Effective Migration Energy Research Articles

Effects of Carbon on Void Nucleation in Self-Ion–Irradiated Pure Iron

Impurities such as carbon atoms play a significant role in the void swelling of irradiated metals. The phenomenon is important to both materials designs in which impurities are intentionally introduced and accelerator-based ion irradiation testing in which impurities are introduced unintentionally as contaminants. Here, we report rate theory simulations of void nucleation in pure Fe, which are irradiated by 5-MeV Fe ions, as one typical irradiation condition used in nuclear material testing. Based on kinetics obtained previously from ab initio calculations, Multiphysics Object-Oriented Simulation Environment (MOOSE)–based numerical solvers were used to simulate defect distributions and void nucleation. Vacancy-carbon interactions increase the effective migration energies of carbon and decrease the diffusivity prefactors. The vacancy mobility reduction decreases both interstitial flux and vacancy flux. However, the vacancy flux reduction is more significant than that of interstitials, leading to reduced void nucleation in bulk. On the other hand, reduced vacancy flux toward the surface leads to local vacancy pileups, leading to locally enhanced void nucleation. These two combined effects make the void nucleation profile deviate from the displacements per atom (dpa) peak, and void swelling peaks shift to the near-surface region. The transition from deep swelling to near-surface swelling is plotted as a function of dpa rate, carbon concentration, and temperature. The study shows that the swelling peak shifting caused by the carbon effect can be avoided by either reducing dpa rates or increasing irradiation temperatures. The study is important to understand swelling behaviors and to optimize irradiation parameters for accelerator-based swelling testing.

Effect of the free surface on near-surface void swelling in self-ion irradiated single crystal pure iron considering the carbon effect

The influence of ion-incident free surfaces on void swelling in near-surface regions was systematically studied using self-ion irradiation of single crystal pure iron. The key interest was to evaluate the effect of free surfaces not only on the formation of void-denuded zones but also on the swelling in the region immediately adjacent to the void-denuded zone. The irradiation matrix included beam energies varying from 1.0 to 5.0 MeV, peak displacements-per-atom levels of 50 and 100 dpa, and irradiation temperatures at 425 °C (at 6 × 10−3 peak dpa/sec, 475 °C (at 1.2 × 10−3 peak dpa/sec) and 525 °C (at 6 × 10−3 peak dpa/sec). The observed denuded depth Δx obtained from transmission electron microscopy was modified to incorporate the sputtering effect. The derived activation energy governing the denuding process is Ex4=1.65±0.03eV, which is significantly higher than the vacancy migration energy EVm known for Fe to be 0.67 eV. This difference is speculated to be due to the strong effect of relatively small amounts of dissolved carbon at 103 appm, which reduces the effective vacancy mobility and thereby increases the effective migration energy. Based on the effective vacancy migration energy extrapolated from a previous first-principle calculation for Fe containing various carbon levels, rate theory calculation was used to model the surface influence and the results support the speculation of carbon influence. For the region immediately adjacent to the void-denuded zone, swelling is locally suppressed, rising to reach the bulk swelling at a depth increment essentially equal to the denuded width. This suppression effect causes shifting of swelling vs. local dpa curves obtained from different peak dpa irradiations. Such shifting is proposed in the present study as a method to define the boundary of the surface-induced suppressed swelling zone beyond which the swelling can be considered to be fully free of surface influence.

Theoretical studies on the stabilization and diffusion behaviors of helium impurities in 6H-SiC by DFT calculations

In fusion environments, large scales of helium (He) atoms are produced by a radical transformation along with structural damage in structural materials, resulting in material swelling and degradation of physical properties. To understand its irradiation effects, this paper investigates the stability, electronic structure, energetics, charge density distribution, PDOS and TDOS, and diffusion processes of He impurities in 6H-SiC materials. The formation energy indicates that a stable, favorable position for interstitial He is the HR site with the lowest energy of 2.40 eV. In terms of vacancy, the He atom initially prefers to substitute at pre-existing Si vacancy than C vacancy due to lower substitution energy. The minimum energy paths (MEPs) with migration energy barriers are also calculated for He impurity by interstitial and vacancy-mediated diffusion. Based on its calculated energy barriers, the most possible diffusion path includes the exchange of interstitial and vacancy sites with effective migration energies ranging from 0.101 eV to 1.0 eV. Our calculation provides a better understanding of the stabilization and diffusion behaviors of He impurities in 6H-SiC materials.

Distinctive features of diffusion-controlled radiation defect recombination in stoichiometric magnesium aluminate spinel single crystals and transparent polycrystalline ceramics

MgAl2O4 spinel is important optical material for harsh radiation environment and other important applications. The kinetics of thermal annealing of the basic electron (F, F+) and hole (V) centers in stoichiometric MgAl2O4 spinel irradiated by fast neutrons and protons is analyzed in terms of diffusion-controlled bimolecular reactions. Properties of MgAl2O4 single crystals and optical polycrystalline ceramics are compared. It is demonstrated that both transparent ceramics and single crystals, as well as different types of irradiation show qualitatively similar kinetics, but the effective migration energy Ea and pre-exponent D0 are strongly correlated. Such correlation is discussed in terms of the so-called Meyer-Neldel rule known in chemical kinetics of condensed matter. The results for the irradiated spinel are compared with those for sapphire, MgO and other radiation-resistant materials.

Anomalous self-diffusion, structural and energy relaxations and temporal scaling laws in pure tantalum and pure vanadium metallic glasses

While most studies have considered diffusion in metallic glasses (MGs) to be normal, with a temporally asymptotic diffusivity at a given temperature (T), we report that the diffusion is anomalous and should be described as subdiffusion in pure Ta and pure V MGs—two examples chosen here because of chemical simplicity, fast relaxation, and minimal ambiguity. The diffusivity at a constant T (below the glass transition temperature) drops continuously with time t according to a negative power law instead of the commonly assumed exponential decay. To understand this, we trace the dynamic evolution of potential energy (Ep) and icosahedral short-range ordering (fico) of the system. We find that at large t, fico increases linearly with ln(t), causing Ep to decrease linearly with ln(t), with a remarkably simple linear correlation between fico and Ep. Based on Ep, we infer a continuously increasing effective migration energy barrier, also scaling linearly with ln(t), which perfectly recovers the negative power law time-dependence of diffusivity. The finding of anomalous diffusion and its origin in the fast-relaxing MGs calls out the need to distinguish potentially anomalous diffusion from normal diffusion in MGs, which is critical in disentangling time and temperature in experimental data and developing a robust theory for diffusion in MGs. The temporal scaling laws for diffusivity and structural and energy relaxations reported here may find their validity in other MGs and aid future theory development. In addition, we also discuss the effect of sample thermal history on the time-dependent diffusivity and how to prevent confusion caused by such effect.

First-principles investigation on stability and diffusion mechanism of helium impurities in 4H-SiC

The stability, structure, energetics and diffusive properties of He impurities in 4H-SiC have been investigated by first principles calculations in order to understand its irradiation effects. The formation energies indicate a He atom is preferable to occupy the Si pre-existing vacancy at first. In turn, by formation of He defects associating at interstitial and vacancy sites require positive but low formation energies, suggesting its propensity diffusion in the material. By calculating its energy barriers corresponding to both the interstitial diffusion and vacancy assisted diffusion, we suggest that the most probable diffusion pathway involves the exchange of interstitial and vacancy positions with the effective migration energies from 0.1 eV to 1.0 eV. Remarkable, our calculated diffusion barriers are consistent well with previous theoretical data for He diffusion in 3C-SiC.

Diffusion mechanisms of C in 100, 110 and 111 Fe surfaces studied using kinetic activation-relaxation technique

The physics of Fe-C surface interactions is of fundamental importance to phenomena such as corrosion, catalysis, synthesis of graphene, new steels, etc. To better understand this question, we perform an extensive characterization of the energy landscape for carbon diffusion from bulk to surfaces for bcc iron at low C concentration. C diffusion mechanisms over the three main Fe-surfaces – (100), (110) and (111) – are studied computationally using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo algorithm. Migration and adsorption energies on surfaces as well as absorption energies into the subsurfaces are predicted and then compared to density functional theory (DFT) and experiment. The energy landscape along C-diffusion pathways from bulk to surface is constructed allowing a more extensive characterization of the diffusion pathways between surface and subsurface. In particular, effective migration energies from (100), (110) and (111) surfaces, to the bulk octahedral site are found to be around ∼1.6 eV, ∼1.2 eV and ∼1.3 eV respectively suggesting that C insertion into the bulk cannot take place in pure crystalline Fe, irrespective of the exposed surface.

Visualization of TlBr ionic transport mechanism by the Accelerated Device Degradation technique

Thallium Bromide (TlBr) is a promising gamma radiation semiconductor detector material. However, it is an ionic semiconductor and suffers from polarization. As a result, TlBr devices degrade rapidly at room temperature. Polarization is associated with the flow of ionic current in the crystal under electrical bias, leading to the accumulation of charged ions at the device׳s electrical contacts. We report a fast and reliable direct characterization technique to identify the effects of various growth and post-growth process modifications on the polarization process. The Accelerated Device Degradation (ADD) characterization technique allows direct observation of nucleation and propagation of ionic transport channels within the TlBr crystals under applied bias. These channels are observed to be initiated both directly under the electrode as well as away from it. The propagation direction is always towards the anode indicating that Br− is the mobile diffusing species within the defect channels. The effective migration energy of the Br− ions was calculated to be 0.33±0.03eV, which is consistent with other theoretical and experimental results.

Interstitial helium diffusion mechanisms in 〈1 1 0〉 tilt grain boundaries in BCC FeCr alloys: A atomistic study

In this work, we studied the migration of He in different 〈110〉 tilt grain boundaries (GBs) (Σ19{331}, Σ9{221}, Σ3{111}, Σ3{112}, Σ11{113}, Σ9{114}) in Fe–(5,10,14)Cr random alloys, with the misorientation angle varying in the range 26°–141°. We performed systematic molecular statics and molecular dynamics simulations to characterize the interaction of He with the core of the GBs and to estimate the diffusion coefficient, migration mechanism, and effective core migration energy. The simulations were performed in the 600–1400K temperature range, applying a set of interatomic potentials for Fe–Cr–He system recently proposed by Juslin et al., specially fitted to the properties of He in bulk Fe. We found that the migration of an interstitial He near the core of the Σ3{112} GB is essentially three-dimensional (3D) within the investigated temperature range. The transition of diffusion mode from one-dimensional (1D) to 3D was observed in other GBs in the studied alloys. The results clearly demonstrate, that the accommodation, migration mechanism, and diffusivity of He is extremely sensitive to variations in atomic structure of a particular GB. Alloying with Cr was found to enhance the mobility of a He interstitial in the GB region.

Elucidating the atomistic mechanisms driving self-diffusion of amorphous Si during annealing

We have analyzed the atomic rearrangements underlying self-diffusion in amorphous Si during annealing using tight-binding molecular dynamics simulations. Two types of amorphous samples with different structural features were used to analyze the influence of coordination defects. We have identified several types of atomic rearrangement mechanisms, and we have obtained an effective migration energy of around 1 eV. We found similar migration energies for both types of samples, but higher diffusivities in the one with a higher initial percentage of coordination defects.

Dimensionality of interstitial He migration in 〈1 1 0〉 tilt grain boundaries in α-Fe

In this work we study the migration of an interstitial helium atom in different 〈1 1 0〉 tilt grain boundaries ( Σ19{3 3 1}, Σ9{2 2 1}, Σ3{1 1 1}, Σ3{1 1 2}, Σ11{1 1 3}, Σ9{1 1 4}) in α-Fe, with the misorientation angle varying in the range 26°–141°. Systematic molecular statics and molecular dynamics simulations were performed to characterize the interaction of He with the core of the grain boundaries (GB) and to estimate the diffusion coefficient, migration mechanism and effective migration energy. The simulations were performed in the temperature range 300–1000 K, applying a recently proposed set of interatomic potentials for Fe–He system by Juslin et al., specially fitted to the properties of He in bulk Fe. It was found that the migration of an interstitial He near the core of Σ3 〈1 1 0〉{1 1 1} GB is essentially three-dimensional in the investigated temperature range. Two-dimensional diffusion prevails in the case of Σ3〈1 1 0〉{112} and Σ9〈1 1 0〉{1 1 4} GBs and it changes to the three-dimensional one above ∼900 K. A completely one-dimensional diffusion along the tilt axis was observed in the core of Σ19〈1 1 0〉{3 3 1} and Σ9〈1 1 0〉{2 2 1} GBs. No core diffusion was detected at Σ11〈1 1 0〉{1 1 3} GB. Thus, only the release from and re-absorption at the GB core was seen in this GB. These results clearly demonstrate that the accommodation, migration mechanism and diffusivity of He is extremely sensitive to variations in the atomic structure of grain boundaries. Some of the results obtained are compared with previously published data, generated using early developed interatomic potentials. In general, the results obtained support and extend most of conclusions on He properties near grain boundaries drawn already, yet several important discrepancies are also found.

Ab initiomodeling of diffusion in indium oxide

Migration barriers of intrinsic defects in cubic indium oxide are calculated by means of first-principles calculations within density-functional theory using the nudged-elastic-band method. Within the open C-type (bixbyite) structure of ${\text{In}}_{2}{\text{O}}_{3}$ there is a large variety of distinct migration paths involving the fourth-neighbor shell. Effective migration energies and diffusion length are calculated by means of kinetic Monte Carlo simulations. We show that cation barriers have generally higher migration energies as compared to oxygen defects, which diffuse via correlated jumps. Moreover, there are distinct diffusion paths for anion and cation interstitials while structural vacancies within the bixbyite structure do not give rise to an enhanced diffusion.

Hydrogen in beryllium: Solubility, transport, and trapping

The paper presents the results of ab initio simulation of hydrogen properties in beryllium. Both interstitial hydrogen positions in the lattice and various hydrogen positions in a vacancy have been studied. The most energetically favorable interstitial hydrogen configuration among the four considered high-symmetry configurations is the basal tetrahedral one, in agreement with the earlier predictions. The most probable diffusion pathway for hydrogen atoms in the bulk involves the exchange of octahedral and basal tetrahedral positions with the effective migration energy of $\ensuremath{\sim}0.4\text{ }\text{eV}$. For hydrogen atom in a vacancy, an off-center (nearly basal tetrahedral) configuration is definitely preferred. Addition of more hydrogen atoms to a vacancy remains energetically favorable up to at least five hydrogen atoms, though the binding energies fall down with the increase in the number of hydrogen atoms in the vacancy.

Kinetic lattice Monte Carlo simulation study on vacancy diffusion in germanium

We report kinetic lattice Monte Carlo simulations of vacancy-assisted self-diffusion in germanium below the melting point. We show that effective migration energies differ greatly from the migration energy of a free vacancy, which was calculated for a system with a low vacancy concentration. Vacancies are agglomerated in clusters and free vacancies are dissociated from clusters at temperatures above 657 °C, and the nucleation temperatures of vacancy clustering in germanium are estimated to be 617–657 °C. At temperatures below 617 °C, there are a few remaining free vacancies for low concentrations, and in that case the effective migration energy of 0.17 eV closely coincides with the migration energy derived from previous theoretical calculations for low vacancy concentrations. The effective migration energy of 1.17 ± 0.1 eV above 657 °C also closely coincides with that measured in previous experiments.

Vacancy clustering and diffusion in germanium using kinetic lattice Monte Carlo simulations

We investigated vacancy-assisted self-diffusion in germanium by means of kinetic lattice Monte Carlo (KLMC) simulations below the melting temperature, for a vacancy concentration of 1 × 1018/cm3. At higher temperatures, fewer clusters formed, but there was less variation in the number of clusters than at lower temperatures as the time increased. Equilibrium diffusivities in the clustering region were 102 lower than those of free vacancies in the initial stage of KLMC simulations. They were expressed according to three temperature regimes: 6.5 × 10− 4 exp(–0.35/k B T) cm2/s at temperatures above 1100 K, 5.2 × 105 exp(–2.32/k B T) cm2/s at temperatures of 900–1100 K and 6.0 × 0–7 exp(–0.19/k B T) cm2/s at temperatures below 900 K. The effective mean migration energy, 1.1 eV, closely coincided with that of the 1.0–1.2 eV in experiments and was very different from the migration energy of the free vacancy.

Diffusion of He interstitial and di-He cluster at grain boundaries in α-Fe

A systematic molecular dynamics study of the diffusion mechanisms of He interstitial and di-He cluster at two representative interfaces has been carried out in α-Fe. The diffusion coefficient of a He interstitial and the effective migration energies were determined. The He atom diffuses along the Σ11 grain boundary one-dimensionally along specific directions, while it migrates two-dimensionally at low temperatures, and three-dimensionally at higher temperatures, in the Σ3 grain boundary. The di-He interstitial cluster can migrate rapidly along the Σ3 interface at low temperatures, but not at the Σ11 interface. It has been observed that a di-He interstitial cluster can kick out a self interstitial atom (SIA) at high temperatures, forming a He 2V complex. The SIA migrates rapidly near interfaces, whereas the He 2V complex is immobile at the temperatures considered. This small cluster may serve as the smallest nucleation for the formation of helium bubbles at interfaces.

Vacancy-Assisted Diffusion in Silicon: A Three-Temperature-Regime Model

In this Letter we report kinetic lattice Monte Carlo simulations of vacancy-assisted diffusion in silicon. We show that the observed temperature dependence for vacancy migration energy is explained by the existence of three diffusion regimes for divacancies. This characteristic has been rationalized with an analytical model. In the intermediate temperature regime the divacancy dissociation plays a key role and an effective migration energy E{v}{m} approximately 2 eV is predicted, computed from either full ab initio values or mixed with experimental ones. The exact position of this temperature regime strongly depends on vacancy concentration. Previous contradictory experimental results are revisited using this viewpoint.

Diffusion of He interstitials in grain boundaries in α-Fe

Helium diffusion in metals is a complex process due to its very low solubility in solids and its ability to be trapped by vacancy type defects or impurities. The preferential positions and predominant migration mechanisms of He atoms depend on temperature, as well as the presence of other intrinsic or irradiation induced defects that can act as traps for He. This work presents results of a systematic molecular dynamics study of the diffusion mechanisms of He atoms in grain boundaries in α-Fe. Two grain boundaries, Σ11〈1 1 0〉 {3 2 3} and Σ3〈1 1 0〉 {1 1 2}, were used for the current investigations. The low-temperature (about 0 K) equilibrium structures of these grain boundaries were determined using standard molecular dynamics relaxation techniques, with a flexible border condition. The migration of He atoms were followed for 1–14 ns, at temperatures between 600 and 1200 K. The diffusion coefficient of He atoms using the mean square displacements of He atoms, and the effective migration energies were determined. We found that He atoms diffuse rapidly in the Σ11 grain boundary, where the binding energy of a He atom to the boundary is high. He migration is primarily one-dimensional along specific directions, but a few directional changes were observed at higher temperatures. In the Σ3 grain boundary, where the He binding energy is low, He atoms migrate one-dimensionally at low temperature, two-dimensionally at intermediate temperature and three-dimensionally at higher temperature. The different activation energies and diffusion mechanisms in these two representative grain boundaries suggests that the atomic structures of the grain boundaries play an important role in the diffusivity of He.

One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper

Atomic-scale computer simulation has been used to study the thermally activated atomic transport of self-interstitial atoms (SIAs) in the form of planar clusters in pure Cu and f-Fe. There is strong evidence that such clusters are commonly formed in metals during irradiation with high-energy particles and play an important role in accumulation and spatial distribution of surviving defects. An extensive study of the mobility of SIA clusters containing two to 331 interstitials has been carried out using the molecular dynamics simulation technique for the temperature range from 180 to 1200 K. The results obtained show that clusters larger than three to four SIAs are one-dimensionally mobile in both Cu and Fe. Large clusters of more than 100 SIAs in Cu and 300 SIAs in Fe have significantly reduced mobility. The problem of describing one-dimensional (1D) motion in three-dimensional space is discussed. An attempt is made to describe the mobility of SIA clusters within the approximation of 1D diffusion. For clusters in both metals the effective migration energy of 1D diffusion as estimated via the jump frequency of the cluster centre of mass is found to be independent of the number of SIAs in the clusters, although the cluster jump frequency decreases with increasing cluster size. Mechanisms of 1D mobility of interstitial clusters are discussed.

Study of point defect behavior in V–Ti alloys using HVEM

Microstructural evolution and point defect behavior in vanadium, V–5Ti binary alloy and V–4Cr–4Ti alloy have been examined by using a high voltage electron microscope. In order to examine the effects of interstitial impurity atoms, V–Ti alloys with different levels of purity have also been examined. During irradiation, interstitial-type dislocation loops formed and grew in all of the materials. In alloys, the loop number density ( C L) was much higher than that in vanadium. In high purity V–4Cr–4Ti, contrary to results from our previous study on vanadium, C L did not significantly decrease or change by purification, indicating solute atoms themselves strongly trap self-interstitial atoms (SIAs). From the temperature dependence of loop density in V–4Cr–4Ti, the effective migration energy of a SIA of 0.50 eVwas obtained. Various observed phenomena are discussed in terms of this activation energy.