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Comment on “Defect ordering in metals under irradiation” by W. Jäger and H. Trinkaus
ELSEVIER
Journal of Nuclear Materials 210 (1994) 230-232
Letter
to the Editors
Comment on “Defect ordering in metals under irradiation” by W. J%ger and H. Trinkaus J.H. Evans Department of Physics, Royal Holloway, Unicersity of London, Egham, Surrey TW20 OEX, United Kingdom
(Received 6 December 1993; accepted 28 February 1994)
In their wide ranging review of defect ordering in metals, Jiiger and Trinkaus [l] include a discussion of possible formation mechanisms for void lattices and, more briefly, bubble lattices. They conclude that in cubic metals, void ordering is probably due to one-dimensional glide of interstitial loops, with the production of such loops in displacement cascades. Although it is satisfying that discussions on void lattice formation are moving toward a consensus of the role of anisotropic interstitial transport, the merits of the model based on two-dimensional diffusion of self-interstitial atoms (2D SIA model), e.g. Refs. [2-51, were not put strongly and there was particular emphasis on challenging evidence previously claimed to support the model. The purpose of the present comment is to answer this challenge by reiterating the strengths of the 2D SIA model. In addition, in the interest of vigorous scientific debate, comments are given on the main conclusion above. In their brief discussion of the 2D SIA model, JIger and Trinkaus [l] concentrate not on the fact that the model, unlike others, is equally applicable to bubble lattices, nor on its strengths with regard to results on hcp metals [6]; instead there is discussion on the saturation effects predicted in the void swelling behaviour. By way of background it is first worth reiterating that these saturation effects arise from the different void sink strengths for vacancies (moving three-dimensionally) and self-interstitials (assumed to move two-dimensionally). As outlined by Evans and Foreman [7], this leads to a maximum void radius given by
where C is the void concentration and Zi the bias of dislocations for interstitials. For Zi between 1 and 1.10, this lead to a maximum swelling of between about 2 and 2.8% (rather more than the 1% quoted in Ref.
[l]). Taking for arguments sake Zi = 1.05, it is easy to show that the ratio of (A/r), where A is the void lattice parameter, should not be less than _ 7 for bee lattices or _ 9 for fee lattices. An early application [8] of Eq. (1) was to explain, both qualitatively and quantitatively, the otherwise curious results of Loomis and Gerber [9] in which the shrinkage of large voids was observed during irradiation to coincide with the growth of a population of small voids - a result seemingly inconsistent with conventional rate theory and isotropic defect diffusion. Although this was an outstanding success for the 2D SIA model, it was only mentioned briefly in Ref. [l] before passing on, firstly, to highlight other results on Nb and Nb-1% Zr [lo], where some values of rmax indeed exceed the predictions of Eq. (11, and secondly, to point out that the results of Bentley et al. [ll] were at too low a dose to warrant previous qualitative claims [7,8] in favour of the 2D SIA model. Essentially based on these results, it was stated in Ref. [l] that “these features cannot be considered as evidence for 2D SIA transport”. Although of no consequence, it seems this statement could be true for the results of Bentley et al. However, of more importance since there is a positive disagreement with Eq. (I), are the higher dose (20 to 140 displacements per atom, dpa) results on Nb and Nb-1% Zr [lo]. The contention in the present comment is that these results, when considered in total values agreeing with Eq. (l)), are by (with many r,, no means an embarrassment for the 2D SIA model. In their detailed work, Loomis et al. have presented over 40 data points on void lattice formation after ion implantation in the temperature range 750 to P 1000°C. In particular, measured void lattice parameter and void diameter values were plotted against temperature (their Figs. 8 and 9). The fact that in each
0022-3115/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00174-M
J.H. Evans /Journal
case almost all points lie on a smooth curve suggests a dose independence for the data. In Table 1, values are given for measured parameters at representative temperatures taken from Ref. [lo], based as accurately as possible on the authors’ original lines through the data. The final column showing the ratio between measured and predicted void diameters is of most interest. It can be seen that for the data areas at 750, 800 and 850°C there is rather good agreement with Eq. (1). With over 20 data points being involved, and with displacement doses in the range 20 to 140 dpa, there must be no doubt that saturation swelling must have been reached in most points if not all. If it is a coincidence that the modelling based on 2D SIA migration fits this data, then there are over 20 such coincidences in the above work alone. A complete survey of the literature is not appropriate here but there are many other measurements from void lattice data, usually expressed in the (A/r) format, that are also consistent with Eq. (11, e.g. see Norris [12], Table IX, and Krishan [13], Table 1. What is clear in Table 1 is that the predictions are far less good when Jhe void lattice parameter increases above about 400 A (T= 825°C and T> 9Oo”C), and become progressively worse at larger void spacings. This was the region that was emphasised in Ref. [l] to suggest that saturation data could not be used to support the 2D SIA model. This emphasis can at best only be described as unfortunate when balanced against the number of correct predictions, a situation made worse when reasons for deviations from Eq. (1) have already been given on several occasions, e.g. Refs. [7,8]. The main reason is that even though the primary jump step is two-dimensional, the probability of rotational (3D) jumps must always exist. If this is so, clearly their effects are more likely to be seen when the void spacing increases, exactly as observed in Table 1. In addition, it is not implausible that the 3-D jump probability might increase with temperature. The above arguments are fully supported by the swelling results of Stubbins et al. [14] on ion bom-
Table
231
of Nuclear Materials 210 (1994) 230-232
barded molybdenum. Below 1120°C where void lattice formation was found, the measured swelling was always less than 3%. The authors drew particular attention to the correlation between void lattice formation and low swelling, a correlation which was strongly emphasised by results for sample temperatures above 1200°C. In this region, the absence of void lattice formation coincided with several observations showed enhanced swelling of the order of 10%. Clear indications of swelling saturation in ion bombarded nickel also coincided with observations of void lattice formation [15]. The overall conclusion of this discussion is that in spite of a few anomalous results, there is easily sufficient data in the literature to positively support the saturation predictions of the 2D SIA model. The only reason for further discussion would be if some other void lattice formation model (the connection between swelling saturation and void lattice formation is very strong) could also satisfy the measured data. The model of interstitial loop glide favoured in Ref. [l] does not appear to do this. The saturation condition in this model predicts a 500 A maximum in the void radius 1161. A major difficulty for the interstitial loop glide model is the appearance of a void lattice under high voltage electron irradiation of nitrided austenitic stainless steel [17]. To overcome this, the authors of Ref. [l] have produced the novel suggestion that the observation is of a nitrogen bubble lattice. This seems most unlikely. If any reports of nitrogen bubble precipitation in steels exist, they must be rare, while it is well known that excess nitrogen in nitrided steel is likely to be present as chromium nitride rather than as free nitrogen. This throws doubt on the meaning of the quoted - 0.5 wt% ‘free’ nitrogen (- 2 at%,) in Ref. [17]) and suggests it could have been a gross overestimate. However, even allowing some uncertainty on this point, it is quite clear that in the HVM irradiations voids were found in unnitrided steel before then moving to nitrided material, showing that the basic conditions for
1
Data points taken from Loomis et al. 1101together with predictions of Eq. (1) Temperature (“C)
750 800 825 850 875 900 950 1000
No of local data points
6 15 4 2 1 7 7 2
Void diameter
Void lattice parameter
(A,
(A,
50 100 180 100 120 180 360 700
210 340 460 340 380 460 800 1400
d,,x, Eq. (1)
d/d,,,
51 97 131 97 108 131 227 397
0.88 1.03 1.37 1.03 1.11 1.37 1.58 1.76
232
J.H. Evans /Journal
of Nuclear Materials 210 (1994) 230-232
void formation and growth must certainly have been present. The reported factor of 50 increase in cavity density (to N 10’6/cm3), relative to the base material, could well have affected growth parameters but the authors of Ref. [l] are effectively suggesting that void growth was suppressed at the expense of bubble growth, at the same time leading to some undetermined mechanism of bubble lattice formation. Given that the cavity density is at least two orders of magnitude less than the bubble density in all bubble lattice measurements, this is implausible. It is worth repeating the report in Ref. [7] that HVM irradiations on ferritic steel have also shown void alignment. These results are unfortunately unpublished but are easily verified by communicating with Little [18]. With regard to the formation of inert gas bubble lattices, the authors of Ref. [l] only mention the model of Dubinko [19] in which loop punching from overpressurised bubbles is claimed to lead to lattice alignment. They also point out possible uncertainties over the loop punching mechanism in this context but in fact these uncertainties are superfluous. As already pointed out [S], the loop punching mechanism cannot work. The punching out of an interstitial loop along a glide cylinder and interacting with a bubble only partially lying on that glide cylinder must push that bubble away from an ordering direction. Such difficulties completely disappear if the 2D SIA model is used. The fact that in bee, fee and hcp metals the respective structures of void and bubble lattices are identical must strongly favour a similar model for both sets of cavity lattices. As detailed elsewhere [5], the 2D SIA jump steps are quite clear in the bee and hcp structures; in the fee structure this is not so although the theoretical finding of a ‘planar crowdion’ by Reeler [20] is worth further investigation. One final comment concerns the reference in Ref. [l] to the apparent absence of bubble lattice formation after xenon implants. It could be relevant that bubble resolution effects have been demonstrated with implants of krypton and, more effectively, xenon into zirconium [21]. Plausibly such effects can prevent or inhibit bubble ordering, the xenon result.
and could
therefore
explain
References
[ll W. Jager
and H. Trinkaus, Proc. Int. Conf. on The Evolution of Microstructures in Metals during Irradiation, Ontario, 1992, eds. C.E. Coleman, R.A. Holt and R.G. Fleck, J. Nucl. Mater. 205 (1993) 394. PI J.H. Evans, J. Nucl. Mater. 119 (1983) 180. 131 J.H. Evans, J. Nucl. Mater. 132 (1985) 147. 141 J.H. Evans, Proc. Int. Conf. on Vacancies and Interstitials in Metals and Alloys, Berlin, September 1986, Mater. Sci. Forum 15-18 (19871 869. [51 J.H. Evans, Proc. NATO Workshop on Patterns, Defects and Materials Instabilities, eds. D. Walgraef and N.M. Ghoniem (Kluwer Academic Publishers, Dordrecht) p. 347. [61 J.H. Evans, A.J.E. Foreman and R.J. McElroy, J. Nucl. Mater. 168 (1989) 340. J. Nucl. Mater. 137 [71 J.H. Evans and A.J.E. Foreman, (1985) 1. PI J.E. Evans, J. Nucl. Mater. 120 (1984) 349. [91 B.A. Loomis and S.B. Gerber, J. Nucl. Mater. 102 (1981) 154. [lOI B.A. Loomis, S.B. Gerber and A. Taylor, J. Nucl. Mater. 68 (1977) 19. [Ill J. Bentley, B.L. Eyre and M.H. Loretto, Proc. Conf. on Fundamental Aspects of Radiation Damage in Metals, Gatlinburg, 1975, US-ERDA Conf-751006, p. 925. [121 D.I.R. Norris, J. Nucl. Mater. 40 (1971) 66. [I31 K. Krishan, Radiat. Eff. 66 (1982) 121. [141 J.F. Stubbins, J. Moteff and A. Taylor, J. Nucl. Mater. 101 (19811 64. l151 G.L. Kulcinski, J.L. Brimall and H.E. Kissinger, J. Nucl. Mater. 40 (1971) 166. ll61 H. Trinkaus, B.N. Singh and A.J.E. Foreman, J. Nucl. Mater. 199 (1992) 1. 1171 S.B. Fisher and K.R. Williams, Radiat. Eff. 32 (1977) 123. I181 E.A. Little, Bldg. 459.4, AEA Technology, Harwell Laboratory, OX11 ORA, UK. [19] V.I. Dubinko, V.V. Slezov, A.V. Tur and V.V. Yanovsky, Radiat. Eff. 100 (19861 85. [20] J.R. Beeler, Radiation Effects Computer Experiments (North-Holland, Amsterdam, 19831 p. 219. [21] J.H. Evans, in Fundamental Aspects of Inert Gases in Solids, eds. S.E. Donnelly and J.H. Evans (Plenum, New York, 1991) p. 307.
Journal of Nuclear Materials 210 (1994) 230-232
Letter
to the Editors
Comment on “Defect ordering in metals under irradiation” by W. J%ger and H. Trinkaus J.H. Evans Department of Physics, Royal Holloway, Unicersity of London, Egham, Surrey TW20 OEX, United Kingdom
(Received 6 December 1993; accepted 28 February 1994)
In their wide ranging review of defect ordering in metals, Jiiger and Trinkaus [l] include a discussion of possible formation mechanisms for void lattices and, more briefly, bubble lattices. They conclude that in cubic metals, void ordering is probably due to one-dimensional glide of interstitial loops, with the production of such loops in displacement cascades. Although it is satisfying that discussions on void lattice formation are moving toward a consensus of the role of anisotropic interstitial transport, the merits of the model based on two-dimensional diffusion of self-interstitial atoms (2D SIA model), e.g. Refs. [2-51, were not put strongly and there was particular emphasis on challenging evidence previously claimed to support the model. The purpose of the present comment is to answer this challenge by reiterating the strengths of the 2D SIA model. In addition, in the interest of vigorous scientific debate, comments are given on the main conclusion above. In their brief discussion of the 2D SIA model, JIger and Trinkaus [l] concentrate not on the fact that the model, unlike others, is equally applicable to bubble lattices, nor on its strengths with regard to results on hcp metals [6]; instead there is discussion on the saturation effects predicted in the void swelling behaviour. By way of background it is first worth reiterating that these saturation effects arise from the different void sink strengths for vacancies (moving three-dimensionally) and self-interstitials (assumed to move two-dimensionally). As outlined by Evans and Foreman [7], this leads to a maximum void radius given by
where C is the void concentration and Zi the bias of dislocations for interstitials. For Zi between 1 and 1.10, this lead to a maximum swelling of between about 2 and 2.8% (rather more than the 1% quoted in Ref.
[l]). Taking for arguments sake Zi = 1.05, it is easy to show that the ratio of (A/r), where A is the void lattice parameter, should not be less than _ 7 for bee lattices or _ 9 for fee lattices. An early application [8] of Eq. (1) was to explain, both qualitatively and quantitatively, the otherwise curious results of Loomis and Gerber [9] in which the shrinkage of large voids was observed during irradiation to coincide with the growth of a population of small voids - a result seemingly inconsistent with conventional rate theory and isotropic defect diffusion. Although this was an outstanding success for the 2D SIA model, it was only mentioned briefly in Ref. [l] before passing on, firstly, to highlight other results on Nb and Nb-1% Zr [lo], where some values of rmax indeed exceed the predictions of Eq. (11, and secondly, to point out that the results of Bentley et al. [ll] were at too low a dose to warrant previous qualitative claims [7,8] in favour of the 2D SIA model. Essentially based on these results, it was stated in Ref. [l] that “these features cannot be considered as evidence for 2D SIA transport”. Although of no consequence, it seems this statement could be true for the results of Bentley et al. However, of more importance since there is a positive disagreement with Eq. (I), are the higher dose (20 to 140 displacements per atom, dpa) results on Nb and Nb-1% Zr [lo]. The contention in the present comment is that these results, when considered in total values agreeing with Eq. (l)), are by (with many r,, no means an embarrassment for the 2D SIA model. In their detailed work, Loomis et al. have presented over 40 data points on void lattice formation after ion implantation in the temperature range 750 to P 1000°C. In particular, measured void lattice parameter and void diameter values were plotted against temperature (their Figs. 8 and 9). The fact that in each
0022-3115/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00174-M
J.H. Evans /Journal
case almost all points lie on a smooth curve suggests a dose independence for the data. In Table 1, values are given for measured parameters at representative temperatures taken from Ref. [lo], based as accurately as possible on the authors’ original lines through the data. The final column showing the ratio between measured and predicted void diameters is of most interest. It can be seen that for the data areas at 750, 800 and 850°C there is rather good agreement with Eq. (1). With over 20 data points being involved, and with displacement doses in the range 20 to 140 dpa, there must be no doubt that saturation swelling must have been reached in most points if not all. If it is a coincidence that the modelling based on 2D SIA migration fits this data, then there are over 20 such coincidences in the above work alone. A complete survey of the literature is not appropriate here but there are many other measurements from void lattice data, usually expressed in the (A/r) format, that are also consistent with Eq. (11, e.g. see Norris [12], Table IX, and Krishan [13], Table 1. What is clear in Table 1 is that the predictions are far less good when Jhe void lattice parameter increases above about 400 A (T= 825°C and T> 9Oo”C), and become progressively worse at larger void spacings. This was the region that was emphasised in Ref. [l] to suggest that saturation data could not be used to support the 2D SIA model. This emphasis can at best only be described as unfortunate when balanced against the number of correct predictions, a situation made worse when reasons for deviations from Eq. (1) have already been given on several occasions, e.g. Refs. [7,8]. The main reason is that even though the primary jump step is two-dimensional, the probability of rotational (3D) jumps must always exist. If this is so, clearly their effects are more likely to be seen when the void spacing increases, exactly as observed in Table 1. In addition, it is not implausible that the 3-D jump probability might increase with temperature. The above arguments are fully supported by the swelling results of Stubbins et al. [14] on ion bom-
Table
231
of Nuclear Materials 210 (1994) 230-232
barded molybdenum. Below 1120°C where void lattice formation was found, the measured swelling was always less than 3%. The authors drew particular attention to the correlation between void lattice formation and low swelling, a correlation which was strongly emphasised by results for sample temperatures above 1200°C. In this region, the absence of void lattice formation coincided with several observations showed enhanced swelling of the order of 10%. Clear indications of swelling saturation in ion bombarded nickel also coincided with observations of void lattice formation [15]. The overall conclusion of this discussion is that in spite of a few anomalous results, there is easily sufficient data in the literature to positively support the saturation predictions of the 2D SIA model. The only reason for further discussion would be if some other void lattice formation model (the connection between swelling saturation and void lattice formation is very strong) could also satisfy the measured data. The model of interstitial loop glide favoured in Ref. [l] does not appear to do this. The saturation condition in this model predicts a 500 A maximum in the void radius 1161. A major difficulty for the interstitial loop glide model is the appearance of a void lattice under high voltage electron irradiation of nitrided austenitic stainless steel [17]. To overcome this, the authors of Ref. [l] have produced the novel suggestion that the observation is of a nitrogen bubble lattice. This seems most unlikely. If any reports of nitrogen bubble precipitation in steels exist, they must be rare, while it is well known that excess nitrogen in nitrided steel is likely to be present as chromium nitride rather than as free nitrogen. This throws doubt on the meaning of the quoted - 0.5 wt% ‘free’ nitrogen (- 2 at%,) in Ref. [17]) and suggests it could have been a gross overestimate. However, even allowing some uncertainty on this point, it is quite clear that in the HVM irradiations voids were found in unnitrided steel before then moving to nitrided material, showing that the basic conditions for
1
Data points taken from Loomis et al. 1101together with predictions of Eq. (1) Temperature (“C)
750 800 825 850 875 900 950 1000
No of local data points
6 15 4 2 1 7 7 2
Void diameter
Void lattice parameter
(A,
(A,
50 100 180 100 120 180 360 700
210 340 460 340 380 460 800 1400
d,,x, Eq. (1)
d/d,,,
51 97 131 97 108 131 227 397
0.88 1.03 1.37 1.03 1.11 1.37 1.58 1.76
232
J.H. Evans /Journal
of Nuclear Materials 210 (1994) 230-232
void formation and growth must certainly have been present. The reported factor of 50 increase in cavity density (to N 10’6/cm3), relative to the base material, could well have affected growth parameters but the authors of Ref. [l] are effectively suggesting that void growth was suppressed at the expense of bubble growth, at the same time leading to some undetermined mechanism of bubble lattice formation. Given that the cavity density is at least two orders of magnitude less than the bubble density in all bubble lattice measurements, this is implausible. It is worth repeating the report in Ref. [7] that HVM irradiations on ferritic steel have also shown void alignment. These results are unfortunately unpublished but are easily verified by communicating with Little [18]. With regard to the formation of inert gas bubble lattices, the authors of Ref. [l] only mention the model of Dubinko [19] in which loop punching from overpressurised bubbles is claimed to lead to lattice alignment. They also point out possible uncertainties over the loop punching mechanism in this context but in fact these uncertainties are superfluous. As already pointed out [S], the loop punching mechanism cannot work. The punching out of an interstitial loop along a glide cylinder and interacting with a bubble only partially lying on that glide cylinder must push that bubble away from an ordering direction. Such difficulties completely disappear if the 2D SIA model is used. The fact that in bee, fee and hcp metals the respective structures of void and bubble lattices are identical must strongly favour a similar model for both sets of cavity lattices. As detailed elsewhere [5], the 2D SIA jump steps are quite clear in the bee and hcp structures; in the fee structure this is not so although the theoretical finding of a ‘planar crowdion’ by Reeler [20] is worth further investigation. One final comment concerns the reference in Ref. [l] to the apparent absence of bubble lattice formation after xenon implants. It could be relevant that bubble resolution effects have been demonstrated with implants of krypton and, more effectively, xenon into zirconium [21]. Plausibly such effects can prevent or inhibit bubble ordering, the xenon result.
and could
therefore
explain
References
[ll W. Jager
and H. Trinkaus, Proc. Int. Conf. on The Evolution of Microstructures in Metals during Irradiation, Ontario, 1992, eds. C.E. Coleman, R.A. Holt and R.G. Fleck, J. Nucl. Mater. 205 (1993) 394. PI J.H. Evans, J. Nucl. Mater. 119 (1983) 180. 131 J.H. Evans, J. Nucl. Mater. 132 (1985) 147. 141 J.H. Evans, Proc. Int. Conf. on Vacancies and Interstitials in Metals and Alloys, Berlin, September 1986, Mater. Sci. Forum 15-18 (19871 869. [51 J.H. Evans, Proc. NATO Workshop on Patterns, Defects and Materials Instabilities, eds. D. Walgraef and N.M. Ghoniem (Kluwer Academic Publishers, Dordrecht) p. 347. [61 J.H. Evans, A.J.E. Foreman and R.J. McElroy, J. Nucl. Mater. 168 (1989) 340. J. Nucl. Mater. 137 [71 J.H. Evans and A.J.E. Foreman, (1985) 1. PI J.E. Evans, J. Nucl. Mater. 120 (1984) 349. [91 B.A. Loomis and S.B. Gerber, J. Nucl. Mater. 102 (1981) 154. [lOI B.A. Loomis, S.B. Gerber and A. Taylor, J. Nucl. Mater. 68 (1977) 19. [Ill J. Bentley, B.L. Eyre and M.H. Loretto, Proc. Conf. on Fundamental Aspects of Radiation Damage in Metals, Gatlinburg, 1975, US-ERDA Conf-751006, p. 925. [121 D.I.R. Norris, J. Nucl. Mater. 40 (1971) 66. [I31 K. Krishan, Radiat. Eff. 66 (1982) 121. [141 J.F. Stubbins, J. Moteff and A. Taylor, J. Nucl. Mater. 101 (19811 64. l151 G.L. Kulcinski, J.L. Brimall and H.E. Kissinger, J. Nucl. Mater. 40 (1971) 166. ll61 H. Trinkaus, B.N. Singh and A.J.E. Foreman, J. Nucl. Mater. 199 (1992) 1. 1171 S.B. Fisher and K.R. Williams, Radiat. Eff. 32 (1977) 123. I181 E.A. Little, Bldg. 459.4, AEA Technology, Harwell Laboratory, OX11 ORA, UK. [19] V.I. Dubinko, V.V. Slezov, A.V. Tur and V.V. Yanovsky, Radiat. Eff. 100 (19861 85. [20] J.R. Beeler, Radiation Effects Computer Experiments (North-Holland, Amsterdam, 19831 p. 219. [21] J.H. Evans, in Fundamental Aspects of Inert Gases in Solids, eds. S.E. Donnelly and J.H. Evans (Plenum, New York, 1991) p. 307.