Chemistry Reference
In-Depth Information
E
tot
is the total energy of the film with
n
layers and
E
bulk
is the total energy
per layer of the bulk. As a result, these total energies should increase linearly with
the film thickness modulated by some small fluctuations. By fitting the data with
a linear function and subtracting the linear part from the total energies, the desired
surface energies
E
s
can be obtained.
Shown in Fig.
4.8
are the surface energies of freestanding Pb films and their
discrete second derivatives. The surface energy oscillates mostly with film thickness
in a bilayer fashion. However, this bilayer pattern is interrupted at least twice by
crossovers at films of 8 layers and 17 layers, as seen in Fig.
4.8
. The separation
between the neighboring crossovers is nine monolayers. Clearly, the oscillation with
film thickness persists for films as thick as 26 monolayers. From Fig.
4.8
b, the films
of 4, 6, 9, 11, 13, 15, 18, 20, and 22 layers are stable. These results agree well with
experimental investigations [
8
].
film
(
n
)
Fig. 4.8
(
a
) Surface energies of freestanding Pb films. (
b
) The discrete second derivative of surface
energy of freestanding Pb films
