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Simulation of mechanical effects of hydrogen in bicrystalline Cu using DFT and bond order potentials

Vasileios Fotopoulos, Alexander L. Shluger

TL;DR

This study addresses hydrogen embrittlement in bicrystalline Cu by benchmarking a bond order potential (BOP) against density functional theory (DFT) for H segregation at a Cu Σ5 grain boundary and evaluating the mechanical impact via large-scale MD. The authors demonstrate that BOP accurately identifies favorable H segregation sites and captures GB relaxation patterns observed in DFT, while revealing that H reduces the grain boundary separation energy via lattice relaxation and charge redistribution. MD simulations across 10–40 mass ppm H show a substantial drop in yield strength (from 8.4 GPa to about 7.3 GPa at the higher concentration) correlated with increased emission of partial and Shockley dislocations from the GB. Collectively, the results validate BOP as a tool for studying H effects in Cu GBs, quantify the concentration threshold (~10 mass ppm) for notable strength loss, and provide atomistic insight into the mechanisms of H-induced decohesion and dislocation activity.

Abstract

Hydrogen embrittlement is a prime cause of several degradation effects in metals. Since grain boundaries (GBs) act efficiently as sinks for hydrogen atoms, H is thought to segregate in these regions, affecting the local formation of dislocations. However, it remains unclear at which concentrations H begins to play any role in the mechanical properties of Cu. In the current study, we use density functional theory (DFT) to assess the accuracy of a bond order potential (BOP) in simulating the segregation of H in Cu GB. BOP accurately predicts the most favorable segregation sites of H in Cu GB, along with the induced lattice relaxation effects. H is found to weaken the crystal by reducing the GB separation energy. Classical molecular dynamics (MD) simulations using BOP are performed to evaluate the concentration of H in bicrystalline Cu required to substantially impact the crystal's mechanical strength. For concentrations higher than 10 mass ppm, H significantly reduces the yield strength of bicrystalline Cu samples during uniaxial tensile strain application. This effect was attributed to the fact that H interstitials within the GB promoted the formation of partial dislocations.

Simulation of mechanical effects of hydrogen in bicrystalline Cu using DFT and bond order potentials

TL;DR

This study addresses hydrogen embrittlement in bicrystalline Cu by benchmarking a bond order potential (BOP) against density functional theory (DFT) for H segregation at a Cu Σ5 grain boundary and evaluating the mechanical impact via large-scale MD. The authors demonstrate that BOP accurately identifies favorable H segregation sites and captures GB relaxation patterns observed in DFT, while revealing that H reduces the grain boundary separation energy via lattice relaxation and charge redistribution. MD simulations across 10–40 mass ppm H show a substantial drop in yield strength (from 8.4 GPa to about 7.3 GPa at the higher concentration) correlated with increased emission of partial and Shockley dislocations from the GB. Collectively, the results validate BOP as a tool for studying H effects in Cu GBs, quantify the concentration threshold (~10 mass ppm) for notable strength loss, and provide atomistic insight into the mechanisms of H-induced decohesion and dislocation activity.

Abstract

Hydrogen embrittlement is a prime cause of several degradation effects in metals. Since grain boundaries (GBs) act efficiently as sinks for hydrogen atoms, H is thought to segregate in these regions, affecting the local formation of dislocations. However, it remains unclear at which concentrations H begins to play any role in the mechanical properties of Cu. In the current study, we use density functional theory (DFT) to assess the accuracy of a bond order potential (BOP) in simulating the segregation of H in Cu GB. BOP accurately predicts the most favorable segregation sites of H in Cu GB, along with the induced lattice relaxation effects. H is found to weaken the crystal by reducing the GB separation energy. Classical molecular dynamics (MD) simulations using BOP are performed to evaluate the concentration of H in bicrystalline Cu required to substantially impact the crystal's mechanical strength. For concentrations higher than 10 mass ppm, H significantly reduces the yield strength of bicrystalline Cu samples during uniaxial tensile strain application. This effect was attributed to the fact that H interstitials within the GB promoted the formation of partial dislocations.
Paper Structure (11 sections, 2 equations, 5 figures)

This paper contains 11 sections, 2 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Bond Order Potentials
  4. Computational Details: First Principles
  5. Computational Details: Bond Order Potentials
  6. Energetic Parameters
  7. Results
  8. Comparison of DFT and BOP calculations
  9. Ab initio strain calculations
  10. MD strain calculations
  11. Conclusions

Figures (5)

  • Figure 1: (a) (i) Shows the examined interstitial H sites (grey spheres) inside the Cu $\Sigma$5 GB; (ii) octahedral and (iii) tetrahedral sites in the bulk. (b) Comparison of segregation and strengthening energies computed using DFT and BOP. To visualize the resulting DFT configurations and charge distributions, VESTA is used momma2008vesta.
  • Figure 2: (a) Relaxed configuration of the lowest energy interstitial H site at Cu GB obtained using BOP; (b) DFT. The distances in Å between H and neighboring Cu atoms are included. Cu and H atoms are shown in blue and white, respectively. (c) Displacements of atoms obtained using DFT; (d) BOP. Atoms are colored based on the displacement magnitude. Yellow arrows illustrate the displacement vectors. The initial configuration prior to relaxation is used as a reference.
  • Figure 3: (a) Separation energies of Cu GB with one and four interstitial H atoms at various separation distances from the equilibrium computed using DFT. Inset image illustrates the GB simulation cell along with the chosen separation plane (yellow line). (b) PDOS of the Cu1 (as seen in Figure \ref{['fig:charges']}(a)) and H atoms in the H-segregated GB model at (i) the equilibrium separation and (ii) a separation of 1.6 Å. The Fermi level is defined as the zero of energy. Hybridization peaks are observed at -9 eV to -7 eV between the Cu1 (see Figure \ref{['fig:charges']}(a)) and H atoms for the equilibrium separation and at -8 eV to -5 eV for the separation of 1.6 Å.
  • Figure 4: Total charge distributions obtained using DFT at equilibrium (first column), 1.6 Å (second column), and 2 Å (third column) separations for Cu GB with (a) one interstitial H (b) four interstitial H atoms. (c) Differential charge distribution of four H interstitial in Cu GB at three different separations, namely equilibrium (first column), 1.6 Å (second column), and 2 Å (third column). The GB separation distances are the same as in (a) and (b). Yellow and cyan iso-surfaces (0.01) correspond to electron accumulation and depletion, respectively.
  • Figure 5: (a) Stress-strain plots for pure Cu GB and Cu GB with different mass ppm concentrations of interstitial H atoms. Inset image illustrates the 120,000-atom Cu GB simulation cell. Green atoms correspond to fcc symmetry whereas amorphous regions (GB) are shown in white. Uniaxial deformation is applied along the y-axis. (b) Dislocation emission from the GB for (i) pure Cu and Cu with (ii) 10 (ii) 25 (iii) 40 mass ppm of H interstitials. Only atoms with non-fcc symmetry are visualized, with red and white corresponding to atoms with hcp symmetry and amorphous structure (GB), respectively. Green lines correspond to Shockley dislocations. Visualization is performed using OVITO stukowski2009visualization.