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Continuous Production of BaTiO3 Nanoparticles by Hydrothermal Synthesis Yukiya Hakuta,* Haruo Ura, Hiromichi Hayashi, and Kunio Arai Supercritical Fluid Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Nigatake 4-2-1, Miyagino-ku, Sendai 983-8551, Japan
Continuous production of BaTiO3 fine particles was performed by hydrothermal synthesis using a flow reaction system. The effect of reaction temperature on particle size and its distribution was investigated. Aqueous 0.1 M TiO2 sols and 0.12 M Ba(OH)2 solutions were used as starting materials. The reaction temperature was in the range 300-420 °C, and the reaction pressure was constant at 30 MPa. The reaction time was varied from 0.1 to 40 s with a flow rate of 15 or 75 g/min. Characterizations of products were performed by X-ray diffractometry, scanning electron microscopy equipped with energy dispersion X-ray spectrometry, and transmission electron microscopy. The conversion of TiO2 into BaTiO3 was also evaluated. At 300 °C, the Ti conversion increased with the reaction time and achieved a 95% yield at 38 s. With the increase in temperature, both the Ti conversion and the crystallinity of BaTiO3 became high. With an increase in temperature from 300 to 380 °C, the average particle size of BaTiO3 decreased from 46 to 36 nm and these particle size distributions became narrow. At 400 and 420 °C, the reaction was complete within several seconds and highly tetragonal crystalline BaTiO3 particles around 50 nm in diameter were produced, whereas the particle size distribution was wide ranging from 10 to 150 nm. However, the finer BaTiO3 particles at a size of 32 nm and a narrow size distribution could be produced by increasing the flow rate to 75 g/min even at 400 °C. We discuss the mechanism of particle formation and growth and the feasibility of continuous production of BaTiO3 particles. 1. Introduction Barium titanate (BaTiO3), having a perovskite type crystal structure, possesses specific ferroelectric properties and is used as the raw material for ceramic condensers, memory, and so on.1 Recently, in proportion to the increase in demand for mobile electronic devices, finer BaTiO3 particles within 100 nm have been required to make a progressive multilayer ceramic condenser with high densification and high capacity.2 BaTiO3 particles have been produced industrially by batch processes such as solid-state reactions and hydrothermal syntheses. From the point of view of mass production, a continuous process is more efficient for producing BaTiO3 particles. Conventionally, BaTiO3 fine particles or thin films have been produced by solid-state reactions,2 sol-gel methods,3-5 and hydrothermal syntheses.6-19 In the solid-state reaction process, BaTiO3 particles have been synthesized by reaction between TiO2 and barium carbonate at 1500 °C for 24 h. This process is simple but useless for expensive materials. Because the particles obtained by the solid-state reaction are large (several micrometers), consequently it is necessary to mill or grind them for ceramic materials, introducing many contaminations. The sol-gel method is one of the low-temperature solution methods. It is possible to obtain high-purity particles and to control their particle size from 10 nm to 100 nm. Furthermore, it is easy to make thin films of BaTiO3 by spin coating. However, the starting materials are expensive and the synthetic * To whom correspondence should be addressed. Tel.: +81-22-237-5214. Fax: +81-22-237-5215. E-mail: y-hakuta@ aist.go.jp.
process is complicated. The sol-gel method has many steps and requires a specific reaction field where the humidity must be adjusted exactly. Afterwards, a hightemperature treatment is sometimes also required for crystallization. Hydrothermal synthesis is one of the best methods for producing metal oxide particles. BaTiO3 particles have been synthesized hydrothermally from titanium and barium compounds from 90 to 200 °C. The hydrothermal method has many advantages: highly crystalline particles, low-cost starting materials, low-temperature treatment, and simple procedure. Since BaTiO3 fine particles synthesized hydrothermally have a metastable cubic form due to the residual OH ions in its crystal structure,17-19 a postheat treatment at around 1000 °C is required for phase transformation from a metastable cubic to a tetragonal phase. Moreover, the conventional hydrothermal method is a time-consuming process. Generally, it takes several hours to days. Hydrothermal synthesis assisted by microwave radiation has been developed to depress both the reaction temperature and reaction time for synthesizing BaTiO3 particles.20-22 We think that it is desirable to construct a continuous process within 1 min of reaction time for completing the reaction, from the point of view of cost for both facilities and operation. A continuous process for producing metal oxide particles by hydrothermal synthesis at higher temperature, from 300 to 450 °C, has been proposed. This method was performed by a flow type reactor. Many applications have been reported, such as phosphors,23-25 magnetic materials,26-29 ionic conductors,20-32 photocatalysts,33 electrode materials,34,35 catalysts,36-38 and insulators.39 The specific feature of this method is the controllability
10.1021/ie049424i CCC: $30.25 © 2005 American Chemical Society Published on Web 01/15/2005
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with the supercritical water at the second mixing point (MP2). As soon as the reactant reached the reaction temperature (Treact), a hydrothermal reaction took place and BaTiO3 particles formed. The reactant was maintained for several seconds in the tube reactor (1.86 mm i.d.), and then the reaction was quenched by cooling at the end of the reactor. The reaction time, t, was defined as
t ) VF/F
Figure 1. Schematic diagram of an experimental apparatus: (1) feedstock of TiO2 sols; (2) feedstock of Ba(OH)2 solution; (3) feedstock of distilled water; (4-6) high-pressure pump; (7, 8) electric furnace; (9) heat exchanger; (10) in-line filter; (11) backpressure regulator; (12) filtrate reservoir.
of solvent properties by changing temperature and pressure, as reviewed by Adschiri et al.40 Moreover, other advantages of this method are continuous production and highly crystalline products without a postheat treatment. We have already demonstrated the hydrothermal synthesis of BaTiO3 under supercritical conditions using a flow type reactor, and tetragonal BaTiO3 particles can be produced under the conditions where the water density is 0.5 g/cm3 or less.41 The final goal of our study is to develop a continuous process for producing BaTiO3 fine particles. Thus, it is very important for the process to control the particle size and its distribution as well as polymorphs of BaTiO3. In this paper, we studied the effect of reaction temperature on the size and size distribution of BaTiO3 particles. Furthermore, we have evaluated Ti conversion from TiO2 to BaTiO3, in order to discuss the mechanism of particle formation and growth from the point of view of reaction kinetics. 2. Experiments 2.1. Materials. Titanium dioxide sols (anataze; Ishihara Sangyo Kaisya STS01; average particle size 3.5 nm, BET surface area 305 m2/g) and barium hydroxide (Ba(OH)2; Wako Pure Chemicals Co. Ltd.) were used as starting materials. The sols and salt were dissolved or dispersed into distilled water, and the concentrations of Ti and Ba(OH)2 were adjusted to 0.1 and 0.12 M, respectively. 2.2. Procedure. Figure 1 gives a schematic diagram of the experimental apparatus used in this study. Ba(OH)2 solution (0.12 M) and 0.1 M TiO2 sols were pressurized to 30 MPa and then fed forward to a reactor by a separate high-pressure pump at a flow rate of 2 g/min. Two streams were mixed at the first mixing point, MP1. Distilled water was fed by another highpressure pump at a flow rate of 11 g/min and then heated to an appropriate temperature (TSCW) by an electric furnace. The temperature of supercritical water (TSCW) was controlled to set up the reaction temperature (Treact). The mixture of TiO2 and Ba(OH)2 was mixed
(1)
Here, V denotes the reactor volume (m3), F is the flow rate (kg/s), and F denotes the solution density (kg/m3) at the reaction temperature and pressure. In this study, since the solution is dilute, pure water density was used to approximately evaluate the reaction time. The produced particles were captured in an in-line filter (pore size 500 nm). Although the primary particle size was 20-100 nm, most products (90 wt % or more) could be captured by the in-line filter due to aggregation. The filtered reactant was depressurized at a backpressure regulator and then recovered in the filtrate reservoir. The recovered products were dried in an oven at 60 °C for 1 day. 2.3. Analyses. Crystal structures of products were determined by the X-ray diffraction method (Rigaku Co. Ltd., Model Lint 2000). The source of X-radiation is Cu KR, and the tube voltage and current are 40 kV and 30 mA, respectively. The scan rate was set to 2°/min. The determination of polymorphs of BaTiO3 (metastable cubic and tetragonal forms) was performed as follows.41 In order to determine the polymorph of BaTiO3, a distinction between cubic and tetragonal forms has been discerned by the existence of several doublets, which are specific to the tetragonal BaTiO3. In the case of fine particles of 50 nm or less, it is well-known that a closed doublet such as that for tetragonal BaTiO3 cannot often be split because of broadening of each peak on the XRD pattern. Therefore, we evaluated the full widths at halfmaximum (fwhm) of the selected two peaks, which corresponded to a singlet (111) and doublet (200, 002) of the tetragonal BaTiO3, respectively. These fwhms were named as fwhm111 and fwhm200, respectively. When both fwhms of the peaks agreed, we decided that the product was cubic BaTiO3. On the other hand, when fwhm200 was larger than fwhm111, the product was regarded as a tetragonal BaTiO3. As a result of the phase transformation from cubic to tetragonal, since two peaks (200, 102) had overlapped, fwhm200 was thought to be large. The particle size and morphology were measured by transmission electron microscopy (TEM; FEI Co., Model TECNAI-G2). The average particle size and its standard derivation were evaluated by measurements of 200 particles or more on the TEM micrographs. Chemical compositions of products were analyzed by a scanning electron microscope equipped with energy dispersion X-ray spectrometry (SEM-EDS; JEOL Ltd., Model JSM5600LV). BaTiO3 formed by the hydrothermal reaction
TiO2 + Ba(OH)2 ) BaTiO3 + H2O
(2)
The conversion of Ti from TiO2 to BaTiO3, which was a raw material, was evaluated by the following procedure. According to XRD analyses, crystalline compounds included in the recovered solid products were BaTiO3 and the residual TiO2. Therefore, we measured the
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Table 1. Experimental Results for Hydrothermal Synthesis of BaTiO3 temp (°C)
press (MPa)
reacn time (s)
TiO2 conversn (%)
products (XRD)a
300
30
0.38 5.11 38.2 0.33 4.49 32.8 0.3 4.0 29.9 0.18 2.40 18.0 0.10 1.38 10.3 2.4
0.54 0.76 0.94 0.60 0.82 1.00 0.57 0.79 0.93 0.69 0.82 1.00 0.69 0.90 0.85 0.90
C-BT, TiO2 C-BT, TiO2 T-BT C-BT, TiO2 C-BT, TiO2 T-BT C-BT, TiO2 C-BT, TiO2 T-BT T-BT, TiO2 T-BT, TiO2 T-BT T-BT, TiO2 T-BT T-BT T-BT
350 380 400 420 400c
30
Ba/Ti ratio
0.94 1.00 0.93 1.05 0.90 0.85 0.90
av particle size, Mb (nm)
std dev, S (nm)a
S/M ratio (%)
12.9 27.7 44.1 15.7 26.8 39.0 18.7 30.0 36.5 40.5 46.6 48.3 46.1 48.4 47.2 32.1
3.6 5.7 8.4 3.0 4.8 8.4 4.8 5.4 5.7 19.5 20.1 12.6 31.5 24.6 14.1 6.7
28 21 19 19 17 21 26 18 15 48 43 26 68 51 30 21
a
C-BT and T-BT denote cubic BaTiO3 and tetragonal BaTiO3, respectively. b The average particle size and standard deviation were evaluated by TEM measurement of around 200 samples. c This experiment was performed at a flow rate (total flow rate 75 g/min) higher than that of other experiments.
Figure 2. Time variation of the Ti conversion at various reaction temperatures.
atomic ratio (Ti/Ba) of products by SEM-EDS and then calculated the Ti conversion as
X)
BaTiO3 (mol) initial TiO3 (mol)
)
Ba atom (%) Ti atom (%)
(3)
From the definition of the TiO2 conversion, X denotes the composition of BaTiO3 in the case of a single phase for XRD (see Table 1) as well. 3. Results 3.1. Ti Conversion and Crystal Structure of Products. We investigated the effect of reaction temperature on hydrothermal reactions for BaTiO3 particle formation by measuring both Ti conversion and the crystal phase of products. Experimental conditions and results are summarized in Table 1. Figure 2 shows the time variation of Ti conversions at various reaction temperatures. At 300 °C, Ti conversion was 54% at 0.3 s of reaction time and then achieved 95% at 38 s. With an increase in temperature, the reaction rate increased and the Ti conversion at 400 and 420 °C reached nearly 100% at 2 s. The hydrothermal reaction of BaTiO3 formation under supercritical conditions proceeded rapidly compared with the conventional hydrothermal synthesis method. Parts a and b of Figure 3 give XRD profiles of products obtained at 300 and 400 °C, respectively. At 300 °C,
Figure 3. XRD profiles of products obtained at temperatures of (a, left) 300 °C and (b, right) 400 °C.
there were both several peaks assigned to the residual TiO2 and peaks of BaTiO3 on the XRD profile of the product obtained at a reaction time of 0.3 s. With an increase in reaction time, the peaks of TiO2 disappeared and then only peaks of BaTiO3 remained in the XRD pattern of the product obtained at 38 s. The intensity of peaks of BaTiO3 increased with an increase in reaction time. This means that the growth of BaTiO3 crystals advanced with the passage of time. We evaluated the crystal phase of BaTiO3 by means of XRD peakbroadening analysis. The fwhm values of the two selected peaks of products obtained at 0.3 s were fwhm111 ) 0.628° and fwhm200 ) 0.610°, respectively. The product obtained at 0.3 s was regarded as cubic BaTiO3, because both fwhms have nearly the same value. On the other hand, the fwhm values of the product obtained at 38 s of reaction time were 0.338 and 0.410°, respectively. Since fwhm200 was greater than fwhm111, the product was decided to be tetragonal BaTiO3. The Ba/Ti ratio of the product at 300 °C and 38 s was 0.94, nearly equal to 1 for a stoichiometric ratio of BaTiO3. At 400 °C, there was no peak assigned to the residual TiO2, even in the product obtained at 2.4 s. The Ti conversion exceeded 90% at 2.0 s of reaction time and reached 100% at 18 s. Since the peak intensity of particle sobtained at 400 °C was strong as compared with that for the particles obtained at 300 °C, the product at 400 °C had a high crystallinity. For the crystal phase of BaTiO3 obtained at 400 °C, the fwhm111
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Figure 4. TEM micrographs of BaTiO3 particles obtained at 300 °C and 30 MPa for reaction times of (a) 0.38 s, (b) 5.11 s, and (c) 38.2 s. Parts d-f show particle size distributions corresponding to a-c, respectively.
and fwhm200 values were 0.487 and 0.557°, respectively. Since fwhm200 was larger than fwhm111, the product was tetragonal BaTiO3. The Ba/Ti ratio of the product at 400 °C and 18 s was 1.05, which was nearly equal to 1, the same as that at 300 °C. With regard to the temperature dependence of the crystal phase of BaTiO3, in the range from 300 to 380 °C, the metastable cubic phase formed at an early stage of reaction and then transformed to the tetragonal phase with an increase in reaction time. On the other hand, at 400 °C, tetragonal BaTiO3 formed even in the early stages of reaction. The relationship between crystal phase and particle size for BaTiO3 is not clear. In most cases, the relationship between crystal phase and size depends strongly on the synthetic method or conditions. For example, Asiaie et al. reported that BaTiO3 particles with diameter of 200 nm or above revealed some tetragonality, for BaTiO3 particles synthesized hydrothermally at 240 °C from barium chloride and titanium tetraisopropoxide under basic conditions.19 We conclude that the BaTiO3 particles obtained by hydrothermal synthesis at higher temperature have some tetragonality in the case of an average particle size of 40 nm or more. One reason for the achievement of producing BaTiO3 particles at a high efficiency is thought to be the performance at higher temperature. In addition, it is important to use TiO2 sols of nano size. For the hydrothermal synthesis of BaTiO3, two reaction mechanisms were reported; one is a dissolution-recrystallization mechanism15 and the other is in situ crystallization.16 The rate-determining processes of these mechanisms are thought to be the TiO2 dissolution process and barium ion diffusion process to TiO2 particles, respectively. When it is assumed that BaTiO3 formation
proceeds by the dissolution-recrystallization mechanism, the reaction rate will increase due to the enhancement of surface area by using nano-sized TiO2 sols. On the other hand, in the case of the in situ crystallization, the diffusion distance of barium ions in the nano-sized TiO2 sols became extremely short. Accordingly, by using nano-sized TiO2 sols, the hydrothermal reaction of TiO2 to give BaTiO3 by either dissolution-crystallization or in situ crystallization can proceed without controlling the reaction process. In this way, the continuous and effective production of BaTiO3 particles was achieved by the flow reaction system, in which the reaction was complete in 38 s of reaction time even at 300 °C. 3.2. Size and Distribution of BaTiO3 Particles. The particle size and distribution of BaTiO3 particles obtained at various reaction temperatures were evaluated by TEM measurements. Parts a-f of Figure 4 show TEM micrographs of BaTiO3 particles obtained at 300 °C and their size distribution. The products obtained at 0.1 s of reaction time were spherical particles 10-20 nm in diameter. With an increase in reaction time, the particle size became large and the shapes of particles transformed from spherical to cubic-like. The particle size distribution was unimodal. As described in Table 1, a ratio of standard deviation to mean particle size, S/M ratio, was around 20% at all reaction times at 300 °C. The shape of the particle size distribution almost did not change with time evolution. Similar trends in the changes of BaTiO3 particle size and their distribution were observed at 350 and 380 °C, as well. In the case of comparing the average particle size at the time which Ti conversion reached around 100%, the average particle size decreased with an increase in the reaction temperature. These results mean that the BaTiO3
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Figure 5. TEM micrographs of BaTiO3 particles obtained at 400 °C and 30 MPa for reaction times of (a) 0.18 s, (b) 2.40 s, and (c) 18.0 s. Parts d-f show particle size distributions corresponding to a-c, respectively.
particle size can be controlled by varying the reaction temperature. Next, TEM micrographs of BaTiO3 particles obtained at 400 °C for various reaction times and their size distributions are shown in Figure 5. At 0.1 s of reaction time, there are large particles 40-120 nm in diameter (Figure 5a). Small particles around 10 nm in diameter were also observed. According to XRD analysis, these particulates were assigned to be BaTiO3. With time evolution, smaller particles disappeared and then larger particles of around 50 nm were only observed in the product obtained at a reaction time of 18 s. The particle size distribution of the product obtained at a reaction time of 0.1 s was wider than that of the product at 300 °C, and the S/M ratio reached 48%. As shown in Figure 5a, the particle size distribution was bimodal, with two peaks at 10 and 50 nm. With an increase in reaction time, a broad peak at the smaller size disappeared and then the particle size distribution changed to unimodal at 18 s, where the unimodal peak was located at around 50 nm. It is expected that the smaller BaTiO3 particles can be obtained under supercritical conditions compared to those obtained under subcritical conditions; however, the average particle size of BaTiO3 obtained under supercritical conditions was as nearly the same as that of BaTiO3 particles obtained under subcritical conditions. 4. Discussion From the results, we can determine BaTiO3 particle formation and growth mechanism in hydrothermal reactions under sub- and supercritical conditions. The particle size and the S/M ratio to Ti conversion for every reaction temperature are plotted in Figure 6. As shown in Figure 6a, at all reaction temperatures, the size of the BaTiO3 particle became greater with an increase
Figure 6. (a) Ti conversion versus average particle size of BaTiO3 particles obtained at various reaction temperatures. (b) Ti conversion versus S/M ratio.
in the Ti conversion. These positive curves mean that particles grow by an inclusion of the monomers which were produced by the hydrothermal reaction. On the other hand, the S/M ratios also became small with thane increase in the Ti conversion, as shown in Figure 6b. This means that the particle growth advanced by not only the inclusion of the monomers but also dissolutionrecrystallization: i.e., Ostwald ripening. From these results, the mechanism of the BaTiO3 particle growth at high temperature was nucleation and crystal growth mechanism with Ostwald ripening, which is similar to the conventional hydrothermal synthesis at low temperature. The relationship between the particle size and reaction temperature can be classified into two groups, (LT region) 300-380 °C and (HT region) 400-420 °C, bordering on 400 °C, as shown in the figures. On the basis of conventional nucleation theory, the particle size is in inverse proportion to the number of nuclei produced. Since the reaction rate becomes large with an increase in reaction temperature, a greater degree of
Ind. Eng. Chem. Res., Vol. 44, No. 4, 2005 845 Table 2. Temperatures of Streams around the Mixing Point Treact
TSCW
Tsol
∆T
300 350 380 400 420
370 ( 3 410 ( 3 420 ( 4 470 ( 5 600 ( 5
25 25 25 25 25
345 385 395 445 575
supersaturation will be achieved at higher temperature and thus a great amount of nuclei will form, assuming that the temperature dependence of the solubility is very small. Therefore, it is expected that smaller particles are obtained at higher temperature. In the LT region, the average particle size became small with an increase in the reaction temperature. The reaction rate in the HT region was higher than that in the LT region, however; the average particle size in the HT region was larger than that in the LT region. Furthermore, in the HT region, some irregularly large particles around 150 nm in diameter were obtained with smaller particles 20 nm in diameter. In particular, the particle size distribution did not have a unimodal shape but a bimodal one. Why did the particle size distribution of BaTiO3 obtained at 400 °C or higher become bimodal? The reason is thought to be that undesired particle formation took place upstream of the mixing point, due to a heat transfer through the wall. As shown in Table 2, the heating of the starting metal salt solutions was accomplished by mixing with the preheated supercritical water (Tscw), whose temperature was much higher than the reaction temperature (Treact). Since the heat capacity of water decreased drastically over the critical temperature, the temperature of the supercritical water for heating the metal salt solution should be high in this case. The heat transfer from the preheated supercritical water to the metal salt solution through the wall was assumed to be in proportion to the temperature difference between TSCW and Tsol. In the case of the reaction temperatures of 400 and 420 °C, ∆T was high at 450 and 570 °C, respectively. Due to the heat transfer through the wall, the starting metal salt solution was heated and then hydrothermal reaction occurred upstream of the mixing point, MP2. Downstream of the mixing point, both particle growth of the preformed particles and new particle formation advanced simultaneously. Consequently, the particle size distribution became bimodal. Therefore, we conducted another experiment to confirm the effect of heat transfer through the wall on the particle formation. The flow rates of both metal salt solution and supercritical water were increased to 20 and 55 g/min, respectively. We expected that the influence of heat transfer through the wall could be prevented by increasing the flow rate of metal salt solution. The reaction temperature and pressure were set to be 400 °C and 30 MPa, respectively, and the reaction time was set to be 2.0 s. According to XRD and SEM-EDS, the product was tetragonal BaTiO3 and the Ti conversion reached 95%. Parts a and b of Figure 7 show the TEM micrograph and the particle size of BaTiO3 particles obtained at a high flow rate of 75 g/min. The average particle size decreased to 32 nm, and the particle size distribution became unimodal in comparison with the flow rate of 15 g/min. From these results, even at 400 °C BaTiO3 particles with smaller particle size and unimodal distribution could be produced by
Figure 7. (a) TEM micrograph of BaTiO3 particles obtained at high flow rate of 75 g/min. (b) Particle size distribution corresponding to part a.
Figure 8. Relationship between the average particle size of BaTiO3 particles and the reaction temperature.
optimizing the mixing conditions, since a stream with high velocity could prevent heat transfer to the starting solution through the wall. Figure 8 shows the relationship between reaction temperature and the average size of BaTiO3 particles obtained at each temperature, where Ti conversion reached at least 90%. As shown in the figure, continuous production of BaTiO3 particles was established, in which the size was controlled from 30 to 50 nm by changing the reaction temperature and the flow rate. 5. Conclusion Continuous production of BaTiO3 fine particles by hydrothermal synthesis was performed by a developed flow reaction system. The effect of reaction temperature on the Ti conversion and the average particle size and size distribution of BaTiO3 were evaluated. Under subcritical conditions at 300-380 °C, the Ti conversion reached 90% at a reaction time of 30-38 s. The BaTiO3 particles grew as Ti conversion increased, where particles might grow by monomer inclusions and Ostwald ripening. The average particle size of BaTiO3 decreased from 44 to 36 nm with an increase in the reaction temperature. Under supercritical conditions at 400 and 420 °C, Ti conversion reached around 100% for several seconds of reaction time and highly crystalline tetragonal BaTiO3 with 48 nm in diameter could be obtained; however, the particle size distribution was broad with 10-150 nm of bimodal particles, due to the undesired heat transfer around the mixing point. However, with an increase in the flow rate of supercritical water and metal salt solution, finer BaTiO3 particles 32 nm in diameter could be obtained even at 400 °C. The continuous and rapid production of BaTiO3 nanoparticles by hydrothermal synthesis in sub- and supercritical water
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Received for review July 1, 2004 Revised manuscript received November 10, 2004 Accepted November 24, 2004 IE049424I
