Kr Bubbles Research Articles

Effects of Point Defects on the Stable Occupation, Diffusion and Nucleation of Xe and Kr in UO2

Xe and Kr gases produced during the use of uranium dioxide (UO2)-fuelled reactors can easily form bubbles, resulting in fuel swelling or performance degradation. Therefore, it is important to understand the influence of point defects on the behaviour of Xe and Kr gases in UO2. In this work, the effects of point defects on the behavioural characteristics of Xe/Kr clusters in UO2 have been systematically studied using molecular dynamics. The results show that Xe and Kr clusters occupy vacancies as nucleation points by squeezing U atoms out of the lattice, and the existence of vacancies makes the clusters more stable. The diffusion of interstitial Xe/Kr atoms and clusters in UO2 is also investigated. It is found that the activation energy is ~2 eV and that the diffusion of the interstitial atoms is very difficult. Xe and Kr bubbles form at high temperatures. The more interstitial Xe/Kr atoms or vacancies in the system, the easier the clusters form.

Irradiation-induced large bubble formation and grain growth in super nano-grained ceramic

In this work, 0.5TRPO•0.5Gd2Zr2O7 ceramic with an average grain size of only ∼15 nm was prepared by a high pressure (5 GPa/520 °C) sintering method. Phase evolutions and microstructure changes of the as-fabricated super nano and micron-grained ceramics under a high-dose displacement damage induced by 300 keV Kr2+ ions were investigated. The results show that the super nano-grained ceramic has low degree of amorphization, obvious grain growth (2–3 times in grain size) and big Kr bubbles (10–68 nm) formation after irradiation. The micron-grained ceramic was severely amorphized after irradiation and many microcracks were formed parallel to its surface. The formation mechanism of Kr bubbles in the super nano-grained ceramic is on account of grain boundary diffusion and migration induced by the accumulation of the injecting Kr ions and irradiation defects. Nevertheless, microcracks formed in the micron-grained sample are caused by the accumulation of Kr atoms.

Noble gas bubbles in bcc metals: Ab initio-based theory and kinetic Monte Carlo modeling

Understanding the interactions of noble gases with metals is of fundamental importance for the design of radiation-resistant structural materials for fission and fusion nuclear reactors. Here we present a unified theory for describing the energetics of He, Ne, Ar, and Kr bubbles in bcc metals in group 5B (V, Nb, Ta), 6B (Cr, Mo, W) and 8B (Fe). Our predictive analytical model is based on the effective-medium and isotropic elasticity theories, and is parameterized using density functional theory (DFT) calculations of small gas-vacancy clusters. By performing kinetic Monte Carlo (KMC) simulations driven by our analytical model, we have predicted the lifetimes of noble gas bubbles and their coarsening by Ostwald ripening. Our most notable finding is the exceptionally higher thermal stability of Ne, Ar and Kr bubbles than He bubbles in bcc metals, conferring them outstanding resistance to Ostwald ripening. The physical origin of the unexpected stability of bubbles formed by large noble gas atoms has been further elucidated. Our theoretical finding is consistent with the experimental observation of He gas bubble superlattice (GBS) coarsening under thermal annealing, and provides new insights on the exceptional stability of fission GBS in bcc U-Mo up to a high homologous temperature of 0.78. The present calculated results also compare favorably with the existing thermal helium desorption spectrometry experiments in the literature.

Noble Gas Bubbles in Bcc Metals: Ab Initio-Based Theory and Kinetic Monte Carlo Modeling

Understanding the interactions of noble gases with metals is of fundamental importance for the design of radiation-resistant structural materials for fission and fusion nuclear reactors. Here we present a unified theory for describing the energetics of He, Ne, Ar, and Kr bubbles in bcc metals in group 5B (V, Nb, Ta), 6B (Cr, Mo, W) and 8B (Fe). Our predictive analytical model is based on the effective-medium and isotropic elasticity theories, and is parameterized using density functional theory (DFT) calculations of small gas-vacancy clusters. By performing kinetic Monte Carlo (KMC) simulations driven by our analytical model, we have predicted the lifetimes of noble gas bubbles and their coarsening by Ostwald ripening. Our most notable finding is the exceptionally higher thermal stability of Ne, Ar and Kr bubbles than He bubbles in bcc metals, conferring them outstanding resistance to Ostwald ripening. The physical origin of the unexpected stability of bubbles formed by large noble gas atoms has been further elucidated. Our theoretical finding is consistent with the experimental observation of He gas bubble superlattice (GBS) coarsening under thermal annealing, and provides new insights on the exceptional stability of fission GBS in bcc U-Mo up to a high homologous temperature of 0.78.

A first-principles study of damage induced by gaseous species He, Kr, and Xe on the structure of nuclear fuel, U3Si

A first-principles approach is employed to study the damage caused by gaseous species, He, Kr, and Xe atoms, on the structures of nuclear fuel U3Si. Formation energies suggest that a U vacancy is more readily generated than is an Si vacancy, and that gaseous atoms, He, Kr, and Xe, favor residing in vacancies compared with interstitial sites. By combining the trapping energies and formation energies of secondary vacancy defects, it can be determined that the number capacity of one U or Si vacancy to trap He atoms in U3Si is two or three, while it is only one with respect to Kr and Xe. When the number of trapped He (Kr and Xe) atoms is increased to four (two), the production of a secondary U vacancy is energetically favorable, and the formation of He (Kr and Xe) bubbles can be initiated. Additionally, when an Xe atom is trapped in an Si vacancy of β-U3Si, Xe bubble evolution is predominantly controlled by diffusion. From this work, one may gain new insight into the mechanism behind bubble formation in uranium silicide fuels.

Evolution of Kr Precipitates in Kr-Implanted Al as Observed by the Channelling Method

The evolution of Kr precipitates at room temperature from nucleation to the formation of solid Kr precipitates in Al implanted with 50 keV Kr+ ions has been studied through the site change of Kr atoms determined by the channelling method. A previous channelling study reported that nucleation centres are various types of Kr–vacancy (V) complexes formed at low implantation doses. In this study, the initial stage of growth of Kr precipitates to bubbles and a key process towards the formation of epitaxially aligned solid Kr precipitates are investigated. The growth of Kr precipitates to bubbles proceeds from the accumulation of Kr atoms migrating to Kr–V complexes by radiation-enhanced diffusion. The Kr bubbles are in the fluid state. As to the epitaxial alignment, the following mechanism is proposed. At implantation doses higher than 2 × 1015 Kr/cm2, small clusters of Kr atoms located at octahedral (O) or displaced O sites are formed on the planes parallel to {111} planes at the bubble-matrix interface at th...

Bubble formation and Kr distribution in Kr-irradiated UO2

In situ and ex situ transmission electron microscopy observation of small Kr bubbles in both single-crystal and polycrystalline UO2 were conducted to understand the inert gas bubble behavior in oxide nuclear fuel. The bubble size and volume swelling are shown as weak functions of ion dose but strongly depend on the temperature. The Kr bubble formation at room temperature was observed for the first time. The depth profiles of implanted Kr determined by atom probe tomography are in good agreement with the calculated profiles by SRIM, but the measured concentration of Kr is about 1/4 of the calculated concentration. This difference is mainly due to low solubility of Kr in UO2 matrix and high release of Kr from sample surface under irradiation.

Transmission Electron Microscopy Investigation of Krypton Bubbles in Polycrystalline CeO2

To gain an understanding of gas bubble transport in oxide nuclear fuel, this paper uses polycrystalline CeO2, composed of both nanograins and micrograins, as a surrogate material for UO2. The CeO2 was implanted with 150-keV Kr ions up to a dose of 1 × 1016 ions/cm2 at 600°C. Transmission electron microscopy characterizations of small Kr bubbles in nanograin and micrograin regions were compared. The grain boundary acted as an efficient defect sink, as evidenced by smaller bubbles and a lower bubble density in the nanograin region as compared to the micrograin region.

In situ TEM observation of growth behavior of Kr bubbles in zirconium alloy during post-implantation annealing

The growth behavior of the Kr bubbles in Kr+ irradiated Zr–1.1Nb–1.51Fe–0.26Cu–0.72Ni alloy was studied by in situ transmission electron microscopy. Results show that the distributions of Kr bubbles are not uniform in the zirconium alloy matrix after annealing at 700K, 875K, 1025K, 1125K and 1225K, respectively. The Kr bubbles started to grow slowly when the sample was annealed at a temperature below 1025K. The average sizes of the gas bubbles were observed to grow only about 0.4nm in diameter at 700K for 170min and 0.9nm at 875K for 240min, respectively. However, gas bubbles grew very quickly at 1225K. The largest size of the gas bubbles is over 200nm after 180min annealing. The relationship between the bubble size and the annealing time was obtained at the designed annealing temperature. An empirical formula for calculating the bubble size was suggested by fitting equations derived from the experiment data. Finally, the growth mechanism of the bubbles in the zirconium alloy was discussed.

Noninvasive microbubble-based pressure measurements: a simulation study

This paper describes a noninvasive method to measure local hydrostatic pressures in fluid filled cavities. The method is based on the disappearance time of a gas bubble, as the disappearance time is related to the hydrostatic pressure. When a bubble shrinks, its response to ultrasound changes. From this response, the disappearance time, and with it the hydrostatic pressure, can be determined. We investigated the applicability of the gases Ar, C 3F 8, Kr, N 2, Ne, and SF 6, based on their diffusive properties. For pressure measurements with a limited duration, e.g. 150 ms, Kr and Ar bubbles are most suitable, since they are most sensitive to pressure change. If there is also a limitation to bubble size, e.g. a maximum diameter of 6 μm, SF 6 is most suitable. We present improvements of a method that correlates the duration of the decay of the fundamental ultrasound response to the hydrostatic overpressure. We propose to correlate the duration until subharmonic occurrence in combination with its decay, to hydrostatic overpressure, since the subharmonic decays more rapidly than the fundamental response. For a dissolving Ar gas bubble with an initial diameter of 14 μm, the overpressure can be determined 4 times as precise from the decay of the subharmonic response as from the decay of the fundamental response. Overpressures as small as 11 mmHg may be discriminated with this method.

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.

Transmission Electron Microscopy Studies of Kr+-Implanted Silicon

The structure and the depth distribution of radiation damage caused in (111) Si by high-dose krypton implantations (E; = 150 keV, T; = RT, D1 = 5 x 1015 , D2 = 1 x 1016 and D3 = 5 x 1016 cm z ) have been investigated using techniques of transmission electron microscopy. Formation of secondary defects (Kr bubbles and microtwins) on subsequent different annealing procedures, i.e. during solid phase epitaxial regrowth of damaged layers by conventional furnace heating and liquid phase epitaxial regrowth by applying laser pulses is compared and discussed. PACS numbers: 61.16.Bg, 61.72.Ff, 61.72.Qq, 61.72.Tt, 68.35.Fx, 81.40.Gh

Recrystallization of Kr in Kr-implanted and annealed aluminum

Abstract Thin Al foils are implanted with 50 keV Kr ions at room temperature to a dose of 1 × 10 16 Kr + ions / cm 2 . Kr bubbles in an as-implanted specimen and also in an annealed specimen at 673 K have been examined for 10 min by transmission electron microscopy at temperatures between 140 and 300 K. A bi-modal size distribution is observed in the annealed specimen, while a single-size distribution is observed in the as-implanted specimen. The lattice parameter of solid fcc Kr in the as-implanted specimen is almost constant during cooling, whereas in the annealed one it increases gradually during cooling down to about 190 K and then becomes nearly constant. These parameters are briefly discussed from the view point of the phase transition of highly pressurized Kr.

A Mossbauer study on solid krypton precipitates in aluminium

Mossbauer spectroscopy on the 9.40 keV transition 83Kr is used to obtain information about solid Kr precipitates in Al. Three different 83RbI sources differing in water content were used, which, when measured against a solid Kr absorber, show a quadrupole component in addition to a dominating single line. An analytical deconvolution technique is presented which takes care of the source characteristics. The spectra of Kr bubbles in Al obtained by high-dose implantation show two components: a single line from Kr atoms inside the bubble and a quadrupole split component from Kr at the Kr-Al interface. Spectra were taken as a function of temperature. The total absorption area could be fitted very well assuming a simple Debye model, yielding a Debye temperature of Theta DT=101(2) K. A decomposition of the total area in the areas of quadrupole and single-line components yields Debye temperatures of Theta DQ=98(6) K and Theta DS=90(10) K respectively.

A Mössbauer Study on Solid Krypton Precipitates in Aluminium and Silicon

ABSTRACTMössbauer spectroscopy on the 9.4 keV transition in 83Kr is used to study inert gases in metals and semiconductors. An absorber was made by implanting 83Kr at 110 keV in Al foils to a total dose of 1.7· 1016 Kr cm−2, leading to the formation of small precipitates (bubbles). Spectra on the as-implanted sample were taken as a function of temperature for three 83RbI sources which differ in line shape due to a different water content. A model is presented to extract the absorber parameters from the spectra in a consistent way, in spite of the different sources used. The spectra of Kr bubbles in Al produced by high dose implantation show two components: a single line from Kr inside the bubble and a quadrupole split component from Kr at the Kr-Al interface. The total absorption area could be fitted very well assuming a simple Debye model, yielding a Debye temperature of ΘDT = 101(2) K. For the individual components we obtained Debye temperatures of ΘDQ = 98(6) K and ΘDS = 90(10) K. The isomer shift of the bulk fraction is significantly larger than that of a solid Kr layer at ambient pressure, reflecting the fact that the s-density increases under compression. The size of the precipitates can be estimated to be 1.5–1.8 nm. Thin KrSi films, produced by Kr plasma sputter deposition, were characterized using cross-sectional X-ray analysis. The results clearly show two different layers. Presumably, the film grows at first as c-Si with a low Kr concentration, but after having reached a certain critical thickness, further growth proceeds as a-Si with a high Kr concentration. For Mössbauer spectroscopy an absorber of 83KrSi was made by plasma deposition on an Al foil. The spectra can be fitted with a single line and a quadrupole component, both with isomer shifts much larger than found in the case of small Kr bubbles in Al. No change in the total absorbed area was observed from 4.2 to 200 K indicating a lower limit of 250 k for the Debye temperature. Both observations indicate that the Kr resides in very small clusters.

Kr bubble formation in Cu after moderate doses of ion irradiation: the role of radiation vacancies

A TEM study of Kr bubble formation in Cu as a result of ion irradiation in a dose range from 2.5 × 1014 to 5 × 1015 Kr cm−2 and subsequent annealing is presented. For irradiation doses below 5 × 1015 Kr cm−2 no bubbles are observed in as-implan samples. Post-implantation annealing results in formation of Kr bubbles containing solid inert gas at room temperature. Two stages of bubble growth are observed during annealing: bubble growth by complexes absorption and bubble growth by coalescence. With increasing dose, the Kr lattice parameter decreases from 0.545 nm to an asymptotic value of 0.523 nm and the fraction of Kr atoms trapped within bubbles reaches saturation. This behaviour is explained in terms of radiation vacancy interaction with bubbles and dislocations.

Ni containing solid Kr bubbles studied with neutron depolarization and small-angle neutron scattering

Neutron depolarization and SANS measurements on Ni containing solid Kr bubbles are presented. The existence of a large fraction of small (∼3 nm) Kr bubbles and a small fraction of much larger (≳30 nm) nuclear inhomogeneities is deduced. The latter, which may be large Kr bubbles, effect the local magnetization.

Ni containing solid Kr bubbles studied with neutron depolarization and small-angle neutron scattering

Neutron depolarization (ND) and small-angle neutron scattering (SANS) experiments on Ni containing solid Kr bubbles are presented and discussed. The aim of the measurements is to study the effect of the Kr bubbles on the local magnetization. For the first time ND measurements in relatively large fields up to 80 kA/m could be performed. However, the ND results do not yield information about the Kr bubbles. The SANS patterns at applied fields larger than 400 kA/m are isotropic and are in agreement with a high fraction of small (radius ≈ 1.5 nm) Kr bubbles. Also a small fraction of larger (radius ≳ 15 nm) Kr bubbles or other nuclear inhomogeneities is likely to be present. The magnetic scattering is in agreement with a local magnetization which is affected by the demagnetization fields of these inhomogeneities.

Small Angle X-Ray Scattering from Kr Bubbles in Amorphous and Crystallized Ni84Y8Kr8

Amorphous and crystallized Ni84Y8Kr8 samples have been examined by the small angle X-ray scattering technique. The size of Kr bubbles in the amorphous sample was estimated to be about 20 Å. The size increased with increasing annealing temperature and annealing time.

Structure and Thermal Stability of Amorphous Ni84Y8Kr8 Alloy

The structural studies of amorphous Ni84Y8Kr8 alloy have been performed by means of X-ray diffraction combined with DTA/TG, TEM and SEM experiments. The local structure of this amorphous alloy appears to be well represented by a mixture of noncrystalline microstructures with short-range interatomic distances similar to crystalline Ni9.4Y, Ni and Kr. The X-ray diffraction pattern at 300°C demonstrated the occurrence of crystallization. Initially, the diffraction peaks can be indexed as a mixture of Ni9.4Y and Ni phases, and Ni9.4Y decomposes into Ni and Ni5Y at higher temperatures. X-ray diffraction measurements exhibit the formation of solid fcc Kr bubbles or precipitates above 540°C. The rapid release of Kr does not occur below 700°C.