Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 69

where j limit can be written as

j limit ¼ j 0 exp a(eU 0 U Max

ORR )

(3 : 21)

k B T

The physical meaning of the term j limit is the current density achieved if all surface
reactions are exothermic, i.e., the highest possible turnover frequency per site. In pre-
vious work on hydrogen evolution, we found that j limit 200 sites 21 s 21 or, in terms
of surface area, 96 mA/cm 2 for Pt(111), fitting experimental data well [Nørskov et al.,
2004, 2005]. Since the lattice parameters of various metals change only by a few per-
cent relative to pure Pt, the number of sites per square centimeter is fairly constant, and
j limit can be effectively considered material-independent, unlike exchange current
density. By incorporating j limit into the analysis, we can thus rewrite the Tafel equation
(3.19) in such a manner that all material dependence is concentrated in only one com-
putable parameter, U ORR

Max .

3.4.3 Improved ORR on Pt 3 X Alloys
Since Pt is so close to the top of the volcano curve for the ORR, it can be difficult to
find a better catalyst that does not contain Pt. A more fruitful approach is to modify Pt
slightly by introducing a subsurface layer of another material. The electronic structure
of the Pt at the surface is then changed so that oxygen binding becomes a little weaker.
In general, the subsurface atoms act by changing the density of states, especially the
position of the d-band center relative to the Fermi level [Hammer and Nørskov,
1995; Kitchin et al., 2004]. Similar effects can be obtained by compressing or stretch-
ing the lattice constant of Pt [Mavrikakis et al., 2000].
In principle, it could be very difficult or impossible to experimentally produce such
surfaces. Fortunately, some Pt alloys spontaneously form Pt skins. For this reason, Pt
skins on Pt 3 X alloys are of significant interest. The Markovic group, in particular, has
made well-controlled and well-characterized experiments for the ORR on Pt skins on
Pt 3 X [Stamenkovic et al., 2006, 2007a, b].
We have performed calculations on this type of alloys. The atomic setup used is a
stochiomeric Pt 3 X slab where the surface X atoms are swapped with Pt subsurface
atoms, leaving a pure Pt skin on top of a subsurface layer enriched with 50% X
atoms. The density of states is affected both by the X atoms in the subsurface layer
and by the changed lattice constant of the alloy compared with Pt. However, both
effects are included when looking at the position of the d-band center. A downward
shift of the d-band results in weaker adsorbate binding, owing to increased occupation
of the antibonding orbital [Hammer and Nørskov, 2000]. The model predicts the U ORR

Max
for the Pt 3 X alloys to be a bit higher than that of pure Pt. Note that a small change in
U ORR

Max can lead to a significant change in the current. Experiments on nanoparticles
[Stamenkovic et al., 2006] showed Pt 3 Co to be the most active, while the theory
indicated that Pt 3 Ni should be closest to the top of the volcano. One possible reason
for this modest discrepancy is that the model only includes (111) surfaces, whereas
the nanoparticles have many different facets. If, for some reason, Pt 3 Co and Pt 3 Ni