Vacancy Binding Energy Research Articles

Helium effects on microstructural change in RAFM steel under irradiation: Reaction rate theory modeling

Reaction rate theory analysis has been conducted to investigate helium effects on the formation kinetics of interstitial type dislocation loops (I-loops) and helium bubbles in reduced-activation-ferritic/martensitic steel during irradiation, by focusing on the nucleation and growth processes of the defect clusters. The rate theory model employs the size and chemical composition dependence of thermal dissociation of point defects from defect clusters. In the calculations, the temperature and the production rate of Frenkel pairs are fixed to be T=723K and PV=10−6dpa/s, respectively. And then, only the production rate of helium atoms was changed into the following three cases: PHe=0, 10−7 and 10−5appmHe/s. The calculation results show that helium effect on I-loop formation quite differs from that on bubble formation. As to I-loops, the loop formation hardly depends on the existence of helium, where the number density of I-loops is almost the same for the three cases of PHe. This is because helium atoms trapped in vacancies are easily emitted into the matrix due to the recombination between the vacancies and SIAs, which induces no pronounced increase or decrease of vacancies and SIAs in the matrix, leading to no remarkable impact on the I-loop nucleation. On the other hand, the bubble formation depends much on the existence of helium, in which the number density of bubbles for PHe=10−7 and 10−5appmHe/s is much higher than that for PHe=0. This is because helium atoms trapped in a bubble increase the vacancy binding energy, and suppress the vacancy dissociation from the bubble, resulting in a promotion of the bubble nucleation. And then, the helium effect on the promotion of bubble nucleation is very strong, even the number of helium atoms in a bubble is not so large.

Controlling diffusion for a self-healing radiation tolerant nanostructured ferritic alloy

Diffusion plays a major role in the stability of microstructures to extreme conditions of high temperature and high doses of irradiation. In nanostructured ferritic alloys, first principle calculations indicate that the binding energy of vacancies is reduced by the presence of oxygen, titanium and yttrium atoms. Therefore, the number of free vacancies available for diffusion can be greatly reduced. The mechanical properties of these alloys, compared to traditional wrought alloys of similar composition and grain structure, is distinctly different, and the ultrafine grained alloy is distinguished by a high number density of Ti–Y–O-enriched nanoclusters and solute clusters, which drives the mechanical response. When a displacement cascade interacts with a nanocluster, the solute atoms are locally dispersed into the matrix by ballistic collisions, but immediately a new nanocluster reforms due to the local supersaturation of solutes and vacancies until the excess vacancies are consumed. The result of these processes is a structural material for advanced energy systems with a microstructure that is self-healing and tolerant to high doses of radiation and high temperatures.

He–vacancy interaction and multiple He trapping in small void of silicon carbide

In fusion environment, large amounts of helium (He) atoms are produced by transmutation along with structural damage in the structural materials, causing material swelling and degrading of physical properties. To understand the microscopic mechanism of He trapping in vacancies and voids, we explored He–vacancy interactions in HenVam (Va for vacancy) clusters (n, m=1–4) and multiple He trapping in a 7-atom void of silicon carbide (SiC) by first-principles calculations. The binding energy between He and the HenVam clusters increases with the number of vacancies, while the vacancy binding energy gradually increases with the number of He atoms. Furthermore, a small cavity of about 0.55nm in diameter can accommodate up to 14 He atoms energetically and the corresponding internal pressure is estimated to be 2.5GPa. The tendency of He trapping in small voids provides an explanation for the experimentally observed He bubble formation at vacancy defects in SiC materials.

Positron studies of interaction between yttrium atoms and vacancies in bcc iron with relevance for ODS nanoparticles formation

The very high calculated binding energy of vacancy (V)–Ysub (1.45eV) in Fe makes it be one possible earliest formation stage of (Y, Ti, O) nanoclusters in ODS alloy. Our direct slow positrons annihilation observations are used to valid the interaction between V and Y. The pure bcc iron samples have been implanted by 1.2MeV Y ions at three fluences from 1×1014 to 3×1015cm−2. Vacancy clusters are observed for all these three fluences. Their size and concentration decrease with Y concentration measured by using SIMS. Two hypotheses are proposed to explain the results, including the formation of complexes Vm–Yn and/or of precipitates Ym–Xn (X=Y, O, etc.). In addition, vacancy clusters are detected deeper than predicted by SRIM calculation due to, at least for a part, channelling which is confirmed by Marlowe calculation and SIMS measurements.

A Simulation Study of Oxygen-Vacancy Behavior in Strontium Titanate: Beyond Nearest-Neighbor Interactions

We investigate the effect of acceptor-dopant cations on oxygen-vacancy migration in the perovskite oxide SrTiO3 by static lattice simulation techniques. We focus on two themes: dopant cations modifying the activation energies for vacancy migration, and dopant cations binding oxygen vacancies in binary associates. In both cases a variety of defect configurations exceeding the scope of first nearest neighbor (1NN) interaction is examined, i.e. 1NN, 2NN, 3NN, 4NN, and 5NN. The behavior of four divalent dopants (Ni2+, Fe2+, Co2+, and Mn2+) and one trivalent dopant (Al3+) is compared. The simulations predict that the binding energy of an oxygen vacancy to any of these dopants is negative at 1NN sites, but only converges to zero for 4NN sites. In addition the simulations show that the migration energy of a vacancy is affected by an acceptor-dopant cation over a length scale of several unit cells. A simple analytical model is used, together with the calculated site and activation energies, to predict how in gene...

Initial precipitation and hardening mechanism during non-isothermal aging in an Al–Mg–Si–Cu 6005A alloy

The characterization of precipitation and hardening mechanism during non-isothermal aging had been investigated using high resolution transmission electron microscopy for an Al–Mg–Si–Cu 6005A alloy. It was proposed that the needle-shaped β″ precipitates with a three-dimension coherency strain-field and an increased number density in the Al matrix provided the maximum strengthening effect for the Al–Mg–Si–Cu 6005A alloy. Simultaneously, it was also found that the formation and evolution of clusters in the early precipitation were associated with the vacancy binding energy, during which Si atoms played an important role in controlling the numbers density of Mg/Si co-clusters, and the excess Si atoms provided the increased number of nucleation sites for the subsequent precipitates to strengthen and improve the precipitation rate. Finally, based on the experimental observation and theoretical analysis, the precipitation sequence during the early precipitation in the Al–Mg–Si–Cu 6005A alloy was proposed as: supersaturated solid solution→Si-vacancy pairs, Mg-vacancy pairs and Mg clusters→Si clusters, and dissolution of Mg clusters→Mg atoms diffusion into the existing Si clusters→Mg/Si co-clusters→GP zone.

Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries

Material strengthening and embrittlement are controlled by intrinsic interactions between defects, such as grain boundaries (GBs), and impurity atoms that alter the observed deformation and failure mechanisms in metals. In this work, we explore the role of atomistic-scale energetics on liquid-metal embrittlement of aluminum (Al) due to gallium (Ga). Ab initio and molecular mechanics were employed to probe the formation/binding energies of vacancies and segregation energies of Ga for 〈100〉, 〈110〉 and 〈111〉 symmetric tilt grain boundaries (STGBs) in Al. We found that the GB local arrangements and resulting structural units have a significant influence on the magnitude of the vacancy binding energies. For example, the mean vacancy binding energies for 〈100〉, 〈110〉 and 〈111〉 STGBs in the 1st layer was found to be −0.63, −0.26 and −0.60eV, respectively. However, some GBs exhibited vacancy binding energies closer to bulk values, indicating interfaces with zero sink strength, i.e. these GBs may not provide effective pathways for vacancy diffusion. The results from the present work showed that the GB structure and the associated free volume also play significant roles in Ga segregation and the subsequent embrittlement of Al. The Ga mean segregation energies for 〈100〉, 〈110〉 and 〈111〉 STGBs in the 1st layer were found to be −0.21, −0.09 and −0.21 eV, respectively, suggesting a stronger correlation between the GB structural unit, its free volume and the segregation behavior. Furthermore, as the GB free volume increased, the difference in segregation energies between the 1st layer and the 0th layer increased. Thus, the GB character and free volume provide an important key to understanding the degree of anisotropy in various systems. The overall characteristic Ga absorption length scale was found to be about ∼10, 8 and 12 layers for 〈100〉, 〈110〉 and 〈111〉 STGBs, respectively. In addition, a few GBs of different tilt axes with relatively high segregation energies (between 0 and −0.1eV) at the boundary were also found. This finding provides a new atomistic perspective for the GB engineering of materials with smart GB networks to mitigate or control liquid-metal embrittlement and more general embrittlement phenomena in alloys.

Interactions of solute (3p, 4p, 5p and 6p) with solute, vacancy and divacancy in bcc Fe

Solute–vacancy binding energy is a key quantity in understanding solute diffusion kinetics and phase segregation, and may help choice of alloy compositions for future material design. However, the binding energy of solute with vacancy is notoriously difficult to measure and largely unknown in bcc Fe. With first-principles method, we systemically calculate the binding energies of solute (3p, 4p, 5p and 6p alloying solutes are included) with vacancy, divacancy and solute in bcc Fe. The binding energy of Si with vacancy in the present work is in good consistent with experimental value available. All the solutes considered are able to form stable solute–vacancy, solute–divacancy complexes, and the binding strength of solute–divacancy is about two times larger than that of solute–vacancy. Most solutes could not form stable solute–solute complexes except S, Se, In and Tl. The factors controlling the binding energies are analyzed at last.

First-principles study of solute–vacancy binding in Cu

Solute–vacancy binding is a key quantity in understanding diffusion kinetics, and may also have a considerable impact on the hardening response in Cu alloys. However, the binding energies between solute atoms and vacancies in Cu are largely unknown and difficult to measure accurately. A large database of solute–vacancy binding energies in Cu from first-principles calculations based on density functional theory was presented in the paper. The trends in the binding energies in terms of super cell size, solutes size and magnetic moments are analyzed. The calculated binding energies agree well with experimental measurements available.

First-principles study of 4d solute diffusion in nickel

Diffusion of the 4d transition elements in Ni has been investigated within the five-frequency model framework using migration energy barriers calculated from the first principles. Agreement with counterintuitive experimental/calculated data is observed; atoms in the middle of 4d row have the smallest atomic radii while exhibiting the lowest diffusivity as compared to larger atoms at the beginning and the end of 4d row. We show that 4d solute diffusion is controlled mainly by the size misfit. The larger atoms have higher solute–vacancy binding energies and lower migration barriers. Both were shown to correlate with a displacement of the equilibrium solute position toward the adjacent vacancy. The difference in mechanisms controlling sp- and transition elements diffusion rates in Ni is discussed.

On the mechanism of sulfur fast diffusion in 3-D transition metals

The origin of abnormally fast diffusion of sulfur in face-centered cubic (fcc) nickel was investigated within an ab initio band structure calculation approach. A vacancy-mediated model of substitutional impurity diffusion with first-principles calculated parameters was used to determine the diffusion coefficients of S and Al impurities in fcc Ni. The sulfur diffusion coefficient was found to be two orders of magnitude higher than that of aluminum, in good agreement with experimental data. We demonstrate that ultrafast diffusivity of sulfur arises from its chemical interaction with the Ni matrix. The valence electron transfer from Ni3d–Ni3d bonds to sulfur softens the Ni–Ni bonding. That increases the sulfur–vacancy exchange rate, the sulfur–vacancy binding energy and the rotation rate of vacancy around sulfur. The latter is shown to be the key factor that governs S diffusion. We also discuss the impact of Ni–Ni bond softening on the mechanical properties of Ni.

Impact of segregation energetics on oxygen conductivity at ionic grain boundaries

In pursuit of whether nanocrystallinity could lead to higher anion conductivity, research has revealed contradicting results exposing the limited understanding of point defect energetics at grain boundaries (GBs)/interfaces. By disentangling and addressing key GB energetics issues related to segregation, migration and binding energies of oxygen vacancies in the presence and absence of dopants at the GBs, as well as the segregation energetics of dopants, we use atomistic simulations of doped nanocrystalline ceria to elucidate that dopant segregation is the key factor leading to degradation of oxygen conductivity in nanocrystalline materials. A framework for designing enhanced conducting nanocrystalline materials is proposed where the focus of doping strategies shifts from the bulk to segregation at GBs.

Energetics of vacancy segregation to symmetric tilt grain boundaries in hexagonal closed pack materials

Molecular static simulations of 190 symmetric tilt grain boundaries in hexagonal closed pack metals were used to understand the energetics of vacancy segregation, which is important for designing stable interfaces in harsh environments. Simulation results show that the local arrangements of grain boundaries and the resulting structural units have a significant influence on the magnitude of vacancy binding energies, and the site-to-site variation within each boundary is substantial. Comparing the vacancy binding energies for each site in different c/a ratio materials shows that the binding energy increases significantly with an increase in c/a ratio. For example, in the [12¯10] tilt axis, Ti and Zr with c/a = 1.5811 have a lower vacancy binding energy than the Mg with c/a = 1.6299. Furthermore, when the grain boundary energies of all 190 boundaries in all three elements are plotted against the vacancy binding energies of the same boundaries, a highly negative correlation (r = −0.7144) is revealed that has a linear fit with a proportionality constant of −25 Å2. This is significant for applications where extreme environmental damage generates lattice defects and grain boundaries act as sinks for both vacancies and interstitial atoms.

Monovacancy in copper: Trapping efficiency for hydrogen and oxygen impurities

The structure and binding energy of vacancy–impurity complexes in copper are studied using first-principles calculations based on density functional theory. A single vacancy is found to be able to trap up to six hydrogen atoms which tend to be situated inside the vacancy at off-center positions (related to the octahedral interstitial positions of the ideal fcc lattice). The binding energy of an H atom dissolved in the Cu lattice (octahedral interstitial position) to a vacancy is calculated to be about 0.24eV, practically independent of the number of H atoms already trapped by the vacancy, up to the saturation with 6 hydrogens. For an oxygen impurity in Cu, a monovacancy is shown to be a deep trap (with a binding energy of 0.95eV). The position of a trapped O atom inside a vacancy is off-center, almost a half-way from the nearest octahedral interstitial to the vacancy center. Such a vacancy–O cluster is shown to be a deep trap for dissolved hydrogen (the calculated binding energy is 1.23eV). The trapping results in the formation of an OH-group, where the H atom is situated near the vacancy center, and the O atom is displaced from the center along a 〈100〉 direction towards a nearby octahedral interstitial position. Further hydrogenation of the monovacancy–OH cluster is calculated to be energetically unfavourable. McNabb–Forster’s equations are generalised to describe the competition between a deep hydrogen trap and a shallow one. It is demonstrated that the deep trap is almost fully filled, which explains why some of hydrogen is strongly bound and cannot be removed without vacuum treatment at elevated temperatures.

Diffusion of Co, Ru and Re in Ni-based superalloys: A first-principles study

Self and impurity diffusivities in Ni-based superalloys have been investigated by first-principles calculations within five-frequency model. The vacancy formation energy, migration energy, correlation factor, solute–vacancy binding enthalpies and entropies in vacancy-mediated diffusions have been considered. The positive solute–vacancy binding energies for Co, Ru and Re indicated that the solute–vacancy pair is not a favorable binding. From the electronic point of view, the origination of the repulsive interaction between solute and vacancy has been comprehensibly expatiated on, which possibly accounts for the low diffusivity of Re element. The calculated self and impurity diffusion coefficients show a good consistent with the reported data from experiments and it is found that the trend in diffusivity is DCo>DNi-self>DRu>DRe.

Electromigration in Dual-Damascene CuMn Alloy IC Interconnects

Electromigration reliability of Cu interconnects is an important issue for continued performance improvement of IC technologies. In this paper, we investigate the impact of Mn impurities on the electromigration drift velocity of Cu conductors. Under accelerated test conditions, the drift velocity in CuMn alloys is reduced by an order of magnitude compared with pure Cu with polycrystalline microstructure. Dilute CuMn alloys exhibit a large activation energy for drift of 1.05 eV, which is significantly increased above that for pure Cu as a result of a 0.2 eV impurity(Mn)-vacancy binding energy. There is no measurable impact of the presence of the Mn dopant on diffusion along the Cu/dielectric cap interface in the samples studied here.

Stabilizing nanocrystalline grains in ceramic-oxides

Nanocrystalline ceramic-oxides are prone to grain growth rendering their highly attractive properties practically unusable. Using atomistic simulations of ceria as a model material system, we elucidate a framework to design dopant-pinned grain boundaries that prevent this grain growth. While in metallic systems it has been shown that a large mismatch between host and dopant atomic sizes prevents grain growth, in ceramic-oxides we find that this concept is not applicable. Instead, we find that dopant-oxygen vacancy interaction, i.e., dopant migration energy in the presence of an oxygen vacancy, and dopant-oxygen vacancy binding energy are the controlling factors in grain growth. Our prediction agrees with and explains previous experimental observations.

Activation energetics of actinide diffusion in UO2 from first-principles calculations

Diffusion of actinides in uranium dioxide plays an important role in determining thermodynamic and mechanic properties of the material. Activation energies of Th, U, Np, and Pu diffusion in uranium dioxide were systematically studied using first-principles calculations. The generalized gradient approximation and projector-augmented wave methods with on-site Coulomb repulsive interaction were applied within Density Functional Theory and Plane Wave framework. Two diffusion paths, one along the lattice 〈110〉 direction and the other along the lattice 〈100〉 direction, were examined in the face-centered cubic UO2 structure. The results show that the 〈110〉 path has lower migration energy than the 〈100〉 path. Under the assumption of a vacancy-assisted jump diffusion mechanism, the major contribution to the activation energy is the migration energy, followed by the vacancy formation energy and vacancy binding energy, where the last has the lowest contribution. However, differences in the activation energies among different actinides stem from both the migration and vacancy binding energies, both of which decrease with atomic number. While discrepancies between the absolute values of the calculated and experimentally observed activation energies remain, this study shows a correlation between activation energy and atomic number and an asymptotic relation between activation energy and ionic radius of the actinides. The present study suggests that the migration of the actinides through the uranium dioxide lattice is closely correlated to the number of 5f electrons and the size of the diffusing atoms.

Interatomic potentials for simulation of He bubble formation in W

A new interatomic pair potential for W–He is described, which includes a short range modification to the Ackland–Thetford tungsten potential. Molecular dynamics simulations using these potentials accurately reproduce ab initio results of the formation energies and ground state positions of He point defects and self interstitial atoms in W. Simulations of larger He–vacancy clusters with up to 20 vacancies and 120 He atoms show strong binding of both He and vacancies to He–vacancy clusters for all cluster sizes. For small clusters, the qualitative agreement with ab initio results is good, although the vacancy binding energy is overestimated by the interatomic potential.

Solute–vacancy binding of the rare earths in magnesium from first principles

The thermodynamic and kinetic properties of Mg–rare earth (RE) alloys are not widely known, despite increased research in recent years into their mechanical strengthening mechanisms. To aid in the development of new alloys and strengthening models, the solute–vacancy binding energies for all 17 RE elements in hexagonal close-packed (hcp) Mg are calculated by density functional theory (DFT) in several solute/vacancy configurations. As the REs can be considerably larger than Mg, special care is taken to ensure convergence with respect to supercell size, and the binding of other large, non-RE solutes is calculated in the large supercells employed in the current work. It is found that the light and heavy lanthanides have favorable and unfavorable nearest-neighbor solute–vacancy binding, respectively. The binding energies exhibit a strong linear correlation to the magnitude of the solute’s displacement towards the vacancy, suggesting that local lattice relaxation is a significant contribution to the binding energy. There are four notable exceptions to this trend: Na, Sb, Pb and Bi. Explicit calculation of the lattice relaxation energy due to the presence of the solute–vacancy pair confirms that local relaxation is an important component of the binding energy, particularly for the larger solutes. Finally, empirical predictions of the dilute mixing energy disagree with those predicted by DFT. New experimental measurements are necessary to resolve the discrepancies, as there are no published thermodynamic data of the REs in hcp Mg.