Investigation of pulsed irradiation effects on interstitial loop growth in metals

A computer program for the solution of non steady-state diffusion equations describing the evolution of point defects and interstitial dislocation loops during pulsed and continuous irradiation is developed. The equations take into account mutual recombination of point defects, defect migration to dislocation loops and line dislocations, and the existence of equilibrium thermal vacancies. It is shown that interstitial loops grow from 2 to 9 run in diameter due to the surplus flux of interstitials in the non steady-state regime (dynamic preference) at 573 K. At 873 K the dislocation loops begin to shrink owing to line tension forces. Comparison of interstitial loop and vacancy behaviour for pulsed and continuous irradiation at 573 and 873 K is performed. It is shown that at pulse duration 2 × 10⁻⁶ s and repetition rate 100 pulses/s, pulsing does not affect the interstitial loop behaviour.     

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.     

Calculations of the trapping and migration of vacancies and nickel self-interstitials in the presence of rare gases and dislocations

Recent models of swelling, void growth, and solute segregation under irradiation all require knowledge of the trapping and migration of vacancies and self-interstitials in the presence of lattice defects. The present calculations include trapping of both vacancies and nickel self-interstitials to substitutional and interstitial rare gas atoms. The results show a systematic dependence on rare gas atom size. It is found for example, that a vacancy is bound to a small fixed rare gas interstitial (He) by ～0.5 eV and to a large fixed interstitial (Xe) by ≥3 eV. In addition, a fixed substitutional rare gas or rare gas interstitial is found to be a strong trap for a self-interstitial. It is found that a single vacancy can significantly affect the migration energy of another vacancy. For example, a 0.4 eV decrease in migration energy is found at a distance of three half-lattice constants. However, this interaction is of limited range; at distances greater than five half-lattice constants vacancy migration is unaffected. The migration of vacancies near the core of a partial dislocation was also investigated. This partial is found to provide a 1 eV (compared to 1.4 eV in the bulk) path for the pipe diffusion of vacancies. In addition, the activation energy for vacancy migration along the slip plane is reduced by as much as 0.2 eV.     

Suppression of void nucleation by injected interstitials during heavy ion bombardment

In a heavy ion irradiation the injected ions come to rest at the end of range as interstitials without a vacancy partner. These extra interstitials perturb the delicate balance of vacancy and interstitial flux to voids. It is shown that the void nucleation rate is drastically reduced by the injected interstitials whenever recombination is an important process. As a result, void nucleation is suppressed in ion-bombardment experiments below a characteristic threshold temperature in the region of the ion deposition. This leads to a void free zone near the end of range in low temperature ion-bombardment experiments. The results obtained are in qualitative agreement with earlier experimental observations.     

Investigation of cascade-induced point-defect fluctuations

High energy irradiation produces collision cascades, which occur randomly in space and time. Any given point in the material will therefore to subject to intermittent arrival of interstitials and vacancies, even under steady irradiation. The conventional rate theory formulation of the point-defect concentrations, which contains spatial and time averaging and a uniform production rate, may not always adequately describe processes such as void nucleation and irradiation creep. We develop in this paper a theoretical approach to describe the cascade-induced point-defect fluctuations by their moments.The first moment, giving the average point-defect concentration, is used in the traditional rate theory. However, the second moment provides the variance of the point defect concentration, and it becomes important for processes such as void nucleation, dislocation climb, and loop growth. An approximate analytical expression is given for the second moment. The obtained concentration variances compare well with numerical results.We demonstrate with the example of climb-induced dislocation glide how the moments can be used to extend rate theory results. Large enhancement in the creep rate due to point defect fluctuations can be obtained if the barrier size and the average climb rate are small and if the cascade size is large.     

Void superlattice formation in electron irradiated CaF2: Theoretical analysis

CaF₂ is widely adopted as deep-UV window material and thin film optical coating. The void superlattice was observed experimentally under electron irradiation at room temperature. We performed kinetic Monte Carlo (kMC) simulations of the initial stages of the process when short- and intermediate-range order of defects in small Ca colloids and larger interstitial aggregates (F₂ gas voids) is created. The kMC model includes fluorine interstitial-vacancy pair creation, defect diffusion, similar defect attraction and dissimilar defect recombination. Special attention is paid to the statistical analysis of the defect aggregate distribution functions under different conditions (dose rate, defect migration and recombination rates). These simulations demonstrate that under certain conditions the dissimilar aggregate recombination is strongly suppressed which stimulates growth of mobile interstitial aggregates that is a precondition for further void ordering into a superlattice.     

The effect of cluster formation on the ‘temperature shift’ for accelerator simulation of neutron irradiation

The effect of the nature of the incident particles on the temperature dependence of irradiation-induced void formation in steel is considered. During neutron irradiation small clusters of vacancies are formed in ‘spikes’. At temperatures below the maximum in the swelling-temperature curve these clusters tend to dissolve slowly and hence provide recombination sites for interstitials as well as vacancies which have escaped from other clusters. Consideration of the dissolution kinetics of these clusters leads to the theoretical prediction of a minimum temperature for void formation (under neutron irradiation) of around 350°C. This result is more consistent with experimental observation than the much lower temperatures predicted by previous theory and hence lends support to the cluster dissolution theory. Due to the nature of the interaction of the high-energy electrons with the lattice, no clusters are formed during HVEM simulation of neutron damage, and cluster dissolution kinetics are therefore not controlling. Clusters are, however, produced in heavy-ion bombardment. Consequently the rate-dependent temperature shifts which are used to compare accelerator void formation data with neutron irradiation are expected to be different for electrons and for heavy ions.     

Nucleation and growth of defect clusters in CeO2 irradiated with electrons

Nucleation and growth process of defect clusters in cerium dioxide (CeO₂) with fluorite-type crystal structure has been investigated in situ under electron irradiation by using high voltage transmission electron microscopy. Planar defect clusters were formed with electron irradiation ranging from 200 to 1000 keV at temperatures below 450 K. The defect clusters were determined to be faulted-interstitial type dislocation loops lying on {1 1 1} planes. The growth rate of dislocation loops was found to increase with decreasing electron energy. An analysis of the fluence dependence of the growth process of dislocation loops suggests an increase in the vacancy mobility with decreasing electron energy. The rate of the electronic excitation is discussed in terms of the radiation-induced diffusion of oxygen-ion vacancies.     

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.     

Role of Lithium in Damage and Recovery of Irradiated Silicon Solar Cells

Lithium plays a role in the degradation and recovery of diffusion length in lithium-doped silicon p/n solar cells irradiated with 1 MeV electrons. Salient experimental results are that (1) the diffusion length degrades when these cells are irradiated at a fast rate; (2) the time constant for recovery of diffusion length decreases with lithium concentration, and increases with fluence, as ?2/3; and (3) recovery is a temperature-sensitive process with an activation energy of (0.61 ± 0.10) eV. These results suggest the following model for the damage and recovery process. Degradation of diffusion length occurs when radiation-induced vacancies pair with lithium and other available impurities to form immobile, negatively-charged recombination sites. These sites are formed at a rate governed by the irradiation rate and the high vacancy mobility. Unpaired lithium ions diffuse to, and pair with, these recombination sites, reducing their cross sections to very low values. Thus, recovery of diffusion length occurs. Recovery follows diffusion-limited kinetics in which the reacting species are of unequal concentrations. The capture radius of the recombination site for a lithium ion is proposed to decrease with fluence as ?-2/3 to achieve better accord between theory and experiment.     

Radiation induced creep and growth of zirconium alloys

The strain under irradiation of zirconium and its alloys is calculated within a simple rate theory approach. Network dislocations and interstitial dislocation loops with their Burgers vector oriented parallel to the crystal basal plane are assumed to climb by preferentially attracting interstitials with respect to vacancies, while the grain boundaries act as neutral sinks and absorb therefore more vacancies than interstitials. This same theory has been applied by Fainstein-Pedraza, Savino and Pedraza for modelling the irradiation growth of cold worked zirconium alloys. It is now extended by including the effect of vacancy traps and the stress induced preferential bias for interstitials of those dislocations favourably oriented with respect to an external or internal stress field. In addition, a model which allows to correlate the deformation of the individual grains with the strain of the polycrystalline specimen where they pertain is developed. The stresses induced within the same grain while it deforms inside the textured crystal are also numerically calculated. Those stresses modify the grain strain via the SIPA mechanism and the stresses-strains are then coupled. The calculated crystal deformation is strongly dependent on texture. For tubes with the c axis oriented preferentially on an axial plane, a rapid increase of the longitudinal strain rate is predicted at high doses.     

辐照条件下空洞超点阵形成过程的相场模拟

钨（W）具有高熔点、高热导率和优异的抗辐照能力等优点,是未来聚变堆面向等离子体部件的重要候选材料。然而中子辐照后的纯W中会产生空洞超点阵,严重影响其服役性能。本文改进了辐照条件下纯W中空洞超点阵形成过程的相场模型,采用更合理的体系总自由能函数表达形式,且考虑了空间与时间上随机分布的辐照点缺陷的产生。模拟结果表明：辐照过程中,间隙原子的定向扩散及其与空位的相互作用是空洞超点阵形成的主要原因;间隙原子沿不同方向的定向扩散形成了不同类型的空洞点阵;点阵中空洞的排列会随模拟时间的延长变得有序,空洞尺寸也会变得基本一致,而空洞形状并非标准的圆形,模拟结果与实验结果基本一致。     

The effects of impurity trapping on irradiation-induced swelling and creep

A theory of the effects of point defect trapping on radiation-induced swelling and creep deformation rates is developed. Trapping increases point defect recombination and decreases the rates of deformation processes. For fixed trapping parameters, the reduction is largest for void nucleation, less for void growth and creep due to dislocation climb-glide, and least for creep due to dislocation climb. The effects of trapping at multiple traps and of spatial and temporal variation in trap concentrations are determined. Alternative pictures in terms of effective recombination and diffusion coefficients are derived. Previous derivations of these coefficients are incorrect. A rigorous explanation is given of the well-known numerical asymmetry in the effects of vacancy and interstitial trapping. Corrections which become necessary at solute concentrations above about 0.1% are described. Numerical results for a wide range of material and irradiation parameters are presented.     

An effect of solute segregation on void growth in irradiated dilute alloys

Void growth in an irradiated solid-solution or two-phase system can be inhibited if solute segregation near the void surface, induced, say, by a lowering of the surface free energy, simultaneously reduces the diffusion of vacancies relative to self-interstitials. The mechanism is found to be efficient in suppressing void growth when re-solution of second-phase precipitates leads to solute supersaturation, or impurity interstitials are generated by collisions cascades in the matrix. While the effect does not require a precipitated second phase for the impurity/interstitial process, changes in the size of precipitates are shown to provide an independent indication of the solute redistribution.     

Anisotropic diffusion of point defects to edge dislocations

Defect diffusion under irradiation is inherently anisotropic due to the non-cubic symmetry of the saddle point configurations. A technique is developed to compute the capture efficiency of a sink in an anisotropic diffusion field of point defects, drawing an analogy between the diffusion problem and the anisotropic dielectricity problem. Analytic expressions in terms of the sink capture efficiency and, alternatively, the effective capture radii are obtained for an edge dislocation. It is found that the effect of the point defect/dislocation interactions can be attributed to the shear polarizability and an effective relaxation volume of the defect. The latter includes both the size effect and the shape effect and is in most cases considerably larger than the isotropic relaxation volume. Values of the effective relaxation volume and the effective capture radii as well as the net bias between vacancies and interstitials are given for Al, Cu, Ni, Fe, and Mo. For self interstitials, the effective relaxation volume is estimated to be 2Ω in all cases. Anisotropic growth due to mechanisms of several similar origins is also predicted.     

Considerations sur la relation entre le fluage sous irradiation et les dommages crees par l'irradiation en l'absence de contrainte

The migration to dislocations of vacancies or interstitials created during neutron-irradiation brings about supplementary creep when one type of point defect is segregated in loops or voids. A balance-sheet of defects arriving at dislocations is set up, not by solving the diffusion equations but rather by taking account of the experimentally observed growth of interstitial loops and of voids in irradiated samples.     

Irradiation damage in proton irradiated palladium-iron solid solutions

Transmission electron microscopy was used to investigate the irradiation damage, in particular irradiation induced precipitation (IIP), in Pd-base alloys containing 2, 8, 12 and 18 at % Fe. The specimens were irradiated mainly using 400 keV protons at a current density of 0.16 μA/mm² over the temperature range 110 to 750°C. A few samples containing 2 and 8% Fe were also irradiated using 3 MeV NiP⁺ ions. The irradiation microstructure of the proton irradiated alloys consists of dislocation loops over the temperature range 110 to 550°C and voids up to 650°C in all the alloys. IIP of Pd₃Fe was observed only in the Pd-18% Fe alloy between 110 and 500°C, irradiated to a dose of 0.9 dpa. Pd₃Fe was associated with dislocation loops, voids and grain boundaries. IIP was not observed in the Pd-2,8 and 12% Fe alloys proton irradiated to the same dose, nor to a higher dose of 1.5 dpa. It was also not observed in the 2 and 8% Fe alloys irradiated at 600 and 700°C by 3 MeV Ni⁺ ions.The absence of IIP in the more dilute alloys is attributed to the fast back diffusion of Fe atoms, which is due to the high mobility of vacancies in these alloys. This causes the Fe concentration at the sinks to remain below the solubility limit. Therefore, even though Fe is an undersized solute, the size effect alone is not sufficient for the production of IIP at point defect sinks in most Pd-Fe alloys. It is proposed that IIP can occur only when the alloy concentration is high enough to minimize the rate of back diffusion, which depends not only on the vacancy mobility but also on the concentration gradient near point defect sinks.     

Dynamic studies of defect mobility using high voltage electron microscopy

The large variety of observed defect-structure development by electron irradiation in fcc and bcc metals is classified from the view point of point-defect mobilities. Vacancy mobility is obtained from the defect structure change caused by the annihilation of vacancies accumulated by irradiation, and their motion activation energy is obtained from the interstitial cluster growth at high temperatures. Mobility of interstitial atoms and their interaction with impurities are obtained from the variation of interstitial cluster formation. Various observed effects of electron radiation induced motion of point defects are explained by the displacement of atoms by the transfer of energy comparable with the migration activation energy of each point defect. The observed superficial temperature dependence of the induced diffusion of vacancies in fcc metals is attributed to divacancies created by the induced diffusion. An efficient method to obtain the self-diffusion energies is proposed with results for some metals.     

Void nucleation, growth, and coalescence in irradiated metals

A novel computational treatment of dense, stiff, coupled reaction rate equations is introduced to study the nucleation, growth, and possible coalescence of cavities during neutron irradiation of metals. Radiation damage is modeled by the creation of Frenkel pair defects and helium impurity atoms. A multi-dimensional cluster size distribution function allows independent evolution of the vacancy and helium content of cavities, distinguishing voids and bubbles. A model with sessile cavities and no cluster–cluster coalescence can result in a bimodal final cavity size distribution with coexistence of small, high-pressure bubbles and large, low-pressure voids. A model that includes unhindered cavity diffusion and coalescence ultimately removes the small helium bubbles from the system, leaving only large voids. The terminal void density is also reduced and the incubation period and terminal swelling rate can be greatly altered by cavity coalescence. Temperature-dependent trapping of voids/bubbles by precipitates and alterations in void surface diffusion from adsorbed impurities and internal gas pressure may give rise to intermediate swelling behavior through their effects on cavity mobility and coalescence.