Zirconium alloys are used as cladding in nuclear reactors. They are vulnerable to hydrogen degradation under the harsh service conditions, which necessitates monitoring for the hydride contentHydride denuded zones found these pressure tubes hinders the monitoring process, which uses scrape samples taken from the pressure tubes. A hypothesis is proposed that oxygen slows the diffusion of hydrogen and thereby encourages the occurrence of hydride denuded zones. We developed an approach to determine the diffusivity of hydrogen in zirconium, combining of first principles calculations and kinetic Monte Carlo (KMC) simulations. Rate constants found through the energy landscapes of hydrogen motion between different interstitial sites, were used in KMC to determine the values of bulk diffusivity. We also found that hydrogen diffusivity in Zr is closely isotropic, with a slightly higher diffusivity in the C-axis direction. With this model we found that oxygen decreases the diffusivity of hydrogen for moderate oxygen concentrations. Though the diffusivity of H seems to be reduced by O, looking at the O concentration profiles found in pressure tubes, we see that the decrease is insufficient to cause a sufficient change to the size of hydrides. Hence, we reject the hypothesis as the main reason for the formation of denuded zones. Thereafter, we used the model to determine the effect of stress on diffusivity of H by applied hydrostatic stresses. We see a decrease in the diffusivity with increase in compressive stress showing us that stress does influence the diffusivity of H. The main reason for this decrease is the increase in activation barriers Lead Zirconate Titanate (PZT) is a widely used piezoelectric material which is also affected by H absorption. This gives the need of understanding the H diffusion in PZT. This research presents the initial results of a study which aims to simulate hydrogen diffusion in PZT using the validated diffusion model used for Zr. First-principles calculations were done to determine the possible hydrogen occupancy locations in the PZT lattice. These results will serve as a basis for future nudged elastic band calculations to determine the diffusion characteristics for H diffusion in PZT.