Size Effects in Electrocatalysis of Fuel Cell Reactions on Supported Metal Nanoparticles - Fuel Cell Catalysis: A Surface Science Approach - page 504

15.2.2 Structural Properties
Structure and morphology of supported metal nanoparticles may differ drastically,
depending on (i) their size, (ii) their interaction with support, (iii) the (electro)chemical
environment, and, (iv) since very often particles do not attain equilibrium shapes, also
on the preparation conditions and sample prehistory.
15.2.2.1 Equilibrium Shape The equilibrium shape of crystals is given by the
Wulff construction, according to which s i /h i ¼ const. [Frenkel et al., 2001; Henry,
1998]. Here h i is the distance from the center to the i th crystal face. A theoretical study
by Romanowski using the concept of localized bonds supposed that only the nearest
neighbor interactions are important to determine the minimum surface free energy for
nanoparticles [Romanowski, 1969]. For free fcc, bcc, and hcp metal crystals, the struc-
tures of minimum surface energy are the cubo-octahedron, the rhombo-dodecahedron,
and the truncated hexagonal bipyramid, respectively [Romanowski, 1969]. In this
chapter, we will mainly focus on fcc metals of interest in electrocatalysis.
In the case of supported metallic particles, the construction is modified by intro-
ducing the adhesion energy (Wulff - Kaishew construction) [Henry, 1998]. The equi-
librium shape is a Wulff polyhedron, which is truncated at the interface by an amount
Dh s , according to the relation Dh s /h i ¼ b/s i , where bis the adhesion energy of the
crystal on the substrate.
For an ideal particle of an equilibrium shape, the contribution of various structural
elements to the surface is a function of the particle size and can easily be computed.
As the particle size decreases, the surface fraction of vertices (CN ¼ 6) and edges
(CN ¼ 7) increases, while that of the atoms associated with (100) and (111) facets
(CN ¼ 8 and 9, respectively) decreases [Van Hardeveld and Hartog, 1969;
Kinoshita, 1988]. Therefore, the average first-shell coordination number scales with
the inverse diameter and decreases well below the theoretical value of CN ¼ 12 to
about 6 for a 1 nm particle [Frenkel et al., 2001]. In order to minimize their surface
energy and maximize the bonding between metal atoms, nanometer-sized particles
may adopt a structure different from that characteristic of bulk metals. For example,
Burton suggested that very small crystallites can possess different thermodynamically
stable shapes than expected from Romanowski's calculations [Burton, 1974]. He
reported small crystallites having five-fold symmetry and icosahedral shape to be
more stable than the expected close-packed structures. The surface of such a crystallite
consists of triangular (111) facets. A low symmetry icosahedral shape has indeed been
observed experimentally, for example, for giant Pd 561 clusters [Vargaftik et al., 1991].
In some cases, the tendency of decreasing surface energy results in the formation of
multiple twins [Nagaev, 1992]. On the other hand, it seems unrealistic to assume
that metal nanoparticles always comprise an exact number of atoms to fit one of the
geometric models described above. As a result, nanoparticles in “real” supported
metal catalysts may not have the shape of the Wulff polyhedron, but adopt the form
corresponding to the minimum surface free energy. In some cases, decreasing the
particle size may result in their amorphization. Calculations have produced a phase
diagram that predicts that small Au clusters at room temperature may be in a state