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

Causal Space-Times on a Null Lattice

I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are constructed from local Lorentz symmetry considerations only. For smooth configurations, the local lattice actions reduce to the Hilbert-Palatini action, a cosmological term and the three topological terms of dimension four of Pontyagin, Euler and Nieh-Yan. Consistency conditions for a topologically hypercubic complex with null 4-simplexes are derived and a topological lattice theory that enforces these non-local constraints is constructed. The lattice integration measure is derived from an \SLC-invariant integration measure by localization of the non-local structure group. This measure is unique up to a density that depends on the local 4-volume. It can be expressed in terms of manifestly coordinate invariant geometrical quantities. The density provides an invariant regularization of the lattice integration measure that suppresses configurations with small local 4-volumes. Amplitudes conditioned on geodesic distances between local observables have a physical interpretation and may have a smooth ultraviolet limit. Numerical studies on small lattices in the unphysical strong coupling regime of large imaginary cosmological constant suggest that this model of triangulated causal manifolds is finite. Two topologically different triangulations of space-time are discussed: a single, causally connected universe and a duoverse with two causally disjoint connected components. In the duoverse, two hypercubic sublattices are causally disjoint but the local curvature depends on fields of both sublattices. This may simulate effects of dark matter in the continuum limit.Comment: Greatly improved version, new numerics, appendices, etc.. 42 pages, 14 figure

Lattice methods for strongly interacting many-body systems

Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic few- and many-body systems, blurring the interfaces between condensed matter, atomic and low-energy nuclear physics. While some of these techniques have been in use in the area of condensed matter physics for a long time, others, such as hybrid Monte Carlo and improved effective actions, have only recently found their way across areas. With this topical review, we aim to provide a modest overview and a status update on a few notable recent developments. For the sake of brevity we focus on zero-temperature, non-relativistic problems. After a short introduction, we lay out some general considerations and proceed to discuss sampling algorithms, observables, and systematic effects. We show selected results on ground- and excited-state properties of fermions in the limit of unitarity. The appendix contains details on group theory on the lattice.Comment: 64 pages, 32 figures; topical review for J. Phys. G; replaced with published versio

Ab initio parametrised model of strain-dependent solubility of H in alpha-iron

The calculated effects of interstitial hydrogen on the elastic properties of alpha-iron from our earlier work are used to describe the H interactions with homogeneous strain fields using ab initio methods. In particular we calculate the H solublility in Fe subject to hydrostatic, uniaxial, and shear strain. For comparison, these interactions are parametrised successfully using a simple model with parameters entirely derived from ab initio methods. The results are used to predict the solubility of H in spatially-varying elastic strain fields, representative of realistic dislocations outside their core. We find a strong directional dependence of the H-dislocation interaction, leading to strong attraction of H by the axial strain components of edge dislocations and by screw dislocations oriented along the critical slip direction. We further find a H concentration enhancement around dislocation cores, consistent with experimental observations.Comment: part 2/2 from splitting of 1009.3784 (first part was 1102.0187), minor changes from previous version

S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD

The isospin-2 pi pi system provides a useful testing ground for determining elastic hadron scattering parameters from finite-volume spectra obtained using lattice QCD computations. A reliable determination of the excited state spectrum of two pions in a cubic box follows from variational analysis of correlator matrices constructed using a large basis of operators. A general operator construction is presented which respects the symmetries of a multi-hadron system in flight. This is applied to the case of pi pi and allows for the determination of the scattering phase-shifts at a large number of kinematic points, in both S-wave and D-wave, within the elastic region. The technique is demonstrated with a calculation at a pion mass of 396 MeV, where the elastic scattering is found to be well described by a scattering length parameterisation.Comment: Tables of little-group CGCs in ancillary file; v2: minor changes to reflect published versio