Page 64 - Book Hosokawa Nanoparticle Technology Handbook

1.11 ELECTRICAL PROPERTIES FUNDAMENTALS

2500
* Solid State Commun. 7 7,139, 1969
B
2000 ** Phys. Rev.B6, 3322,1972
150 ε a 1500 ε a
Dielectric Constant 100 ε Dielectric Constant 1000 ε

60

ε c 40 ε a = 1500 * ε c
fir
20
fir
ε c = 38 ± 16 **
0
50
10 15 20 25 30 40 50 60 70 80 90 100 110
Particle Size (nm) Particle Diameter (nm)
Figure 1.11.3 Figure 1.11.5
Particle size dependence for dielectric constant of PT Particle size dependence for dielectric constant of BT
nanoparticles. nanoparticles.

that of the normal one for the larger particles without
500 size effect. Therefore, it is concluded that the dielec-
Pb(Zr x ,Ti 1-x )O 3
450 X=0.50 tric constant calculated using LST relation is reason-
X=0.40 able. The intrinsic dielectric constant of lead titanate
X=0.30 increased with decreasing particle size, since the size
400
Dielectric Constant 350 is well known that the dielectric constant is abruptly
X=0.00
effect lead to the decrease in Curie temperature [2]. It
increased at around Curie temperature. Therefore, the
300
size region to increase the dielectric constant also
250
ding to the Curie temperature shift.
200 decreases with decreasing particle size, correspon-
Furthermore, particle size dependences of the
150
dielectric constant of lead zirconate titanate and bar-
100 ium titanate are shown in Figs 1.11.4 and 1.11.5,
respectively. These results indicated that the intrinsic
0 10 20 30 40 50
dielectric constant increases with decreasing particle
Particle Diameter (nm)
size by the size effect. Other electrical properties
should be affected by size effect. It is expected to
Crytical Size
develop other novel characterization methods to esti-
mate the electrical properties of nanoparticles.
Figure 1.11.4
Particle size dependence for dielectric constant of PZT
nanoparticles.
References
[1] T. Nakamura: Jpn. J. Appl. Phys., 23, 1265 (1984).
using LST relation in Fig. 1.11.2. From this figure, [2] K. Ishikawa, K. Yoshikawa and N. Okada: Phys. Rev. B,
the dielectric constant started to increase at around 37, 5852 (1988).
15–20nm of the particle size. This result is in good [3] H. Suzuki, T. Ohno: J. Soc. Powder Technol. Jpn., 39
agreement with the tendency in the c/a ratio change (12), 877–884 (2002).
estimated by XRD analysis. In general, the critical [4] T. Sakudo (ed.): Kotai-Butsuri-Koushi-shindo/Yuudentai,
size of lead titanate is reported to be up to 9nm, p. 72, Syoukabou (2003).
whereas the electrical properties started to change as [5] T. Nakamura: Kyou-yuudentai to Kouzou-souteni,
the particle size reached at around 15–20nm. The
dielectric constants of lead titanate single crystal are Syoukabou (1988).
reported as 111, 55, respectively [6]. In con- [6] R.J. Pressley: Handbook of Lasers with Selected Data
c
a
trast, the dielectric constant of lead titanate estimated on Optical Technology, The Chemical Rubber Co.,
by LST relation exhibited almost the same value as Cleveland (1971).
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