Bubble Coarsening Research Articles

Ageing of free bubble clusters

Abstract The ageing of two-dimensional free foam clusters has been studied experimentally. We have determined the kinetics of coarsening of inner and peripheral bubbles in a cluster, and the respective distributions of area and number of sides as a function of time. The distributions remain stationary at long times when the kinetics are approximately parabolic and the mean sizes of the two types of bubble are the same. The total area of peripheral bubbles remains nearly constant as the cluster shrinks. We also found that Lewis' law applies equally to peripheral and inner bubbles in the cluster.

Hydrodynamic bubble coarsening in off-critical vapor-liquid phase separation.

Late-stage coarsening in off-critical vapor-liquid phase separation is reexamined. In the limit of bubbles of vapor distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft-sphere fluid.

Hydrogen isotopes behavior in nickel in nuclear fusion reactor conditions

The behavior of hydrogen isotopes in metals is very important for future nuclear fusion reactors. To study deuterium influence on helium pre-irradiated nickel, 0– 28 MeV He 2+ and 7 MeV D + beams were used. The He samples pre-implanted at 30, 100 and 300 appm (atomic parts per million) D + ( 10 18 ions/ cm 2 ) irradiated and annealed (1273 K) in high vacuum for 1, 10, 100 and 1000 h. After an electrochemical preparation (Struers jet), they were examined by transmission electron microscopy (TEM). Values for He bubble radii and densities depending on He ions doses and annealing periods are reported. Two types of bubbles were observed, namely: “small” bubbles, predominantly in the matrix (from 5 nm radius for 30 appm, 1 h annealing to 35 nm for 300 appm, 100 h annealing), and “large” bubbles, predominantly in the grain boundary regions, but even in some dislocations (from 30 nm radius for 30 appm, 1 h annealing to 120 nm for 300 appm, 100 h annealing). A unique bubble coarsening mechanism — the Ostwald ripening — is considered. The influence of deuterium on the “small” and “large” bubble radius values is discussed.

On the behaviour of intragranular fission gas in UO 2 fuel

Data obtained from the literature concerning the behaviour of intragranular gas in sintered LWR UO 2 fuel are reviewed comprehensively. The characteristics of single gas atoms and bubbles, as a function of irradiation time, temperature, fission rate and burn-up are described, based on the reported experimental data. The relevance of various phenomena affecting gas behaviour is evaluated. The current status of modelling of the behaviour of intragranular gas is considered in light of the present findings. Simple calculations showed that the conventional approximation for the effective diffusion coefficient does not adequately describe the gas behaviour under transient conditions, when bubble coarsening plays a key role in the release. The difference in the release fraction, compared with a more mechanistic approach, could be as large as 30%. A number of recommendations regarding possible defects in the mechanistic approach to modelling of intragranular gas are highlighted. The lack of an effective numerical method for solving the set of relevant non-linear differential equations is shown to be a serious obstacle in implementing the mechanistic models for fission gas release (FGR), in integral fuel performance codes.

Bubble size distribution and coarsening of aqueous foams

This paper characterises the bubble size distribution of aqueous foams, produced by a compressed-air foam generator. The time evolution of bubble size distribution in aqueous foams is experimentally measured using a CCD video camera. A computer model, which predicts the change in bubble size distribution with time, is used to simulate the coarsening and disproportionation of aqueous foams. As an extension of previous computer simulations, our model incorporates the variation in liquid fraction during the foam aging process, thereby enabling the simulation of both wet and dry foams. It is found that a Weibull-type distribution best approximates the narrow bubble-size distribution produced by a compressed-air foam generator. The modelled predictions show good agreement with the experimental measurements and a sensitivity analysis indicates a significant dependence of the model on drainage (hence on the thickness of the lamellae), the Henry constant, the gas diffusivity and the surface tension of the foam solution.

Radiation damage studies on Ni implanted with high energy He and D ions

The behavior of hydrogen isotopes in metals is very important for the future nuclear fusion reactor. To study deuterium influence on helium pre-irradiated nickel, 0–28 MeV He ++ and 7 MeV D + beams were used. Thirty, 100 and 300 appm He pre-implanted samples were D + (10 18 ions per cm 2) irradiated and 1, 10, 100 and 1000 h high vacuum annealed (1273 K). After an electrochemical preparation (Struers jet), they were examined by transmission electron microscopy (TEM). Values for He bubbles’ radii and densities depending on He ions’ doses and annealing periods are reported. Two types of bubbles were observed: ‘small’ bubbles, predominantly in the matrix (from 5 nm radius for 30 appm, 1 h annealing to 35 nm for 300 appm, 100 h annealing) and ‘large’ bubbles, predominantly in the grain boundaries regions, but even in some dislocations (from 30 nm radius for 30 appm, 1 h annealing to 120 nm for 300 appm, 100 h annealing). A unique bubble coarsening mechanism, the Ostwald ripening, is considered. The influence of deuterium on the ‘small’ and ‘large’ bubbles’ radii values is discussed.

Potassium bubble growth in doped tungsten

Potassium filled submicroscopic bubbles play a decisive role in determining the metallurgical properties of doped tungsten wires. Besides the influence of bubbles on the recrystallization behaviour and the high temperature creep strength, the bubbles may also form the nuclei for the generation of large cavities or voids which influence the fracture behaviour and lamp failure. The most accepted mechanism of bubble coarsening is stress assisted bubble growth; however, this needs as prerequisite a critical bubble size dependence on the stress system of the tungsten coil. It will be shown that a possible mechanism for the coarsening until the critical size is the diffusion controlled transport of potassium provided there are corresponding diffusion paths, as for example grain boundaries or dislocations. In addition, the new model also explains the formation of voids in doped tungsten wire and gives the basis for a material limited failure mechanism in halogen lamps.

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.

Small angle neutron scattering from helium bubbles in metals

Small angle neutron scattering (SANS) has been widely used in investigating defects in metals, and in particular, to characterize the helium bubble population in implanted materials. The main advantage in using SANS is the non-destructive feature of the tests and the quantitative results obtained by averaging over a large sample volume. SANS is a powerful technique, very sensitive to microstructural changes and its use was of fundamental importance to show the bimodal distribution of the bubble population: in the vicinity of grain boundaries and free surface and inside grains, respectively. Here the most important applications of the SANS technique to the study of the helium bubbles in implanted materials are reviewed. Most of the work has been done on nickel samples, but also a ternary alloy Fe-Ni 15%wt-Cr 15%wt and a steel (MANET) with a more complicated structure have been successfully investigated. Different annealing treatments, isothermal and isochronal, were investigated in order to determine the active mechanisms of the bubble coarsening and their activation energies. From the SANS data the bubble size distributions have been determined, from which parameters such as mean radius and density of the bubble population have been calculated. The gas pressure inside the bubbles was also determined by the contrast variation technique in SANS and by a computational procedure, and an excellent agreement was found between the results. These results show a marked overpressure inside the bubbles as compared to thermodynamical equilibrium values of about 3 GPa. A comparison with results obtained by other techniques confirms the validity of SANS, which has to be considered as a complementary technique for its indirect image of the sample.

Gas release processes for high concentrations of helium bubbles in metals

Although many aspects of helium behaviour in metals relevant to fusion reactor technology have been studied, relatively little information is available on the kinetics of high temperature release of helium precipitated into bubbles. Recently, based on the many observations showing that bubble coarsening during annealing is induced initially in regions nearest thermal vacancy sources (e.g. grain boundaries or surfaces), a qualitative model has been suggested in which the vacancy gradient between the vacancy source and initially overpressurised bubble concentrations must lead to directed bubble migration up the gradient towards the source. It is clear that this gives a potential for gas release, either directly for surfaces, or indirectly for grain boundaries. The present paper extends work on this mechanism by discussing quantitative aspects of bubble movement in vacancy gradients and using computer simulations to provide information on the parameters of importance in the gas release mechanism. Among these are the helium content and the associated local swelling, while release kinetics and temperature are primarily controlled by self-diffusion parameters.

Helium bubbles in FeNiCr after post-implantation annealing

A FeNiCr sample was implanted at room temperature with 1200 appm helium and subsequently annealed at 973 K for times ranging from 15 min up to 2780 h. Formation and coarsening of the helium bubbles were investigated by small angle neutron scattering (SANS) and transmission electron microscopy (TEM). The helium bubbles were found in a bimodal size distribution: small bubbles in the bulk and large bubbles close to the grain boundaries. The bulk bubbles contain helium under marked overpressure (as compared to the thermal equilibrium value) and their coarsening was identified to occur via migration and coalescence controlled by surface diffusion with an activation energy of 1.9 ± 0.4 eV. The measured size distributions are in reasonable agreement with the corresponding results obtained by computer simulation. The large bubbles develop in regions close to the grain boundaries. From the measured width of these regions the self diffusion coefficient could be estimated and good agreement with literature values was found.

An investigation into the influence of implanted oxygen on krypton behaviour in uranium dioxide during annealing

Abstract It is generally agreed that fission gas release in hyperstoichiometric uranium dioxide is strongly influenced by the excess oxygen. However, the exact mechanisms have not been studied at the fundamental level. The aim of the work reported here was to obtain information on this topic by controlled experiments using an ion implantation approach rather than working with irradiated nuclear fuel. Krypton implants were used to create krypton bubbles in UO 2 samples to which oxygen was then added, again by implantation, to induce local changes in stoichiometry. The effect of the oxygen on subsequent krypton desorption was studied during annealing to high temperatures using transmission electron microscopy and thermal desorption spectroscopy. This combination of techniques on individual samples allowed bubble substructure changes to be followed and directly matched to the gas release measurements. Two clear effects of oxygen were seen. At around 1300 K, a new gas release stage was found; it appeared to be related to the 1600 K peak seen after Kr-only implants and could be attributed to the loss of near-surface krypton gas atom clusters, with accelerated migration in hyperstoichiometric UO 2 . However, at higher temperatures the coarsening of bubbles in (Kr + O) regions was surprisingly suppressed with the bubbles appearing more uniform and smaller than in Kr-only areas. It is suggested that excess oxygen might form a complex bubble coating effectively pinning the bubbles to slow bubble migration.

Effect of Grain Size on Microstructural Change and Damage Recovery in UO2 Fuels Irradiated to 23 GWd/t.

The effect of grain size on microstructural change and damage recovery in U0 fuels was studied by X-ray diffractometry (XRD) and transmission electron microscopy (TEM). The as-irradiated lattice parameter of the standard fuel (grain size: 16 /im) was larger than that of the large-grained fuel (43 μm), indicating a larger number of fission-induced point defects in the lattice of the former fuel. This tendency was in contrast to previously reported results for low burnup fuels below 1 GWd/t. The lattice dilation in the present high burnup fuels was mainly due to the accumulation of vacancies. The lattice parameter of both fuels began to recover around an irradiation temperature of 450~650°C, and both had a complete recovery at 850°C. On annealing at high temperatures of 1,450~1,800°C, the bubble diameter in the standard fuel was larger than that in the large-grained fuel. This indicated that vacancy diffusion from the grain boundaries plays an important role during bubble coarsening at high temperatures.

Formation and growth of intragranular fission gas bubbles in UO 2 fuels with burnup of 6–83 GWd/t

The detailed characteristics of intragranular fission gas bubbles in UO 2 fuel pellets (burnup: 6–83 GWd/t) before and after postirradiation annealing at 1600 and 1800°C have been examined by TEM and SEM fractography. In the base-irradiated fuels, a high density of small bubbles of about 2 nm in diameter precipitated uniformly in the matrix. When increasing burnup above 44 GWd/t, larger bubbles of 10–20 nm newly appeared in addition to the small bubbles. On heating at high temperatures, bubble growth was saturated within a few minutes. Enhanced coarsening of bubbles was found preferentially near the grain boundaries in the middle burnup fuels of 16–28 GWd/t and throughout the grains in the high burnup fuels of 44 and 83 GWd/t. The bubble growth during annealing was associated with a remarkable decrease of the bubble number density, and the relationship between bubble density N b and mean diameter d b was expressed as N b α d b −2.6. The coarsening was attributed to coalescence via bubble migration for moderately large bubbles of up to 50–60 nm, and to Ostwald ripening accompanied by a sufficient vacancy supply from external vacancy sources such as free surfaces, grain boundaries or irradiation-induced sub-grain boundaries for huge bubbles above 100 nm.

Coarsening of helium bubbles in [formula omitted]CrNi measured by small angle neutron scattering

A 100 μm thick specimen of Fe-15% Cr-15% Ni (serving as a model alloy for austenitic stainless steels) has been homogeneously implanted with 1200 appm He and then isothermally annealed at 973 K for periods between 0.25 and 2780 h. After each annealing step the size distribution and the density of helium bubbles have been determined by small angle neutron scattering (SANS). After the last annealing step the bubble structure was also measured by TEM and good agreement with SANS results was found. The observed changes of the mean bubble radius and the bubble density with annealing time can be described by power laws. The corresponding exponents of 0.14 and −0.37, respectively, indicate bubble migration and coalescence as the dominating coarsening mechanism. It is further concluded that the gas pressure in the bubbles is significantly higher than the thermal equilibrium value, in agreement with earlier results on pure nickel.

Helium desorption from Fe and V by atomic diffusion and bubble migration.

Thermal helium desorption from homogeneously implanted iron and vanadium foils was investigated during linear heating and isothermal annealing, respectively. The isothermal experiments showed an initial period with a square-root dependence of the desorbed helium on time, characteristic of atomic helium diffusion, followed by a reduction of desorption due to clustering. The substitutional helium atoms migrate by a dissociative mechanism, with dissociation energies of 1.4\ifmmode\pm\else\textpm\fi{}0.3 eV for both metals. Up to temperatures of 600 K (Fe) and 700 K (V), retrapping was dominated by irradiation-induced vacancies. At higher temperatures diffusion times became unmeasurably small. Retention of helium in the specimens indicated that di-helium clusters are stable up to 673 K in Fe and up to 773 K in V. Desorption after clustering was analyzed by comparison with models of bubble coarsening. The vanadium results were best described by bubble migration via surface diffusion at all temperatures investigated (573--1173 K), while the iron data from 900 to 1184 K indicated bubble migration by volume diffusion as the prevalent coarsening mechanism.

Diffusion of helium in magnesium and titanium before and after clustering

Magnesium and titanium foils were homogeneously implanted by α-particles at room temperature and afterwards helium desorption was investigated during linear heating (0.83 K/s) and isothermal annealing. Desorption started by atomic diffusion with diffusion enthalpies of 0.6 ± 0.1 eV (Mg) and 1.0 ± 0.3 eV (Ti), respectively. For both metals this is consistent with a dissociative diffusion mechanism, but in Ti a vacancy mechanism can not be fully ruled out. After isothermal annealing a temperature dependent fraction of the implanted helium was retained in the specimens due to clustering. Desorption after formation of clusters or small bubbles was compared to models of bubble coarsening. At temperatures from 523 to 653 K in Mg and from 623 to 773 K in Ti, bubble migration by surface diffusion was found to be the dominant coarsening mechanisms characterized by surface diffusion enthalpies of about 0.7 and 0.64 eV, respectively. Helium dissociation from bubbles (Ostwald ripening) was identified as dominant mechanism in Ti from 973 to 1073 K.

Dynamics and coarsening in three-dimensional foams

The authors show that diffusing-wave spectroscopy can be used as a non-invasive probe of the bulk properties of three-dimensional foams. A new picture accounting for the origin of the temporal fluctuations of multiply scattered light is developed and corroborated with direct observations through a microscope. The interpretation and measurements yield the growth law for the coarsening of foam bubbles and new insight into their dynamics.

Inert gas bubbles

Nuclear reactions result in inert gas bubbles appearing in the microstructure of metals and alloys and this can have a profound influence on, for example, mechanical properties. For this reason, bubbles have been extensively studied within the nuclear industry and much progress has been made in understanding their behaviour. However, significant advances have also been made within academia. It has been shown previously that Brownian motion of gas bubbles does indeed occur on annealing, leading to bubble coarsening. There have been examples where the pressure inside the bubbles has been so high that the atoms become so close together that the ‘gas’ takes on some of the properties of a solid. In such circumstances, the rate of migration of the bubbles is greatly diminished. The development of bubble growth mechanism maps is described.MST/1317

The formation of helium bubbles near the surface and in the bulk in nickel during post-implantation annealing

A systematic TEM study on nickel specimens homogeneously implanted with about 1000 appm helium at room temperature and annealed for about 1 h between 873 and 1273 K is reported and interpreted. During annealing the observed bubble structure coarsens substantially. The coarsening rate is, however, much faster close to the surface than in the bulk. The apparent activation energies of the average bubble radius in these regions are 1.1 and 0.23 eV, respectively. Results from other investigations confirm and complete these findings. The enhanced coarsening near the surface is attributed to the relaxation of initially overpressurized bubbles by vacancies supplied by the nearby surface. The coarsening mechanism in this region is identified as Ostwald ripening. In the bulk, the latter is suppressed due to a reduction of the vacancy concentration by the overpressure in the bubbles. In this region bubble coarsening is attributed to coalescence via bubble migration controlled by surface diffusion.