Roger E. Stoller

A comparison of displacement cascades in copper and iron by molecular dynamics and its application to microstructural evolution

Abstract The use of molecular dynamics simulation and improved many-body potentials make it possible to compare displacement cascade evolution in different materials. However, the extreme variability between individual cascades requires multiple simulations at nominally identical conditions of temperature and energy in order to assure that the comparison is statistically valid. We describe such a comparison of copper and iron in this paper. Over 600 cascades have been investigated, with simulation energies in the range 60 eV to 10 keV and temperatures from 100 to 900 K. The evolution of the cascades is similar in both materials, with the development of a highly disordered core and the emission of focusons and replacement collision sequences during the collisional phase of the cascade. The majority of vacancy-type defects are found in the cascade core when in-cascade recombination is complete, while the interstitial-type defects tend to be distributed around the periphery of this region. The final defect structure has been characterized by the total surviving defect fraction, and the number and size of the point defect clusters produced. Since these parameters have significant implications for the nuclear industry in its assessment of radiation damage, we show how they depend on cascade energy and temperature. To illustrate their importance, we provide an example of how the molecular dynamics results can be used in a rate theory model of ferritic steel embrittlement.

Primary damage formation in bcc iron

Abstract Primary defect formation in bee iron has been extensively investigated using the methods of molecular dynamics (MD) and Monte Carlo (MC) simulation. This research has employed a modified version of the Finnis-Sinclair interatomic potential. MD was used in the simulation of displacement cascades with energies up to 40 keV and to examine the migration of the interstitial clusters that were observed to form in the cascade simulations. Interstitial cluster binding energies and the stable cluster configurations were determined by structural relaxation and energy minimization using a MC method with simulated annealing. Clusters containing up to 19 interstitials were examined. Taken together with the previous work, these new simulations provide a reasonably complete description of primary defect formation in iron. The results of the displacement cascade simulations have been used to characterize the energy and temperature dependence of primary defect formation in terms of two parameters: (1) the number of surviving point defects and (2) the fraction of the surviving defects that are contained in clusters. The number of surviving point defects is expressed as a fraction of the atomic displacements calculated using the secondary displacement model of Norgett-Robinson-Torrens (NRT). Although the results of the high energy simulations are generally consistent with those obtained at lower energies, two notable exceptions were observed. The first is that extensive subcascade formation at 40 keV leads to a higher defect survival fraction than would be predicted from extrapolation of the results obtained for energies up to 20 keV. The stable defect fraction obtained from the MD simulations is a smoothly decreasing function up to 20 keV. Subcascade formation leads to a slight increase in this ratio at 40 keV, where the value is about the same as at 10 keV. Secondly, the potential for a significant level of in-cascade vacancy clustering was observed. Previous cascade studies employing this potential have reported extensive interstitial clustering, but little evidence of vacancy clustering. Interstitial clusters were found to be strongly bound, with binding energies in excess of 1 eV. The larger clusters exhibited a complex, 3D structure and were composed of 〈111〉 crowdions. These clusters were observed to migrate by collective 〈111〉 translations with an activation energy on the order of 0.1 eV.

Dose dependence of the microstructural evolution in neutron-irradiated austenitic stainless steel

Abstract Microstructural data on the evolution of the dislocation loop, cavity, and precipitate populations in neutron-irradiated austenitic stainless steels are reviewed in order to estimate the displacement damage levels needed to achieve the “steady state” condition. The microstructural data can be conveniently divided into two temperature regimes. In the low temperature regime (below about 300°C) the microstructure of austenitic stainless steels is dominated by “black spot” defect clusters and faulted interstitial dislocation loops. The dose needed to approach saturation of the loop and defect cluster densities is generally on the order of 1 displacement per atom (dpa) in this regime. In the high temperature regime (~ 300 to 700°C), cavities, precipitates, loops and network dislocations are all produced during irradiation; doses in excess of 10 dpa are generally required to approach a “steady state” microstructural condition. Due to complex interactions between the various microstructural components that form during irradiation, a secondary transient regime is typically observed in commercial stainless steels during irradiation at elevated temperatures. This slowly evolving secondary transient may extend to damage levels in excess of 50 dpa in typical 300-series stainless steels, and to > 100 dpa in radiation-resistant developmental steels. The detailed evolution of any given microstructural component in the high-temperature regime is sensitive to slight variations in numerous experimental variables, including heat-to-heat composition changes and neutron spectrum.

The role of cascade energy and temperature in primary defect formation in iron

Molecular dynamics (MD) simulations have been used to investigate the formation of atomic displacement cascades in iron with energies up to 50 keV (corresponding to a primary knock-on atom (PKA) energy of 79 keV) at 100 K, up to 20 keV at 600 K, and up to 10 keV at 900 K. The cascade damage production has been characterized in terms of several parameters: the number of surviving point defects, the fraction and type of surviving point defects found in clusters, and the size distributions of the in-cascade point defect clusters. A sufficient number of simulations have been completed at each condition to evaluate the statistical variation in these primary damage parameters as a function of irradiation temperature and cascade energy. The energy dependence of stable defect formation can be conveniently separated into three regimes with the number of defects in each regime correlated by a simple power law with a characteristic exponent. The primary effects of cascade energy on defect formation at high energies are explained in terms of subcascade formation. Only a modest effect of temperature is observed on defect survival, while irradiation temperature increases lead to a slight increase in the in-cascade interstitial clustering fraction and a decrease in the vacancy clustering fraction. Cascade energy has little effect on the in-cascade clustering fractions above about 5 keV. However, there is a systematic change in the cluster size distribution, with higher energy cascades producing larger clusters. The loosely coupled nature of the in-cascade vacancy clusters persists at higher energies.

On the relationship between uniaxial yield strength and resolved shear stress in polycrystalline materials

Attempts to correlate radiation-induced microstructural changes with changes in mechanical properties rely on a well-established theory to compute the resolved shear stress required to move dislocations through a field of obstacles. However, this microstructure-based shear stress must be converted to an equivalent uniaxial tensile stress in order to make comparisons with mechanical property measurements. A review of the radiation effects literature indicates that there is some confusion regarding the choice of this conversion factor for polycrystalline specimens. Some authors have used values of 1.73 and 2.0, based on an inappropriate application of the von Mises and Tresca yield criteria, respectively. The basic models pertinent to this area of research are reviewed, and it is concluded that the Taylor factor with a value of 3.06 is the correct parameter to apply in such work.

Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys

A grand challenge in materials research is to understand complex electronic correlation and non-equilibrium atomic interactions, and how such intrinsic properties and dynamic processes affect energy transfer and defect evolution in irradiated materials. Here we report that chemical disorder, with an increasing number of principal elements and/or altered concentrations of specific elements, in single-phase concentrated solid solution alloys can lead to substantial reduction in electron mean free path and orders of magnitude decrease in electrical and thermal conductivity. The subsequently slow energy dissipation affects defect dynamics at the early stages, and consequentially may result in less deleterious defects. Suppressed damage accumulation with increasing chemical disorder from pure nickel to binary and to more complex quaternary solid solutions is observed. Understanding and controlling energy dissipation and defect dynamics by altering alloy complexity may pave the way for new design principles of radiation-tolerant structural alloys for energy applications.

The influence of helium on microstructural evolution: Implications for DT fusion reactors☆

Abstract The influence of helium on the microstructural evolution of irradiated metals is reviewed. The review encompasses data from past work involving charged particle irradiations and neutron irradiations in fission reactors, but emphasizes more recent results. This latter data was obtained from experiments in which either the reactor neutron spectrum or the isotopic content of the nickel in the irradiated alloys was tailored to yield a ratio of helium to displacement production (He/dpa ratio) that is near the value that will be obtained in a DT fusion reactor. Both the absolute level of helium present and the He/dpa ratio are shown to be important parameters. All major components of the irradiated microstructure: cavities, precipitates, and dislocations are shown to be sensitive to helium as a result of either its direct influence on cavity formation, or its indirect effect on point defect and solute partitioning. The results emphasize the importance of careful experimental and theoretical analysis if data from fission reactor experiments are to be used in fusion reactor design. In particular, the effects of helium appear to be greatest during the swelling incubation period, the time of most practical interest for fusion reactor designers.

Statistical analysis of a library of molecular dynamics cascade simulations in iron at 100 K

Abstract An extensive database of atomic displacement cascades in iron has been developed using molecular dynamics (MD) simulations. Simulations have been carried out at temperatures of 100, 600, and 900 K, and at energies between 0.10 and 50 keV. The results presented here focus on the simulations conducted at 100 K. A sufficient number of cascades has been completed under each condition of cascade energy and temperature to obtain statistically significant average values for the primary damage production parameters. The statistical analysis has been used to examine the influence of primary knockon direction, simulation cell-size, and lattice heating by the high energy recoil. A surprising effect of primary knockon atom (PKA) direction was observed up to 1 keV, but little effect of lattice heating was detected. We have previously reported preliminary results indicating that the ratio of surviving point defects to the number calculated by the Norgett–Robinson–Torrens (NRT) displacement model appears to pass through a minimum value of about 20 keV. The present analysis supports the statistical significance of this minimum, which can be attributed to the onset of extensive subcascade formation.

Subcascade formation in displacement cascade simulations: Implications for fusion reactor materials

Displacement cascade formation in iron has been investigated by the method of molecular dynamics (MD) for cascade energies up to 40 keV, corresponding to PKA energies up to 61 keV. The results of these simulations have been used in the SPECOMP code to obtain effective, energy-dependent cross sections for two measures of primary damage production: (1) the number of surviving point defects expressed as a fraction of the those predicted by the standard secondary displacement model by Norgett, Robinson, and Torrens (NRT), and (2) the fraction of the surviving interstitials contained in clusters that formed during the cascade event. The primary knockon atom spectra for iron obtained from the SPECTER code have been used to weight these MD-based damage production cross sections in order to obtain spectrally averaged values for several locations in commercial fission reactors, materials test reactors, and a DT fusion reactor (ITER) first wall. An evaluation of these results indicates that neutron energy spectrum differences between the various environments do not lead to significant differences between the average primary damage formation parameters. This conclusion implies that the displacement damage component of radiation damage produced in a DT fusion reactor should be well simulated by irradiation in a fission reactor neutron spectrum, and that differences in nuclear transmutation production may be the primary source of uncertainty in the prediction of material performance at high doses in DT fusion reactors.

Atom probe characterization of the microstructure of nuclear pressure vessel surveillance materials after neutron irradiation and after annealing treatments

Abstract Microstructural changes due to neutron irradiation of weld and forging materials were characterized using the atom probe field ion microscope (APFIM). Neutron-induced clusters containing Cu, P, Ni, Mn and Si were detected in the high copper weld (0.24 at.% Cu) after irradiation to fluences of 6.6 × 1022 and 3.47 × 1023 n m−2; only phosphorus atmospheres were observed in the low copper forging material (0.02 at.% Cu) irradiated to an intermediate fluence of 1.5 × 1023 n m−2. These results are in agreement with previous studies and with their respective measured transition temperature shifts. In addition, APFIM experiments were carried out on the high fluence weld material after two post-irradiation annealing treatments. The first annealing treatment of 168 h at 454°C is similar to the proposed condition for in situ pressure vessel annealing and the second, 29 h at 610°C, is similar to the final stress relief heat treatment employed in vessel fabrication. Annealing at 454°C led to coarsening of the copper-enriched precipitates and a 92% recovery of the radiation-induced transition temperature shift. Essentially complete rehomogenization of the solutes was obtained in the simulated stress relief treatment at 610°C.