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A ReaxFF Molecular Dynamics Study of Hydrogen Diffusion in Ruthenium—The Role of Grain Boundaries

Scope

New ReaxFF for Ru/H with MD of hydrogen in pristine hcp Ru versus Σ7 tilt and twist grain boundaries—GBs trap H and redirect diffusion anisotropically, informing EUV mirror capping layers.

Summary

Ruthenium caps on EUV multilayer mirrors must limit hydrogen uptake that drives blistering. Prior DFT indicated low bulk H solubility; this work parametrizes a ReaxFF model against quantum data for Ru/H and runs reactive MD on nanocrystalline motifs to isolate grain-boundary effects on H transport.

Methods

1 — MD application (atomistic dynamics)

  • Engine / code: ReaxFF molecular dynamics was run with the AMS2020 reactive MD package; trajectory analysis (including hydrogen MSD) used MDAnalysis.
  • System size and composition: Three Ru/H cells were simulated: pristine hcp Ru (40.6 x 37.5 x 34.3 A, 3840 Ru + 40 H), Sigma7 tilt GB (27.0 x 46.8 x 42.8 A, 3690 Ru + 40 H), and Sigma7 twist GB (36.1 x 36.1 x 34.8 A, 2800 Ru + 28 H).
  • Boundaries / periodicity: 3D periodic boundary conditions for all cells.
  • Ensemble: Pre-equilibration in NpT, then diffusion production in NVT.
  • Timestep: 0.25 fs (velocity-Verlet integration).
  • Duration / stages: At least 0.1 ns pre-equilibration before NVT diffusion sampling; configurations saved every 1000 steps.
  • Thermostat: Nose-Hoover chain thermostat (chain length 10; damping 25 fs).
  • Barostat: Berendsen barostat during NpT pre-equilibration.
  • Temperature: Maxwell-Boltzmann initialization at target temperature; 700 K is explicitly shown in GB snapshots.
  • Pressure: 1 atm during NpT pre-equilibration; N/A for pressure control in the NVT diffusion stage.
  • Electric field: N/A - no external field protocol reported.
  • Replica / enhanced sampling: N/A - no umbrella, metadynamics, or replica exchange reported.

2 — Force-field training (Ru/H ReaxFF)

  • Parent FF / elements: New Ru/H ReaxFF parameterization targeting ruthenium with dissolved/interstitial hydrogen.
  • QM reference: BAND calculations using a PBE + TS + SOC + ZORA style reference level as described in the paper/SI.
  • Training set: Bulk hcp Ru structural and elastic targets (a, c/a, cell volume, bulk modulus) plus hydrogen site energetics in Ru (tetrahedral and octahedral environments).
  • Optimization: ReaxFF parameter fitting workflow is reported in the article and SI; exact optimizer weighting details are not fully expanded in this page text.
  • Reference data used: DFT-derived quantities above were used for fit/validation, and the paper compares H site energetics to earlier reported values.

3 — Experiments

  • EUV lithography is cited as motivation; N/A in-house H-in-Ru measurement in this computational paper (indirect H-in-Y H-proxy only in ref [13] cited in the intro per JPCC text)**.

Findings

1 — Outcomes and mechanisms

The simulations indicate that Sigma7 tilt and twist grain boundaries in Ru are hydrogen-favoring regions relative to pristine hcp Ru. Hydrogen diffusion is anisotropic in GB-containing models: transport along the boundary plane is faster, while crossing the boundary plane is more hindered, which produces effective trapping/accumulation at the boundary environment.

2 — Comparisons

Compared with the pristine Ru cell, both GB models show stronger hydrogen localization at interfacial regions and altered diffusion pathways. The fitted Ru/H ReaxFF also reproduces key Ru bulk structural/mechanical quantities reported in the study benchmark set, supporting use of the potential for this GB-versus-bulk transport comparison.

3 — Sensitivity and design levers

Microstructure is the key design lever highlighted by this paper: introducing specific GB motifs changes both preferred hydrogen residence sites and directional mobility. The article framing links this to Ru cap performance in EUV systems, where reducing adverse hydrogen uptake/transport pathways is a practical objective.

4 — Limitations and outlook (as authored)

The reported conclusions are based on selected Sigma7 GB archetypes rather than a full grain-boundary character distribution. The paper positions the model as a step toward broader microstructure-aware assessments, not as a final map of all Ru film textures and service conditions.

5 — Corpus / KB honesty

This page is grounded in the on-file DOI-matched galley PDF plus linked SI context. It supports claims about relative GB-vs-bulk hydrogen behavior and anisotropic diffusion trends in the modeled cells; it does not establish universal trapping strengths for all Ru grain-boundary types or direct one-to-one operating-pressure equivalence for deployed EUV mirror stacks.

Limitations

The study samples specific Σ7 boundaries; other misorientation distributions could show different trapping strengths. Ru microstructure in EUV mirrors includes texture, grain-size gradients, and interlayers not represented in the idealized bicrystal cells used to isolate GB H partitioning. Hydrogen chemical potential in service may differ from simulation reservoirs; map MD chemical potentials cautiously to operating partial pressures. Ru/H parameter sets should be versioned alongside the AMS/ReaxFF or LAMMPS ReaxFF build used in downstream runs (this article states AMS2020 for the reported MD).

Relevance to group

Co-authored ReaxFF development and application for hydrogen in technologically relevant Ru films.

Reader notes (navigation)

Citations and evidence anchors