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The association of compositional fluctuations with clusters of cavities in irradiated alloys
143
Journal of Nuclear Materials 172 (1990) 143-150 Non-Homed
THEIASSOCIATION QF CO~S~ON~ OF CAlTIlES IN IRRAIMATER ALLOYS
~U~A~ONS
WITH CLUSTERS
CM. SHEPHERD and SM. MURPHY Mated& Devekpnent Dtvision,AEA Techolagy
Hawell Laboratory, OxfordshireOXI 1 ORA, United Kingdom
Rea%iv& 2 March 1990; z%Jqa?d7 March 1990
The clime of Fe-X!% Cr-15% Ni alloys irradiated with neutrons at &WC has been studied in detail. These materials display intragramdar fl~tuations in composition with an irregular size and spacing. Tbe alloys also contain a distributionof small, helium~filled cavities. It is shown that these cavities are clustered, and that the clusters of cavities are associatedwith regions rich in nickel and depleted in iron and chromium. It is believed that the cavities are the dominant point defect sinks and that the nickel enrichmmt associated with the clusters of cavities is a result of ~~~ation-~du~ segregation.Possibleexplanationsfor the clusteringof cavities are discussed.
1. lnuon .Dramatic fluctuations in composition have been observed in a mnnber of austenitic alloys after irmdiation. Such fluctuations were first observed in binary Fe-Ni alloys and ternary Fe-Cr-Ni alloys comaining approximately 35% Ni after both neutron and ion irradiations [l-4]. More recently, similar fluctuations have been observed in 15% Ni stainless steels following neutron irradiation f5]. The suggestedexplanations of this phenomenon can be divided into three main groups: (i) The ~uct~tions are the result of irradiation induced segregation to point defect sinks. In this case each nickel-rich region would contain either one huge sink or a cl~ter of smaller sinks. However, in both the 35% Ni and tbe 15% Ni alloys there was no apparent correlation between the compositional fluctuations and any visible ~~os~~t~~ sink [1,5]. (ii) The material undergoes a spinodal decomposition which is accelerated by the irradiation. Brager and Garner [1,2] argue that the spinodal reaction occurs extremely slowly in the absence of irradiation. Postirradiation anneahng experiments on the 15% Ni alloys irradiated at 644’C have demonstrated that the compositional fl~~t~ti~s are not stable at the irradiation temperature and therefore a spinodal-like decomposition can not explain the observations 161.The similarity of the fluctuations in both sets of alloys casts doubt on the validity of this explanation even for the 35% Ni alloys.
(iii) The fluctuations are the result of an irradiation-induced instability. An instability in the diffusion behaviour of the alloy could produce such fluctuations dim&y [7-91. Alternatively, an instability in the sink structure could lead to fluctuations in composition via mechanism (i} [lo]. A more detailed examination of the 15% Ni, stainless steel specimens has revealed a population of small cavities which were previously unobserved [II]. The cavities were typically 6 nm in diameter and the regions around them were rich in nickel and silicon but depleted in chromium and iron. These cavities could therefore be the ~d~~i~ features required for the first explanation above. This paper describes the distribution of these cavities and their relationship with the fluctuations in composition. 2. Expewntal The compositions of the alloys used in this work are detailed in table 1. The alloys form the basis of a much larger experiment to examine the infium~ of silicon on Table1 Tableof compositions a>(wt%) Ahoy
Cr
Ni
C
Si
Mn
7E 7c
11.89 11.8
15.2 15.1
0.052 0.061
0.95 1.42
1.03 0.99
N
@Pm)
‘) MO,Ti, Nb, V and W all K 0.02 wt%.
30 35
C.M. Shepherd
144
neutron-induced The specimens
microstructural
S.M. Mvphy
development
/ Association of compositional fluctuations
[5,11,12].
described in this paper were solution treated prior t,o irradiation at 644°C to 50.1 dpa in EBIZII. Two analytical electron microscopes were used during this work. A Vacuum Generators HB501 Scanning Transmission Electron Microscope was used when only X-ray mapping was required. However, when both X-ray maps and cavity images were to be recorded on the same microscope, a Philips EM430 was used because of its superior photographic capabilities. Both microscopes are equipped with Link X-ray detectors and computers. The X-ray maps were collected at magnifications of - ~25000. At this magnification it is dificult to identify all of the small cavities. In order to locate as many of the cavities as possible, the mapped area was photographed at higher magnifications and the positions of all the cavities were translated onto a single photograph
also
- ~25000.
with cavity clusters
The distribution
then be superimposed
of the cavities
could
on the X-ray maps.
3. Results 3. I. Microscopy In previous studies, spatial variations in composition have been investigated by measuring the local composition at points along a line perpendicular to a grain boundary. The elemental X-ray maps used here provide two-dimensional information on the local composition; this is valuable in relating compositional changes to the microstructural features in the material. Fig. 1 shows a typical X-ray map for the elements Fe, Cr and Ni from an area in a solution treated specimen irradiated to 50.1 dpa at 644’C. There is a grain boundary on the right of this figure with ferritic or martensitic regions on either
Fig. 1. STEM image and associated elemental X-ray maps of a grain boundary in alloy 7E irradiated to 50.1 dpa at 644°C.
C.M. Shepherd
SM. Murphy /Association
of compositional fluctuations with cavity clusters
145
Fig. 2. (a) Ni X-ray map, (b) the distribution of cavities within the mapped area, from alloy 7G irradiated to 50.1 dpa at 644°C.
146
C.M. Shepherd S.M. Murphy / Association of
side (see ref. [5] for a more detailed description.) These maps show that the grain boundary is rich in nickel but depleted in chromium and iron, and that the transformed region is depleted in nickel but rich in chromium and iron. Further away from the grain boundary, the material was entirely austenitic, but contained irregular-shaped regions rich in nickel and depleted in chromium and iron. In between these regions the concentration of nickel was reduced and the concentrations of iron and chromium increased. The size of these nickelrich regions vary and their spatial distribution was irregular. Thus, it is clear that the apparent wavelength of any linear profile across this region would be very sensitive to the choice of the line and it would be inappropriate to ascribe anything other than an average “wavelength” to this structure. However, the linear profiles obtained from similar specimens irradiated to a dose of 26.7 dpa [5] are consistent with the observations described here. This implies that these compositional fluctuations were not significantly affected by the increase in irradiation dose. The X-ray intensity from a particular region depends on the number of atoms of each element in this region. Consequently both changes in compositions and variations in specimen thickness caused by uneven electro-
compositional fluctuations with cauity clusters polishing will produce variations in the X-ray intensity. However, it is clear from fig. 1 that the nickel concentration is high where iron and chromium concentrations are low and vice versa, so that the changes in X-ray intensity must clearly be the result of variations in the local composition of the material. Fig. 2(a) shows another X-ray map of the nickel concentration from a different specimen also irradiated to 50.1 dpa at 644Y. Again the fluctuations in nickel concentration are clearly visible. Fig. 2(b) is a schematic diagram of the same area which shows prominent features and indicates the positions of the small cavities. It is clear that almost all of the cavities are located in nickel-rich regions. In general each nickel-rich region contains not a single cavity, but a cluster of cavities. Two of these clusters of cavities and their associated nickel-rich regions have been labelled by the symbols A and B. To illustrate the association further, figs. 2(a) and 2(b) are superimposed in fig. 3. 3.2. Analysis of cavity distribution The extent of cavity clustering in has been assessed using a statistical relative positions of the cavities in the foil specimen. The region used for this
these specimens analysis of the plane of the thin analysis is shown
Fig. 3. The superimposition of figs. 2(a) and (b) to demonstrate the association of clusters of cavities with nickel-rich regions.
C.M. Shepherd
S.M. Mwphy
/ Association
of compositional fluctuations
with cavity cluters
Fig. 4. Photograph of cavities used in assessment of cavity clustering. Alloy 7E irradiated to 50.1 dpa at 644°C. in fig. 4 and the cavity distribution here is typical of that observed in these specimens. It is very difficult to determine the depth of all the cavities within the foil; therefore only the separations of the cavities in the plane of the foil are considered. Clearly, variations in the thickness of the foil could give rise to apparent clustering of the cavities so the thickness of the specimen was measured at a number of points. It was found that the foil thickness was constant to within +20!% across the area studied, with an average value of 260 run. The positions of the cavities in fig. 4 were transferred to a computer file using a Kontron digitiser attached to a Hewlett Packard computer. The positions of 1093 cavities were recorded in a rectangular area covering 3680 nm x 4120 run. The degree of clustering was investigated by calculating the distances separating pairs of cavities. Fig. 5 shows the ratio of the calculated and expected values of the frequency of distances separating pairs of cavities. The spacings of all possible pairs of cavities in the region depicted in fig. 4 are included in this calculation. There is clearly an excess in the number of cavity pairs
0
100
300
200 Separation
of cavity
pars
4ccl
500
(nm)
Fig. 5. Ratio of calculated and expected values of frequency o distances separating pairs of cavities. Each point includes datr for a 10 mu range of separations.
148
CM. Shepherd
S.M. Mtuphy /Association
2oti
,I 0
200
600 Separotmn
600
of
cowty pars
ml
1000
(nm)
Fig. 6. Ratio of calculated and expected values of frequency of distances separating pairs of cavities. Each point includes data for a 30 nm range of separations.
separated by lo-50 nm; this indicates that the cavities are clustered. There are also fewer than expected cavity pairs separated by approximately 100-140 run, which suggests that this is the typical size of a cavity cluster. In fig. 6, the same results are plotted using a coarser averageing procedure. In this figure it is clear that there are more cavity pairs than expected separated by - 370 nm, and this indicates that the clusters are separated by - 370 nm. However, there is clearly a large variation in the distances between the cavity clusters. In this figure, the average value of the pair correlation function appears to be higher than the expected average value. This is probably the result of edge effects arising from the relatively small size of the region investigated here. The results of computer simulations of clustered cavity distributions indicate that measuring the cavity separations in only two dimensions will tend to reduce the apparent degree of clustering in the sample. However, the distance between the clusters of cavities deduced from the position of the peak in the pair correlation function should not be greatly affected.
4. Discussion As discussed in a previous paper, the small cavities observed in this material are surrounded by shells of - 20 mn diameter which are rich in nickel and silicon
of
compositional fluctuationswith cavity clusters [ll]. However, this observation does not explain the formation of compositional fluctuations because these nickel-rich shells around the cavities are much smaller than the nickel-rich regions described here and shown in fig. 1. The results presented in the previous section show that the cavities in this material are clustered, and that the cavity clusters coincide with these large nickelrich regions. Thus, the compositional fluctuations shown in fig. 1 are associated not with segregation to individual cavities, but with segregation around clusters of cavities. The irregular shapes and sizes of the cavity clusters are reflected in the irregular shapes and sixes of the nickel-rich regions. The results discussed so far were obtained from samples irradiated at 644°C but similar behaviour was observed after irradiation at lower temperatures. After irradiation at 575°C the alloy, which was originally entirely austenitic, contained ferritic regions (see ref. [5] for a description of these microstructures.) In these specimens the smaIl cavities were observed only in the austenitic regions (i.e. the nickel-rich regions) and not in the ferritic phase. This again illustrates the association of cavity clusters with nickel-rich regions. It is possible that the transformation to ferrite might itself alter the cavity distribution, but it is thought that cavity clustering and fluctuations in the composition precede the transformation. After irradiation at 400°C (the lowest temperature in this experiment) the alloy again contained austenitic and ferritic regions, but in this case no cavities were visible. It is likely, however, that very small (submicroscopic) cavities were formed in the material, and that clusters of these cavities were associated with the austenitic regions. Clearly, in the 15% Ni alloys studied here, the formation of clusters of cavities is linked to the formation of fluctuations in composition. It is possible that cavity clusters are also associated with the compositional fluctuations observed in the 35% Ni alloys studied by Brager and Garner [1,2], and further studies in this area would be valuable. There are two possible sequences which could lead to the observations described in this paper. Firstly, the clusters of cavities could form during the early stages of the irradiation, and the nickel segregation to these clusters would produce fluctuations in composition. Secondly, the compositional fluctuations could occur first, with cavities nucleating preferentially in the nickel-rich regions. The first of these possibilities appears to be more likely since in the pure alloys discussed here cavity nucleation occurs rapidly in the early stages of the irradiation before a significant degree of solute segregation takes place.
CM. Shepherd
S.M. Murphy / Association
If cavity nucleation precedes the development of the compositional fluctuations, then some explanation is required for the clustering of the cavities. It is possible that cavities tend to form in clusters, i.e. new cavities tend to form close to pre-existing cavities. For example, cavities might nucleate on dislocation loops or perhaps the presence of a nickel-rich shell around one cavity could encourage the nucleation of new cavities around it, e.g. by attracting gas atoms towards the nickel-rich regions. Alternatively, it is possible that cavities nucleate randomly, but migrate through the material to form clusters. Such clustering may occur because of some attractive interaction between cavities. A more probable explanation is that cavities nucleate randomly, but there is some mechanism that increases the growth rate of cavities in some regions while cavities in other regions shrink and disappear. A recent theoretical study has explored this possibility [13]. At small sizes cavities grow by the accumulation of helium atoms, and because larger cavities are more efficient at collecting gas atoms, they tend to grow at the expense of smaller cavities. This mechanism leads to fluctuations in cavity size and eventually to fluctuations in cavity concentrations (assuming some cavities can disappear altogether). The results of the numerical calculations suggest that after irradiation at 644OC, fluctuations in cavity concentrations with a range of wavelengths - 1 pm should develop in the material. This agrees reasonably well with the observations described here. In general, the void swelling in low nickel, high chromium alloys is greater than that in high nickel, low chromium alloys. Consequently, when Brager and Garner [l] speculated on how an alloy containing compositional fluctuations would respond to further irradiation they argued that voids will tend to nucleate in regions which are depleted in nickel but rich in chromium, and segregation of nickel towards the growing voids will then produce nickel-rich regions around the voids. This would imply that new cavities and new nickel-rich regions would appear as the irradiation dose increases. It seems more likely that the small cavities observed in the present study which already reside in nickel-rich regions eventually develop into voids. These cavities grow as the helium generated by transmutation reactions accumulates and eventually they will become voids. The size of the chromium-rich or nickel-rich regions described in this paper is comparable to the diffusion distance of vacancies and interstitials before they disappear by recombination or by absorption at sinks. Thus, these small regions of varying composition in the material cannot be regarded as isolated, since many of
of compositional fluctuations
with cavity clusters
149
the vacancies and interstitials produced in one region migrate into other regions before they are annihilated. This suggests that it is not possible to extrapolate from the void swelling response of alloys with different bulk compositions to predict the probability of void formation in small microstructural regions of different compositions, as Brager and Garner proposed [l].
5. Summary and conclusions A careful study of the cavity distribution in an irradiated 12% Cr-15% Ni alloy has revealed that the cavities are clustered. These cavity clusters are associated with nickel-rich regions, implying that the cavity clusters and the formation of fluctuations in composition in this material are linked. The reasons for this behaviour are not clear but a number of possible explanations are discussed in this paper. Whatever the precise mechanism, it is likely that the nucleation of the cavities precedes the redistribution of the alloying elements, and that the clustering of the cavities is the key to understanding the formation of compositional fluctuations during irradiation.
Acknowledgements We wish to thank Dr. T.M. Williams and Mr. R.M. Boothby for many useful discussions during this work. This work described in this report was undertaken as part of the Underlying Research Programme of the UKAFA.
References [l] H.R. Brager and F.A. Garner, in: Proc. Symp. on Gptimising Materials for Nuclear AppIications, Los Angelos, CA, 1984, Eds. F.A. Garner, D.S. GeUes and F.W. Wiffen (MetaIhtrgicaI Society of AIME, Warrendale, PA, 1985) p. 141. (21 F.A. Garner, H.R. Brager and J.M. McCarthy, in: Proc. 13th Symp. on Radiation-Induced Changes in Microstructure, ASTM STP 955, Eds. F.A. Garner, N.H. Packan and A.S. Kumar (ASTM, Philadelphia, 1987) p. 75. [3] F.A. Garner, H.R. Brager, R.A. Dodd and T. Lam&en, Nucl. Instr. and Meth. B16 (1986) 244. [4] R.A. Dodd, F.A. Garner, J.J. Kai, T. Lauritzen and W.G.. Johnston, ibid. ref. [2], p. 788. [5] T.M. Williams, R.M. Boothby and J.M. Tit&marsh, in: Proc. Int. Conf. on Materials for Nuclear Reactor Core Applications (BNES, London, 1987) p. 293.
150
C.M. Shepherd
S.M. Murphy / Association of
[6] C.M. Shepherd and T.M. Williams, J. Nucl. Mater. 168 (1989) 337. [7] G. Martin, Phys. Rev. B21 (1980) 2122. [8] C. Abromeit and G. Martin, Solid State Phenomena 3&4 (1988) 321. [9] S.M. Murphy, Harwell Report AERE-R 13282 (1988), to be published in MetaB. Trans. [lo] S.M. Murphy, Solid State Phenomena 3&4 (1988) 295.
compositional fluctuations with cavity clusters [ll]
C.M. Shepherd, S.M. Murphy and T.M. Williams, Hanvell Report AERE-R 13538. [12] RM. Boothby, T.M. Williams and G.C. Bromly, ibid. ref. [51, P 223. [13] S.M. Murphy, presented at the NATO ASI Meeting on Patterns, Defects and Materials Instabilities, Cargese, Corsica, September 4-15, 1989.
Journal of Nuclear Materials 172 (1990) 143-150 Non-Homed
THEIASSOCIATION QF CO~S~ON~ OF CAlTIlES IN IRRAIMATER ALLOYS
~U~A~ONS
WITH CLUSTERS
CM. SHEPHERD and SM. MURPHY Mated& Devekpnent Dtvision,AEA Techolagy
Hawell Laboratory, OxfordshireOXI 1 ORA, United Kingdom
Rea%iv& 2 March 1990; z%Jqa?d7 March 1990
The clime of Fe-X!% Cr-15% Ni alloys irradiated with neutrons at &WC has been studied in detail. These materials display intragramdar fl~tuations in composition with an irregular size and spacing. Tbe alloys also contain a distributionof small, helium~filled cavities. It is shown that these cavities are clustered, and that the clusters of cavities are associatedwith regions rich in nickel and depleted in iron and chromium. It is believed that the cavities are the dominant point defect sinks and that the nickel enrichmmt associated with the clusters of cavities is a result of ~~~ation-~du~ segregation.Possibleexplanationsfor the clusteringof cavities are discussed.
1. lnuon .Dramatic fluctuations in composition have been observed in a mnnber of austenitic alloys after irmdiation. Such fluctuations were first observed in binary Fe-Ni alloys and ternary Fe-Cr-Ni alloys comaining approximately 35% Ni after both neutron and ion irradiations [l-4]. More recently, similar fluctuations have been observed in 15% Ni stainless steels following neutron irradiation f5]. The suggestedexplanations of this phenomenon can be divided into three main groups: (i) The ~uct~tions are the result of irradiation induced segregation to point defect sinks. In this case each nickel-rich region would contain either one huge sink or a cl~ter of smaller sinks. However, in both the 35% Ni and tbe 15% Ni alloys there was no apparent correlation between the compositional fluctuations and any visible ~~os~~t~~ sink [1,5]. (ii) The material undergoes a spinodal decomposition which is accelerated by the irradiation. Brager and Garner [1,2] argue that the spinodal reaction occurs extremely slowly in the absence of irradiation. Postirradiation anneahng experiments on the 15% Ni alloys irradiated at 644’C have demonstrated that the compositional fl~~t~ti~s are not stable at the irradiation temperature and therefore a spinodal-like decomposition can not explain the observations 161.The similarity of the fluctuations in both sets of alloys casts doubt on the validity of this explanation even for the 35% Ni alloys.
(iii) The fluctuations are the result of an irradiation-induced instability. An instability in the diffusion behaviour of the alloy could produce such fluctuations dim&y [7-91. Alternatively, an instability in the sink structure could lead to fluctuations in composition via mechanism (i} [lo]. A more detailed examination of the 15% Ni, stainless steel specimens has revealed a population of small cavities which were previously unobserved [II]. The cavities were typically 6 nm in diameter and the regions around them were rich in nickel and silicon but depleted in chromium and iron. These cavities could therefore be the ~d~~i~ features required for the first explanation above. This paper describes the distribution of these cavities and their relationship with the fluctuations in composition. 2. Expewntal The compositions of the alloys used in this work are detailed in table 1. The alloys form the basis of a much larger experiment to examine the infium~ of silicon on Table1 Tableof compositions a>(wt%) Ahoy
Cr
Ni
C
Si
Mn
7E 7c
11.89 11.8
15.2 15.1
0.052 0.061
0.95 1.42
1.03 0.99
N
@Pm)
‘) MO,Ti, Nb, V and W all K 0.02 wt%.
30 35
C.M. Shepherd
144
neutron-induced The specimens
microstructural
S.M. Mvphy
development
/ Association of compositional fluctuations
[5,11,12].
described in this paper were solution treated prior t,o irradiation at 644°C to 50.1 dpa in EBIZII. Two analytical electron microscopes were used during this work. A Vacuum Generators HB501 Scanning Transmission Electron Microscope was used when only X-ray mapping was required. However, when both X-ray maps and cavity images were to be recorded on the same microscope, a Philips EM430 was used because of its superior photographic capabilities. Both microscopes are equipped with Link X-ray detectors and computers. The X-ray maps were collected at magnifications of - ~25000. At this magnification it is dificult to identify all of the small cavities. In order to locate as many of the cavities as possible, the mapped area was photographed at higher magnifications and the positions of all the cavities were translated onto a single photograph
also
- ~25000.
with cavity clusters
The distribution
then be superimposed
of the cavities
could
on the X-ray maps.
3. Results 3. I. Microscopy In previous studies, spatial variations in composition have been investigated by measuring the local composition at points along a line perpendicular to a grain boundary. The elemental X-ray maps used here provide two-dimensional information on the local composition; this is valuable in relating compositional changes to the microstructural features in the material. Fig. 1 shows a typical X-ray map for the elements Fe, Cr and Ni from an area in a solution treated specimen irradiated to 50.1 dpa at 644’C. There is a grain boundary on the right of this figure with ferritic or martensitic regions on either
Fig. 1. STEM image and associated elemental X-ray maps of a grain boundary in alloy 7E irradiated to 50.1 dpa at 644°C.
C.M. Shepherd
SM. Murphy /Association
of compositional fluctuations with cavity clusters
145
Fig. 2. (a) Ni X-ray map, (b) the distribution of cavities within the mapped area, from alloy 7G irradiated to 50.1 dpa at 644°C.
146
C.M. Shepherd S.M. Murphy / Association of
side (see ref. [5] for a more detailed description.) These maps show that the grain boundary is rich in nickel but depleted in chromium and iron, and that the transformed region is depleted in nickel but rich in chromium and iron. Further away from the grain boundary, the material was entirely austenitic, but contained irregular-shaped regions rich in nickel and depleted in chromium and iron. In between these regions the concentration of nickel was reduced and the concentrations of iron and chromium increased. The size of these nickelrich regions vary and their spatial distribution was irregular. Thus, it is clear that the apparent wavelength of any linear profile across this region would be very sensitive to the choice of the line and it would be inappropriate to ascribe anything other than an average “wavelength” to this structure. However, the linear profiles obtained from similar specimens irradiated to a dose of 26.7 dpa [5] are consistent with the observations described here. This implies that these compositional fluctuations were not significantly affected by the increase in irradiation dose. The X-ray intensity from a particular region depends on the number of atoms of each element in this region. Consequently both changes in compositions and variations in specimen thickness caused by uneven electro-
compositional fluctuations with cauity clusters polishing will produce variations in the X-ray intensity. However, it is clear from fig. 1 that the nickel concentration is high where iron and chromium concentrations are low and vice versa, so that the changes in X-ray intensity must clearly be the result of variations in the local composition of the material. Fig. 2(a) shows another X-ray map of the nickel concentration from a different specimen also irradiated to 50.1 dpa at 644Y. Again the fluctuations in nickel concentration are clearly visible. Fig. 2(b) is a schematic diagram of the same area which shows prominent features and indicates the positions of the small cavities. It is clear that almost all of the cavities are located in nickel-rich regions. In general each nickel-rich region contains not a single cavity, but a cluster of cavities. Two of these clusters of cavities and their associated nickel-rich regions have been labelled by the symbols A and B. To illustrate the association further, figs. 2(a) and 2(b) are superimposed in fig. 3. 3.2. Analysis of cavity distribution The extent of cavity clustering in has been assessed using a statistical relative positions of the cavities in the foil specimen. The region used for this
these specimens analysis of the plane of the thin analysis is shown
Fig. 3. The superimposition of figs. 2(a) and (b) to demonstrate the association of clusters of cavities with nickel-rich regions.
C.M. Shepherd
S.M. Mwphy
/ Association
of compositional fluctuations
with cavity cluters
Fig. 4. Photograph of cavities used in assessment of cavity clustering. Alloy 7E irradiated to 50.1 dpa at 644°C. in fig. 4 and the cavity distribution here is typical of that observed in these specimens. It is very difficult to determine the depth of all the cavities within the foil; therefore only the separations of the cavities in the plane of the foil are considered. Clearly, variations in the thickness of the foil could give rise to apparent clustering of the cavities so the thickness of the specimen was measured at a number of points. It was found that the foil thickness was constant to within +20!% across the area studied, with an average value of 260 run. The positions of the cavities in fig. 4 were transferred to a computer file using a Kontron digitiser attached to a Hewlett Packard computer. The positions of 1093 cavities were recorded in a rectangular area covering 3680 nm x 4120 run. The degree of clustering was investigated by calculating the distances separating pairs of cavities. Fig. 5 shows the ratio of the calculated and expected values of the frequency of distances separating pairs of cavities. The spacings of all possible pairs of cavities in the region depicted in fig. 4 are included in this calculation. There is clearly an excess in the number of cavity pairs
0
100
300
200 Separation
of cavity
pars
4ccl
500
(nm)
Fig. 5. Ratio of calculated and expected values of frequency o distances separating pairs of cavities. Each point includes datr for a 10 mu range of separations.
148
CM. Shepherd
S.M. Mtuphy /Association
2oti
,I 0
200
600 Separotmn
600
of
cowty pars
ml
1000
(nm)
Fig. 6. Ratio of calculated and expected values of frequency of distances separating pairs of cavities. Each point includes data for a 30 nm range of separations.
separated by lo-50 nm; this indicates that the cavities are clustered. There are also fewer than expected cavity pairs separated by approximately 100-140 run, which suggests that this is the typical size of a cavity cluster. In fig. 6, the same results are plotted using a coarser averageing procedure. In this figure it is clear that there are more cavity pairs than expected separated by - 370 nm, and this indicates that the clusters are separated by - 370 nm. However, there is clearly a large variation in the distances between the cavity clusters. In this figure, the average value of the pair correlation function appears to be higher than the expected average value. This is probably the result of edge effects arising from the relatively small size of the region investigated here. The results of computer simulations of clustered cavity distributions indicate that measuring the cavity separations in only two dimensions will tend to reduce the apparent degree of clustering in the sample. However, the distance between the clusters of cavities deduced from the position of the peak in the pair correlation function should not be greatly affected.
4. Discussion As discussed in a previous paper, the small cavities observed in this material are surrounded by shells of - 20 mn diameter which are rich in nickel and silicon
of
compositional fluctuationswith cavity clusters [ll]. However, this observation does not explain the formation of compositional fluctuations because these nickel-rich shells around the cavities are much smaller than the nickel-rich regions described here and shown in fig. 1. The results presented in the previous section show that the cavities in this material are clustered, and that the cavity clusters coincide with these large nickelrich regions. Thus, the compositional fluctuations shown in fig. 1 are associated not with segregation to individual cavities, but with segregation around clusters of cavities. The irregular shapes and sizes of the cavity clusters are reflected in the irregular shapes and sixes of the nickel-rich regions. The results discussed so far were obtained from samples irradiated at 644°C but similar behaviour was observed after irradiation at lower temperatures. After irradiation at 575°C the alloy, which was originally entirely austenitic, contained ferritic regions (see ref. [5] for a description of these microstructures.) In these specimens the smaIl cavities were observed only in the austenitic regions (i.e. the nickel-rich regions) and not in the ferritic phase. This again illustrates the association of cavity clusters with nickel-rich regions. It is possible that the transformation to ferrite might itself alter the cavity distribution, but it is thought that cavity clustering and fluctuations in the composition precede the transformation. After irradiation at 400°C (the lowest temperature in this experiment) the alloy again contained austenitic and ferritic regions, but in this case no cavities were visible. It is likely, however, that very small (submicroscopic) cavities were formed in the material, and that clusters of these cavities were associated with the austenitic regions. Clearly, in the 15% Ni alloys studied here, the formation of clusters of cavities is linked to the formation of fluctuations in composition. It is possible that cavity clusters are also associated with the compositional fluctuations observed in the 35% Ni alloys studied by Brager and Garner [1,2], and further studies in this area would be valuable. There are two possible sequences which could lead to the observations described in this paper. Firstly, the clusters of cavities could form during the early stages of the irradiation, and the nickel segregation to these clusters would produce fluctuations in composition. Secondly, the compositional fluctuations could occur first, with cavities nucleating preferentially in the nickel-rich regions. The first of these possibilities appears to be more likely since in the pure alloys discussed here cavity nucleation occurs rapidly in the early stages of the irradiation before a significant degree of solute segregation takes place.
CM. Shepherd
S.M. Murphy / Association
If cavity nucleation precedes the development of the compositional fluctuations, then some explanation is required for the clustering of the cavities. It is possible that cavities tend to form in clusters, i.e. new cavities tend to form close to pre-existing cavities. For example, cavities might nucleate on dislocation loops or perhaps the presence of a nickel-rich shell around one cavity could encourage the nucleation of new cavities around it, e.g. by attracting gas atoms towards the nickel-rich regions. Alternatively, it is possible that cavities nucleate randomly, but migrate through the material to form clusters. Such clustering may occur because of some attractive interaction between cavities. A more probable explanation is that cavities nucleate randomly, but there is some mechanism that increases the growth rate of cavities in some regions while cavities in other regions shrink and disappear. A recent theoretical study has explored this possibility [13]. At small sizes cavities grow by the accumulation of helium atoms, and because larger cavities are more efficient at collecting gas atoms, they tend to grow at the expense of smaller cavities. This mechanism leads to fluctuations in cavity size and eventually to fluctuations in cavity concentrations (assuming some cavities can disappear altogether). The results of the numerical calculations suggest that after irradiation at 644OC, fluctuations in cavity concentrations with a range of wavelengths - 1 pm should develop in the material. This agrees reasonably well with the observations described here. In general, the void swelling in low nickel, high chromium alloys is greater than that in high nickel, low chromium alloys. Consequently, when Brager and Garner [l] speculated on how an alloy containing compositional fluctuations would respond to further irradiation they argued that voids will tend to nucleate in regions which are depleted in nickel but rich in chromium, and segregation of nickel towards the growing voids will then produce nickel-rich regions around the voids. This would imply that new cavities and new nickel-rich regions would appear as the irradiation dose increases. It seems more likely that the small cavities observed in the present study which already reside in nickel-rich regions eventually develop into voids. These cavities grow as the helium generated by transmutation reactions accumulates and eventually they will become voids. The size of the chromium-rich or nickel-rich regions described in this paper is comparable to the diffusion distance of vacancies and interstitials before they disappear by recombination or by absorption at sinks. Thus, these small regions of varying composition in the material cannot be regarded as isolated, since many of
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the vacancies and interstitials produced in one region migrate into other regions before they are annihilated. This suggests that it is not possible to extrapolate from the void swelling response of alloys with different bulk compositions to predict the probability of void formation in small microstructural regions of different compositions, as Brager and Garner proposed [l].
5. Summary and conclusions A careful study of the cavity distribution in an irradiated 12% Cr-15% Ni alloy has revealed that the cavities are clustered. These cavity clusters are associated with nickel-rich regions, implying that the cavity clusters and the formation of fluctuations in composition in this material are linked. The reasons for this behaviour are not clear but a number of possible explanations are discussed in this paper. Whatever the precise mechanism, it is likely that the nucleation of the cavities precedes the redistribution of the alloying elements, and that the clustering of the cavities is the key to understanding the formation of compositional fluctuations during irradiation.
Acknowledgements We wish to thank Dr. T.M. Williams and Mr. R.M. Boothby for many useful discussions during this work. This work described in this report was undertaken as part of the Underlying Research Programme of the UKAFA.
References [l] H.R. Brager and F.A. Garner, in: Proc. Symp. on Gptimising Materials for Nuclear AppIications, Los Angelos, CA, 1984, Eds. F.A. Garner, D.S. GeUes and F.W. Wiffen (MetaIhtrgicaI Society of AIME, Warrendale, PA, 1985) p. 141. (21 F.A. Garner, H.R. Brager and J.M. McCarthy, in: Proc. 13th Symp. on Radiation-Induced Changes in Microstructure, ASTM STP 955, Eds. F.A. Garner, N.H. Packan and A.S. Kumar (ASTM, Philadelphia, 1987) p. 75. [3] F.A. Garner, H.R. Brager, R.A. Dodd and T. Lam&en, Nucl. Instr. and Meth. B16 (1986) 244. [4] R.A. Dodd, F.A. Garner, J.J. Kai, T. Lauritzen and W.G.. Johnston, ibid. ref. [2], p. 788. [5] T.M. Williams, R.M. Boothby and J.M. Tit&marsh, in: Proc. Int. Conf. on Materials for Nuclear Reactor Core Applications (BNES, London, 1987) p. 293.
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[6] C.M. Shepherd and T.M. Williams, J. Nucl. Mater. 168 (1989) 337. [7] G. Martin, Phys. Rev. B21 (1980) 2122. [8] C. Abromeit and G. Martin, Solid State Phenomena 3&4 (1988) 321. [9] S.M. Murphy, Harwell Report AERE-R 13282 (1988), to be published in MetaB. Trans. [lo] S.M. Murphy, Solid State Phenomena 3&4 (1988) 295.
compositional fluctuations with cavity clusters [ll]
C.M. Shepherd, S.M. Murphy and T.M. Williams, Hanvell Report AERE-R 13538. [12] RM. Boothby, T.M. Williams and G.C. Bromly, ibid. ref. [51, P 223. [13] S.M. Murphy, presented at the NATO ASI Meeting on Patterns, Defects and Materials Instabilities, Cargese, Corsica, September 4-15, 1989.