Potential energy surface and hopping path for hydrogen inLaNi5

Abstract

Hydrogen hopping paths in ${\text{LaNi}}_{5}\text{H}$ solid solution were analyzed via first-principles calculations. Potential energy surfaces were determined for hydrogen on the plane with hydrogen sites $6m$, $12o$, and $4h$ and on the plane with hydrogen sites $12n$, $3f$, and $6i$. From the zero-point vibration energy along the hopping path, it was found that hydrogen locations are grouped only at three regions; quasi-$m$ site $(o\text{\ensuremath{-}}m\text{\ensuremath{-}}o)$, $h$ site, and quasi-$f$ site $(i\text{\ensuremath{-}}f\text{\ensuremath{-}}i)$. By applying the nudged elastic band method to hydrogen hopping paths between all the possible two sites, the most probable diffusion route was determined as quasi-$f$--quasi-$m$--quasi-$f$ in the $\mathbit{c}$ direction and quasi-$f$--quasi-$m$--quasi-$f$--quasi-$m$--quasi-$f$ in the $\mathbit{a}$ and $\mathbit{b}$ directions with the same saddle point energy of 0.37 eV, which is in good agreement with the measured activation energy, 0.3--0.5 eV, of the hydrogen diffusion in the solid solution phase of ${\text{LaNi}}_{5}\text{-H}$ system.