Formation of steady state size distribution of precipitates in alloys under cascade-producing irradiation

The effect of coherency loss on the development of precipitate size distribution under cascade-producing irradiation is considered. The nucleation of coherent precipitates, their growth followed by coherency loss and cascade-induced dissolution of large incoherent precipitates can occur simultaneously resulting in formation of a quasi-stationary size distribution of semicoherent precipitates. To describe this process we consider co-evolution of a mixed population of coherent, semicoherent and incoherent precipitates. Mathematically, the problem is formulated as a set of discrete rate equations of nucleation kinetics (the Master equation approach) which is also used for later stages of evolution. To solve the corresponding large set of equations (typically, more than 10⁵ equations) an efficient numerical method is developed. The simulation results obtained for material parameters and irradiation conditions typical for nuclear reactors show that the coherency loss affects considerably evolution of the precipitate population. Under certain irradiation conditions, both in solution-annealed alloys and in aged ones, the mean precipitate size and the number density during prolonged irradiation tend to steady state values, whereas the size distribution function of large precipitates narrows. The width of the quasi-stationary size distribution is controlled by cascade parameters. It was found that the asymptotic quasi-stationary state of the precipitate population may depend on initial state of the alloy.     

Radiation-induced cation disorder in the spinel MgAl2O4

There is some controversy in the literature concerning the nature of radiation-induced cation disorder and phase transformation in the spinel MgAl₂O₄. Attempts have been made to interpret the experimental data either in terms of a pure inversion involving the exchange between the Mg and Al atoms, or the disordering of the cation sublattice leading to a change in crystallographic symmetry to a defective NaCl-type lattice. We have performed first principles electronic structure calculations in order to examine the nature of this cationic disorder. We find that at low energies an exchange between the Mg and Al atoms is more favourable leading to an inversion in the spinel. With further increase in energy, the cations can be displaced from the tetrahedral sites to the unoccupied octahedral sites in the lattice, both in the normal and inverse spinels. In the case of the inverse spinel, such a displacement leads to a spontaneous change in the value of the u parameter of the oxygen lattice to the ideal value, and thus to an ideal defective NaCl-type lattice. On the other hand, in the case of a normal spinel, the displacement of Mg atoms to the unoccupied octahedral sites leads initially to a pseudo-cubic arrangement which then transforms later with further energy to an ideal defective NaCl-type structure. Thus in both cases a defective NaCl-type structure is obtained as the final structure. We find that the total energy barrier for obtaining this structure is the same in both cases.     

Computer simulation of the interaction of carbon atoms with self-interstitial clusters in α-iron

Static and dynamic properties of clusters of self-interstitial atoms and their complexes with carbon (C) atoms in α-iron are studied by molecular dynamics method using a pairwise interatomic potential for iron-carbon interaction and a many-body potential for iron. The effect of C atoms on the configuration, stability and migration of , and 〈1 0 0〉 interstitial clusters is investigated. In the framework of the simple model of interstitial solute used here, C atoms enhance the relative stability of 〈1 0 0〉 over clusters, but not enough to explain their common occurrence under irradiation. Clusters of seven interstitials or smaller are able to co-migrate with C atoms with a reduced mobility compared with pure iron. Bigger clusters have dislocation structure and are immobilised: C migrates along the core of their periphery as in the core of a straight edge dislocation. C dissociates from all clusters at high enough temperature.     

Ab initio formation energies of Fe-Cr alloys

We have calculated ab initio lattice parameters, formation energies, bulk moduli and magnetic moments of Fe-Cr alloys. The results agree well with available experimental data. In addition to body centered cubic (bcc) alloys, which are representative of ferritic steels used in fast neutron reactors, face centered cubic (fcc) and hexagonal close packed (hcp) phases were considered in order to complete a theoretical database of thermodynamic properties. Calculations were done for the ferromagnetic phase, as well as for a phase with local moment disorder, simulating the magnetic structure at high temperatures. For the latter case, the formation energy of the alloy is strictly positive smooth function of chromium concentration, in agreement with experiments performed at high temperature. In the ferromagnetic case, a negative mixing enthalpy is found for chromium concentrations below 6%. Our observation is consistent with the experimentally observed inversion of the ordering trend, as well as with formation of the chromium rich α^′ phase at Cr-concentrations above 9%, occurring at T<900 K.     

Comparative study and imaging by PhotoElectroChemical techniques of oxide films thermally grown on zirconium and Zircaloy-4

The oxidation of iron and chromium that are present as impurities in zirconium metal or as alloying elements in Zircaloy-4 was investigated with PhotoElectroChemical techniques (PEC), highlighting the chemical nature, the size and the lateral distribution of Fe and Cr-containing phases in thin zirconia scales formed during the oxidation of pure zirconium and Zircaloy-4 at 470 °C in oxygen. In the case of zirconium, iron and chromium impurities led to the formation of oxides distributed in a homogeneous way in the zirconia scale, while in the case of Zircaloy-4 these elements, present in the form of intermetallic particles in the substrate, led to the formation of localised haematite Fe₂O₃, rhomboedric solid solution (Fe_xCr_1−x)₂O₃ and chromia Cr₂O₃ phases. These phases were accurately studied via the measurement of their respective band-gap (Fe₂O₃: 2.2 eV, (Fe_xCr_1−x)₂O₃: 2.6 eV and Cr₂O₃: 3.0 eV). It is concluded that PEC techniques represent a sensitive and powerful way to locally analyse the various semiconductor phases in the oxide scale at a micron scale.     

Object kinetic Monte Carlo study of sink strengths

The sink strength for three-dimensionally (3D) versus one-dimensionally (1D), or mixed 1D/3D, migrating defects in irradiated materials has attracted much attention in the recent past, because many experimental observations cannot be interpreted unless 1D or mixed 1D/3D migration patterns are assumed for self-interstitial atom clusters produced in cascades during irradiation. Analytical expressions for the sink strengths for defects migrating in 3D and also in 1D have been therefore developed and a ‘master curve’ approach has been proposed to describe the transition from purely 1D to purely 3D defect migration. Object kinetic Monte Carlo (OKMC) methods have subsequently been used to corroborate the theoretical expressions but, although good agreement was generally found, the ability of this technique to reach the 1D migration limit has been questioned, the limited size of the simulation box used in OKMC studies having been mainly blamed for the inadequacies of the model. In the present work, we explore the capability of OKMC to reproduce the sink strengths of spherical absorbers in a wide range of volume fractions, together with the sink strength of grain boundaries, for defects characterised by different migration dimensionality, from fully 3D to pure 1D. We show that this technique is not only capable of reproducing the theoretical expressions for the sink strengths in the whole range of conditions explored, but is also sensitive enough to reveal the necessity of correcting the theoretical expressions for large sink volume fractions. We thereby demonstrate that, in spite of the limited size of the OKMC simulation box, the method is suitable to describe the microstructure evolution of irradiated materials for any defect migration pattern, including fully 1D migrating defects, as well as to allow for the effect of extended microstructural features, much larger than the simulation box, such as grain boundaries.     

Measurement of implanted helium particle transport by a flowing liquid lithium film

Due to its low atomic number, low sputtering yield, high sputtered ion fraction and excellent thermal properties, liquid lithium has been proposed as a potential candidate for advanced plasma-facing components (PFC). Using a liquid material opens the possibility of a continuously flowing, self-regenerating plasma-facing surface with a small residence time. This would allow such component to handle very high heat loads that are expected. There are, however, multiple unanswered questions regarding how such a liquid PFC would interact with the plasma in the reactor. The issue of particle control is critical, and it can be a factor to determine the feasibility of these advanced concepts. Hydrogen and helium are important in this regard: hydrogen transport by a flowing PFC impacts the reactor fuel recycling regime and tritium inventory; helium transport can help quantify ash removal by the flowing PFC. The flowing liquid-metal retention experiment (FLIRE) was built at the University of Illinois to answer some of the questions regarding particle transport by flowing liquid films exposed to plasmas. Experimental results regarding helium transport by a flowing lithium film after irradiation with an energetic He ion beam are presented in this work. Retained fraction values up to 2% were measured for the experimental conditions, and the retention was found to increase linearly with implanted ion energy. A pure diffusion model was used to describe the helium transport by the Li film, and it was found that such model predicts a diffusion coefficient of (2.8 ± 0.6) × 10⁻¹¹ m²/s, based on the experimental retention measurements. Preliminary evidence of long-term trapping of helium will also be presented.     

Synthesis and characterization of low-temperature precursors of thorium-uranium (IV) phosphate-diphosphate solid solutions

Several compositions of new precursor of thorium-uranium (IV) phosphate-diphosphate solid solutions (Th_4−xU_x(PO₄)₄P₂O₇, called β-TUPD) were synthesized in closed PTFE containers either in autoclave (160 °C) or on sand bath (90-160 °C). All the samples appeared to be single phase. From XRD data and TEM observations, the diffraction lines matched well with that of pure thorium phosphate-hydrogenphosphate hydrate (TPHPH), Th₂(PO₄)₂(HPO₄) · H₂O, which confirmed the preparation of a complete solid solution between pure thorium and uranium (IV) compounds. TGA/DTA experiments showed that samples of thorium-uranium (IV) phosphate-hydrogenphosphate hydrate (TUPHPH) prepared at 150-160 °C were monohydrated leading to the proposed formula Th_2−x/2U_x/2(PO₄)₂(HPO₄) · H₂O. The variation of the XRD diagrams versus the heating temperature showed that TUPHPH remained crystallized and single phase from room temperature to 200 °C. After heating between 200 °C and 800 °C, the presence of diphosphate groups in the solid was evidenced. In this range of temperature, the solid was transformed into the low-temperature monoclinic form of thorium-uranium (IV) phosphate-diphosphate (α-TUPD). This latter compound finally turned into well-crystallized, homogeneous and single-phase β-TUPD (orthorhombic form) above 930-950 °C for x values lower than 2.80. For higher x values, a mixture of β-TUPD, α-Th_1−zU_zP₂O₇ and U_2−wTh_wO(PO₄)₂ was obtained. By this new chemical route of preparation of β-TUPD solid solutions, the homogeneity of the samples is significantly improved, especially considering the distribution of thorium and uranium.     

Molecular dynamics simulations of CH3 sticking on carbon surfaces, angular and energy dependence

Sticking cross-sections for CH₃ radicals at different angles of incidence and different energies were calculated using molecular dynamics simulations, employing both quantum-mechanical and empirical force models. The chemisorption of a CH₃ radical at 2100 K onto a dangling bond is found to be highly dependent on the angle of incidence of the incoming radical. The sticking cross-section decreases from (10.4 ± 1.2) to (1.4 ± 0.3) Ų when the angle of incidence of the methyl radical increases from 0° to 67.5°. A simple geometrical model is presented to explain the angular dependence. In the sticking process of CH₃ radicals with higher kinetic energies (1, 5, and 10 eV) both a fully hydrogen-terminated surface and a surface with dangling bond were studied. The sticking probability is enhanced as the radical energy increases. We observed sticking onto the fully hydrogen-terminated surface for all cases except for the case when the methyl radicals had energies corresponding to a temperature of 2100 K.     

Stress-reorientation of hydrides and hydride embrittlement of Zr-2.5 wt% Nb pressure tube alloy

Hydrogen in excess of the terminal solid solubility precipitates out as a brittle hydride phase in zirconium alloys. The hydrides acquire platelet shaped morphology due to their accommodation in the matrix and can cause severe embrittlement, especially when these are oriented normal to the tensile stress axis. The precipitation of hydride platelets normal to the tensile stress when cooled under stress from a solution-annealing temperature is commonly referred to as ‘stress-reorientation’. The stress-reorientation is associated with a threshold stress below which no reorientation is observed. In this work, stress-reorientation of hydrides was investigated for unirradiated, cold worked and stress-relieved Zr-2.5 wt% Nb pressure tube material for a reorientation temperature of 423-723 K. The effect of the reoriented hydrides on the tensile properties of the Zr-2.5 wt% Nb pressure tube alloy was evaluated in the temperature range of 298-573 K.     

Ab initio calculations of self-interstitial interaction and migration with solute atoms in bcc Fe

The embrittlement of pressure vessel steels under radiation has been long ago correlated with the presence of solute Cu. Indeed the atom probe and the small angle neutron scattering, principally, have revealed the formation of Cu clusters under neutron flux in reactor pressure vessel (RPV) steels and dilute FeCu alloys. Other solutes such as Ni, Mn and Si which are also found within the clusters, are now suspected to contribute to the embrittlement. The interactions of these solutes with radiation induced point defects need thus to be characterized properly in order to understand the elementary mechanisms behind the formation of these clusters. We have investigated by ab initio calculations based on the density functional theory the interactions of self-interstitials with solute atoms in dilute FeX alloys (X = Cu, Mn, Ni or Si). Different possible configurations of solute-dumbbell complexes have been studied. Their binding energies are discussed, as well as their relative stability. The migration of dumbbells with a solute atom in their vicinity was also investigated. All these results are compared to some experimental ones obtained on dilute FeX model alloys. Our results indicate that for Mn solute atoms, diffusion via an interstitial mechanism is very likely.     

Thermo-oxidation of hard carbon films with tungsten surface impurity

The removal of codeposited tritiated carbon films from the next generation of fusion reactors may involve baking in an O₂ environment. Experimental results have indicated that thermo-oxidation can be effective in the removal of such films, however, wide variations have been observed in the oxidation rates of various types of carbon films. In the current experiments, we have investigated the role of metallic impurities by sputter-depositing tungsten onto hard a-C:D films, and exposing them to O₂ gas at 623 K. It was found that rather than catalysing the oxidation of the hydrogenated carbon film, the W deposit tended to inhibit the film removal at this temperature. This suggests that film structure is the predominant factor determining the oxidation rate of tokamak codeposits.     

Effect of alloying elements (Cu, Fe, and Nb) on the creep properties of Zr alloys

The thermal creep behaviors of Zr-based alloys containing Cu, Fe and Nb were investigated under constant load stress at temperatures of 280 and 330 °C, and a stress range of 100-140 MPa. To evaluate an alloying effect on a creep, Zr-based alloys were selected as the binary and ternary systems of Zr-0.3Cu, Zr-0.3Fe, Zr-0.5Nb-0.3Cu and Zr-0.5Nb-0.3Fe. The final annealing of these alloys was performed at 510 °C for 8 h to obtain a recrystallization structure for all the tested alloys. A microstructure characterization test was carried out for the samples before and after the creep test by using TEM, and the results were used to understand the creep mechanism. Creep tests were performed for up to 70 h, which showed a steady-state secondary creep rate in all the alloys. The value of the stress exponent was about 5.5 in all the alloys. The dislocation density was increased by increasing the applied stress, regardless of the alloy system. From the results of this study, it was revealed that the Nb as an alloying element showed the strongest effect on the creep resistance among the added alloying elements, and Fe was more effective than Cu from the viewpoint of creep resistance.     

Ab initio energetics of some fission products (Kr, I, Cs, Sr and He) in uranium dioxide

A computational study of some fission products (FP) energetics in uranium dioxide is presented. Krypton, iodine, caesium, strontium and helium are considered. Calculations are made within the density functional theory in the local density approximation with the plane wave pseudopotential method. Three insertion sites are considered: the octahedral interstitial position and the oxygen and uranium substitution sites. The importance of atomic relaxations is estimated on the He and Kr cases. They prove quantitatively important but can be neglected to draw qualitative trends. For each fission product incorporation and solution energies are calculated. The obtained values of the solutions energies of the various FP are in good agreement with their experimental behaviour: Kr, Cs and I atoms are insoluble in uranium dioxide, Sr solubility depends on the stoichiometry of urania. He atoms are found to have little interaction with their environment in uranium doxide.     

Solubility of actinide surrogates in nuclear glasses

This paper discusses the results of a study of actinide surrogates in a nuclear borosilicate glass to understand the effect of processing conditions (temperature and oxidizing versus reducing conditions) on the solubility limits of these elements. The incorporation of cerium oxide, hafnium oxide, and neodymium oxide in this borosilicate glass was investigated. Cerium is a possible surrogate for tetravalent and trivalent actinides, hafnium for tetravalent actinides, and neodymium for trivalent actinides. The material homogeneity was studied by optical, scanning electron microscopy. Cerium L_III XANES spectroscopy showed that the Ce³⁺/Ce_total ratio increased from about 0.5 to 0.9 as the processing temperature increased from 1100 to 1400 °C. Cerium L_III XANES spectroscopy also confirmed that the increased Ce solubility in glasses melted under reducing conditions was due to complete reduction of all the cerium in the glass. The most significant results pointed out in the current study are that the solubility limits of the actinide surrogates increases with the processing temperature and that Ce³⁺ is shown to be more soluble than Ce⁴⁺ in this borosilicate glass.     

Manufacturing pressurized creep tubes from highly purified V-4Cr-4Ti alloys, NIFS-Heat2

A fabrication process for pressurized creep tubes (PCTs) for a highly purified V-4Cr-4Ti alloy, NIFS-heat2 was established. No increase in impurity contents in PCTs was detected during the tube manufacturing process. In a preliminary thermal creep test, homogeneous deformation was observed over entire tube length, which verifies reliability of creep measurement by using the present PCTs.     

Transmission electron microscopy examination of oxide layers formed on Zr alloys

A transmission electron microscopy investigation was performed on oxides formed on three zirconium alloys (Zircaloy-4, ZIRLO and Zr-2.5Nb) in pure water and lithiated water environments. This research is part of a systematic study of oxide microstructures using various techniques to explain differences in corrosion rates of different zirconium alloys. In this work, cross-sectional transmission electron microscopy was used to determine the morphology of the oxide layers (grain size and shape, oxide phases, texture, cracks, and incorporation of precipitates). These characteristics were found to vary with the alloy chemistry, the corrosion environment, and the distance from the oxide/metal interface. These are discussed and used in conjunction with observations from other techniques to derive a mechanism of oxide growth in zirconium alloys.     

Channelling studies on the lattice location of B atoms in graphite

In order to obtain information on the lattice location of B atoms in graphite, channelling experiments have been performed at room temperature with a proton beam of an energy of 0.65-0.77 MeV for the 〈0 0 0 1〉 axial channel in highly oriented pyrolytic graphite (HOPG) crystals doped with 0.32 at.% B. The B atoms are detected by measuring α-particles which are emitted as a result of a nuclear reaction ¹¹B(p,α)αα. It is clearly demonstrated that most of B atoms are shadowed behind the 〈0 0 0 1〉 C atomic rows. Taking account of the already reported experimental results on a change of lattice parameters by B-doping, it is concluded that most of B atoms are located at substitutional sites. It is also observed that B-doping introduces lattice strain on the c-plane. In addition, the presence of a small portion of interstitial B atoms is suggested.