considering materials with grain sizes of around 10 nm (which is 1/1000 of the
conventional grain size), then according to Eq. (2.4) the time for homogenization is
reduced by a factor of (10
3 )
2 ¼ 10
6 . Hence, a homogenization time of hours is
reduced to one of milliseconds; the homogenization occurs instantaneously. Indeed,
this phenomenon is often referred to as “instantaneous alloying.” It might also be
said that “. . . each reaction that is thermally activated will happen nearly instantaneously” and therefore it is not possible to produce or store nonequilibrium systems
(which are well known for conventional materials) at elevated temperature. While
this is an important point in the case of high-temperature, gas-phase synthesis
processes, there are even more consequences with respect to synthesis at lower
temperatures or the long-term stability of nonequilibrium systems at room
temperature. The diffusion coefficient D has a temperature dependency of
D ¼ D 0 exp ÀQ=RT
ð
Þ , with the activation energy Q, the gas constant R, and the
temperature T. The quantity D 0 is a material-dependent constant. However, on
returning to the previous example, for a material with 10 mm grain size, we can
assume a homogenization time of 1000 s at a temperature of 1000 K, and two
different activation energies of 200 kJ mol
À1 (which is typical for metals) and
300 kJ mol
À1 (which is characteristic for oxide ceramics). The homogenization
times for the 10-mm and 5-nm particles are compared in Table 2.1. In terms of
temperature, 1000 K for gas-phase synthesis, 700 K for microwave plasma synthesis
at reduced temperature, and 400 K as a storage temperature with respect to longterm stability, were selected. The results of these estimations are listed in Table 2.1.
The data provided in Table 2.1 indicate that, under the usual temperatures for gasphase synthesis (1000 K and higher), there is no chance of obtaining any nonequilibrium structures. However, when considering microwave plasma processes,
where the temperatures rarely exceed 700 K, there is a good chance of obtaining
nonequilibrium structures or combinations of such materials. A temperature of
400 K represents storage and synthesis in liquids, and at this temperature, the 5-nm
particles are stable; however, from the point of thermal stability, it should be
straightforward to synthesize nonequilibrium structures. However, according to
Gleiter, diffusion coefficients up to 20 orders of magnitude larger than those for
Table 2.1 Relative homogenization time (s) for 5-nm nanoparticles at activation energies of 200
and 300 kJ mol
À1 compared to 10-mm material at 1000 K
a)
.
Particle size
Activation energy (kJ mol
À1
)
Temperature (K)
1000
700
400
10 mm
300
10
3
5.0 Â 10
9
2.8 Â 10
26
200
10
3
2.9 Â 10
7
4.3 Â 10
18
5 nm
300
2.4 Â 10
À4
1.3 Â 10
3
7.0 Â 10
19
200
2.4 Â 10
À4
7.3 Â 10
0
1.1 Â 10
12
a) Assumed homogenization time ¼ 1000 s.
2.2 Elementary Consequences of Small Particle Size j15
conventional grain size), then according to Eq. (2.4) the time for homogenization is
reduced by a factor of (10
3 )
2 ¼ 10
6 . Hence, a homogenization time of hours is
reduced to one of milliseconds; the homogenization occurs instantaneously. Indeed,
this phenomenon is often referred to as “instantaneous alloying.” It might also be
said that “. . . each reaction that is thermally activated will happen nearly instantaneously” and therefore it is not possible to produce or store nonequilibrium systems
(which are well known for conventional materials) at elevated temperature. While
this is an important point in the case of high-temperature, gas-phase synthesis
processes, there are even more consequences with respect to synthesis at lower
temperatures or the long-term stability of nonequilibrium systems at room
temperature. The diffusion coefficient D has a temperature dependency of
D ¼ D 0 exp ÀQ=RT
ð
Þ , with the activation energy Q, the gas constant R, and the
temperature T. The quantity D 0 is a material-dependent constant. However, on
returning to the previous example, for a material with 10 mm grain size, we can
assume a homogenization time of 1000 s at a temperature of 1000 K, and two
different activation energies of 200 kJ mol
À1 (which is typical for metals) and
300 kJ mol
À1 (which is characteristic for oxide ceramics). The homogenization
times for the 10-mm and 5-nm particles are compared in Table 2.1. In terms of
temperature, 1000 K for gas-phase synthesis, 700 K for microwave plasma synthesis
at reduced temperature, and 400 K as a storage temperature with respect to longterm stability, were selected. The results of these estimations are listed in Table 2.1.
The data provided in Table 2.1 indicate that, under the usual temperatures for gasphase synthesis (1000 K and higher), there is no chance of obtaining any nonequilibrium structures. However, when considering microwave plasma processes,
where the temperatures rarely exceed 700 K, there is a good chance of obtaining
nonequilibrium structures or combinations of such materials. A temperature of
400 K represents storage and synthesis in liquids, and at this temperature, the 5-nm
particles are stable; however, from the point of thermal stability, it should be
straightforward to synthesize nonequilibrium structures. However, according to
Gleiter, diffusion coefficients up to 20 orders of magnitude larger than those for
Table 2.1 Relative homogenization time (s) for 5-nm nanoparticles at activation energies of 200
and 300 kJ mol
À1 compared to 10-mm material at 1000 K
a)
.
Particle size
Activation energy (kJ mol
À1
)
Temperature (K)
1000
700
400
10 mm
300
10
3
5.0 Â 10
9
2.8 Â 10
26
200
10
3
2.9 Â 10
7
4.3 Â 10
18
5 nm
300
2.4 Â 10
À4
1.3 Â 10
3
7.0 Â 10
19
200
2.4 Â 10
À4
7.3 Â 10
0
1.1 Â 10
12
a) Assumed homogenization time ¼ 1000 s.
2.2 Elementary Consequences of Small Particle Size j15