Ab initio molecular dynamics simulation of hydrogen diffusion in $\alpha$-iron

First-principles atomistic molecular-dynamics simulation in the microcanonical and canonical ensembles has been used to study the diffusion of interstitial hydrogen in $\alpha$-iron. Hydrogen to iron ratios between $\theta =\frac{1}{16}$ and $\frac{1}{2}$ have been considered by locating interstitial hydrogen atoms at random positions in a $2\times 2\times 2$ supercell. We find that the average optimum absorption site and the barrier for diffusion depend on the concentration of interstitials. Iron Debye temperature decreases monotonically for increasing concentration of interstitial hydrogen, proving that iron-iron interatomic potential is significantly weakened in the presence of a large number of diffusing hydrogen atoms.

Figure 1

(Color online) Simulated random walks $\left(T=700\text{K}\right)$ for eight interstitial hydrogen atoms simultaneously located in a $2\times 2\times 2$ bcc supercell.

Figure 2

(a) (Short dashed line) Diffusion coefficient, $D$ $\left(\frac{m^2}{s}\right)$, obtained for a set of averaged diffusion MD trajectories for a single H atom in a $2\times 2\times 2$ bcc iron supercell. A barrier for diffusion of $B_1=0.145\text{eV}$ is obtained from a least-squares fit. (b) (Long dashed line) Same for eight H interstitial atoms diffusing in the supercell. A barrier of $B_8=0.047\text{eV}$ is deduced from the fit. Error bars have been estimated from standard errors $\left(\frac{1.96\sigma }{\sqrt{N}}\right)$.

Figure 3

As a percentage over the total simulation time, residence time around octahedral sites, $P_O$ for: (i) a single interstitial hydrogen [small gray dots; thin gray line corresponds to $k_B\Delta =0.06\text{eV}$ in Eq. (2)]; (ii) two H (small black dots; thin black line is for $k_B\Delta =0.07\text{eV}$); (iii) four H (large gray dots; thick gray line is for $k_B\Delta =0.04\text{eV}$); and (iv) eight H (large black dots; thick black line is for $k_B\Delta =-0.035\text{eV}$). The dashed line separates the two asymptotic regions ($\Delta \ge 0$ and $\Delta \le 0$).

Figure 4

Iron root-mean-squared displacement from equilibrium positions $u\left(\text{Å}\right)$ vs temperature (K). The density of interstitial hydrogen for each case is: (i) $n_H=1$ (small gray dots), (ii) $n_H=2$ (small black dots), (iii) $n_H=4$ (large gray dots), and (iv) $n_H=8$ (large black dots). Corresponding continuous lines coded similarly in size and gray/black are least-square fits to the data using Eq. (3) with Debye temperatures $\Theta =381$, 399, 360, and 259 K, respectively.

Figure 5

Debye-Waller temperature (K) vs number of interstitial H diffusing in the unit cell. Dashed line is a linear least-squares fit to guide the eye.