A statistical theory of void growth and time-lag

The Langevin method using the system-size expansion is applied to the nucleation and growth of voids in irradiated metals. The evolution of the average void size and the fluctuations are ordered with respect to the “system-size” inverse, where the system-size is defined as the concentration of nucleating centers. To the lowest order, the average void size satisfies the equations used for swelling calculations, and the fluctuations about the mean are Gaussian. The growth of critical sized clusters into voids is due to the higher order terms. Void growth under steady-state irradiation depends on the higher order non-Gaussian corrections until the voids become large enough. The cooling cycle of an ICFR is also considered. It is found that the non-Gaussian correction terms may play a significant role in the final void size at the end of the pulse period. The two-time cluster size correlation function φ(t, t') is evaluated near the critical size. φ(t, t') is exponentially increasing with an e-folding time, which is within a factor of about two of nucleation time-lag estimates using multistate kinetics. For sizes greater than the critical size, an exact equation is derived relating φ(t, t') to the void size current I(x, t).     

The influence of silicon and helium on the microstructural stability of ion-irradiated incoloy DS alloys

In order to test their void swelling behaviour under irradiation, several alloys based on the solid-solution nickel alloy Incoloy DS (18Cr-38Ni-Fe) with additions of 0.05, 0.43, 0.92 and 2.24 wt% Si have been studied using 4 MeV helium and 46 MeV nickel ion irradiation in the Harwell VEC. For irradiations of 60 dpa with 10 appm He the void swelling decreased from ˜ 0.9% to negligible levels with increasing silicon content. After irradiation to 90 dpa following injection with 10 appm He the 2.24% Si alloy showed <1.0% swelling at an apparent peak swelling temperature of 625° C. This alloy was subsequently irradiated to check the swelling response with concentrations of helium and hydrogen appropriate to fusion-reactor conditions. Following irradiation to 60 dpa after 1000 appm He injection the swelling peak was shifted to 575° C where a swelling maximum of 4% was observed. At 625° C with 1000 appm He alone, swelling was 2.0% compared with 1.2% in samples injected with 1000 appm He +1000 appm H. This small reduction in swelling was associated with a higher cavity (bubble) concentration in the hydrogen implanted sample. Fine-scale precipitation of Ni₃Si(γ'), η-carbide and G-phase was observed after irradiation together with helium bubbles attached to the η- and G-phase precipitates. The precipitation and void swelling was significantly greater in irradiated samples containing 1000 appm He than in those with 10 appm and irradiated to 90 dpa. It is concluded that although the Incoloy DS alloy possibly has a potential for fission-reactor core applications it has little to commend it for fusion-reactor use where the high swelling response, microstructural instability and likely long-term induced activation arising from the higher nickel content are clearly undesirable factors.     

Void Swelling and Precipitation in Ti-Modified Austenitic Fe-Ni-Cr Alloys

Irradiation temperature dependence of void swelling, and the effects of aging before irradiation on void swelling and on precipitation were examined in three Ti-modified austenitic steels called No. 1 (Fe-14Ni-16Cr-1.8Mn-2.4Mo-0.1Nb-0.1Ti-0.9Si-0.07C), No. 2 (Fe-14Ni-15Cr-1.6Mn-2.6Mo-0.24Ti-1.0Si-0.06C) and No. 3 (Fe-25Ni-15Cr-1.6Mn-2.4Mo-0.4Ti-1.0Si-0.06C). After irradiation to 10 dpa with 150–200 keV proton, the cold worked No. 1 showed swelling peak of 0.4% at 823 K, the cold worked No. 2 0.15% at 773 K and the cold worked No. 3 0.08% at 723 K. Sample Nos. 2 and 3 which were aged at 923 K for 5.4 Ms (1,500 h) showed larger void swelling because of higher void number density than the unaged ones after the irradiation to 20–40 dpa at 923 K. The amount of intragranular TiC precipitates in the irradiated specimens did not vary significantly with preirradiation treatments. Voids were mostly attached to eta (M₆C) phase which was produced during irradiation. The number density of eta phase produced during the irradiation in aged specimens was much higher than that in unaged ones. This is thought to give a main reason why void swelling in aged specimens was larger than that in unaged ones.     

The influence of pre-injected helium on void nucleation and growth in FV548 steel irradiated with 1 MeV electrons

A study has been made of the effect of helium pre-injection on the void populations produced in solution-treated specimens of FV548 austenitic steel irradiated with 1 MeV electrons in the temperature range 450–650°C. The results suggest that helium atom clusters, created during pre-injection, act as void nuclei during subsequent irradiation, although the helium cluster-void transition is limited at high irradiation temperatures by a rapid temperature-dependent increase in the critical void nucleus size. In most cases the void swelling rates at 600 and 650°C decreased with increasing void number density. This was not the case in those specimens in which helium had been pre-injected at elevated temperatures, suggesting that void swelling is an extremely sensitive function of the balance between the void and dislocation sink strengths.     

Void-swelling in solution-treated FV548 steel irradiated in a high-voltage electron microscope

A study has been made of void formation and growth in 1150°C solution-treated FV548 steel irradiated with 1 MeV electrons in the Harwell AEI EM7 high-voltage microscope (HVM). Voids are observed to form in the temperature range 200–650°C and measurements have been made of the void numbers and sizes and associated swelling as a function of temperature. Over most of the temperature range the void numbers increase rapidly to a maximum value while the voids grow continuously throughout irradiation. A particularly interesting feature of the results is that the variation in void numbers with irradiation temperature is slight up to 550°C and then the numbers decrease markedly at higher temperatures. The associated swelling increases linearly with dose and the swelling rate is a function of temperature.The present results are compared and contrasted with those from other simulation experiments on stainless steels. The most prominent distinguishing features in terms of the influence exerted by gas and by the damage process occurring during irradiation on void nucleation and growth are identified and discussed.     

Void swelling and precipitation in a titanium-modified austenitic stainless steel under proton irradiation

The correlation between void swelling and precipitation behavior in a 10% cold worked Fe-16.2Ni-14.6Cr-2.37Mo-1.79Mn-0.53Si-0.24Ti-0.06C alloy was examined with 200 keV proton irradiation. Swelling peak temperature after the proton irradiation to 10 dpa was about 823 K, and void swelling decreased steeply with increase in irradiation temperature from 823 to 923 K. Void swelling increased rapidly from 1.9 to 12.1% with increase in irradiation dose from 20 to 45 dpa at 873 K. Fine intragranular TiC precipitates, which were formed during initial stage of irradiation, dissolved gradually with increase in irradiation dose from 10 to 45 dpa at 873 K, while the amount of precipitation of needle-shaped Fe₂P phase containing titanium increased with increasing dose. The reduction of sink strength of the TiC precipitates due to the dissolution during irradiation was thought to cause the increase of swelling rate with increase in irradiation dose from 20 to 45 dpa at 873 K.     

Void Swelling of Solution-Annealed Type 316 Stainless Steel under Long Time Proton Irradiation

Solution-annealed type 316 stainless steel was irradiated by 150 keV proton to a dose of about 6 dpa at the irradiation temperature ranging 450–700°C. To examine the effect of aging during irradiation, the present proton irradiation was carried out for about 25 h at a low dose rate of 7×10–^?5dpa/s. The specimens without He preinjection showed much smaller void swelling than those preinjected with He to the content of 10 at.ppm. Similarly to the case of neutron irradiations, the void swelling in the He preinjected specimens showed the temperature dependence with double peaks, and the peak swelling temperatures were about 550 and 650°C. In these specimens with He preinjection. void number density decreased and average void diameter increased with the increase of irradiation temperature in the range of 450–600°C, but these trends were reversed between 600 and 650°C. The volume of the grain boudary M₂₃C6 precipitates increased with the increase of irradiation temperature from 600 to 700°C, and it was concluded that the decrease of soluble carbon due to the precipitation of M₂₃C6 caused the second swelling peak at 650°C.     

Quantitative modelling of swelling in M316 steel

The chemical rate theory is widely used to describe the microstructural evolution in a material during irradiation. We describe recent improvements to the theory that increase its predictive capability. The incubation dose prior to the onset of void swelling is modelled by allowing partition of the gas between the various sinks in the microstructure. New dislocation and void sink strengths have been derived incorporating the field effects. These improvements to the theory have been incorporated into a new FACSIMILE computer code designated VS5. The new code has been successfully employed to model void swelling during HVM, VEC and fast reactor irradiation of 316 steel.     

Effect of helium on void swelling in molybdenum

Simultaneous irradiation of molybdenum with helium and heavy ions (Ta³⁺) using a dual beam facility resulted in continued void nucleation in molybdenum to high dose levels, but the added helium had no measurable effect on the void swelling or swelling rate when compared with results for heavy ion irradiation without helium. Pretreatment by neutron irradiation or preinjection with helium resulted in no significant microstructural changes compared to no pretreatment. Also the temperature dependence of swelling was essentially unchanged when helium was added to the irradiation. The lack of a strong helium effect was attributed to the high inherent void nucleation rate in molybdenum. The overall swelling rate was similar to that observed for neutron irradiation and correlated well with the microstructural features that were observed. At the highest temperature and dose (1475 K and 40 dpa), simultaneous helium and heavy ion irradiation did result in a very nonuniform void distribution; thus, helium may have a greater effect on the microstructure at temperatures above those reported here.     

Very high swelling and embrittlement observed in a Fe–18Cr–10Ni–Ti hexagonal fuel wrapper irradiated in the BOR-60 fast reactor

The highest void swelling level ever observed in an operating fast reactor component has been found after irradiation in BOR-60 with swelling in Kh18H10T (Fe–18Cr–10Ni–Ti) austenitic steel exceeding 50%. At such high swelling levels the steel has reached a terminal swelling rate of 1%/dpa after a transient that depends on both dpa rate and irradiation temperature. The transient duration at the higher irradiation temperatures is as small as 10–13 dpa depending on which face was examined. When irradiated in a fast reactor such as BOR-60 with a rather low inlet temperature, most of the swelling occurs above the core center-plane and produces a highly asymmetric swelling loop when plotted vs. dpa. Voids initially harden the alloy but as the swelling level becomes significant the elastic moduli of the alloy decreases strongly with swelling, leading to the consequence that the steel actually softens with increasing swelling. This softening occurs even as the elongation decreases as a result of void linkage during deformation. Finally, the elongation decreases to zero with further increases of swelling. This very brittle failure is known to arise from segregation of nickel to void surfaces which induces a martensitic instability leading to a zero tearing modulus and zero deformation.     

Interstitial cluster nucleation at the onset of irradiation

The rate equations for the concentrations of single and small clusters of vacancies and interstitials are investigated during the transient period at the onset of irradiation. For reasonable cluster binding energies, it is found that stable interstitial clusters nucleate homogeneously in high concentrations at the lower temperature range of void swelling and their concentration decreases with increasing temperature. The effect of irradiation rate is similar to that for void swelling: lowering the irradiation rate shifts the concentration curves to lower temperatures. Increasing the concentration of preexisting sinks decreases cluster nucleation, and the cluster concentrations are found to be sensitive to cluster binding energies.     

氦对低活性Fe-Cr-Mn(W,V)合金辐照损伤影响

采用低能离子加速器和超高压电镜相连接复合辐照装置,研究注入He后经电子束辐照,观察低放射性Fe-Cr-Mn（W,V）合金的辐照损伤特征;研究He对辐照过程中产生二次缺陷,空洞肿胀,诱起晶界偏析的影响。实验结果证明He的存在,增加辐照初期位错密度,促进空洞核心形成及空洞肿胀增加,抑制晶界近旁溶质元素偏析。     

The effects of cold working and pre-irradiation heat treatment on void formation in neutron-irradiated type 316 stainless steel

The effect of fast-neutron irradiation on void formation in Type 316 stainless steel having undergone specific thermalmechanical treatments was investigated by transmission electron microscopy. The study showed that, for irradiation at the three lower temperatures (420, 475 and 580°C): (1) the void volume decreased with increasing cold work; (2) the reduction in swelling was due to a decrease in both void-number density and void size; (3) the decrease in void size with increasing cold-work level was enhanced at higher irradiation temperatures; (4) cold working from 0 to 10% decreased the voidnumber density, and void volume, more than in the range from 10 to 20%; (5) void formation in the 20% cw steel which had been heat treated 100 h at 650°C before irradiation was similar to that of the solution-treated steel. The temperature dependence of swelling of the cold-worked material was different from that of the solution-treated steel. Irradiation at 650°C resulted in a larger void volume in the cold-worked material than for irradiation at 475 or 580°C. The effects of cold work and irradiation temperature on void growth are consistent with the predictions of a diffusion-controlled model.     

Void Swelling in Electron Irradiated High Purity Fe-Cr-Ni Austenitic Alloys

High-purity Fe-Cr-Ni austenitic alloys corresponding to commercial Type-316 stainless steel and Hastelloy-X were used to investigate the void swelling mechanism of the austenitic steels. The alloys were irradiated with 1 MeV electrons in a high voltage electron microscope in the temperature range of 300~600°C to a total dose of about 30 dpa. Low void swelling in Ni-base alloy is attributed to both low void number density and small void size. Void embryos in Fe-base alloy are stabilized by strain field arised from Ni solute segregation around the void surface. The stabilization does not occur in Ni-base alloy, which results in extremely low void number density at high temperatures (>500°C). Higher void growth rates in Fe-base alloy than in Ni-base alloy are attributable to large climbing rate of dislocations produced during the irradiation.     

Importance of zirconium cross sections in calculating reactivity effects for inert matrix fuels

Zirconium is employed as the “inert” component in several different inert matrix fuel concepts currently under development (cermet, oxide solution, etc.). Relative to the situation in standard light water reactors, this implies a very significant increase in the zirconium inventory, with a correspondingly enhanced importance of the nuclear data for zirconium in calculating safety related parameters. The present paper discusses new numerical results for various reactivity effects. On the basis of the current findings, it is recommended that a high priority be assigned to both the reduction of uncertainties in the epithermal data for zirconium and to the improvement of methods for resonance self-shielding of these data.     

Interpreting and predicting irradiation creep by fuel element modelling

In order to provide quantitative predictions of the deformation in fuel element cladding it is necessary to take into account several coupled mechanisms. In particular void swelling and irradiation creep components can only be isolated if they are individually understood and modelled correctly. The fuel element modelling program FRUMP has been used to investigate the contribution from void swelling when an appropriately stress dependent model is used. The voidage strain can then be isolated and the remaining irreversible strains examined to give information on irradiation creep. It is emphasized that a proper understanding of the stress effects on void swelling is essential for this procedure.     

Void formation and precipitation during electron-irradiation in austenitic stainless steels modified with Ti,Zr and V

Solution-annealed type 316 stainless steels modified with one or two elements of titanium, zirconium and vanadium were electron-irradiated up to a dose of about 50 dpa at temperatures of 773 to 823 K in a high voltage electron microscope. Addition of 0.3 wt% of titanium or zirconium to 316 steel remarkably reduce the void density at 823 K, compared with that in the standard 316 steel. Conversely, addition of 0.3 wt% of vanadium enhances void formation at 823 K; the void density is two orders of magnitude higher than that in the 316 steel. The enhancement is related to the radiation-induced V-carbides in the early stage of irradiation. Further addition of 0.15 wt% titanium to the V- and Zr-modified steels completely suppresses void formation up to 50 dpa at 823 K, because fine Ti-carbides precipitated along dislocations beyond about 10 dpa change dislocation bias to reduce the vacancy supersaturation rate. A beneficial effect of zirconium on void formation is disappeared by the addition of 0.15 wt% vanadium to the Zr-modified steel irradiated at 773 to 823 K.     

Fluence and temperature dependence of swelling in irradiated molybdenum

Volume changes have been analyzed in molybdenum which has been neutron irradiated to various fluences over the temperature range 50 to 1300°C. This data together with all previously reported data has been compiled into a three-dimensional plot of swelling versus temperature versus fluence. Significant low temperature swelling, < 400°C, is observed and is consistent with the presence of isolated immobile vacancies. Void swelling only becomes significant at temperatures > 400°C. The nature of the dislocation and void microstructure at high irradiation temperatures are analyzed quantitatively as a function of irradiation temperature and the results are reasonably consistent with a recent model of Brailsford and Bullough. The same model is also consistent with an observed trend towards saturation in the void swelling at high fluences at the low temperature end of the void region.     

Void-swelling in cold-worked copper during HVEM irradiation

Void formation and growth in pure cold-worked copper and the parallel evolution in dislocation structure during HVEM irradiation have been investigated. Degrees of cold work in the range 10–90% rolling reduction and irradiation temperatures in the range 250–450°C have been covered. The cold-worked structure basically survives irradiation. Initially (for low degrees of cold work), void density and swelling rate increase with increasing degree of cold work; they then level off and eventually start decreasing with further cold work. The decrease in swelling rate cannot be explained in terms of a simple increase in dislocation density; one will have to consider the real, heterogeneous dislocation distribution.     

Numerical simulation of void nucleation in irradiated metals

An atomistics-based theory for void nucleation has been used to calculate — for the first time — terminal void number densities for irradiated nickel, type 316 stainless steel, and the Ni-base alloy, PE-16. Both the absolute magnitudes and temperature dependences of the void number densities are in agreement with experiment. The void nucleation parameter, ψ, which governs spontaneous void nucleation was evaluated for the three materials; the results are in agreement with experiment. The critical gas content for rapid void growth was calculated for PE-16 and type 316 stainless steel, and was found to increase from about 10 helium atoms at the lower end of the void swelling range to some 10⁴ atoms at the upper end. The theory was also found to predict re-nucleation of a new distribution of voids after a drop in temperature during irradiation.