Divacancy Migration Research Articles

Determining the diffusion behavior of point defects in zirconium by a multiscale modelling approach

Zr alloys are commonly used materials for in-core components of pressurized water reactors. The evolution of defects in Zr under irradiation conditions will directly contribute to the degradation of reactor components. For a better understanding of the evolution process of defects in Zr, a multiscale simulation was performed to study the diffusion behavior of radiation-induced point defects. Because the existing potentials cannot accurately describe the energy differences of stable states self-interstitial atoms (SIAs) in Zr, an embedded atom method potential that can exactly reproduce the energy difference between metastable states and ground states, and the binding energy of divacancy of Zr, was first developed by fitting a potential to point defect properties calculated by density functional theory and other basic crystal properties. Based on the constructed potential, molecular dynamics (MD) and kinetic Monte Carlo simulations were conducted to investigate the migration of point defects. We determined several frequent migration paths of SIAs by kinetic study, which is rarely reported in previous MD studies. The SIA exhibits obvious anisotropic diffusion characteristics at low temperatures (<600 K). The most frequent migration path for SIAs is the jump between the two nearest basal octahedral (BO) sites in the basal plane, which means that SIAs diffuse faster along the basal plane than along the c axis. It is found that diffusion within the basal plane tends to be two-dimensional (2D) diffusion rather than 1D diffusion, and there is a significant correlation effect for diffusion of SIAs along the basal plane. Additionally, the existence of trivacancy-SIA complex was found in the process of divacancy migration, which can inhibit divacancy migration. Monovacancies and divacancies exhibit anisotropic diffusion characteristics in the considered temperature range Divacancies have a much faster diffusion rate than monovacancies in the present MD simulation and can easily dissociate at high temperatures (>900 K). The rapid migration of the divacancies may contribute to the formation of vacancy dislocation loops. These results are meaningful to understand the evolution process of radiation-induced defects.

Intrinsic defect migration in Be12Ti

Be12Ti is a leading candidate neutron-multiplier material for fusion breeder blankets; yet the evolution of the crystal defects under irradiation is poorly understood. Here, the migration of intrinsic defects in tetragonal Be12Ti was predicted using atomic scale computer simulation. Transport of titanium and beryllium through the interstitial, interstitialcy and vacancy-mediated models was considered, along with the migration of divacancy clusters, previously identified as important to the defect chemistry of Be12Ti. It was found that titanium defects exhibit much higher migration energies than beryllium for most migration pathways, leading to a dramatic difference in the self-diffusivity of the two species. Both beryllium vacancy and interstitial diffusion is close to isotropic with vacancy transport exhibiting the highest self-diffusion coefficient. Migration of beryllium di-vacancies is also isotropic with activation energy equal to that of isolated vacancies. The titanium interstitial exhibits significantly lower migration energy than its vacancy (1.00 eV and 6.75 eV respectively), with both mechanisms strongly anisotropic: the activation energy for [001] migration is at least 5 eV lower than other directions. Even the more exotic mixed titanium beryllium vacancy migration exhibits a much higher migration energy than [001] titanium interstitial transport. The framework used for predicting defect transport kinetics, including vacancy-mediated, interstitial and interstitialcy mechanisms, can be applied to any complex-structured intermetallic compound.

Vacancies and interstitials in yttrium

The paper deals with the first principles simulation of formation energies and migration barriers of self point defects, including vacancies, di-vacancies and single interstitial atoms, in metallic yttrium. The vacancy formation energy in yttrium is shown to be relatively high (~1.8 eV), whereas the migration barriers are very similar for the jumps inside the basal planes and between basal planes, being equal to ~0.65 eV. The sum of these numbers reasonably reproduces the experimental values of the self-diffusion activation barriers. The vacancy pairs at the first nearest neighbor separation (divacancies) have binding energy of ~0.2 eV, which is only weakly sensitive to the divacancy orientation in the lattice, whereas vacancy pairs at the second and third nearest-neighbor separations are energetically unfavorable, suppressing the dissociation of divacancies. Together with the noticeably lower divacancy migration barriers with respect to single vacancies, this makes divacancies efficient mediators for mass transfer in Y. Among multiple possible configurations of a single interstitial, only the basal octahedral one is found to be the true energy minimum, while all the other considered possibilities are either unstable, or saddle points on the potential energy surface. This is in contrast to other hcp metals, where several metastable interstitial configurations often coexist. The lowest migration barriers for single interstitial diffusion along the basal plane and between planes are practically equal, ~0.4 eV, implying isotropic diffusion of interstitials in yttrium. Overall, the predicted properties of point defects in yttrium are in line with the general trends for hcp metals with the c/a ratio below .

Investigation of the Character of Stored-Energy Release from Graphite Irradiated at High Temperature

The results of an investigation of the stored energy in GR-280 graphite irradiated at 560°C to neutron fluence ~3·1026 m–2 are presented. The measurements were performed by means of differential scanning calorimetry with constant heating rate 20°C/min. The release of the stored energy reaches a maximum at annealing temperature 1100°C. The maximum output is equal to 0.34–0.48 J/(g·°C). The total stored energy released in the annealing temperature range 560–1300°C does not exceed 183 J/g. A kinetic analysis of the spectrum of the stored energy was performed. This analysis established that increasing the radiation temperature from 450 to 560°C results in almost complete vanishing of individual vacancies, redistribution of the migration of di-vacancies, and evolution of a cluster structure upon post-radiation annealing in the range 560–1300°C in the direction of processes with lower activation energy.

Defect Physics, Delithiation Mechanism, and Electronic and Ionic Conduction in Layered Lithium Manganese Oxide Cathode Materials

Layered LiMnO$_2$ and Li$_2$MnO$_3$ are of great interest for lithium-ion battery cathodes because of their high theoretical capacities. The practical application of these materials is, however, limited due to poor electrochemical performance. We herein report a comprehensive first-principles study of defect physics in LiMnO$_2$ and Li$_2$MnO$_3$ using hybrid-density functional calculations. We find that manganese antisites have low formation energies in LiMnO$_2$ and may act as nucleation sites for the formation of impurity phases. The antisites can also occur with high concentrations in Li$_2$MnO$_3$; however, unlike in LiMnO$_2$, they can be eliminated by tuning the experimental conditions during preparation. Other intrinsic point defects may also occur and have an impact on the materials' properties and functioning. An analysis of the formation of lithium vacancies indicates that lithium extraction from LiMnO$_2$ is associated with oxidation at the manganese site, resulting in the formation of manganese small hole polarons; whereas in Li$_2$MnO$_3$ the intrinsic delithiation mechanism involves oxidation at the oxygen site, leading to the formation of bound oxygen hole polarons $\eta_{\rm O}^{+}$. The layered oxides are found to have no or negligible bandlike carriers and they cannot be doped n- or p-type. The electronic conduction proceeds through hopping of hole and/or electron polarons; the ionic conduction occurs through lithium monovacancy and/or divacancy migration mechanisms. Since $\eta_{\rm O}^{+}$ is not stable in the absence of negatively charged lithium vacancies in bulk Li$_2$MnO$_3$, the electronic conduction near the start of delithiation is likely to be poor. We suggest that the electronic conduction associated with $\eta_{\rm O}^{+}$ and, hence, the electrochemical performance of Li$_2$MnO$_3$ can be improved through nanostructuring and/or ion substitution.

Migration of defect clusters and xenon-vacancy clusters in uranium dioxide

The possible transition states, minimum energy paths (MEPs) and migration mechanisms of defect clusters and xenon-vacancy defect clusters in uranium dioxide ( UO 2) have been investigated using the dimer and the nudged elastic-band (NEB) methods. The nearby O atom can easily hop into the oxygen vacancy position by overcoming a small energy barrier, which is much lower than that for the migration of a uranium vacancy. A simulation for a vacancy cluster consisting of two oxygen vacancies reveals that the energy barrier of the divacancy migration tends to decrease with increasing the separation distance of divacancy. For an oxygen interstitial, the migration barrier for the hopping mechanism is almost three times larger than that for the exchange mechanism. Xe moving between two interstitial sites is unlikely a dominant migration mechanism considering the higher energy barrier. A net migration process of a Xe-vacancy pair containing an oxygen vacancy and a xenon interstitial is identified by the NEB method. We expect the oxygen vacancy-assisted migration mechanism to possibly lead to a long distance migration of the Xe interstitials in UO 2. The migration of defect clusters involving Xe substitution indicates that Xe atom migrating away from the uranium vacancy site is difficult.

Calculation of migration rates of vacancies and divacancies in α-Iron using transition path sampling biased with a Lyapunov indicator

ABSTRACTPredicting the microstructural evolution of radiation damage in materials requires handling the physics of infrequent-events, in which several time scales are involved. The reactions rates characterizing these events are the main ingredient for simulating the kinetics of materials under irradiation over large time scales and high irradiation doses. We propose here an efficient, finite temperature method to compute reaction rate constants of thermally activated processes. The method consists of two steps. Firstly, rare reactive trajectories in phase-space are sampled using a transition path sampling (TPS) algorithm supplemented with a local Lyapunov bias favoring diverging trajectories. This enables the system to visit transition regions separating stable configurations more often, and thus enhances the probability of observing transitions between stable states during relatively short simulations. Secondly, reaction constants are estimated from the unbiased fraction of reactive trajectories, yielded by an appropriate statistical data analysis tool, the multistate Bennett acceptance ratio (MBAR) package. We apply our method to the calculation of reaction rates for vacancy and di-vacancy migration in α-Iron crystal, using an Embedded Atom Model potential, for temperatures ranging from 300 K to 800 K.

Intrinsic defects and krypton impurity atoms in hcp titanium: A first-principles study

We report on the migration of monovacancies, divacancies, and substitutional krypton atoms in hcp titanium using the nudged elastic band method, in the framework of ab initio density functional theory. The divacancy migration energy barrier is found to be lower than that of a monovacancy. The migration of substitutional krypton in titanium is governed by the vacancy mechanism, if there is an excess of nonequilibrium vacancies after the implantation. However, if thermal vacancies dominate, krypton atom migration is expected to proceed via the dissociation mechanism. We also present ab initio calculations on the formation of clusters of multiple substitutional impurity krypton atoms and the interactions between krypton impurities and vacancies in titanium. We have found that, analogous to multiple interstitial krypton clusters, clusters of substitutional krypton atoms are energetically unstable, but are stabilized by vacancies. However, the efficiency of stabilization by vacancies depends strongly on the spatial distribution of the vacancies within the clusters. This study indicates the possibility of inert gases to nucleate in voids created by vacancies in ion implantation processes.

Kinetics versus thermodynamics in materials modeling: The case of the di-vacancy in iron

Monte Carlo models are widely used for the study of microstructural and microchemical evolution of materials under irradiation. However, they often link explicitly the relevant activation energies to the energy difference between local equilibrium states. We provide a simple example (di-vacancy migration in iron) in which a rigorous activation energy calculation, by means of both empirical interatomic potentials and density functional theory methods, clearly shows that such a link is not granted, revealing a migration mechanism that a thermodynamics-linked activation energy model cannot predict. Such a mechanism is, however, fully consistent with thermodynamics. This example emphasizes the importance of basing Monte Carlo methods on models where the activation energies are rigorously calculated, rather than deduced from widespread heuristic equations.

Contributions of different mechanisms of self-diffusion in face-centered cubic metals under equilibrium conditions

The contributions of different mechanisms of self-diffusion in face-centered cubic metals Ni, Cu, and Al at thermodynamic equilibrium have been analyzed using the molecular dynamics method. The vacancy, divacancy, and cyclic mechanisms of self-diffusion, as well as the mechanisms involving the vacancy migration to the second coordination sphere and the formation and recombination of Frenkel pairs, have been considered. It has been shown that the second in contribution to the self-diffusion after the vacancy mechanism in the metals under consideration is the migration of divacancies. The third is the mechanism involving the formation and recombination of dynamic Frenkel pairs. The cyclic mechanisms (with simultaneous atomic displacements) and the vacancy migration directly to the second coordination sphere in face-centered cubic metals are unlikely.

Activation Energies for the Formation and Evaporation of Vacancy Clusters in Silicon

The thermal evolution of vacancy-type defects in Czochralski (Cz-) and epitaxially grown (epi-) silicon has been investigated using variable-energy positron annihilation spectroscopy. Heating at 300-500 degrees C caused rapid migration of divacancies and clustering of the resulting defects with activation energies of 2.1(2) and 2.7(7) eV in epi- and Cz-Si. Clustering occurred more rapidly in Cz-Si, attributed to the seeding effect of impurities. Heating at 500-640 degrees C annealed the clusters with activation energies of 3.9(3) and 3.6(3) eV in epi- and Cz-Si, linked to the vacancy-cluster binding energy.

Monovacancy and divacancy formation and migration in copper: A first-principles theory

The formation and migration of monovacancies and divacancies in copper have been studied from first-principles in order to resolve the discrepancies between previously published experimental and theoretical data. The monovacancy and divacancy formation, migration and binding enthalpies as well as the formation volumes have been calculated in the framework of a plane-wave pseudopotential implementation of the density functional theory, with full structural relaxations included. The monovacancy and divacancy formation entropies have been estimated from experimental data by performing a least-squares analysis. We show that the complete set of first-principles data, taking into account the presence of both vacancies and divacancies as well as the temperature dependence of the formation enthalpies and entropies allow one to reproduce the Arrhenius plot of the total vacancy concentration and the diffusion coefficient, both in good agreement with the most accurate experiments.

Lithium Diffusion in Layered Li[sub x]CoO[sub 2

The results of a first principles investigation of lithium diffusion within the layered form of are presented. Kinetic Monte Carlo simulations predict that lithium diffusion is mediated through a divacancy mechanism between and and with isolated vacancies at infinite vacancy dilution. The activation barrier for the divacancy migration mechanism depends strongly on lithium concentration resulting in a diffusion coefficient that varies within several orders of magnitude. We also argue that the thermodynamic factor in the expression of the chemical diffusion coefficient plays an important role at high lithium concentration. ©2000 The Electrochemical Society

Vacancy clustering in quenched Al-Li solid solution alloys studied by Doppler broadening spectroscopy

The clustering of vacancies in severely quenched Al-Li solid solution alloys, with Li content between 230 and 2760 ppm, has been studied using Doppler broadening spectroscopy. The alloy samples were initially annealed at 873 K in dry air or dry, pure nitrogen. The onset temperature for vacancy clustering in samples initially annealed in air was found to be , lower than for the nitrogen-annealed samples. This result is consistent with the migration of divacancies, formed as a result of the significant increase in vacancy concentration caused by Li migration to, and oxidation at, the surfaces of samples annealed in air. Li-vacancy binding may also contribute, to a lesser extent, to the retardation of vacancy migration in the nitrogen-annealed samples. No dependence on Li content was seen in the results for the two sets of samples.

On the anisotropic migration of point defects in h.c.p. zirconium

Abstract Point-defect calculations in h.c.p. zirconium have been carried out with a pair potential constructed in terms of the generalized pseudopotential theory. Two models of the h.c.p. lattice with either the ideal or the experimental c/a ratio were considered. It has been found with both models that the monovacancy has the same migration energy in and out of the basal plane, whereas the divacancy migration is anisotropic and favours out-of-plane mobility. A significant anisotropy for interstitial migration is observed, with greater in-plane mobility at the experimental c/a ratio. The di-interstitial migrates in the basal plane by the crowdion mechanism. The results of the calculations permit interpretation of some annealing stages of irradiated zirconium and allow conclusions to be drawn on the possibility of the diffusional anisotropy difference in h.c.p. zirconium.

Investigation of intrinsic point defects in rapidly quenched copper by nuclear quadrupole double resonance

Abstract This letter reports nuclear quadrupole double-resonance (NQDOR) measurements on Cu specimens that were rapidly quenched from the melt either by Duwez's gun technique or by melt spinning. Comparison with measurements of the recovery of the residual electrical resistivity and with previous NQDOR studies of electron-irradiated Cu leads to the conclusion that the defects annealing out in the so-called recovery stage III after low-temperature electron irradiation are self-interstitials. Among the vacancy-type imperfections introduced by the rapid-quenching techniques employed in the present work there is at least one defect (presumably the divacancy) that becomes mobile in the same temperature range as self-interstitials. This is in agreement with the evidence from other work that in Cu the enthalpies of migration of divacancies and of self-interstitials are almost the same.

Energetics of the formation and migration of defects in Pb(110).

As part of our investigations on the disordering of metal surfaces, we report the results of our calculations of the energetics of formation and migration of defects in Pb(110) using molecular-dynamics and molecular-statics simulations. We used the embedded-atom method to describe the interatomic interactions. Defect formation and migration energies have been calculated at the surface as well as in the near-surface region. Vacancy, divacancy, and interstitial formation and migration energies converge to bulk values already at a few layers below the surface. Our results are compared with recent simulations of Cu and Ni and with experimental data. We also calculated the surface Debye temperature and surface energy. We find that the surface Debye temperature, surface single-vacancy formation energy, and surface divacancy formation energy are all lower than their bulk values. Our result for the surface energy is lower than the experimental values.

Scanning-tunneling-microscope tip-induced migration of vacancies on GaP(110).

Scanning-tunneling-microscope tip-induced migration of divacancies is observed on n-doped GaP(110). The motion occurs only at negative polarity of the tunneling voltage and along the [11\ifmmode\bar\else\textasciimacron\fi{}0] direction, independent of the scanning direction, and is thus purely nonthermal. It is suggested that a field-induced reduction of the barrier for the migration initiates the motion. A quantitative analysis of the migration indicates long-lived excited states, consistent with charged trap states in doped semiconductors.

Many-body effects on calculated defect properties in h.c.p. metals

Abstract Defect calculations have been carried out with a simple short-range atomistic computer model which includes n-body forces from the embedded-atom method. The model was constrained to an ideal c/a ratio and parameters were chosen to approximate Ti for comparison with earlier short-range two-body calculations. The results contrast sharply with the earlier work and with other pairwise calculations in h.c.p. metals. Here vacancy diffusion is anisotropic with greater mobility in the basal plane and the migration energy is about half the formation energy. Divacancy binding is approximately isotropic and follows ‘vacancy bond counting’ (as does the binding energy of larger clusters), and the divacancy migration energy is only about 10% less than the vacancy migration energy. Both calculations give the configuration with the interstitial centred in a equilateral basal triangle under an octahedral site as most stable, but in the present work there is much less spread in energy between different configurations. Interstitial migration is complex, but not the same in the different models.

First- and second-nearest-neighbor divacancies in silicon: Origin and ordering of gap levels.

Two configurations of the silicon divacancy, namely the first- and second-nearest-neighbor divacancies, are examined using a semi-self-consistent Hamiltonian describing the neutral undistorted situation. With Gaussian-type basis orbitals and a supercell containing 686 atoms plus the defect, the energy levels of major interest around the band gap were extracted using the Lanczos algorithm and a continued-fraction representation of the local density of states. The first-nearest-neighbor divacancy is found to introduce two doubly degenerate gap levels. The corresponding wave functions are bonding (g) and antibonding (u) combinations of \ensuremath{\pi}-like monovacancy orbitals, with the ${\ensuremath{\pi}}_{u}$-like state below ${\ensuremath{\pi}}_{g}$. The corresponding combinations of the \ensuremath{\sigma}-like orbitals (${\ensuremath{\sigma}}_{u}$ and ${\ensuremath{\sigma}}_{g}$) are found to be band resonances. By requiring calculated results to be compatible with experimental data, the symmetry of each gap level corresponding to the various charge states in the fully Jahn-Teller distorted system is inferred. We also discuss the possibility that the doubly negative charge state can appear in two lattice-distorted configurations of different symmetries. The second-nearest-neighbor (or split) divacancy, which is an intermediate state in divacancy dissociation and probably also in divacancy migration, is found to introduce five nondegenerate gap states. The results can be summarized in terms of a simple molecular model based on interacting monovacancy orbitals. It is also argued that the particular ordering of these levels is due to a solid-state node in the monovacancy gap-state wave function.