Dipole-Dipole Interaction Model for Oriented Aggregation of BaTiO 3 Nanocrystals
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Dipole-Dipole Interaction Model for Oriented Aggregation of BaTiO3 Nanocrystals Kyuichi Yasui and Kazumi Kato National Institute of Advanced Industrial Science and Technology (AIST) 2266-98 Anagahora, Shimoshidami, Moriyama-ku, Nagoya 463-8560, Japan ABSTRACT In order to study the oriented aggregation of BaTiO3 nanocrystals in the ultrasoundassisted synthesis in an aqueous solution [F.Dang et al., Jpn.J.Appl.Phys. 48, 09KC02 (2009)], the electric dipole-dipole interaction model has been studied by numerical simulations. The results of the numerical simulations are consistent with the experimental ones if the electric dipole moment of a primary particle (a nanocrystal) of 5 nm in diameter is about 10 D =3.3 x 10-29 (C m). It suggests that a 5-10 nm BaTiO3 nanocrystal synthesized in an aqueous solution with ultrasound has spontaneous polarization. INTRODUCTION The ultrasound-assisted synthesis of BaTiO3 nanoparticles in an aqueous solution results in the formation of aggregates of BaTiO3 nanocrystals [1]. The size of an aggregate is 100-400 nm and that of the constituent primary particle (a nanocrystal) is 5-10 nm. Surprisingly, the electron diffraction pattern from an aggregate is the same as that from a single crystal. It means that the crystal axes of the constituent nanocrystals are aligned in an aggregate. Such an aggregate is referred to as a mesocrystal [2]. In order to study the mechanism of the mesocrystal formation, the authors have performed numerical simulations of nucleation and aggregation of BaTiO3 nanocrystals [3-5]. Firstly, the particle (aggregate) size distribution has been simulated and it has been concluded that (large) aggregates do not attach each other and that they aggregate only with primary particles (or small aggregates) [3, 5]. Next, a collision between two particles (aggregate(s) or primary particle(s)) has been numerically simulated based on the electric dipole-dipole interaction model [4, 5]. It has been concluded that large aggregates do not attach each other due to stronger repulsive interaction of the double-layer caused by the non-zero zeta potential of a nanocrystal. It has also been concluded that the crystal axes are aligned by the dipole-dipole interaction. However, in the paper [4, 5], the shape of a primary particle was assumed as cubic although in the experiment [1] it was sphere. Thus in the present paper, numerical simulations have been performed for spherical primary particles. THEORETICAL MODEL We consider a collision between an aggregate and a primary particle, as shown in Fig. 1. It is assumed that each primary particle has an electric dipole moment (p) on its surface because
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(a primary particle or an aggregate)
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(An aggregate) Figure 1. A collision between an aggregate and a primary particle. One of the constituent primary particles is shown on the outer surface of an aggregate. mobile charge carriers screen the polarization inside a particle [6]. For an aggregate, the elect
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