Vacancy Sources Research Articles

Interdiffusion and Kirkendall Effect in Doped BaTiO3–BaZrO3 Perovskites: Effect of Vacancy Supersaturation

Interdiffusion in Sc‐doped and Ta‐doped BaTiO3‐BaZrO3 perovskites was examined, both theoretically and experimentally. Analytical expressions for the lattice velocity, v, and the interdiffusion coefficient,D̃, were obtained. The v and the D̃ were numerically evaluated as a function of dopant type (trivalent‐acceptor or pentavalent‐donor) and concentration using literature values of oxygen vacancy diffusivity, DVO, the A‐site vacancy diffusivity, DVA, and assumed values for the B‐site vacancy diffusivities, DVB and DVB′. Regardless of the chosen values of DVB and DVB′, the calculated D̃ increased with the Ta concentration and decreased with the Sc concentration. The dependence (shape) of the calculated v vs dopant type and concentration, however, was a function of the magnitudes of DVA and DVB. For DVA < (DVB, DVB′) < DVO, the calculated v exhibited a maximum at ∼0.8% acceptor dopant. Diffusion couples in the BaTiO3‐BaZrO3 system doped with either Sc (acceptor) or Ta (donor) were annealed in air over a temperature range between 1300° and 1500°C. Extensive Kirkendall porosity was observed in several samples. The measured porosity vs dopant concentration (acceptor/donor) trace was similar to that of calculated v vs dopant concentration (acceptor/donor). However, the measured D̃ vs dopant concentration (acceptor/donor) was not in accord with the calculations. This difference is attributed to a nonequilibrium vacancy supersaturation and the accompanying porosity formation. To obtain further evidence of the deviation from equilibrium, experiments were also conducted on both coarse‐grained and fine‐grained samples. The coarse‐grained samples, which are expected to have fewer vacancy sinks and sources, exhibited greater Kirkendall porosity and greater D̃ values compared to the fine‐grained samples, consistent with a greater deviation from equilibrium.

Effects of point defect distribution on arsenic precipitation in low-temperature grown III–V arsenides

The behavior of As precipitation in low-temperature grown III–V arsenides is investigated and correlated with the doping level, crystal bond strength, and dislocation density. Experimental results reveal that the doping level affects the concentration of charged defects, such as vacancy and antisite point defects, and hence leads to the selective precipitation of excess As in homojunctions. For heterostructures, As precipitates tend to condense in materials with a lower bond strength due to differences in point defect concentrations between the materials. In addition, dislocations are found to be a vacancy source that facilitates As precipitation around them. These results indicate that column III vacancies play an important role in As precipitation of low-temperature grown III–V arsenides.

Solid phase epitaxy for low pressure chemical vapor deposition Si films induced by ion implantation

This work investigated the ion implantation induced solid phase epitaxy (SPE) of Si thin films prepared by low pressure chemical vapor deposition (LPCVD). Previous studies indicate that the residual layer at the interface between the Si thin film and single crystalline substrate is the major obstacle to the SPE process of Si film. In this work, Ge + and Si + ion were implanted to completely amorphize the Si film prepared by LPCVD. Ion implantation also mixed the interfacial oxide layer and its effects on subsequent epitaxial growth of Si film subjected to various annealing conditions were discussed as well. In addition, the specimen surface was modified by inductive couple plasma (ICP) process. The ICP modification using nitrogen gas could form a vacancy source on the sample surface to enhance the atomic diffusion rate and change the stress state in the vicinity of surface, thereby accelerating the SPE process.

Elevated temperature deformation of Cr 3Si alloyed with Mo

Four-point bend, constant load compressive creep and constant engineering strain rate tests were conducted on arc-melted and powder-metallurgy (PM) processed Cr 40Mo 30Si 30 specimens in the temperature range 1400–1700 K. This is a two-phase alloy consisting of (Cr,Mo) 3Si and (Cr,Mo) 5Si 3 phases. The PM specimens, which were substantially weaker than the arc-melted materials, exhibited a stress exponent, n, of about 2 and an apparent activation energy for creep, Q a, of 485 kJ/mol. The mechanism in these specimens appeared to be controlled by creep of a glassy phase. In the case of arc-melted specimens for which n ~ 3 and Q a ~ 430 kJ/mol, the rate-controlling creep mechanism appeared to be that dominant in the (Cr,Mo) 5Si 3 phase. In this case, it is suggested that the Nabarro creep mechanism, where dislocation climb is controlled by Bardeen–Herring vacancy sources, is the dominant creep mechanism. Finally, an analysis of the present and literature data on Cr 3Si alloyed with Mo appeared to suggest that the creep rate decreases sharply with an increase in the Mo/Si ratio.

Identification of Nature of Dislocation Loops Grown as Vacancy Source after Up-Quenching

The dislocation loops grown as vacancy source after up-quenching in 99.9999 % aluminum single crystals with a low dislocation density were examined by synchrotron topography in order to determine the Burgers vector and the nature directly. The specimen crystal was heated to 295°C and hold for 15min. at the temperature, then cooled down to room temperature to freeze the loops in the specimen. Topographs were taken on the high-speed X-ray topographic station (BL-15B) at the Photon Factory (KEK-PF). White beam topographs were taken using four of symmetrically equivalent 111 and 220 reflections for the determination of the Burgers vector. Monochromatic section topographs were also taken with 111, 222, 333 and 444 reflections at a wavelength of 0.62Å. The image of the loops was simulated by numerical solution of the Takagi-Taupin equations. Burgers vector of the frozen loops was determined to be a/2<110>. And comparison between the observed loop image and the simulated one showed that the dislocation loop grown as a vacancy source was interstitial-type and the size ranged from 3 µ m to 10 µ m in radius.

The influence of microstructure on the sintering process in crystalline metal powders investigated by positron lifetime spectroscopy: II. Tungsten powders with different powder-particle sizes

Compacts of tungsten powder with five different powder-particle sizes (from to ) are subjected to pressureless sintering. We investigate the change in microstructure during the sintering process by positron lifetime spectroscopy. So as to be able to distinguish between defects having the same positron lifetime, we investigate their kinetics when the sample is annealed. In particular, we consider the annealing out of vacancy clusters after low-temperature electron irradiation, as well as recovery and recrystallization of a tungsten sheet, in as-manufactured form. Making measurements on uncompacted powder, we find an increasing fraction of positrons annihilating in surface states with decreasing powder-particle size. The powder-particle and grain sizes (influencing the x-ray domain size) are monitored additionally by means of metallography and x-ray diffraction. We find that all of the methods give results in agreement with each other. The small grain sizes at lower temperature, about one fifth of the powder-particle size, cause positrons to annihilate at grain boundaries, leading to vacancy-cluster-like signals. At the intensive-shrinkage stage, there are certainly contributions from different shrinkage mechanisms. The observed shrinkage rates can be explained by Coble creep. It is possible that dislocations also play a role as vacancy sources and sinks, since the intensive-shrinkage stage occurs in a temperature region wherein recrystallization takes place.

Synchrotron Radiation Topographic Camera for Continuous Observation

An X-ray topographic camera in the high-speed X-ray topographic station (BL-15B) at the Photon Factory, High Energy Accelerator Research Organization was improved for continuous observation with nuclear plates. Using this camera, several topographs were taken during heating process of nearly-perfect aluminum single crystals. As a result, an obscure topograph, in which not only defect images but also fringe are unclear, was taken in spite of very short exposure time (2.0 s) just prior to the appearance of interstitial-type dislocation loops grown as vacancy sources.

Damage and annealing in two-dimensional Coulomb crystals

Experiments have shown that the attenuation of shear modes in a 2D classical Coulomb crystal, formed from helium ions trapped below the free surface of superfluid helium, is sensitive to damage in the crystal, and it can therefore be used to monitor the annealing process that follows deliberate damage to the crystal. The characteristic time required for annealing in a circular crystal of radius 13 mm is found to be of order 500 s, and it rises only slowly with decreasing temperature. It is suggested that such behaviour requires the production of configurations of dislocations that can disappear only through dislocation climb, which requires the absorption and emission of vacancies or interstitials, and that the relatively small temperature dependence implies that there must be some source of vacancies or interstitials within the crystal even at the lowest temperatures.

The effect of capillarity on the chemical potential in interfaces

A theory of the effect of curvature on the chemical potential of atoms inside an interface, e.g. a grain boundary, is developed under the assumption that the interface is an ideal source or sink for vacancies. Three simple geometries are considered to illustrate the theory. Corrections to the chemical potential appear already in the first order in curvature. The magnitude of the correction term depends on the elastic properties of the phases forming the interface, its intrinsic structure and the relative size of the grains it separates. For migrating interfaces between dissimilar phases, the correction depends on the diffusivities and the molar volumes of the two phases, rather than on their elastic moduli. The implications of the theory for fine-grained materials are discussed.

Allowance for gas solubility and the finite strength of vacancy sinks in the sintering of a ceramic

The process of diffusional evolution (shrinkage or growth) of gas-filled pores in a hot-pressed ceramic is analyzed, assuming that the gas is soluble in the matrix. It is additionally assumed that the strength of vacancy sources and sinks is finite. An equation is derived for the porosity of the ceramic at a late stage of sintering.

On the problem of high-rate reactive diffusion

Competitive mechanisms for fast diffusional growth of an interphase layer during the initial stage of reactive diffusion were analysed. The effect of fast growth is attributable to grain boundary diffusivity and/or accelerated volume diffusion due to vacancy supersaturation. In analysing the latter case, vacancy source movement and the space distribution of non-equilibrium vacancies were considered. The system parameters which determine the governing mechanism of the process were obtained. It was shown that if, due to vacancy supersaturation, bulk diffusion dominates, the process is intensified by the grain boundary diffusion.

Fraction of Interstitialcy Component of Phosphorus and Antimony Diffusion in Silicon

The effect of nitride films on the diffusion of phosphorus and antimony in silicon has been investigated, in order to extract the fractional interstitialcy component of these dopant diffusion. Nitride film deposited on silicon substrate is used as an extrinsic source of vacancies. The phosphorus diffusion is retarded and the antimony diffusion is enhanced in silicon under nitride films. By observing the variation of the retardation in phosphorus diffusion and the enhancement in antimony diffusion, it is determined that the fraction of interstitialcy component in phosphorus and antimony diffusion is approximately 0.96 and 0, respectively.

Evidence for Non-Equilibrium Vacancy Concentrations Controlling Interdiffusion in III-V Materials

ABSTRACTInterdiffusion and self-diffusion in III-V semiconductors has usually been assumed to operate through the diffusion of point defects, the concentrations of which are at thermal equilibrium values. We have studied the interdiffusion of multiple quantum well samples, grown under a range of growth conditions, each containing a thin source of vacancies. This has enabled simultaneous measurements of the interdiffusion coefficient, diffusion coefficient for vacancies and the concentration of those vacancies in a single experiment. We have shown that independent of growth conditions, within a wide window of III-V flux ratio and temperature, the diffusion at all temperatures is governed by a constant background concentration of vacancies.

Helium bubbles in nickel annealed at T>0.7 Tm

Helium-induced cavities in fusion materials are considered to be detrimental. Valuable information on He bubbles and on the basic mechanisms underlying their evolution is obtained by post-implantation annealing, subsequent to He implantation at about 300 K. For Ni and Cu, it has been shown that up to annealing temperatures T a≤0.7 T m ( T m is the melting point), highly overpressurized bubbles form in the volume and coarsen very slowly by migration and coalescence, whereas near vacancy sources the overpressure relaxes and the coarsening occurs rapidly by Ostwald ripening (OR) which leads to the appearance of small and large He cavities. Annealing of He loaded Ni at T a from 0.72 T m to 0.92 T m leads to the formation of only one population of nearly equilibrium bubbles which is related to the recovery of the ability of dislocations to emit vacancies into their surroundings. The effective activation energy of the increase of the mean bubble radius was found to be 0.60±0.02 eV, which is lower than that for the OR at lower temperatures (1.1 eV). Analysis shows that the mechanism covering the coarsening of He bubbles at very high temperatures is still OR, but limited by the rate of ledge nucleation on the bubble walls.

Point defect concentration development in electron-irradiated bucky onions

Rate equations for the generation and recombination of vacancies and selfinterstitial atoms in a spherical bucky onion under electron irradiation are proposed. They are used to study the temporal development of the point defect concentrations in different shells of onions. The self-interstitial concentration was found to remain low and to be only slightly enriched near the onion centre. The loss of atoms from the outer surface of the bucky onions by sputtering acts as a vacancy source for the whole onion. Irradiation-induced diffusion leads to a net flux of vacancies towards the onion core. The coupling between neighbouring shells necessary for this radial diffusion can be described by the concept of intermediate shells introduced here.

Correlation between coherency strain effects and the Kirkendall effect in binary infinite diffusion couples

A robust correlation between the sign of the binary Vegard's Law coefficient and the direction of the Kirkendall shift has been discovered. In an examination of 48 experimental binary pairs it has been found that within a very few explainable exceptions the marker movement is towards the paired atom which expands the lattice. We claim robustness because this size effect overrides a conventional contrary mass effect on the relative jump frequencies in nearly all cases. The effect is explained by attributing significant attractive, internal stress-relaxing reorganization of a random vacancy array so as to substantially increase the large atom encounters and thus the effective exchange frequencies as indexed by the relative intrinsic diffusion coefficients. From the data we conclude that this local effect on the diffusion coefficients could exceed the magnitude of the global diffusional effect of coherency strain which is deemed to enter processes like spinodal decomposition. Serendipitously, the primary Vegard-originated misfit dislocations at the weld reorganize and multiply, providing the vacancy sources and sinks which sustain the near-vacancy equilibrium and well-defined chemical diffusion coefficients which have long been associated with the Kirkendall effect.

Post-irradiation fission gas release from high burn-up UO 2 fuel annealed under oxidising conditions

In post-irradiation fission gas release experiments on UO 2 fuel, large increases in effective diffusion coefficients have been reported when anneals have been carried out under oxidising conditions. These conditions affect in some way the processes involved in the diffusive phase of gas release associated with the important step of intragranular fission gas transfer to the grain boundaries. The purpose of this paper is to extend a recent model involving fission gas bubble movement to propose a possible explanation. A central part of the model concerns the importance of grain boundaries as a dominant vacancy source. Under normal conditions, boundary concentrations are due to thermal vacancy production but under oxidising conditions, it is suggested that if fast oxygen diffusion takes place along grain boundaries then the subsequent oxidation reaction at the boundary has the potential to cause a huge enhancement of the local vacancy level. As will be demonstrated, an acceleration in the rate of fission gas bubble movement to the grain boundaries will result. A comparison of model calculations with a few selected literature results suggests that the mechanism has more than sufficient strength to give the large effects observed.

Diffusion-induced amorphization in yttrium-iron garnet imbedded with ZrO 2 particles

Yttria-iron garnet (YIG)/ZrO 2 (5 mol.%) composites, fired at 1450°C in oxygen atmosphere for 8, 16 and 96 h, were studied by transmission electron microscope with regard to a possible diffusion-induced amorphization (DIA) process within the YIG lattice. Lattice image shows an amorphous zoning of YIG around the intragranular ZrO 2 particles where possible grain-boundary wetting effect can be avoided, and next to the YIG/ZrO 2 interface where the gradient of inward Zr flux or outward Fe flux is presumed to be large. As a result of such a solid-state amorphization, the lattice planes are still parallel-aligned in the opposite sides of the amorphous zoning. Structural and chemical considerations further suggest that amorphization proceeds by cellular disordering of Zr 4+, Fe 3+ and Fe 2+ (charge compensating defect due to Zr 4+ substitution for Fe 3+) in the array of octahedral sites and facilitated indirectly by dislocations acting as source and sink of vacancies. An ordering process, subsequent to DIA, caused the formation of non-dendritic α-Fe 2O 3 islands in the relatively high Fe/Zr ratio region of the amorphized zoning.

Interdiffusion: A probe of vacancy diffusion in III-V materials

We have used the interdiffusion of a multiple quantum well sample due to a thin source of vacancies, as a probe, to simultaneously measure the interdiffusion coefficient, diffusion coefficient for group III vacancies in GaAs and the background concentration of these vacancies in a single experiment. We have shown that the interdiffusion at all temperatures is governed by a constant background concentration of vacancies in the material and that this background concentration is the concentration of vacancies in the substrate material. The measured vacancy concentration is around 2\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. This result shows that the vacancy concentrations in GaAs are not at thermal equilibrium concentrations as has been widely assumed. Rather it has value which is ``frozen in,'' probably at the GaAs crystal growth temperature. The activation energy found for the intermixing of InGaAs/GaAs is shown to be governed solely by the activation term for vacancy diffusion which is calculated to have an activation energy of 3.4\ifmmode\pm\else\textpm\fi{}0.3 eV.

Characterization and removal of residual defects in high dose, very low energy BF 2+-implanted (001) Si

Residual defects in 5 keV, 5 × 10 15/cm 2 BF 2 + implanted (001)Si samples have been investigated by transmission electron microscopy. The residual defects were identified to be {113} interstitial defects, (001) defect clusters, fluorine bubbles and stacking faults. For the removal of the end-of-range (EOR) defects, the activation energy was determined to be 4.5 ± 0.4 eV. It is suggested that the free surface and fluorine bubbles act as effective vacancy sources to accelerate the removal of EOR defects.