Migration Of Point Defects Research Articles

Ultrahigh temperature in situ transmission electron microscopy based bicrystal coble creep in Zirconia II: Interfacial thermodynamics and transport mechanisms

This work uses a combination of stress dependent single grain boundary Coble creep and zero-creep experiments to measure interfacial energies, along with grain boundary point defect formation and migration volumes in cubic ZrO2. These data, along with interfacial diffusivities measured in a companion paper are then applied to analyzing two-particle sintering. The analysis presented indicates that the large activation volume, v*=vf+vmprimarily derives from a large migration volume and suggests that the grain boundary rate limiting defects are delocalized, possibly due to electrostatic interactions between charge compensating defects. The discrete nature of the sintering and creep process observed in the small-scale experiments supports the hypothesis that grain boundary dislocations serve as sources and sinks for grain boundary point defects and facilitate strain during sintering and Coble creep. Model two-particle sintering experiments demonstrate that initial-stage densification follows interface reaction rate-limited kinetics.

Production, Annihilation and Migration of Point Defects in Cyclic Straining

Interactions of mobile dislocations in persistent slip bands with ladder-like structure are analyzed and production rates of point defects, preferably vacancies, are derived. Previous resistivity measurements in copper single crystals and polycrystals are used to derive the growth of vacancy concentration during cyclic loading at low temperatures. The parameters of the growth law are derived from the initial growth rate and saturated vacancy concentration. The consequences of vacancy production in localized cyclic straining on the surface relief formation are analyzed. At very low temperature vacancies are produced and annihilated only athermally and vacancy concentration saturates. Localized deformation in persistent slip bands produces high vacancy concentration which outcomes in formation of tiny extrusions. At ambient and slightly elevated temperatures vacancies are steadily produced and migrate from the persistent slip bands to the matrix. This results in formation of persistent slip markings consisting of extrusions and intrusions. The shape of extrusions and intrusions depends on the on the dislocation arrangement in the PSB and in the neighbor matrix and their history during cyclic straining. Fatigue cracks start from sharp-edged intrusions.

Atomistic simulations to study point defect dynamics in bi-crystalline niobium

Niobium is an important element in Zr–Nb alloy, which is widely employed for structural material in many nuclear reactors. Superior mechanical properties and creep resistance in conjunction with low neutron cross-section, makes Zr–Nb alloy a suitable candidate for the manufacturing of pressure tubes and fuel cladding in nuclear reactors. Molecular dynamics based simulations were performed to study the point defect dynamics in niobium. Atomistic simulations were performed in the environment of classical mechanics to investigate the effect of grain boundary configurations on the point defect dynamics. Symmetric and asymmetric tilt grain boundaries were generated between the two crystals of niobium, and defect formation and migration energies were calculated as a function of distance from the grain boundary plane. A relationship between the grain boundary energies and point defect formation energies was predicted, and it was concluded that higher energy grain boundaries have higher tendency to behave as sink for point defects. Lower offset in vacancy formation energies between the initial and terminating position of vacancy, energetically favours the migration of point defects, whereas higher energy offset between bulk and grain boundaries require more energy to migrate vacancy towards the grain boundary.

(Invited) Electro-Chemo-Mechanical Equilibrium of Point Defects at Interfaces

Formation and migration of point defects underlie nearly all materials for energy transformation, such as electrodes and solid electrolytes for lithium-ion batteries and solid oxide fuel cells. The distribution of point defects such as lithium and oxygen vacancies reflect electro-chemo-mechanical equilibria. In this talk, I will present a general theory framework for understanding how mechanical contribution plays a key role in determining the space-charge effect at interfaces.

Role of electronic and magnetic interactions in defect formation and anomalous diffusion in δ-Pu

Previous experimental work has shown self-irradiation in Pu solids produces point defect populations that correlate with increases in local disorder, long-range structural changes, induced magnetic moments, and other thermo-physical property changes. Thermally activated kinetic processes drive these defects to diffuse and interact toward either damage evolution or lattice recovery. Using DFT and cNEB, as implemented in VASP, barriers for mono-vacancy and split-interstitial diffusion and Frenkel pair recombination were calculated in fcc δ-Pu. The results indicate the migration barrier of a monoclinic mono-vacancy is lower when compared to the migration barrier of a tetragonal split-interstitial in δ-Pu, contrary to typical fcc metal point defect migration. This fundamentally different diffusion mechanism is a result of local symmetry breaking induced by electronic and magnetic interactions leading to the development of Pu–Pu short bonds (<3.0 Å) within a many-atom complex defect forming and migrating. The migration of the monoclinic mono-vacancy maintains short bonds with anti-parallel spins throughout the transition; whereas, during the migration transition state for the tetragonal split-interstitial, formation of short bonds with parallel spins and a spin-flip of the migrating Pu interstitial occurs. The associated energy cost is reflected in an increase in the migration barrier energy. Frenkel pair recombination is not spontaneous at 0K, but correlates with magnetic moment interactions, leading to an energy barrier for recombination. From these results, it is concluded that migration of defects in unalloyed δ-Pu are highly dependent on the electronic and magnetic interactions that induce associated low-symmetry structures and consequently influence the diffusional properties. Typical fcc defect diffusion mechanisms do not apply to the monoclinic mono-vacancy and tetragonal split-interstitial in the complex 5f δ-Pu system suggesting that the experimental observation of radiation damage induced localized magnetic moments and anomalous diffusion properties measured in δ-Pu could be understood in terms of defect kinetics and interactions.

Influence of Radiation Porosity Created in Austenitic Steel upon Neutron Irradiation on the Concentration of Intrinsic Point Defects

This paper investigates the dependence of the concentration of point defects in the EK64 steel on the characteristics of neutron irradiation in the framework of the model of migration of point defects. The results obtained were used to analyze the data on the experimental determination of the characteristics of radiation porosity in the samples of the EK164 steel irradiated using various dose–temperature parameters. The values of the critical diameters of the vacancy nuclei of pores have been calculated. It has been shown that, with an increase in the integral area of the pore surface, the concentration of point defects decreases and the size of the critical diameter increases. This leads to a multi-modal distribution of pore sizes. The obtained numerical estimates of the peak values of the concentration of small pores correspond satisfactorily to the experimental pore-size distributions.

Decomposition mechanisms and the role of transition metal impurities in the kinetics of Ca(BH4)2·2NH3

We present first-principles density-function theory studies of the formation and migration of native point defects in Ca(BH4)2·2NH3, which is a promising material for hydrogen storage. According to analysis of the energetics, structures, formation and migration of hydrogen-, calcium-, boron- and nitrogen-related defects, we find that the diffusion of hydrogen interstitial (Hi−) in the bulk is the rate-limiting step for decomposing Ca(BH4)2·2NH3. Our calculated results show that the activation energy for the decomposition process of Ca(BH4)2·2NH3 is 1.41 eV (in a closed vessel). Moreover, electrically active impurities such as Fe, Co and Ni can tailor the kinetics of dehydrogenation of Ca(BH4)2·2NH3 by shifting the Fermi level. These mechanisms provide an appropriate explaining for the experimentally observed improving of the kinetics for hydrogen desorption of Ca(BH4)2·2NH3 through doping transition metal chlorides in a closed vessel.

Molecular Dynamics Study of the Point Defect Migration in the Ordered CuPt Alloy during Deformation

Abstract—The migration energies of a vacancy and an interstitial atom in the ordered CuPt alloy are calculated using molecular dynamics simulation. A high interstitial atom migration anisotropy is detected: as a rule, an interstitial atom migrates along the (111) planes containing copper atoms. A similar anisotropy is also observed for the vacancy migration during elastic tensions along these planes.

The short-range clustering in Fe–Cr alloys enhanced by severe plastic deformation and electron irradiation

ABSTRACTThe short-range clustering enhanced by migration of non-equilibrium point defects generated under the high-pressure torsion in Bridgman anvils and ball milling is detected by means of Mössbauer spectroscopy in Fe100−cCrc (c = 12–20.6) binary alloys. The degree of short-range clustering is increased with increasing the temperature of severe plastic deformation. The short-range clustering enhanced by severe plastic deformation is similar to that obtained after the thermal annealing and electron irradiation at close temperatures.

Diffusion controlled helium bubble formation resistance of FeCoNiCr high-entropy alloy in the half-melting temperature regime

For the structure materials applied in advanced nuclear energy system, helium bubble formation is always a big concern which will severely degrade the performance of materials around or above the half-melting temperature regime (∼0.5 Tm). To explore the He bubble formation resistance in the FeCoNiCr alloy, that is a novel face-centered cubic (fcc) high-entropy alloy (HEA) showing excellent radiation damage tolerance, we conducted a series of 2 MeV He ions irradiation experiments on them at three different temperatures (0.46, 0.51 and 0.57 Tm). For reference purpose, a model fcc metallic system of pure Ni was irradiated simultaneously. Through transmission electron microscopy (TEM), He bubble formation in the irradiated samples was systematically investigated. The results show that in any designated temperature, He bubbles have a smaller size, higher number density, and denser distribution in the HEA when comparing to that of pure Ni. The volume fraction of He bubbles is also less in the HEA, suggesting a suppressed bubble evolution. For the underlying mechanism of the He bubble formation resistance of HEA, we suggest that the featured energy barriers for point defects migration in the HEA will promote the recombination of defects and somewhat reduce the vacancy concentration during irradiation. Such unique effect could suppress the He diffusion through vacancy mechanism, it will finally influence the evolution of He bubbles in the HEA.

Quasi-viscous deformation mode in nonequilibrium nanocrystalline structures

Based on the analysis of the elastic-stressed state of partial disclinations of nanodipoles the rate of the quasi-viscous deformation mode in nanocrystalline structures is estimated. It’s shown that velocity of movement of point defects (V) and nanodipole propagation within the quasi-viscous deformation mechanism, depending on the activation energy of the migration of point defects (vacancies, interstitial atoms) and deformation temperature, can reach high values close to the speed of sound in metals.

Effect of the Neutron Irradiation Characteristics on the Irradiation-Induced Swelling in a Kh18N9 Steel

Abstract—The swelling of Kh18N9 steel fragments cut from the reactor internals after irradiation at 370–442°C and an atomic displacement generation rate of 4.8 × 10–9–4.16 × 10–8 dpa/s are determined by hydrostatic weighing. The vacancy migration energy for a Kh18N9 steel (1.24 eV) is estimated using the energies for austenitic steels (ChS68, EK164) with various nickel contents. The neutron irradiation-induced void growth in a Kh18N9 steel during its operation in the BN-600 nuclear power reactor internals is analyzed in terms of a point defect migration model with allowance for the estimated vacancy migration energy. The vacancy void growth rate at the beginning of the transient swelling stage is used as a characteristic of the susceptibility to radiation swelling. This rate is diameter independent for the samples under study.

Mass transport properties of quasiharmonic vs. anharmonic transition-metal nitrides

I present a development of the color-diffusion algorithm, used in non-equilibrium (accelerated) ab initio molecular dynamics simulations of point-defect migration in crystals [Sangiovanni et al., Phys. Rev. B 93, 094305 (2016)], to determine the temperature dependence of anion vacancy jump frequencies in rocksalt-structure (B1) TiN and VN characterized by quasiharmonic (TiN) vs. strongly anharmonic (VN) lattice dynamics. Over a temperature range [≈0.6·Tm < T < ≈0.9·Tm] relatively close to the materials melting points Tm, the simulations reveal that anion vacancy migration in TiN and VN exhibits an Arrhenius-like behavior, described by activation energies EaTiN = 4.2 ± 0.3 eV and EaVN = 3.1 ± 0.3 eV, and attempt frequencies νTiN = 8·1015±0.7 s−1 and νVN = 2·1017±0.8 s−1. A comparison of activation energies Ea extracted by Arrhenius linear regression at elevated temperatures with ab initio Ea0K values calculated at 0 Kelvin reveals that, while the nitrogen migration energy EaTiN varies modestly with temperature {∆EaTiN = [Ea(Tm) – Ea(0 K)]/Ea(0 K) ≈ 0.1}, the changes in EaVN vs. T are considerable (∆EaVN ≈ 1). The temperature-induced variations in vacancy migration energies and diffusivities are discussed in relation to the TiN and VN vibrational properties determined via ab initio molecular dynamics at different temperatures. It is argued that static 0-K calculations, which account for thermal expansion effects within the framework of quasiharmonic transition-state theory, accurately reproduce the finite-temperature mass transport properties of TiN. Conversely, the use of molecular dynamics simulations, which explicit treat lattice vibrations at any temperature of interest, is necessary to achieve reliable atomic diffusivities in B1 VN, a crystal phase dynamically stabilized by anharmonic vibrations [Mei et al., Phys. Rev. B 91, 054101 (2015)].

Development of the ReaxFF Reactive Force Field for Inherent Point Defects in the Si/Silica System.

We redeveloped the ReaxFF force field parameters for Si/O/H interactions that enable molecular dynamics (MD) simulations of Si/SiO2 interfaces and O diffusion in bulk Si at high temperatures, in particular with respect to point defect stability and migration. Our calculations show that the new force field framework (ReaxFFpresent), which was guided by the extensive quantum mechanical-based training set, describes correctly the underlying mechanism of the O-migration in Si network, namely, the diffusion of O in bulk Si occurs by jumping between the neighboring bond-centered sites along a path in the (110) plane, and during the jumping, O goes through the asymmetric transition state at a saddle point. Additionally, the ReaxFFpresent predicts the diffusion barrier of O-interstitial in the bulk Si of 64.8 kcal/mol, showing a good agreement with the experimental and density functional theory values in the literature. The new force field description was further applied to MD simulations addressing O diffusion in bulk Si at different target temperatures ranging between 800 and 2400 K. According to our results, O diffusion initiates at the temperatures over 1400 K, and the atom diffuses only between the bond-centered sites even at high temperatures. In addition, the diffusion coefficient of O in Si matrix as a function of temperature is in overall good agreement with experimental results. As a further step of the force field validation, we also prepared amorphous SiO2 (a-SiO2) with a mass density of 2.21 gr/cm3, which excellently agrees with the experimental value of 2.20 gr/cm3, to model a-SiO2/Si system. After annealing the a-SiO2/Si system at high temperatures until below the computed melting point of bulk Si, the results show that ReaxFFpresent successfully reproduces the experimentally and theoretically defined diffusion mechanism in the system and succeeded in overcoming the diffusion problem observed with ReaxFFSiOH(2010), which results in O diffusion in the Si substrate even at the low temperature such as 300 K.

Visualizing Nonradiative Mobile Defects in Organic–Inorganic Perovskite Materials

AbstractOrganic–inorganic perovskite materials have mobile charged point defects that migrate in response to voltage biasing and illumination, causing device performance variation over time. Improvements in device stability and reliability require methods to visualize point defect migration, estimate ionic mobilities, and identify factors influencing their migration. In this work, a versatile method is demonstrated to track nonradiative point defect migration in situ. Photoluminescence mapping of laterally biased perovskite films is used to track continuous changes in nonradiative recombination as charge‐trapping defects migrate between the device electrodes. A Monte Carlo framework of defect drift and diffusion is developed that is consistent with experimental photoluminescence observations, which combined enables point defect mobility estimation in methylammonium lead iodide films. Furthermore, measurements performed on materials with varied grain sizes demonstrate that point defect mobility is 1500× faster at grain boundaries compared to bulk. These findings imply that grain morphology can be used to tune point defect mobility such that large‐grained or single‐crystal materials inhibit point defect migration. The methods used in this work can be applied to visualize and quantify the migration of charge‐trapping point defects in a wide range of state‐of‐the‐art perovskite materials targeted toward reduced ionic mobilities and superior device stability.

Radiation defect dynamics in solids studied by pulsed ion beams

The buildup of radiation damage is often a dynamic phenomenon proceeding via migration and interaction of point defects ballistically generated in collision cascades. Here, we describe how the dynamic aspects of damage formation via inter-cascade defect interaction can be studied by pulsed ion beam bombardment. We illustrate the pulsed beam method by an example for Si bombarded at 100 °C with 1.35 MeV Xe ions and compare with previously reported data for 0.5 MeV Xe ion irradiation. Results reveal that the time constant of defect relaxation strongly depends on both ion energy and the depth from the sample surface. This observation cannot be entirely explained as an effect of the collision cascade density on defect interaction dynamics, based on depth dependencies of cascade densities calculated with a recently developed model that accounts for the fractal nature of cascades. There results call for future systematic studies to better understand ion energy and cascade density effects on defect relaxation dynamics in Si.

Formation and migration of point defects in tungsten carbide: Unveiling the sluggish bulk self-diffusivity of WC

The formation and migration of point defects in α-WC was investigated using density functional theory atomic simulations. The material exhibits extremely limited deviation from stoichiometry and only at high temperatures and for carbon deficient conditions (WC1-x). Bulk self-diffusivity was found to be remarkably slow (∼1014 cm2/s at 2400 °C) and strongly anisotropic, with basal diffusivity 3–4 orders of magnitude faster than c-axis diffusivity. Our findings help re-interpret previous experimental observations, which were deemed anomalous due to the surprisingly low diffusivity. At equilibrium, the self-diffusivity is dominated by C vacancies, with C interstitials and W defects providing negligible contribution to the total diffusivity. However, under irradiation conditions, interstitial diffusion is predicted to dominate owing to the higher mobility of interstitials once formed (Em(Ci)=1.19 eV vs Em(VC)=3.48 eV). Such diffusion also exhibits strong anisotropy. This may be exploited by means of texture engineering to control the swelling of WC components exposed to radiation fields.

Growth in Vacancy Voids at the Initial Stage of Transient Swelling

Swelling at the beginning of the transient stage has been described using point-defect migration theory. The rate of the growth in void diameter at various irradiation temperatures has been calculated for EK-164 steel cladding of the BN-600 reactor. It has been shown that this rate does not depend on the void diameter in a wide temperature range. The characteristics of porosity formed in the steel upon irradiation have been analyzed. The calculated results have been compared with the experimental data obtained for fuel claddings after service in the BN-600 reactor.

Deterministic Role of Collision Cascade Density in Radiation Defect Dynamics in Si.

The formation of stable radiation damage in solids often proceeds via complex dynamic annealing (DA) processes, involving point defect migration and interaction. The dependence of DA on irradiation conditions remains poorly understood even for Si. Here, we use a pulsed ion beam method to study defect interaction dynamics in Si bombarded in the temperature range from ∼-30 °C to 210 °C with ions in a wide range of masses, from Ne to Xe, creating collision cascades with different densities. We demonstrate that the complexity of the influence of irradiation conditions on defect dynamics can be reduced to a deterministic effect of a single parameter, the average cascade density, calculated by taking into account the fractal nature of collision cascades. For each ion species, the DA rate exhibits two well-defined Arrhenius regions where different DA mechanisms dominate. These two regions intersect at a critical temperature, which depends linearly on the cascade density. The low-temperature DA regime is characterized by an activation energy of ∼0.1 eV, independent of the cascade density. The high-temperature regime, however, exhibits a change in the dominant DA process for cascade densities above ∼0.04 at.%, evidenced by an increase in the activation energy. These results clearly demonstrate a crucial role of the collision cascade density and can be used to predict radiation defect dynamics in Si.

Density Functional Theory Modeling of Cation Diffusion in Bulk Lanthanum Manganite and Tetragonal Zirconia for Solid Oxide Fuel Cell Applications

Cation diffusion in perovskites such as La1-xSrxMnO3±δ (LSM) and fluorites such as Yttria Stabilized Zirconia (YSZ) plays a key role in controlling performance and long-term stability of solid oxide fuel cells (SOFCs) and of the corresponding electrode/electrolyte interfaces. For point defects based cation migration mechanisms, discrepancies between experimental studies and atomistic modeling results are generally observed when trying to identify the apparent activation energies of the cation diffusivities. In particular, computational modeling of the simple point defect migration generally overestimates the apparent activation energies by several eVs [1-3] relative to experimental results. Despite the existence of few proposed defect cluster pathways in the SOFC literature, the corresponding energetics based on atomistic level modeling is quite limited. As a result, outstanding questions related to the influence of the local bonding environment of the material upon the activation energies of cation diffusion and upon the energetics of the defect cluster carriers are still open. In this presentation, density functional theory (DFT) calculations of the cation diffusion involving mechanisms beyond the isolated point defect migration mechanism are discussed in connection to SOFC applications. The barriers of the cations, cation vacancy clusters, and cation impurities migration as well as their corresponding saddle point configurations in bulk LaMnO3±δ (LMO) and tetragonal ZrO2 are investigated. For cation vacancy migration in both LaMnO3 and tetragonal ZrO2 systems, it was revealed that significant reduction in the barriers of 1~3 eV takes place when there exists an additional nearest neighbor vacancy or a nearest neighbor vacancy pair bound to the original cation vacancy transport carrier (i.e., partially or fully bound Schottky defects). Such a significant reduction in the migration barriers of isolated cation vacancy migration due to the presence of an additional nearest neighbor vacancy or a vacancy pair invokes the need to examine other possible defect cluster diffusion mechanisms that exhibit attractive or weakly repulsive interactions between point defects. For example, our recent studies [1,3] suggest that the presence of a nearest neighbor B-site cation vacancy in bulk LMO decreases the electrostatic repulsion and steric constraints to the migrating A-site cations in the transition state configurations, leading to a more active A-site cation diffusion with apparent activation energies in good agreement with the experimental measurements. An analogous scenario is also observed for the Lanthanide impurity migration (via a cation vacancy related mechanism) in tetragonal ZrO2, where the migration barriers of partial and full Schottky bound defects are about 1.5 and 2.4 eV lower than those of simple cation vacancy migration (about 3 eV). By considering the attractive interactions of -1.0 and -1.4 eV for the partial (VZr-VO) and full (VO-VZr-VO) bound Schottky defects along with the separated Schottky defect formation energies of 4~5 eV (in a 288-atom ZrO2 supercells), it follows that cation impurity diffusion via partially and fully bonded Schottky defects could be more active than the cation vacancy migration of the separated Schottky defects in tetragonal ZrO2. Finally, the trends in the migration barriers of the defect cluster mechanisms among several types of cation impurities relevant for SOFC applications in LMO and tetragonal ZrO2 will be also discussed.