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Modeling of Phase Transitions during Hydride Formation in Palladium-Hydrogen Systems

Johannes Gisy 1*, Magdalena Seiler2, Stefan Wagner2, Astrid Pundt2, Thomas Böhlke 1

1 Karlsruhe Institute of Technology (KIT), Institute of Engineering Mechanics, Chair of Continuum Mechanics; 2 Karlsruhe Institute of Technology (KIT), Institute for Applied Materials, Materials Science and Engineering

Phase-Field, Phase Change & Chemo-Mechanical Microstructure Evolution · C223
Thursday, 3 September 2026, 14:50–15:15 · Chair: Milan Jirásek

Keywords: chemo-mechanical coupling, visco-plasticity, phase transitions

Thin metal films are exposed to hydrogen (H) such that hydride formation and phase stability can be investigated. The hydride-forming metal, i.e., palladium (Pd), is sputtered on an inert substrate. Due to the H-induced lattice expansion of the adhered film, stresses arise, and the composite structure bends. Depending on the stress state, the H concentration and the temperature, hydride formation is possible or suppressed [1]. However, inelastic deformations alter the phase stability for a fixed temperature. Experimental studies by Colla et al. [2] investigate the creep behavior of thin Pd films, revealing a rate dependency of the plastic flow. To support these investigations, a Finite­-Element (FE) model to represent physically, but also geometrically, the composite structure is needed. A chemo­-mechanical model for the thin film accounting for H diffusion and inelastic deformation is introduced. The focus is on the chemo-mechanical coupling as hydride formation in the PdH system at room temperature depends strongly on the plastic deformations [1]. The diffusion model fully couples the chemical and mechanical constitutive response following [3] and [4]. The chemical potential depends on the mechanical stress state which impacts the phase stability during hydride formation. However, only the hydrostatic stresses contribute to the chemical potential while plasticity coupling is solely due to geometrical constraints. Thus, the thickness's contrast and its influence on the stress state needs to be studied. Current results regarding the role of phase formations on the stress evolution as well as a comparison between model and experimental measurements will be presented.

References

  1. A. Dyck, T. Böhlke, A. Pundt, and S. Wagner, Phase transformation in the palladium hydrogen system: effects of boundary conditions on phase stabilities, Scripta Materialia, 247:116117, 2024, https://doi.org/10.1016/j.scriptamat.2024.116117.
  2. M. S. Colla, et al., Dislocation-mediated relaxation in nanograined columnar palladium films revealed by on-chip time-resolved HRTEM testing, Nature Communications, 6(1), 2015, https://doi.org/10.1038/ncomms6922.
  3. J. Gisy, A. Dyck, and T. Böhlke, A numerical study on the physical couplings of a geometrically linear thermo-chemo-mechanical model, International Journal of Solids and Structures, 309:113162, 2025, https://doi.org/10.1016/j.ijsolstr.2024.113162.
  4. A. Dyck, et al., Hydride formation in open thin film metal hydrogen systems: Cahn–Hilliard-type phase-field simulations coupled to elasto-plastic deformations, Mechanics of Materials, 203:105258, 2025, https://doi.org/10.1016/j.mechmat.2025.105258.