Number Density Of Loops Research Articles

A study on the microstructure and mechanical property of proton irradiated A508-3 steel

Transmission electron microscopy and the nanoindentation technique were employed to study the dislocation loops and hardening induced in proton irradiated A508-3 steel. The A508-3 steel specimens were irradiated to the dose of 0.054, 0.163, 0.271dpa at room temperature (RT), 0.163 pa at 250°C and 0.163, 0.271dpa at 290°C. The effect of dose and temperature on the dislocation loops and irradiation hardening was investigated. The results indicated that the dislocation loops were formed in proton irradiated A508-3 steel. The size and number density generally increased with increasing dose at RT. When the irradiation temperature changed from RT to 290°C, the loop size increased and the loop number density decreased. The irradiation hardening increased with dose. The effect of temperature on the irradiation induced hardening was discussed.

Contributions of Cu-rich clusters, dislocation loops and nanovoids to the irradiation-induced hardening of Cu-bearing low-Ni reactor pressure vessel steels

Dislocation loops, nanovoids and Cu-rich clusters (CRPs) are known to represent obstacles for dislocation glide in neutron-irradiated reactor pressure vessel (RPV) steels, but a consistent experimental determination of the respective obstacle strengths is still missing. A set of Cu-bearing low-Ni RPV steels and model alloys was characterized by means of SANS and TEM in order to specify mean size and number density of loops, nanovoids and CRPs. The obstacle strengths of these families were estimated by solving an over-determined set of linear equations. We have found that nanovoids are stronger than loops and loops are stronger than CRPs. Nevertheless, CRPs contribute most to irradiation hardening because of their high number density. Nanovoids were only observed for neutron fluences beyond typical end-of-life conditions of RPVs. The estimates of the obstacle strength are critically compared with reported literature data.

TEMPERATURE EFFECT OF Xe ION IRRADIATION TO 316 AUSTENITIC STAINLESS STEEL

Molten Salt Reactors (MSR) is one of the six most promising Generation IV fission reactors. In the ultimate goals, MSR should run at temperatures over 1000 K, and its neutron irradiation damage doses could reach 100 dpa or more for the core components. Hence, the evaluation of irradiation damage under high temperature for structural materials is of particular importance for ensuring the safe operation of MSR. It is generally accepted the structural materials used for MSR should be Ni-based alloys, especially the Hastelloy N alloy. Recently, the 316 austenitic stainless steel (316SS) was considered as a candidate structural material for MSR. In this study, bulk and TEM specimens of 316SS have been characterized by nanoindentation and TEM to determine the change of microhardness and microstructural evolution after 7 MeV Xe26+ and 1 MeV Xe20+ iron irradiation, respectively. The irradiation experiments were carried out at room temperature (about 22 degrees C) and 600 degrees C, and the ion fluences correspond to calculated peak damge dose of 0.62 and 3.7 dpa. The nanoindentation results for bulk specimens showed the irradiation induced hardening of 316SS irradiated at room temperature, and the hardenability increases with increasing ion damage dose. However, in the case of the irradiation at 600 degrees C, the hardness of 316SS keep the same level with that of the unirradiated specimen. The recovery of irradiation induced hardening occurred at 600 degrees C compared with the room temperature irradiation. The TEM results showed that the presence of high number density of nanoscale dislocation loops, with the diameter of 3 similar to 8 nm, in 316SS irradiated at room temperature. The number density of these dislocation loops increase with the increase of ion damage dose. As far as the irradiated 316SS under 600 degrees C, several solute clusters were observed with the size range from 4 to 12 nm, which a little larger than the dislocation loops. It should be noted that the number density is far smaller than that of the dislocation loops in former case. The radiation induced defects (dislocation loops, solute clusters) were believed to be responsible for the hardening in 316SS. The temperature effect of Xe ion irradiation to 316SS was discussed using the Orowan mechanism. The stronger diffusion of point defects caused by ion implantation at 600 degrees C was considered to be the main reason for the recovery of irradiation induced hardening, in which the vacancies and interstitials have greater probability for recombination and then disappear, resulting in the exiguous nucleation sites for the formation of solute clusters.

Elastic trapping of dislocation loops in cascades in ion-irradiated tungsten foils

Using in situ transmission electron microscopy (TEM), we have observed nanometre scale dislocation loops formed when an ultra-high-purity tungsten foil is irradiated with a very low fluence of self-ions. Analysis of the TEM images has revealed the largest loops to be predominantly of prismatic 1/2〈111〉 type and of vacancy character. The formation of such dislocation loops is surprising since isolated loops are expected to be highly mobile, and should escape from the foil. In this work we show that the observed size and number density of loops can be explained by the fact that the loops are not isolated—the loops formed in close proximity in the cascades interact with each other and with vacancy clusters, also formed in cascades, through long-range elastic fields, which prevent the escape of loops from the foil. We find that experimental observations are well reproduced by object Kinetic Monte Carlo simulations of evolution of cascades only if elastic interaction between the loops is taken into account. Our analysis highlights the profound effect of elastic interaction between defects on the microstructural evolution of irradiated materials.

Effects of Ti element on the microstructural stability of 9Cr–WVTiN reduced activation martensitic steel under ion irradiation

Microstructure of 9Cr–WVTiN reduced-activation martensitic steels with two different Ti concentrations irradiated with Fe+, He+ and H+ at 300°C was studied with transmission electron microscopy. Small dislocation loops were observed in the irradiated steels. The mean size and number density of dislocation loops decreased with the increase of Ti concentration. The segregation of Cr and Fe in carbides was observed in both irradiated steels, and the enrichment of Cr and depletion of Fe were more severe in the low Ti-concentration 9Cr–WVTiN steel.

Effect of impurities on vacancy migration energy in Fe-based alloys

Effects of impurities, such as carbon, nitrogen, helium and hydrogen, on microstructural evolution in pure iron were investigated by means of a multi-beam electron microscope. Growth rate of dislocation loops were measured to calculate vacancy migration energies. In all irradiation temperature conditions, both the size and the number density of dislocation loops were increased as a function of dose. Irradiation with more impurities showed an increase in the temperature dependence of the dislocation loop growth rate compared to irradiation with little impurities. The in situ experiment indicated that the net migration energy of vacancies could be increased due to trapping by impurities, and the effect of C and N on the migration energy of vacancy would be larger than that of W, V, Ta. Furthermore, H and He would increase vacancy migration energy greater than C and N, as well as W, V, Ta. The density functional theory (DFT), applied to the atomic models of BCC iron, indicated an increase in vacancy migration energy by the trapping of impurity atoms, that is a good agreement with this in situ experiment.

Finite size scaling study ofNf=4finite density QCD on the lattice

We explore the phase space spanned by the temperature and the chemical potential for four-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite-size scaling analyses to gluonic and quark observables, including plaquette, Polyakov loop, and quark number density, and examine their susceptibility, skewness, kurtosis, and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at ${N}_{\mathrm{t}}=4$ and spatial sizes chosen from ${6}^{3}$ up to ${10}^{3}$. Configurations were generated using the phase-reweighting approach, while the value of the phase of the quark determinant was carefully monitored. The $\ensuremath{\mu}$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $\ensuremath{\mu}$ reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(\ensuremath{\beta},\ensuremath{\kappa},\ensuremath{\mu}/T)=(1.58,0.1385,0.584\ifmmode\pm\else\textpm\fi{}0.008)$, where $({m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}},T/{m}_{\ensuremath{\rho}})=(0.822,0.154)$. It weakens considerably at $(\ensuremath{\beta},\ensuremath{\kappa},\ensuremath{\mu}/T)=(1.60,0.1371,0.821\ifmmode\pm\else\textpm\fi{}0.008)$, where $({m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}},T/{m}_{\ensuremath{\rho}})=(0.839,0.150)$, and a crossover rather than a first-order phase transition cannot be ruled out.

Microstructural evolution of CANDU spacer material Inconel X-750 under in situ ion irradiation

Work on Inconel®1Inconel® is a registered trademark of Special Metals Corporation that refers to a family of austenitic nickel–chromium-based superalloys.1 X-750 spacers removed from CANDU®2CANDU® is a registered trademark of Atomic Energy of Canada Limited standing for ‘‘CANada Deuterium Uranium’’.2 reactors has shown that they become embrittled and there is development of many small cavities within the metal matrix and along grain boundaries. In order to emulate the neutron irradiation induced microstructural changes, heavy ion irradiations (1MeV Kr2+ ions) were performed while observing the damage evolution using an intermediate voltage electron microscope (IVEM) operating at 200kV. The irradiations were carried out at various temperatures 60–400°C. The principal strengthening phase, γ′, was disordered at low doses (∼0.06dpa) during the irradiation. M23C6 carbides were found to be stable up to 5.4dpa. Lattice defects consisted mostly of stacking fault tetrahedras (SFTs), 1/2<110> perfect loops and small 1/3<111> faulted Frank loops. The ratio of SFT number density to loop number density for each irradiation condition was found to be neither temperature nor dose dependent. Under the operation of the ion beam the SFT production was very rapid, with no evidence for further growth once formed, indicating that they probably formed as a result of cascade collapse in a single cascade. The number density of the defects was found to saturate at low dose (∼0.68dpa). No cavities were observed regardless of the irradiation temperature between 60°C and 400°C for doses up to 5.4dpa. In contrast, cavities have been observed after neutron irradiation in the same material at similar doses and temperatures indicating that helium, produce during neutron irradiation, may be essential for the nucleation and growth of cavities.

Numerical simulation of irradiation hardening in Zirconium

A phase field model is developed to simulate interactions between gliding dislocations and irradiation induced damage loops (i.e., vacancy and self-interstitial loops) in Zirconium. Pinning contact interactions and long-range elastic interactions are simulated, with populations of defects generated based on experimental observations of typical damage microstructures in irradiated Zr. The model is employed to simulate irradiation hardening as a function of damage loop density. We find that the stress fields of damage loops contribute significantly to their effective obstacle strength, and that the elastic interactions cause the dependence of critical resolved shear stress on damage loop number density to deviate from analytical predictions of dispersed barrier hardening. The simulation predictions of the yield strength agree well with experimental measurements for different damage loop densities.

Effect of Carbon Impurity Content on Microstructural Evolution in Neutron-Irradiated Alpha Iron: Cluster Dynamics Modeling

ABSTRACTCluster dynamics (CD) modeling has been used to estimate the long-term evolution of point defect (PD) clusters. However, previous studies have often simplified the governing equations by assuming the maximum size of mobile self-interstitial atom (SIA) clusters and by ignoring the one-dimensional (1D) reaction kinetics of SIA loops. They have also conducted parameter fittings, such as the clustered fraction and the maximum size of clusters produced by collision cascade, to reproduce experimental data. In this study, in addition to modeling the 1D motion of SIA loops in the framework of the production bias model (PBM), reaction rates associated with carbon impurity atoms present in alpha iron were formulated to consider the trapping effect of one-dimensionally migrating SIA loops by a vacancy-carbon (V-C) complex that was shown to have strong bindings with SIA loops by previous atomistic simulations. Calculations results for neutron-irradiated alpha iron showed that the developed CD model can successfully reproduce the saturation trend of the number density of immobile SIA loops in contrast to the prediction using a model without the trapping effect.

Analysis of helium and hydrogen effect on RAFS by means of multi-beam electron microscope

Effects of helium and hydrogen gas on microstructural evolution in pure iron, Fe–8Cr, and F82H IEA were investigated by means of a multi-beam electron microscope. Growth rate and saturated number density of dislocation loops were measured to calculate migration energies of point defects. In all irradiation temperature conditions, both the size and the number density of dislocation loops were increased as a function of dose. Irradiation with helium and hydrogen showed an increase in the temperature dependence of the dislocation loop growth rate compared to irradiation without helium and hydrogen. On the other hand, little difference was observed in the saturated loop number density at each irradiation temperature. The migration energy of interstitials was determined to be 0.3eV for both types of irradiation. The migration energy of vacancies was determined to be 0.9eV for electron irradiation. This in situ experiment indicated that the net migration energy of vacancies could be increased due to trapping by helium and hydrogen. Irradiation experiments indicated that net migration energy of vacancy in F82H IEA irradiated with helium or hydrogen tended to be higher compared to that in pure iron and Fe–8Cr, which could relate not only to helium and hydrogen, but also to carbon and nitrogen concentration in matrix.

Development of microstructure and irradiation hardening of Zircaloy during low dose neutron irradiation at nominally 358 °C

Wrought Zircaloy-2 and Zircaloy-4 were neutron irradiated at nominally 358 °C in the high flux isotope reactor (HFIR) at relatively low neutron fluences between 5.8 × 10 22 and 2.9 × 10 25 n/m 2 ( E > 1 MeV). The irradiation hardening and change in microstructure were characterized following irradiation using tensile testing and examinations of microstructure using Analytical Electron Microscopy (AEM). Small increments of dose (0.0058, 0.11, 0.55, 1.08, and 2.93 × 10 25 n/m 2) were used in the range where the saturation of irradiation hardening is typically observed so that the role of microstructure evolution and 〈 a〉 loop formation on irradiation hardening could be correlated. An incubation dose between 5.8 × 10 23 and 1.1 × 10 24 n/m 2 was needed for loop nucleation to occur that resulted in irradiation hardening. Increases in yield strength were consistent with previous results in this temperature regime, and as expected less irradiation hardening and lower 〈 a〉 loop number density values than those generally reported in literature for irradiations at 260–326 °C were observed. Unlike previous lower temperature data, there is evidence in this study that the irradiation hardening can decrease with dose over certain ranges of fluence. Irradiation induced voids were observed in very low numbers in the Zircaloy-2 materials at the highest fluence.

The swelling, microstructure, and hardening of wrought LCAC, TZM, and ODS molybdenum following neutron irradiation

TEM examinations and swelling measurements were performed on commercially available wrought Low Carbon Arc Cast (LCAC), La-oxide Oxide Dispersion Strengthened (ODS), and TZM molybdenum alloys following irradiation in the High Flux Isotope Reactor (HFIR) at 300 °C, 600 °C, and 900 °C to neutron fluences between 1.05 and 24.7 × 10 25 n/m 2 ( E > 0.1 MeV), or 0.6–13.1 dpa. The defect structure, hardening, and swelling were shown to be strongly dependent on irradiation temperature and starting microstructure. Irradiation at 300 °C results in the formation of a high number density of fine loops and voids (∼1 nm) that produce significant hardening and low swelling that is comparable for all alloys. Irradiation at 600 °C–784 °C produces a high number density of larger voids (5–6 nm) that results in significant hardening with the highest swelling. A low number density of the largest void sizes (8–30 nm) are formed for the 900 °C irradiation that result in low hardening and less swelling than observed for the 600 °C irradiation. The fine grain size of ODS Mo results in a higher concentration of denuded zones along grain boundaries and improved ductile-laminate toughening that results in improved resistance to irradiation embrittlement for the 600 °C irradiations. Irradiation-induced formation of precipitates rich in transmutation products is observed at the highest dose, and it is likely that these features exert an influence on subsequent void growth.

Neutron irradiation hardening and microstructure changes in Fe–Mn binary alloys

Irradiation hardening and microstructure changes in Fe–Mn binary alloys were investigated after neutron irradiation at 290 °C and up to 0.13 dpa. Significant irradiation hardening comparable to that of Fe–1 at.%Cu alloy was observed in Fe–1 at.%Mn alloy. Manganese increases the number density of dislocation loops, which contributed to the observed irradiation hardening. Manganese serves as a nucleus of the loop by trapping interstitial atoms and clusters, preventing 1D motion of the loops.

Effects of multi-beam irradiation on defect formation in Fe–Cr alloys

An Fe–8Cr model alloy was irradiated under two modes: simple electron irradiation and dual-beam-irradiation by electrons and helium ions, and in situ observed in the high voltage electron microscope (JEOL JEM-ARM-1300 operated at 1250kV) at temperatures ranging from 300 to 500°C.At all temperatures, the size and number density of dislocation loops increased as a function of dose on both specimens. It appears that the dual-irradiated specimens showed greater temperature dependence on the growth rate of dislocation loop than that of electron-irradiated. However, there was little difference in temperature dependence of the saturated loop number density. The migration energy of interstitials was determined to be 0.23eV for both types of irradiation. The migration energy of vacancies was determined to be 0.95eV for electron irradiation. From this in situ experiment, it is indicated that the net migration energy of vacancies could be increased due to trapping by helium.

Effects of alloying elements on radiation hardening based on loop formation of electron-irradiated light water reactor pressure vessel model steels

Electron irradiations using a high voltage electron microscope were conducted on several reactor pressure vessel model alloys in order to investigate the effects of alloying elements on the formation and development of defect clusters. In addition, the effects of alloying elements on yield stress change after irradiation were considered, comparing the mean size and number density of dislocation loops with the irradiation-induced hardening. High Cu alloys formed Cu and Mn–Ni–Si rich clusters, and these are important in determining the yield stress increase. High Ni alloys formed a high density of small dislocation loops and probably Mn–Ni–Si rich cluster, which have the effect of increasing the yield stress. High P enhanced radiation-induced segregation on grain boundary, helping prevent dislocation movement.

Multiple-beam irradiation effects in electron-beam-welded F82H joint

Electron-beam-welded reduced-activation ferritic/martensitic steel F82H, which is one of prime candidate materials for experimental fusion reactors, have been irradiated by electron and helium ion beams using a High Voltage Electron Microscope (HVEM) as the experimental evaluation of the modeling and simulations. Growth rate and saturated number density of dislocation loops have been measured to calculate the migration energies of point defects. Electron irradiation experiment indicated that net migration energy of vacancy in the welded metal of F82H tended to be lower compared to that in base metal, which could be relating to difference of carbon concentration in matrix. In the case of dual beam (electron and helium) irradiation, net migration energies of vacancy were slightly higher than that in electron beam irradiation. This result indicates that vacancy would be trapped by implanted helium due to their strong interaction and appeared to have higher migration energy.

Cosmic string loop distribution on all length scales and at any redshift

We analytically derive the expected number density distribution of Nambu-Goto cosmic string loops at any redshift soon after the time of string formation to today. Our approach is based on the Polchinski-Rocha model of loop formation from long strings which we adjust to fit numerical simulations and complement by a phenomenological modelling of gravitational backreaction. Cosmological evolution drives the loop distribution towards scaling on all length scales in both the radiation and matter era. Memory of any reasonable initial loop distribution in the radiation era is shown to be erased well before Big Bang Nucleosynthesis. In the matter era, the loop distribution reaches full scaling, up to some residual loops from the radiation era which may be present for extremely low string tension. Finally, the number density of loops below the gravitational cutoff is shown to be scale independent, proportional to a negative power of the string tension and insensitive to the details of the backreaction modelling. As an application, we show that the energy density parameter of loops today cannot exceed 10−5 for currently allowed string tension values, while the loop number density cannot be less than 10−6 per Mpc3. Our result should provide a more robust basis for studying the cosmological consequences of cosmic string loops.

Dislocation loop evolution under ion irradiation in austenitic stainless steels

A solution annealed 304 and a cold worked 316 austenitic stainless steels were irradiated from 0.36 to 5 dpa at 350 °C using 160 keV Fe ions. Irradiated microstructures were characterized by transmission electron microscopy (TEM). Observations after irradiation revealed the presence of a high number density of Frank loops. Size and number density of Frank loops have been measured. Results are in good agreement with those observed in the literature and show that ion irradiation is able to simulate dislocation loop microstructure obtained after neutron irradiation. Experimental results and data from literature were compared with predictions from the cluster dynamic model, MFVIC (Mean Field Vacancy and Interstitial Clustering). It is able to reproduce dislocation loop population for neutron irradiation. Effects of dose rate and temperature on the loop number density are simulated by the model. Calculations for ion irradiations show that simulation results are consistent with experimental observations. However, results also show the model limitations due to the lack of accurate parameters.

Microstructural Characterization of RPV Materials Irradiated to High Fluences at High Flux

Abstract Understanding the embrittlement of reactor pressure vessel (RPV) steels at high fluence region is very important for the long term operation of nuclear power plants. In this study, extensive microstructural analyses were performed on the RPV steels irradiated to very high fluences beyond 1020n/cm2, E&amp;gt;1 MeVat high fluxes under the Pressurized Thermal Shock and Nuclear Power Plant Integrity Management projects in Japan. Three dimensional atom probe analyses were performed to characterize the solute atom cluster formation in these materials. The effects of fluence, flux, and chemical compositions on the characteristics of clusters were analyzed. The formation of dislocation loops was identified in the transmission electron microscopy analyses of high and low Cu steels, and the changes in loop size and number density with fluence were studied. P segregation on grain boundaries was also studied by surface analyses as well as grain boundary chemical analyses. We found that nonhardening embrittlement due to grain boundary fracture is not a major contributor to the embrittlement in these materials and irradiation conditions. The correlation of the microstructural changes and the Charpy transition temperature shifts was studied. The volume fraction of solute atom clusters has an excellent correlation with the transition temperature shifts. The Orowan model calculations of the contributions of dislocation loops to the transition temperature shifts show that in low Cu materials, dislocation loops may be a major contributor, but in Cu containing materials its contribution is weak. Root-sum-square of the contributions of solute atom clusters and dislocation loops seems to be a reasonable model to describe the total ΔRTNDT.