Point defects created by atomic displacements are lost either through mutual recombination or by migration to sinks. Void swelling requires a mobile population of excess vacancies and can only occur over a limited temperature range, typically 350—

700 °C in neutron-irradiated steels and nickel-based alloys. Rapid diffusion at higher temperatures reduces the concentration of radiation-induced vacancies to near thermal equilibrium levels. Recombination dom­inates at lower temperatures, where reduced vacancy mobility prevents the formation of voids as the neces­sary counter-migration of matrix atoms cannot occur. In the swelling regime, an increased bias for intersti­tials over vacancies at dislocation sinks gives rise to the surplus vacancies which agglomerate to form voids.

The flux of point defects to sinks, including void surfaces, dislocations, and grain boundaries, results in the segregation of particular solute atoms at the sinks and the depletion of others. In austenitic steels and nickel-based alloys, it is generally found that nickel segregates at the point defect sinks. This is generally attributed to the inverse Kirkendall effect described by Marwick,29 whereby faster diffusing solutes such as Cr move in the opposite direction to the vacancy flux and are depleted at the sink, and slower diffusing solutes such as Ni are enriched. One of the earliest observations of nickel segregation at void surfaces due to the inverse Kirkendall effect was made by Marwick et al.30 in an alloy with a composition cor­responding to that of the matrix phase in Nimonic PE16. (For more detailed discussions on radiation — induced segregation effects, see the reviews of Wiedersich and Lam,31 and Rehn and Okamoto.32)

Venker and Ehrlich33 recognized that differences in the partial diffusion coefficients of alloy constitu­ents might account for the effects of composition on swelling. Any effect of this kind would generally be expected to be more significant the larger are the differences between the partial diffusion coefficients of the alloy components. Garner and Wolfer34 exam­ined Venker and Ehrlich’s conjecture and concluded that the addition of even small amounts of a fast — diffusing solute such as silicon to austenitic alloys would greatly increase the effective vacancy diffusion
coefficient (i. e., would enhance the diffusion rate for all matrix elements). The overall effect is analogous to an increase in temperature — resulting in an effective decrease in the vacancy supersaturation and hence a reduction in the void nucleation rate. This mecha­nism is generally accepted as the explanation for the beneficial effect of silicon in reducing swelling in austenitic steels and nickel-based alloys. Although this relies on the diffusion of silicon via vacancy ex­change, silicon is also generally observed to segregate to point defect sinks and since it is an undersized solute, this is believed to occur by the migration of interstitial-solute complexes. There is, however, no reason to suppose that both diffusion mechanisms cannot operate simultaneously.

Garner and Wolfer34 originally considered that since nickel diffuses relatively slowly in austenitic alloys, an increase in nickel content would have the opposite effect to silicon. However, a later assessment made by Esmailzadeh and Kumar,35 based on diffu­sion data reported by Rothman eta/.,36 indicated that the void nucleation rate in Fe-15Cr-Ni alloys would decrease with an increase in nickel content from 20 to 45%. This result is obtained because, although nickel remains the slowest diffusing species, the effective vacancy diffusion coefficient of the system is calcu­lated to increase at the higher nickel content. Esmail — zadeh and Kumar’s calculations also confirmed the beneficial effect of silicon, with the addition of 1% Si predicted to be as effective in suppressing void nucleation as increasing the nickel content from 20 to 45%. Effects at nickel contents above 45% could not be examined due to a lack of appro­priate diffusion data.

As well as affecting the nucleation of voids, differ­ences in the diffusion rates of the various solutes might also be expected to influence void growth. Simplistically, this can be thought of as being partly due to the segregation of slower diffusing solutes reducing the rate of vacancy migration in the vicinity of the voids. However, a further consequence of such nonequilibrium solute segregation was identified by Marwick,2 who realized that it would give rise to an additional vacancy flux which would oppose the radiation-induced flux to the sink. As discussed by Marwick, this additional flux (the Kirkendall flux) may itself be an important factor in limiting void growth, since it will reduce the probability ofvacancy annihilation at sinks and increase the likelihood of point defect recombination.

The effect of nickel content on void swelling was considered further in a model developed by Wolfer and coworkers.37,38 The model examined the compo­sitional dependence of the void bias and focused on the effects of nickel segregation at void surfaces. Wolfer’s model indicated that the compositional gra­dients produced by radiation-induced segregation give rise to additional drift forces which affect the point defect fluxes and thereby modify the bias terms. These additional drift forces arise from the effects of composition on point defect formation and migration energies, on the lattice parameter and the elastic mod­uli, and from the Kirkendall flux. Wolfer’s calculations for binary Fe-Ni alloys indicated that the effect of the Kirkendall flux is small for interstitials but significant for vacancies. Nevertheless, it was considered that the overall effect of compositional gradients on the bias terms is likely to be greater for interstitials than for vacancies due to other factors, particularly the effect of variations in the elastic moduli. As noted by Garner and Wolfer,39 an increase in the shear modulus in the segregated regions around voids would reduce the bias for interstitials and therefore help to stabilize voids. It is difficult to predict the significance of this effect in complex alloys, however, since depletion of Cr in the segregated region will tend to reduce the shear modu­lus, whereas enrichment of Ni in high-Ni alloys will tend to increase it.38 A more significant result of the model with regard to the effect of nickel on swelling is that there is a reversal in the sign of the Kirkendall force for vacancies in Fe-Ni alloys at ^35% Ni. Below this level, vacancies are predicted to be attracted into regions of higher Ni concentration, but above it, the opposite occurs. Wolfer et a/. considered that this effect may account for the dependence of swelling on Ni content in austenitic alloys containing less than 35% Ni.

A generalized description of the swelling behavior of austenitic alloys, which was consistent with the model developed by Wolfer et a/., was put forward by Garner40 (see also Chapter 4.02, Radiation Damage in Austenitic Steels). Garner’s ideas were largely based on the results of the EBR-II irradiation experiments and the earlier ion bombardment work of Johnston et a/., both of which showed a strong dependence of swelling on nickel content. It was considered that swelling was characterized by a tran­sient period followed by a regime in which the swelling rate became constant. In neutron-irradiated alloys, the swelling rate in the posttransient regime was generally found to be ~ 1% per dpa. In swelling — resistant alloys, however, it was argued that such high swelling rates might not be observed owing to ex­tended transient periods. The duration of the transient regime was shown to be dependent on alloy composition and could extend for many tens of dpa in low-swelling materials. The duration of the transient regime was implicitly linked to the completion of void nucleation but, at the time these ideas were put forward, relatively few measurements of void concentrations were available, as swelling data were mainly derived from dimensional or density changes.

Factors that were proposed to account for the influence of nickel on the void nucleation rate in­cluded the effect on vacancy diffusivity described by Esmailzadeh and Kumar35; a possible correlation with the development of fine scale compositional fluctua­tions by a spinodal-like decomposition process (observed by Dodd et a/.41 in ion-irradiated ternary Fe-Cr-Ni alloys); and an effect of nickel on the minimum critical radius for the formation of stable voids.42 Voids are unstable below a critical size, and will generally shrink unless stabilized by gas atoms; the minimum stable void radius is dependent on a number of factors, including temperature and defect bias, and Coghlan and Garner suggested that the compositional dependence of the vacancy diffusivity would also affect this critical size. In other words, it was considered that the transition from gas bubble to void would require a larger bubble size in high — nickel alloys, particularly at relatively high tempera­tures in the swelling regime where void nucleation becomes increasingly difficult. Hoyt and Garner43 subsequently argued that the minimum critical void radius concept might account for the minimum in swelling found at the intermediate nickel contents, provided that a compositional-dependent bias factor for dislocations was also incorporated into the model. The compositional dependence of the bias factor arises from solute segregation, which reduces the strain energy of dislocations and decreases the ratio of the bias for interstitials compared to vacancies.

It is of interest that early evidence for the opera­tion of the bubble to void transition was obtained by Mazey and Nelson,44 who implanted Nimonic PE16 (STA condition) and a PE16 matrix alloy (ST condi­tion) with 1000 appm He to produce a high density of gas bubbles before subsequent irradiation with

46.5 MeV Ni6+ ions. The PE16 matrix alloy used in this particular experiment was a low Si variant (<0.02 wt%) which was known to exhibit relatively high swelling. The mean bubble size following helium implantation at 625 ° C was higher by a factor of about two in the matrix alloy (~11 nm diameter) than in the commercial PE16 alloy (~5 nm diameter). Examination of the alloys following subsequent irradiation also at 625 °C revealed high swelling (12% at 60 dpa) with a uniform distribution of large voids but no remaining helium bubbles in the matrix alloy, and low swelling (~1% at 60 dpa) with a bimodal distribution of bubbles plus voids in the standard PE16 alloy (see Figure 5). These results were interpreted as providing evidence for the con­cept of a critical stable void size, with only a small fraction of bubbles in the commercial PE16 alloy, but all of the bubbles in the matrix alloy, being sufficiently large to grow as voids. Although not specifically discussed by Mazey and Nelson, the compositional differences between the two alloys suggest that the presence of Si and/or the g forming solutes Al plus Ti may help to reduce void nucleation in PE16.

The belief advanced by Garner,40 that sluggish void nucleation generally accounted for low swelling in nickel-based alloys, persisted for some time. However, data reported by Muroga et a/45,46 largely overturned this view. Muroga et a/. carried out microstructural examinations of a series of EBR-II-irradiated Fe-15Cr-Ni ternary alloys with Ni contents ranging from 15 to 75 wt%, and of archived samples of similar alloys from the heavy-ion bombardment experiments of Johnston eta/.12 Examination of alloys irradiated in EBR-II at 510 ° C showed that the saturation void con­centration was dependent on nickel content and was minimized at 35—45 % Ni, but revealed that there was no increase in void numbers in any of the materials above a fluence of 2.6 x 1026nm~2 (E>0.1 MeV) (see Figure 6). Alloys containing 19% and 30% Ni exhib­ited high swelling rates at higher fluences, but swelling remained low in higher nickel alloys. Similar effects were found in the ion-bombarded samples, where, for example, it was shown that there was no significant change in the void concentration in Fe—15Cr—45Ni at doses above 50 dpa in irradiations at 675 °C, yet a marked increase in swelling rate occurred above 120 dpa. Thus, contrary to earlier ideas, these investi­gations clearly demonstrated that the onset of a high swelling rate was not related to the cessation of void nucleation. It follows that the transition to a high rate of swelling must be due to an increase in the growth rate of existing voids.

Muroga et a/.45,46 observed that the total disloca­tion density in the irradiated Fe—15Cr—Ni alloys was only weakly dependent on nickel content. This sug­gested that at the intermediate nickel levels, where the void concentration was low, dislocations were weak sinks (for both vacancies and interstitials) relative to voids. In addition, it was observed that

dislocation loops persisted to higher doses at the intermediate nickel contents, indicating a lower growth rate for the loops — again implying an effect of nickel on dislocation sink strength. Based on these observations, Muroga et al. suggested that a reduced dislocation bias for interstitials at the intermedi­ate nickel contents might explain the influence of nickel on the early stages of void development. An additional factor was required to account for the eventual transition to a high swelling rate. Microche­mical data presented by Muroga et al46 suggested that this transition was related to the depletion of nickel in the matrix owing to its enrichment at void surfaces.

A complete description which incorporates all of the composition-dependent factors which affect the nucleation and growth of voids is lacking. However, there is a general consensus that the major influence of alloy composition arises through its effects on the effective vacancy diffusivity and on segregation aris­ing from the inverse Kirkendall effect. A correlation between the magnitude of void swelling and radia­tion-induced segregation was shown for Fe-Cr-Ni
ternary alloys by Allen et a/.48 The compositional dependence of radiation-induced segregation was determined using a model based on the earlier work of Marwick,2 which incorporates both the vacancy flux to the voids and the back-diffusion of vacancies due to the solute gradients set up by the inverse Kirkendall effect. Vacancy diffusivities for various alloy compositions were determined by the measure­ments of grain boundary segregation in proton- irradiated samples. Swelling data for ion and neutron-irradiated alloys were then compared with the expected swelling propensity defined by the ratio ofthe forward to back diffusion terms calculated at the appropriate irradiation temperature. The materials for which vacancy diffusivity data were determined included Fe-based alloys containing 16-24% Cr and 9-24% Ni, and Ni-based alloys containing 18% Cr and either zero or 9% Fe. This work did not specifi­cally examine 40-50% Ni alloys corresponding to the highest swelling resistance, though the results indi­cated that swelling generally decreased with increas­ing levels of nickel enrichment and chromium depletion at void surfaces.