Hydride formation in open thin film metal hydrogen systems: Cahn–Hilliard-type phase-field simulations coupled to elasto-plastic deformations

Abstract

For the usage of intercalating material systems to store and convert energy of renewable sources, their phase stabilities need to be engineered to adjust to the desired operation conditions. This can, e.g., be achieved by miniaturization, leading to constraints that modify the systems thermodynamics. The experimental investigation of such systems is cumbersome, as experiments on nano-sized systems are time intensive. Numerical simulations based on chemo-mechanically coupled continuum models can serve as a tool helping to understand these systems and to study different effects of miniaturization. In this work we present a phase-field model for the example of open, constrained metal hydrogen thin film systems, that allows the prediction of the hydrogen intercalation and hydride formation. The model relies on a free energy density consisting of chemical, mechanical and interfacial parts. The first two contributions are based on measurements of the thermodynamics of open Niobium–Hydrogen thin films, that are chosen as a model. The interfacial contribution of Cahn–Hilliard-type introduces a phase-field description for both phases. To study the systems behavior a numerical implementation in the commercial Finite Element solver ABAQUS is presented. Numerical results are presented and compared to previously obtained experimental results on the open systems thermodynamics. We show, that the model is capable of reproducing experimentally observed behavior of thin films especially regarding the coexistence of $\alpha$- and hydride-phase in thermodynamic equilibrium, where the equilibrium concentrations in both phases drastically differ from bulk values, and gradients in concentration and stresses result due to the interfacial constraint conditions.