Vacancy Flow Research Articles

Kinetics of coloration of anodic electrochromic films of WO3·H2O

Polycrystalline layers of WO3·H2O are obtained by anodization of tungsten in 1 N H2SO4 at 70° C. The cathodic reduction of these layers in acid solutions causes the formation of blue WO3−x·H2O (0<x⩽:0.12) oxides. The kinetics of coloration are investigated by galvanostatic and potentiostatic techniques. The experimental results are compared with the theoretical data obtained by solving the diffusion equation for a constant flow of oxygen vacancies and for a time-dependent surface vacancy concentration. Except in the initial stage of coloration, the process controlling rate can be ascribed to the diffusion of oxygen vacancies from the oxide-electrolyte interface into the bulk of the layers. At low vacancy concentration, a barrier-limited proton transfer across the oxide-electrolyte interface seems to determine the kinetics of coloration.

A simple operational gas release and swelling model: II. Grain boundary gas

The model described in this paper is intended for use in fuel behaviour codes and extends work given in an earlier paper to include the behaviour of fission gas on grain boundaries. The model includes: a description of the configuration of porosity on the grain faces and edges, both before and after interlinkage; a rate theory treatment of the flow of vacancies between the grain faces and the various types of porosity; a treatment of the distribution of fission gas between the grain faces and edges; and the interlinkage of both types of pores, leading to the release of gas from the fuel. In addition to reproducing experimentally measured gas release and swelling well, the model allows a quantitative understanding of the observation of interlinked face porosity in large-grained material and the dominance of the growth of edge porosity in small-grained material.

The Climbing Motion of Faulted Dislocation Loops Induced by Elastic Interaction

The movement of faulted dislocation loops during annealing has been studied with transmission electron microscopy using the usual stereotechnique. It is revealed that the distance between two nearby faulted dislocation loops in a thin foil varies during annealing at 95°C for 2 hours without their sizes changing. This variation in distance is considered to occur by pipe diffusion due to the elastic interaction between the loops. The vacancy concentration and the vacancy flow along the perimeter of the loops are calculated by considering the interaction force between their segments. It is shown that the vacancy flow that moves loops exists when the distance between loops is less than 200 Å. The activation energy for pipe diffusion is estimated to be about 0.90 eV.

Void swelling and irradiation-induced void shrinkage in neutron irradiated molybdenum and TZM

Molybdenum and TZM samples have been neutron-irradiated in the Dounreay Fast Reactor to doses up to 8 × 10 26n/m 2 ( E > 0.1 MeV) and at temperatures between 450 and 900°C. This paper presents and discusses the results of a transmission electron microscope study of the void parameters in the irradiated samples. In general, these parameters were not too dependent on either purity or irradiation temperature. Results showing the effects of dose were rather limited but at 450°C sufficient evidence was obtained to show convincingly that in both molybdenum and TZM the usual void growth processes were being replaced during the irradiation by a mechanism tending to produce void shrinkage. The shrinkage process is discussed in terms of the segregation of a transmutation impurity, possibly technetium, to the void surface where its accumulation gradually inhibits the flow of vacancies into the voids.

Interdiffusion and Kirkendall Effect in Cu&amp;ndash;Sn Alloys

Interdiffusion coefficients in copper-rich copper-tin solid solutions containing up to 6 at% of Sn have been determined by Matano’s analysis in the temperature range between 973 and 1101 K using semi-infinite couples with Kirkendall markers consisting of pure copper and Cu–Sn alloys. An anomalously large Kirkendall effect reported by several authors has been shown to be an overestimation resulting from the disregard for the large difference in partial molar volumes between Cu and Sn in the alloy. Using the data on the interdiffusion coefficient, the marker shift, the partial molar volumes and Darken’s relation, the intrinsic diffusion coefficients, DSn, and DCu, in the Cu-alloys containing 0.9, 1.7, 3.1 and 4.9 at% of Sn have been determined, and the ratio of DSn⁄DCu has been found to be about three. In addition to the above experiments with semi-infinite couples, the intrinsic diffusion coefficients in the Cu-alloys containing 0.6, 1.4, 2.6 and 3.5 at% of Sn at 1089 K have been determined by Heumann’s method using finite thin plate couples. Using the tracer diffusion data in pure Cu and the value of DCu in the infinite dilution of Sn evaluated from the detailed concentration dependence of DCu thus obtained, the vacancy flow factor which is expressed by the ratio of the phenomenological coefficients of flux equations in the infinite dilution of Sn, (LCuSn⁄LSnSn)NSn=0, at 1014 and 1089 K, has been estimated to be −1.06−0.24+0.18 and −0.84−0.13+0.12, respectively. Such a negative large ratio suggests that the jump between a tin atom and a vacancy in copper is strongly correlated.

転位への原子空孔消滅の計算機シミュレーション

The computer simulation of vacancy annihilation to dislocations has been made by the Monte Carlo method to interpret the annealing kinetics of vacancies in deformed gold, which is described by the Harper form as C=C0exp(−K·tm), where C is the vacancy concentration, t is time, K and m are constants, as reported in the preceding paper. Three factors most important for the kinetics have been taken into account in the calculation; (a) vacancy flow due to the concentration gradient, (b) vacancy flow due to the gradient of the vacancy-dislocation interaction (elastic) potential, and (c) sink efficiency of dislocation. In the simulation, the sink efficiency has been treated in such a way that a vacancy at a nearest-neighbour site of dislocation must overcome an energy barrier ΔE on annihilation. The results are summarized as follows:(1) In the case where dislocation acts as a perfect sink (ΔE=0), the value of exponent m in the early stage of annealing indeed ranges from 0.55 to 0.69, depending on the dislocation density, in accord with the experiment, but in the later stage approaches 1.0 in marked contrast to the experiment. The similar tendency is found even when the interaction potential is assumed to be ten times as large as the theoretically reasonable value. The present results, therefore, do not support the Harper’s analysis that the value of m is uniquely defined by the form of the vacancy-dislocation interaction potential.(2) When a fixed sink efficiency (ΔE=const.>0) of dislocation is assumed, bearing in mind the extended dislocation, the obtained value of m becomes much higher than the experimental value, increasing with the increase in the energy barrier ΔE.(3) A variable sink efficiency model has been found to be most appropriate, in which the energy barrier ΔE is assumed to increase with the degree of bowing-out of dislocation as a function of the number of vacancies absorbed. The exponent m in this case varies with the dislocation density in a similar way as the experimental results; for the low dislocation density the whole process of annealing can be described by a single value of m, while for the high dislocation density the annealing process consists of two stages, i.e., the early stage with the exponent m′=0.7 and the later stage with the exponent m=0.5.

A kinetic model for solute redistribution to sinks and void growth in irradiated dilute alloys

During irradiation of dilute alloys redistribution of solute elements from solution to the vicinity of point defect sinks can take place. This process can modify defect capture efficiencies of sinks, provided it occurs at an adequate rate and is accompanied by changes in defect diffusivities and/or transfer velocities across the sink-matrix interface. We consider a rate theoretical model for void growth, in which solute redistribution is driven by interstitial and vacancy flow to sinks. Application of the model to several mechanisms, triggered by solute redistribution, reveals conditions under which void growth will be hindered. Finally, the model is used to discuss some problems associated with correlations of void growth in cases of charged particle and neutron irradiations.

Radiation enhanced outdiffusion during ion implantation

For a systematic prediction of the radiation-enhanced outdiffusion occurring during implantation, the use of a model based on the effect of vacancy flow on diffusion is described. The model agrees reasonably well with experiments in all twentysix measured cases. For the systematic understanding of the radiation enhanced outdiffusion, an approximative diagram based on the activation energy of self-diffusion is constructed for all pure elements and its application possibilities are discussed.

Thermomigration of Scandium in Aluminum

The redistribution of scandium in polycrystalline A1-0.04 at ppm Sc dilute alloy which was annealed under a temperature gradient was investigated by means of the neutron activation analysis. The remarkable result is that the concentration of scandium increased at both the hot and the cold sides of specimen. Such a distribution is caused by a movement of scandium toward the both ends through the specimen. The movement of scandium toward the cold end is explained qualitatively in terms of the scandium flow associated with vacancy flow. It is pointed out that such an induced solute flow plays an important role on the thermomigration in substitutional alloys, and that the vacancy distribution under a temperature gradient should be investigated quantitatively to establish a well understanding of thermomigration in substitutional alloys.

Plutonia particle behavior during the sintering of mixed oxide fuels

The phenomenon of cavity formation during sintering of mixed oxide fuel in a reducing atmosphere was investigated experimentally and theoretically. Sintering in Ar-8% H 2 at 1675°C for 8 h was found to produce cavities in the center or at the periphery of the PuO 2 particles. After considering (and rejecting) several possible mechanisms, a model based upon nucleation and growth of water bubbles at or in the PuO 2 particles during hydrogen reduction was developed and shown to qualitatively account for the observations: water bubbles develop because of the low permeability of this species in the oxide and bubble growth arises from vacancy flow (creep) from the matrix in response to the excess water vapor pressure inside the bubble.

Intrinsic diffusion and vacancy flow effects in vanadium-titanium alloys

Intrinsic diffusion coefficients and vacancy flow parameters have been determined in the vanadium-titanium system from 900 to 1500°C. The experimental results reflect a greater influence of the vacancy flow phenomenon on the intrinsic flux of each species than that predicted on the basis of the random alloy model. The principal assumptions of the random alloy model are that a single vacancy mechanism is the operative diffusion mechanism and that all diffusing species find themselves in random environments with the absence of preferred sites for either atoms or vacancies. Solvent diffusivity enhancement calculations have been performed, however, and suggest that existence of two compcting, vacancy mechanisms in this system. The observed discrepancies between theoretical and experimental values are examined in light of the occurrence of a combined monovacancy-divacancy mechanism. In addition, other nonrandom effects are discussed which result in violations of the random alloy model assumptions and which lead to differences between theoretical and experimental quantities.

Defect flow induced outdiffusion in the Al → Zn implantations

Abstract Concentration profiles of the 100 keV Al → Zn implantations have been measured using the (p, γ) resonance broadening method. The profiles were studied as a function of concentration and implantation dose rate. Strong radiation-enhanced outdiffusion was observed during the room temperature implantations, which can be explained as the effect of vacancy flow on diffusion.

Graduates in demand

The high level of demand for graduates in the job market in 1977 has surprised even the careers advisers in Britain's universitiesand polytechnics. The flow of vacancies in the summer of 1977 for people graduating was 'probably the strongest for three years'.

On the mass dependence of the energy factor ΔK of the isotope effect for impurity diffusion in copper

AbstractUsing diffusion and isotope effect measurements of Au and Co in Cu a lower limit of the correlation factor of impurity diffusion as well as the corresponding limits of the kinetic energy factor ΔK are calculated from Manning's jump frequency model of vacancies near impurity atoms. The results show that a variation in impurity mass by a factor of three does not change ΔK for impurity diffusion significantly. For Au and Co in Cu ΔK is found to be about the same as for self‐diffusion in copper. This result allows to estimate the jump frequency ratios and the corresponding vacancy flow factors.

Dislocation networks in phosphorus-implanted silicon

Abstract Observations, by transmission electron microscopy have been made on defects generated in 50 keV, high-dose (1 × 1015 to 3 × 1016 ions/em2) phosphorus-implanted silicon (111) wafers followed by 1100°C isothermal annealing in inert (dry N2) and oxidizing (wet O2) atmospheres. The formation of dislocation networks is closely associated with the generation of interstitial type dislocation loops which grow from point defects produced by ion implantation in silicon wafers. Also, dislocations grow more easily in wet O2 annealing than in dry N2. In wet O2 annealing, dislocation networks are formed by annealing within 1–2 min for samples implanted with doses above 3 × 1015 ions/cm2, and they move to deeper depths in the wafers during annealing. On the other hand, in dry N2 annealing, the critical ion dose for generation of dislocation networks is 1 × 1016 ions/cm2 and the location of dislocation networks in the wafers is usually unchanged during annealing. Such a difference in the generation and motion of dislocations between the two atmospheres can be explained in terms of the analysis of Sanders and Dobson (1969) for the vacancy flow between defect and surface. It is also shown that by implanting silicon into phosphorus-diffused layers, the generation of dislocation networks is strongly correlated with the formation of secondary defects caused by implantation and annealing.

Autodiffusion dans les alliages concentres fer-palladium

Measurements of the diffusion coefficients of 39Fe and 103Pd in various iron-palladium alloys (between 0 and 100at.% iron) between 1100 and 1250°C, have shown that the activation energies for selfdiffusion for the two tracers are practically equal, independent of composition. The values obtained are very close to those corresponding to the activation energy of chemical diffusion. This result is in good agreement with the fact that the thermodynamic activities of iron and palladium have small temperature dependance and that the vacancy flow, as calculated with the model of Manning, is rather small. In spite of a strong ordering tendency in the solid solution of Fe-Pd, as indicated by a thermodynamic calculation, this model allows to calculate, with the aid of the measured self-diffusion coefficients, various parameters, such as the correlation factors for both iron and palladium, the vacancy correlation factors, and the atomic jump frequencies.

On the elastic interactions of a Broberg crack with vacancies and solute atoms

Elastic interactions (dilatation and inhomogeneity) of vacancies and solute atoms with a uniformly moving crack were analyzed on the basis of Broberg's moving crack model. In the region sufficiently near the crack tip, vacancies, substitutional solute atoms with smaller radii, and soft inclusions are attracted to the singularity, while interstitials, substitutional solutes with larger radii, and hard inclusions are repelled from it. The potential for flow of vacancies or solute atoms decreases initially with increasing crack propagation velocity and then increases in the high velocity range. Comparison of the present results with those based on Yoffe's model indicates a distinct difference between the dynamic effects on the elastic interactions predicted by these models. The dynamic effects predicted by both theories, however, are small in the low velocity range (say less than 10 percent of the shear wave velocity in the medium), and are not expected to be important for environment-assisted subcritical crack growth.

Void growth rates in irradiated materials at the peak swelling temperature

The extent to which interface control of vacancy and interstitial flow into voids inhibits void growth in irradiated metallic materials is discussed along with the dose dependence of swelling contrasted with diffusion-controlled growth. It is suggested that the observed linear variation of swelling with dose may be partially accounted for by the insensitivity of the swelling to the void growth controlling mechanism. (JRD)

Interdiffusion and intrinsic diffusion in binary vanadium-titanium solid solutions at 1350°C

Interdiffusion coefficients, intrinsic diffusion coefficients, and vacancy wind parameters have been determined in the vanadium-titanium system at 1350°C with the use of infinite, solid-solid diffusion couples. The experimentally determined diffusion coefficients were compared with the values predicted from the models of Darken, Manning and Dayananda with the use of available tracer diffusion and thermodynamic information and were found to be larger than those calculated from the three models. Vacancy wind parameters, determined experimentally, were seen to reflect a greater influence of the vacancy wind phenomenon on the intrinsic diffusion flux of each species than that calculated on the basis of Manning’s theory. In particular, the faster diffusing component is enhanced and the slower diffusing component is retarded to a greater degree than is theoretically predicted. Furthermore, experimental and predicted values of intrinsic diffusivity ratios,D V /D Ti ,were compared and the results suggest an increased effect of vacancy flow on the intrinsic fluxes with respect to the magnitude of this phenomenon calculated from Manning’s treatment. The vacancy wind effect is shown to be an important factor in the consideration of intrinsic diffusion fluxes and their relation to tracer diffusion and thermodynamic information in the vanadium-titanium system.

Suppression of Stacking Fault Generation in Silicon Wafer by HCl Added to Dry O2 Oxidation

Dislocation free (001) plane surface silicon wafers were oxidized in dry O2 mixed with small amounts of HCl (HCl oxidation) to clarify the effect of HCl on Frank type stacking fault generation during oxidation. The defect size was decreased with HCl concentration increase. Complete stacking fault generation suppression was observed for higher HCl concentration. Shrinkage and elimination of existing stacking faults occurred during the oxidation. Suppression, shrinkage, and elimination could be explained by the vacancy flow from the oxide silicon interface to the faulted defect during HCl oxidation.