Strain Controlling Catalytic Efficiency …
5
“D” is similar to intermediate “B” but the additional oxygen atom penetrating the
surface. The free energy for the reactions was calculated by adding the previously
reported zero-point energy (ZPE) corrections and entropic contributions of pure βNiOOH since these additions were shown stable with variations in composition [17,
42]. The free energies were calculated at the operating conditions for the OER:
1 V and pH = 14, by adding a constant energy −eU for the applied voltage and a
term of −k B T · ln 10 · pH for the pH where k B is Boltzmann constant and T is the
temperature of 298.15 K. The free energies without pH and T corrections are provided
in the supporting information (Tables 13, 14, 15, 16 and 17). The overpotential is
defined as voltage needed to add to the calculated electrochemical potential so that
all reaction free energies are negative. The intermediate reaction cells are expanded
or contracted significantly (up to 10%) in order to be able to see the effect of strain.
The expansion or contraction was performed by elongating or contracting the surface
lattice vectors and allowing only the ions to optimize in their positions. The lattice
vectors were changed only in the directions of the
a and
b vectors. For example, the
expansion is reflected by the distance between the sheets elongated from 2.624 to
2.722 Å (see Fig. 2).
3 Results
In this section, we present free energy calculations of the water oxidation reaction
for the Ni 1−x Fe x OOH alloy under applied strain. First, we focus on the pure NiOOH
case and analyze the effect of strain on each intermediate reaction of water oxidation.
Next, we show for 8 at% Fe doping the effect of both doping and strain. We then
extend the analysis to higher Fe contents and discuss how both alloying percentage
and strain affect the overpotential required for water oxidation.
The overpotential required for water oxidation on pure NiOOH is 0.61 eV (see
Table 1). The process determining the overpotential is the chemical reaction with the
highest free energy, which is the first deprotonation step for pure NiOOH (−0.11 eV in
Table 1). In contrast, with the application of 10% contraction, the highest free energy
belongs to the second reaction step. As seen in Fig. 3, the most dominant change is for
Table 1 Free energies and overpotentials for pure NiOOH with or without strain at pH = 14 and
V = 1 V
Reaction
−10%
−5%
0
5%
10%
A to B
−0.18
−0.23
−0.11
−0.19
0.04
B to C
0.36
−0.24
−0.71
−1.12
−1.70
C to D
−0.41
−0.36
−0.40
−0.51
−0.44
D to A
−2.57
−1.97
−1.58
−0.98
−0.71
Over potential
1.08
0.49
0.61
0.52
0.76
Units are eV
5
“D” is similar to intermediate “B” but the additional oxygen atom penetrating the
surface. The free energy for the reactions was calculated by adding the previously
reported zero-point energy (ZPE) corrections and entropic contributions of pure βNiOOH since these additions were shown stable with variations in composition [17,
42]. The free energies were calculated at the operating conditions for the OER:
1 V and pH = 14, by adding a constant energy −eU for the applied voltage and a
term of −k B T · ln 10 · pH for the pH where k B is Boltzmann constant and T is the
temperature of 298.15 K. The free energies without pH and T corrections are provided
in the supporting information (Tables 13, 14, 15, 16 and 17). The overpotential is
defined as voltage needed to add to the calculated electrochemical potential so that
all reaction free energies are negative. The intermediate reaction cells are expanded
or contracted significantly (up to 10%) in order to be able to see the effect of strain.
The expansion or contraction was performed by elongating or contracting the surface
lattice vectors and allowing only the ions to optimize in their positions. The lattice
vectors were changed only in the directions of the
a and
b vectors. For example, the
expansion is reflected by the distance between the sheets elongated from 2.624 to
2.722 Å (see Fig. 2).
3 Results
In this section, we present free energy calculations of the water oxidation reaction
for the Ni 1−x Fe x OOH alloy under applied strain. First, we focus on the pure NiOOH
case and analyze the effect of strain on each intermediate reaction of water oxidation.
Next, we show for 8 at% Fe doping the effect of both doping and strain. We then
extend the analysis to higher Fe contents and discuss how both alloying percentage
and strain affect the overpotential required for water oxidation.
The overpotential required for water oxidation on pure NiOOH is 0.61 eV (see
Table 1). The process determining the overpotential is the chemical reaction with the
highest free energy, which is the first deprotonation step for pure NiOOH (−0.11 eV in
Table 1). In contrast, with the application of 10% contraction, the highest free energy
belongs to the second reaction step. As seen in Fig. 3, the most dominant change is for
Table 1 Free energies and overpotentials for pure NiOOH with or without strain at pH = 14 and
V = 1 V
Reaction
−10%
−5%
0
5%
10%
A to B
−0.18
−0.23
−0.11
−0.19
0.04
B to C
0.36
−0.24
−0.71
−1.12
−1.70
C to D
−0.41
−0.36
−0.40
−0.51
−0.44
D to A
−2.57
−1.97
−1.58
−0.98
−0.71
Over potential
1.08
0.49
0.61
0.52
0.76
Units are eV