First-principles study of vacancy-hydrogen interaction in Pd

Hydrogen absorption in face-centered-cubic palladium is studied from first principles, with particular focus on interaction between hydrogen atoms and vacancies, formation of hydrogen-vacancy complexes, and multiple hydrogen occupancy of a Pd vacancy. Vacancy formation energy in the presence of hydrogen, hydrogen trapping energy, and vacancy formation volume have been calculated and compared to existing experimental data. We show that a vacancy and hydrogen atoms form stable complexes. Further we have studied the process of hydrogen diffusion into the Pd vacancy. We find the energetically preferable position for hydrogen to reside in the palladium unit cell in the presence of a vacancy. The possibility of the multiple hydrogen occupancy (up to six hydrogen atoms) of a monovacancy is elucidated. This theoretical finding supports experimental indication of the appearance of superabundant vacancy complexes in palladium in the presence of hydrogen.

Figure 1

Variation in the total energy in the 32 site supercell with one vacancy and 1 interstitial H atom as a function of hydrogen distance to the vacancy. Hydrogen atom is moved from the octahedral site, whose position is marked with a dashed line, toward the vacancy center. The total energy is given relative to the energy of the system where hydrogen is placed in the center of the vacancy (point zero). The estimated energy minimum corresponds to the H-vacancy distance equal to $1.564\text{Å}$.

Figure 2

(Color online) Vacancy-nH complex in fcc Pd. Dark circles represent Pd atoms, small light circles represent hydrogen positions. In $1\mathit{H}\text{−}\mathit{v}$ cluster hydrogen occupies position 1. For $2\mathit{H}\text{−}\mathit{v}$ there are two different possible configurations: two hydrogen atoms in positions 1 and 2 (the compact cluster) or in 1 and 3 (the linear configuration). For $3\mathit{H}\text{−}\mathit{v}$ cluster three hydrogen atoms are placed in positions 1-2-3 or 1-2-5.