Hydrogen storage in epitaxial films: a finite element study

In epitaxial niobium (Nb) films on sapphire substrates, there is an enhancement in the solubility of hydrogen (at a given pressure and temperature) due to biaxial tensile stresses. These stresses are partly relieved on growth of the film beyond critical thickness, leading to a reduction in the amount of excess hydrogen that can be stored in the film. Additionally, a depletion of hydrogen from the compressive regions of interfacial misfit dislocations further reduces the hydrogen storage capacity of the film. In this work, a finite-element methodology developed earlier is extended and further utilized to get a spatial map of hydrogen before and after critical thickness is exceeded. Critical thickness for "Nb(111)" ||sapphire(0001) (finite) system is calculated using a three-dimensional numerical model. With the aid of standard theoretical equations, the spatial variation of the enrichment of hydrogen is determined using the stress fields computed from the finite-element model. This calculation is performed in a system with and without an interfacial misfit dislocation, after the critical thickness is exceeded, to evaluate the reduction in the storage capacity of hydrogen in the niobium film.