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.     

The irradiation-creep strain produced by vacancy loops

When metals are irradiated with neutrons or ions, vacancy loops are formed by the athermal collapse of displacement cascades. On the application of a uniaxial stress, those loops with normals aligned with the applied stress absorb irradiation-produced interstitials and thermally emit vacancies at a greater rate than the non-aligned loops. This mechanism ensures that the vacancy loop distribution will be non-isotropic, thereby producing a shape change. In this paper the magnitude of the creep strain produced by this mechanism is calculated: it is shown that the vacancy loop mechanism gives rise to transient irradiation-creep strains only and that the magnitude of the transient strain is small. The results of the present analysis are critically compared with previous work.     

Irradiation-induced swelling and creep of metals

Conclusions The assumption of the existence in the microstructure of cold-worked material of dislocations having a preference for interstitial atoms (edge), and dislocations not having any preference (screw or mixed) can explain the observed decrease in dislocation density during the early stages of irradiation. This assumption also enables us to understand why the formation of a high dislocation density in a metal has a relatively small effect on the concentration and dimensions of interstitial dislocation loops formed in irradiation. Within the framework of the existing theory it is difficult to justify the assumption that screw dislocations are neutral sinks for point defects, since these dislocations have an edge component, and it would seem they should have a preference for interstitial atoms as pure edge dislocations do. However, the efficiency of dislocations as sinks may possibly not be determined by the drift of vacancies and interstitial atoms in elastic dislocation fields, but by a structural core of dislocations where trapping of point defects occurs. Unfortunately, the problem of the effect of a core of dislocations on the trapping of vacancies and interstitial atoms has not been adequately studied. Within the framework of the Heald and Speight mechanism of irradiation creep, relations were derived and analyzed which characterize the rates of irradiation swelling and irradiation creep in the presence of different types of dislocations, including those having a preference for interstitial atoms. It was established that taking account of neutral dislocation sinks does not change the theoretical conclusion that there is no simple linear relation between swelling and irradiation creep of a metal. The direct proportionality between swelling and creep deformation observed in certain cases can be explained by assuming that the strength of the sinks for dislocations predominates over the sink for point defects.Translated from Atomnaya Énergiya, Vol. 50, No. 1, pp. 17–21, January, 1981.     

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.     

The damage structure formed in molybdenum by irradiation in a fast reactor at 650°c

Transmission electron microscopy has been used to study the damage structure of commercially pure and zone-refined molybdenum irradiated in a fast reactor to a total dose of $\text{～3 × 10}{}^{22}\text{n/cm}{}^2$ at ～650°C. In all cases the structures consist of coarsely distributed dislocation segments and loops, and a considerably finer distribution of small voids. The voids tend to be ordered on a bcc superlattice parallel to the underlying host lattice. Although the loops are predominantly interstitial in nature, a significant number of small vacacy loops are present in both the commercially pure and zone-refined materials. The formation of vacancy loops during irradiation can only be accounted for by in-site collapse of displacement spikes. The occurrence of such a process implies that the formation and growth of voids is dependent on emission of vacancies from the loops. An important practical consequence of having a high density of voids compared to other sinks for point defects is that the voids themselves act as dominant neutral sinks for vacancies and interstitials, leading to an early saturation in void growth.     

Simulation of displacement cascades in tungsten irradiated by fusion neutrons

Numerical calculations of damage in tungsten irradiated by fusion neutrons were performed using molecular dynamics simulations combined with an embedded atom method potential. The displacement cascade efficiency has been calculated using the ratio of the number of Frenkel pairs determined by molecular dynamics simulations to the number of Frenkel pairs derived from Norgett-Robinson-Torrens formula. The cascade efficiency decreases as the Primary Knock Atoms increases. The Norgett-Robinson-Torrens calculations overestimate the Frenkel pair defect production by a factor of 2. The changes in the cascades dimensions at the early stages after irradiation indicate that the tungsten interstitials are more mobile than the vacancies. We found that the most common types of defects are single vacancies, di-vacancies, vacancy-clusters, interstitials and small number of interstitial clusters containing more than three atoms.     

Interstitial loop nucleation and growth in solution-treated type 316 stainless steel irradiated to low doses with 22 MeV C2+ and 46.5 MeV Ni6+ ions

The nucleation and growth of interstitial dislocation loops have been studied in solution-treated type 316 austenitic steel irradiated to low doses in the Harwell Variable Energy Cyclotron. Specimens have been irradiated with 46.5 MeV Ni⁶⁺ ions and 22 MeV C²⁺ ions, after room temperature pre-injection with 10 ppm helium and without helium pre-injection, at temperatures in the range 300–600°C. The effects of these irradiation variables on the interstitial loop populations produced are discussed. At low doses, where loop intersection is rare and dislocation network formation is minimal, the number of interstitial atoms stored in loops can give an indication of the swelling rate in circumstances where voids remain submicroscopic. It is shown that extrapolation of the low-dose swelling rates indicated by interstitial loop populations gives reasonable fit with experimentally determined high-dose void swelling values.     

Bias factors for radiation creep, growth and swelling

Central to the present concepts of the origin of the radiation-induced creep, growth and swelling phenomena is the relative interaction of interstitials and vacancies with various sinks. Radiation-induced climb of dislocations, which figures in many theories of radiation creep and growth, requires the absorption of an excess of either vacancies or interstitials. On the other hand, radiation swelling requires the absorption of an excess of vacancies to effect void growth. These relative preferences are normally expressed in theoretical models by certain bias factors, or capture efficiencies, usually assumed to be constant. Several attempts have been made to estimate their magnitude theoretically but all are seen to involve errors or physically unrealistic assumptions. We present here a unified treatment in which these various bias factors are estimated in a self-consistent model which incorporates, for the first time, all the essential physics, i.e., defect production, interactions of both vacancies and interstitials with sinks and the presence of two types of sinks. We present quantitative evaluations for the SIPA creep model and for radiation swelling, and compare with previous estimates of these phenomena.     

Irradiation Creep-Swelling Interaction in Modified 316 Stainless Steel up to 200 dpa

The irradiation creep-swelling interaction parameters were pecisely derived for MONJU fuel pin cladding PNC316 by irradiation tests of pressurized tubes in FFTF. It was found out that a creep-swelling coupling coefficient decreased and asymptotically approached a constant value as the swelling progresses, although it was widely believed that the irradiation creep rate could be proportional to the swelling rate. This non-proportionality in the irradiation creep-swelling interaction was investigated by means of the rate theory analyses under sequential climb-controlled glide process of dislocation due to absorption of interstitial atoms. It was clarified through a constructed robust model that the presence of a precipitate sink should upset the proportionality of the net interstitial flux into dislocations to the net vacancy flux into the voids. In addition, irradiation creep parameters derived by material irradiation was demonstrated to be applicable for reasonably predicting the irradiation creep deformation in the fuel pins.     

Interconnection between irradiation creep and interstitial loop formation in fcc metals

The creep strain resulting from stress-assisted, preferential loop nucleation was — following an idea proposed by Lewthwaite —calculated for both the uniaxial and the biaxial stress state. Taking the texture into account the calculated creep is about one half as large as the observed creep. This small discrepancy can be reduced further by assuming that more than just three interstitials constitute a nucleus and/or by also taking into account the stress-assisted loop growth. A contribution to the creep strain may further arise from stress-assisted, anisotropic ‘swelling’. It is concluded that these processes might account for all or a larger part of irradiation-induced creep.     

A swelling model for stoichiometric SiC at temperatures below 1000°C under neutron irradiation

A simple phenomenological model for the saturation swelling below 1000°C of neutron-irradiated silicon carbide (SiC) is presented in this paper. Under fast neutron irradiation, SiC is known to undergo volumetric expansion (swelling) which quickly saturates at a fast fluence of approximately 10²⁵ n/m² for irradiation temperatures below 1000°C. A previous model due to Balarin attributes swelling to lattice dilation as a result of single point defects. We show in this paper that the experimentally observed linear temperature dependence of saturation swelling can be explained in terms of the formation and growth of small interstitial clusters, resulting directly from collision cascades initiated by energetic neutrons. These loops grow by absorption of mobile carbon interstitials and their composition is subject to stoichiometry constraints, requiring absorption of slower silicon interstitials. Because of cascade re-solution events, the density of loops decreases sharply with temperature as a result of overlap of cascades with larger size loops at higher temperatures. The average radius of these loops increases with temperature. Volumetric swelling is shown to obey a linear temperature dependence as a consequence of the strong decrease in density and the simultaneous increase in average radius, and to saturate with fluence. The model is shown to be consistent with experimental observations. In the temperature range below 500–600°C, swelling seems to be dominated by single point defects, or defect clusters containing only a few atoms, in accordance with the explanation offered by Balarin.     

Thermal accommodation coefficients of inert gases on stainless steel and UO2

A model for primary creep of clad materials in an irradiation environment is developed subject to the following assumptions: Creep is due to the glide of edge dislocations which encounter irradiation-produced depleted zones, as barriers to their motion. The rate controlling:Step is the climb of the dislocations through the zones. Irradiation affects the creep rate in two opposing ways: (1) the vacancy-rich depleted zones serve as pinning sites for the dislocations slowing their glide, (2) the radiation-produced interstitials and vacancies cause faster dislocation climb than would be expected out-of-pile. During the early stages of irradiation before the damage has saturated, far more isolated interstitials are produced than isolated vacancies. Consequently, the flux of interstitials to dislocations is substantially greater than that of vacancies causing the dislocations to climb relatively fast. Contributing also to the rapid creep rate in the early stages is the reduced number of obstacles available to pin the dislocations.     

In-pile temperature dependence of the yield strength and growth of zircaloy

A previously reported growth model is modified and low temperature growth predictions in zircaloy are made to support the proposal that the smaller irradiation damage observed at lower temperature results from the damage sites, or depleted zones, being larger at lower temperatures. This proposal holds that the vacancies making up the zones cannot migrate at the lower temperature and, therefore, cannot condense into small voids or dislocation loops. The larger zones serve as better sinks for interstitials because they have a larger capture radius and, since they contain the same number of vacancies as the smaller, higher temperature zones, they heal faster resulting in less total damage. The resulting theoretical predictions are compared with experimental data and found to be in good agreement.     

Etude de la formation des cavites d'irradiation dans le cuivre I-irradiation aux electrons de 1 MeV

We have studied the lormation of voids and interstitial loops in thin copper foils irradiated by 1 MeV electrons as a function of temperature and of gas content. We have observed a close relationship between voids and the dislocation network. By irradiating specimens degassed by annealing, we were able to show that for irradiation temperatures ? 100°C, it is the gas dissolved in the matrix which is responsible for nucleating both loops and voids. It follows that the upper temperature limit and the temperature of maximum swelling are displaced to higher temperatures when the gas content of the material increases. The temperature range of swelling and the position of peak swelling are therefore linked above all to the nucleation conditions of the defect accumulations.     

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.     

金红石辐照损伤的分子动力学模拟

为了研究辐照条件下金红石的耐辐照损伤能力，采用GULP软件包拟合出了与实验值吻合的势函数，并采用LAMMPS软件包计算出了金红石的离位阈能和高能粒子反冲条件下的位移级联。通过统计球坐标系下266个出射方向的离位能，利用缺陷形成概率的定义得出Ti和O原子的离位阈能分别为(78.3±1.0) eV和(42.6±2.0) eV。采用VORONOI缺陷统计方法，计算了300 K、10 keV出射能量条件下缺陷数量随辐照时间演化信息，结果表明：Ti原子作为初始出射原子产生的缺陷数量整体高于O原子产生缺陷的数量，在最大无序阶段产生的空位、填隙和不同类型反位缺陷通过空位-填隙复合作用和kick-out机制逐渐减少，有效地降低了晶体的无序度，提高了基材耐辐照损伤性能。     

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.     

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.     

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.     

Radiation damage in non-fissile metallic alloys

A general survey is presented of radiation-induced displacement damage in non-fissile metallic alloys. The importance of the spatial arrangement of the vacancies and interstitials so produced is highlighted, especially as a guide to formulating an appropriate gauge for the various radiation-induced phenomena considered—i.e. hardening, embrittlement, growth, creep, swelling and fracture. The present level of theoretical understanding and the technological import of these phenomena are also assessed.