Is Hydrogen Diffusion along Grain Boundaries Fast or Slow? Atomistic Origin and Mechanistic Modeling

We perform comprehensive first-principles calculations and kinetic Monte Carlo simulations to explicitly elucidate the distinct roles of grain boundaries (GBs) in affecting hydrogen (H) diffusion in fcc nickel (Ni). We demonstrate the transition between slow and fast H diffusion along the GB with an abrupt change in H diffusivity. Low-angle GBs are shown to comprise isolated high-barrier regions to trap and inhibit H diffusion, with H diffusivity well prescribed by the classical trapping model, while high-angle GBs are shown to provide interconnected low-barrier channels to facilitate H transport. On the basis of the dislocation description of the GB and the Frank-Bilby model, the slow-fast diffusion transition is identified to result from dislocation core overlapping and is accurately predicted. The present Letter provides key mechanistic insights towards interpreting various experimental studies of H diffusion in metals, new critical knowledge for predictive modeling of H embrittlement, and better understanding of the kinetics of H and other interstitial impurities in microstructures.

Figure 1

Representative GB configurations examined in this Letter, (a) $\mathrm{\Sigma }3[110](111)$, (b) $\mathrm{\Sigma }11[110](113)$, (c) $\mathrm{\Sigma }5[100](210)$, (d) $\mathrm{\Sigma }5[100](310)$, (e) $\mathrm{\Sigma }25[100](430)$, and (f) $\mathrm{\Sigma }41[100](540)$, with the polyhedral units constituting the GB illustrated. The gray spheres indicate the host Ni atom. Different polyhedral units, i.e., octahedron (OCT), tetrahedron (TET), capped-trigonal prism (CTP), bitetrahedron (BTE), and pentagonal bipyramid (PBP) are indicated by different geometrical shapes in green, blue, gray, purple, and red shades, respectively.

Figure 2

Contour mapping of the energy barrier $E_b$ of H migration at representative GBs. (a) $\mathrm{\Sigma }3[110](111)$, (b) $\mathrm{\Sigma }11[110](113)$, (c) $\mathrm{\Sigma }5[100](210)$, (d) $\mathrm{\Sigma }5[100](310)$, (e) $\mathrm{\Sigma }25[100](430)$, (f) $\mathrm{\Sigma }41[100](540)$. Big gray spheres represent host Ni atoms.

Figure 3

H diffusivity ($D$) as H bulk concentration ($C_b$) varies, calculated from KMC simulations and predicted from Eq. (1), for GBs: (a) $\mathrm{\Sigma }3[110](111)$, (b) $\mathrm{\Sigma }11[110](113)$, (c) $\mathrm{\Sigma }5[100](210)$, (d) $\mathrm{\Sigma }5[100](310)$, (e) $\mathrm{\Sigma }25[100](430)$, and (f) $\mathrm{\Sigma }41[100](540)$, at different temperatures.

Figure 4

(a) H diffusivities at different H bulk concentration $C_b$ as functions of the GB tilt angle $\theta$ at 300 K. The horizontal red dashed line indicates bulk H diffusivity at 300 K and the solid lines are predictions from Eq. (3). (b) Dislocation separation distance along the GB as a function of $\theta$ according to the Frank-Bilby model (2), where $\overrightarrow{b}$ denotes the Burgers vector of the constituting dislocation.

Figure 5

Schematic illustration of dislocation cores at GBs and the evolution of energy barrier with tilt angle increase. The gray shape represents dislocation cores at GBs. The gray spheres are the host Ni atom and the small red ball illustrates the H atom.