The Importance of the Solids Loading on Confirming the Dielectric Nanosize Dependence of BaTiO3 Powders by Slurry Method

The dielectric nanosize dependence of BaTiO3 powders was investigated by the slurry method, where two series of BaTiO3 slurries with 10 vol% and 30 vol% solids loadings were prepared as model samples. Applying the Bruggeman-Hanai equation, the high-frequency limiting permittivity (ε h) of the slurries was extracted from the dielectric spectra. The ε h of the 10 vol% slurry showed abnormal size independence in the range from 100 nm to 700 nm, and the ε h of the 30 vol% slurry exhibited good agreement with the previous prediction. Through analysing quantitatively the response of ε h to the changing permittivity of the powders under different solids loading, it was found that the ε h of the slurry with lower solids loading is more inclined to be interfered by the systematic and random errors. Furthermore, a high permittivity value was found in the BaTiO3 powders with 50 nm particle size.


Introduction
With the achievement of the particle size from several microns downward tens of nanometers, the issue about the nanosize effect of BaTiO 3 has attracted intensive attentions [1][2][3]. However, the reported critical size for BaTiO 3 powders spreads out in the wide range between 25 and 110 nm [4,5]. The intrinsic reason is that the grain of BaTiO 3 powders would grow up irreversibly during the high temperature sintering. So it is very difficult to obtain the exact critical size of BaTiO 3 by means of using traditional solid-state pellet technique. Recently, the dielectric evaluation of ceramic slurries as an in situ method has been of primary interest [6,7]. However, the slurry method presented that the permittivity of BaTiO 3 powders keeps basically constant when the particle size is above 200 nm [8]. The result deviates the present theories about the size dependence of BaTiO 3 powders and implies that some defects in the slurry method need to be improved. In this paper, we focused on the effect of the solids loading on the slurry method and offered some accurate and valuable information to the dielectric nanosize dependence of BaTiO 3 powders.

Experimental
BaTiO 3 powders with seven kinds of particle sizes, 50, 100, 200, 300, 400, 500, and 700 nm, were commercially obtained from Inframat Advanced Materials, USA. The purities of all powders are higher than 99.95%, and the room-temperature density is 5.85 g/cm 3 . BaTiO 3 slurries at two solids loadings, 10 vol% and 30 vol%, were prepared by ultrasonically mixing powders with a propylene carbonate ( = 66.7 at 25 ∘ C, from Fisher Scientific) for 30 min. The slurries were then placed in a liquid dielectric test fixture (Agilent Tech., 16452A), and the frequency dependence of the permittivity of the slurries was measured with an impedance analyzer (Agilent Tech. 4294A) from 40 Hz to 20 MHz at 25 ∘ C. Figure 1 shows the 3D representations of the particle sizedependent dielectric relaxation spectra of BaTiO 3 powders dispersed in propylene carbonate (PC) with 10 vol% and 30 vol% solids loadings, respectively. A clear relaxation behavior can be seen at near 10 4 Hz, which is aroused from the interfacial polarization between the BaTiO 3 powders and the PC. By using Bruggeman-Hanai equation [9] ℎ − − (

Result and Discussion
the permittivity of BaTiO 3 powders ( ) can be calculated directly from the high-frequency limiting permittivity of the slurry ( ℎ ) in the case that the volume fraction of the powders in the slurry ( ) and the permittivity of the PC ( ) are known accurately. So ℎ is a significant dielectric parameter in order to obtain the with small margin of error. Figure 2(a) shows the particle size dependence of ℎ of BaTiO 3 slurries with different . According to the nonlinear relationship between ℎ and in (1), the ℎ will increase with increasing if the is larger than the . The permittivity of the PC is about 67 at room temperature, which is much smaller than the permittivity of BaTiO 3 powders (1000∼5000). So it is reasonable that the ℎ of 30 vol% BaTiO 3 slurry is much higher than the one of 10 vol% slurry at each particle size. Furthermore, the BaTiO 3 slurries with different volume fractions display distinct particle size dependence. For the slurry with 10 vol% solids loading, ℎ keeps constant basically on the size range from 700 nm to 300 nm, which agrees with the results in Wada's research [8]. For the slurry with 30 vol% solids loading, however, the ℎ displays a nonlinear size dependence similar with the results from solids method [10]. The difference implies that the analysis of the solids loading might explain the discrepancy between the previous results from the slurry and pellet methods. Now, the permittivity of the BaTiO 3 powders is supposed to decrease from 4000 to 3000 with decreasing particle size, and the permittivity of the BTiO 3 slurries with different given solids loading is calculated by (1). According to the results listed in Table 1, dependence of change rate in ℎ (Δ ℎ % = ( ℎ,2 − ℎ,1 )/ ℎ,2 × 100%) can be found. With the volume fraction becoming diluted from 25% to 4%, the Δ ℎ % decreases gradually from 1.90% to 0.20%. It means that the diluter the slurry is, the higher the requirement to the measurement accuracy will be. In experimental measurements, there are always both systematic and random errors, which are mixed into the original data usually. For the dilute slurry, the small Δ ℎ % is more inclined to be interfered by the systematic and random errors and offers inaccurate information. So the solids loading of the slurry should be increased high enough in order to weaken the confused influence of the systemic error on the original data.
Considering the positive effect of higher solids loading on the accuracy of the slurry method, the ℎ from Figure 1(b) was assigned into (1) for calculating the permittivity of BaTiO 3 powders, . Figure 2(b) shows the size dependence of , which has the similar size dependence with the corresponding ℎ . It can be found that the increased obviously with the particle size decreasing from 700 nm to 500 nm, and then decreased gradually with the particle size decreasing from 500 nm to 100 nm. The result agrees with the current postulation from the pellet method. The dependence in fine BaTiO 3 structures is driven by a combined effect of the ferroelectric core whose nonlinearity is gradually reducing, together with the increasing amount of the nonferroelectric "dead-layer" grain boundaries, when reducing the grain size down to tenths of nanometers [1]. However, the with 50 nm particle size appeared with significant high value, which was reported only in Wada's slurries method. There is not enough attention for explaining the phenomenon yet, and we will focus on it in our following research.

Conclusions
The importance of the solids loading in the accuracy of the sully method was researched in order to get the accurate nanosize effect of BaTiO 3 powders. By means of comparing the dielectric data and calculation of the BaTiO 3 slurries with two different solids loadings, 10 vol% and 30 vol%, the higher one was found to possess lower calculation error. Based on the finding, the conflicting nanosize dependence of the BaTiO 3 powders obtained from previous slurry and pellet method was attributed to the low solid loading used in the slurry method.