Interatomic potentials for hydrogen in $\alpha$–iron based on density functional theory

We present two interatomic potentials for hydrogen in $\alpha$–iron based on the embedded atom method potentials for iron developed by Mendelev et al. [Philos. Mag. 83, 3977 (2003)] and Ackland et al. [J. Phys.: Condens. Matter 16, S2629 (2004)]. Since these latter potentials are unique among existing iron potentials in their ability to produce the same core structure for screw dislocations as density functional theory (DFT) calculations, our interatomic potentials for hydrogen in iron also inherit this important feature. We use an extensive database of energies and atomic configurations from DFT calculations to fit the cross interaction of hydrogen with iron. Detailed tests on the dissolution and diffusion of hydrogen in bulk $\alpha$–iron, as well as the binding of H to vacancies, free surfaces, and dislocations, indicate that our potentials are in excellent overall agreement with DFT calculations.

Figure 1

(Color online) Schematic of bcc Fe lattice showing four tetrahedral sites and one octahedral site on a face.

Figure 2

(Color online) Dissolution energies of H in $\alpha \text{-Fe}$ as a function of (a) hydrostatic and (b) uniaxial strain. Numerical values in the legend indicate RMS errors for each potential with respect to DFT values. The lines are a guide to the eye.

Figure 3

(Color online) Diffusion barriers for H in $\alpha \text{-Fe}$ as a function of (a) hydrostatic and (b) uniaxial strain. Numerical values in the legend indicate RMS errors for each potential with respect to DFT values. The lines are a guide to the eye.

Figure 4

(Color online) Schematic of possible binding sites for H on (a) Fe (100) and (b) Fe (110) surfaces.

Figure 5

(Color online) Schematic of H-binding sites at a vacancy. The binding site is displaced by $\delta$ from the O-site toward the vacancy. The numbering of the binding sites indicates the sequence in which H atoms are added to compute the binding energy for the $\left(n+1\right)\text{th}$ H atom (see text).

Figure 6

(Color online) Binding energy (in eV) for multiple hydrogen atoms at a vacancy. The binding energy, as displayed here, is the energy required to trap an additional H atom at the vacancy, referenced to the bulk dissolution energy, i.e., $E_b=\left[E\left({\text{Fe}}_m\text{H}\right)-E\left({\text{Fe}}_m\right)\right]-\left[E\left({\text{Fe}}_{m-1}{\text{H}}_n\right)-E\left({\text{Fe}}_{m-1}{\text{H}}_{n-1}\right)\right]$. Dissolution of up to three H atoms is seen to be exothermic (referenced to bulk Fe and ${\text{H}}_2$). Trapping at a vacancy, even in the presence of other trapped atoms, is almost always less endothermic than dissolution in a bulk T-site.

Figure 7

(Color online) Binding sites for H atoms at a screw dislocation core. The blue and white spheres represent the first and second shell of binding sites around the core. The “bonds” are merely a guide for visualization.

Figure 8

(Color online) Binding sites for H atoms at an edge dislocation core. The extra half-plane of atoms is above the glide plane thus making the stresses compressive (tensile) above (below) the glide plane. The lowest-energy binding sites along the glide plane are indicated in blue (octahedral coordination). The pink spheres (tetrahedral coordination) represent weak binding sites immediately below the glide plane of the dislocation. The white spheres (tetrahedral coordination) represent sites with negative binding energy, i.e., dissolution is less energetically favorable than at a bulk T-site. The “bonds” are merely a guide to viewing the coordination.

Figure 9

(Color online) (a) Two-body, (b) electron density, and (c) embedding functions for Potentials A and B.