The influence of different inert gases on void nucleation in stainless steel bombarded by 46.5 MeV Ni6+ ions

The implications of irradiation-induced re-solution of inert gas atoms for the nucleation of voids is discussed. The differences between light gases such as helium and the heavier gases such as argon is highlighted as these are shown to give rise to quite different behaviour. For instance, helium is considered to migrate through the solid predominantly by enhanced interstitial diffusion, whereas argon migrates by enhanced vacancy diffusion. This difference gives rise to quite different nucleation densities and has a dramatic effect on the total void swelling. The main predictions of the model have been checked experimentally using ion-bombardment techniques and the results of these experiments are discussed in some detail.     

Phase-field modeling of void migration and growth kinetics in materials under irradiation and temperature field

A phase-field model is developed to investigate the migration of vacancies, interstitials, and voids during irradiation in a thermal gradient. Void growth kinetics during irradiation are also modeled. The model accounts for the generation of defects including vacancies and interstitials associated with the radiation damage, recombination of vacancies and interstitials, defect diffusion, and defect sinks. The effect of void size, vacancy concentration, vacancy generation rate, recombination rate, and temperature gradient on a single void migration and growth is parametrically studied. The results demonstrate that a temperature gradient causes void migration and defect fluxes, i.e., the Soret effect, which affects void stability and growth kinetics. It is found that (1) void migration mobility is independent of void size, which is in agreement with the theoretical prediction under the assumption of bulk diffusion controlled migration; (2) void migration mobility strongly depends on the temperature gradient and (3) the effect of defect concentration, generation rate, and recombination rate on void migration mobility is minor although they strongly influence void growth kinetics.     

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.     

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.     

The effect of damage rate on void growth in metals

The rate theory formulation of void growth was utilized to analyze the effects of damage rate on metal swelling. In particular, the swelling behavior of 316 SS was modeled as a function of temperature, over a range of displacement damage rates between 10^?6dpa/s and 10^?3dpa/s. Detailed analysis of the rate processes for point defect annihilation, migration, and loss to sinks indicated that small vacancy loops limit void growth at high damage rates. The reduction of void growth rates by vacancy emission from voids was found to be shifted towards higher temperature at higher displacement rates. In effect, the peak swelling temperature as well as the upper cutoff temperature for swelling are increased as the displacement rate is increased. The influence of constant or rate dependent nucleation conditions on the final swelling was investigated and it was shown that the initial microstructure before the growth stage essentially determines the peak swelling temperature. When appropriate empirical expressions for void and loop densities were used, the final peak swelling temperature shift agrees reasonably well with experimental data.     

Effect of trapping on interstitial cluster nucleation at the onset of irradiation

Kinetic calculations have been carried out to study heterogeneous nucleation of interstitial clusters at solute trapping sites during the transient period from the onset of irradiation until the vacancy and interstitial concentrations approach their “quasi” steady-state values. The irradiation rate, temperature, and interstitial-solute binding energy were the primary parameters varied. It has been reported earlier that, for reasonable cluster binding energies, interstitial clusters nucleate homogeneously in high concentrations at the lower temperature range of void swelling and their concentration decreases with increasing temperature. In the present calculations it is found that the decrease in the free interstitial concentration due to trapping reduces the homogeneous nucleation but, except at very high interstitial-solute binding energies, this decrease is more than offset by heterogeneous nucleation, yielding a net increase in nucleated interstitial clusters. These effects are greater at lower temperatures and lower irradiation rates.     

Effects of temperature and helium on void formation in self-ion irradiated aluminum

High-purity aluminum was irradiated with 9 MeV aluminum ions at several temperatures in the range 25–125°C, both with and without pre-injected helium. The aluminum ion irradiation doses ranged from 0.2 to 20 dpa. Void swelling in the temperature range studied was found to occur only when the aluminum contains helium gas, and as little as 0.1 appm helium is sufficient to nucleate a substantial void population. In the absence of helium, even doses of 20 dpa do not result in void formation. The void number density and size follow the general trends in conventional nucleation theories, and are similar to trends observed in nickel and stainless steels. The microstructure quite often contained heterogeneous distributions of void stringers, suggesting nucleation of voids on dislocations.     

The principles of nucleation theory relevant to the void swelling problem

The nucleation of small stable species is described in the problem of void growth by discrete rate equations. The purpose of this review is to clarify and draw together existing ideas on incubation dose and critical cavity radius for void nucleation and those of classical nucleation theory. When gas is being produced the problem reduces to one of calculating the incubation dose for the gas bubble-to-void transition. A general expression for the steady state nucleation rate is derived for the case when voids are formed by vacancy fluctuations which enable an effective nucleation barrier to be crossed.     

Gonflement du nickel irradie par des ions Ni+ de moyenne energie

After briefly summarising the advantages and drawbacks of bombardment with heavy ions, we describe the experimental apparatus we used for studying swelling in nickel. Next we discuss the problems connected with the determination of the number of atoms displaced during ion-bombardment.We studied the influence of the following parameters on the swelling of nickel: temperature, gas content, fluence, ion energy. Swelling varied with temperature and increases to a maximum at 620°C for 500 keV nickel ions. Prior helium-loading of the samples (10ppm) reduces swelling and the mean void size and increases the number of cavities. Swelling grows linearly with fluence up to 25 displacements per atom. The number and size of voids grows rapidly in the early stages of irradiation.We explain how helium reduces swelling in our experiments, and we determine how far the fluences calculated for ion-bombardments need to be corrected to allow valid comparisons with in-pile results.     

Effect of Solute Titanium on Void Swelling in 316 Stainless Steel

To investigate the solute Ti effect on void swelling in stainless steels, the well-annealed 316 stainless steels modified with various amounts of Ti were electron-irradiated in a high voltage electron microscope (HVEM). It was found that the swelling decreased dramatically with increasing Ti content up to 0.25w/0. This strong dependence of swelling on Ti content arises mainly from the changes in void number density, although the void growth rate also decreases with increase in Ti content. The dependence of the void number density on Ti content is interpreted in terms of the vacancy trapping effect of Ti, which decreases the steady state free vacancy concentration and results in the effective suppression of the void nucleation rate.     

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.     

The quantitative analysis of loop-growth and void-swelling in nickel

Dislocation loop and void growth experiments at several temperatures in the HVEM have been used to investigate point defect behaviour in nickel. It has been found that the dislocation bias is about 5% for interstitials and that voids also have a preference for interstitial defects. The value of the void bias is much less than the dislocation bias, being about 0.5%, so that swelling still occurs. The vacancy migration energy, $\text{E}{}^{\mathrm{v}}{}_{\mathrm{m}}$, has been confirmed to be $\text{1.1 ± 0.1 eV}$.     

Trapping of helium atoms in aluminum

Using molecular dynamic simulation, the effect of vacancy clusters on the interstitial helium atoms was studied in the early stages of helium bubble formation in the vessel of fission reactor, aluminum. The simulation shows, that there is a slight propensity of helium interstitial clustering without initial vacancies in aluminum. When vacancy cluster was introduced, the behavior of interstitial helium atoms was strongly dependent on the ratio of vacancy to helium. The interstitial helium atoms will be attracted in the center of the vacancy cluster when the ratio of vacancy to helium is much larger than 1, and when the ratio approaches 1, the helium will recombine with the vacancies, and, form in substitutions. In the case of the ratio of vacancy to helium less than 1, some aluminum interstitials will be created. The result shows, that the vacancy cluster plays a role of a nucleation center for helium atoms to accelerate the helium bubble growth.     

Void swelling in zirconium

The void swelling behaviour of crystal bar zirconium, during electron irradiation in the High Voltage Electron Microscope, is described. Void growth is observed to occur during irradiation in the temperature range 625–770 K in specimens pre-injected with 100 atomic ppm helium. The results are incorporated into rate theory calculations to determine the dislocation “bias factor” for interstitials and to suggest a possible reason for the apparent resistance of zirconium to void swelling under in-reactor conditions.     

Spontaneous cationic Frenkel pair recombinations in lanthanum pyrozirconate (La2Zr2O7)

Spontaneous cationic Frenkel pair recombinations in lanthanum zirconate (La₂Zr₂O₇) pyrochlore are studied with empirical potential molecular dynamics. A complex behavior is observed depending on the distance between the vacancy and the interstitial and on the nature of the cations lying in between them. While interstitials of the first shell near a vacancy readily recombine, interstitials of the second shell never do. The third shell interstitials recombine in half the configurations, i.e. when the intermediate cation is lanthanum, leading to antisites when a zirconium defect pair is considered. The behavior is globally the same in the corresponding disordered fluorite structure, but we observed that in this structure, the number of spontaneous recombinations increases with temperature.     

The influence of temperature on void-lattice formation and swelling

In two previous papers (see refs. [2] and [3]) the present authors have presented a theory of void lattices that is based on the two-interstitial model of point defects in metals and explains void-lattice formation in terms of a self-organization far from thermal equilibrium. Major features of the void lattices (e.g., the identity of the structure and orientation of void lattices and their host crystal lattices, the growth saturation and size uniformity of voids in a void lattice, the displacive stability of void lattices within a wide parameter range) are traced to a common cause—the existence of one-dimensionally migrating crowdion interstitials.In the present paper, the void-lattice theory is extended by including reactions among point defects (vacancy-interstitial recombination, athermal conversion of interstitials from the crowdion to the dumbbell configuration, and vice versa) as well as the evaporation of vacancies from dislocations and voids. It is shown that this extension accounts for the temperature dependences of swelling and void-lattice formation. For Mo and Ni it is demonstrated that, in accordance with observations, an optimum temperature for void-lattice formation exists which is located on the low-temperature side of the regime of strong swelling.     

Radiation-induced defect buildup and radiation-enhanced diffusion in a foil under energetic bombardment

The distribution of interstitials, monovacancies and vacancy aggregates containing two to six vacancies in a silver foil under irradiation was calculated as a function of both distance from the surface of the foil and irradiation time by numerically solving the rate equations for various temperatures (0–250°C) and internal sink concentrations (0,10 ^?5 and 10^?3). The calculations would be useful in areas of high-voltage electron microscopy, radiation-enhanced diffusion and void formation. The mobile defects (interstitials, monovacancies, divacancies and trivacancies) were assumed to react with each other, to annihilate at fixed sinks and to diffuse to the surface. Vacancy clusters larger than trivacancies were considered to be immobile, able to grow, but not dissociate. Humps on the steady-state concentration profiles for monovacancies and immobile vacancy clusters were found near the surface of a foil, provided the irradiation temperature and sink density were low and/or the defect production rate was quite high. The radiation-enhanced diffusion coefficient, $\text{D}{}_{\mathrm{rad}}$, of the material was calculated from the diffusivities of mobile defects and their steady-state concentrations, as a function of temperature, sink concentration, and Frenkel-pair production rate.     

Saturation of proton-induced swelling in AISI 316

There is some evidence which suggests that void swelling may not increase continuously with increasing irradiation but may saturate at a level dependent on irradiation conditions, helium/dpa level or artifacts of the simulation such as the presence of injected interstitials. An experiment was therefore performed to determine the saturation level of swelling of annealed AISI 316 at 625°C in the absence of helium and injected interstitials. Using 140 keV protons and step-height measurements it was found that saturation did not occur until 260% swelling was achieved at ~ 600 dpa. Prior to saturation the swelling curve exhibited the anticipated bilinear form with a steady state swelling rate of 0.64%/dpa based on a 20 eV threshold energy.     

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.     

Effect of mobile helium on void nucleation in materials during irradiation

The steady-state rate of void nucleation is calculated for irradiated materials containing mobile helium. At the low displacement rates typical of a fast-breeder reactor a concentration of less than 10^?10 atom fraction helium can cause a 10²⁰ increase in nucleation rate. The helium is less effective at the high displacement rates typical of accelerator experiments, but can increase the void-nucleation rate by 10⁴ at a helium concentration of 10^?8. The calculated void-nucleation rates for low displacement rates and without helium are too low to explain the void number densities observed in breeder-reactor irradiated materials. Therefore, void nucleation in reactor environments is helium-assisted. Accelerator experiments intended to simulate void nucleation under reactor conditions must be carefully designed to observe gas-assisted rather than homogeneous void nucleation.