144 7 Thermodynamics of Nanoparticles and Phase Transformations
temperatures and even more striking, at temperatures above 250 K, which is
explained by increased freedom for vibration of the ions at the grain boundaries.
This material had a reduced density of 89% (this density reduction is not due
to porosity), which is explained by the reduced density of the material at grain
boundaries.
Precise and very detailed theoretical calculations of heat capacity as a function
of the particle size of indium oxide, In 2 O 3 [12] led, as expected, to a decrease of
heat capacity with decreasing particle size. Most importantly, however, is the deviation of this tendency at the smallest grain sizes. This increase at particle sizes
below 1.5 nm is due to the fact that, at this particle size, the material consists of
surface only. Surface is, as demonstrated for example, in Figures 7.4 and 7.5,
highly disordered; and disordered material has, because of the increased number
of possible vibration modes, higher heat capacity (Figure 7.22).
Figure 7.22 Calculated values for the heat capacity of indium oxide, In 2 O 3 as function of the
particle size [12]. As the reference temperature, a value of 298 K was selected. Please note the
dramatic increase of the heat capacity at particle sizes below 1.2 nm.
0
10
20
30
40
particle diameter [nm]
75
80
85
90
95
heat
capacity
c v
[J
mol
–1
K
–1
]
References
1 Castro, T., Reifenberger, R., Choi, E., and
Andres, R.P. (1990) Phys. Rev., 42,
8548–8556.
2 Coombes, C.J. (1972) J. Phys. F, 2,
441–448.
3 Chang, J., and Johnson, E. (2005) Philos.
Mag., 85, 3617–3627.
4 Eckert, J., Holzer, J.C., Ahn, C.C., Fu, Z.,
and Johnson, W.L. (1993) Nanostruct.
Mater., 2, 407–413.
5 Vollath, D., and Fischer, F.D. (2011) Prog.
Mater. Sci., 56, 1030–1076.
6 Iijima, S., and Ichihashi, T. (1986) Phys.
Rev. Lett., 56, 616–619, figure 1.
7 Oshima, Y., and Takayanagi, K. (1993) Z.
Phys. D, 27, 287–294.
8 Ajayan, P.M., and Marks, L.D. (1988)
Phys. Rev. Lett., 60, 585–587.
9 Xu, Q., Sharp, D., Yuan, C.W., Yi, D.O.,
Liao, C.Y., Glaeser, A.M., Minor, A.M.,
temperatures and even more striking, at temperatures above 250 K, which is
explained by increased freedom for vibration of the ions at the grain boundaries.
This material had a reduced density of 89% (this density reduction is not due
to porosity), which is explained by the reduced density of the material at grain
boundaries.
Precise and very detailed theoretical calculations of heat capacity as a function
of the particle size of indium oxide, In 2 O 3 [12] led, as expected, to a decrease of
heat capacity with decreasing particle size. Most importantly, however, is the deviation of this tendency at the smallest grain sizes. This increase at particle sizes
below 1.5 nm is due to the fact that, at this particle size, the material consists of
surface only. Surface is, as demonstrated for example, in Figures 7.4 and 7.5,
highly disordered; and disordered material has, because of the increased number
of possible vibration modes, higher heat capacity (Figure 7.22).
Figure 7.22 Calculated values for the heat capacity of indium oxide, In 2 O 3 as function of the
particle size [12]. As the reference temperature, a value of 298 K was selected. Please note the
dramatic increase of the heat capacity at particle sizes below 1.2 nm.
0
10
20
30
40
particle diameter [nm]
75
80
85
90
95
heat
capacity
c v
[J
mol
–1
K
–1
]
References
1 Castro, T., Reifenberger, R., Choi, E., and
Andres, R.P. (1990) Phys. Rev., 42,
8548–8556.
2 Coombes, C.J. (1972) J. Phys. F, 2,
441–448.
3 Chang, J., and Johnson, E. (2005) Philos.
Mag., 85, 3617–3627.
4 Eckert, J., Holzer, J.C., Ahn, C.C., Fu, Z.,
and Johnson, W.L. (1993) Nanostruct.
Mater., 2, 407–413.
5 Vollath, D., and Fischer, F.D. (2011) Prog.
Mater. Sci., 56, 1030–1076.
6 Iijima, S., and Ichihashi, T. (1986) Phys.
Rev. Lett., 56, 616–619, figure 1.
7 Oshima, Y., and Takayanagi, K. (1993) Z.
Phys. D, 27, 287–294.
8 Ajayan, P.M., and Marks, L.D. (1988)
Phys. Rev. Lett., 60, 585–587.
9 Xu, Q., Sharp, D., Yuan, C.W., Yi, D.O.,
Liao, C.Y., Glaeser, A.M., Minor, A.M.,