(Digital Presentation) Predicting Hydrogen Diffusivity in Amorphous Titania Using Markov Chain Kinetic Monte Carlo Simulations

Understanding hydrogen transport is vital to industries focused on discovering new materials for energy storage and corrosion mitigation. However, knowledge of the physical nature of hydrogen’s diffusion pathways is often limited, especially for materials that exhibit a multitude of phases/defect classes. These materials typically have three rate-limiting structural domains: (1) bulk (2) grain boundaries, and (3) surfaces. In this work we have chosen to study hydrogen diffusion through titania due to its importance in the aforementioned application spaces. Here, we aim to understand diffusion through titania grain boundaries, which are approximated via the amorphous phase. Density functional theory (DFT) was used to calculate thousands of activation energies of hydrogen diffusion in the amorphous phase via nudged elastic band calculations using an automated hydrogen pathway generation scheme. Amorphous structures, on the order of tens of nanometers, were generated using a machine learning force field via classical molecular dynamics (MD). Markov chains were generated using the MD-derived atomic structures as their reference. Kinetic Monte Carlo (KMC) simulations were then performed over a variety of temperatures and stoichiometries, for system sizes in the tens of nanometers, allowing us to connect directly with experimental measurements. Using our KMC simulations we can directly calculate the hydrogen diffusion constant, as a function of temperature and stoichiometry, and compare these values with those determined via experiments. We also employ a graph-based characterization scheme that can quantify the subtle differences in local hydrogen diffusion networks throughout the KMC simulation, allowing us to link local hydrogen diffusivity with structural differences within the material observed along the diffusion pathway. This work sets the stage for one to perform long time-scale and/or length-scale simulations to understand how temperature and atomic structure affect properties such as diffusivity, solubility, and permeation, and connect these values directly with experiments.