M.R. Wenman

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

Strain fields and line energies of dislocations in uranium dioxide

Computer simulations are used to investigate the stability of typical dislocations in uranium dioxide. We explain in detail the methods used to produce the dislocation configurations and calculate the line energy and Peierls barrier for pure edge and screw dislocations with the shortest Burgers vector ½⟨110⟩. The easiest slip system is found to be the {100}⟨110⟩ system for stoichiometric UO(2), in agreement with experimental observations. We also examine the different strain fields associated with these line defects and the close agreement between the strain field predicted by atomic scale models and the application of elastic theory. Molecular dynamics simulations are used to investigate the processes of slip that may occur for the three different edge dislocation geometries and nudged elastic band calculations are used to establish a value for the Peierls barrier, showing the possible utility of the method in investigating both thermodynamic average behaviour and dynamic processes such as creep and plastic deformation.

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.

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

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.

High temperature measurements and condensed matter analysis of the thermo-physical properties of ThO2

Values are presented for thermal conductivity, specific heat, spectral and total hemispherical emissivity of ThO2 (a potential nuclear fuel material) in a temperature range representative of a nuclear accident - 2000 K to 3050 K. For the first time direct measurements of thermal conductivity have been carried out on ThO2 at such high temperatures, clearly showing the property does not decrease above 2000 K. This could be understood in terms of an electronic contribution (arising from defect induced donor/acceptor states) compensating the degradation of lattice thermal conductivity. The increase in total hemispherical emissivity and visible/near-infrared spectral emissivity is consistent with the formation of donor/acceptor states in the band gap of ThO2. The electronic population of these defect states increases with temperature and hence more incoming photons (in the visible and near-infrared wavelength range) can be absorbed. A solid state physics model is used to interpret the experimental results. Specific heat and thermal expansion coefficient increase at high temperatures due to the formation of defects, in particular oxygen Frenkel pairs. Prior to melting a gradual increase to a maximum value is predicted in both properties. These maxima mark the onset of saturation of oxygen interstitial sites.