Diffusion of Krypton in Cesium and Rubidium Iodide; A Comparison of Results Obtained Following Reactor Irradiation and Ion Bombardment

Hj. MATZKE * and F. SPRINGER

High Temperature Chemistry Group, CCR EURATOM, Ispra (Va), Italy

(Z. Naturforsch. 25 a, 252—256 [1970] ; received 29 October 1969)

The present study shows that under suitably chosen conditions, the same results of rare gas diffusion coefficients can be obtained in samples which are reactor irradiated to produce a homo- geneous concentration of rare gas, and in samples that are labeled with rare gas by controlled ion bombardment. In the present study, the diffusion of krypton in Rbl and Csl was found to follow

the empirical rule of yielding activation enthalpies in the range (1.4±0.2) x 10~3 Tm eV, with

Tm = melting point in °K. Trapping of rare gases (gas-gas or gas-damage interactions) was observed at high gas concentration.

Rare gas diffusion constants are usually deter- and used without waiting times between labeling mined by measuring the integral amount of gas that and release experiment whereas reactor irradiated diffuses out of the specimen, i. e. the amount of gas samples are frequently highly radioactive and wait- that is released from the solid. In the early investi- ing times are necessary if all or part of the gas gations, reactor irradiation was used to produce the atoms are not produced directly but originate by rare gas atoms in the solid by a suitable nuclear radioactive decay of a mother substance; the effect reaction [fission, (n,y), (n,oc), (n,p) etc.]. Since of damage or specific impurities on release can these reactor irradiated specimens contained gas easily be studied in double bombardments. throughout the solid, there was frequently an over- Careful investigations performed in this way and lapping of surface and bulk effects, e. g. a fast ini- using the ion bombardment technique lead to a clear tial release, the so-called "burst", was observed. In separation of the various processes that contribute samples containing pre-existing defects or at longer to the overall release. These processes were grouped irradiation exposure leading to higher concentrations into a system of stages. On the other hand, some of radiation damage or higher gas concentrations, difficulties were observed in ion bombardment stu- the release was retarded due to a "trapping" of gas dies as well, the main one being the possibility of atoms, i. e. to gas-damage or gas-gas interactions. evaporation leading to the release of the rare gas. Since these processes frequently occurred simultane- Since the ranges (penetration depths) of the rare ously in reactor irradiated samples, the diffusion gas atoms in ion bombardment work usually vary constants deduced from the composite release curves between a few Ä up to about 1 //m, and in most ex- had sometimes little or no physical significance. periments are of the order of 102 Ä, evaporation To separate these processes, controlled ion-bom- losses of the order of one or a few jug/cm2 surface bardment with well defined ion beams was chosen as cause an essential release but are difficult to mea- a second alternative to label solids with rare gas be- sure. If the activation enthalpy, AH, for gas diffu- cause of its various advantages: with varying en- sion is less than the AH for vaporization, evapora- ergy, the position of the gas (or median range of tion will dominate the release at high temperatures. the gas ions) with respect to the surface can be Therefore, it was early felt that a combination chosen at will thus enabling a separation of surface of the techniques of reactor irradiation (in the last and bulk effects; by varying the ion dose, the gas years mainly employed by the schools of K. E. Zi- concentration can easily be varied without changing MEN, Hahn-Meitner-Institut, Berlin (F. FELIX and the purity of the specimen thus avoiding the many coworkers) and of T. S. ELLEMAN, North Carolina disturbing impurities that are produced during reac- State University) and of controlled ion bombard- tor irradiation; the specimen can easily be handled ment (in the last years mainly employed by C. JECH, R. KELLY, E. V. KORNELSEN, G. SÖRENSEN and the * Present address: Hj. MATZKE, Transuraninstitut, Euratom, D-7500 Karlsruhe, Postfach 2266. author) should be performed in order to obtain a maximum of reliable information. The first obvious Experimental system was that of fission xenon and U02 since Single crystals of Csl and Rbl were cut or cleaved many investigations had been made in this system from pieces purchased from Harshaw (Cleveland, Ohio) because of its importance in reactor technology. The and pre-annealed in vacuo. Radioactive Kr-85 was in- results 1 lead to a first understanding of the mecha- troduced into the crystals using the heavy ion accelera- nism of undisturbed fission gas diffusion in uranium tor 11 of the Institute of Physics, University of Aarhus. A constant energy of 500 keV was used, and the inte- oxide, UOo , and the retarded release of gas (trap- grated ion doses were varied between 2 x 1012 and ping) and the formation and annealing of radia- 4 x 1015 Kr-ions/cm2. Release measurements were per- tion induced defects as observed in transmission formed isochronally in vacuo (about 10-5 Torr) with electron microscopy could be correlated. Later, a 5 min holding times at each temperature. The heatings were spaced at intervals of 50 to keep the effect similar combination of the two techniques was per- of preceeding annealings small. formed in a study of the diffusion of fission xenon in uranium monocarbide, UC 2. Theoretical Another challenging system for a comparison of data obtained with reactor irradiated or ion bom- The mathematics needed to evaluate diffusion co- barded crystals would be the alkali halides. efficients and to calculate activation enthalpies, AH, have been published previously3,12. The median Unfortunately, for many years, argon diffusion range, Rm, of the krypton ions was assumed to be was predominantly studied in reactor irradiated 7600 A in Cs I and 8000 A in Rb I, based on range potassium halides since suitable isotopes of argon measurements with other alkali halides 13. An error are easily formed by (n,p) reactions of the cation, in the range would yield a parallel shift of the Ar- whereas the heavy rare gases krypton, xenon, and rhenius line and hence affect the pre-exponential radon were mostly used in the ion bombardment term, D0, only. Besides the evaluation in the Arrhe- studies since the only argon isotope readily available nius diagram, activaton enthalpies were deduced for ion bombardment work, Ar-41, has an incon- directly from the release curves (curves of fractio- veniently short half life of 1.82 h only. Preliminary nal release, F, versus temperature, T) assuming an ion bombardment studies showed that the mobility idealized range of the pre-exponential rate constant, 15±1 -1 of argon in alkali halides can be greatly different k0 — 10 sec , as is usual in this type of work (e. g. 3' 4'12) 12a. from the mobility of the heavier rare gases3-5. Therefore, a comparison between the two techniques as applied to alkali halides seemed premature so far. Results and Discussion Recently, however, detailed results on the diffu- Fig. 1 shows the results obtained for ion bom- sion of heavy rare gases in reactor irradiated cesium barded Rb I together with literature data for reactor iodide6-8 and rubidium iodide 9 have been publish- irradiated Rb I. The present ion bombardment data ed thus greatly extending the earlier data of KAL- can be grouped around two parallel lines c and d BITZER 10. Therefore, it seemed to be of interest to representing the lower and the higher bombardment perform an investigation on the release following doses (gas concentrations) (provided it is correct ion bombardment and to compare the results. to draw a single line for the high dose data since at

1 Hj. MATZKE, Trans. ANS 8, 26 [1965] and Nucl. Appl. 2, 11 P. DAHL, H. E. JORGENSEN, and K. O. NIELSEN [1968], to 131 [1966]. be published. 2 Hj. MATZKE and F. SPRINGER, Rad. Effects 2, 11 [1969]. 12 R. KELLY and Hj. MATZKE, J. Nucl. Mat. 20,171 [1966]. 3 Hj. MATZKE, Z. Naturforsch. 22 a, 507 [1967]. 13 J. L. WHITTON and Hj. MATZKE, Can. J. Phys. 44, 2905 4 R. KELLY, C. JECH, and Hj. MATZKE, Phys. Stat. Sol. 25, [1966].

641 [1968]. 12a This range of k0 corresponds to a range of D0 of 3xl0_1±1 5 Hj. MATZKE, unpublished results. cm2 sec"1 as is typical for most data on solute diffusion. 6 T. S. ELLEMAN, C. H. Fox, JR.. and L. D. MEARS, J. Nucl. The assumption of this range enabled a first separation of Mat. 30. 89 [1969]. the various processes contributing to the overall release in 7 F. FELIX and K. MEIER, Z. Naturforsch. 22 a. 2075 [1967], complex systems. As shown in Ref. 19, the effective D0 can 8 F. FELIX and K. MEIER, Phys. Stat. Sol. 32, K 139 [1969]. be different by a factor of yi/yj CT where the 7's are the 9 F. FELIX, Phys. Stat. Sol. 27, 529 [1968], appropriate entropy factors exp (S/k) for the interstitial 10 S. KALBITZER, Z. Naturforsdi. 17 a, 1071 [1962]. sites (i) and traps (T), the molar fraction of which is CT • both high and low temperatures the data points tend dose. At the lowest temperature of 135 °C and for to fall above this line). The corresponding AH is all doses used, the diffusion coefficients are higher 1.45 +0.05 eV for both lines, the pre-exponential than expected and do not fit to lines c and d. The constants, D0, are 5 X 104 and 3 X 103 cm2/sec for scatter of the data is comparable to that of data line c and d, respectively. The AWs deduced from obtained following reactor irradiation, as indicated the gas release curves (F vs. T curves) are some- by the blade dots around line b. what lower due to the assumed idealized range of Fig. 2 shows the results obtained for krypton dif-

D0 = 3 x 10x±1 cm2 sec"1, and are 1.05 ± 0.1 eV for fusion in ion bombarded Cs I together with literature the lower dose and 1.15 +0.1 eV for the higher data on xenon diffusion in reactor irradiated or

T(°C

curve atoms/cm^

o -10 a ref. 9 b • 3 c A A 2.5x100"» Fig. 1. Arrhenius diagram of the dif- d a 2.5X1C?8 fusion of krypton in Rb I. Included • 2.5x10r0 9 are literature results of FELIX 9 and e 3 x 10,? ref. 10 KALBITZER 10. A gas concentration of 1017 atoms/cm3 corresponds to a bombardment dose of about 1.6 x 1013 ions/cm2.

- T(°C) 300

Fig. 2. Arrhenius diagram of the dif- fusion of krypton in Cs I. Included are literature results of ELLEMAN, Fox, and MEARS 6, of FELIX and MEIER 7 and of KALBITZER 10 on the diffusion of xenon in Cs I. The arrow aloms/cm^ indicates the scatter in the literature results. The self-diffusion measure- o 1x1016 ~ ments of LYNCH 14 are indicated A ixio17 j around 400 °C by the two small a 2.5xK)18 1 d dashed lines. • 2.5X1019 j curve atoms/cm3 Ref. "iodine labeled" (see below) Cs I as well as on self- summarized in Table 1 together with the present re- diffusion in Cs I. No data are available for the sys- sults. In addition, evaluation of the present data tem Kr/Cs I, but the differences in diffusion rates 13a from an Arrhenius-type diagram and direct compu- between Xe and Kr should be negligible since even tation of AH's from the F vs. T curves yields com- AT Ar diffuses in Cs I at rates (identical AH, D0 =1.5 parable results, the agreement being particularly sa- XE 8 D0 ) very similar to those of xenon . Again, the tisfying for Cs I. The AH's for the lower doses can data for the two lower doses can be grouped together be expressed in relation to the melting point, Tm in 2 -1 -3 (line a, AH = 1.0 ± 0.05 eV, D0 = 0.65 cm sec ). °K, as AH = 1.13 x 10 Tm eV for Cs I and AH

The diffusion coefficients for the two higher doses = 1.58 X 10~3 Tm eV for Rb I which is in approxi- are smaller, especially between about 250 to 400 °C, mate agreement with an empirical rule 15 stating that where they can be grouped around line d {AH again the AH for gas diffusion at low gas concentration 1.0 eV, 0.02 cm2 sec-1). At 220 °C and espe- should fall into the range cially at 450 °C, however, the diffusion coefficients AH= (1.4 ±0.2) x 10-3 Tm eV . are much higher than would correspond to line d. The AH's deduced from the gas release curves (F For such a diffusion, the undisturbed mobility of vs. T curves) assuming the idealized range of single gas atoms was assumed 15. One of the authors Z)0 = 3 x 10_1±1 cm2 sec-1 would be 1.02 ± 0.1 eV suggested previously on basis of doping and chan- for the lower doses (hence good agreement with the neling experiments3'16'17 that the mechanism for value deduced from Fig. 2) and 1.13±0.1eV for such a diffusion, in the alkali halides KCl, KBr, and the higher doses. The scatter of the data is again NaCl, involves the mobility of single gas atoms in comparable to that of data obtained following reac- small vacancy clusters, most probably divacancies tor irradiation or "damage-free labeling" by intro- (neutral vacancy pairs). A similar mechanism was ducing into Cs I 1-133 that decays into Xe-133 (see later suggested by ELLEMAN et al. 6 for Cs I, and by arrow in Fig. 2). PRONKO and KELLY for RbCl18, based on a com- The present results on ion bombarded samples parison of their data with theoretical calculations of agree well with the literature data on specimen where NORGETT and LIDIARD 19. The latter authors cal- reactor irradiation and nuclear reactions were used culated, for Kr-diffusion in Rb I, the following ran- to produce the rare gases in the crystals. The dif- ges (depending on the potential and gas-ion inter- fusion constants, AH and D0, published so far, are action constants used) of energies:

Substance gas gas concentration Do AH ref. technique of (atoms/cm3) (cm2sec_1) (eV)

Rbl Kr lto 2.5 Xl017 5x 104 1.45 p. s. ion bomb. 2.5 to 25 x 1018 3x 103 1.45 p. s. ion bomb. 1 X ion 1.3 xlO6 1.41 9 react, irr. IXIOI5 8 X 104 1.41 9 react, irr. 3 x IOI7 8 XlO2 1.35 10 react, irr. Cs I Kr 1 to 10x1016 0.65 1.0 p. s. ion bomb. 2.5 to 25 x 1018 (0.02) * (1.0)* p. s. ion bomb. Xe 9X1012 0.57 1.01 6 I-doping 4 to 150x lOi4 ^0.05 ^1.0 6 react, irr. 2xl0i5 2 1.14 7 react, irr. 2x1016 0.65 1.14 7 react, irr. 8XIOI3 0.3 0.98 8 react, irr. 1 X lOi8 1 x 10-5 0.8 10 react, irr.

Table 1. Diffusion constants for rare gas diffusion in Rb I and Cs I. (p. s. = present study.) * Tentative values since the straight line d in Fig. 2 is not well defined.

13a In contrast to Rb I, practically identical diffusion rates are 16 Hj. MATZKE, G. RICKERS, and G. SORENSEN, Z. Naturforsdi. observed for various rare gases in Cs I. Ref. 8 shows that 24 a, 820 [1969]. the diffusion coefficients for Ar and Xe differ only slightly, 17 Hj. MATZKE and J. A. DAVIES, J. Appl. Phys. 38, 805 and the present study proves that also the diffusion coeffi- [1967]. cients for Kr are very similar to those for Ar and Xe. 18 P. P. PRONKO and R. KELLY, to be published. 14 D. W. LYNCH, Phys. Rev. 118, 468 [I960], 19 M. J. NORGETT and A. B. LIDIARD, Phil. Mag. 18, 1193 15 Hj. MATZKE, Can. J. Phys. 46, 621 [1968]. [1968], binding in anion vacancy 1.00 to 1.81 eV ves a and d thus indicating trapping. In principle binding in cation vacancy 0.96 to 1.23 eV such a result would be expected because of the dif- binding in vacancy pair 1.13 to 1.76 eV ferent experimental conditions of having a thin solution in interstitial site 0.95 to 1.80 eV interstitial diffusion 0.22 to 0.30 eV layer containing the gas in the ion bombardment experimental result 1.45 ± 0.05 eV. work on the one hand and a homogeneously labeled big crystal in reactor irradiation studies on the other Evidently, the experimental results would be com- hand. As shown previously 12'15, the fraction, G, of patible with the gas interacting with single vacancies gas atoms that will escape without getting trapped or with vacancy pairs. In analogy to the above men- at radiation damage or in defect clusters is simply tioned alkali halides, we would favour the mecha- nism involving divacancies as the most probable G = exp( — p/L) one. Similar conclusions can be drawn for heavy where p = depth of the gas atom beneath the surface rare gas diffusion in Cs I. Here, in addition, the dif- and L = diffusion length for trapping. Hence, the fusion coefficients for self-diffusion have been mea- fraction G is expected to be higher in ion bombard- sured 14 and are much lower than those of rare gases, ment work because of the smaller mean p. However, thus again favouring an independent mechanism for no such effect was observed with Rb I. Though the gas mobility. reason for this discrepancy is unclear one should It should be noted that the present study did not bear in mind the different crystal structures of the yield any indication of a high temperature release two substances (Rb I = NaCl-type; Cs I = CsCl-type). process in Rb I having a low AH of about 0.3 eV The agreement of the present low dose data for (see upper part of curve a in Fig. 1 and ref. 9) Cs I with those of ELLEMAN, FOX, and MEARS 6 who which would be compatible with the above calculated used "iodine doped" Cs I is particularly striking. value for interstitial diffusion. In Cs I, such a pro- Elleman et al. employed an ingenious technique to cess was not observed either in the previous litera- obtain Xe-labeled Cs I with a minimum of damage. ture studies. They grew Cs I single crystals containing 1-133 The present data extend the range of gas con- which, by /^-emission, decays into Xe-133. These centrations used previously to still higher values. Xe-atoms receive a maximum recoil energy of 12 eV With increasing gas concentration (bombardment which should be insufficient to produce more than dose), lower diffusion coefficients are observed with about one vacancy. The agreement of the data ob- a saturation being indicated at concentrations of tained with these crystals with those of the present about 2.5 X 1018 atoms/cm3 since a further increase study (or with Elleman's low dose fission recoil in gas concentration to 2.5 X 1019 atoms/cm3 does doped specimens6) indicates one of two possibili- not lead to a substantial further decrease in D- ties: either trapping of rare gases in Cs I does not values. Such a decrease indicates the well known become important before unusually high gas con- trapping of rare gas atoms (gas-gas or gas-damage centrations are readied, or essential damage is creat- interactions). Parallel lines in the Arrhenius dia- ed in Cs I even by I-doping, e. g. by mechanisms si- grams are indicated for the different concentrations milar to those of colour center production or sput- implying similar (or identical) AWs. Most other tering in alkali halides (measurable ejection of substances (e. g. 2) show an increased AH whenever atoms from e. g. NaCl or KI can be obtained with trapping occurs. Even in the present study, the 10 eV electrons or 5 eV photons and holes can easily data points tended to fall together at high tem- be obtained in alkali halides during electron bom- peratures, independent of dose. At low temperatures, bardment at slightly higher energies 20). too high D-values were found indicating a faster mechanism of release. Similar observations were re- The authors would like to thank Prof. K. O. NIELSEN cently reported for Kr-diffusion in KCl and RbCl18. for an invitation to the University of Aarhus in Decem- For Cs I, the present results for fairly high gas ber 1968, and for providing beam time at the heavy ion accelerator. Thanks are due to the team of the ac- concentrations of 1 X 1016 and 1 X 1017 atoms/cm3 celerator (P. KJOER and P. NORGAARD) for performing agree with the literature data for lower concentra- the bombardments. tions (9 x 1012 and 1 x 1014 atoms/cm3) whereas the 20 literature data for concentrations between 2 x 1015 P. D. TOWNSEND and D. J. ELLIOTT, presented at the Int. Conf. on Atomic Collision Phenomena in Solids, Sussex, 16 3 and 2 x 10 atoms/cm fall between the present cur- U. K.1969.