6
E. K. Hamal and M. C. Toroker
Fig. 3 Free energies for water oxidation reaction for pure NiOOH as a function of % contraction/expansion
reactions (2) and (4), where oxygen penetrates and leaves the surface, respectively.
The changes for reaction (2) and (4) are dramatic and can span over 2.5 eV difference
when comparing 10% contraction versus 10% expansion (see Table 1). Expansion
makes more space for an oxygen atom to penetrate, but disfavors oxygen release.
Therefore, the reaction 2 free energy reduces with expansion and the reaction 4 free
energy increases with expansion.
The rest of the reactions (1) and (3) are less sensitive to strain for pure NiOOH,
although the effect is significant enough to reduce the overpotential at 5% contraction
or expansion (as seen in Table 1, ~0.1 eV decrease in the overpotential and free
energy of the first reaction upon expansion). A correlation between the free energies
of reactions (1) and (3) and the application of strain can be identified while fixing
the fractional coordinates of the atoms. In this case, there is a general linear relation
between the free energies of reaction (1) and (3) and strain that is there is a general
increase in the overpotential when expansion is applied. This expansion increases
the interatomic distance, which localizes the atomic orbitals, and inhibits the release
of localized electrons during deprotonation reactions.
Similar to pure NiOOH, the 8% Fe-doped case also has an overpotential that is
determined by the first two reactions (see Table 2; Fig. 4). However, as seen in Table
2, the intersection of the reaction 1 and 2 free energies occurs at zero compression
(the free energies for the first two reactions are ~ −0.4 eV), since the bond distances
around the active site are shorter for the doped case. The average Fe–O bond distance
at the active site is 1.912 Å, which is shorter than the 1.952 Å average Ni–O distance
at the active site of pure NiOOH. The Fe–O bonds are even shorter than typical Fe–O
bonds of pure FeOOH where it is expected that the distances would be larger than pure
NiOOH according to the order of Ni and Fe atoms in the periodic table of elements
(Ni has a larger atomic number and therefore smaller ionic radius). The short Fe–O
bonds at the active site result from a high +4 oxidation state of iron at the active
E. K. Hamal and M. C. Toroker
Fig. 3 Free energies for water oxidation reaction for pure NiOOH as a function of % contraction/expansion
reactions (2) and (4), where oxygen penetrates and leaves the surface, respectively.
The changes for reaction (2) and (4) are dramatic and can span over 2.5 eV difference
when comparing 10% contraction versus 10% expansion (see Table 1). Expansion
makes more space for an oxygen atom to penetrate, but disfavors oxygen release.
Therefore, the reaction 2 free energy reduces with expansion and the reaction 4 free
energy increases with expansion.
The rest of the reactions (1) and (3) are less sensitive to strain for pure NiOOH,
although the effect is significant enough to reduce the overpotential at 5% contraction
or expansion (as seen in Table 1, ~0.1 eV decrease in the overpotential and free
energy of the first reaction upon expansion). A correlation between the free energies
of reactions (1) and (3) and the application of strain can be identified while fixing
the fractional coordinates of the atoms. In this case, there is a general linear relation
between the free energies of reaction (1) and (3) and strain that is there is a general
increase in the overpotential when expansion is applied. This expansion increases
the interatomic distance, which localizes the atomic orbitals, and inhibits the release
of localized electrons during deprotonation reactions.
Similar to pure NiOOH, the 8% Fe-doped case also has an overpotential that is
determined by the first two reactions (see Table 2; Fig. 4). However, as seen in Table
2, the intersection of the reaction 1 and 2 free energies occurs at zero compression
(the free energies for the first two reactions are ~ −0.4 eV), since the bond distances
around the active site are shorter for the doped case. The average Fe–O bond distance
at the active site is 1.912 Å, which is shorter than the 1.952 Å average Ni–O distance
at the active site of pure NiOOH. The Fe–O bonds are even shorter than typical Fe–O
bonds of pure FeOOH where it is expected that the distances would be larger than pure
NiOOH according to the order of Ni and Fe atoms in the periodic table of elements
(Ni has a larger atomic number and therefore smaller ionic radius). The short Fe–O
bonds at the active site result from a high +4 oxidation state of iron at the active