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

Variation in ambulance call rates for care homes in Torbay, UK

Emergency ambulance calls represent one of the routes of emergency hospital admissions from care homes. We aimed to describe the pattern of ambulance call rates from care homes and identify factors predicting those homes calling for an ambulance most frequently. We obtained data from South Western Ambulance Service NHS Foundation Trust on 3138 ambulance calls relating to people aged 65 and over from care homes in the Torbay region between 1/4/12 and 31/7/13. We supplemented this with data from the Care Quality Commission (CQC) website on home characteristics and outcomes of CQC inspections. We used descriptive statistics to identify variation in ambulance call rates for residential and nursing homes and fitted negative binomial regression models to determine if call rates were predicted by home type (nursing versus residential), the five standards in the CQC reports, dementia care status or travel time to hospital. One hundred and forty-six homes (119 residential and 27 nursing) were included in the analysis. The number of calls made ranged from 1 to 99. The median number (IQR; range) of calls per resident per year was 0.51 (0.21 to 0.89; 0.03 to 2.45). Nursing homes had a lower call rate than residential homes (adjusted rate ratio (ARR) 0.29; 95% CI: 0.22 to 0.40 ; p<0.001); care homes failing the quality and suitability of management standard had a lower call rate compared to those who passed (ARR 0.67; 95% CI: 0.50 to 0.90; p=0.006); and homes specialising in dementia had a higher call rate compared to those not specialising (ARR 1.56; 95% CI: 1.23 to 1.96; p<0.001). These findings require replication in other regions to establish their generalisability and further investigation is required to determine the extent to which callrate variability reflects the different needs of resident populations or differences in care home policies and practice

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

The bonding of H in Zr under strain

Accurate computer simulation is important for understanding the role of irradiation-induced defects in zirconium alloys found in nuclear reactors. Of particular interest is the distribution and trapping of hydrogen, and the formation of zirconium hydride. These simulations require an accurate representation of Zr-H bonding in order to predict the behaviour of H around atomic-scale defects, dislocation lines, and dislocation loops. Here we explore the bonding of H in Zr under strain, how well it is represented by state-of-the-art Embedded Atom Method (EAM) potentials, and what physics is needed for an accurate representation in a Linear Combination of Atomic Orbitals (LCAO) Density Functional Theory (DFT) framework. For H in dilute solution under hydrostatic strain in the range -10% to +10%, solution energies and Zr-H bond lengths computed using EAM potentials are found to be in poor agreement with plane-wave DFT results. We note that the bond lengths are in a poor agreement even in equilibrium. LCAO basis sets are used to explore the importance of electron distribution around H atoms, and the transfer of electrons between H and Zr. The electron distribution around H atoms is found to be important to the explanation of the difference between octahedral and tetrahedral interstitial sites for H, with H in a tetrahedral site having very similar bonding to H in zirconium hydrides. The interatomic electron transfer has a smaller impact but is needed for maximum accuracy

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

Systematic development of ab initio tight-binding models for hexagonal metals

A systematic method for building an extensible tight-binding model from ab initio calculations has been developed and tested on two hexagonal metals: Zr and Mg. The errors introduced at each level of approximation are discussed and quantified. For bulk materials, using a limited basis set of s p d orbitals is shown to be sufficient to reproduce with high accuracy bulk energy versus volume curves for fcc, bcc, and hcp lattice structures, as well as the electronic density of states. However, the two-center approximation introduces errors of several tenths of eV in the pair potential, crystal-field terms, and hopping integrals. Environmentally dependent corrections to the former two have been implemented, significantly improving the accuracy. Two-center hopping integrals were corrected by taking many-center hopping integrals for a set of structures of interest, rotating them into the bond reference frame, and then fitting a smooth function through these values. Finally, a pair potential was fitted to correct remaining errors. However, this procedure is not sufficient to ensure transferability of the model, especially when point defects are introduced. In particular, it is shown to be problematic when interstitial elements are added to the model, as demonstrated in the case of octahedral self-interstitial atoms

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

Peridynamic modelling of cracking in TRISO particles for high temperature reactors

A linear-elastic computer simulation (model) for a single particle of TRISO fuel has been built using a bond-based peridynamic technique implemented in the finite element code ‘Abaqus’. The model is able to consider the elastic and thermal strains in each layer of the particle and to simulate potential fracture both within and between layers. The 2D cylindrical model makes use of a plane stress approximation perpendicular to the plane modelled. The choice of plane stress was made by comparison of 2D and 3D finite element models. During an idealised ramp to normal operating power for a kernel of 0.267 W and a bulk fuel temperature of 1305 K, cracks initiate in the buffer near to the kernel-buffer interface and propagate towards the buffer-iPyC coating interface, but do not penetrate the iPyC and containment of the fission products is maintained. In extreme accident conditions, at around 600% (1.60 W) power during a power ramp at 100% power (0.267 W) per second, cracks were predicted to form on the kernel side of the kernel-buffer interface, opposite existing cracks in the buffer. These were predicted to then only grow further with further increases in power. The SiC coating was predicted to subsequently fail at a power of 940% (2.51 W), with cracks formed rapidly at the iPyC-SiC interface and propagating in both directions. These would overcome the containment to fission gas release offered by the SiC ‘pressure vessel’. The extremely high power at which failure was predicted indicates the potential safety benefits of the proposed high temperature reactor design based on TRISO fuel