Radiation-induced Segregation Model Research Articles

Impact of micro-alloying in ion-irradiated nickel: From the inhibition of point-defect cluster diffusion by thermal segregation to the change of dislocation loop nature

Micro-alloying strongly affects the incubation period of void swelling in irradiated face-centered cubic materials. However, the underlying mechanism, which relates to the formation of dislocation loops, is still unclear. Here, we investigate pure Ni, Ni-0.4wt.%Cr and Ni-0.4/0.8/1.2wt.%Ti as model materials, to gain insight into the solute effects on the loops evolution in the early stage of irradiation. The dislocation loop characteristics (mobility, Burgers vector, nature) are studied using in-situ transmission electron microscopy and ex-situ irradiation with Ni+ ions at 450°C and 510°C for doses from 0.06 to 0.7 dpa. It appears that a tiny amount of Ti effectively increases the loop density, reduces the loop mobility and the stacking fault energy. It leads to an equal distribution among a/2<110> perfect loop families. It also stabilizes self-interstitial loops against vacancy loops depending on Ti content and temperature. Our modeling of radiation-induced segregation, based on experiments and recent ab initio calculations of flux couplings, predicts a Cr enrichment and a Ti depletion nearby dislocation loops. It is in good agreement with our observations by X-ray spectroscopy in TEM and by atom probe tomography. However, the lowered loop mobility must be the signature of a thermal segregation rather than the impact of radiation-induced depletion. Indeed, oversized Ti atoms subsequently trapped at strained lattice sites around the dislocation line of the loop due to thermal segregation would inhibit its diffusion. This opens new perspectives for future experimental investigations and radiation-effect modeling.

Microstructure-dependent rate theory model of defect segregation and phase stability in irradiated polycrystalline LiAlO2

Gamma lithium aluminate (LiAlO2) is a breeder material for tritium and is one of key components in a tritium-producing burnable absorber rod (TPBAR). Dissolution and precipitation of second phases such as LiAl5O8 and voids are observed in irradiated LiAlO2. Such microstructure changes cause the degradation of thermomechanical properties of LiAlO2 and affect tritium retention and release kinetics, and hence, the TPBAR performance. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed for investigating the accumulation of species and phase stability in polycrystalline LiAlO2 structures under irradiation. Three sublattices (i.e. [Li, Al, V]I [O, Vo]II [Lii, Ali, Oi, Vi]III), and concentrations of six diffusive species (i.e. Li; vacancy of Li or Al at [Li, Al, V]I sublattice, O vacancy at [O, Vo]II sublattice, and Li, Al and O interstitials at [Lii, Ali, Oi, Vi]III interstitial sublattices; are used to describe spatial and temporal distributions of defects and chemistry. Microstructure-dependent thermodynamic and kinetic properties including the generation, reaction, and chemical potentials of defects and defect mobility are taken into account in the model. The parametric studies demonstrated the capability of the developed RIS model to assess the effect of thermodynamic and kinetic properties of defects on the segregation and depletion of species in polycrystalline structures and to explain the phase stability observed in irradiated LiAlO2 samples. The developed RIS model will be extended to study the precipitation of LiAl5O8 and voids and tritium retention by integrating the phase-field method.

Microstructure-Dependent Rate Theory Model of Radiation-Induced Segregation in Binary Alloys

Conventional rate theory often uses the mean field concept to describe the effect of inhomogeneous microstructures on the evolution of radiation induced defect and solute/fission product segregation. However, the spatial and temporal evolution of defects and solutes determines the formation and spatial distribution of radiation-induced second phase such as precipitates and gas bubbles/voids, especially in materials with complicated microstructures and subject to high dose radiation. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed to investigate the effect of inhomogeneous thermodynamic and kinetics properties of defects on diffusion and accumulations of solute A in AB binary alloys. Four independent concentrations: atom A, interstitial A, interstitial B, and vacancy on [A, B] sublattice are used as field variables to describe temporal and spatial distribution and evolution of defects and solute A. The independent concentrations of interstitial A and interstitial B allow to describe their different generation rates, thermodynamic and kinetic properties, and release the assumptions of interstitial generation and sink strength used in the conventional rate theory. Microstructure and concentration dependent chemical potentials of defects are used to calculate the driving forces of defect diffusions. With the model, the effects of defect chemical potentials and mobilities on the RIS in polycrystalline AB model alloys have been simulated. The results demonstrated the model capability in predicting defect evolution in materials with inhomogeneous thermodynamic and kinetic properties of defects. The model can be extended to materials with complicated microstructures such as a wide range of grain size distribution, coating structure and multiphases as well as radiation-induced precipitation subject to severe radiation damage.

Моделирование радиационно-индуцированной сегрегации в сплавах Fe-Cr-Ni

In the model of radiation-induced segregation, based on the first and second Fick’s laws and with inverse Kirkendall effect considered, the concentration profiles of the components of the concentrated Fe-Cr-Ni alloy and radiation point defects are obtained at different temperatures, dislocation densities, dose rates. The concentration profiles were calculated from the start of irradiation to the steady state. The sensitivity of concentrations of alloy components near the surface is analyzed as function of input parameters (vacancies migration energy for Cr, Ni, Fe, interstitial migration energy, etc.).

MODELING RADIATION-INDUCED SEGREGATION IN BINARY ALLOYS

A computer code to calculate the time and space dependencies of the defect and component concentrations of a binary alloy is developed. This code is based on the theoretical model for radiation-induced segregation governed by first and second Fick’s laws with taking into account inverse Kirkendall effect. The system of three coupled partial differential equations for concentrations of one of components and point defects is converted to the system of ordinary differential equations in time by a discretization procedure. Numerical solutions of this system are obtained under appropriate initial and boundary conditions by means of the MATLAB. The modeling of radiation-induced segregation in binary Fe-Cr alloys is carried out for various initial concentrations of components, temperatures, dose rates and doses. The process of achievement of steady state at dose rising is demonstrated. The calculated concentration profiles are compared with experimental profiles published in literature. The sensitivity of model to input parameters is done and the capabilities of proposed model are estimated. This computer code for multicomponent alloys is developed.

Modeling radiation induced segregation in Ni–Cr model alloys from first principles

In this paper, a rate theory model is employed to study radiation induced segregation (RIS) in Ni–Cr model alloys. In contrast with similar previous models, model parameters have been obtained from first principles via density functional theory (DFT) calculation. Qualitative model behavior is compared and contrasted with the physical mechanisms that underlie conventional RIS models, and the effects of Cr–Cr interstitial trapping and defect sink bias are investigated. It is concluded that: (1) the parameters required in this RIS model are too sensitive to be rigorously determined by present DFT approaches alone, and fitting to experimental RIS data is necessary to produce an accurate model. (2) In contrast with the emphasis of previous RIS models, the best fit DFT-based RIS model suggests that under radiation, the interstitial flux should drive Cr strongly toward enrichment near defect sinks, while the vacancy flux should drive Cr strongly toward depletion, and that the vacancy effect should be slightly stronger resulting in moderate Cr depletion. (3) The effects on RIS of Cr–Cr interstitial trapping and biased defect sinks are relatively small compared with the effects associated with variations in the species dependent diffusivities.

A Multicomponent Model of Radiation-induced Segregation for Commercial Stainless Steels

A radiation-induced segregation model of the Fe-Cr-Ni-Si-Mo system was developed to predict the change in grain boundary composition in commercial stainless steels under neutron irradiation. Parametric survey showed that there were strong influences on segregation behavior for the binding of Si to an interstitial and the jump frequency of Ni and Si via interstitial mechanisms. Careful setting of these parameters using effective point defect migration energies resulted in a good agreement between calculated results and measured data for SUS316 stainless steels irradiated to 74 dpa in light water reactor. Model calculation qualitatively reproduced the effects of dose rate, temperature, and bulk composition reported in the literature.

Effects of oversized solutes on radiation-induced segregation in austenitic stainless steels

Zirconium or hafnium additions to austenitic stainless steels caused a reduction in grain boundary Cr depletion after proton irradiations for up to 3 dpa at 400 °C and 1 dpa at 500 °C. The predictions of a radiation-induced segregation (RIS) model were also consistent with experiments in showing greater effectiveness of Zr relative to Hf due to a larger binding energy. However, the experiments showed that the effectiveness of the solute additions disappeared above 3 dpa at 400 °C and above 1 dpa at 500 °C. The loss of solute effectiveness with increasing dose is attributed to a reduction in the amount of oversized solute from the matrix due to growth of carbide precipitates. Atom probe tomography measurements indicated a reduction in amount of oversized solute in solution as a function of irradiation dose. The observations were supported by diffusion analysis suggesting that significant solute diffusion by the vacancy flux to precipitate surfaces occurs on the time scales of proton irradiations. With a decrease in available solute in solution, improved agreement between the predictions of the RIS model and measurements were consistent with the solute-vacancy trapping process, as the mechanism for enhanced recombination and suppression of RIS.

Segregation at grain boundaries: from equilibrium to irradiation induced steady states

We present a model of radiation-induced segregation (RIS) at the grain boundary (GB), treating both segregation produced by interstitials and segregation due to vacancies. Predicted kinetics of RIS in austenitic steels reveal how thermodynamic properties control the formation of a transient ‘W-shaped’ profile, the oscillatory behaviour being a signature of an establishment of a local equilibrium at proximity of the GB. The impact of a pre-irradiation profile on the formation of a ‘W-shaped’ profile is shown to be negligible at least at the GB plane and the plane adjacent.

Modeling of radiation-induced segregation at grain boundaries in Fe–Cr–Ni alloys

Modeling of radiation-induced segregation at grain boundaries in Fe–Cr–Ni alloys was carried out for wide ranges of temperatures, point defects generation rates and doses taking into account both the vacancy and interstitial mechanisms of the alloy components diffusion. To explain available data on deterioration of both the radiation-induced segregation and void swelling in austenitic stainless steels doped with oversized substitutional atoms (Ti, Nb, Ta, Zr or Hf) a physical model is proposed. Results of calculating the time of desegregation of components in Fe–Cr–Ni alloys near grain boundary during isothermal post-irradiation annealing are presented.

Effects of Pre-Existing Thermal Sensitization on the Radiation Induced Sensitization in Type 304 Stainless Steels

AbstractI is generally recognized that radiation induced sensitization plays an important role in initiating irradiation assisted stress corrosion cracking (IASCC) of austenitic stainless steels in reactor core internal of light water reactor. However, the synergism between radiation sensitization and prior thermal sensitization is unclear. This situation is likely to occur in most welded core internal structures subjected to neutron irradiation. In this study, the effect of prior thermal treatment on radiation sensitization were investigated on proton irradiated Type 304 stainless steel (SS) of initially as-received (AR) and thermal-sensitized (SEN) conditions. The Cr depletion profiles were measured by field emission gun transmission electron microscopy/ energy dispersive spectroscopy (FEGTEM / EDS), and were calculated by a radiation induced segregation (RIS) model.The different initial conditions were input in the RIS model calculations. For the asreceived condition, the initial Cr profile was modeled by a uniform concentration distribution. For the initially thermal-sensitized condition, the wider Cr depletion profile measured by FEGTEM / EDS was input as the initial condition. The results showed that radiation sensitization is characterized by a very narrow Cr depleted zone. The Cr content at grain boundary tends to be lower as radiation dose increases. Comparing with the non-sensitized (asreceived) specimens with the same dosage, the grain boundary Cr content without prior sensitization is higher than that with sensitization pre-treatment. The deeper grain boundary Cr concentration of irradiated thermally sensitized sample is induced not only from proton irradiation effect, but also resulted from the pre-existing Cr depletion.

Effect of Zirconium Addition to Austenitic Stainless Steels on Suppression of Radiation Induced Chromium Segregation at Grain Boundaries under Ion Irradiation

The effect of Zr addition to austenitic stainless steels on the suppression of radiation induced Cr segregation at grain boundaries under 400 keV He+ irradiation was studied. Type 316L stainless steel and steels with addition of 0.07, 0.21 or 0.41 mass% Zr were kept at 1,423K for 30 min, and then they were quenched into the water. Irradiation was done at 773K with the dose rate of 2.4×10−4dpa/s. The total dose was 0.85 or 3.4dpa. After irradiation, profiles of Cr concentration across the grain boundaries were measured using an analytical electron microscope with 1 nm beam diameter. Concentration of Cr at the grain boundary is decreased by radiation induced segregation. However, it increased with the addition of Zr, and the Cr segregation is almost completely suppressed when Zr is added more than 0.21 mass%.The effect of Zr addition on suppression of Cr segregation was analyzed focussing on the interaction between dissolved Zr atoms and point defects. The effect is based on vacancy trapping by the Zr atom, and the extent to which it suppresses Cr segregation can be empirically evaluated using a radiation induced segregation model by changing the effective vacancy migration energy.

Modeling of Radiation-Induced Segregation in Austenitic Fe-Cr-Ni Alloys

AbstractTo improve the ability to predict radiation-induced segregation (RIS) in austenitic Fe-Cr-Ni alloys, a model for predicting RIS is developed which calculates diffusion parameters based on local atomic configuration. Comparisons of RIS measurements in austenitic iron-base and nickelbase Fe-Cr-Ni alloys with calculations using the Perks vacancy-driven RIS model have shown that to accurately predict segregation trends, composition specific diffusion parameters must be used. This requirement limits the ability of the Perks model to predict segregation in Fe-Cr-Ni alloys for which no prior segregation measurements exist. To overcome this limitation, the improved model calculates migration energies using pair interaction energies to account for composition dependent diffusivities. The advantages of this approach are that a single set of input parameters can be used to describe a wide range of bulk alloy compositions, and the effects of local order can be easily incorporated into the calculations. A description of the model is presented, and model calculations are compared to segregation data to show that significant trends in the measured segregation data can be modeled using a single set of input parameters.

The Effect of Migration Energies on Reducing Overprediction in Radiation-Induced Segregation Models

AbstractModels for calculating radiation-induced segregation (RIS) in concentrated alloys based solely on differences in the magnitude of the vacancy driven flux typically overpredict the amount of grain boundary segregation. A simple sensitivity analysis is used to show that the overprediction may be linked to the choice of input parameters. By varying the Cr-vacancy migration energy from 1.300eV to 1.320 eV and the Fe-vacancy migration energy from1.300eV to 1.305 eV, well within their experimental uncertainty, RIS model calculations are brought into better agreement with AES and STEM-EDS measurements of grain boundary segregation in Fe-Cr-Ni alloys irradiated with protons at 7x 10−6 dpa/s at various temperatures and doses.