which shows a decrease in enthalpy for transformation with decreasing particle size.
In addition to determining the melting point of aluminum nanoparticles with
calorimetric methods, Eckert et al. [11] also measured the enthalpy of melting as a
function of particle size (see Figure 7.8). In Figure 7.8, the enthalpy of melting is plotted
against the inverse particle size, thus confirming the linear relationship between
melting enthalpy and inverse particle size as predicted by Eqs. (7.12) and (7.13).
The “perfect fits” as shown in Figures 7.7b and 7.8 are rather rare cases, and most
experimental data show more or less severe deviations. For example, Figure 7.9
a and b show the melting point of lead nanoparticles over a size range of about
3–50 nm.
The data in Figure 7.9b show that the above-mentioned linear relationship
between melting point and inverse particle size is valid only for the range of
very small particles. There are many possible reasons for this deviation, including
0.02
0.03
0.04
0.05
0.06
0.07
0.08
(particle diameter) -1 [nm -1 ]
820
840
860
880
900
920
940
melting
temperature
[K]
10
15
20
25
30
35
40
particle diameter [nm]
820
840
860
880
900
920
940
melting
temperature
[K]
Melting temperature of
bulk aluminum
of
Melting temperature
bulk aluminum
(a)
(b)
Figure 7.7 Melting temperature of aluminum
as a function of grain size, according to Eckert
et al. [11]. The melting temperature of the
bulk material is indicated by the bold line.
(a) Aluminum melting points plotted versus
particle size. (b) Aluminum melting points
plotted versus inverse particle size. Note the
inverse proportionality as described in Eq. (7.7).
7.3 Phase Transformations of Nanoparticles j143