Title:

Multiscale modelling of hydrogen in zirconium

The presence of hydrogen (H) is deleterious to many metals and alloys, and results in the loss of integrity by a number of embrittlement processes. The zirconium (Zr) alloys used throughout the nuclear industry to produce protective fuel cladding are highly susceptible to one form of H embrittlement: Delayed Hydride Cracking (DHC), which occurs because Zr is a hydrideforming metal. H atoms are introduced into the fuel clad by the corrosion reaction and diffuse along stress, temperature and concentration gradients. DHC occurs when H diffuses along the stress gradient caused by a crack in the clad. Once enough H accumulates and the precipitation solvus is reached, brittle hydrides grow ahead of the crack and eventually enable the crack to propagate. The process then begins again with H diffusion. The present work is aimed at modelling H diffusion in Zr under the influence of the elastic field caused by dislocations, as a precursor to the diffusion of H to cracks. A combination of first principles Density Functional Theory (DFT) simulations, atomistic simulations with Embedded Atom Method (EAM) Empirical Potentials (EPs), and analytical models are used to simulate H diffusion to a dislocation on the continuum scale, incorporating the elastic interaction energy between H and the dislocation as a driver. The defect forces exerted by interstitial H on neighbouring Zr atoms are calculated using DFT and EP methods. The free energy of H in Zr as a function of applied strain is also calculated using both DFT and EP. These quantities are then used to evaluate the elastic dipole tensor of H in Zr using two approaches: the defect forces method, and the strain method. Expressions for the dipole tensor are derived using the two approaches and their methods of calculation are also described. The purpose of evaluating the elastic dipole tensor is to illustrate the anisotropy of the elastic field of H in Zr. It is shown that the elastic field of H can be more accurately described as a misfitting prolate spheroid, than by the typical misfitting sphere approach. The calculated dipole tensors using both methods and both simulation techniques show that the dipole tensor components ρ11 = ρ22 ≠ 33, which is representative of the fact that the hexagonal closepacked (HCP) crystal is isotropic in the basal plane and has a nonideal c/a ratio. It is shown that the defect forces method yields a conditionally convergent sum, requiring the forces to fall as 1=R3 or faster to obtain a converged dipole tensor, where R is the radial distance between H and surrounding Zr atoms. This is not satisfied when using DFT, whereas converged forces are obtained using the EP. It is found that there is no numerical agreement between the strain and defect forces method dipole tensors using either DFT or EP, and that this mismatch can be attributed to the series of assumptions that lead to each expression for the elastic dipole tensor. Using DFT, the ρ11 component of the dipole tensor is found to be lower than the ρ33 component (ρ11 = 1.68 eV and ρ33 = 1.74 eV for a 96atom supercell), whereas the EP technique yielded a higher ρ11 component (ρ11 = 3.94 eV and ρ33 = 3.68 eV for a 96atom supercell). The reason for this is attributed to an underestimation of the strength of the ZrH bond by the EAM potential developed by [1]. The workdone formulation for the elastic interaction energy is used to compute the elastic interaction energy between H interstitials and dislocations in Zr, without needing to simulate H and a dislocation together in a single simulation cell, which can become computationally expensive, particularly for edge dislocations. This new approach also combines atomistic simulations with continuum models, and can be scaled up to evaluate the interaction between H interstitials and cracks, or any other displacement field, whilst also accounting for anisotropy. The computed elastic interaction energy is used in a stress driven diffusion calculation to model the diffusion of H to dislocations. Two dislocation elastic fields are compared: a prism dislocation with dislocation line oriented along the caxis and b= (a/3) [2⁻1 ⁻10], and a basal dislocation with dislocation line oriented in the basal plane and b= (a/3) [2⁻1 ⁻10]. It is shown that since the elastic field of the prism dislocation is isotropic, the elastic interaction between H and the dislocation will also be isotropic. Therefore a dislocation oriented in another direction, with a nonzero displacement field component along the crystal caxis, is required to highlight the anisotropy of its elastic interaction with H. This is shown to be the case with the basal edge dislocation. It is shown that both the prism and basal dislocations become saturated with H within 2 picoseconds at 300K, with H accumulating around the basal dislocation more rapidly at all temperatures. Furthermore it is shown that at low temperatures, the basal dislocation in particular can act as a nucleation site for hydrides, by attracting enough H to its atmosphere to exceed the solubility limit. The work presented in this thesis is a theoretical characterisation of the elastic field of H in Zr, its elastic interaction with dislocations, and its diffusion to dislocations, whilst accounting for anisotropy. The above is work that has not yet been performed on the ZrH system.
