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Dose dependence of impurity detrapping stages in irradiated metals
Journal of Nuclear Materials 73 (1978) 118-120 0 North-Holland Publishing Company
DOSE DEPENDENCE OF IMPURITY DETRAPPINC
1. Introduction
The dose dependence of an impurity detrapping stage is given by a combination of the dose dependence of the trapping process and that of the detrapping process. The answers to the following questions are therefore required: (1) What percentage of migrating interstitials (normalised to the initially introduced resistivity increase) is trapped at the particular trapping site and how does this percentage change with dose? (2) What is the probability of a detrapped interstitial reaching a vacancy with subsequent annihilation and how does this probability change with dose *? The answer to these questions are often straightforward and sufficient to explain the observed dose dependence. If, e.g., one impurity species is dominating and a comparable quantity of interstitials are reacting in the recovery stage of free migration (“1,“) after a 4 K irradiation, the percentage of impurity trapping increases with decreasing dose, due to the decreasing competition of the interstitial-vacancy annihilation, which provides the answer to the first question. As for the second question, the detrapped interstitial will find its way to a vacancy with a high probability if no other traps are present in a quantity comparable to the vacancy concentration, and consequently no dose dependence results from the detrapping process alone. Combining the answers to the two questions, we obtain a decreasing normalised stage height with increasing dose [4].
3.0
irradiation
2.5 2.0 4; % 1.0 0.5
70
100
120
TEMPERATURE
or the
2. Basic concept
u +100 at bmUAa_
0
METALS
ture, the concentration of traps considered, concentration of other traps.
Recently a study of the dose dependence of Cu alloyed with Ag, electron irradiated at 50 K, was presented in this journal [ 11; elsewhere, an investigation of the dose dependence of Cu alloyed with Au after thermal-neutron irradiation at 4 K was published [2]. Both impurities lead to the same principal recovery stages (at only slightly shifted temperatures) in the stage II regime of Cu, and these recovery stages show the same dependence on the alloying concentration [3]. It is therefore astonishing at first sight, that an opposite dose dependence has been found for the main detrapping stage (at -110 K and at -120 K for the Au and the Ag impurities, respectively) as is illustrated in fig. 1 and 2 [ 1,2]. It is the purpose of this comment to point out that these results are not contradictory, and to discuss why and how the dose dependence of a detrapping stage may be influenced by experimental parameters as, e.g., the concentration of radiation induced defects, the irradiation tempera-
50 K
STAGES IN IRRADIATED
150 K
* Similarly, if ‘dose’ is replaced by ‘alloying concentration’, the dependence on the alloying concentration [ 1,3] may be looked at. The results of both types of experiments should be consistent.
Fig. 1. Differentiated isochronal resistivity recovery curves after electron irradiation at 50 K for initial defect concentrations of -12 at ppm and -54 at ppm, normalised to the resistivity increments at 50 K (Dworschak et al. [ 1 I). 118
U. Giisele, J. Aspeling /Dose dependence of impurity detrapping stages in metals
3. Irradiation at 4 K and high impurity concentration For fairly high impurity concentrations (say, e.g., 100-1000 at ppm brought in by alloying with the impurity to be investigated) additional traps may be provided, with a higher interstitial binding energy than a single impurity atom, by alloying atoms lying accidentally close together [2,3,5]. If in addition, the concentration of radiation-induced defects is much lower than the alloying concentration, the percentage of trapped interstitials is almost dose-independent. Therefore the dose dependence of the final detrapping stage from single impurities (at -110 K for Au and -120 K for Ag in Cu) is given by the dose dependence of the detrapping alone. If the vacancy concentration is comparable to the concentration of deeper traps (consisting of several impurity atoms), the probability of interstitals recombining with vacancies increases with increasing dose, leading to just the opposite dose dependence found in the case of comparable defect and impurity concentrations. In this way the dose dependence of the 110 K stage in fig. 2 has been explained [2]. The recovery stage at 150 K is connected with the detrapping of interstitials from traps consisting of several Au atoms [2,3]. A similar dose dependence may be expected for the case of two impurity species A and B, where the concentration of A is much higher than the vacancy concentration and
119
where interstitials are detrapped from A at lower temperatures than from B. Then, again, the detrapping stage connected with the impurity A increases with increasing dose. If the initial radiation-induced defect concentration at 4 K is increased in subsequent experiments so that it finally becomes comparable to the concentration of the main impurity we expect a changeover of the dose dependence to the opposite behaviour, as discussed above. In fig. 3 the expected normalised stage height of a final detrapping stage versus the initial Frenkel-pair concentration is qualitatively shown for an alloyed metal, say, e.g., Au or Ag in Cu, after irradiation at 4 K. Since no systematic experimental study has as yet been reported on one alloyed system ranging from sufficiently low to sufficiently high defect concentrations the changeover in the dose dependence has never been observed experimentally.
4. Irradiation in stage II Dworschak et al. [ 1 ] used high defect concentrations, irradiated at $0 K, a temperature above that of free interstitial migration and normalised to the initial resistivity increment at this temperature. Since all remaining interstitials are trapped at impurities, this normalisation naturally results in a dose-independent percentage of trapped interstitials. Since the vacancy concentration is much higher than that of possible
4 K irradiation
.-F 2
e z z 0
E
.F
2 $2
‘G
m
z 70
100 120 TEMPERATUREK
150
Fig. 2. Differentiated isochronal resistivity recovery curves after thermal-neutron irradiation at 4 K for initial defect concentrations of - 1 at ppm, 3 at ppm and 10 at ppm, normalised to the resistivity increments at 4 K (Aspeling et al. [ 21).
Frenkel pair concentration at 4K
*
Fig. 3. Normalised stage height of a final detrapping stage in an irradiated metal alloyed with the traps considered versus initial Frenkeldefect concentration at 4 K, schematically, as expected from theoretical consideration for, e.g., Cu alloyed with Au or with Ag.
120
U. Cosele, J. Aspeling /Dose dependence of impurity detrapping stages in metals
traps still effective after the final detrapping stage from single Ag atoms, the probability for a detrapped interstitial to reach a vacancy is fairly high. A slight increase in the stage can be expected with increasing dose, contrary to the actually observed decrease with dose (fig. 1). For the explanation of this behaviour we must introduce some complications in the simple trapping and detrapping picture given above. For a sufficiently high ratio of interstitials to impurity atoms, the probability that two or more interstitials are trapped at the same impurity atom can no longer be disregarded. Dworschak et al. conclude that several interstitials around one impurity atom may hinder further rearrangement and detrapping processes 111. Thus, the normalised final detrapping stage of a single interstitial from a single impurity atom decreases with increasing dose. The formation of interstitial clusters around impurities, resolving only at higher temperatures, may also occur during the normal detrapping stages [6]. This would account, in part, for the fact that even after the final detrapping stage of single interstitials from single impurities, a certain percentage of the damage remains until stage III fl,3,7-93.
5. Partial detrapping Let us finally discuss the possibi~ty that an annoying atom has a variety of trapping sites with different activation energies for detrapping around it. For many metal/alloy systems this has been found experimentally as a decrease of the trapping radius with increasing temperature [l,lO,ll]. The trapping radius vanishes at a temperature where the single interstitial is released from its deepest trapping site. If this partial detrapping is investigated by resistivity-recovery experiments, and if the vacancy concentration is much lower than the alloying concentration, an interstitial detrapped from a shallow trapping site will be trapped again at deeper trapping sites [ 11. Thus, a recovery experiment may show a region of no annealing until the detrapping from the deepest trap occurs [lo]. For higher vacancy concentrations, a region of continuous annealing may be found [ 11. From these con-
Received 4 August 1977
siderations it follows that a decrease in the trapping radius as detected by damage-rate experiments does not necessarily lead to a corresponding observable annealing in recovery experiments. 6. Conclusions
Detrapping of interstitials from impurities may or may not lead to a recovery stage, the normafised stage height of which may decrease with increasing dose, or just the opposite, depending on the experimental parameters and the normalisation procedure, as discussed above. Acknowledgements
We wish to thank Dr. F. Dworschak, Prof. W. Frank and Prof. A. Seeger for valuable suggestions. References [ 1.1F. Dworschak, R, Lennartz and I. Selke, J. Nuci. Mat., to be published. (21 J. Aspeling, C.S.B. Piini and U. Gosele, Rad. Effects 33 (1977) 53. [3] C.P. Cannon and A. Sosin, Rad. Effects 25 (1975) 253. [4] C.L. Snead, Jr., F.W. Wiffen and J.W. Kaufman, Phys. Rev. 164 (1967) 900. (S] D.G. Martin, Phil. Mag. 7 (1962) 803. {6] W. Schilling, G. Burger, K. lsebeck and H. Wenzl, in: Vacancies and lnterstitials in Metals, A. Seeger, D. Schumacher, W. SchiJling and I. Diehl, eds. North-Holland, Amsterdam, 1970) p. 255. 17) A. Sosin, J. Phys. Sot. Japan 18, Supplement HI (1963) 277. [S] P.B. Peters and P.E. Shearin, Phys. Rev. 174 (1968) 691. [9] W. SchilJing, K. Sonnenberg and H.J. Dibbert, Rad. Effects 16 (1977) 65. (lo] F. Dworschak, R. Lennartz and H. Wollenberger, I. Phys. F 5 (1975) 400. [ 111 I:. Dworschak, Th. Monsau and H. Wollenberger, J. Phys. F 6 (1976) 2207.
* On leave of absence from (and also present address) MaxPlanck-Institut fur Metallforschung, Institut fii Physik, Stuttgart, Germany
U. G5sele * and J. Aspeling South African Atomic Energy Board, Pretoria, Rep. South Africa
DOSE DEPENDENCE OF IMPURITY DETRAPPINC
1. Introduction
The dose dependence of an impurity detrapping stage is given by a combination of the dose dependence of the trapping process and that of the detrapping process. The answers to the following questions are therefore required: (1) What percentage of migrating interstitials (normalised to the initially introduced resistivity increase) is trapped at the particular trapping site and how does this percentage change with dose? (2) What is the probability of a detrapped interstitial reaching a vacancy with subsequent annihilation and how does this probability change with dose *? The answer to these questions are often straightforward and sufficient to explain the observed dose dependence. If, e.g., one impurity species is dominating and a comparable quantity of interstitials are reacting in the recovery stage of free migration (“1,“) after a 4 K irradiation, the percentage of impurity trapping increases with decreasing dose, due to the decreasing competition of the interstitial-vacancy annihilation, which provides the answer to the first question. As for the second question, the detrapped interstitial will find its way to a vacancy with a high probability if no other traps are present in a quantity comparable to the vacancy concentration, and consequently no dose dependence results from the detrapping process alone. Combining the answers to the two questions, we obtain a decreasing normalised stage height with increasing dose [4].
3.0
irradiation
2.5 2.0 4; % 1.0 0.5
70
100
120
TEMPERATURE
or the
2. Basic concept
u +100 at bmUAa_
0
METALS
ture, the concentration of traps considered, concentration of other traps.
Recently a study of the dose dependence of Cu alloyed with Ag, electron irradiated at 50 K, was presented in this journal [ 11; elsewhere, an investigation of the dose dependence of Cu alloyed with Au after thermal-neutron irradiation at 4 K was published [2]. Both impurities lead to the same principal recovery stages (at only slightly shifted temperatures) in the stage II regime of Cu, and these recovery stages show the same dependence on the alloying concentration [3]. It is therefore astonishing at first sight, that an opposite dose dependence has been found for the main detrapping stage (at -110 K and at -120 K for the Au and the Ag impurities, respectively) as is illustrated in fig. 1 and 2 [ 1,2]. It is the purpose of this comment to point out that these results are not contradictory, and to discuss why and how the dose dependence of a detrapping stage may be influenced by experimental parameters as, e.g., the concentration of radiation induced defects, the irradiation tempera-
50 K
STAGES IN IRRADIATED
150 K
* Similarly, if ‘dose’ is replaced by ‘alloying concentration’, the dependence on the alloying concentration [ 1,3] may be looked at. The results of both types of experiments should be consistent.
Fig. 1. Differentiated isochronal resistivity recovery curves after electron irradiation at 50 K for initial defect concentrations of -12 at ppm and -54 at ppm, normalised to the resistivity increments at 50 K (Dworschak et al. [ 1 I). 118
U. Giisele, J. Aspeling /Dose dependence of impurity detrapping stages in metals
3. Irradiation at 4 K and high impurity concentration For fairly high impurity concentrations (say, e.g., 100-1000 at ppm brought in by alloying with the impurity to be investigated) additional traps may be provided, with a higher interstitial binding energy than a single impurity atom, by alloying atoms lying accidentally close together [2,3,5]. If in addition, the concentration of radiation-induced defects is much lower than the alloying concentration, the percentage of trapped interstitials is almost dose-independent. Therefore the dose dependence of the final detrapping stage from single impurities (at -110 K for Au and -120 K for Ag in Cu) is given by the dose dependence of the detrapping alone. If the vacancy concentration is comparable to the concentration of deeper traps (consisting of several impurity atoms), the probability of interstitals recombining with vacancies increases with increasing dose, leading to just the opposite dose dependence found in the case of comparable defect and impurity concentrations. In this way the dose dependence of the 110 K stage in fig. 2 has been explained [2]. The recovery stage at 150 K is connected with the detrapping of interstitials from traps consisting of several Au atoms [2,3]. A similar dose dependence may be expected for the case of two impurity species A and B, where the concentration of A is much higher than the vacancy concentration and
119
where interstitials are detrapped from A at lower temperatures than from B. Then, again, the detrapping stage connected with the impurity A increases with increasing dose. If the initial radiation-induced defect concentration at 4 K is increased in subsequent experiments so that it finally becomes comparable to the concentration of the main impurity we expect a changeover of the dose dependence to the opposite behaviour, as discussed above. In fig. 3 the expected normalised stage height of a final detrapping stage versus the initial Frenkel-pair concentration is qualitatively shown for an alloyed metal, say, e.g., Au or Ag in Cu, after irradiation at 4 K. Since no systematic experimental study has as yet been reported on one alloyed system ranging from sufficiently low to sufficiently high defect concentrations the changeover in the dose dependence has never been observed experimentally.
4. Irradiation in stage II Dworschak et al. [ 1 ] used high defect concentrations, irradiated at $0 K, a temperature above that of free interstitial migration and normalised to the initial resistivity increment at this temperature. Since all remaining interstitials are trapped at impurities, this normalisation naturally results in a dose-independent percentage of trapped interstitials. Since the vacancy concentration is much higher than that of possible
4 K irradiation
.-F 2
e z z 0
E
.F
2 $2
‘G
m
z 70
100 120 TEMPERATUREK
150
Fig. 2. Differentiated isochronal resistivity recovery curves after thermal-neutron irradiation at 4 K for initial defect concentrations of - 1 at ppm, 3 at ppm and 10 at ppm, normalised to the resistivity increments at 4 K (Aspeling et al. [ 21).
Frenkel pair concentration at 4K
*
Fig. 3. Normalised stage height of a final detrapping stage in an irradiated metal alloyed with the traps considered versus initial Frenkeldefect concentration at 4 K, schematically, as expected from theoretical consideration for, e.g., Cu alloyed with Au or with Ag.
120
U. Cosele, J. Aspeling /Dose dependence of impurity detrapping stages in metals
traps still effective after the final detrapping stage from single Ag atoms, the probability for a detrapped interstitial to reach a vacancy is fairly high. A slight increase in the stage can be expected with increasing dose, contrary to the actually observed decrease with dose (fig. 1). For the explanation of this behaviour we must introduce some complications in the simple trapping and detrapping picture given above. For a sufficiently high ratio of interstitials to impurity atoms, the probability that two or more interstitials are trapped at the same impurity atom can no longer be disregarded. Dworschak et al. conclude that several interstitials around one impurity atom may hinder further rearrangement and detrapping processes 111. Thus, the normalised final detrapping stage of a single interstitial from a single impurity atom decreases with increasing dose. The formation of interstitial clusters around impurities, resolving only at higher temperatures, may also occur during the normal detrapping stages [6]. This would account, in part, for the fact that even after the final detrapping stage of single interstitials from single impurities, a certain percentage of the damage remains until stage III fl,3,7-93.
5. Partial detrapping Let us finally discuss the possibi~ty that an annoying atom has a variety of trapping sites with different activation energies for detrapping around it. For many metal/alloy systems this has been found experimentally as a decrease of the trapping radius with increasing temperature [l,lO,ll]. The trapping radius vanishes at a temperature where the single interstitial is released from its deepest trapping site. If this partial detrapping is investigated by resistivity-recovery experiments, and if the vacancy concentration is much lower than the alloying concentration, an interstitial detrapped from a shallow trapping site will be trapped again at deeper trapping sites [ 11. Thus, a recovery experiment may show a region of no annealing until the detrapping from the deepest trap occurs [lo]. For higher vacancy concentrations, a region of continuous annealing may be found [ 11. From these con-
Received 4 August 1977
siderations it follows that a decrease in the trapping radius as detected by damage-rate experiments does not necessarily lead to a corresponding observable annealing in recovery experiments. 6. Conclusions
Detrapping of interstitials from impurities may or may not lead to a recovery stage, the normafised stage height of which may decrease with increasing dose, or just the opposite, depending on the experimental parameters and the normalisation procedure, as discussed above. Acknowledgements
We wish to thank Dr. F. Dworschak, Prof. W. Frank and Prof. A. Seeger for valuable suggestions. References [ 1.1F. Dworschak, R, Lennartz and I. Selke, J. Nuci. Mat., to be published. (21 J. Aspeling, C.S.B. Piini and U. Gosele, Rad. Effects 33 (1977) 53. [3] C.P. Cannon and A. Sosin, Rad. Effects 25 (1975) 253. [4] C.L. Snead, Jr., F.W. Wiffen and J.W. Kaufman, Phys. Rev. 164 (1967) 900. (S] D.G. Martin, Phil. Mag. 7 (1962) 803. {6] W. Schilling, G. Burger, K. lsebeck and H. Wenzl, in: Vacancies and lnterstitials in Metals, A. Seeger, D. Schumacher, W. SchiJling and I. Diehl, eds. North-Holland, Amsterdam, 1970) p. 255. 17) A. Sosin, J. Phys. Sot. Japan 18, Supplement HI (1963) 277. [S] P.B. Peters and P.E. Shearin, Phys. Rev. 174 (1968) 691. [9] W. SchilJing, K. Sonnenberg and H.J. Dibbert, Rad. Effects 16 (1977) 65. (lo] F. Dworschak, R. Lennartz and H. Wollenberger, I. Phys. F 5 (1975) 400. [ 111 I:. Dworschak, Th. Monsau and H. Wollenberger, J. Phys. F 6 (1976) 2207.
* On leave of absence from (and also present address) MaxPlanck-Institut fur Metallforschung, Institut fii Physik, Stuttgart, Germany
U. G5sele * and J. Aspeling South African Atomic Energy Board, Pretoria, Rep. South Africa