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Radiation-induced diffusion of quenched-in vacancies in metals
Volume 46A, number 6
PHYSICS LETTERS
28 January 1974
RADIATION-INDUCED DIFFUSION OF QUENCHED-IN VACANCIES IN METALS A. SEEGER Max-Planck-Institut für Metallforschung, Inst itut für Physik, Institut für theoretisch und angewandte Physik der Universitdt Stuttgart, Stuttgart, Germany Received 3 December 1973 It is shown that the plateau observed by Lucasson and coworkers in the resistivity versus fluence curve during electron irradiation of pre-quenched metals can be explained in terms of radiation-induced diffusion of vacancies.
In recent notes Lucasson and coworkers have shown that at temperatures corresponding to the recovery stage lIthe damage curves (residual electrical resistivity versus electron fluence) of pure Al [I], Pt [2], or Au [3] specimens containing quenced-in vacancies may exhibit a plateau at quite small fluences. The authors attempt to relate this unexpected feature to the fact that the quenched-in resistivities exceeded the residual resistivities of the annealed specimens, i.e., that already at the start of the irradiations the vacancy concentration was larger than or at least comparable with the impurity concentration. They seek for an explanation in terms of the rapid migration of radiation-produced interstitials at the temperature of irradiation. The present note proposes an alternative interpretation in terms of the recently discovered phenomenon of radiation-induced defect diffusion [4, 5].
For conciseness we concentrate on the case of gold. For this metal, inspite of intense search [6—11], sofar no evidence for the thermally activated migration of self-interstitials at low temperatures has been found. Schepp [11] has performed similar experiments as Daoud et al. [3] and did not find any indication of the plateau effect. It appears therefore that the interpretation of Lucasson et al. cannot hold for Au. In fig. 1 we have subtracted the damage curves obtamed in ref. [3] after three different pre-quenches from the damage curve measured on the annealed specimens. All three curves show the characteristic S-shape frequently observed after quenches from similar temperatures Tq as those used in the pre-quenches [12, 13]. This suggests that they should be interpreted in terms of nucleation and growth of vacancy agglomerates, e.g., small stacking-fault tetrahedra. The high-
9flcm
72o~c.~
T
5 25-lO
~
0
7
2
3
4
0tL1077e/cm2]
Fig. 1. Difference ~p between the damage curves (change of the electrical resistivity as a function of the electron fluence ~t) of a gold wire in the annealed state and after different quenches with quenched-in resistivities ~pq. Irradiation temperature -~ 120 K, electron energy — 1.6 MeV.
395
Volume 46A, number 6
PHYSICS LETTERS
voltage electron microscopy work on lead [4,5] has indeed demonstrated that radiation-induced diffusion of vacancies leads to the formation of stacking-fault tetrahedra at temperatures at which the thermally activated diffusivity of vacancies is negligibly small, Let us now discuss the influence of the electron energy Eirr and thus the difference between the experiments of Schepp (Eirr 2.9 MeV) [111 and Daoud et al. (Eirr 1.6 MeV) [3]. In Daoud’s experiments [31 the defect production rate was much smaller than in Schepp’s [11], since they were carried out much closer to the threshold energy of Au (Ed 1.3 MeV). An important contribution of the radiation-induced diffusion, however, comes from sub-threshold energy transfers [5, l4],so that the radiation-induced diffusion coefficients in the two experiments should differ much less than the defect production rates. Because of the long range of dynamic crowdions in gold [151 one expects in Schepp’s experiments a strong effect of the quenched-in vacancies on the shape of the damage curves at small fluences, which presumably overshadows the effects of radiation-induced vacancy diffusion. In [3] the dynamic crowdion effects are expected to be much smaller; they call nevertheless for corrections in fig. 1 if one attempts a quantitative analysis in terms of the radiation-induced diffusion coefficient. A quantitative comparison of the radiation-induced migration of quenched-in vacancies with the results of isothermal anneals of identically quenched specimens should afford a means of determining the radiationenhanced diffusion relative to the thermally activated one of. say, mono-vacancies. In such a determination one should on the one hand use sub-threshold irradiations, thus obviating the need for correcting for the effects of the quenced-in vacancies on the retention of radiation-produced defects, and on the other hand work under quenching conditions which can be analyzed quantitatively in terms of monovacancy nugration, i.e., with very low vacancy concentrations. The ob-
28 January 1974
lar case of platinum the apparent discrepancy between electron irradiation of quenched specimens [2, I 7], which seemed to indicate a very small production rate of immobile interstitials at Stage-Il temperatures, and that of annealed specimens [17], which clearly support an appreciable direct production of socalled Stage-Ill interstitials, is believed to have been resolved in favour of the latter. Finally it should be mentioned that the preceding conclusions call for caution in transmission electron microscopy studies of quenced specimens. While the maximum energy transfered to an atom in a 100 keV electron microscope is only 1.1 eV in Au and thus presumably negligible, it is more than one half of the threshold energy in Al and thus likely to cause radialion-induced defect migration. .
The author acknowledges gratefully discussions with Drs. W. Frank and K. Urban.
References [1 R. Brugière and P. Lucasson, Rad. Eff. 11(1971)55. [2] N. Kachoukh, M. Daoud, A. Lucasson and P. Lucasson, Rad. Eff. 16(1972)193.
131 M. Daoud, N. Kachoukh, A. Lucasson and P. Lucasson. Phys. Lett. 42 A (1972) 169.
14] K. Urban, Proc. 3rd Intern. Conf. High-voltage electron microscopy, Oxford 1973, to be published. A. Seeger, to be published. [6] J.B. Ward and J.W. Kauffman, Phys. Rev. 123 (1961) 90. 171 W. Bauer, iS. Koehler and J.W. Kauffman. Phys. Rev.J.W. 128 DeFord, (1962) 1497. 181 CL. Snead, F.W. Wiffen and J.W. Kauffman, Proc. mt. Conf. Solid state physics research with accelerators.
[51K. Urban and
Brookhaven 1967 (BNL 50083 C-52) p. 230.
191 C. Lee and J.S. Koehler, Phys. Rev. 176 (1968) 813. 1101 H. Wollenberger, in Vacancies and interstitials in metals.
eds. A. Seeger, D. Schumacher, W. Schilling and J. Diehi, (North-Holland, Amsterdam 1970) p. 215.
[ii] H.-E. Schepp, Rep. Jbl-866-FF, 1972.
servation of a resistivity decrease of quenched samples during sub-threshold electron irradiations would form a very direct confirmation of the view-point of the present note. The present considerations invalidate the conclu-
112]
sions, drawn from electron irradiations of pre-quenched metals, on the production of immobile interstitials
[16] W. Schilling and K. Sonneberg, J. Phys. F. Metal Phys. 3 (1973) 322. 1171 G. Duesing, H. Hemmerich, D. Meissner and W. Schilling, Phys. Stat. Sol. 23 (1967)481.
in the Stage-Il temperature region [161. In the particu396
i.E. Bauerle and J.S. Koehier, Phys. Rev. 107 (1957) 1493. [13] M. Dc Jong and J.S. Koehler, Phys. Rev. 129 (1963) 49. 114] K. Dettmann, G. Leibfried and K. Schröder, Phys. Stat. Sol. 22 (1967) 432.
1151 A. Seeger, Red. Eff. 2 (1970) 165.
PHYSICS LETTERS
28 January 1974
RADIATION-INDUCED DIFFUSION OF QUENCHED-IN VACANCIES IN METALS A. SEEGER Max-Planck-Institut für Metallforschung, Inst itut für Physik, Institut für theoretisch und angewandte Physik der Universitdt Stuttgart, Stuttgart, Germany Received 3 December 1973 It is shown that the plateau observed by Lucasson and coworkers in the resistivity versus fluence curve during electron irradiation of pre-quenched metals can be explained in terms of radiation-induced diffusion of vacancies.
In recent notes Lucasson and coworkers have shown that at temperatures corresponding to the recovery stage lIthe damage curves (residual electrical resistivity versus electron fluence) of pure Al [I], Pt [2], or Au [3] specimens containing quenced-in vacancies may exhibit a plateau at quite small fluences. The authors attempt to relate this unexpected feature to the fact that the quenched-in resistivities exceeded the residual resistivities of the annealed specimens, i.e., that already at the start of the irradiations the vacancy concentration was larger than or at least comparable with the impurity concentration. They seek for an explanation in terms of the rapid migration of radiation-produced interstitials at the temperature of irradiation. The present note proposes an alternative interpretation in terms of the recently discovered phenomenon of radiation-induced defect diffusion [4, 5].
For conciseness we concentrate on the case of gold. For this metal, inspite of intense search [6—11], sofar no evidence for the thermally activated migration of self-interstitials at low temperatures has been found. Schepp [11] has performed similar experiments as Daoud et al. [3] and did not find any indication of the plateau effect. It appears therefore that the interpretation of Lucasson et al. cannot hold for Au. In fig. 1 we have subtracted the damage curves obtamed in ref. [3] after three different pre-quenches from the damage curve measured on the annealed specimens. All three curves show the characteristic S-shape frequently observed after quenches from similar temperatures Tq as those used in the pre-quenches [12, 13]. This suggests that they should be interpreted in terms of nucleation and growth of vacancy agglomerates, e.g., small stacking-fault tetrahedra. The high-
9flcm
72o~c.~
T
5 25-lO
~
0
7
2
3
4
0tL1077e/cm2]
Fig. 1. Difference ~p between the damage curves (change of the electrical resistivity as a function of the electron fluence ~t) of a gold wire in the annealed state and after different quenches with quenched-in resistivities ~pq. Irradiation temperature -~ 120 K, electron energy — 1.6 MeV.
395
Volume 46A, number 6
PHYSICS LETTERS
voltage electron microscopy work on lead [4,5] has indeed demonstrated that radiation-induced diffusion of vacancies leads to the formation of stacking-fault tetrahedra at temperatures at which the thermally activated diffusivity of vacancies is negligibly small, Let us now discuss the influence of the electron energy Eirr and thus the difference between the experiments of Schepp (Eirr 2.9 MeV) [111 and Daoud et al. (Eirr 1.6 MeV) [3]. In Daoud’s experiments [31 the defect production rate was much smaller than in Schepp’s [11], since they were carried out much closer to the threshold energy of Au (Ed 1.3 MeV). An important contribution of the radiation-induced diffusion, however, comes from sub-threshold energy transfers [5, l4],so that the radiation-induced diffusion coefficients in the two experiments should differ much less than the defect production rates. Because of the long range of dynamic crowdions in gold [151 one expects in Schepp’s experiments a strong effect of the quenched-in vacancies on the shape of the damage curves at small fluences, which presumably overshadows the effects of radiation-induced vacancy diffusion. In [3] the dynamic crowdion effects are expected to be much smaller; they call nevertheless for corrections in fig. 1 if one attempts a quantitative analysis in terms of the radiation-induced diffusion coefficient. A quantitative comparison of the radiation-induced migration of quenched-in vacancies with the results of isothermal anneals of identically quenched specimens should afford a means of determining the radiationenhanced diffusion relative to the thermally activated one of. say, mono-vacancies. In such a determination one should on the one hand use sub-threshold irradiations, thus obviating the need for correcting for the effects of the quenced-in vacancies on the retention of radiation-produced defects, and on the other hand work under quenching conditions which can be analyzed quantitatively in terms of monovacancy nugration, i.e., with very low vacancy concentrations. The ob-
28 January 1974
lar case of platinum the apparent discrepancy between electron irradiation of quenched specimens [2, I 7], which seemed to indicate a very small production rate of immobile interstitials at Stage-Il temperatures, and that of annealed specimens [17], which clearly support an appreciable direct production of socalled Stage-Ill interstitials, is believed to have been resolved in favour of the latter. Finally it should be mentioned that the preceding conclusions call for caution in transmission electron microscopy studies of quenced specimens. While the maximum energy transfered to an atom in a 100 keV electron microscope is only 1.1 eV in Au and thus presumably negligible, it is more than one half of the threshold energy in Al and thus likely to cause radialion-induced defect migration. .
The author acknowledges gratefully discussions with Drs. W. Frank and K. Urban.
References [1 R. Brugière and P. Lucasson, Rad. Eff. 11(1971)55. [2] N. Kachoukh, M. Daoud, A. Lucasson and P. Lucasson, Rad. Eff. 16(1972)193.
131 M. Daoud, N. Kachoukh, A. Lucasson and P. Lucasson. Phys. Lett. 42 A (1972) 169.
14] K. Urban, Proc. 3rd Intern. Conf. High-voltage electron microscopy, Oxford 1973, to be published. A. Seeger, to be published. [6] J.B. Ward and J.W. Kauffman, Phys. Rev. 123 (1961) 90. 171 W. Bauer, iS. Koehler and J.W. Kauffman. Phys. Rev.J.W. 128 DeFord, (1962) 1497. 181 CL. Snead, F.W. Wiffen and J.W. Kauffman, Proc. mt. Conf. Solid state physics research with accelerators.
[51K. Urban and
Brookhaven 1967 (BNL 50083 C-52) p. 230.
191 C. Lee and J.S. Koehler, Phys. Rev. 176 (1968) 813. 1101 H. Wollenberger, in Vacancies and interstitials in metals.
eds. A. Seeger, D. Schumacher, W. Schilling and J. Diehi, (North-Holland, Amsterdam 1970) p. 215.
[ii] H.-E. Schepp, Rep. Jbl-866-FF, 1972.
servation of a resistivity decrease of quenched samples during sub-threshold electron irradiations would form a very direct confirmation of the view-point of the present note. The present considerations invalidate the conclu-
112]
sions, drawn from electron irradiations of pre-quenched metals, on the production of immobile interstitials
[16] W. Schilling and K. Sonneberg, J. Phys. F. Metal Phys. 3 (1973) 322. 1171 G. Duesing, H. Hemmerich, D. Meissner and W. Schilling, Phys. Stat. Sol. 23 (1967)481.
in the Stage-Il temperature region [161. In the particu396
i.E. Bauerle and J.S. Koehier, Phys. Rev. 107 (1957) 1493. [13] M. Dc Jong and J.S. Koehler, Phys. Rev. 129 (1963) 49. 114] K. Dettmann, G. Leibfried and K. Schröder, Phys. Stat. Sol. 22 (1967) 432.
1151 A. Seeger, Red. Eff. 2 (1970) 165.