole. This portion of the curve will bediscussed later. Further, a number of singletemperature experiments were performed at aslow dose as possible (6 x 1013 cm-2). The valuesof D are in accordance with the values shown inFig. 2 and are separately plotted in Fig. 3. 1t istherefore assumed that the line drawn in Fig. 3corresponds to diffusion in a lattice which is notinfluenced by radiation damage in such a way thatthe diffusion of krypton is affected.DIFFUSION OF KRYPTON IN RUBIDIUM CHLORIDE 20012031510"TFIG. 2. Arrhcnius plot of results from four multl-temperaturc anneals(llvt = 9 X 1014 cm-2).-5-6-70.2 -8-9-10-1110As described above, the value of D was notinfluenced by an increase of the integrated fastf1ux from 6 x 1013 to 9 X 1014 cm-2• However, amarked influence was observed after irradiationto 5 x 1016 cm-2 resulting in an inhibition of the700 350 300 250I I I-5-60-7'"2 -8-9-10I I-11 10 15 2010'TFIG. 3. Arrhenius plot of results from five single tem-perature anneals (unfilled symbols) and one multI-temperature anncal (fillcd symbols). The specimens hadbeen irradiated to an intcgrated fast flux of 6 x 1013 cm-2•rate of diffusion. Figure 5 shows a multi-tempera-ture anneal and the release characteristics may benoted as fo11ows:(a) In the first stage a temperature of 260°C wasmaintained and the diffusion coefficient whichwas of the order of only 10-13 cm2 sec-1 showed atendency to decrease.(b) In the second temperature stage (360°C) thediffusion coefficient increased continuously from5·7 x 10-12 to 4·4 X 10-10 cm2 sec]; a constantvalue was never reached.(e) In the third stage, a temperature of SlOve waskept for only 30 min and a practically constantvalue of D = 1·3 X 10-6 cm2 sec1 was observed.(d) In the fourth stage the original temperatureof 260°C was once more reached and a constantbut considcrably higher diffusion coefficient wasobserved, cf. Fig. 6.(e) In the fifth stage 360°C was again maintainedwhereby the diffusion coefficient quickly in-creased from 3 x 10-8 cm2 sec1 to a constant valueof about 1·3 x 10-7 cm2 sec1•(f) In the last stage the temperature was kept at610°C for a short time and a slightly increasingdiffusion coefficient was observed.The results of this experiment are shown inFig. 6 together with two single temperatureanneals at 460°C and 600°C resp.; the latterexperiments were performed with crystals irradia-ted to an integrated fast flux of more than1018 cm-2 •Experimental data for a11 runs are summarizedin Table 1. The resulting diffusion coefficientsare satisfactorily reproducible and have evidently2002 W. BANNASCH and P. SCHMELINGFlG. 5. Release curve demonstrating the influence ofradiation damage upon the release of krypton. Thespccimen was irradiated to an integrated fast flux of5 x 1016 cm-2 and subsequently annealed at five tem-perature levels; the corresponding diffusion coefficientsare shown in Fig. 6 (designation lOa-f).260°C to 360°C low values of D were noted and anactivation energy of the order of 60 kcal/mole.The rubidium chloride lattice is of the NaCltype and exhibits a Schottky disorder. Thoughthe self-diffusion has not been measured inrubidium chloride, it is reasonable to be1ieve thatthe lattice ions move in aecordanee with other(b) Infiuence of radiation damage, cf. Fig. 6At low temperatures low values of D were ob-served and there were indications of a slightlydecreasing diffusion coefficient during the run.At higher temperatures a marked, continuousincrease of D during an isothermal anneal wasobvious, cf. Fig. 5. Above about 460°C idealdiffusion kineties was predominant and values ofD were found whieh are only slightly lower thanthose at low irradiation dose../ 600~ 50040C -r-" 30020030F2 4>2t t25 • .20151005I300250150 200t, mm10050o15-20f-"rr5. DISCUSSIONOne may characterize the release of kryptonfrom rubidium chloride by summarizing theexperimental facts:FlG. 4. Release of krypton from a slightly irradiatedspecimen (nvt = 6 x 1013 cm-2) at 415°C with a tem-perature break at 582°C.not been influenced by other gas releasing pro-cesses such as vaporization of the specimen.(a) Low irradiation dose, cf. Fig. 3Ideal diffusion kinetics is observed at alltemperatures with indications of a slightly in-creasing diffusion coefficient during an isothermalanneal at the lowest temperatures. Above 360°Ca straight line relationship log D vs. 1/T wasfound, corresponding to an activation energy of10 ± 2 kcal/mole. In the temperature region ofDIFFUSION OF KRYPTON IN RUBIDIUM CHLORIDE 2003Table 1. Summary 0/ experimentc.l dataDimensions of Irradiation AnnealNo. specimen nvt* Temp. Time at(ern) (em-Z) (oe) tempo (min)1 0'75 x 1'08 x 1'11 9 x 1014 400 210510 130610 1032 0'47x1'07x1'13 9 x 1014 560 26660 493 0'51 x 1'05 x 1·12 9 x 1014 240 280560 40690 504 0'52 x 1'06 x 1-17 9 x 1014 285 245338 120460 925 0'51 x 1'07 x 1·12 6 x 1013 360 2706 0'53 x 1'07 x 1·12 6 x 1013 260 3307 0'52xl'06x1-13 6 x 1013 460 2408 0'56 x 1'07 x 1·15 6 x 1013 560 2379 0·51 x 1'07 x 1·12 6 x 1013 310 33010 0'53 x 1'08 x 1·19 5·0xl016 260 190360 119510 30260 120360 92610 3011 0'53 x 1·07 x 1·18 6 x 1013 415 40582 20415 13512 0·56xl·lOxl·16 1·2 x 1018 595 42313 O' 50 x 1· 07 x 1·17 1·6 x 1018 460 510* The fast flux information is based on measurement of Si31, whereby a erossseetion of 30mb was assumed for the reaetion P31 (n, p) Si31. The thermal fluxwas about 20 times higher than the fast one.alkali halides, e.g. a vacancy mechanism is govern-ing the self-diffusion which proceeds with anactivation energy of the order of 50 kcalfmole forcations and with still higher values for anions.As the krypton release at higher temperatures ischaracterized by ideal diffusion kinetics with highdiffusion coefficient and a surprisingly low activa-tion energy, one is obliged to assurne that the rare-gas atoms do not make use of a vacancy mechanismfor their movements in the lattice. The onlypossibility is diffusion by an interstitial mechanismor movement along lattice defects of various kinds.However, the influence of radiation damageupon the diffusion at lower temperatures is suchas to make an interstitial diffusion mechanismseem unlikely as sole process in the damagedlattice. After irradiation to higher doses thediffusion coefficient is lowered with many ordersof magnitude and during an isothermal anneal thediffusion coefficient is continuously increasing,indicating a healing out of the radiation damage.A damaged lattice still contains enough inter-stitial paths to permit practically free movement ofthe rare-gas atoms and one must conclude thatthe diffusing krypton atoms in some way associatewith the created lattice defects and are thus moreor less immobilized. As the value of D is depend-ent on the irradiation dose the rare-gas atoms donot create these defects themselves and the forma-tion of micro-bubbles by random encounter isimprobable considering the low concentration ofkrypton which for the experiment shown in Fig. 62004 W. BANNASCH and P. SCHMELINGt, min005REFERENCES1. LAGERWALL T. and SCHMELING P., Euratom Rept.,p. 51, EUR 595e (1964).2. KALBITZER 5., Z. Naturf. 17a, 1071 (1962).3. LAGERWALL T., Nukleonik 4, 158 (1962).4. LAGERWALL T., Diss. Hahn-Meitner Institut fürKernforschung, Berlin (1964).5. LAGERWALL T., Nukleonik 5, 179 (1964).6. MATZKE HJ., J. Nucl. Mat. 11,344 (1964).7. MUNDT H. P., and RICHTER A. K. H., Z. Naturf.20a, 267 (1965).FIG. 7. Healing out of damaged lattice regions, demon-strated as a rapidly increasing krypton release during anisothermal anneal; the plot corresponds to the secondtemperature stage of Fig. 5.It has been shown that the system ArfKCl iseven more sensitive to radiation damage than isKrjRbCI, (9) and, investigations of irradiationsensitive diffusion and its causes are now continuedon single crystal KCI.Acknowledgement-The authors would like to thankProf. W. SEELMAN:'I-EGGEBERT, Director of the Institute,for his encouragement of this work.010oneself how significant the measured activationenergy of 10 kcalfmole is and if the lowered diffu-sion coefficient in the region below 360°C is also aresult of radiation damage, cf. Fig. 3. The resultof the experiment shown in Fig. 4 indicates thatthe slope above 360°C is really the one whichcorresponds to diffusion in an undisturbed lattice.The region be10w 360°C is still a matter of ques-tion and the present investigation does not produceenough information to determine the diffusionmechanism.20alOdI~b-5_~2-6010f-7-8c -9co~ -10-11-12-I~-1410 15104TFIG. 6. Arrhenius plot of the results from specimensdamaged by radiation; the drawn line corresponds tothe diffusion coefficient in the undisturbed lattice.is certainly less than 1010 atomsjcm3. The exis-tence of rare-gas traps has been discussed byHURST(12) and others(13); the well-known pheno-menon of bubble formation could be a late stageof trapping,(14) and LAGERWALL(4,5) has proposedthat vacancy clusters constitute such sinks inCaF2 •Without trying to identify the physical natureof these irradiation-induced defects, one maythink of the entity kryptonjdefect as being formedat an early stage of the post-activation diffusionanneal and as being immobile or diffusing at avery low rate (Fig. 5, 1st temperature stage). Athigher temperatures the healing out process ismeasurably influencing the diffusion which meansthat either the diffusing entity is reducing in sizeor the krypton atom is breaking away, resultingin a continuous increase of the diffusion coeffi-cient (Fig. 5, 2nd temperature stage). Though onefeds that the latter mechanism is the most plau-sible one, it is not possible to say which processoccurs at the present state of knowledge, onlythat it is connected with its own kinetics. Figure 7shows this healing process as a straight line in ay(F) vs. t plot.Considering the influence of radiation damageand the fact that this damage is only partly healedout during an isothermal anneal, one may askDIFFUSION OF KRYPTON IN RUBIDIUM CHLORIDE 20058. RICHTER A. K. H. and ZIMEN K. E., Z. Naturf. 20a,666 (1965).9. SCHMELING P., Phys. Stat. Sol., in press.10. INTHOFF W. and ZIMEN K. E., Kinetik der Dif-fusion radioaktiver Edelgase aus festen Stoffennach Bestrahlung, p. 15. Trans. Chalmers Univ.Techn. No. 176, Gumperts, Göteborg (1956).11. LAGERWALL T. and ZIMEN K. E., Euratom Rept.,p. 40, EUR 1372e (1964).12. HURST D. G., AtOlnic Energy of Canada Ltd. Rept.,p. 40, AECL-1550 (1962).13. MAcEwAN R. J. and STEVENS W. H., J. Nucl. Mat.11,77 (1964).14. BARNES R. S., J. NUcl' iHat. 11, 135 (1964).

Diffusion of Krypton in Rubidium Chloride and its dependence of radiation damage

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Diffusion of Krypton in Rubidium Chloride and its dependence of radiation damage

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