Therefore,
N
n
=
4D
2
=d
2
D 3 =d 3 =
4d
D
Using the expressions in the table and Equation 2.7, one can determine the
predicted melting temperatures of a variety of nanostructures. In order to
calculate nanostructure-melting temperature, the corresponding bulk
melting temperatures are required. For example, Figure 2.5a and b show
550
500
450
400
350
T
m (K)
T
m (K)
0
1 0
2 0
3 0
4 0
5 0
D (nm)
D (nm)
(a)
600
550
500
450
0
1 5
(b)
30
45
Sn nanoparticles
Pb nanoparticles
Figure 2.5 The melting temperatures of (a) Sn nanoparticles, and (b) Pb nanoparticles, as a function of particle diameter. The symbols represent experimental
values and the solid lines are the calculated melting temperatures based on Equation
2.7 and Table 2.1. (Reprinted from Physica B: Condensed Matter, 368, Qi, W.H., Size
effect on melting temperature of nanosolids, 46–50, Copyright 2005, with permission
from Elsevier.)
TEMPERATURE AND NANOMATERIALS
27