Size Effects in Electrocatalysis of Fuel Cell Reactions on Supported Metal Nanoparticles - Fuel Cell Catalysis: A Surface Science Approach - page 506

Figure 15.1 High resolution transmission electron microscopy images (HR-TEM) of 5 wt%
Pd (a) and 50 wt% Pt-Ru (b) particles supported on carbon supports of the Sibunit family
with surface areas of about 6 m 2 g 21 (a) and 72 m 2 g 21 (b). (c) Fourier-transformed image of
(b). ((a) Reprinted from Pronkin et al. [2007], Copyright 2007, with permission from
Elsevier. (b) and (c) reprinted from Gavrilov et al. [2007]—Reproduced by permission of the
PCCP Owner Societies.)
The Fourier-transformed image in Fig. 15.1c shows that individual grains are
randomly oriented, breaking the continuity of lattice planes in the crystallites.
Unless high temperature annealing procedures are employed (which often is not the
case), these grain boundary regions may have very long lifetimes. The described
materials are usually called “nanostructured” or “nanocrystalline” [Gleiter, 1992].
The high volume density of disordered grain boundary regions leads to unique phys-
ical properties, differentiating these materials from single crystals, coarsely grained
polycrystalline materials, and nanometer-sized supported metal particles. As we
will show in Section 15.5, the presence of grain boundary regions may strongly
influence the electrocatalytic activities of heterogeneous (electro)catalysts.
15.2.2.2 Lattice Parameter Along with the particle shape, another quantity of
relevance to catalysis is the lattice parameter. In the early studies of size effects (see,
e.g., the discussion in the review [Uvarov and Boldyrev, 2001]), changes in the lattice
parameter were explained by the influence of the Laplace excess pressure compressing
crystallites of high curvature. Indeed, lattice constant contraction was reported for
nanoparticles of some fcc metals—Au [Mays et al., 1968], Pt [Wasserman and
Vermaak, 1972], and Ag [Mays et al., 1968]—relative to the values characteristic of
bulk materials. However, the simplified approach resting upon the notion of
Laplace excess pressure neglects the strain energy. When the latter is considered,
the excess pressure may exceed the Laplace pressure and thus lead to lattice com-
pression, but may also become negative, resulting in lattice dilatation [Mays et al.,
1968; Vermaak et al., 1968; Vermaak and Kuhlmann-Wilsdorf, 1968; Nagaev,
1992]. Thus, for Cu particles [Wasserman and Vermaak, 1972], the lattice constant
appeared to remain unchanged or to increase slightly with decreasing particle size,
while for diamond and silicon particles, dilatation was reported [Gamarnik, 1990].
All-electron density functional (DFT) calculations by Krueger and co-workers, per-
formed for high symmetry Au and Pd crystals, have shown a linear correlation between
bond length and average coordination numbers (and thus with inverse particle size)
[Krueger et al., 1997]. For further details on the influence of size on the lattice