22 3 Surfaces in Nanomaterials
Figure 3.1 Ratio of the surface shell volume over the total volume of the particle. The
thickness of the surface layer was selected to be 0.5 or 1.0 nm.
0
5
10
15
20
particle diameter [nm]
0
0.2
0.4
0.6
0.8
1
surface
layer
/
total
volume
Thickness of surface layer
0.5 nm
1.0 nm
Figure 3.2 Nanocrystalline material. The full circles represent atoms in the crystallized phase,
whereas the open circles represent atoms at the grain boundary.
Figure 3.1 depicts the ratio of the surface-influenced volume over the total
volume of the particle. For reasons of simplicity, the shape of the particles was
assumed to be spherical.
Scrutinizing this graph, one realizes that in case of a 5-nm particle, 49% or
78%, respectively, of the volume belongs to the surface-influenced volume. In the
case of smaller particles, the relative amount of material influenced by surface
phenomena is significantly larger. There are applications where this has severe
consequences. For example, in a first approximation the magnetic moment at
saturation and the susceptibility depend primarily on the part of the particles,
which is not influenced by the surface; hence, magnetic nanoparticles exhibit only
low values for these parameters (see Chapter 8). Lastly, the considerations, valid
for free nanoparticles, may be adapted for nanocrystalline bulk materials; one has
just to replace the term “free surface” by grain boundaries. Schematically, this
situation is depicted in Figure 3.2. It is interesting to note that the atoms located