1, respectively 0, and the points of contact of the vertical tangents (ranges 1 and 3) are
the ones where fluctuations occur. Experimentally, during a heating or cooling process,
when the point of contact is reached, the concentration jumps immediately to the stable
branch, as indicated by arrows in Figure 7.28a.
The situation is less complex in the case of the global enclosure. As may be seen in
Figure 7.28b, a global enclosure leads to hysteresis between the heating and the
cooling cycle, when the temperature of phase transformation is passed. Figure 7.28b
displays a broad temperature range where the transformation occurs. Furthermore,
one has to distinguish a lower and an upper fluctuation range on both sides of the
transformation range. The branch indicated by DT < 0 is connected to the lowtemperature phase, whereas the other branch, indicated by DT > 0, refers to the
high-temperature phase.
Looking at experimental results, one finds types resembling one or the other type
of enclosing in Figure 7.29a and b. Certainly, experimental reality never reflects the
pure types, as they are result from computing. Nevertheless, the graph based on results
obtained on melting of germanium particles in silica, reported by Xu et al. [25] comes
close to the case of local enclosure as depicted in Figure 7.28a. This result may be
understood quite well, as the thermal conductivity of germanium is certainly higher
than that of silica. The reasoning of the data displayed in Figure 7.28b is not that
straight forward. In this case, melting and freezing of InSb particles in silica (Tetu et al.
[26]) is displayed as a function of the temperature. Yes, this graph is quite similar to
Figure 7.28b, the global case. However, the different behavior, as compared to the case
of germanium in silica, can be explained only by the poorer thermal conductivity of
InSb particles as compared to the previous case. Furthermore, the germanium
particles were significantly smaller than the InSb particles. This difference in size
may act in the same direction as the difference in thermal conductivity.
References
1 Malinovskaya, T.D. and Sachkov, V.I. (2003)
Russ. Phys. J., 46, 1280–1282.
2 Tsch€ ope, A. and Birringer, R. (1993) Philos.
Mag. B, 68, 223–229.
3 Rupp, J. and Birringer, R. (1987) Phys. Rev.,
36, 7888–7890.
4 Wang, L., Tan, Z., Meng, S., Liang, D., and
Li, G. (2001) J. Nanoparticle Res., 3,
483–487.
5 Thomson, W. (1871) Philos. Mag., 42,
448–452.
6 Castro, T., Reifenberger, R., Choi, E., and
Andres, R.P. (1990) Phys. Rev., 42,
8548–8556.
7 Reiss, H. and Wilson, I.W. (1948) J. Colloid
Sci., 3, 551–561.
8 Pawlow, P. (1908) Z. Phys. Chem., 65, 1.
9 Hanszen, K.-J. (1960) Z. Phys., 157,
523–553.
10 Zhao, M., Zhou, X.H., and Jiang, Q. (2001)
J. Mater. Res., 16, 3304–3308.
11 Eckert, J., Holzer, J.C., Ahn, C.C., Fu, Z.,
and Johnson, W.L. (1993) Nanostruct.
Mater., 2, 407–413.
12 Coombes, C.J. (1972) J. Phys. F, 2, 441–448.
13 Vollath, D. (2012) Int. J. Mater. Res., 103,
278–282.
14 Suresh, A. and Mayo, M.J. (2003) J. Mater.
Sci., 18, 2913–2921.
15 Mayo, M.J., Suresh, A., and Porter, W.D.
(2003) Rev. Adv. Mater. Sci., 5, 100–109.
16 Ayyub, P., Palkar, V.R., Chattopadhyay, S.,
and Multani, M. (1995) Phys. Rev., 51,
6135–6138.
References j165
the ones where fluctuations occur. Experimentally, during a heating or cooling process,
when the point of contact is reached, the concentration jumps immediately to the stable
branch, as indicated by arrows in Figure 7.28a.
The situation is less complex in the case of the global enclosure. As may be seen in
Figure 7.28b, a global enclosure leads to hysteresis between the heating and the
cooling cycle, when the temperature of phase transformation is passed. Figure 7.28b
displays a broad temperature range where the transformation occurs. Furthermore,
one has to distinguish a lower and an upper fluctuation range on both sides of the
transformation range. The branch indicated by DT < 0 is connected to the lowtemperature phase, whereas the other branch, indicated by DT > 0, refers to the
high-temperature phase.
Looking at experimental results, one finds types resembling one or the other type
of enclosing in Figure 7.29a and b. Certainly, experimental reality never reflects the
pure types, as they are result from computing. Nevertheless, the graph based on results
obtained on melting of germanium particles in silica, reported by Xu et al. [25] comes
close to the case of local enclosure as depicted in Figure 7.28a. This result may be
understood quite well, as the thermal conductivity of germanium is certainly higher
than that of silica. The reasoning of the data displayed in Figure 7.28b is not that
straight forward. In this case, melting and freezing of InSb particles in silica (Tetu et al.
[26]) is displayed as a function of the temperature. Yes, this graph is quite similar to
Figure 7.28b, the global case. However, the different behavior, as compared to the case
of germanium in silica, can be explained only by the poorer thermal conductivity of
InSb particles as compared to the previous case. Furthermore, the germanium
particles were significantly smaller than the InSb particles. This difference in size
may act in the same direction as the difference in thermal conductivity.
References
1 Malinovskaya, T.D. and Sachkov, V.I. (2003)
Russ. Phys. J., 46, 1280–1282.
2 Tsch€ ope, A. and Birringer, R. (1993) Philos.
Mag. B, 68, 223–229.
3 Rupp, J. and Birringer, R. (1987) Phys. Rev.,
36, 7888–7890.
4 Wang, L., Tan, Z., Meng, S., Liang, D., and
Li, G. (2001) J. Nanoparticle Res., 3,
483–487.
5 Thomson, W. (1871) Philos. Mag., 42,
448–452.
6 Castro, T., Reifenberger, R., Choi, E., and
Andres, R.P. (1990) Phys. Rev., 42,
8548–8556.
7 Reiss, H. and Wilson, I.W. (1948) J. Colloid
Sci., 3, 551–561.
8 Pawlow, P. (1908) Z. Phys. Chem., 65, 1.
9 Hanszen, K.-J. (1960) Z. Phys., 157,
523–553.
10 Zhao, M., Zhou, X.H., and Jiang, Q. (2001)
J. Mater. Res., 16, 3304–3308.
11 Eckert, J., Holzer, J.C., Ahn, C.C., Fu, Z.,
and Johnson, W.L. (1993) Nanostruct.
Mater., 2, 407–413.
12 Coombes, C.J. (1972) J. Phys. F, 2, 441–448.
13 Vollath, D. (2012) Int. J. Mater. Res., 103,
278–282.
14 Suresh, A. and Mayo, M.J. (2003) J. Mater.
Sci., 18, 2913–2921.
15 Mayo, M.J., Suresh, A., and Porter, W.D.
(2003) Rev. Adv. Mater. Sci., 5, 100–109.
16 Ayyub, P., Palkar, V.R., Chattopadhyay, S.,
and Multani, M. (1995) Phys. Rev., 51,
6135–6138.
References j165