Fig. 1 Two-dimensional system of the hydrogen diffusion simulation

Fig. 2 Temporal evolution of hydrogen concentration in normalized time, a 0, b 0.00126, c 0.0126, d 0.0504, e 0.126, f 1.26. g A magnified image of the hydrogen concentration in the triple-junction taken at the red box in f

Fig. 3 Evolution of spatial concentration profiles: a along the permeation direction (red A-B line in Fig. 2f), b along the exiting side (red C-D line in Fig. 2f)

Fig. 4 a-c Normalized diffusive flux as a function of normalized time in the two-dimensional system with a $D_{{{\text{gb}}}} /D_{{\text{b}}} =$ 0.1, b $D_{{{\text{gb}}}} /D_{{\text{b}}} =$ 1, c $D_{{{\text{gb}}}} /D_{{\text{b}}} =$ 10. d Effective diffusivities of hydrogen in iron as a function of the assumed binding energies and GB intrinsic diffusivities with the solid symbol in two-dimensional system and hollow one in one-dimension