Vacancy Sinks Research Articles

Simulation of interdiffusion and voids growth based on cellular automata

Abstract In the interdiffusion of two solid-state materials, if the diffusion coefficients of the two materials are not the same, the interface of the two materials will shift to the material with the lower diffusion coefficient. This effect is known as the Kirkendall effect. The Kirkendall effect leads to Kirkendall porosity. The pores act as sinks for vacancies and become voids. In this paper, the movement of the Kirkendall plane at interdiffusion is simulated based on cellular automata. The number of vacancies, the critical radius of voids nucleation and the nucleation rate are analysed. The vacancies diffusion, vacancies aggregation and voids growth are also simulated based on cellular automata.

Atomistic simulations of screw dislocations in bcc tungsten: From core structures and static properties to interaction with vacancies

Atomistic simulations have been used to investigate the core structures, static properties of isolated 1/2 <111> screw dislocations, and their interaction with vacancies in bcc tungsten (W) based on three empirical interatomic potentials. Differential displacement maps show that only one embedded atom method potential is able to reproduce the compact non-degenerate core as evidenced by ab initio calculations. The obtained strain energy and stress distribution from atomistic simulations are, in general, consistent with elasticity theory predictions. In particular, one component of the calculated shear stress, which is not present according to elasticity theory, is non-negligible in the core region of our dislocation model. The differences between the results calculated from three interatomic potentials are in details, such as the specific value and the symmetry, but the trend of spatial distributions of static properties in the long range are close to each other. By calculating the binding energies between the dislocations and vacancies, we demonstrate that the dislocations act as vacancy sinks, which may be important for the nucleation and growth of hydrogen bubbles in W under irradiation.

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the extended defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.

Energetics of point defect interacting with bi-crystal Σ3 copper grain boundaries

Point defects interacting with grain boundary (GB) may shed light on point defect sink strength of GB. In this work, vacancy and self-interstitial atom (SIA) formation energies within 25 Σ3 〈110〉 copper grain boundaries (GBs) were calculated using embedded atom method (EAM) potential. The energetics of point defects interacting with these GBs was analyzed. It is found that the lowest vacancy formation energies in 25 Σ3 GBs in general decrease with increasing their inclination angles with respect to Σ3 coherent twin GB (CTB). Lowest SIA formation energies in 25 Σ3 GBs except CTB, however, shows an increasing trend. The lowest vacancy within Σ3 GBs correlates well with average GB energy, but not so for SIA formation energies. Moreover, overall trend of the correlation between lowest vacancy formation energies and GB energies for Σ3 GBs and other ten GBs with Σ ranging from 5 to 13 shows a remarkable decreasing trend, but not obvious for SIA. Void denuded zone (VDZ) widths of GBs that can be used to evaluate the vacancy sink strength of them, correlates with lowest vacancy formation energies as well as average energies of GBs at their equilibrated states.

Amorphous intergranular films act as ultra-efficient point defect sinks during collision cascades

Atomistic simulations are used to explore the effect of interfacial structure on residual radiation damage. Specifically, an ordered grain boundary is compared to a disordered amorphous intergranular film, to investigate how interface thickness and free volume impacts point defect recombination. Collision cascades are simulated and residual point defect populations are analyzed as a function of boundary type and primary knock on atom energy. While ordered grain boundaries easily absorb interstitials, these interfaces are inefficient vacancy sinks. Alternatively, amorphous intergranular films act as ultra-efficient, unbiased defect sinks, providing a path for the creation of radiation-tolerant materials.

The voids kinetics during diffusion process

In this paper it is shown that the small voids, cracks or inclusions may act as sinks for vacancies or sources for interstitial atoms if the density is very close to equilibrium by numerical simulations. The two dimensional model is presented based on the generalized Darken concept. The void radius is estimated and compared with experimental results in Fe–Pd and β-NiAl–Cu systems. During the studies the following question arises: where is the most favorable place of the void formation. This question will be discussed.

Stress, deformation and diffusion interactions in solids – A simulation study

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain–stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.

Stoichiometry effect on the irradiation response in the microstructure of zirconium carbides

Zone-refined ultra high pure ZrC with five C/Zr ratios ranging from 0.84 to 1.17 was irradiated using a 2MeV proton beam at 1125°C. The stoichiometry effect on the irradiation response of ZrC microstructure was examined using transmission electron microscopy following the irradiation. The irradiated microstructures generally feature a high density of perfect dislocation loops particularly at away from the graphite precipitates, and the C/Zr ratio shows a notable effect on the size and density of dislocation loops. The dislocation loops are identified as interstitial type perfect loops, and it was indirectly proved that the dislocation loop core likely consists of carbon atoms. Graphite precipitates that form with excess carbon in the super-stoichiometric ZrC are detrimental, and the dramatic increases in the size of and density of dislocation loops in the vicinity of graphite precipitates in ZrC phase were observed. Irradiation-induced faceted voids were only observed in ZrC0.95, which is attributed to the pre-existing dislocation lines as biased sinks for vacancies.

Effect of Surface and Grain Boundary on the Reversion of Al-Zn Alloys

Age-hardening of Al-Zn alloy after quenching develops inhomogeneously due to the effect of surface as a vacancy sink and grain boundary as an easy path. In this study, reversion of the age-hardened Al-Zn alloys, in which ellipsoidal GP zones were formed, was investigated by Vickers micro-hardness test. Ellipsoidal GP zones were reverted more quickly near the surface and grain boundary than in the interior, as spherical GP zones in Al-10%alloy did. It is considered that the surface and grain boundary plays a role of effective source for vacancies, in addition to the interior source such as dislocations, as in the case of the reversion of spherical GP zones.

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.

Irreversible thermodynamics of creep in crystalline solids

We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-hydrostatically stressed multi-component solid medium with non-conserved lattice sites and inhomogeneities handled by employing gradient thermodynamics. Phase fields describe microstructure evolution which gives rise to redistribution of vacancy sinks and sources in the material during the creep process. We derive a general expression for the entropy production rate and use it to identify of the relevant fluxes and driving forces and to formulate phenomenological relations among them taking into account symmetry properties of the material. As a simple application, we analyze a one-dimensional model of a bicrystal in which the grain boundary acts as a sink and source of vacancies. The kinetic equations of the model describe a creep deformation process accompanied by grain boundary migration and relative rigid translations of the grains. They also demonstrate the effect of grain boundary migration induced by a vacancy concentration gradient across the boundary.

An energetic and kinetic perspective of the grain-boundary role in healing radiation damage in tungsten

Radiation-induced damage in tungsten (W) and W alloys has been considered as one of the most important issues in fusion research, because radiation-produced defects not only degrade the mechanical property but also change the behaviours of H and He in W significantly, such as the retention of H. Nano-structured W has been developed to reduce accumulation of defects within grains and further mitigate radiation-induced damage. However, the fundamental role of a grain boundary (GB) in healing radiation damage in W is not yet well understood. Using molecular dynamics and statics, we evaluate energetically and kinetically the role of a GB in defect evolution (vacancy and interstitial segregation and their annihilation) near the GB in W, by calculating the vacancy (interstitial) formation energy, segregation energy, diffusion barrier, vacancy–interstitial annihilation barrier near the GB and the corresponding influence range of the GB. We find that, as reported and expected, interstitials are preferentially trapped into GBs over vacancies during irradiation, with vacancies dominant near the GB and interstitials highly localized at the GB. On the one hand, the GB serves as a sink both for vacancies and interstitials near itself by reducing their formation energy and diffusion barrier. The formation energy of the vacancy decreases only by ∼0.86 eV, but 7.5 eV is reduced for the formation energy of the interstitial in the GB core, indicating that the sink is unexpectedly stronger for interstitials than vacancies. The average barrier of vacancy diffusion is 0.98 eV much less than 1.8 eV in the bulk; the interstitial migrates into the GB via a barrier-free process. On the other hand, the GB acts as a catalyst for the vacancy–interstitial recombination at the GB by lowering the annihilation barrier. The annihilation with the average barrier as low as 0.31 eV works even at a low temperature of 121 K; besides, the annihilation of a close vacancy–interstitial pair is spontaneous. Meanwhile, the annihilation mechanism near the GB is modified due to the exceptionally large reduction in the interstitial formation energy. The influence range of the GB is small (1–1.5 nm), leading to a small volume fraction of the GB region working as the sink and the catalyst. This indicates that GBs in fine W grains may play a limited role in improving radiation performance.

Irradiation damage of single crystal, coarse-grained, and nanograined copper under helium bombardment at 450 °C

Abstract

The influence of Cu–Nb interfaces on local vacancy concentrations in Cu

The sink strength of Cu–Nb interfaces was investigated by measuring the steady-state vacancy concentration profile adjacent to Cu–Nb interfaces during 1.8 MeV Kr + irradiation. Broadening of dilute nanoscale Au tracer layers in Cu quantified position-dependent values for radiation-enhanced diffusivity and, accordingly, vacancy concentration. The measured vacancy profile corresponds to results calculated from a steady-state kinetic rate equation that assumes perfect sink efficiency at the Cu–Nb interface, indicating that it behaves like an ideal sink for vacancies in Cu.

A popular metastable omega phase in body-centered cubic steels

Steel remains to be one of the most common structural materials in the world as human civilization advances from the Iron Age to the ongoing Silicon Age. Our knowledge of its microstructure evolution and structure–performance relationship is nevertheless still incomplete. We report the observation and characterization of a long ignored metastable phase formed in steels with body-centered cubic (bcc) structure using both transmission electron microscopy and density functional theory calculations. This ω phase has a hexagonal structure and coherent interface with the matrix: aω = √2 × abcc and cω = √3/2 × abcc. It is 3.6% smaller in volume and 0.18 eV higher in energy than bcc-Fe, with atoms in alternating close- and loose-packed layers couple anti-ferromagnetically. Carbon plays a crucial role in promoting bcc to ω transformation. At a concentration higher than 4 at.% they tend to segregate from the bcc matrix to the ω-phase; at about 14 at.%, they can induce bcc to ω transformation; and finally at 25 at.%, they stabilize the ω phase as ω-Fe3C. The ω phase in bcc Fe can serve as sinks for vacancies, H, and He atoms, leading to improved resistance of martensitic steels to irradiation damage.

Eliminate Kirkendall voids in solder reactions on nanotwinned copper

Electroplating was used to fabricate a high density of nanotwins that exhibited the preferred (1 1 1) orientation in Cu. We found no formation of Kirkendall voids in solder reactions on the nanotwinned Cu. This was due to the high density of steps and kinks on the nanotwin boundaries, which serve as vacancy sinks. Thus the vacancy concentration cannot reach supersaturation and nucleate voids. The finding is a significant advance in the problem of solder joint reliability in microelectronic three-dimensional integrated circuit devices.

Modelling of fission gas release from irradiated UO2 fuel under high-temperature annealing conditions

The new model for the vacancy field evolution in grains during annealing of irradiated fuel was developed and implemented in the MFPR code. The model simulates time and spatial variation of the vacancy concentration in the presence of extended vacancy sources (grain boundaries and dislocations) and sinks (growing intragranular bubbles). Being combined with the models for dislocation creep and for bubbles biased migration in the vacancy gradient, the new model self-consistently describes the processes of gas release and microstructure evolution observed in the annealing tests.

Atomic structure variations of mechanically stable fcc-bcc interfaces

It has recently been shown that under severe plastic deformation processing bi-metal fcc/bcc composites develop a mechanically stable heterophase interface that joins the {112}fcc//{112}bcc planes in the Kurdjumov-Sachs orientation relationship. In this article, we study variations in the relaxed equilibrium atomic structure of this interface with changes in fcc stacking fault energy (SFE) and lattice mismatch between the two crystals. Using molecular statics/dynamics simulations for three fcc/bcc systems, Cu-Nb, Al-Fe, and Al-Nb, we find that the number of distinct sets of intrinsic interfacial dislocations and their core structures vary significantly among these three systems. The impact of these atomic-scale structural differences on interfacial properties is demonstrated through their interactions with point defects. The interfaces studied here are shown to exhibit a wide variation in ability, ranging from being a poor to an excellent sink for vacancies.

Inhibition of Electromigration in Eutectic SnBi Solder Interconnect by Plastic Prestraining

Plastic prestraining was applied to a solder interconnect to introduce internal defects such as dislocations in order to investigate the interaction of dislocations with electromigration damage. Above a critical prestrain, Bi interfacial segregation to the anode, a clear indication of electromigration damage in SnBi solder interconnect, was effectively prevented. Such an inhibiting effect is apparently contrary to the common notion that dislocations often act as fast diffusion paths. It is suggested that the dislocations introduced by plastic prestraining acted as sinks for vacancies in the early stage of the electromigration process, but as the vacancies accumulated at the dislocations, climb of those dislocations prompted recovery of the deformed samples under current stressing, greatly decreasing the density of dislocation and vacancy in the solder, leading to slower diffusion of Bi atoms.

Effect of deformation-induced vacancies on diffusion properties of nonequilibrium grain boundaries

The kinetics of variation of the diffusion properties of nonequilibrium grain boundaries (GBs) related to the absorption of vacancies generated in the course of plastic deformation of a material has been studied. It is demonstrated that the sink of the deformation-induced vacancies to GBs can increase the GB diffusion coefficient by one to two orders of magnitude. An approximate analytical expression is obtained that describes the dependence of the coefficient of diffusion along nonequilibrium GBs on the strain rate and value of strain.