Ab Initio Atomistic Thermodynamics for Fuel Cell Catalysis - Fuel Cell Catalysis: A Surface Science Approach - page 143

Haftel and Rosen used the embedded atom method (EAM) to study the structure
and dynamics of metallic systems and investigated the surface reconstructions of
various faces of Au and Pt theoretically with a number of different interaction poten-
tials [Haftel and Rosen, 2001]. Later, they employed the surface embedded atom
method (SEAM) to calculate the total energy of Au(100)-hex, Au(100)-(1 1), and
Au(111)-(1 1) [Haftel and Rosen, 2003]. In order to account for the electrode poten-
tial, they added additional charge to the atoms at the electrode surface. From their
studies, they concluded that surface charge plays an important role in the lifting of
reconstruction. In addition, they estimated the reconstruction energy as function of
change in surface strain, and found this factor to be important only for higher
potentials.
While in previous ab initio studies the reconstructed surface was mostly simulated
as Au(111), Feng et al. [2005] have recently performed periodic density functional
theory (DFT) calculations on a realistic system in which they used a (5 1) unit
cell and added an additional atom to the first surface layer. In their calculations, the
electrode potential was included by charging the slab and placing a reference electrode
(with the counter charge) in the middle of the vacuum region. From the surface free
energy curves, which were evaluated on the basis of experimentally measured capacities,
they concluded that there is no necessity for specific ion adsorption [Bohnen and
Kolb, 1998] and that the positive surface charge alone would be sufficient to lift
the reconstruction.
Although (5.19) is exact, the practical evaluation of the free energy G of the
entire electrode/electrolyte interface with the accuracy required to tackle the effect
of surface reconstruction is far beyond present capabilities. Therefore, instead of
studying the influence of specific electrolyte ion adsorption directly, we focus on
the electronic effects arising from the positive surface charge, and investigate whether
these are already sufficient to lift the surface reconstruction. We further assume that the
numbers of anions and cations within the interface stay constant over the entire range
of electrode potentials and that the structure of the electrolyte does not change. These
are certainly rather strong assumptions, but allow for quantum mechanical calculations
of the electronic structure of Au(100)-hex and Au(100)-(1 1). As a consequence, the
last two terms in (5.19) (hereafter denoted by K ) become constant and the influence on
the electrolyte on the electrode surface cancels out when we focus on relative stabilities
only. Therefore, with
g 0 ¼ g þ N a m ac (T, a ac ) þ N c y

m c (T, a c ) ; g þ K

x N a

(5 : 20)

we can rewrite (5.19) as

g 0 (T, a Au , f e ) ¼ 1
A

G(T, a Au , N Au , q e ) N Au g bulk

Au (T, a Au ) q e (Df F = e)

(5 : 21)

This expression has the advantages that the electrode potential only appears in the last
term and that the Gibbs free energy G depends only on the temperature and quantities
related to the electrode, allowing one to neglect the electrolyte part of the interface.