30 3 Surfaces in Nanomaterials
One may expect that the hydrostatic pressure, caused by the surface stress
deforms the particle. In fact, this phenomenon leads, in the case of metallic nanoparticles, to particle contraction. However, this contraction is so small that is can
be determined only by high-precision X-ray lattice constant measurements. In the
case of ceramic particles, this reduction is, generally, superimposed by phenomena leading to lattice expansion.
Considering the experimental difficulty determining lattice constants with high
precision in the case of small particles, this phenomenon is well documented.
Figure 3.9 displays, as examples, the lattice constants of gold [2] and palladium [3]
as a function of the particle diameter. In both cases, a significant reduction of the
lattice constant was observed.
Particles of ceramic oxides behave differently. Figure 3.10 depicts the dependency of the unit cell volume of γ-Fe 2 O 3 as function of the particle size [4]. It is
important to realize that, in contrast to metals, the lattice expands with decreasing
particle size. This phenomenon is explained by a change in the lattice structure at
the surface with decreasing particle size. The starting point for the explanation is
the observation that, in most cases, the cations at the surface of an oxide are terminated by oxygen ions or other anions, such as (OH)
−
. Therefore, the surface of
an oxide is covered with ions, all bearing negative electrical charges. These negative charges repel each other; hence, the lattice expands [5].
3.3
Vapor Pressure of Small Particles
From the Clausius–Clapeyron law, Lord Kelvin derived an equation for the vapor
pressure of a curved surface as a function of the curvature radius. In connection
to particulate matter, this equation connects the vapor pressure of a free surface
Figure 3.9 Experimental values for the lattice constant of gold [2] and palladium [3]
nanoparticles. Due to the deformation due to the hydrostatic pressure originated by the
surface tension, decreasing lattice parameters are observed with decreasing particle size.
0
2
4
6
8
10
12
14
particle diameter [nm]
–4
–3
–2
–1
0
lattice
contraction
∆a/a [%]
Au
Pd
One may expect that the hydrostatic pressure, caused by the surface stress
deforms the particle. In fact, this phenomenon leads, in the case of metallic nanoparticles, to particle contraction. However, this contraction is so small that is can
be determined only by high-precision X-ray lattice constant measurements. In the
case of ceramic particles, this reduction is, generally, superimposed by phenomena leading to lattice expansion.
Considering the experimental difficulty determining lattice constants with high
precision in the case of small particles, this phenomenon is well documented.
Figure 3.9 displays, as examples, the lattice constants of gold [2] and palladium [3]
as a function of the particle diameter. In both cases, a significant reduction of the
lattice constant was observed.
Particles of ceramic oxides behave differently. Figure 3.10 depicts the dependency of the unit cell volume of γ-Fe 2 O 3 as function of the particle size [4]. It is
important to realize that, in contrast to metals, the lattice expands with decreasing
particle size. This phenomenon is explained by a change in the lattice structure at
the surface with decreasing particle size. The starting point for the explanation is
the observation that, in most cases, the cations at the surface of an oxide are terminated by oxygen ions or other anions, such as (OH)
−
. Therefore, the surface of
an oxide is covered with ions, all bearing negative electrical charges. These negative charges repel each other; hence, the lattice expands [5].
3.3
Vapor Pressure of Small Particles
From the Clausius–Clapeyron law, Lord Kelvin derived an equation for the vapor
pressure of a curved surface as a function of the curvature radius. In connection
to particulate matter, this equation connects the vapor pressure of a free surface
Figure 3.9 Experimental values for the lattice constant of gold [2] and palladium [3]
nanoparticles. Due to the deformation due to the hydrostatic pressure originated by the
surface tension, decreasing lattice parameters are observed with decreasing particle size.
0
2
4
6
8
10
12
14
particle diameter [nm]
–4
–3
–2
–1
0
lattice
contraction
∆a/a [%]
Au
Pd