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Kr bubble formation in Cu after moderate doses of ion irradiation: the role of radiation vacancies
Nuclear Instruments and Methods in Physics Research B62 (1992) 469-477 North-Holland
Nuclear Instruments &Methods in Physics Research Section B
Kr bubble formation in Cu after moderate doses of ion irradiation: the role of radiation vacancies D. Kuzminov ', C . Templier, E. Raqi and H. Garem
Laboratoire de Métallurgie Physique, URA 13140, Ac . du Recteur Pineau, 86022 Poitiers Cédex, France
Received 6 May 1991 and in revised form 25 July 1991 A TEM study of Kr bubble formation in Cu as a result of ion irradiation in a dose range from 2.5 x 10 14 to 5 x 10 15 Kr cm -2 and subsequent annealing is presented . For irradiation doses below 5 x 10 15 Kr cm -2 no bubbles are observed in as-implanted samples . Post-implantation annealing results in formation of Kr bubbles containing solid inert gas at room temperature . Two stages of bubble growth are observed during annealing: bubble growth by complexes absorption and bubble growth by coalescence . With increasing dose, the Kr lattice parameter decreases from 0.545 nm to an asymptotic value of 0.523 nm and the fraction of Kr atoms trapped within bubbles reaches saturation . This behaviour is explained in terms of radiation vacancy interaction with bubbles and dislocations. 1. Introduction The technological interest in rare gases in metals stems to a large degree of fusion first wall and fission reactor applications. Tritium in fusion reactors permeates the first wall and decays into helium ; alpha particles are injected into the first wall from the plasma itself. Fission fragments are the primary source of the heavier rare gases in metals. The interest in heavy rare gases is also dictated by their use in ion-beam mixing technology, production of metallization layers in microelectronics by sputter deposition, sintering of powders, etc . Rare gases have a very low solubility in metals and therefore strongly tend to precipitate within cavities (bubbles) following ion implantation [1]. The phenomena of helium bubble formation is very well known and has been broadly investigated . One of the crucial points in understanding gas-atom clustering in metals is the question of pressure and density inside the bubbles [2], which has been discussed for more than thirty years . The presence of high pressure and density inside bubbles was finally confirmed by the discovery in 1984 that implanted heavy rare gas atoms (Ar and Xe) precipitated in Al in solid form [3,4] at room temperature: in order to confine solid precipitates the pressure inside * This work is financially supported by Conseil Régional de Poitou-Charentes. 1 On leave from Institute of Physical Chemistry of the Academy of Sciences of the USSR 117915. Moscow, Leninsky Prospekt 31, USSR.
bubbles must exceed 2-3 GPa. This discovery was subsequently extended to observation of Ar, Kr and Xe precipitates in other metals [5-8]. The aim of this article is to report experimental observations of Kr bubble formation in Cu after moderate doses of ion irradiation (2 .5 x 10 14-5 x 10 15 ions cm -2 ). Particular attention is paid to accurate calculation of vacancy-krypton (V/K0 ratio inside bubbles and to its comparison with the number of vacancies produced versus irradiation dose. It allows us to draw some conclusions about the participation of radiation vacancies in bubble formation, the question which was discussed in recent theoretical studies [9,10]. 2 . Experimental technique Copper discs of 3 mm in diameter and 0.1 mm thick were punched out of polycristalline Cu foil and then annealed at 1150 K for 6 h under vacuum better than 10 -4 Pa . This allowed us to obtain samples with cristallite size ranging from 0.1 to a few micron . Then the samples were clectropolished from both sides and implanted. The implantation was carried out at room temperature with Kr ions subsequently at two energies 240 kcV and 80 kcV and ion fluxes around 10 12 ions cm -2 s -1 . The implantation energies were selected on the basis of results from TRIM computer code [ll] in order to produce distribution profile close to homogeneous with the largest penetration range of 60 nm . The results of TRIM89 calculation for irradiation doses used are summarized in table 1 .
0168-583X/92/$05 .00 0 1992 - Elsevier Science Publishers B .V. All rights reserved
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D. Kuzminor et al. / Kr bubble formation in Cu
Table 1 Irradiation conditions as calculated with TRIM computer code for 1 .3 x 1015 ions cm -2 implanted sample . For other doses, the same ratio between the two energies have been used Energy [keV]
Dose [cm - 'l
Mean range [nn]
240 I .0 x 10" 51 19 80 2 .6 x 10 14
At . cone. [at .%]
Disp . dam . per ion
0.3 0.3
3500 1300
TEM examination of the samples at magnification of 5 x 10 4 times was performed in a JEOL 2000X operating at 200 kV . Cavities were identified by their defocuse contrast and were usually imaged at defocuse
distances e 5 0.8 wm in sample areas of = 100 nm thick. Selected-area diffraction patterns were taken with the electron beam parallel to (110) or (112) matrix orientation . The solid rare gas lattice parameter was calculated by the simple ratio method from (111) Cu matrix and solid Kr reflections under the assumption that the Cu lattice constant was not affected measurably by the precipitation process. These measurements were made either by using microdensitometer or computer image analysis with an estimated accuracy of about 0 .5-1%. Nevertheless, for very weak reflections which were observed after 2 .5 x 10 14 ions cm -2 implantation, the accuracy could reach 2-3% . In situ annealing of the samples at 620 ± 10 K was performed using commercial heating stage of the microscope.
Fig . 1. TEM micrographs obtained from Cu samples following implantation of 5 x 10 14 Kr CM - 2 cm and annealing at 620 K for (a) 5, (b) 20 and (c) 780 min . From up to down: (I11) Cu and Kr reflections in selected area diffraction patterns (Kr reflections are arrowed), bright-field underfocused ((a) and (b)) and overfocused (c) images, dark-field images obtained with (I11) Kr reflection .
47 1
D. Kuzminov et al. / Kr bubble formation in Cu
3. Experimental results
0.55
3.1. Microstructure development during long-time annealing
TEM analysis of the samples has been performed at room temperature both before and after annealing for different time at 620 K (i .e . 0.45T,H , TM being the Cu melting temperature). This temperature has been chosen in order to avoid the effect of thermal vacancies on the bubble growth process. Before annealing, all the ' samples (for exception of that implanted at the highest dose, 5 x 10'5 Kr em - Z) could be characterized by the absence of extra reflections corresponding to solid Kr. Inspite of a large number of small defect clusters revealed with weak beam technique (fig . 5a), neither visible Kr precipitates, nor dislocations were detected. After the first annealing (2-5 min), both the appearance of Kr bubbles and a well developed dislocation structure could be observed. An example of microstructural changes of Kr-implanted Cu (5 x 10'4 ions cm -Z ) after 5, 20 and 780 min of annealing is presented in fig. 1. Microdiffraction pattern analyses together with the analyses of bright-field and dark-field images obtained at room temperature with <111) Kr reflections show that Kr within bubbles is present in the crystalline state. Nevertheless, during annealing at 620 t 10 K no extra reflections were observed . The variations with annealing time t,, of bubble density N, mean bubble diameter (2rß,), Kr lattice parameter and the fraction of Kr atoms trapped inside bubbles S &duc~d from the latter quantities are given in figs . 2 and 3. It is seen from these figures that the
w y o .~
100 200 800 Annealing time, min Fig. 3. Variation of Kr lattice parameter and the fraction of Kr atoms trapped in bubblesduring post-implantation annealingat 620K. Irradiation dose was5x 10'4 cm -2 . 0
variation of microstructure with t;, may be represented by two stages: stage A (t,, < 20 min) and stage B (t a > 20 min). Stage A is characterized by the increase of both bubble density Nb up to 1 .3 x 10'2 cm -2 and S up to 100% for the given sample (fig. 2). At the same time, the mean bubble diameter and the Kr lattice parameter stay practically unchanged (2r,, = 3.0 nut and aKr = 0.530 nm respectively). Higher annealing time (stage B) results in a slight increase of bubble diameter and Kr lattice parameter, reaching mean values of 2r b = 3.5 nm and a,U = 0.535 nm respectively after t o _ 780 min. Meanwhile, the bubble density drops from 1.3 x 10'2 to 8.4 x 10" cm -2 and this decrease mainly occurs during the first minutes of annealing. Exactly the same general annealing behaviour was observed for the samples implanted at 3 x 10'4 and 1.3 x 10 15 Kr CM-2 . 3.2. Dose dependence
Fig. 2. Variation of bubble density and bubble diameter during post-implantation annealing at 620 K. Irradiation dose was5x10'4 Kr cm -2 .
Quantitative information about the thermodynamic state of solid Kr inside bubbles and the number of Kr atoms comprised by bubbles can be deduced from the lattice parameter, bubble diameter and density measueements. These measurements (table 2) have been performed at room temperature following implantation of Kr to various doses plus annealing at 620 K for - 20 min (i.e . at the end of stage A). It allowed us to avoid the influence of bubble coalescence on Kr lattice changes. The resultsof TEM examinations are given in fig. 4. Also, dislocation structure was imaged after the treatments mentioned above. The results of dislocations observation in TEM for various irradiation doses are presented in fig. 5. TEM images were obtained
D. Kuzminoc et al. / Kr bubble formation in Cu
472
Table 2 Variation of bubble density N6 , mean bubble diameter d, Kr lattice parameter axr and Ronchi pressure P inside bubbles measured after annealing stage A vs krypton irradiation dose P Dose Nb d aKr 11014Cm-=] [1011 Cm -Z] [nm] [nm] [GPa] 2.5 3.0 5.0 6.0 7.5 13.0 50.0
7.0±0 .5 7.3±0 .7 13 ± 1 13 ± 1 .5 17 ±2 19 ±2 23 ±1
3.0±0 .5 3.0±0 .5 3.0±0 .5 3.0±0 .5 3.0±0 .5 3.2±0 .5 3 .2±0.5
0.545±0.010 1 .8 0.540±0.008 1 .8 0.530±0.005 2.3 0.528±0.005 2.5 0.524±0.005 2.8 0.523±0.005 2.8 0.523±0.005 2 .8
using weak-beam technique. The observation conditions were : g = 1111 , sR = 0.14 run -1 . For all the irradiation doses extra reflections corresponding to solid Kr can be observed at room temperature . In case of the lowest irradiation dose, i .e . 2.5 x 10 14 ions cm -2, the extra reflections are extremely weak and hardly detectable (fig . 4a). However, darkfield images obtained using Kr reflections confirm that Kr inside bubbles is present in the crystalline state. Variation of Kr lattice parameter and V/Kr ratio inside bubbles with irradiation dose is shown in fig . 6a. With increasing Kr dose from 2.5 x 10 14 to 5 x 10 15 ions cm -2, the average Kr lattice parameter decreases from 0.545 nm toward some asymptotic value of 0.523 run, corresponding to a decrease of V/Kr ratio from = 3.5 to = 3.0. This result seems to be completely contradictory to the increases of the rare gas lattice parameter with increasing dose observed by Templier et al . for Xe in Al [121 and Birtcher and Liu [131 for Kr irradiated Ni,
but at fluences from 10 15 to 1016 CM -Z and from 10 16 to 5 x 1016 CM-2 respectively. Variation of the fraction of Kr atoms precipitated within bubbles with increasing irradiation dose has been calculated using the data in table 2 and is plotted in fig. 6b . Approximately 100% Kr trapping within bubbles is detected up to a dose of 7.5 x 10 14 ions cm -2, while at higher irradiation doses the number of Kr atoms trapped by bubbles approaches some saturation value of = 1.1 x 10 15 ions em - Z, indicating only = 24% trapping at 0 = 5 x 10 15 ions cm -Z . Variation of dislocation density versus irradiation dose, calculated using the micrographs in fig. 5, is plotted in fig . 7. According to this plot, the density of dislocations drops as ion fluence is increased from 2.5 x 10 14 to 5 x 10 15 Kr CM-2 . It is worth noting that only visible dislocations were taken into account. Meanwhile, it is obvious from fig. 4a that for the smallest dose practically no random distribution of defect clusters (mainly supposed to be bubbles) is observed . Almost all of them are aligned along visible dislocations or invisible lines, which could probably be imaged as dislocations under different observation conditions. Therefore, we expect that for the smallest irradiation dose the density of dislocations might have been slightly underestimated . 4. Discussion 4.1 . As-implanted Cu and annealing behaviour As it has been mentioned in section 3.1, no visible bubbles were detected in as-implanted samples, for
Fig. 4. (111) Cu and Kr reflections in selected area diffraction patterns (top, Kr reflections arrowed) and dark-field images (bottom) taken with (111) Kr reflections, obtained from Cu samples following implantation at doses (cm'z1: (a) 3x10 14, (b) 6x10 14, (c) 5X10'5 and post-implantation annealing at 620 Kuntil the endof stage A.
D . Kuzminov et
473
al. / Kr bubble formation in Cu
a
14
10
c
15
10
cm2
Irradiation dose,
16
10
Fig. 6. Variation of V/Kr ratio inside bubbles and the Kr lattice parameter (a), mean fraction of Kr atoms trapped by bubbles (b) vs ion irradiation dose .
c
16
0
-,L 12" y
Q
w 81 t~p
Fig . 5 . Cu defect structure after Kr implantation and annealing at 620 K until the end of stage A, as revealed with TEM. Implantation doses were [cm 1; (a) 2.5 x 10 (no annealing); .5X1014 (c) 6 x 10 ; (d) I .3 x 10 ; (e) 5X1015 2 (b) ; . The images were obtained using weak-beam technique, g =111 (6g excited), Sg = 0.14 nm'
14
-2
14
15
1.
A
41 10
14
1015 Irradiation dose,
ctri2
16
10
Fig . 7. Variation of dislocation density with irradiation dose .
474
D. Kuzininoi- et aL / Kr bubble formation in Cu
exception of irradiation with 5 x 10 5 Kr CM -2. Due to a large number of defects and resolution limit, it was not possible to detect bubbles with diameters less then 1.5-2.0 rim. Therefore, we assume that Kr atoms before annealing arc present either in submicroscopic clusters or in solution in Cu. This assumption does not contradict with recent observations by ion channelling method [14] that after low doses of implantation, a large fraction of Kr is contained in KrV complexes. Nevertheless, at doses somewhat higher than 10 5 Kr cm -2 , formation of bubbles is detected, in agreement with our observations . On the basis of these arguments and general annealing behaviour described in section 3.1 (figs. 2 and 3), the two stages observed during annealing may be attributed to two different processes of bubble growth : stage A: bubble growth by Kr atoms and vacancies entrapment; stage B: bubble growth by coalescence . The fact that these stages are very distinguishable in time probably arises from low bubble concentration and big difference between Kr and Kr bubble diffusivities in Cu . During stage A the bubble diameter increases from = 1.5-2.0 nm (the detection limit) up to 3.0-3 .5 nm . But as the bubble concentration increases substantially, the mean bubble diameter remains constant . Since no extra reflections arc detected at the annealing temperature, Kr inside the bubbles is probably present in the fluid state . This may be also derived from Simon type equation [15] on substituting of Kr pressure deduced from aK, room temperature value (table 2). Therefore, bubble migration should be favourable. During the coalescence process, bubble density drops approximately 1.5 times. Assuming, that total volume occupied by bubbles remains constant, we find bubble diameter to be 2r,, = 3.4 nm by the end of stage B. in a good agreement with the experimental value 2rh = 3.5 nm . The increase of Kr lattice parameter with annealing time during the stage B can be also easily explained in terms of Cu elastic expansion due to bubble coalescence, without acid of extra vacancies. Indeed, for elastic media the volume increase dV of a hole of initial volume V and radius r due to internal pressure P can be given as [16] : dV/V=(3/4 w)(P-2F/r),
(1)
where W = 48 .3 GPa and ir= 1 J m-2 are respectively the copper shear modulus and surface energy and P is the pressure inside bubbles deduced from the Ronchi equation of state [17] (P=2 .5 GPa when using a K,= 0.53 nm). From eq. (1) it is obvious that bubble coalescence will result in an increase of Kr lattice parameter up to
aKr=0.533 nm, which is very close to the value of aK, obtained after ta = 780 min, see fig. 2. Consequently, one can draw the conclusion that no influence of thermal vacancies on bubble formation is detected . 4.2. The role of radiation vacancies in Kr bubble formation
Three mean features can be outlined from the results presented in section 3 and are due to be discussed below: i) the annealing behaviour of Kr-implanted Cu samples exhibits no pronounced influence of thermal vacancies; ii) with increasing irradiation dose, the V/Kr ratio inside bubbles decreases remarkably to some constant value; iii) with increasing irradiation dose both the fraction of Kr atoms trapped within bubbles and dislocation density decrease. The deviation from 100% Kr trapping and reaching of Kr lattice parameter asymptotic value are observed above the same dose, i .e. 7.5 x 10 1° ions cm -2 . The formation of precipitates, especially at low doses of irradiation, requires long range migration of inert gas atoms. On the contrary to He, one can hardly expect Kr atom to occupy interstitial site in an fee metal, since a reaction of its transformation into substitutional position at the expense of self interstitial atom production is favourable . Once in a vacancy, Kr atom will be completely immobile unless it traps additional vacancy to form KrV2 complex, whose mobility is high enough at T > 0.3TM [18]. On the other hand, the annealing temperature of 0.45TM is too low to provide for a noticeable thermal vacancy equilibrium concentration : assuming Ev = 1 eV in Cu, the equilibrium vacancy concentration at 0.45T M does not exceed 5 x 10-° at.% . Therefore, the only vacancies available are those produced in displacement cascades . For the reason quoted above, their concentration should determine the concentration of mobile Kr atoms, and consequently the actual number of Kr atoms participating in the process of bubble formation. The relevant equation relating the net concentration C of radiation vacancies, survived after spontaneous recombination inside a cascade and irradiation dose is well known [19]
dC/dtß = vd(1 - 1,.C)2 - Q,C, (2) where trd = 6.9 x 10- is cm -2 is the number of displacements per one matrix atom created by a unit dose of krypton ion (obtained from TRIM calculation [111). V = 200 is the spontaneous recombination volume in number of Cu atomic volumes [19,20] and tr, is cross section for subthreshold transfers.
D. Kuzminot, et al.
/ Kr bubble formation in Cu
The square in this equation is obtained by taking into account the change of recombination volumes due to overlapping of cascades . The second term in the right-hand part of eq. (2) can be neglected [21]. The solution of eq . (2) gives the saturation value C= 1/V =0.5 at.% which is practically reached at doses close to 10 1 ' ions cm -2 in our experimental conditions . In fig. 8 the number of radiation vacancies and the number of implanted Kr atoms (assuming 100% retention) are plotted versus Kr irradiation dose . It is seen, that in the dose range used in our experiments the concentration of radiation vacancies remains constant . Therefore, the increase of irradiation dose from 2.5 x 1014 to 5 x 10 15 Kr cm -2 results in a decrease of the number of free vacancies available per Kr atom from - 10 to - 0.5 . As a consequence, during the subsequent annealing the probability of vacancy trapping by Kr atoms will increase, but fewer free vacancies will remain to be trapped by the bubbles. This consideration may give a clue to understanding of aK, reduction with increasing fluence observed in our experiment. For further discussion, two assumptions should be made. First, once the processes of spontaneous recombination have occurred, Kr atoms may be found mainly in substitutional position, i .e. in the form of KrV complexes. It means that the overall vacancy concentration equals the saturation concentration of radiation vacancies plus the concentration of retained (implanted) Kr atoms. This assumption gives the lower limit of vacancy concentration. Secondly, dislocations and bubbles are the main vacancy sinks, i .e. after annealing all the vacancies are trapped either by bubbles or by dislocations . As no dislocations are observed in as-implanted samples, vacancy trapping implies that vacancies mainly assist formation of dislocations . Taking into account 8,
10141010
1012
1010.02
1014 2
Irradiation dose, cm Fig. 8. Calculated variation of the number of radiation vacan cies (N,,) and the number of Kr atoms retained in Cu matrix (N,K,) with irradiation dose .
475
Table 3 Calculation of vacancy balance forvarious krypton irradiation doses . C_ C,,, and Cvd are respectively the concentrations of radiation vacancies as calculated from eq. (2), trapped by bubbles and trapped by dislocations. Latter value is calculated under assumption that for the lowest dose Cvr = C vb + Cad (see the text) Dose [10' 4cm -2 ]
Cvr
Cvn
Cvr -Cvb
[at.%]
Cvd [at.%]
2.5 6.0 7.5 13.0 50 .0
0.5 0.5 0.5 0.5 0.5
0.12 0.25 0.30 0.36 0.48
0.38 0.25 0.20 0.14 0.02
0.38 0.24 0.23 0.22 0.13
[at.%]
[at.%]
the fraction of Kr atoms trapped within bubbles, a, the V/Kr ratio inside bubbles and the concentration of Kr atoms implanted CK,, the concentration of radiation vacancies trapped by bubbles C' may be calculated as SCKr(a - 1) . If the concentration of vacancies trapped by dislocations Cvd is proportional to the density of dislocations Cd, C vd =pCd. /3 may be found from an assumption that for the lowest irradiation dose the concentration of radiation vacancies is C= C°b +/3Cd . The results of vacancy balance calculations are presented in table 3. As follows from table 3, for irradiation doses below 1015 Kr cm -2 a very good balance is met between the concentrations of vacancies trapped by bubbles and by dislocations. But for higher doses there are remarkable discrepancies. Nevertheless, it is obvious that these discrepancies may appear due to formation of Kr precipitates in the course of irradiation at doses above 10 15 Kr cm -2 . In this case, the number of vacancies available is, of course, underestimated. Therefore, all the radiation vacancies are involved in the process of bubble and dislocations formation . Competition between these two processes determines the V/Kr ratio inside bubbles, bubble and dislocation densities. For this reason, the increase of Kr irradiation dose will eventually result in a decrease of the fraction of Kr atoms trapped by bubbles (fig . 6b), because the irradiated matrix will be merely running out of free (radiation) vacancies assisting mobile Kr-V complexes formation . The appearance of saturation of the total amount of krypton trapped (fig. 9) due to processes limiting Kr retention is no valid since these processes become significant only at doses above 10" ions cm -2 [22]. The V/Kr saturation value observed inside bubbles (fig . 6) might be attained in two major ways: a) by pressure-driven bubble growth, i .e. dislocation loop punching; b) through mere Kr-V complexes absorption . Roughly, the validation of these two mechanisms
476
D. Kuzminoi , et aL / Kr buffle formation in Cu 5 . Conclusion
Irradiation dose, crn2 Fig. 9. Variation of the number of Kr atoms trapped by bubbles vs ion irradiation dose. can be made on the basis of V/Kr balance inside matrix and inside bubbles. For the first case, we assume that the majority of radiation vacancies are trapped by KrVZ complexes, but additional vacancies inside the bubbles are gained via dislocation loop punching . In this case, the upper level of the number of Kr atoms trapped by bubbles is determined by the number of radiation vacancies, that is two times in excess of the value registered experimentally (figs. 9a and c) . Also, the pressure inside bubbles (P = 2.8 GPa) is, in fact, not high enough to induce dislocation loop punching [23,24] . The second way seems to be more probable, as substitutional Kr tends to gain more than one vacancy [141 . In this case only radiation vacancies contribute to the bubbles. The calculated upper limit of the number of Kr atoms trapped by bubbles under assumption that V/Kr ratio cannot exceed 3 . is presented in fig. 9b (note, that in order to reach the ratio V/Kr = 3, only two radiation vacancies must be accounted for, since Kr atoms are supposed to occupy substitutional position). It is worth nothing, that both experimental (fig. 9a) and calculated (fig . 9b) saturation levels are in very good agreement. Even in cast , that the majority of Kr atoms are present in the form of KrV, complexes, there is an imaginary possibility of their dissociation to KrV + V in the vicinity of bubbles due to interaction with elastic stresses, and in this way supply of the bubbles with additional vacancies . In the presence of stresses, this process can become more favourable with respect to migration of inert gas-divacancy complex, since in fee metals the difference between activation energies of dissociation and migration of VZ or impurity-divacancy complex is of the order of tenths of eV [18,251. But for confirmation serious theoretical study is necessary.
Kr bubble formation in Cu after irradiation in a dose range 2 .5 x 10 14 to 4.5 x 1015 Kr cm -` and in situ annealing at 0 .45TM has been studied with TEM . After all the implantations and subsequent thermal treatments, the presence of solid Kr inside bubbles was detected . With increasing . irradiation dose the Kr lattice parameter was found to decrease from a mean value of 0.545 nm to a saturation value of 0 .523 nm, while the number of Kr atoms trapped by bubbles also reached some saturation value . This behaviour was explained in terms of interaction of increasing number of Kr atoms with a constant number of radiation vacancies. Some mechanisms of bubble growth during post implantation low temperature annealing (0.45TM ) have also been discussed .
Acknowledgement One of us (D.K .) acknowledges Conseil Régional Poitou-Charentes for financial support of this work.
References [l] H . Ullmaier, Radiat . Eff. 78 (1983) 1 . [2] S .E . Donnelly, Radiat . Eff. 90 (1985) 1 . [31 C. Templier . C . Jaouen, J .P . Rivi6re, J . Delafond and J . Grilh6, C . R. Acad . Sci. Paris 299 (1984) 613. [41 A. vom Felde, J. Fink. Th. Muller-Heinzerling, J. Pfluger, B . Scheerer, G. Linker and D. Kaletta, Phys. Rev. Lett . 53 (1984) 922. [5] C . Templier, J .C. Desoyer, H. Garem and J .P . Rivii;re . Acta Metall . 37 (1989) 393. [61 J .H. Evans and D.J . Mazey. J . Phys. F15 (1985) Lt . [7] S.E. Donnelly and C .J. Rossouw, Nucl . Instr . and Meth . B13 (1986) 485 . [81 R .C. Birtcher and W . Jäger, Nucl . Instr. and Meth . B15 (1986) 435. [9] H . Trinkaus, B .N . Singh and A.J.E . Foreman, J . Nucl. Mater. 174 (1990) 80 . [101 H. Trinkaus . J. Nucl. Mater. 17 4 (1990) 178. [111 J. Biersack and L.G. Haggmark . Nucl . Instr . and Meth. 174 (1980) 257 . 1121 C. Templier . H. Garem and J .P . Rivi6re, Philos. Mag . A53 (1986) 667. [131 A.S . Liu and R .C. Birtcher, Mat . Res . Soc . Symp. Proc . 12 8 (1989) 303 . [14] E. Yagi, Nucl. Instr . and Meth . B39 (1989) 68. [15] R .K. Crawford, in : Rare Gas Solids, vol. 1, eds . M .L. Klein and J .A . Venables (Academic Press. London, 1977) pp . 663-822 . [161 J .D. Eshelby, in: Physics of Metals, ed. P .B . Hirsch (Cambridge University Press. 1975) p. 1 . [171 C . Ronchi, J . Nucl . Mater. 96 (1981) 134 .
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[18] [191 [201 [211 [221
C.F. Melius, W.D. Wilson and C.L. Bisson, AERE Report R9433 (Harwell, 1981) vol. 1, p . 14. K . Dettmann, G . Leibfreid and K. Shroeder, Phys. Status Solidi 22 (1967) 423. K. Dettmann and K. Shroeder, Radiat . Eff. Lett . 67 (1967) 135 . J.P. Rivière and J .F . Dinhut, J. Nucl. Mater. 118 (1983) 333. R.C . Birtcher and W. Jäger, Ultramicroscopy 22 (1987) 267.
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[231 D .W. Greenwood, A.J.E . Foreman and D .E. Rimmer, J . Nucl . Mater. 4 (1959) 305 . [24] K . Kamada, A. Sagara, H. Kinoshita and H. Takahashi, Radiat . Eff. 106 (1988) 219. [25] W. Schiile and R . Scholz, in: Point Defects Interaction in Metals, ed . H . Takamara (University of Tokyo Press, North-Holland, 1982) p. 257.
Nuclear Instruments &Methods in Physics Research Section B
Kr bubble formation in Cu after moderate doses of ion irradiation: the role of radiation vacancies D. Kuzminov ', C . Templier, E. Raqi and H. Garem
Laboratoire de Métallurgie Physique, URA 13140, Ac . du Recteur Pineau, 86022 Poitiers Cédex, France
Received 6 May 1991 and in revised form 25 July 1991 A TEM study of Kr bubble formation in Cu as a result of ion irradiation in a dose range from 2.5 x 10 14 to 5 x 10 15 Kr cm -2 and subsequent annealing is presented . For irradiation doses below 5 x 10 15 Kr cm -2 no bubbles are observed in as-implanted samples . Post-implantation annealing results in formation of Kr bubbles containing solid inert gas at room temperature . Two stages of bubble growth are observed during annealing: bubble growth by complexes absorption and bubble growth by coalescence . With increasing dose, the Kr lattice parameter decreases from 0.545 nm to an asymptotic value of 0.523 nm and the fraction of Kr atoms trapped within bubbles reaches saturation . This behaviour is explained in terms of radiation vacancy interaction with bubbles and dislocations. 1. Introduction The technological interest in rare gases in metals stems to a large degree of fusion first wall and fission reactor applications. Tritium in fusion reactors permeates the first wall and decays into helium ; alpha particles are injected into the first wall from the plasma itself. Fission fragments are the primary source of the heavier rare gases in metals. The interest in heavy rare gases is also dictated by their use in ion-beam mixing technology, production of metallization layers in microelectronics by sputter deposition, sintering of powders, etc . Rare gases have a very low solubility in metals and therefore strongly tend to precipitate within cavities (bubbles) following ion implantation [1]. The phenomena of helium bubble formation is very well known and has been broadly investigated . One of the crucial points in understanding gas-atom clustering in metals is the question of pressure and density inside the bubbles [2], which has been discussed for more than thirty years . The presence of high pressure and density inside bubbles was finally confirmed by the discovery in 1984 that implanted heavy rare gas atoms (Ar and Xe) precipitated in Al in solid form [3,4] at room temperature: in order to confine solid precipitates the pressure inside * This work is financially supported by Conseil Régional de Poitou-Charentes. 1 On leave from Institute of Physical Chemistry of the Academy of Sciences of the USSR 117915. Moscow, Leninsky Prospekt 31, USSR.
bubbles must exceed 2-3 GPa. This discovery was subsequently extended to observation of Ar, Kr and Xe precipitates in other metals [5-8]. The aim of this article is to report experimental observations of Kr bubble formation in Cu after moderate doses of ion irradiation (2 .5 x 10 14-5 x 10 15 ions cm -2 ). Particular attention is paid to accurate calculation of vacancy-krypton (V/K0 ratio inside bubbles and to its comparison with the number of vacancies produced versus irradiation dose. It allows us to draw some conclusions about the participation of radiation vacancies in bubble formation, the question which was discussed in recent theoretical studies [9,10]. 2 . Experimental technique Copper discs of 3 mm in diameter and 0.1 mm thick were punched out of polycristalline Cu foil and then annealed at 1150 K for 6 h under vacuum better than 10 -4 Pa . This allowed us to obtain samples with cristallite size ranging from 0.1 to a few micron . Then the samples were clectropolished from both sides and implanted. The implantation was carried out at room temperature with Kr ions subsequently at two energies 240 kcV and 80 kcV and ion fluxes around 10 12 ions cm -2 s -1 . The implantation energies were selected on the basis of results from TRIM computer code [ll] in order to produce distribution profile close to homogeneous with the largest penetration range of 60 nm . The results of TRIM89 calculation for irradiation doses used are summarized in table 1 .
0168-583X/92/$05 .00 0 1992 - Elsevier Science Publishers B .V. All rights reserved
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D. Kuzminor et al. / Kr bubble formation in Cu
Table 1 Irradiation conditions as calculated with TRIM computer code for 1 .3 x 1015 ions cm -2 implanted sample . For other doses, the same ratio between the two energies have been used Energy [keV]
Dose [cm - 'l
Mean range [nn]
240 I .0 x 10" 51 19 80 2 .6 x 10 14
At . cone. [at .%]
Disp . dam . per ion
0.3 0.3
3500 1300
TEM examination of the samples at magnification of 5 x 10 4 times was performed in a JEOL 2000X operating at 200 kV . Cavities were identified by their defocuse contrast and were usually imaged at defocuse
distances e 5 0.8 wm in sample areas of = 100 nm thick. Selected-area diffraction patterns were taken with the electron beam parallel to (110) or (112) matrix orientation . The solid rare gas lattice parameter was calculated by the simple ratio method from (111) Cu matrix and solid Kr reflections under the assumption that the Cu lattice constant was not affected measurably by the precipitation process. These measurements were made either by using microdensitometer or computer image analysis with an estimated accuracy of about 0 .5-1%. Nevertheless, for very weak reflections which were observed after 2 .5 x 10 14 ions cm -2 implantation, the accuracy could reach 2-3% . In situ annealing of the samples at 620 ± 10 K was performed using commercial heating stage of the microscope.
Fig . 1. TEM micrographs obtained from Cu samples following implantation of 5 x 10 14 Kr CM - 2 cm and annealing at 620 K for (a) 5, (b) 20 and (c) 780 min . From up to down: (I11) Cu and Kr reflections in selected area diffraction patterns (Kr reflections are arrowed), bright-field underfocused ((a) and (b)) and overfocused (c) images, dark-field images obtained with (I11) Kr reflection .
47 1
D. Kuzminov et al. / Kr bubble formation in Cu
3. Experimental results
0.55
3.1. Microstructure development during long-time annealing
TEM analysis of the samples has been performed at room temperature both before and after annealing for different time at 620 K (i .e . 0.45T,H , TM being the Cu melting temperature). This temperature has been chosen in order to avoid the effect of thermal vacancies on the bubble growth process. Before annealing, all the ' samples (for exception of that implanted at the highest dose, 5 x 10'5 Kr em - Z) could be characterized by the absence of extra reflections corresponding to solid Kr. Inspite of a large number of small defect clusters revealed with weak beam technique (fig . 5a), neither visible Kr precipitates, nor dislocations were detected. After the first annealing (2-5 min), both the appearance of Kr bubbles and a well developed dislocation structure could be observed. An example of microstructural changes of Kr-implanted Cu (5 x 10'4 ions cm -Z ) after 5, 20 and 780 min of annealing is presented in fig. 1. Microdiffraction pattern analyses together with the analyses of bright-field and dark-field images obtained at room temperature with <111) Kr reflections show that Kr within bubbles is present in the crystalline state. Nevertheless, during annealing at 620 t 10 K no extra reflections were observed . The variations with annealing time t,, of bubble density N, mean bubble diameter (2rß,), Kr lattice parameter and the fraction of Kr atoms trapped inside bubbles S &duc~d from the latter quantities are given in figs . 2 and 3. It is seen from these figures that the
w y o .~
100 200 800 Annealing time, min Fig. 3. Variation of Kr lattice parameter and the fraction of Kr atoms trapped in bubblesduring post-implantation annealingat 620K. Irradiation dose was5x 10'4 cm -2 . 0
variation of microstructure with t;, may be represented by two stages: stage A (t,, < 20 min) and stage B (t a > 20 min). Stage A is characterized by the increase of both bubble density Nb up to 1 .3 x 10'2 cm -2 and S up to 100% for the given sample (fig. 2). At the same time, the mean bubble diameter and the Kr lattice parameter stay practically unchanged (2r,, = 3.0 nut and aKr = 0.530 nm respectively). Higher annealing time (stage B) results in a slight increase of bubble diameter and Kr lattice parameter, reaching mean values of 2r b = 3.5 nm and a,U = 0.535 nm respectively after t o _ 780 min. Meanwhile, the bubble density drops from 1.3 x 10'2 to 8.4 x 10" cm -2 and this decrease mainly occurs during the first minutes of annealing. Exactly the same general annealing behaviour was observed for the samples implanted at 3 x 10'4 and 1.3 x 10 15 Kr CM-2 . 3.2. Dose dependence
Fig. 2. Variation of bubble density and bubble diameter during post-implantation annealing at 620 K. Irradiation dose was5x10'4 Kr cm -2 .
Quantitative information about the thermodynamic state of solid Kr inside bubbles and the number of Kr atoms comprised by bubbles can be deduced from the lattice parameter, bubble diameter and density measueements. These measurements (table 2) have been performed at room temperature following implantation of Kr to various doses plus annealing at 620 K for - 20 min (i.e . at the end of stage A). It allowed us to avoid the influence of bubble coalescence on Kr lattice changes. The resultsof TEM examinations are given in fig. 4. Also, dislocation structure was imaged after the treatments mentioned above. The results of dislocations observation in TEM for various irradiation doses are presented in fig. 5. TEM images were obtained
D. Kuzminoc et al. / Kr bubble formation in Cu
472
Table 2 Variation of bubble density N6 , mean bubble diameter d, Kr lattice parameter axr and Ronchi pressure P inside bubbles measured after annealing stage A vs krypton irradiation dose P Dose Nb d aKr 11014Cm-=] [1011 Cm -Z] [nm] [nm] [GPa] 2.5 3.0 5.0 6.0 7.5 13.0 50.0
7.0±0 .5 7.3±0 .7 13 ± 1 13 ± 1 .5 17 ±2 19 ±2 23 ±1
3.0±0 .5 3.0±0 .5 3.0±0 .5 3.0±0 .5 3.0±0 .5 3.2±0 .5 3 .2±0.5
0.545±0.010 1 .8 0.540±0.008 1 .8 0.530±0.005 2.3 0.528±0.005 2.5 0.524±0.005 2.8 0.523±0.005 2.8 0.523±0.005 2 .8
using weak-beam technique. The observation conditions were : g = 1111 , sR = 0.14 run -1 . For all the irradiation doses extra reflections corresponding to solid Kr can be observed at room temperature . In case of the lowest irradiation dose, i .e . 2.5 x 10 14 ions cm -2, the extra reflections are extremely weak and hardly detectable (fig . 4a). However, darkfield images obtained using Kr reflections confirm that Kr inside bubbles is present in the crystalline state. Variation of Kr lattice parameter and V/Kr ratio inside bubbles with irradiation dose is shown in fig . 6a. With increasing Kr dose from 2.5 x 10 14 to 5 x 10 15 ions cm -2, the average Kr lattice parameter decreases from 0.545 nm toward some asymptotic value of 0.523 run, corresponding to a decrease of V/Kr ratio from = 3.5 to = 3.0. This result seems to be completely contradictory to the increases of the rare gas lattice parameter with increasing dose observed by Templier et al . for Xe in Al [121 and Birtcher and Liu [131 for Kr irradiated Ni,
but at fluences from 10 15 to 1016 CM -Z and from 10 16 to 5 x 1016 CM-2 respectively. Variation of the fraction of Kr atoms precipitated within bubbles with increasing irradiation dose has been calculated using the data in table 2 and is plotted in fig. 6b . Approximately 100% Kr trapping within bubbles is detected up to a dose of 7.5 x 10 14 ions cm -2, while at higher irradiation doses the number of Kr atoms trapped by bubbles approaches some saturation value of = 1.1 x 10 15 ions em - Z, indicating only = 24% trapping at 0 = 5 x 10 15 ions cm -Z . Variation of dislocation density versus irradiation dose, calculated using the micrographs in fig. 5, is plotted in fig . 7. According to this plot, the density of dislocations drops as ion fluence is increased from 2.5 x 10 14 to 5 x 10 15 Kr CM-2 . It is worth noting that only visible dislocations were taken into account. Meanwhile, it is obvious from fig. 4a that for the smallest dose practically no random distribution of defect clusters (mainly supposed to be bubbles) is observed . Almost all of them are aligned along visible dislocations or invisible lines, which could probably be imaged as dislocations under different observation conditions. Therefore, we expect that for the smallest irradiation dose the density of dislocations might have been slightly underestimated . 4. Discussion 4.1 . As-implanted Cu and annealing behaviour As it has been mentioned in section 3.1, no visible bubbles were detected in as-implanted samples, for
Fig. 4. (111) Cu and Kr reflections in selected area diffraction patterns (top, Kr reflections arrowed) and dark-field images (bottom) taken with (111) Kr reflections, obtained from Cu samples following implantation at doses (cm'z1: (a) 3x10 14, (b) 6x10 14, (c) 5X10'5 and post-implantation annealing at 620 Kuntil the endof stage A.
D . Kuzminov et
473
al. / Kr bubble formation in Cu
a
14
10
c
15
10
cm2
Irradiation dose,
16
10
Fig. 6. Variation of V/Kr ratio inside bubbles and the Kr lattice parameter (a), mean fraction of Kr atoms trapped by bubbles (b) vs ion irradiation dose .
c
16
0
-,L 12" y
Q
w 81 t~p
Fig . 5 . Cu defect structure after Kr implantation and annealing at 620 K until the end of stage A, as revealed with TEM. Implantation doses were [cm 1; (a) 2.5 x 10 (no annealing); .5X1014 (c) 6 x 10 ; (d) I .3 x 10 ; (e) 5X1015 2 (b) ; . The images were obtained using weak-beam technique, g =111 (6g excited), Sg = 0.14 nm'
14
-2
14
15
1.
A
41 10
14
1015 Irradiation dose,
ctri2
16
10
Fig . 7. Variation of dislocation density with irradiation dose .
474
D. Kuzininoi- et aL / Kr bubble formation in Cu
exception of irradiation with 5 x 10 5 Kr CM -2. Due to a large number of defects and resolution limit, it was not possible to detect bubbles with diameters less then 1.5-2.0 rim. Therefore, we assume that Kr atoms before annealing arc present either in submicroscopic clusters or in solution in Cu. This assumption does not contradict with recent observations by ion channelling method [14] that after low doses of implantation, a large fraction of Kr is contained in KrV complexes. Nevertheless, at doses somewhat higher than 10 5 Kr cm -2 , formation of bubbles is detected, in agreement with our observations . On the basis of these arguments and general annealing behaviour described in section 3.1 (figs. 2 and 3), the two stages observed during annealing may be attributed to two different processes of bubble growth : stage A: bubble growth by Kr atoms and vacancies entrapment; stage B: bubble growth by coalescence . The fact that these stages are very distinguishable in time probably arises from low bubble concentration and big difference between Kr and Kr bubble diffusivities in Cu . During stage A the bubble diameter increases from = 1.5-2.0 nm (the detection limit) up to 3.0-3 .5 nm . But as the bubble concentration increases substantially, the mean bubble diameter remains constant . Since no extra reflections arc detected at the annealing temperature, Kr inside the bubbles is probably present in the fluid state . This may be also derived from Simon type equation [15] on substituting of Kr pressure deduced from aK, room temperature value (table 2). Therefore, bubble migration should be favourable. During the coalescence process, bubble density drops approximately 1.5 times. Assuming, that total volume occupied by bubbles remains constant, we find bubble diameter to be 2r,, = 3.4 nm by the end of stage B. in a good agreement with the experimental value 2rh = 3.5 nm . The increase of Kr lattice parameter with annealing time during the stage B can be also easily explained in terms of Cu elastic expansion due to bubble coalescence, without acid of extra vacancies. Indeed, for elastic media the volume increase dV of a hole of initial volume V and radius r due to internal pressure P can be given as [16] : dV/V=(3/4 w)(P-2F/r),
(1)
where W = 48 .3 GPa and ir= 1 J m-2 are respectively the copper shear modulus and surface energy and P is the pressure inside bubbles deduced from the Ronchi equation of state [17] (P=2 .5 GPa when using a K,= 0.53 nm). From eq. (1) it is obvious that bubble coalescence will result in an increase of Kr lattice parameter up to
aKr=0.533 nm, which is very close to the value of aK, obtained after ta = 780 min, see fig. 2. Consequently, one can draw the conclusion that no influence of thermal vacancies on bubble formation is detected . 4.2. The role of radiation vacancies in Kr bubble formation
Three mean features can be outlined from the results presented in section 3 and are due to be discussed below: i) the annealing behaviour of Kr-implanted Cu samples exhibits no pronounced influence of thermal vacancies; ii) with increasing irradiation dose, the V/Kr ratio inside bubbles decreases remarkably to some constant value; iii) with increasing irradiation dose both the fraction of Kr atoms trapped within bubbles and dislocation density decrease. The deviation from 100% Kr trapping and reaching of Kr lattice parameter asymptotic value are observed above the same dose, i .e. 7.5 x 10 1° ions cm -2 . The formation of precipitates, especially at low doses of irradiation, requires long range migration of inert gas atoms. On the contrary to He, one can hardly expect Kr atom to occupy interstitial site in an fee metal, since a reaction of its transformation into substitutional position at the expense of self interstitial atom production is favourable . Once in a vacancy, Kr atom will be completely immobile unless it traps additional vacancy to form KrV2 complex, whose mobility is high enough at T > 0.3TM [18]. On the other hand, the annealing temperature of 0.45TM is too low to provide for a noticeable thermal vacancy equilibrium concentration : assuming Ev = 1 eV in Cu, the equilibrium vacancy concentration at 0.45T M does not exceed 5 x 10-° at.% . Therefore, the only vacancies available are those produced in displacement cascades . For the reason quoted above, their concentration should determine the concentration of mobile Kr atoms, and consequently the actual number of Kr atoms participating in the process of bubble formation. The relevant equation relating the net concentration C of radiation vacancies, survived after spontaneous recombination inside a cascade and irradiation dose is well known [19]
dC/dtß = vd(1 - 1,.C)2 - Q,C, (2) where trd = 6.9 x 10- is cm -2 is the number of displacements per one matrix atom created by a unit dose of krypton ion (obtained from TRIM calculation [111). V = 200 is the spontaneous recombination volume in number of Cu atomic volumes [19,20] and tr, is cross section for subthreshold transfers.
D. Kuzminot, et al.
/ Kr bubble formation in Cu
The square in this equation is obtained by taking into account the change of recombination volumes due to overlapping of cascades . The second term in the right-hand part of eq. (2) can be neglected [21]. The solution of eq . (2) gives the saturation value C= 1/V =0.5 at.% which is practically reached at doses close to 10 1 ' ions cm -2 in our experimental conditions . In fig. 8 the number of radiation vacancies and the number of implanted Kr atoms (assuming 100% retention) are plotted versus Kr irradiation dose . It is seen, that in the dose range used in our experiments the concentration of radiation vacancies remains constant . Therefore, the increase of irradiation dose from 2.5 x 1014 to 5 x 10 15 Kr cm -2 results in a decrease of the number of free vacancies available per Kr atom from - 10 to - 0.5 . As a consequence, during the subsequent annealing the probability of vacancy trapping by Kr atoms will increase, but fewer free vacancies will remain to be trapped by the bubbles. This consideration may give a clue to understanding of aK, reduction with increasing fluence observed in our experiment. For further discussion, two assumptions should be made. First, once the processes of spontaneous recombination have occurred, Kr atoms may be found mainly in substitutional position, i .e. in the form of KrV complexes. It means that the overall vacancy concentration equals the saturation concentration of radiation vacancies plus the concentration of retained (implanted) Kr atoms. This assumption gives the lower limit of vacancy concentration. Secondly, dislocations and bubbles are the main vacancy sinks, i .e. after annealing all the vacancies are trapped either by bubbles or by dislocations . As no dislocations are observed in as-implanted samples, vacancy trapping implies that vacancies mainly assist formation of dislocations . Taking into account 8,
10141010
1012
1010.02
1014 2
Irradiation dose, cm Fig. 8. Calculated variation of the number of radiation vacan cies (N,,) and the number of Kr atoms retained in Cu matrix (N,K,) with irradiation dose .
475
Table 3 Calculation of vacancy balance forvarious krypton irradiation doses . C_ C,,, and Cvd are respectively the concentrations of radiation vacancies as calculated from eq. (2), trapped by bubbles and trapped by dislocations. Latter value is calculated under assumption that for the lowest dose Cvr = C vb + Cad (see the text) Dose [10' 4cm -2 ]
Cvr
Cvn
Cvr -Cvb
[at.%]
Cvd [at.%]
2.5 6.0 7.5 13.0 50 .0
0.5 0.5 0.5 0.5 0.5
0.12 0.25 0.30 0.36 0.48
0.38 0.25 0.20 0.14 0.02
0.38 0.24 0.23 0.22 0.13
[at.%]
[at.%]
the fraction of Kr atoms trapped within bubbles, a, the V/Kr ratio inside bubbles and the concentration of Kr atoms implanted CK,, the concentration of radiation vacancies trapped by bubbles C' may be calculated as SCKr(a - 1) . If the concentration of vacancies trapped by dislocations Cvd is proportional to the density of dislocations Cd, C vd =pCd. /3 may be found from an assumption that for the lowest irradiation dose the concentration of radiation vacancies is C= C°b +/3Cd . The results of vacancy balance calculations are presented in table 3. As follows from table 3, for irradiation doses below 1015 Kr cm -2 a very good balance is met between the concentrations of vacancies trapped by bubbles and by dislocations. But for higher doses there are remarkable discrepancies. Nevertheless, it is obvious that these discrepancies may appear due to formation of Kr precipitates in the course of irradiation at doses above 10 15 Kr cm -2 . In this case, the number of vacancies available is, of course, underestimated. Therefore, all the radiation vacancies are involved in the process of bubble and dislocations formation . Competition between these two processes determines the V/Kr ratio inside bubbles, bubble and dislocation densities. For this reason, the increase of Kr irradiation dose will eventually result in a decrease of the fraction of Kr atoms trapped by bubbles (fig . 6b), because the irradiated matrix will be merely running out of free (radiation) vacancies assisting mobile Kr-V complexes formation . The appearance of saturation of the total amount of krypton trapped (fig. 9) due to processes limiting Kr retention is no valid since these processes become significant only at doses above 10" ions cm -2 [22]. The V/Kr saturation value observed inside bubbles (fig . 6) might be attained in two major ways: a) by pressure-driven bubble growth, i .e. dislocation loop punching; b) through mere Kr-V complexes absorption . Roughly, the validation of these two mechanisms
476
D. Kuzminoi , et aL / Kr buffle formation in Cu 5 . Conclusion
Irradiation dose, crn2 Fig. 9. Variation of the number of Kr atoms trapped by bubbles vs ion irradiation dose. can be made on the basis of V/Kr balance inside matrix and inside bubbles. For the first case, we assume that the majority of radiation vacancies are trapped by KrVZ complexes, but additional vacancies inside the bubbles are gained via dislocation loop punching . In this case, the upper level of the number of Kr atoms trapped by bubbles is determined by the number of radiation vacancies, that is two times in excess of the value registered experimentally (figs. 9a and c) . Also, the pressure inside bubbles (P = 2.8 GPa) is, in fact, not high enough to induce dislocation loop punching [23,24] . The second way seems to be more probable, as substitutional Kr tends to gain more than one vacancy [141 . In this case only radiation vacancies contribute to the bubbles. The calculated upper limit of the number of Kr atoms trapped by bubbles under assumption that V/Kr ratio cannot exceed 3 . is presented in fig. 9b (note, that in order to reach the ratio V/Kr = 3, only two radiation vacancies must be accounted for, since Kr atoms are supposed to occupy substitutional position). It is worth nothing, that both experimental (fig. 9a) and calculated (fig . 9b) saturation levels are in very good agreement. Even in cast , that the majority of Kr atoms are present in the form of KrV, complexes, there is an imaginary possibility of their dissociation to KrV + V in the vicinity of bubbles due to interaction with elastic stresses, and in this way supply of the bubbles with additional vacancies . In the presence of stresses, this process can become more favourable with respect to migration of inert gas-divacancy complex, since in fee metals the difference between activation energies of dissociation and migration of VZ or impurity-divacancy complex is of the order of tenths of eV [18,251. But for confirmation serious theoretical study is necessary.
Kr bubble formation in Cu after irradiation in a dose range 2 .5 x 10 14 to 4.5 x 1015 Kr cm -` and in situ annealing at 0 .45TM has been studied with TEM . After all the implantations and subsequent thermal treatments, the presence of solid Kr inside bubbles was detected . With increasing . irradiation dose the Kr lattice parameter was found to decrease from a mean value of 0.545 nm to a saturation value of 0 .523 nm, while the number of Kr atoms trapped by bubbles also reached some saturation value . This behaviour was explained in terms of interaction of increasing number of Kr atoms with a constant number of radiation vacancies. Some mechanisms of bubble growth during post implantation low temperature annealing (0.45TM ) have also been discussed .
Acknowledgement One of us (D.K .) acknowledges Conseil Régional Poitou-Charentes for financial support of this work.
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D. Kuzminoc et aL / Kr bubble formation in
[18] [191 [201 [211 [221
C.F. Melius, W.D. Wilson and C.L. Bisson, AERE Report R9433 (Harwell, 1981) vol. 1, p . 14. K . Dettmann, G . Leibfreid and K. Shroeder, Phys. Status Solidi 22 (1967) 423. K. Dettmann and K. Shroeder, Radiat . Eff. Lett . 67 (1967) 135 . J.P. Rivière and J .F . Dinhut, J. Nucl. Mater. 118 (1983) 333. R.C . Birtcher and W. Jäger, Ultramicroscopy 22 (1987) 267.
Cu
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[231 D .W. Greenwood, A.J.E . Foreman and D .E. Rimmer, J . Nucl . Mater. 4 (1959) 305 . [24] K . Kamada, A. Sagara, H. Kinoshita and H. Takahashi, Radiat . Eff. 106 (1988) 219. [25] W. Schiile and R . Scholz, in: Point Defects Interaction in Metals, ed . H . Takamara (University of Tokyo Press, North-Holland, 1982) p. 257.