Fig. 1 Effect of nanoscale chemical heterogeneities on a distribution of H solution energies in various high alloyed FCC [31], b H segregation tendency to GBs [31], c H migration energy profiles along different paths [33], d trajectories of H diffusion showing the blocking effect from high-energy positions [34], and e H-induced change of fracture free energy and unstable stacking fault energy [37]. f Ab initio-based predictions of embrittled (red) and un-embrittled (blue) domains of H concentrations and comparison with experiments [37]

Fig. 2 Interaction between GB-segregated alloying and H atoms. a Prediction chart of solute/solvent (GB/matrix) combinations that could enhance (green) or hinder (red) H diffusion compared to a homogeneous solid solution alloy [41]. b Effect of H-solute interaction on the GB segregation energy, GB strengthening energy, and the bulk partial cohesive energy [39]

Fig. 3 Ab initio calculations of the correlation between the size of TiC carbides and $E_{{\text{b}}}$ [46]. The energy profiles for a perfect coherent interface (red) and misfit dislocation core of semi-coherent interface (black), b coherent interface with a single C vacancy at the interface and within the carbide (black), connected C vacancies (dashed black), and a single C vacancy within the carbide with two occupied H atoms (dashed red), and c the (110)Fe/(001)TiC incoherent interface with (black) and without (red) C vacancies at the interface and with C vacancies within the carbide (gray). The H desorption energies at various H trapping sites obtained by d theoretical predictions and e experimental characterizations

Fig. 4 H trapping of NaCl-type MC carbides and multicomponent (M,X)C carbides. a DFT calculations of $E_{{\text{b}}}$ at different sites of coherent phase boundaries [49]. The APT analysis of deuterium-charged samples with precipitation of b VC carbides showing trapping at broad interface [60] and c (V,Mo)C carbides showing trapping inside the particles [61]

Fig. 5 Relationship between the homogeneous electron gas density and the interaction energy to H in metals [68]

Fig. 6 Ab initio investigation for the effect of stress anisotropy on H energetics in BCC metals [74]. Formation energies of H under uniaxial stress along [001] and [100] directions for a interstitial H; b planar H cluster; c di-hydrides; d the minimum formation energies from a-c; e corresponding formation volume tensor of stress-free condition; f sensitivity of formation energies to stresses

Fig. 7 Charge transfer mechanism of H trapping at phase boundaries [49]. a One H atom gains electrons from surrounding atoms; b interfacial segregated X atoms change the partial electron density distribution at region of phase boundaries; c the relationship between the charge transfer ratio R and mechanical-free binding energy for Tet-2 and C-Vac sites