P.A. Burr

The thermodynamics of hydride precipitation: The importance of entropy, enthalpy and disorder

The precipitation of zirconium hydrides from Zr solid solution was investigated using first-principles lattice dynamics simulations. These included the temperature-dependent vibrational enthalpy and vibrational entropy combined with the configurational entropy terms. In contrast with previous approaches, it was found that the latent enthalpy alone is not sufficient to fully describe precipitation of hydrides; a full thermodynamic assessment is required. In particular, the vibrational enthalpy of precipitation assists in stabilizing hexagonal close-packed hydrides and is especially important in forming the metastable zeta phase. The configurational entropy change during precipitation favours face-centred cubic hydrides. Given this, at concentrations below 300 ppm H, no hydride precipitation is predicted, suggesting that when hydrides are seen in those materials it is because the local concentration of H is greater than that measured globally. While gamma hydride is the most stable phase, it is very close in energy to the delta phase

Hydrogen accommodation in Zr second phase particles: Implications for H pick-up and hydriding of Zircaloy-2 and Zircaloy-4.

Ab-initio computer simulations have been used to predict the energies associated with the accommodation of H atoms at interstitial sites in , -Zr and Zr-M intermetallics formed with common alloying additions (M = Cr, Fe, Ni). Intermetallics that relate to the Zr2(Ni,Fe) second phase particles (SPPs) found in Zircaloy-2 exhibit favourable solution enthalpies for H. The intermetallic phases that relate to the Zr(Cr,Fe)2 SPPs, found predominantly in Zircaloy-4, do not oer favourable sites for interstitial H. It is proposed that Zr(Cr,Fe) 2 particles may act as bridges for the migration of H through the oxide layer, whilst the Zr2(Ni,Fe)-type particles will trap the migrating H until these are dissolved or fully oxidised.

Peroxide defect formation in zirconate perovskites

Atomic scale modelling suggests that excess oxygen can be accommodated in the group II perovskite zirconates by the formation of peroxide ion defects. This is unprecedented given the lack of charge compensating defects required for standard excess oxygen accommodation. The solution energy of O2 was predicted to be close to zero for BaZrO3, accommodating the peroxide ion defect more easily than in SrZrO3 or CaZrO3. This was experimentally examined by exposing SrZrO3 and BaZrO3 to hydrogen peroxide solution and then carrying out Raman spectroscopy measurements to look for a peak indicative of peroxide ions. A peak was observed at ∼1000 cm−1 in both compositions, suggesting the theoretically predicted peroxide ion is present.

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 SnZr× defect was shown to be dominant across most oxygen partial pressures, with SnZr″ charge compensated by VO•• 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 SnZr″ 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.

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). Zr-2(Fe,Ni) and Zr(Nb,Fe)(2) are also discussed

Development of Xe and Kr empirical potentials for CeO2, ThO2, UO2 and PuO2, combining DFT with high temperature MD

The development of embedded atom method (EAM) many-body potentials for actinide oxides and associated mixed oxide (MOX) systems has motivated the development of a complementary parameter set for gas-actinide and gas-oxygen interactions. A comprehensive set of density functional theory (DFT) calculations were used to study Xe and Kr incorporation at a number of sites in CeO2, ThO2, UO2 and PuO2. These structures were used to fit a potential, which was used to generate molecular dynamics (MD) configurations incorporating Xe and Kr at 300 K, 1500 K, 3000 K and 5000 K. Subsequent matching to the forces predicted by DFT for these MD configurations was used to refine the potential set. This fitting approach ensured weighted fitting to configurations that are thermodynamically significant over a broad temperature range, while avoiding computationally expensive DFT-MD calculations. The resultant gas potentials were validated against DFT trapping energies and are suitable for simulating combinations of Xe and Kr in solid solutions of CeO2, ThO2, UO2 and PuO2, providing a powerful tool for the atomistic simulation of conventional nuclear reactor fuel UO2 as well as advanced MOX fuels.

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

To understand the mechanisms by which the re-solution of Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, the solubility and clustering of Fe and Cr in model binary Zr alloys was investigated using a combination of experimental and modelling techniques — atom probe tomography (APT), x-ray diffraction (XRD), thermoelectric power (TEP) and density functional theory (DFT). Cr occupies both interstitial and substitutional sites in the α-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 Fe and Cr content in the α-Zr matrix deviates from Vegards law and is strongly anisotropic for Fe additions, expanding the c-axis while contracting the a-axis. Matrix content of solutes cannot be reliably estimated from lattice parameter measurements, instead a combination of TEP and APT was employed. Defect clusters form at higher solution concentrations, which induce a smaller 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 apparent solubility of defect clusters; the implications for irradiation induced microstructure changes in Zr alloys are discussed.

Importance of elastic finite-size effects: Neutral defects in ionic compounds

Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.

Defect processes in Be12X (X = Ti, Mo, V, W)

The stability of intrinsic point defects in Be

Experimental and DFT investigation of (Cr,Ti)3AlC2 MAX phases stability

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