Monte-Carlo Simulation of Diffusion as an Aid to Interpreting Quasi-elastic Neutron Scattering from Lattice Gas Systems with Diffusion on Multiple Time-Scales

Pd and Pd-Ag have recently found application in hydrogen processing technologies, both in terms of purification membranes and isotope-separation systems. Direct measurement of the diffusion processes in these systems is provided by quasi-elastic neutron scattering (QENS); the timescales that can be observed are dependent on the energy range and resolution of the instru- mentation. Historical QENS measurements of PdH have been interpreted in terms of single process involving nearest-neighbour jumps between octahedral sites in the fcc lattice. The observation of an additional QENS component arising from motion on significantly more rapid timescale has recently been reported (Steel, 2018), whereby a localised-type motion between tetrahedral and octahedral sites has been suggested. The work presented in this thesis involves the calculation of pair correlation functions G(r, t) from Monte Carlo simulations of diffusion in lattice gas systems. Fourier transforming G(r, t) in both time and space yields a scatting function S(Q, ω), comparable to that which would be obtained from QENS measurements from diffusion. S(Q, ω) comprises, in general, a number of Lorentzian functions whose widths are related to decay-constants of exponential functions in the intermediate scattering function, I(Q, t). The separation of components in I(Q, t) offers a route to interpreting diffusive motions on different time-scales. In PdH, only jumps between octahedral and tetrahedral sites are allowed in the Monte Carlo simulations, with the relevant interstitial site energies and barrier heights for diffusion being included in the model. It is shown that I(Q, t) can be interpreted in terms of two decaying exponential functions. T he decay constant, f (Q), from the more slowly decaying exponential component has the form of the Chudley-Elliott model, an analytical expression based on a differential equation describing long-range diffusive motion via a series of uncorrelated jumps. These jumps in the Chudley-Elliott model are interpreted as translational motion via octahedral sites, but given that these jumps are excluded within in the simulation, the actual jump path could instead be interpreted by jumps via a neighbouring tetrahedral site, referred to here as a Octahedral-Tetrahedral-Octahedral (O-T-O) jump mechanism. A more rapid process is suggested to be due to jumps between Octahedral and tetrahedral sites, where there is a much smaller residence time in the tetrahedral sites. Its form as a function of concentration and temperature are discussed in terms of previous experimental spectra. Whilst the main focus of the work is to examine the effect of jump diffusion processes on the QENS signal from hydrogen in PdH, diffusion of hydrogen in the C15 Laves phase alloy ZrV2 was also examined in some detail. The rationale here is that this is a system where long-range translational diffusion and localised diffusion have been shown to coexist, and acts as a good test for the techniques developed and presented in this work. The PdHx system has important practical applications in the filtering and recycling of the exhaust gasses produced in fusion reactions, which is implemented using an alloy of palladium and silver (PdAg) in particle beds an example of which can be seen in the exhaust processing system in the tritium recovery plant of ITER (Glugla et al., 2006b) in which tritiated waste products are passed through palladium-sliver permiators in multiple stages lowering the tritium content