First-principles calculation of the elastic dipole tensor of a point defect: Application to hydrogen in α-zirconium

The elastic dipole tensor is a fundamental quantity relating the elastic field and atomic structure of a point defect. We review three methods in the literature to calculate the dipole tensor and apply them to hydrogen in α -zirconium using density functional theory (DFT). The results are compared with the dipole tensor deduced from earlier experimental measurements of the λ tensor for hydrogen in α -zirconium. There are significant errors with all three methods. We show that calculation of the λ tensor, in combination with experimentally measured elastic constants and lattice parameters, yields dipole tensor components that differ from experimental values by only 10%–20%. There is evidence to suggest that current state-of-the-art DFT calculations underestimate bonding between hydrogen and α -zirconium

Hydrogen solubility in zirconium intermetallic second phase particles

The enthalpies of solution of H in Zr binary intermetallic compounds formed with Cu, Cr, Fe, Mo, Ni, Nb, Sn and V were calculated by means of density functional theory simulations and compared to that of H in {\alpha}-Zr. It is predicted that all Zr-rich phases (formed with Cu, Fe, Ni and Sn), and those phases formed with Nb and V, offer lower energy, more stable sites for H than {\alpha}-Zr. Conversely, Mo and Cr containing phases do not provide preferential solution sites for H. In all cases the most stable site for H are those that offer the highest coordination fraction of Zr atoms. Often these are four Zr tetrahedra but not always. Implications with respect to H-trapping properties of commonly observed ternary phases such as Zr(Cr,Fe)2, Zr2(Fe,Ni) and Zr(Nb,Fe)2 are also discussed.Comment: manuscript accepted for publication in Journal of Nuclear Materials (2013

From solid solution to cluster formation of Fe and Cr in α\alpha-Zr

To understand the mechanisms by which Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, a combination of experimental (atom probe tomography, x-ray diffraction and thermoelectric power measurements) and modelling (density functional theory) techniques are employed to investigate the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys. Cr occupies both interstitial and substitutional sites in the {\alpha}-Zr lattice, Fe favours interstitial sites, and a low-symmetry site that was not previously modelled is found to be the most favourable for Fe. Lattice expansion as a function of alloying concentration (in the dilute regime) is strongly anisotropic for Fe additions, expanding the $c$-axis while contracting the $a$-axis. Defect clusters are observed at higher solution concentrations, which induce a smaller amount of lattice strain compared to the dilute defects. In the presence of a Zr vacancy, all two-atom clusters are more soluble than individual point defects and as many as four Fe or three Cr atoms could be accommodated in a single Zr vacancy. The Zr vacancy is critical for the increased solubility of defect clusters, the implications for irradiation induced microstructure changes in Zr alloys are discussed.Comment: 15 pages including figure, 9 figures, 2 tables. Submitted for publication in Acta Mater, Journal of Nuclear Materials (2015

Understanding the importance of the energetics of Mn, Ni, Cu, Si and vacancy triplet clusters in bcc Fe

Numerous experimental studies have found the presence of (Cu)-Ni-Mn-Si clusters in neutron irradiated reactor pressure vessel steels, prompting concerns that these clusters could lead to larger than expected increases in hardening, especially at high fluences late in life. The mechanics governing clustering for the Fe-Mn-Ni-Si system are not well-known; state-of-the-art methods use kinetic Monte Carlo (KMC) parameterised by density functional theory (DFT) and thermodynamic data to model the time evolution of clusters. However, DFT based KMC studies have so far been limited to only pairwise interactions due to lack of DFT data. Here we explicitly calculate the binding energy of triplet clusters of Mn, Ni, Cu, Si and vacancies in bcc Fe using DFT to show that the presence of vacancies, Si, or Cu stabilises cluster formation, as clusters containing exclusively Mn and/or Ni are not energetically stable in the absence of interstitials. We further identify which clusters may be reasonably approximated as a sum of pairwise interactions, and which instead require an explicit treatment of the three-body interaction, showing that the three-body term can account for as much as 0.3 eV, especially for clusters containing vacancies

Examining the thermal properties of unirradiated nuclear grade graphite between 750 and 2500 K

This study presents the first high temperature measurements (between 750 K and 2500 K) of thermal conductivity, thermal diffusivity, specific heat and spectral emissivity of virgin graphite samples (type IM1-24) from advanced gas-cooled reactor (AGR) fuel assembly bricks. Scanning electron microscope (SEM) and X-ray computed tomography (XRT) techniques were used to verify the presence of Gilsocarbon filler particles (a characteristic microstructural feature of IM1-24 graphite). All thermal properties were investigated in two orthogonal directions, which showed the effective macroscopic thermal conductivity to be the same (to within experimental error). This can be linked to the morphology of the filler particles that consist of concentrically aligned graphitic platelets. The resulting spherical symmetry allows for heat to flow in the same manner in both macroscopic directions. The current thermal conductivity results were compared to other isotropic grade graphite materials. The significant discrepancies between the thermal conductivities of the individual grades are likely the result of different manufacturing processes yielding variations in the microstructure of the final product. Differences were identified in the filler particle size and structure, and possibly the degree of graphitization compared to other reported nuclear graphites

Modelling the role of pellet crack motion in the (r-θ) plane upon pellet-clad interaction in advanced gas reactor fuel

A finite element model of pellet fragment relocation in the r-θ plane of advanced gas-cooled reactor (AGR) fuel is presented under conditions of both ‘hard’ and ‘soft’ pellet-clad interaction. The model was able to predict the additional radial displacement of fuel fragments towards the cladding as well as the stress concentration on the inner surface resulting from the azimuthal motion of pellet fragments. The model was subjected to a severe ramp in power from both full power and after a period of reduced power operation; in the former, the maximum hoop stress in the cladding was found to be increased by a factor of 1.6 as a result of modelling the pellet fragment motion. The pellet-clad interaction was found to be relatively insensitive to the number of radial pellet crack. However, it was very sensitive to both the coefficient of friction used between the clad and pellet fragments and power ramp duration

Application of Weibull fracture strength distributions to modelling crack initiation behaviour in nuclear fuel pellets using peridynamics

The thermomechanical behaviour of uranium dioxide nuclear fuel pellets irradiated in a pressurised water reactor has been simulated using a two-dimensional application of bond-based peridynamics implemented in the Abaqus commercial finite element software. Near-surface bond failure, and hence crack initiation, were modelled assuming a probabilistic (variable) failure strain described by a Weibull distribution – with bond failure, and hence crack propagation, in the bulk of the fuel pellets modelled assuming a deterministic (fixed) failure strain. The measured dependency of the number of radial pellet cracks on heat generation rate per unit length – which we show cannot be reproduced by the common assumption in pellet modelling of a deterministic failure strain throughout the pellet volume – was accurately predicted when a size-scaled Weibull distribution with a modulus of 5 was used. However, this low modulus value was associated with the prediction of some cracks initiating away from the pellet surface, which is unphysical. Use of a Weibull modulus of 10 avoided this simulation artefact while still reproducing the experimentally observed dependency with reasonable accuracy

Accommodation of tin in tetragonal ZrO2

Atomic scale computer simulations using density functional theory were used to investigate the behaviour of tin in the tetragonal phase oxide layer on Zr-based alloys. The Sn×ZrSnZr× defect was shown to be dominant across most oxygen partial pressures, with Sn′′ZrSnZr″ charge compensated by V∙∙OVO•• occurring at partial pressures below 10−31 atm. Insertion of additional positive charge into the system was shown to significantly increase the critical partial pressure at which Sn′′ZrSnZr″ is stable. Recently developed low-Sn nuclear fuel cladding alloys have demonstrated an improved corrosion resistance and a delayed transition compared to Sn-containing alloys, such as Zircaloy-4. The interaction between the positive charge and the tin defect is discussed in the context of alloying additions, such as niobium and their influence on corrosion of cladding alloys

The effect of pressure on hydrogen solubility in Zircaloy-4

The effect of pressure on the room temperature solubility of hydrogen in Zircaloy-4 was examined using synchrotron X-ray diffraction on small ground flake samples in a diamond anvil cell at pressures up to 20.9 GPa. Different combinations of hydrogen level/state in the sample and of pressure transmitting medium were examined; in all three experiments, it could be concluded that pressure resulted in the dissolution of δ hydrides and that interstitial hydrogen seemingly retards the formation of ω Zr. A pressure of around 9 GPa was required to halve the hydride fraction. These results imply that the effect of pressure is thermodynamically analogous to that of increasing temperature, but that the effect is small. The results are consistent with the volume per Zr atom of the α, δ and ω phases, with the bulk moduli of α and δ, and with previous measurements of the hydrogen site molar volumes in the α and δ phases. The results are interpreted in terms of their implication for our understanding of the driving forces for hydride precipitation at crack tips, which are in a region of hydrostatic tensile stress on the order of 1.5 GPa