Vacancy Migration Energy Research Articles

Phase-field simulation of Cu enriched nanoparticles with variation of defects migration energy under neutron irradiation

Neutron radiation induces point defects and affects the diffusivity of atoms and the kinetics of precipitation. The phase-field simulation reveals the influence of migration energy of vacancy on the radiation-enhanced precipitation in Fe–Cu alloy. The study shows that radiation-enhanced diffusion (RED) also depends on the diffusivity of vacancy-associated migration energy and not only on the dose rate; the low migration energy of vacancy results in accelerated precipitation and a higher volume fraction of Cu precipitates. Interestingly, decreasing migration energy from 1.0 eV to 0.9 eV results in a 30% increase in the precipitates’ volume fraction. Also, the combination of the lowest dose rate 5.0 × 10−3 dpa s−1 and highest migration energy 1.0 eV delays the precipitation. The study also examines the influence of migration energy of vacancy on the radius of Cu precipitates. The lowest migration energy, 0.9 eV, increases the radius up to one-third. Finally, the work presents the drawbacks of the analytical digital image processing technique in the quantitative comparison with the script.

Vacancy migration energies in CrMnFeCoNi, CrFeCoNi, and CrFeNi alloys and their effect on atomic diffusion

The mechanism of sluggish diffusion in high-entropy alloys has not been understood completely. In this study, we aimed to understand the mechanism by estimating the vacancy migration energies in such alloys. The vacancy migration and annihilation behavior in equimolar CrMnFeCoNi, CrFeCoNi, and CrFeNi alloys during an annealing process after electron irradiation were investigated via positron annihilation lifetime spectroscopy. The migration energies of monovacancies in these alloys were evaluated to be 0.93, 0.92, and 0.79 eV, respectively, which are comparable with or slightly smaller than that in pure Ni, one of the constituents metals that has the same face-centered cubic structure. On the other hand, the vacancy migration energies increase with the number of constituent elements, suggesting the possibility of shallow vacancy trapping by local chemical environments in the CrMnFeCoNi alloy. These results do not fully support the sluggish diffusion mechanism that has been proposed for high-entropy alloys.

Effects of Re on Vacancy Mobility in a Ni-Re System: An Atomistic Study

The performance of modern Ni-based superalloys depends critically on the kinetic transport of point defects around solutes such as rhenium. Here, we use atomistic calculations to study the diffusion of vacancy in the low-concentration limit, using the crystalline fcc-framework nickel as a model. On-the-fly kinetic Monte Carlo is combined with an efficient energy-valley search to find energies of saddle points, based on energetics from the embedded atom method. With this technique, we compute the local energy barriers to vacancy hopping, tracer diffusivities, and migration energies of the low-concentration limit of Ni-Re alloys. It was estimated that the computed diffusion rates are comparable to the reported rates. The presence of Re atoms affects the difference between the energy of the saddle point and the initial energy of point defect hopping. In pure Ni, this difference is about 1 eV, while at 9.66 mol% Re, the value is raised to about 1.5 eV. The vacancy migration energy of vacancy in the 9.66 mol % Re sample is raised above that of pure Ni. Our findings demonstrate that even in the low-concentration limit, Re solute atoms continue to play a crucial role in the mobility of the vacancies.

Enhanced recombination suppresses the void swelling in bcc multi-component alloys

Multi-component alloys, e.g., high-entropy alloys, exhibit excellent mechanical and radiation tolerance properties, making them potential candidate materials in nuclear applications. In this work, the void swelling in a single-phase body-centered cubic (bcc) reduced activation multi-component alloy FeCrV under high dose Au-ion irradiation was investigated. It is found that FeCrV has a significantly suppressed void swelling compared to α-Fe, with voids of smaller size distributed in a narrower region. To understand the difference between these two alloys in the defect evolution and its possible effect on the void swelling, the diffusion of point defects in α-Fe and FeCrV was investigated. Combined Density Functional Theory (DFT) and kinetic Monto Carlo (kMC) method based on the environment-dependent vacancy migration energies was used to simulate the vacancy diffusion. It is shown that vacancy diffusion is enhanced, which is because vacancies prefer to migrate through the easy migration channels which have lower values of the wide migration energy distribution in multi-component alloys. Ab initio molecular dynamics (AIMD) was employed to simulate the interstitial diffusion. The results show the interstitial diffusion is sluggish in FeCrV due to the atomic traps existing that slow down interstitials’ migration. The migration process of point defects in bcc multi-component alloy shows clear chemical environment dependence. The closer mobilities of vacancies and interstitials enhance the local recombination of point defects and suppress the void swelling.

Atomic-Scale Hidden Point-Defect Complexes Induce Ultrahigh-Irradiation Hardening in Tungsten.

Tungsten displays high strength in extreme temperature and radiation environments and is considered a promising plasma facing material for fusion nuclear reactors. Unlike other metals, it experiences substantial irradiation hardening, which limits service life and presents safety concerns. The origin of ultrahigh-irradiation hardening in tungsten cannot be well-explained by conventional strengthening theories. Here, we demonstrate that irradiation leads to near 3-fold increases in strength, while the usual defects that are generated only contribute less than one-third of the hardening. An analysis of the distribution of tagged atom-helium ions reveals that more than 87% of vacancies and helium atoms are unaccounted for. A large fraction of helium-vacancy complexes are frozen in the lattice due to high vacancy migration energies. Through a combination of in situ nanomechanical tests and atomistic calculations, we provide evidence that irradiation hardening mainly originates from high densities of atomic-scale hidden point-defect complexes.

Machine Learning Based Methodology to Predict Point Defect Energies in Multi-Principal Element Alloys

Multi-principal element alloys (MPEAs) are a new class of alloys that consist of many principal elements randomly distributed on a crystal lattice. The random presence of many elements lends large variations in the point defect formation and migration energies even within a given alloy composition. Compounded by the fact that there could be exponentially large number of MPEA compositions, there is a major computational challenge to capture complete point-defect energy phase-space in MPEAs. In this work, we present a machine learning based framework in which the point defect energies in MPEAs are predicted from a database of their constituent binary alloys. We demonstrate predictions of vacancy migration and formation energies in face centered cubic ternary, quaternary and quinary alloys in Ni-Fe-Cr-Co-Cu system. A key benefit of building this framework based on the database of binary alloys is that it enables defect-energy predictions in alloy compositions that may be unearthed in future. Furthermore, the methodology enables identifying the impact of a given alloying element on the defect energies thereby enabling design of alloys with tailored defect properties.

Defect dynamics and uniaxial tensile deformation of equi and non-equi-atomic configuration of multi-elemental alloys

In this article, molecular dynamics and statics-based simulations were carried out to study the effect of equi-atomic and non-equi-atomic compositions of multi-elemental alloys on defect dynamics and tensile deformation. High and medium entropy alloy configurations were subjected to uni-axial tensile loading, and deformation governing mechanism was identified with the help of dislocation extraction algorithm and common neighbour analysis. Due to low or negative stacking fault energy, phase transformation from FCC to HCP in conjunction with solid solution hardening was identified as the governing mechanism for the plastic deformation in most of the multi-elemental alloys. Atomistic snapshots of simulation box containing deformed configurations of medium and high entropy alloys also show heterogenous nucleation, pinning of dislocations, cross channelling of twin boundaries. It was predicted that in alloys with higher Cr content twinning and stacking fault is prominent mode of deformation. Nudged elastic band algorithm was used to predict the vacancy migration energies in each of the atomistic configurations. The results presented in the article are in qualitatively in agreement with the experimental results, and higher fidelity simulations helps in developing better understanding about the plastic deformation in equi and non-equi-atomic composition of multi-elemental alloys.

Mobility of point defects in CoCrFeNi-base high entropy alloys

The in-situ observation of microstructural evolution under electron irradiation was performed in order to experimentally estimate the mobility of vacancy and interstitial in 316 stainless steel and CoCrFeNi-base high entropy alloys. The vacancy migration energy in CoCrFeNiMn and CoCrFeNiAl0.3 was estimated to be lower and higher compared with that in 316 stainless steel, respectively. While, the interstitial migration energy in those alloys seems to be almost the same. The increase in vacancy migration energy in CoCrFeNiAl0.3 is probably due to a strong interaction between vacancy and Al. The positron annihilation analysis revealed that vacancies might exist close to Co and Ni atoms in CoCrFeNi-base high entropy alloys. In addition, vacancies could also be captured by Mn and Al atoms in CoCrFeNiMn and CoCrFeNiAl0.3, respectively. The electron- and ion-irradiation at 400 and 300 °C up to 1.5 dpa resulted in the precipitation of the intermetallic compounds, such as CoFe, NiFe in CoCrFeNiMn, and Ni3Al in CoCrFeNiAl0.3. From these results, it is suggested that Co, Ni, Mn, and Al atoms could affect the vacancy mobility in HEAs, leading to the delay of microstructural evolution and the enhancement of precipitation under irradiation.

Point defect mobility in hydrogen pre-implanted vanadium under electron irradiation

Mobility of point defect (vacancy and interstitial) is a critical factor for irradiation resistance of nuclear materials like vanadium. Hydrogen (H) atoms generated by nuclear transmutation can strongly affect the migration mechanism of point defect. Microstructural evolution and point defect behavior in vanadium with and without H-pre-implantation have been investigated by in-situ annealing and electron irradiation by using high voltage electron microscopy (HVEM). The migration energy of vacancies and the one of interstitials were calculated to be about 1.5 eV and 0.3 eV based on the growth speed and the number density of dislocation loops at 573–773 K, respectively. The surface effect of samples on measurement of migration energy and the interaction between hydrogen and point defect were also discussed.

Solubility and vacancy-mediated inter-diffusion in the Zr-Nb-Cr system

To better understand the microstructural evolution of Cr-coated Zr alloy cladding, we investigate, using density functional theory calculations, the vacancy-mediated diffusion behaviour of Zr and Nb solutes in BCC-Cr as well as Zr and Cr solutes in BCC-Nb. The calculated vacancy formation and migration energies are in good agreement with available literature, as are the self-diffusivities. We show that in BCC-Cr both Nb and Zr are faster diffusers than Cr (vacancy-mediated self-diffusion). It was also found that both Zr and Nb segregate towards vacancy sinks in BCC-Cr at normal reactor operating temperatures, but at elevated temperatures their flux is expected to be in opposite directions. In BCC-Nb, we show that Cr is a slower diffuser than Nb self-diffusion, while Zr is faster; and both Zr and Cr are expected to decorate vacancy sinks in BCC-Nb at all temperatures relevant to reactor operation. A similar behaviour is likely to occur in β-Nb phase found in Zr-Nb alloys. The implications of these findings for Cr-coated Zr alloy cladding are discussed.

Interactions between twin boundary and point defects in magnesium at low temperature

The interactions between a $$\left\{ {10\overline{1}2} \right\}$$ twin boundary and point defects including vacancies and self-interstitial atoms in magnesium were investigated by molecular dynamics simulations at low temperature. The simulation results suggest that vacancies have a softening effect on TB migration, while interstitials lead to a hardening effect. During the interactions, vacancies were observed to be not absorbed by the TB. In contrast, interstitials are able to be absorbed by TB and migrate on TB. Finally, those absorbed interstitials aggregate and form interstitial clusters, which are released from the TB. The migration energies of vacancy and interstitial are calculated through nudged elastic band method. The aforementioned observations can be well explained by the migration energies, where the energies of a vacancy in a bulk crystal and on TB are both two order in magnitude higher than those of an interstitial. The current work provides new insights into the irradiation effects in magnesium.

Lithium tracer diffusion in LiNi0.33Mn0.33Co0.33O2 cathode material for lithium-ion batteries.

The LiNi0.33Mn0.33Co0.33O2 compound is one of the most interesting cathode materials for Li-ion batteries. Li diffusion in this material directly influences charging/discharging times (and consequently power densities), maximum capacities, stress formation and possible side reactions. In the present study Li tracer self-diffusion is investigated in polycrystalline sintered bulk samples with an average grain size of about 50 nm in the temperature range between 110 and 350 °C. For analysis, stable 6Li tracers are used in combination with Secondary Ion Mass Spectrometry (SIMS). The diffusivities can be described by the Arrhenius law with an activation enthalpy of (0.85 ± 0.03) eV, which is interpreted as the migration energy of a single Li vacancy. Lithium diffuses via structural vacancies whose concentration is fixed by a Li deficiency of about 10%. An extrapolation of the diffusivities to room temperature gives significantly lower values than the diffusivities obtained by electrochemical measurements in literature.

Nucleation and growth mechanisms of γ’’ phase with single-unit-cell height in Mg-RE-Zn(Ag) series alloys: a first-principles study

The highly thermal stability precipitates strengthen creep resistance for alloys, which require precipitates to resist coarsen at elevated temperature. In the Mg-RE-Zn (Ag) series alloys, the key strengthening phase - γ’’ phase, remains its single-unit-cell height throughout aging process. The origin of such extremely thermal stability of γ’’ phase is still unclear. By using the first-principles calculations, it is found that the formation of γ’’ phase introduces compressive strain to its surrounding α-Mg lattice and simultaneously alter charge distribution of α-Mg lattice near the α-Mg/γ’’ hetero-interface. These two variations over α-Mg lattice lead to lower vacancy formation energies and migration energy barriers for solute atoms near the α-Mg/γ’’ hetero-interface in comparison with that of bulk condition. Consequently, the variations facilitate rapid diffusion of solute atoms near the γ’’ phase and promote nucleation rate of other γ’’ plates around it. On the basis of ledge-thickening model, the origin of nucleation/growth of γ’’ phase with single-unit-cell height was explained. Thermodynamically and kinetically, the solute atoms are not apt to migrate into the nearest basal plane adjacent to the γ’’ phase. Moreover, the lower aging temperature (∼200 °C) and almost completely coherent α-Mg/γ’’ hetero-interface lead to the ledges are extremely hard to nucleate on the hetero-interface. Therefore, γ’’ plates maintain single-unit-cell height throughout aging process.

In situ transmission electron microscopy study of the formation and migration of vacancy defects in atomically thin black phosphorus

Structural defects play an important role in the optimization of material structures and properties, especially in low-dimensional systems such as two-dimensional (2D) materials. In this work, we investigated the formation, aggregation, and diffusion of vacancy defects in atomically thin black phosphorus (BP) via in situ high-resolution transmission electron microscopy. Vacancy defects including di-vacancies (DVs), vacancy clusters (e.g. tetra-vacancy and TV), and vacancy lines were confirmed as the primary forms of structural defects in BP. DV and TV defects were found to be highly mobile. The defects preferentially diffused and migrated along the diagonal and in a zigzag pattern (rather than an armchair pattern). After prolonged thermal excitation and electron-beam irradiation, all these as-formed vacancies tended to aggregate and line up parallel to the zigzag pattern direction to form extended vacancy lines with a total length reaching hundreds of nanometers or even the micrometer scale. Ab initio calculations were conducted to reveal the vacancy migration pathway, energy landscape, and modifications to the electronic structure of the host BP monolayers (MLs). It was found that the migration of a 5-8-5 DV was accomplished via sequential structural transformations including several transitions and intermediate configurations, such as 5-7-7-5 DVs. The associated migration barriers were determined as 2.1 eV for diagonal migration and 2.6 eV along the zigzag path, respectively. Calculations further confirmed that the presence of vacancy defects induced considerable electronic structure modification of the host ML-BP; for example, the bandgap was reduced from 0.9 eV (for defect-free ML-BP) to 0.7 eV in the presence of vacancy lines with a concentration of 1.2 at.%. The present study expands the current understanding of the formation and dynamic behaviors of primary vacancy defects and illustrates methods available to alter the electronic structures of 2D BP materials. It can further serve as a guideline for the function-oriented design and fabrication of BP-based devices via precisely controlled defect engineering.

Rate Theory Model of Irradiation-Induced Solute Clustering in b.c.c. Fe-Based Alloys

Solute nanoclusters are critical to the structural and mechanical integrity of numerous alloys based on the b.c.c. Fe matrix, which have risen to prominence as candidates for advanced nuclear reactor applications. Because irradiation can profoundly alter the morphology and composition of these solute nanoclusters, it is critical to understand and predict solute clustering behavior in the presence of irradiation. In this study, we advance a simple theory to model irradiation-induced nanocluster evolution subject to different irradiating particles. The model is trained and validated with experimental data following an approach similar to training a machine learning algorithm, resulting in an agile model that can be used for rapid screening of new alloys. Using the model, nanocluster evolution is found to depend upon the disordering parameter (i.e., cluster morphology and dose rate) and irradiation temperature, and is most sensitive to the solute migration, vacancy formation, and vacancy migration energies. Results are discussed with respect to the irradiation temperature shift for varying irradiating particle types and dose rates.

Statistical study of vacancy diffusion in TiC and TaC

Density functional theory (DFT) simulations, Metropolis Monte Carlo (MMC), and kinetic Monte Carlo (kMC) simulations were performed to understand the mechanisms of mass diffusion in a group IVB transition metal carbide, TiC, and a group VB transition metal carbide, TaC. The DFT calculations were used to obtain the vacancy formation energy and migration energy of a variety of microstates for off-stoichiometric TiC and TaC. MMC simulations, based on our DFT results, were used to determine the ensemble average of the metal vacancy formation energy and determine the average size metal-vacancy clusters present in these materials. kMC simulations were used to determine the ensemble average of the migration energy barrier as well as understand how the vacancies in these materials, on average, migrate. These collective results show that metal vacancy migration in TiC and TaC are quite different, where Ti vacancies should be surrounded by four to five carbon vacancies whereas, on average, tantalum vacancies are surrounded by one or zero carbon vacancies. However, the carbon vacancies substantially contribute to metal vacancy diffusion in both these materials, as the metal vacancy statistically will have a carbon vacancy near it before and after migration. From these results, we find that the activation energy of metal vacancy diffusion is 7.66 eV in ${\mathrm{Ti}}_{0.995}{\mathrm{C}}_{0.97}$ and 6.41 eV in ${\mathrm{Ta}}_{0.995}{\mathrm{C}}_{0.97}$, which agrees reasonably well with experimentally reported activation energies. These results give further insights into the mechanisms associated with mass diffusion within the transition metal carbide families, an important insight needed to better elucidate high temperature diffusional creep responses which is often difficult to assess experimentally.

Effect of C on the formation of Cu precipitates and vacancy clusters in neutron-irradiated Fe–Cu alloys

Two types of Fe–Cu binary alloys: Fe-0.15Cu and Fe-0.3Cu with and without 0.25 wt% C were irradiated with fission neutrons at damages ranging from 4 × 10−6 to 0.16 dpa at 573 K. The effect of C on the formation of Cu precipitates and vacancy clusters in the alloys was investigated. The addition of C delayed the formation of vacancy clusters in both the alloys. This is because the addition of C increased the migration energy of vacancies, i.e., decreased the migration of vacancies. However, C did not affect the growth of microvoids. Although the effect of C on the formation of Cu precipitates depended on the irradiation dose, the effect was insignificant at high irradiation doses.

Defect properties in a VTaCrW equiatomic high entropy alloy (HEA) with the body centered cubic (bcc) structure

We report first-principles results of the point defect properties in a V-Ta-Cr-W high-entropy alloy (HEA) with the body-centered cubic (bcc) structure. Different from the widely-investigated face-centered cubic (fcc) HEAs, the local lattice distortion is more pronounced in bcc ones, which has a strong influence on the defect properties and defect evolution under irradiation. Due to the large size of Ta, the exchange between vacancies and Ta exhibits lower energy barriers. On the other hand, interstitial dumbbells containing V and Cr possess lower formation energies. These defect energetics predicts an enrichment of V and Cr and a depletion of Ta and W in the vicinity of defect sinks. Besides, we find that interstitial dumbbells favor the [110] orientation in the HEA, instead of [111] direction in most nonmagnetic bcc metals, which helps to slow down interstitial diffusion significantly. Consequently, the distribution of migration energies for vacancies and interstitials exhibit much larger overlap regions in the bcc HEA compared to fcc HEAs, leading to the good irradiation resistance by enhancing defect recombination. Our results suggest that HEAs with the bcc structure may bear excellent irradiation tolerance due to the particular defect properties.

Mechanisms behind the spontaneous growth of Tin whiskers on the Ti2SnC ceramics

The spontaneous growth of Tin whiskers has been a reliability issue in electronic assemblies for around 70 years, but the underlying physics is still ambiguous. Herein, Sn whiskers formed on the Ti2SnC, a layered ternary carbide ceramic MAX phase, were studied to trace the atomic motion in whisker growth process. Free Sn source was found to be necessary for the formation of Sn whiskers, however, the interface microstructure suggests that Sn atoms feeding whiskers are diffusing through the Ti2SnC lattice. According to the simulation results on the formation and migration energies of vacancies in Ti2SnC, a low diffusion barrier is expected for Sn atoms to diffuse along the basal planes. When Sn atoms diffuse out of the substrate, Sn whiskers bounded by low-energy planes form to minimize the total energy. In contrast, the whiskers maintain the striated morphology inherited from the whisker root in the environment containing oxygen, which is mainly attributed to the confinement of the oxide film on whisker surface. The findings will also shed new light on understanding the general whiskering problems found in other materials.

The origin of the exceptionally low activation energy of oxygen vacancy in tantalum pentoxide based resistive memory

It is well known that collective migrations of oxygen vacancies in oxide is the key principle of resistance change in oxide-based resistive memory (OxRAM). The practical usefulness of OxRAM mainly arises from the fact that these oxygen vacancy migrations take place at relatively low operating voltages. The activation energy of oxygen vacancy migration, which can be inferred from the operational voltage of an OxRAM, is much smaller compared to the experimentally measured activation energy of oxygen, and the underlying mechanism of the discrepancy has not been highlighted yet. We ask this fundamental question in this paper for tantalum oxide which is one of the most commonly employed oxides in OxRAMs and try the theoretical answer based on the first-principles calculations. From the results, it is proven that the exceptionally large mobility of oxygen vacancy expected by the switching model can be well explained by the exceptionally low activation barrier of positively charged oxygen vacancy within the two-dimensional substructure.