Radiation Damage Cascades Research Articles

A modified two temperature molecular dynamics (2T-MD) model for cascades

Two-Temperature molecular dynamics (2T-MD) is a common approach for describing how electrons contribute to the evolution of a damage cascade by addressing their role in the redistribution of energy in the system. However, inaccuracies in 2T-MD’s treatment of the high-energy particles have limited its utilisation. Here, we propose a reformulation of the traditional 2T-MD scheme to overcome this limitation by addressing the spurious double-interaction of high-energy atoms with electrons. We conduct a series of radiation damage cascades for 30, 50, and 100 keV primary knock-on atoms in increasingly large cubic W cells. In the simulations, we employ our modified 2T-MD scheme along with other treatments of electron–phonon coupling to explore their impact on the cascade evolution and the number of remnant defects. The results suggest that with the proposed modification, 2T-MD simulations account for the temperature time evolution during the ballistic phase and remove arbitrary choices, thus providing a better description of the underlying physics of the damage process.

Molecular dynamics simulations of radiation damage in YBa2Cu3O7

The advent of high-temperature superconductors (HTS) with high field strengths offers the possibility of building smaller, cheaper magnetically confined fusion reactors. However, bombardment by high energy neutrons ejected from the fusion reaction may damage the HTS tapes and impair their operation. Recreating the conditions present in an operational fusion reactor is experimentally challenging, therefore, this work uses molecular dynamics simulations to understand how radiation modifies the underlying crystal structure of YBa2Cu3O7. To facilitate the simulations a new potential was developed that allowed exchange of Cu ions between the two symmetrically distinct sites without modifying the structure. Radiation damage cascades predict the formation of amorphous regions surrounded by regions decorated with Cu and O defects found in the CuO-chains. The simulations suggest that the level of recombination that occurs is relatively low, resulting in a large number of remnant defects and that there is a no substantial temperature effect.

Multiple cascade radiation damage simulations of pyrochlore

ABSTRACT We report molecular dynamics simulations of multiple radiation damage cascades in the pyrochlores Gd2Ti2O7 and Gd2Zr2O7 and the solid solution Gd2(Zr x Ti1–x )2O7 (x = 0.25, 0.50, 0.75). Using a simulation cell of 360,448 atoms, for each compound 2200 decay events are simulated over a total time of 10 ns, with each recoiling uranium atom (primary-knock-on atom) assigned initial kinetic energy of 5 keV. The structures generated are analysed using Steinhardt local order parameters. There is a large increase in volume for the Ti pyrochlore associated with a transition to an amorphous structure which resembles the melt while preserving the local environment of the Ti. The calculated dose for amorphisation is 20 eV atom−1 which compares well with experiment overlap of cascade and damage accumulation drives the amorphisation suppressessing the healing mechanisms. The behaviour of the zirconate is different – the substantial anion disorder produced by each recoil event is followed by healing and reversion to the parent pyrochlore. In the solid solution the onset of amorphisation is delayed to later times on increasing the Zr concentration and overall swelling reduced. Our simulations highlight the importance of ion mobility, associated with the weaker Zr–O bonds, in healing.

Multiscale simulations of electron and ion dynamics in self-irradiated silicon

The interaction of energetic ions with the electronic and ionic system of target materials is an interesting but challenging multi-scale problem and understanding of the early stages after impact of heavy, initially charged ions is particularly poor. At the same time, energy deposition during these early stages determines later formation of damage cascades. We address the multi-scale character by combining real-time time-dependent density functional theory for electron dynamics with molecular dynamics simulations of damage cascades. Our first-principles simulations prove that core electrons affect electronic stopping and have an unexpected influence on the charge state of the projectile. We show that this effect is absent for light projectiles, but dominates the stopping physics for heavy projectiles. By parameterizing an inelastic energy loss friction term in the molecular dynamics simulations using our first-principles results, we also show a qualitative influence of electronic stopping physics on radiation-damage cascades.

Explicit Multielement Extension of the Spectral Neighbor Analysis Potential for Chemically Complex Systems.

A natural extension of the descriptors used in the Spectral Neighbor Analysis Potential (SNAP) method is derived to treat atomic interactions in chemically complex systems. Atomic environment descriptors within SNAP are obtained from a basis function expansion of the weighted density of neighboring atoms. This new formulation instead partitions the neighbor density into partial densities for each chemical element, thus leading to explicit multielement descriptors. For Nelem chemical elements, the number of descriptors increases as [Formula: see text], while the computational cost of the force calculation as implemented in LAMMPS is limited to [Formula: see text] and the favorable linear scaling in the number of atoms is retained. We demonstrate these chemically aware descriptors by producing an interatomic potential for indium phosphide capable of capturing high-energy defects that result from radiation damage cascades. This new explicit multielement SNAP method reproduces the relaxed defect formation energies with substantially greater accuracy than weighted-density SNAP, while retaining accurate representation of the bulk indium phosphide properties.

Radiation damage reduction by grain-boundary biased defect migration in nanocrystalline Cu

Nanocrystalline materials with a high density of grain boundaries have long been reported to alleviate radiation damage. However, a full mechanistic understanding of defect reduction, particularly the interaction mechanisms between grain boundaries and clustered defects during irradiation, remains an open question. Here we present atomistic simulations of prolonged radiation damage evolution in Cu bicrystals with increasing radiation dose. Our results reveal the atomic details of defect nucleation and migration, and the mechanisms for the annihilation of defect clusters during irradiation. Stacking fault tetrahedra formed due to radiation damage cascades show preferential migration to irradiated grain boundary. Interstitial-loaded grain boundaries are observed to be dynamically resilient, and persistently interact with the stacking fault tetrahedra, revealing a self-healing response to radiation damage. The results show a synergistic effect of grain boundaries on defect annihilation at small grain spacings of less than 6 nm, giving rise to a drastic decrease in the density of defect clusters. These findings, along with the mechanistic insights, present an integrated perspective on interface-mediated damage reduction in radiation-resistant nanomaterials.

Iron phosphate glasses: Structure determination and radiation tolerance

Iron phosphate glass (IPG) has gained recent interest for use in encapsulating radioactive waste for long term storage. In this work, we investigate 5 different compositions of iron phosphate glass. We consider amorphous structures of 3 known crystalline phases: Fe2+Fe23+(P2O7)2, Fe43+(P2O7)3 and Fe3+(PO3)3, and structures of IPG (40mol% Fe2O3 and 60mol% P2O5), with 4% and 17% Fe2+ ion concentrations.Using constant volume molecular dynamics (MD), we quench a set of structures for each glass composition, to find the optimal density structure. We found that the lowest energy structures of IPG with 4% and 17% concentration of Fe2+, have a density of 3.25 and 3.28g/cm3 respectively. This is slightly higher than the experimentally measured values of 2.9 and 2.95g/cm3 respectively.We also estimate an upper and lower bound on the melting temperatures of each glass, then for each glass, we simulate radiation damage cascades at 4keV. The cascade structures can be in the form of either a concentrated thermal spike or more diffuse with sub-cascade branching. We found that the glass compositions with a higher Fe/P atomic ratio, contained a greater number of displacements after the cascade. We also found that the IPG with 4% Fe2+, contained slightly fewer displacements than the IPG with 17% Fe2+. This is consistent with our previous work, which showed that the threshold displacement energies are lower for glasses with a lower Fe2+ content. In all the simulations, many PO4 polyhedra are destroyed during the early stages of irradiation, but recover strongly over a time scale of picoseconds, leaving very few over or under co-ordinated P atoms at the end of the ballistic phase. This is in contrast to recent work in apatite. The strong recovery indicates that phosphate glasses with a low Fe2+ content could be good materials for waste encapsulation.

Molecular dynamics simulation of radiation damage cascades in diamond

Radiation damage cascades in diamond are studied by molecular dynamics simulations employing the Environment Dependent Interaction Potential for carbon. Primary knock-on atom (PKA) energies up to 2.5 keV are considered and a uniformly distributed set of 25 initial PKA directions provide robust statistics. The simulations reveal the atomistic origins of radiation-resistance in diamond and provide a comprehensive computational analysis of cascade evolution and dynamics. As for the case of graphite, the atomic trajectories are found to have a fractal-like character, thermal spikes are absent and only isolated point defects are generated. Quantitative analysis shows that the instantaneous maximum kinetic energy decays exponentially with time, and that the timescale of the ballistic phase has a power-law dependence on PKA energy. Defect recombination is efficient and independent of PKA energy, with only 50% of displacements resulting in defects, superior to graphite where the same quantity is nearly 75%.

Incorporating non-adiabatic effects in embedded atom potentials for radiation damage cascade simulations

In radiation damage cascade displacement spikes ions and electrons can reach very high temperatures and be out of thermal equilibrium. Correct modelling of cascades with molecular dynamics should allow for the non-adiabatic exchange of energy between ions and electrons using a consistent model for the electronic stopping, electronic temperature rise, and thermal conduction by the electrons. We present a scheme for correcting embedded atom potentials for these non-adiabatic properties at the level of the second-moment approximation, and parameterize for the bcc transition metals above the Debye temperature. We use here the Finnis–Sinclair and Derlet–Nguyen–Manh–Dudarev potentials as models for the bonding, but the corrections derived from them can be applied to any suitable empirical potential. We show with two-temperature MD simulations that computing the electronic thermal conductivity during the cascade evolution has a significant impact on the heat exchange between ions and electrons.

Investigations on Radiation Tolerance of Mn+1AXn Phases: Study of Ti3SiC2, Ti3AlC2, Cr2AlC, Cr2GeC, Ti2AlC, and Ti2AlN

Nanolaminated Mn+1AXn phases as candidate materials for next generation nuclear reactor applications show great potential in tolerating radiation damage. However, different Mn+1AXn materials behave very differently when exposed to energetic neutron and ion irradiations. Based on first‐principle calculations, the radiation tolerance of two M3AX2 and four M2AX phases were studied in this work, covering all the Mn+1AXn phases previously investigated with experiments. We have calculated the formation energies of Frenkel pairs and antisite pairs in these materials. The improved radiation tolerance from Ti3AlC2 to Ti2AlC observed by experiments can be understood in terms of different Al/TiC layer ratio as the A atomic plane in the nanolaminated crystal Mn+1AXn accommodates radiation‐induced point defects. The formation of MA–AM antisite pair in Mn+1AXn materials would provide an alternative way to accommodate the defects resulted from radiation damage cascades, whereas this ideal substitution channel does not exist for Cr2GeC due to its pronouncedly higher MA–AM antisite pair formation energy. To further elucidate their radiation damage tolerance mechanism, we have made a detailed analysis on their interatomic M–X, M–A, and X–A bonding characters. Criteria based on the bonding analysis are proposed to assess the radiation tolerance of the six Mn+1AXn materials, which can be further applied to explore other Mn+1AXn phases with respect to their performances under radiation environment.

Order parameter and connectivity topology analysis of crystalline ceramics for nuclear waste immobilization

We apply bond order and topological methods to the problem of analysing the results of radiation damage cascade simulations in ceramics. Both modified Steinhardt local order and connectivity topology analysis techniques provide results that are both translationally and rotationally invariant and which do not rely on a particular choice of a reference structure. We illustrate the methods with new analyses of molecular dynamics simulations of single cascades in the pyrochlores Gd2Ti2O7 and Gd2Zr2O7 similar to those reported previously (Todorov et al 2006 J. Phys.: Condens. Matter 18 2217). Results from the Steinhardt and topology analyses are consistent, while often providing complementary information, since the Steinhardt parameters are sensitive to changes in angular arrangement even when the overall topological connectivity is fixed. During the highly non-equilibrium conditions at the start of the cascade, both techniques reveal significant localized transient structural changes and variation in the cation connectivity. After a few picoseconds, the connectivity is largely fixed, while the order parameters continue to change. In the zirconate there is a shift to the anion disordered system while in the titanate there is substantial reversion and healing back to the parent pyrochlore structure.

Simulating radiation damage cascades in graphite

Molecular dynamics simulation is used to study radiation damage cascades in graphite. High statistical precision is obtained by sampling a wide energy range (100–2500eV) and a large number of initial directions of the primary knock-on atom. Chemical bonding is described using the Environment Dependent Interaction Potential for carbon. Graphite is found to exhibit a radiation response distinct from metals and oxides primarily due to the absence of a thermal spike which results in point defects and disconnected regions of damage. Other unique attributes include exceedingly short cascade lifetimes and fractal-like atomic trajectories. Unusually for a solid, the binary collision approximation is useful across a wide energy range, and as a consequence residual damage is consistent with the Kinchin–Pease model. The simulations are in agreement with known experimental data and help to clarify substantial uncertainty in the literature regarding the extent of the cascade and the associated damage.

Molecular dynamics and object kinetic Monte Carlo study of radiation-induced motion of voids and He bubbles in bcc iron

We show that voids adjacent to radiation damage cascades can be moved in their entirety by several lattice spacings. This is done using molecular dynamics cascade simulations in iron at energies of 1-5 keV. The effect of this mechanism is studied further using an OKMC code and shows enhancement of void diffusion by 2 orders of magnitude from 1x10^-22 cm^2/s to 3x10^-20 cm^2/s. Repeating the study on He bubbles shows that the movement is damped by the presence of helium in the void.

Nonadiabatic Forces in Ion-Solid Interactions: The Initial Stages of Radiation Damage

The Born-Oppenheimer approximation is the keystone for molecular dynamics simulations of radiation damage processes; however, actual materials response involves nonadiabatic energy exchange between nuclei and electrons. In this work, time dependent density functional theory is used to calculate the electronic excitations produced by energetic protons in Al. We study the influence of these electronic excitations on the interatomic forces and find that they differ substantially from the adiabatic case, revealing a nontrivial connection between electronic and nuclear stopping that is absent in the adiabatic case. These results unveil new effects in the early stages of radiation damage cascades.

Topological connectivity analysis of accumulated radiation damage from multiple molecular dynamics recoil cascades

ABSTRACTThe results of sequential large-scale molecular dynamics (MD) simulations of radiation damage cascades in Gd2Ti2O7 and Gd2Zr2O7 are presented. Twelve alpha recoil cascades, each due to a recoil atom with 40 keV of kinetic energy, are performed in both materials and a stark contrast in behaviour observed. Topological connectivity analysis is used to analyse the structural evolution of the two systems. Our results provide important insight into accumulation of disorder in pyrochlore-structured ceramics.

Radiation damage formation in fusion structural materials due to elastic and inelastic processes

A new theoretical model based on Boltzmann transport equation for moving displaced atoms is developed for the investigations of main important characteristics of radiation damage production in fusion structural materials. The main characteristics sub-cascades are determined here including the distribution of sub-cascades per PKA, average number of point defects per sub-cascade combining suggested model and NRT approach, sub-cascade’s cross-sections and generation rates for both elastic and inelastic processes. On the basis of this developed model the numerical calculations for the main important characteristics of radiation damage production, cascade and sub-cascade formations in different fusion structural materials such as Fe, V, C, Al, Be and W are performed using the neutron energy spectra for fusion reactors: ITER and DEMO. For the comparison of difference in radiation damage production in fusion and fission reactors the additional numerical calculations have been made for neutron energy spectrum in fast atomic reactor HFIR.

Evolution of atomic collision cascades in vanadium crystal with internal structure

The formation of radiation-damage regions (radiation-damage cascades) in vanadium crystallites with internal structures (intergrain boundary) has been simulated by the molecular-dynamic method. The interatomic interaction is described within the embedded-atom method. A relatively small number of clusters of intrinsic point defects (vacancies and self-interstitial atoms) are formed both in ideal vanadium crystallites and in crystallites with boundaries after the relaxation of atomic-displacement cascades. The evolutionary character of atomic-displacement cascades is determined in many respects by the presence of extended boundaries in materials. The intergrain boundaries hinder the propagation of atomic-displacement cascades and store many radiation-induced defects.

Electronic excitations and their effect on the interionic forces in simulations of radiationdamage in metals

Using time-dependent tight-binding simulations of radiation damage cascades in amodel metal we directly investigate the nature of the excitations of a system ofquantum mechanical electrons in response to the motion of a set of classical ions. Wefurthermore investigate the effect of these excitations on the attractive electronic forcesbetween the ions. We find that the electronic excitations are well described by aFermi–Dirac distribution at some elevated temperature, even in the absence of the directelectron–electron interactions that would be required in order to thermalize anon-equilibrium distribution. We explain this result in terms of the spectrum ofcharacteristic frequencies of the ionic motion. Decomposing the electronic forceinto four well-defined components within the basis of instantaneous electroniceigenstates, we find that the effect of accumulated excitations in weakening theinterionic bonds is mostly (95%) accounted for by a thermal model for the electronicexcitations. This result justifies the use of the simplifying assumption of a thermalizedelectron system in simulations of radiation damage with an electronic temperaturedependence and in the development of temperature-dependent classical potentials.

How good is damped molecular dynamics as a method to simulate radiation damage in metals?

Classical molecular dynamics (MD) is a frequently used technique in the study of radiation damage cascades because it provides information on very small time and length scales inaccessible to experiment. In a radiation damage process, energy transfer from ions to electrons may be important, yet there is continued uncertainty over how to accurately incorporate such effects in MD. We introduce a new technique based on the quantum mechanical Ehrenfest approximation to evaluate different methods of accounting for electronic losses. Our results suggest that a damping force proportional to velocity is sufficient to model energy transfer from ions to electrons in most low energy cascades. We also find, however, that a larger rate of energy transfer is seen when the ionic kinetic energy is confined to a focused sequence of collisions. A viscous damping coefficient dependent on the local atomic environment is shown to be an excellent model for electronic energy losses in low energy cascades in metals.

Mechanisms of He escape during implantation in CuNb multilayer composites

CuNb multilayer composites with layer thicknesses as small as 4nm have shown remarkable resistance to radiation damage at room temperature. The technological importance of these materials, however, depends on their radiation damage resistance properties at elevated temperatures. We investigated the degree of retention of 33keV 4He+ implanted at temperatures ranging from 490°C to 660°C in CuNb multilayer composites with layer thicknesses from 4nm to 100nm. Analysis by elastic recoil detection (ERD) with 12MeV 12C3+ beam demonstrates that the fraction of retained He decreases with increasing temperature and decreasing layer thickness, suggesting that interfaces between neighboring Cu and Nb layers serve as pathways for fast diffusion of implanted He out of the CuNb multilayer composites. Atomic-scale simulations of radiation damage cascades indicate that this property stems from the ability of CuNb interfaces to quickly absorb defects created during these cascades.