First-principles study of hydrogen diffusion in polycrystalline Nickel

TL;DR

The study tackles hydrogen diffusion and embrittlement in polycrystalline nickel by developing a multiscale framework that links first-principles migration barriers to continuum transport. It combines DFT-derived atomistic data with kinetic Monte Carlo (KMC) simulations to obtain anisotropic diffusivities in bulk and grain-boundary environments, which are then embedded into finite-element models of polycrystalline microstructures. The approach yields Arrhenius-type bulk diffusion with $E_a = 0.37~\text{eV}$ and reproduces grain-size and grain-boundary–type trends observed experimentally, notably fast in-plane diffusion along Sigma5 boundaries and diffusion-barrier behavior for Sigma3 boundaries, captured through the relation $k_{ij} = \nu_{ij} \exp(-\Delta E_{ij}/(k_B T))$ and effective diffusion $D_\mathrm{eff}$. This parameter-free, physically grounded framework demonstrates how microstructural topology controls hydrogen transport and provides a path toward microstructure-informed alloy design to mitigate hydrogen-related degradation, with potential extensions to other materials and defect types. It also establishes a clear workflow for transferring atomistic transport information to engineering-scale simulations, enabling predictive assessments of hydrogen diffusion in complex polycrystalline systems.

Abstract

Hydrogen embrittlement in metals is strongly governed by hydrogen diffusion and trapping, yet predicting these effects in polycrystalline systems remains challenging. This work introduces a multiscale modeling framework that links atomistic energetics to continuum-scale transport. Migration barriers for bulk and grain-boundary environments, obtained from first-principles calculations, are used in kinetic Monte Carlo simulations to compute anisotropic effective diffusivities. These diffusivities are then incorporated into finite element models of polycrystalline microstructures, explicitly accounting for grain-boundary character and connectivity. The approach captures both fast-path and trapping effects without relying on empirical parameters and reproduces experimental trends for nickel, including the dependence of effective diffusivity on grain size and boundary type. This methodology provides a physically grounded route for predicting hydrogen transport in engineering alloys and can be extended to other materials and defect types.

Figures (14)

• Figure 1: Workflow for converting a crystal structure into its KMC diffusion graph for bulk Ni. The starting point (a) is the Ni perfect lattice. The lattice is then (b) decorated with the relevant interstitial sites, octahedral in this case. The original Ni atoms are removed (c). Finally, (d) the diffusion lattice is constructed. Note, only in-cell jumps are represented, but periodic images are considered in the code
• Figure 2: Graph representation of interstitial diffusion sites in FCC Ni. Most of possible sites are Ni octahedral sites (red circles). Approaching the GB plane, octahedral site are distorted in to square-pyramidal sites (olive diamonds), and finally in the GB plane effective sites (blue squares) nodes. Grey lines represent the possible hydrogen migration paths.
• Figure 3: Diffusion lattice representation for the $\Sigma5$ grain boundary, in blue. Large gray circles denote Ni atoms on the GB plane, and small gray circles indicate Ni atoms on the next plan. Black dots mark all interstitial sites within the GB plane connected with the possible paths. Blue squares represent the effective sites used in the simplified diffusion graph, and blue lines indicate the idealized migration pathways between them.
• Figure 4: Continuum model preparation and setup: (a) generated microstructure, (b) microstructure with inflated GBs and TJs meshed using Octree meshing algorithm. Finally, (c) assigned local coordinate systems for anisotropic diffusivity directions.
• Figure 5: Boundary conditions for the permeation test applied to the 2.5D microstructure: normalize concentration $C=1$ on one face and $C=0$ on the opposite face, with zero flux ($J=0$) on the remaining boundaries. This setup enforces through-thickness transport, effectively reducing the problem to one-dimensional diffusion across the slab.