Frenkel Pair Defects Research Articles

Ab initio modeling of radiation damage in MgF2 crystals

MgF2 with a rutile structure is important radiation-resistant material with numerous applications due to its transparency from vacuum ultraviolet to infrared range of photon energies. We present and discuss the results of calculations for basic radiation defects in this crystal. The study is based on the large scale ab initio DFT calculations using hybrid B3PW exchange–correlation functional and atomic basis set. We analyzed the electronic structure, atomic displacements, charge density distribution as well as defect formation energies using large supercells. We compared properties of close and well separated F−H (Frenkel) defect pairs as well as individual defects. We simulated also formation and energetic preference of inert F2 interstitial molecules as sinks of mobile interstitial fluorine atoms which is relevant for material radiation stability. We discussed also diffusion of the primary electronic defects—F centers.

Accommodation of excess oxygen in fluorite dioxides

Accommodation of excess oxygen in CeO2, ThO2 and UO2 has been investigated using ab-initio modelling. Calculations indicate that hyperstoichiometry is preferentially accommodated by the formation of peroxide species in CeO2 and ThO2 but not in UO2, where oxygen interstitial defects are dominant. Migration of the excess oxygen defects was also studied; the peroxide ion in CeO2 and ThO2 is transported via a different mechanism, due to the formation of peroxide molecules, to the oxygen interstitial in UO2. Frenkel pair defects were investigated to understand if the interstitial component could assume a peroxide like configuration in the vicinity of the vacancy. While it was already expected that this would not be the case for UO2 since peroxide was not stable, it was also not found to be the case for CeO2 and ThO2 with the peroxide disassociating into a lattice species and a separate interstitial ion.

First-principles study of energetic and electronic properties of δ-Re6MO12 (Re = Ho, Gd, Y; M = U, W)

First-principles calculations have been performed to study the structural, energetic, and electronic properties of δ-Re6MO12 (Re = Ho, Gd, Y; M = U, W). The calculated results indicated that the energetic tendencies for the formation of Frenkel-pair defects of δ-Re6MO12 are consistent with the experimental results, and the Frenkel-pair defects have a significant influence on radiation-induced phase transformation. Density of states (DOS) analysis showed hybridizations between W 5d and O 2p states in Y6WO12 and between U 6d and O 2p states in Re6UO12 (Re = Ho, Gd, Y) are observed, but the interaction ⟨M-O⟩ orbital is much stronger in Re6UO12 (Re = Ho, Gd, Y) than that in Y6WO12. Bader charge analysis revealed that ⟨U-O⟩ bond in Re6UO12 (Re = Ho, Gd, Y) is more covalent than ⟨W-O⟩ bond in Y6WO12. It was proposed that ⟨M-O⟩ bond may play a more significant role in determining their radiation tolerance.

Ion irradiation induced order-to-disorder transformation in δ-phase Lu4Hf3O12

In this study, polycrystalline δ-phase Lu4Hf3O12 was irradiated with 6MeV Xe26+ ions to fluences ranging from 2×1013 to 1×1015ions/cm2. Ion irradiation-induced microstructural evolution was examined by using grazing incidence X-ray diffraction (GIXRD). A complete phase transformation from ordered rhombohedral to disordered fluorite (O–D) was observed by a fluence of 1×1015ions/cm2, equivalent to a peak ballistic damage dose of ∼3.49 displacements per atom (dpa). To research the different irradiation effect between light ion and heavy ion on δ-Lu4Hf3O12, 400keV Ne2+ ions were implanted to ion fluences ranging from 1×1014 to 1×1015ions/cm2. A complete O–D crystal structure transformation was observed by a fluence of 5×1014ions/cm2 (∼0.22dpa). This threshold dose was found to be observably lower than the threshold dose to produce order-to-disorder transformation using Xe26+ ions on δ-Lu4Hf3O12. This suggests that heavy ions are less efficient than light ions in producing the retained defects that are responsible for the O–D transformation. The theoretical calculations show that the O–D transformation of δ-phase was attributed to the anion oxygen Frenkel pair defect. The ion irradiation-induced transformation of δ-phase Lu4Hf3O12 into disordered fluorite structure observed here is also discussed in relation to the temperature–composition (T–C) phase diagrams for the compound.

Simulating Radiation-Induced Defect Formation in Pyrochlores

ABSTRACTThe accuracy and robustness of new Buckingham potentials for the pyrochlores Gd2Ti2O7 and Gd2Zr2O7 is demonstrated by calculating and comparing values for a selection of point defects with those calculated using a selection of other published potentials and our own ab inito values. Frenkel pair defect formation energies are substantially lowered in the presence of a small amount of local cation disorder. The activation energy for oxygen vacancy migration between adjacent O48f sites is calculated for Ti and Zr pyrochlores with the energy found to be lower for the non-defective Ti than for the Zr pyrochlore by ∼0.1 eV. The effect of local cation disorder on the VO48f → VO48f migration energy is minimal for Gd2Ti2O7, while the migration energy is lowered typically by ∼43 % for Gd2Zr2O7. As the healing mechanisms of these pyrochlores are likely to rely upon the availability of oxygen vacancies, the healing of a defective Zr pyrochlore is predicted to be faster than for the equivalent Ti pyrochlore.

Thermodynamic assessment of oxygen diffusion in non-stoichiometric UO2±x from experimental data and Frenkel pair modeling

The self and chemical diffusion of oxygen in the non-stoichiometric domain of the UO2 compound is analyzed from the point of view of experimental determinations and modeling from Frenkel pair defects. The correlation between the self-diffusion and the chemical diffusion coefficients is analyzed using the Darken coefficient calculated from a thermodynamic description of the UO2±x phase. This description was obtained from an optimization of thermodynamic and phase diagram data and modeling with different point defects, including the Frenkel pair point defects. The proposed diffusion coefficients correspond to the 300–2300K temperature range and to the full composition range of the non stoichiometric UO2 compound. These values will be used for the simulation of the oxidation and ignition of the uranium carbide in different oxygen atmospheres that starts at temperatures as low as 400K.

Li+ionic conductivities and diffusion mechanisms in Li-based imides and lithium amide

In this study, both experimental ionic conductivity measurements and the first-principles simulations are employed to investigate the Li(+) ionic diffusion properties in lithium-based imides (Li(2)NH, Li(2)Mg(NH)(2) and Li(2)Ca(NH)(2)) and lithium amide (LiNH(2)). The experimental results show that Li(+) ions present superionic conductivity in Li(2)NH (2.54 × 10(-4) S cm(-1)) and moderate ionic conductivity in Li(2)Ca(NH)(2) (6.40 × 10(-6) S cm(-1)) at room temperature; while conduction of Li(+) ions is hardly detectable in Li(2)Mg(NH)(2) and LiNH(2) at room temperature. The simulation results indicate that Li(+) ion diffusion in Li(2)NH may be mediated by Frenkel pair defects or charged vacancies, and the diffusion pathway is more likely via a series of intermediate jumps between octahedral and tetrahedral sites along the [001] direction. The calculated activation energy and pre-exponential factor for Li(+) ion conduction in Li(2)NH are well comparable with the experimentally determined values, showing the consistency of experimental and theoretical investigations. The calculation of the defect formation energy in LiNH(2) reveals that Li defects are difficult to create to mediate the Li(+) ion diffusion, resulting in the poor Li(+) ion conduction in LiNH(2) at room temperature.

Novel potentials for modelling defect formation and oxygen vacancy migration in Gd2Ti2O7 and Gd2Zr2O7 pyrochlores

Ceramic materials play a critical role in the safe long-term immobilisation of nuclear waste and fundamental understanding of both radiation damage and healing processes are required in order to determine the suitability of proposed storage materials, such as pyrochlores. Here, new interatomic potentials are derived for the pyrochlores Gd2Ti2O7 and Gd2Zr2O7. Their accuracy and robustness is demonstrated by calculating and comparing values for a selection of point defects with those calculated using a selection of other published potentials. Frenkel pair defect formation energies are substantially lowered in the presence of a small amount of local cation disorder. The activation energy for oxygen vacancy migration between adjacent O48f sites is calculated for Ti and Zr pyrochlores using an improved tangent nudged elastic band method. This energy is lower for the non-defective Ti than for the Zr pyrochlore by ∼0.1 eV, consistent with the majority of the potentials tested. The effect of local cation disorder on the VO48f → VO48f migration energy is minimal for Gd2Ti2O7, while in contrast the migration energy is lowered typically by ∼43% for Gd2Zr2O7. Since the healing mechanisms of these pyrochlores are likely to rely upon the availability of oxygen vacancies, the healing of a defective Zr pyrochlore is predicted to be faster than for the equivalent Ti pyrochlore.

On the interaction between radiation-induced defects and foreign interstitial atoms in α-iron

Interaction between Frenkel pair (FP) defects and nitrogen atoms in α-iron has been investigated by means of resistivity recovery method. Both FP defects are attracted to nitrogen atoms. Dissociation of self-interstitial atoms from nitrogen atoms is observed at 165 K while that of vacancies at 250 K. The binding energies of FP defects with nitrogen are both about 0.1–0.15 eV. A weak RR stage is observed at 340 K assigned to the presence of carbon in concentration of about 1 appm. Analysis of its features leads to a conclusion on a dissociation (binding) energy of vacancy-carbon atom pairs of about 0.9 (0.35) eV.

An ab initio study of the effect of charge localization on oxygen defect formation and migration energies in magnesium oxide

Plane-wave density functional theory was used to study the properties of oxygen vacancies and interstitials, with different charge states, in MgO. The calculated properties were the relaxed configurations, the Frenkel defect formation energies and the energies of the migration barriers, and all properties were found to be strongly dependent on the defect charge state. The lowest energy configuration of the O 2− interstitial was found to be the cube centre; however, the O − and O 0 interstitials formed dumb-bell configurations. The Frenkel defect energies were also strongly dependent on the defect charge, with the neutral pair energy calculated to be 3 eV lower than the doubly charged Frenkel pair defect energy. The migration barriers of the oxygen vacancies were found to increase as the net charge of the oxygen vacancies decreased, which suggests that vacancies with trapped electrons are much less mobile than the F 2+ vacancies modelled by classical potentials. The migration of the oxygen interstitials showed particularly interesting behaviour. The O 0 interstitial was found to have a higher migration barrier than the O 2− interstitial but a very low barrier (0.06 eV) was found for the O − interstitial. The results have significant implications for the reliability of classical radiation damage simulations.

Recovery of electrical resistivity, short-range order formation and migration of defects in electron-irradiated Fe–4Cr alloy doped with carbon

Resistivity recovery (RR) data of Cr4 alloy doped with carbon (Cr4C) after irradiation with 5 MeV electrons are presented and compared with RR data of non-doped Cr4 alloy. Analysis of the defect- and short-range order-induced parts of RR has confirmed the proposed earlier scheme of the evolution of Frenkel pair defects on post-irradiation anneal in Cr4 and Cr9. Vacancies start free migration around 205–210 K; however, the related peak of stage III is invisible in conventional RR plots. Interstitials atoms (IAs) trapped in stage I at configurations of several Cr atoms start their long-range migration at 220 K. Migrating vacancies are captured by carbon atoms in Cr4C while IAs are not. Dissociation of vacancies from carbon atoms at 350 K gives rise to a decoration of carbon atoms with Cr atoms. Indications are seen that a release of vacancies captured by atoms of residual nitrogen takes place around 250–260 K.

Simulation of displacement cascades in tungsten irradiated by fusion neutrons

Numerical calculations of damage in tungsten irradiated by fusion neutrons were performed using molecular dynamics simulations combined with an embedded atom method potential. The displacement cascade efficiency has been calculated using the ratio of the number of Frenkel pairs determined by molecular dynamics simulations to the number of Frenkel pairs derived from Norgett–Robinson–Torrens formula. The cascade efficiency decreases as the Primary Knock Atoms increases. The Norgett–Robinson–Torrens calculations overestimate the Frenkel pair defect production by a factor of 2. The changes in the cascades dimensions at the early stages after irradiation indicate that the tungsten interstitials are more mobile than the vacancies. We found that the most common types of defects are single vacancies, di-vacancies, vacancy-clusters, interstitials and small number of interstitial clusters containing more than three atoms.

Heat capacity measurements and XPS studies on uranium–lanthanum mixed oxides

Heat capacity measurements were carried out on (U 1− y La y )O 2± x ( y = 0.2, 0.4, 0.6, and 0.8) using differential scanning calorimeter (DSC) in the temperature range 298–800 K. Enthalpy increment measurements were carried out on the above solid solutions using high temperature drop calorimetry in the temperature range 800–1800 K. Chemical states of U and La in the solid solutions of mixed oxides were determined using X-ray photoelectron spectroscopy (XPS). Oxygen to metal ratios of (U 1− y La y )O 2± x were estimated from the ratios of different chemical states of U present in the sample. Anomalous increase in the heat capacity is observed for (U 1− y La y )O 2± x ( y = 0.4, 0.6 and 0.8) with onset temperatures in the range of 1000–1200 K. The anomalous increase in the heat capacity is attributed to certain thermal excitation process, namely, Frenkel pair defect of oxygen. The heat capacity value of (U 1− y La y )O 2± x ( y = 0.2, 0.4, 0.6, and 0.8) at 298 K are 65.3, 64.1, 57.7, 51.9 J K −1 mol −1, respectively. From the XPS investigations, it was observed that the O/M ratios at the surface are higher than that in the bulk. In uranium rich mixed oxide samples, the surface O/M ratios are greater than 2 whereas that in La rich mixed oxides, they are less than 2, though the bulk O/M in all the samples are less than 2.

Energetics and concentration of defects in Gd2Ti2O7 and Gd2Zr2O7 pyrochlore at high pressure

Using first-principles calculations and complementary experiments, the defect formation energies and defect concentrations were calculated as a function of pressure. The results show that at high pressure, the defect formation energies decrease with pressure for both systems. In Gd2Ti2O7, the dominant defect type is cation anti-site defect, the local structure around a defect is highly distorted, and the energetically favorable defect–defect interactions at shorter distance suggest the possibility of defect clustering. In Gd2Zr2O7, anion Frenkel-pair defects are favored at all pressures and the dominant defect type involving a cation is a coupled defect of a cation anti-site and an anion Frenkel-pair defect. There are only minor distortions around the defects, and the defect–defect interactions are weak, which suggests almost-ideal non-interacting defect formation. Comparison of experimentally observed defect concentrations and those based on the calculated defect formation energies suggests that the defects formed at high pressure are better estimated with a concentrated limit approximation, while those formed at ambient pressure can be evaluated at a dilute limit approximation.

Derivation of enhanced potentials for uranium dioxide and the calculation of lattice and intrinsic defect properties

Previously reported forms of the cation–anion Buckingham potential provide a significantly greater contribution than the repulsive Coulombic component at short-range thus predicting an unphysical attraction between the pair of ions. A detailed reappraisal of the computer modelling of uranium dioxide (UO 2) employing atomistic simulation techniques is presented. An improved set of interatomic potentials is derived in order to describe the lattice correctly under conditions subsequent to radiation damage with the creation of Frenkel pair defects. Novel methodology is employed in the derivation of potentials ensuring applicability over the entire region of interest. The cation–anion potential is obtained via a combination of empirical fitting to crystal structural data and parametric fitting to additional physical properties. These potentials are subsequently verified and validated by calculation of additional bulk lattice properties, whose values agree favourably with those measured experimentally. Atomistic computer simulation techniques are then used to investigate the defect properties of UO 2. The theoretical techniques are based upon efficient energy minimization procedures and Mott–Littleton methodology for accurate defect modelling and employed to calculate intrinsic defect formation energies and enable predictions of the expected type of intrinsic disorder to be made.

Short-living defects and recombination processes in Li6Gd(BO3)3 crystals

Abstract Results of a study of transient optical absorption (TOA) and luminescence of lithium-gadolinium orthoborate Li 6 Gd(BO 3 ) 3 (LGBO) in the visible and ultraviolet spectral regions are presented. As revealed by absorption optical spectroscopy with nanosecond time resolution, the LGBO TOA derives from optical transitions in hole centers, with the optical density relaxation kinetics being mediated by interdefect tunneling recombination involving these centers and neutral lithium atoms acting as electronic Li 0 centers. At 290 K, the Li 0 centers are involved in thermally stimulated migration, which is not accompanied by carrier transfer to the conduction or valence band. The slow TOA decay kinetics components, with characteristic times ranging from a few milliseconds to seconds, have been assigned to diffusion-limited annihilation of lithium interstitials with vacancies. The mechanisms responsible for the creation and relaxation of short-living Frenkel defect pairs in the LGBO cation sublattice have been analyzed.

Physical Properties, Intrinsic Defects, and Phase Stability of Indium Sesquioxide

We report an accurate and robust interatomic pair potential for the technologically important transparent conducting oxide indium sesquioxide (In2O3). The potential is optimized for the thermodynamically stable bixbyite phase, and it is then used to explore the relative stability and physical properties of five sesquioxide polymorphs and their high-pressure phase transitions. The potential is further employed to investigate the formation of intrinsic defects at the limit of infinite dilution through the embedded Mott−Littleton approach. The anion Frenkel pair is determined to be the lowest energy source of ionic disorder with an energy of formation of 3.2 eV per defect, which can be explained by the presence of intrinsic anion vacancy sites in the bixbyite structure. In contrast, both the cation Frenkel pair (6.9 eV) and Schottky defect (4.4 eV) are less thermodynamically stable. The Schottky formation energy is less in the high pressure phases; however, it remains above 4 eV at elevated pressures.

Transient hole-polaron optical absorption in Li6Gd(BO3)3 crystals

Results of a study of transient optical absorption (TOA) and luminescence of lithium gadolinium orthoborate Li6Gd(BO3)3 (LGBO) in the visible and UV spectral regions are presented. As revealed by absorption optical spectroscopy with nanosecond time resolution, the LGBO TOA derives from optical transitions in hole centers, with the optical density relaxation kinetics being mediated by interdefect tunneling recombination involving these centers and neutral lithium atoms acting as electronic Li0 centers. At 290 K, the Li0 centers are involved in thermostimulated migration, which is not accompanied by carrier transfer to the conduction or valence band. The slow components of the TOA decay kinetics, with characteristic times ranging from a few milliseconds to seconds, have been assigned to diffusion-limited annihilation of lithium interstitials with vacancies. The mechanisms responsible for the creation and relaxation of short-lived Frenkel defect pairs in the LGBO cation sublattice have been analyzed.

Difference approach to the analysis of resistivity recovery data for irradiated short-range ordered alloys

Electrical resistivity recovery (RR) data for irradiated concentrated alloys typically consist of two inseparable parts, one resulting from defect annihilation and the other from short-range order (SRO) effects. These parts exhibit different behaviour and often follow opposite trends. Therefore, in this case, analysis of RR data within the conventional method is too complicated. A new approach to data analysis of such a two-component RR is proposed. The approach involves a new quantity, the difference RR (DRR), which is composed of RR dependences of two similar samples irradiated to different defect concentrations. It is shown that the SRO formation proper and the stages corresponding to the onset of long-range migration of Frenkel pair defects, formed in each part of RR, can be clearly related to certain features of the DRR plots. This interrelationship allows detecting and identifying these stages in each part of RR separately. The validity of the approach is illustrated by analysis of the available pairwise RR data for Fe–16Cr–20Ni and Fe–4Cr alloys. It makes it possible to detect the small contribution from the SRO formation to RR in Fe–4Cr, which we failed to observe previously. It is shown that stage III of Fe–4Cr, which has a negligible contribution to the part of RR induced by defect annihilation, is clearly observed in the part induced by SRO formation.

Void nucleation, growth, and coalescence in irradiated metals

A novel computational treatment of dense, stiff, coupled reaction rate equations is introduced to study the nucleation, growth, and possible coalescence of cavities during neutron irradiation of metals. Radiation damage is modeled by the creation of Frenkel pair defects and helium impurity atoms. A multi-dimensional cluster size distribution function allows independent evolution of the vacancy and helium content of cavities, distinguishing voids and bubbles. A model with sessile cavities and no cluster–cluster coalescence can result in a bimodal final cavity size distribution with coexistence of small, high-pressure bubbles and large, low-pressure voids. A model that includes unhindered cavity diffusion and coalescence ultimately removes the small helium bubbles from the system, leaving only large voids. The terminal void density is also reduced and the incubation period and terminal swelling rate can be greatly altered by cavity coalescence. Temperature-dependent trapping of voids/bubbles by precipitates and alterations in void surface diffusion from adsorbed impurities and internal gas pressure may give rise to intermediate swelling behavior through their effects on cavity mobility and coalescence.