24 3 Surfaces in Nanomaterials
lattice, the energy of bonding, u is needed to break the bonds. This is demonstrated
in Figure 3.3.
Therefore, to break a larger part of material into smaller pieces, each bond
between two neighboring atoms must be broken. After breaking, two new surfaces
emerge. Hence, on both sides, for each atom at the new surface, half of the binding
energy is stored at the surface. In the interior of a particle, the atoms are in a
mechanical equilibrium of binding forces, fixing them at their lattice positions.
Arrows mark these forces in Figure 3.4. It is obvious that atoms at the surface
have lost bonds at the outside. Because of the reduced number of neighbors, at
each atom at the surface, a force acts perpendicular to the surface. At a plane
surface (to be mathematically exact: the surface of a plane infinite half-space),
Figure 3.3 Creating new surfaces, for example, by breaking a larger part into smaller pieces
requires the energy u for each bond to be broken.
u
u
u
u
u
u
u
u
Figure 3.4 Forces acting between atoms at
lattice positions. Because of the reduced
number of neighbors, the atoms at the
surface are pulled in the direction to the
interior of the particle. However, this does
not lead to a pressure comparable with a
hydrostatic pressure, rather, it leads to a
stress in the surface, the surface stress. For
the estimation of thermal effects, for
example, during coagulation of two particles,
the sum value of the surface energy of both
particles, Eq. (3.6), is the ruling one.