Absorption Of Vacancies Research Articles

Modelling of Vacancy Diffusion and Pore Formation during Parabolic Oxide Growth

Vacancy diffusion and the possibility of pore formation during oxide growth by cation diffusion are investigated. For a parabolic time dependence of the oxide thickness growth, the evolution of the vacancy concentration in the metal is analysed by taking into account the annihilation of vacancies at sinks located at the oxide–metal interface and within the metal. By omitting vacancy absorption at growing vacancy agglomerates, upper estimates of the vacancy supersaturation are calculated, from which the nucleation and growth rates of pores are derived. The nucleation rate strongly decreases with increasing oxidation time and temperature whereas the growth rate increases with increasing temperature. The analysis suggests that the appearance of pores is crucially controlled by the strength of vacancy sinks at the oxide–metal interface and by the presence of impurities lowering the surface energy by impurity segregation to the metal surface of vacancy clusters. Possible flaws of the approach which are related to the assumption of parabolic oxide growth are discussed.

Diffusional attractions between voids on a Si(111)7×7 surface

Ostwald ripening or coarsening is a term which describes the growth of large domains at the expanse of small ones in the final stages of any phase separation process. Several theories were developed in order to explain this process. All of them are based on the Lifshitz, Slyozov, and Wagner (LSW) model which predicts an increase in the average radius of domains r̄(t)∝t1/3 and a reduction of the number density of domains as a function of time N(t)∝t−1. The LSW model assumes static and circular domains, which are distributed at random. These assumptions were found to be incorrect by many experiments. And more advanced theories were necessary to explain these observations. In our work, we study the coarsening of voids formed in a Si(111)7×7 surface covered by 0.8 bilayers (BL). Besides the expected increase in the diameter of voids and the decrease in the number density, very strong attractions and rapid motion of voids towards each other were clearly observed. The result of the attraction between the voids is coagulation of voids and an increase in the spatial correlations between voids, as the coarsening process progresses, as we indeed observed. This is contradictory to the “ideal gas” picture which is the basis of the LSW model. Basically, this can be explained by a concentration gradient which develops between two voids of different size and the growth of voids in the direction of the larger concentration. However, this model cannot explain the large diffusional motions observed in our experiments. It is proposed that an amplification mechanism exists, whereby the arrival of a diffusing vacancy to the boundary of the void causes the release of several adatoms from the boundary. This process causes a much larger motion than expected by a single vacancy absorption. This picture, which is consistent with the structure of the steps, demonstrates how the microscopic details might have a significant affect on the global coarsening process.

Vacancy clustering to faulted loop, stacking fault tetrahedron and void in fcc metals

An atomistic step of growth to a faulted loop, a stacking fault tetrahedron (sft) and a void by clustering of vacancies in fcc metals was studied by molecular dynamics computer simulation with an isotropic EAM potential due to Daw and Baskes [1]. In aluminum, a tri-vacancy relaxes to the Damask-Dienes-Weizer structure (3v-sft). A penta-vacancy relaxes to an octahedral 6v in which an atom is included. The relaxed 5v is stable so that a 6v grows to doubly linked relaxed 5v. This is a critical step of faulted loop formation. By further absorption of vacancy, a cluster grows to an array of relaxed 5vs on a (111) plane and finally collapses to a faulted loop. In gold, a stable structure of vacancy cluster below 15v is a void. A tri-vacancy in gold does not relax to the Damask-Dienes-Weizer structure. Above the size of 6v, partial relaxation of 3v-sft type was observed. The relaxation of a micro-void to a sft is the thermal activated process. In nickel, a void is the most stable cluster below 20v and a sft is the most stable structure above the size of 20v. In Ni, a micro-void grows to a large void due to the difficulty of relaxation to a sft. Vacancies in Ag grow to a sft in the similar way as vacancy clustering in Au.

A computational study of dislocation evolution and radiation-induced segregation at a grain boundary

Radiation-induced segregation (RIS) influences the chemical and mechanical properties of the structural materials of fusion and fission reactors. In this study, such RIS and dislocation sink strength evolution were investigated on the basis of computer simulation for solute segregation at and near a grain boundary. A new continuity equation model for RIS, based on the rate theory, which includes the simultaneous evolution of faulted dislocation loops and network dislocations, has been developed. A di-interstitial was assumed to be the nucleus of a dislocation loop in the present work, and we calculated dislocation evolution due to absorption of interstitials and vacancies. The dependencies of irradiation temperature, irradiation rate and dose on the RIS at a grain boundary under electron irradiation in high-voltage electron microscope (HVEM) were clarified. We also considered the effect of probe size used in TEM-EDS analysis in order to satisfy the relationship with measured compositional profiles. The present work sheds a light on the accomplishment of performing ‘combined calculation’ which deals with both RIS and various kinds of internal sink evolution.

A small-angle neutron scattering and transmission electron microscopy study of krypton precipitates in copper

The annealing behaviour of bulk copper containing 2.6 at.% krypton has been studied by small-angle neutron scattering (SANS) and transmission electron microscopy (TEM). In addition positron annihilation spectroscopy (PAS) and mass-density measurements (MDM) were made. In the as-prepared and annealed material a high density of krypton precipitates (`bubbles') exists. Special emphasis is put on different approaches to the analysis of the SANS data. Differences between the results from the various analyses are pointed out and discussed. Polydisperse models clearly give the most extensive information, i.e. the size distribution of the Kr bubbles and integral parameters derived from it (i.e. bubble volume, total surface area and average radius). It is demonstrated that a correct choice of form factor is important for the reliability of the derived size distribution. In TEM a high degree of overlap of bubble images is observed and corrected for. Good agreement between the shapes of SANS and TEM size distributions is found, while differences in amplitude are ascribed to experimental uncertainties. Average krypton densities in the bubbles as well as fractional cavity volumes derived from PAS and MDM are found to be in good agreement, but the cavity volumes are clearly larger than the total bubble volumes obtained from the SANS and TEM size distributions. Above roughly bubble growth takes place. Two different mechanisms for the initiation of growth are discussed. At the higher annealing temperatures the growth in bubble size and total volume fraction is explained by bubble migration and coalescence followed by absorption of thermal vacancies.

On the symmetry of denuded zones in diffusional creep

Recently, Wolfenstine and coworkers have published a paper in which they attempted to refute the relationship between denuded zones and diffusional creep. Many of their arguments have been commented on by other authors, but one of them has not been analyzed satisfactorily yet. Wolfenstine et al. have noted, that denuded zones are frequently observed on the one side of grain boundary, and they consider the fact to be in contradiction with the diffusional creep theory, Diffusional creep is considered to consist in three processes--the emission and absorption of vacancies in grain boundaries, diffusion of them between grain boundaries with various normal stress and grain boundary sliding as an accommodation process. The original Nabarro-Herring and Coble theories are completely independent of the processes in grain boundaries, because they assume the processes are easy in comparison with diffusion. On the other hand, the creation of denuded zones is the result of the emission of vacancies and depends on the details of that process. In the present paper it is argued that the asymmetrical occurrence of denuded zones is fully compatible with the theory of diffusional creep.

Thermal oxidation of CuInSe 2: Experiment and physico-chemical model

The thermal oxidation of CuInSe 2 single crystals and bulk polycrystalline plates of n- and p-type conductivity with polished facets have been carried out at elevated temperatures of 400 to 610°C in dry oxygen/air atmosphere. All crystals demonstrated an enhancement in hole conductivity near the surface. Additionally, transparent layers of In 2O 3 chemical composition grew on the surface. Electron-probe analysis, Rutherford backscattering, X-ray diffraction, and optical and photoelectric experimental data have provided a basis to develop a physico-chemical model for the thermal oxidation of CuInSe 2 crystals. The model includes the In 2O 3 compound appearance, V Se, V Cu vacancy absorption, Se i, Cu i extra atom and Cu x Se generation. The chemical reactions are accompanied by arising dislocations and mechanical stresses at the In 2O 3/CuInSe 2 interface.

Grain shape effects on interface-controlled diffusional creep under multiaxial stresses

Interface control of the emission and absorption of vacancies reduces, but does not eliminate, the dependency of diffusional creep on grain size and shape and it increases the sensitivity to stress. Previous analyses of interfacially controlled diffusional creep of polycrystals with equiaxed grains under a uniaxial stress are extended and further developed to determine approximately the behaviour of material with anisotropic grain shapes under multiaxial stresses. Whilst all details of this creep process are not fully understood, it is shown that, by noting a set of conditions to be fulfilled, the form of equation required to describe anisotropic creep strength can be identified. Although interfacial control implies a power law dependance on stress, it is noted that the directionality in creep deformation is governed by grain shape orientation and by linear functions of the applied stresses and so anisotropic aspects of creep response under multiaxial stresses can be described by “creep compliance coefficients” analogous to those representing anisotropic elastic behaviour. Since anisotropy is influenced by three parameters, representing the principal orthogonal grain dimensions, only three of these coefficients are independent. From this approach a Von Mises type function can be formulated through which anisotropic interface-controlled diffusional creep strength may be evaluated.

Role of Al2O3 particulate reinforcements on precipitation in 2014 Al-matrix composites

Precipitation in commercial aluminum alloy 2014, without and with alumina particulate reinforcements, was studied using microhardness, electrical resistivity, differential scanning calorimetry (DSC), and transmission electron microscopy. The precipitation sequence in 2014 Al was confirmed to be αss→α + GPZ →α + λ’→a + λ’ + gH→α + λ (AlCuMgSi) + θ (CuAl2). Reinforcement addition decreased the time to peak hardness, but also reduced the peak matrix microhardness. This was traced to a decrease in the amount of λ’ formed in the composites. Further, it was observed that while Guinier-Preston (GP) zone and θ’ formations are accelerated in the composites, λ’ precipitation is decelerated. The acceleration is attributable primarily to enhanced nucleation resulting from an increase in the matrix dislocation density due to coefficient of thermal expansion (CTE) mismatch between the matrix and the reinforcements, whereas the deceleration is associated with a decrease of low-temperature solute diffusivity due to absorption of vacancies at dislocations and interfaces. It was also observed that the degree of overall acceleration in hardening and the reduction in peak matrix microhardness with reinforcement addition decreased with decreasing aging temperatures. The causal relationships of these observations with the associated mechanisms are discussed.

Saturation of radiation strengthening in copper irradiated with high-energy heavy ions

Yield strength variations in Cu due to irradiation with high-energy 11B, 20Ne and 40Ar ion beams are discussed. Based on the high mobility of small interstitial clusters it is supposed that immobile clusters with an appropriate size are “mobilized” due to vacancy absorption, providing an additional source of interstitials. The solution of the rate equations is given. It is shown that if the loss of migrating defects at lattice sinks can be neglected then the variation of the overall numbers of interstitials and vacancies forming clusters is given by identical differential equations.

Atomistics of void formation in irradiated copper

Computer simulations of molecular dynamics and molecular statics are carried out to study the atomistics of void formation in irradiated copper. The isotropic many-body potential of the embedded atom method due to Daw and Baskes [5] is implemented. It is found that a relaxation of tri-vacancy to the Damask-Dienes type of stacking fault tetrahedron (3v-sft) is an important step for the formation of sft. In a 3v-sft, an atom inside a tetrahedral 4v moves with large amplitude at low frequency. To form a void in irradiated copper, gaseous atoms such as hydrogen and helium have to be included in a vacancy cluster. Hydrogen atoms are introduced in the present work. Gaseous atoms suppress the 3v-sft type of relaxation. The structure of hexa-vacancy fluctuates between a sft and a void. A hydrogen atom trapped in a hexa-vacancy preserves the structure of a void. In order to grow such a microvoid to a large void, several hydrogen atoms have to be included in a microvoid. A 8v-void which traps only singly hydrogen atom grows to sft by further absorption of vacancies, while it grows to a void when two hydrogen atoms are trapped. A sft of nine-vacancy which is composed by the mixture of a 6v-sft and 3v-sfts converts to a void when four hydrogen atoms come to the cluster. For the case of the formation of a tetrahedral 10v-void in the core of a displacement damage cascade, the vacancy cluster itself is stable. By absorbing vacancies, it grows to a large sft in which the 10v-void is still included. Even when only one hydrogen atom is trapped in vacancy clusters which grow from the 10v-void and whose size is below the 17-vacancy, it relaxes to avoid. Trapped hydrogen atoms move on the surface of a void and suppress the relaxation of sft. When hydrogen atoms come to a sft which grows from the 10v-void and whose size is larger than the 18-vacancy, it does not relax to a void. It is concluded that the critical step of void nucleation is in the range of six to fifteen vacancies in the presence of gaseous atoms. The preferential formation of voids along dislocation lines, which is observed in irradiated metals, is due to the existence of a high concentration of trapped gaseous atoms along dislocation lines.

Precipitate strain relief via point defect interaction: models for SiO 2 in silicon

Precipitation in the solid state is often accompanied by a volume mismatch, creating strain which inhibits precipitation. For the SiO 2 Si system, this strain, if unrelieved, is large enough to prevent precipitation altogether. The strain is usually assumed to be relieved via emission or absorption of point defects. Here, we suggest a model in which only one species of point defect is involved and the emission/absorption relieves the strain only partially. We generate a Gibbs free energy equation in two variables and by monitoring the atom movements during precipitation, are able to derive two relationships: an expression for the critical radius and, more importantly, a direct correlation between strain and point defect supersaturations. We use this approach to study three systems: SiO 2 strain relief via interstitial emission, vacancy absorption and carbon absorption. Finally, the importance of the strain/supersaturation relationship is emphasized by noting its impact upon nucleation rates. Even small point defect supersaturations can eliminate nucleation and must therefore be considered carefully in studies of precipitation.

Calorimetric absorption spectroscopy and photoluminescence study of defects in diamond

Defects in diamond, both plasma-assisted chemical vapor deposition grown polycrystalline and electron-irradiated type IIa natural diamond, were studied using calorimetric absorption spectroscopy and photoluminescence. Calorimetric absorption spectroscopy is a highly sensitive low temperature technique which measures the non-radiative recombination component of a given optical absorption. For the first time calorimetric absorption spectroscopy has been used to investigate a wide band gap crystalline material, namely diamond. The radiative efficiency of the 1.68 and 1.639 eV absorption in plasma assisted chemical vapor deposition diamond grown on silicon and the 1.673 eV absorption in electron irradiated natural diamond have been studied using a combination of calorimetric absorption spectroscopy and photoluminescence measurements. The radiative efficiency of the 1.68 eV absorption is found to be much greater than that of the 1.639 eV absorption. Also, the 1.673 eV neutral vacancy absorption in irradiated bulk diamond is seen to have a highly non-radiative recombination character.

Fluctuation effect of point defect reaction on nucleation of interstitial clusters during neutron irradiation

Effects of stochastic fluctuation of point defect reaction on the destination of small interstitial clusters were discussed. Nuclei of interstitial clusters are known to be formed directly from cascade collisions during neutron irradiation. However, the number of experimentally observed interstitial clusters is always much less than the number of cascade collisions in all the materials observed. Success fraction of interstitial cluster nuclei for growth was less than 1/10 in thin foil irradiated samples and less than 1/1000 in bulk irradiated samples, even in the atmosphere of excess free interstitials. These results cannot be explained by rate theory, and stochastic fluctuation of the absorption of free vacancies and interstitials is expected to be playing the major role. The repetition of the shrinkage and growth can make most of the small interstitial clusters produced by cascade collision shrink to zero size.

Thermal release behavior of helium implanted into nickel

The thermal release behavior of helium implanted into nickel with 20 keV He + ions at fluences ranging from 1 × 10 17 to 5× 10 17 ions/cm 2 has been studied. The number of helium release peaks increased and the temperature at which the release began became lower with increasing fluence. The surfaces of nickel samples heated after ion implantation were also examined. The release peaks were associated with distinct surface damage features such as holes and blisters. The release peak at high temperatures appeared to be controlled by the thermal vacancy absorption of bubbles. The release peaks at lower temperatures was attributable to the interbubble fracture associated with helium precipitation into bubbles.

The Influence of Grain Boundary Structure on Strain-Induced Grain Growth During Superplastic Deformation

ABSTRACTA model is presented to explain the grain growth that is often observed during superplastic deformation. The atomic structure of grain boundaries leads to a coupling between boundary sliding and boundary migration. There is a similar coupling between the absorption or emission of vacancies from a boundary and boundary migration. Because of these couplings, the grain boundary sliding and diffusional flow of superplastic deformation produce extensive boundary migration. We propose that this forced migration leads to random changes in the sizes of grains, and that this evolution of the grain size distribution leads to grain growth.

Theoretical modelling of solute segregation to a free surface in irradiated dilute alloys

Abstract In recent years, segregation to a variety of sinks has been observed in a wide range of alloys during irradiation. There have also been a number of theoretical calculations of the segregation to free surfaces in both dilute and concentrated alloys. In this paper, we show that the boundary conditions used have a strong effect on the calculated solute concentration profiles. In most calculations the free surface is assumed to be an ideal sink for vacancies and interstitials, and the calculated solute concentration profiles are very steep close to the free surface. In this paper, we examine the physically more realistic case of rate-limitation boundary conditions for the absorption of vacancies and interstitials at the free surface and show that this reduces considerably the solute concentration gradients close to the surface. We also discuss the implications of this behaviour for the modelling of experimental results of solute segregation.

Determination of the bias factor by the moments solution to the Fokker-Planck equation

An important parameter in the rate theory of swelling is the dislocation loop bias factor, Z 1 j , which is a measure of the rate of interstitial atom absorption relative to vacancy absorption at interstitial loops. The Fokker-Planck (F-P) equation is used to describe interstitial loop evolution, with a kinetic nucleation current boundary condition at di-interstitial atomic clusters. The majority of loop nucleation is shown to be finished after one milli-dpa, which allows the shape of the loop distribution function to be governed mainly by the drift ( F ) and dispersion ( D ) functions in the F-P equation. Since collision cascades contribute significantly to D , their effects must be suppressed by using low-energy ions or high-energy electrons to produce spatially homogeneous atomic displacements. Under these conditions, both F and D are shown to be proportional to the square root of the number of atoms in a loop. The proportionality parameters depend on material and irradiation conditions, and are linearly proportional to Z 1 j . The ratio F D , which resembles the Peclet number in fluid flow, can be used in a unique way to determine Z 1 j without the usual complications of uncertainties in material and irradiation conditions. This is shown to constitute an internal variable measurement of the bias factor.

Absorption of Frenkel' defects at dislocations and strength of dislocational sink. Model determination of absorption zone

Analysis shows that the channel of accelerated vacancy migration in the dislocation core is surrounded by a broader region of vacancy absorption. The positions of dislocations close to the axis and steps at these dislocations from which intrinsic interstitial atoms perform spontaneous transition toward the point of their disappearance have been found. Close to the step, the same positions have been found for vacancies. However, spontaneous transition is often only one of the stages of the multistep process leading to defect absorption. Only when the contribution of all the paths of defect transfer to the point at which its disappearance is possible and all the stages on each of these paths are taken jointly into account can the size and shape of the absorption zone be estimated. These problems will be studied further, since they are keys to estimating the strength of the dislocational sink.

Stress Induced Anisotropic Diffusion of Intrinsic Point Defects towards Dislocations in H.C.P. Crystals

AbstractThe diffusion equations for vacancies and interstitials in the field of straight edge dislocations are numerically solved for a crystal under irradiation and uniaxially stress. The main dislocation systems in hexagonal closed packed metals are considered. The diffusion model takes into account the full lattice and defect symmetry in the equilibrium and migration configurations. A diffusivity tensor for strained h.c.p. metals is deduced, which depends linearly on the strain field. This tensor allows to solve analytically the steady state defect flux towards a hollow cylinder in a homogeneously strained crystal. The resulting vacancy and interstitial absorption (sink strength) are calculated and compared with the ones obtained numerically when the dislocation field is taken into account. It is shown that both approaches result in a similar dependence of the sink strengths on the homogeneous strain as far as a correct capture radius is adopted for the hollow cylinder. The dependence of the results on the boundary conditions and the defect symmetry considered is discussed. For the numerical calculations defect symmetries consistent with those calculated for magnesium are used.