Atomistic Simulations of H-Cu Vacancy Cosegregation and H Diffusion in Cu Grain Boundary

TL;DR

This work tackles hydrogen embrittlement in copper by resolving the atomistic sequence from H2 adsorption to incorporation, diffusion, and cosegregation with Cu vacancies at grain boundaries. Using a hybrid DFT–BOP framework, the authors model H behavior across bulk, surface, and GB regions, identifying low incorporation barriers at GBs ($E_{inc}$ around $0.35$ eV) and strong H–vacancy coupling at GBs (cosegregation energies up to $-0.8$ eV). They show H diffuses rapidly within GB networks with barriers as low as $0.2$ eV, contrasting with higher bulk barriers ($\sim 0.42$ eV), and form H–V$_{Cu}$ complexes that can seed void formation. The results illuminate a pathway where H2 exposure leads to H accumulation at GBs, promoting hydrogen-enhanced localized plasticity and decohesion, and provide atomic-scale parameters for integrating into kinetic Monte Carlo and phase-field multiscale models for predicting hydrogen embrittlement in Cu.

Abstract

Hydrogen embrittlement remains a critical challenge in structural and electronic applications of copper (Cu) but its mechanism is still not fully understood. In this study, we combine density functional theory (DFT) and bond-order potential (BOP) simulations to determine the atomistic pathways for hydrogen adsorption/incorporation and fast interfacial diffusion at Cu grain boundaries (GBs), including its interaction with vacancies. Undercoordinated regions, such as surfaces and GBs, serve as preferential adsorption/incorporation sites for atomic hydrogen, especially in the presence of Cu vacancies. The presence of hydrogen in GB further enhances the segregation of Cu vacancies, leading to the formation of stable H-$V_\mathrm{Cu}$ complexes with cosegregation energy gains of up to $-0.8$ eV. Furthermore, our simulations reveal that the migration barriers for hydrogen within the GB networks are as low as $0.2$ eV and significantly lower than in bulk Cu ($0.42$ eV). The results presented in this paper suggest an atomistic mechanism that links $H_2$ exposure to H accumulation in GBs, providing information on the early stages of hydrogen-induced degradation.

Figures (6)

• Figure 1: Hydrogen adsorption, dissociation, and relative energetics across different crystallographic environments in Cu. (a) Molecular hydrogen (H$_2$) in the gas phase. (b) Dissociation of adsorbed H$_2$ on Cu (100): the reported barrier for this process is 0.12 eV alvarez2016hydrogen. Panel (ii) shows the top view after dissociation. (c) Atomic H adsorption on Cu (100): (i) pristine surface with $E^{\mathrm{H}}_{\mathrm{ads}}=-0.24$ eV; (ii) surface containing a Cu vacancy with stronger adsorption, $E^{\mathrm{H}}_{\mathrm{ads}}=-0.30$ eV. The arrows labelled $E_{\mathrm{diff}}$ indicate energy differences between the two states: from H on the pristine surface to H in bulk, $E_{\mathrm{diff}}=+0.54$ eV; from H in a surface vacancy to H in bulk, $E_{\mathrm{diff}}=+0.62$ eV. (d) Incorporation of H in bulk Cu $E^{\mathrm{H}}_{\mathrm{inc}}=0.68$ eV. (e) Incorporation of H at the $\Sigma 5$(210)[100] grain boundary (GB) is less unfavorable, $E^{\mathrm{H}}_{\mathrm{inc}}=0.35$ eV. The arrow from bulk to GB shows the energetic offset $E_{\mathrm{diff}}=-0.58$ eV, i.e., H in GB configuration is lower in energy than H in bulk by 0.58 eV. All adsorption/incorporation energies are referenced to molecular H$_2$ in the gas phase; $E_{\mathrm{diff}}$ values quantify final–initial total-energy differences between the indicated configurations.
• Figure 2: Copper vacancy segregation energetics at the Cu (100) surface and the $\Sigma 5$(210)[100] GB, with and without the presence of hydrogen. Segregation energies ($E_{\text{seg}}^{\text{V}_{\text{Cu}}}$) are referenced to a vacancy located in bulk Cu. (a) (i) Surface vacancy segregation at the pristine Cu (100) surface is energetically favorable with $E_{\text{seg}}^{\text{V}_{\text{Cu}}} = -0.59$ eV. (ii) The presence of hydrogen slightly enhances vacancy segregation to $-0.63$ eV. (b) (i) Vacancy segregation at the $\Sigma 5$(210)[100] GB is more favorable ($E_{\text{seg}}^{\text{V}_{\text{Cu}}} = -0.72$ eV) compared to the surface. (ii) The presence of hydrogen at the GB further lowers the energy to $-0.83$ eV. The negative segregation energies indicate a clear thermodynamic driving force for vacancy accumulation at grain boundaries and surfaces, enhanced by hydrogen incorporation.
• Figure 3: (a) The 76-atom Cu $\Sigma5$(210)[100] GB simulation cell showing the examined segregation sites for Cu vacancies (red) and hydrogen interstitial atoms (cyan). (b) Computed cosegregation energies for H interstitials occupying different sites (1--4) interacting with Cu vacancies located at various GB sites (V1--V7). Negative energies indicate favorable cosegregation at the GB. (c) Atomic configurations of the two representative H--V$_\text{Cu}$ complexes: (i) H initially at interstitial site 2 cosegregating with a Cu vacancy at site 2; (ii) H initially at interstitial site 4 cosegregating with a Cu vacancy at site 2. Initial and relaxed configurations illustrate significant local atomic rearrangements upon relaxation.
• Figure 4: (a) Simulation cell used for MD and NEB barrier calculations, comprising 932 atoms with two free surfaces and a central $\Sigma5$(210)[100] GB. (b) MD trajectories illustrating hydrogen diffusion within Cu at 700 K. Trajectories are colored according to temperature, highlighting preferential H migration paths along the grain boundary. Labels 'I' (initial) and 'F' (final) indicate start and end positions of a hydrogen atom during the MD simulation.
• Figure 5: (a) The various diffusion paths examined for H. (b) Diffusion barriers calculated through NEB and BOP for H in two potential diffusion paths within the GBs. (c) (i),(ii) Configurations of the images (replicas) during the diffusion process for the two paths, demonstrating the intermediate states that H assumes as it migrates through the GB.