Electrical and Dielectric Characterization of Bi 12 GeO 20 Prepared by Modified Pechini Method

Bismuth germanate (Bi12GeO20) ceramics were produced using modified Pechini route, and the synthesis parameters, crystalline phases, microstructure, and sintering conditions were investigated. Bi12GeO20 powders with submicrometric particle sizes were investigated for calcination temperatures from400 to 600C,with soaking times of 1 h and 5 h. Controlling the synthesis parameters, dense ceramics with two different grain sizes of 3.4 ± 0.5 μm and 5.7 ± 0.8 μm could be produced after sintering at 750C/1 h. The electric and dielectric properties of these ceramics were determined by impedance spectroscopy (IS). From the results, it was concluded that the dielectric permittivity measured at high frequencies is insensitive to the grain size, while the AC dark conductivity presents a noticeable dependency on this feature. This behaviour was discussed on the basis of a Maxwell-Wagner interfacial relaxation, whose intensity depends directly on the volume fraction of grain boundaries in the sample.


Introduction
Bismuth germanate (Bi 12 GeO 20 ) belongs to a class of materials known as sillenites with general formula Bi 12 MO 20 , where M represents a tetravalent ion or a combination of ions yielding average charge 4+ [1,2].Sillenites crystallize in the cubic system (space group I23) and usually present photorefractive and electrooptical properties [3][4][5] that make them useful as recording media, optical switching, and sensors, among others [6][7][8][9].For optical applications, transparency and crystalline coherence are required, so the devices employ single crystals.Nevertheless, for UV and high energy sensors, transparency is not a requirement since either the electrical conductivity or the dielectric permittivity can be used to monitor radiation doses.On the other hand, a good control of grain size and purity of the material can determine the sensitivity and good resolution of such devices.Some synthesis routes have been proposed to obtain Bi 12 GeO 20 single crystals and ceramics [10][11][12][13][14], but to our knowledge Pechini route has not been reported up to now for the production of Bi 12 GeO 20 or any other sillenites.Pechini process has emerged as a powerful method to obtain nanocrystalline powders in several compositions.This synthesis route allows the formation of a polymeric net (resin) containing the metallic ions homogeneously distributed.The resin formation occurs in three steps: metallic chelate formation, ester formation, and polyesterification [14][15][16].The original Pechini method mixes metallic citrates first and then adds polyhydroxy alcohols [14].The main advantage of this method is the good control of the stoichiometry, high purity, easy dopant incorporation, and formation of nanometric or submicrometric particles with controlled particle size.
In a previous paper, the mechanisms of dark conductivity and dielectric relaxation of Bi 12 GeO 20 ceramics produced by solid state reaction were reported [9].It was observed that high resistivity of the grain interfaces leads to Maxwell-Wagner polarization of the grain boundaries due to local charge rearrangement [9].In this work impedance spectroscopy (IS) was utilized to determine the AC conductivity and dielectric permittivity of the bismuth germanate ceramics obtained by modified Pechini method, comparing the obtained parameters with those reported in the literature and investigating the influence of the grain size on these properties [9,[17][18][19][20].Additionally, the synthesis parameters

Experimental
Bi 12 GeO 20 powders were synthesized by the polymeric precursor method using bismuth oxide (Bi 2 O 3 ; VETEC, 3N) and germanium oxide (GeO 2 ; Alfa Aesar, 5N).Firstly, Ge and Bi solutions were prepared, respectively, by dissolving GeO 2 in distilled water at 90 ∘ C in a concentration of 0.005 g mL −1 [16] and Bi 2 O 3 in nitric acid (diluted with distilled water) in a concentration of 0.120 g mL −1 .These cationic solutions were separately mixed with citric acid (CA; VETEC, 3N) previously dissolved in distilled water (0.1 g mL −1 ) at a molar ratio of 1 : 3 (Cation : CA) [16].Ethylenediamine (ED; VETEC, 3N) was slowly added to adjust pH of bismuth citrate at 9.0, which is essential to the solution stability.To activate the polymerization reaction, each citrate solution was kept at 90 ∘ C and separately mixed with ethylene glycol (EG; C 2 H 6 O 2 ; VETEC, 3N), at the molar ratio of 6 : 4 (Cation : EG).After that, Ge solution was slowly added to Bi solution under stirring, keeping pH = 9.0.After the complete homogenization, this material was dried at 100 ∘ C for 24 h, resulting in a yellowish polymeric resin.
The dried resin was characterized by thermogravimetry (TG) and differential thermal analysis (DTA) using a simultaneous DTA/TG (SDT 2960; TA Instruments).In these analyses the samples were kept under synthetic air flow (120 mL min −1 ) and heated from 25 up to 1000 ∘ C with heating rate of 10 ∘ C min −1 .The results from DTA/TG have guided the calcination tests of this resin carried out in a muffle-type furnace, using different temperatures and soaking times, as it will be discussed in the next section.
After the calcination, the Bi 12 GeO 20 powder was milled again for 20 min, mixed to a binder solution of polyvinyl alcohol, conformed by uniaxial pressing under 15 MPa in disks 4 mm in diameter and 2 mm thick for sintering and 8 mm thick for dilatometric analyses.These dilatometric studies were performed in a NETZSCH-402PC dilatometer, with heating rate of 10 ∘ C/min and air flux of 120 mL/min.The results obtained from the dilatometric tests guided the sintering, which was performed in a muffle-type furnace.A batch of three samples was made at each sintering condition.
The relative density of the sintered ceramics was determined by the fluid displacement (Archimedes) method, using distilled water [21,22].The crystalline phases of the powder and sintered ceramics were inspected by X-ray diffraction (XRD; Rigaku RINT 2000/PC), in continuous scanning mode using Cu K  radiation, in the 2 range between 10 ∘ and 80 ∘ .The particle size of the calcined powders was obtained from the analysis of 5 SEM images (JEOL 6510LV and PHILIPS XL 30 FEG).The average grain size of the sintered ceramics was determined from the analysis of at least 3 SEM images, using the linear intercept technique [23], in which the grain shape was assumed to be spherical.
For the impedance spectroscopy measurements, the opposite faces of the cylindrical samples were polished with silicon carbide, cleaned with acetone in ultrasonic bath for 15 minutes, and dried at 100 ∘ C. Electric contact was made by applying Pt paste on the parallel faces of the pellets and firing them at 700 ∘ C for 30 minutes.The measurements were performed in a two-electrode configuration cell, in the frequency range from 10 Hz to 30 kHz, using a Solartron Impedance/Gain-Phase Analyzer SL 1260.The applied potential was 2 V and all the measurements were taken isothermally, with a tolerance of 1% in temperature.

Results and Discussion
The thermal behavior of the polymeric resin is presented in Figure 1 The main thermal event in DTA curve is an exothermic peak observed between 420 and 480 ∘ C, accompanied by a mass loss of 32%.This event can be associated to combustion reactions, organic decomposition, and subsequent formation of crystalline phase.Three exothermic events with a total mass loss of ∼45% can be observed below 400 ∘ C and are possibly related to dehydration, oxidation reactions, and NO  elimination.These results suggest that Bi 12 GeO 20 crystallizes at temperatures near 450 ∘ C, which is 230 ∘ C below the lowest value reported in literature [9] for the production of this material.Figure 1(b) presents the DTA curves obtained after thermal treatment at 450 ∘ C and 750 ∘ C, respectively.According to the equilibrium phase diagram of the binary mixture Bi 2 O 3 /GeO 2 , Bi 12 GeO 20 is the most stable phase in the region with GeO 2 concentrations from 32 to 1 mol% [7,24].However, according to these authors, the metastable phase Bi 2 GeO 5 , as well as the Bi 2 O 3 component, can also be found between 437 and 792 ∘ C [24].As one can see in Figure 1(b), the powder calcined 450 ∘ C undergoes a thermal event at 755 ∘ C, while the sample treated at 750 ∘ C presents only an endothermic peak with onset at 910 ∘ C, which corresponds to the melting point of Bi 12 GeO 20 .To reach a deeper understanding of the reactions occurring during the synthesis, a systematic study of the calcined powders was carried out using XRD technique.Figure 2 presents XRD patterns of the powders calcined at different temperatures during 1 h or 5 h, as indicated in each curve.The presence of major phase Bi 12 GeO 20 can be observed for all the samples analysed.Minor phases -Bi 2 O 3 and Bi 2 GeO 5 were also observed for the samples calcined at  ≤ 600 ∘ C for 1 h or  ≤ 500 ∘ C for 5 h.Comparing these results with the DTA curves presented in Figure 1(b), it can be concluded that the endothermic event at 755 ∘ C is related to the reaction between -Bi 2 O 3 and Bi 2 GeO 5 to form Bi 12 GeO 20 .This reaction occurred at lower temperatures when longer soaking times were employed, so, for the samples calcined during 1 h or 5 h, single phase Bi 12 GeO 20 was obtained at 600 ∘ C or 550 ∘ C, respectively.
Figure 3 presents SEM images of the powders calcined for 1 h at 450 ∘ C and 600 ∘ C. As a general feature, it can be observed that the samples have well-dispersed submicrometric particles, with sizes of about 200 (±100) nm for the sample produced at 450 ∘ C and 500 (±100) nm when  = 600 ∘ C was used for the synthesis.It can also be noticed that some platelike structures are present in the sample produced at lower temperatures (see Figure 3(c)).These particles are possibly -Bi 2 O 3 , also detected by XRD measurements (see Figure 2).On the other hand, the samples produced at 600 ∘ C (see Figure 3(e)) presented only rounded particles, corresponding to the single phase Bi 12 GeO 20 observed in the XRD patterns.
Smaller particles can favour the packing process during the sintering of the ceramic bodies.Figure 4 presents the measured shrinkage and its derivative as a function of the sintering temperature for compacts prepared with the powders produced at 450 or 600 ∘ C. The maximum shrinkage rate was determined at 723 ∘ C and 756 ∘ C, respectively, for the samples synthesized at 450 ∘ C (Figure 4(a)) and 600 ∘ C (Figure 4(b)).Based on these values, the sintering tests were carried out at 750 ∘ C, with soaking time of 1 h.Hereafter, the sintered ceramics produced using the powders calcined at 450 ∘ C and 600 ∘ C will be called C450 and C600, respectively.
Figure 5 presents the XRD patterns of the samples C450 and C600, confirming that single phase Bi 12 GeO 20 was obtained for both the sintered ceramics.Figure 6 presents SEM images of these sintered samples, where the grains at the final stage of sintering can be observed.The density of the sintered samples was the same (8.3 ± 0.1 g/cm 3 ) for both samples, but a noticeable difference between the average grain sizes was registered.The sample C450 presented average grain size 3.4 ± 0.5 m, while the value 5.7 ± 0.8 m was determined for the sample C600.It is well known that the average size, as well as the properties of the material, may depend on  the preparation method and synthesis conditions [25][26][27].Impedance spectroscopy (IS) was employed to determine the AC conductivity and dielectric permittivity of the Bi 12 GeO 20 ceramics, in order to investigate the influence of the grain size on these properties.
The AC conductivity is the real part of the complex admittance and can be obtained from the impedance data using (1).In this equation,  and  are the thickness of the sample and the area of the electrodes, respectively: Figure 7 presents the AC dark conductivity as function of the frequency for samples C450 and C600.It can be observed that both curves present the same profile, but the sample C450 has higher conductivity.The conductivity measured at 250 ∘ C and low frequencies were about 5 × 10 −9 S/cm for sample C450 and 4 × 10 −10 S/cm for sample C600.These values are comparable with some values reported in [9,17,18], although the experimental conditions were not exactly the same.The higher conductivity was observed for the ceramic with smaller grains.Considering that the internal conductivity of each grain would be the same for both samples, since they were sintered at the same conditions, the higher conductivity of sample C450 can be attributed to local charge transport in the grain boundaries.In fact, it was already reported that space charge rearrangement occurs at the intergrain region of Bi 12 GeO 20 ceramics [9], resulting in Maxwell-Wagner polarization of the grain boundaries.To check this possibility, the dielectric permittivity of the samples was analyzed.
The dielectric permittivity of a material is calculated from the impedance data, using where  0 is the empty cell capacitance and  is the angular frequency  = 2.Corrections for the ceramic porosity were made using Maxwell's model [28,29].This model considers that, in a ceramic with porosity , the pores are spheres with    = 1 embedded in the ceramic matrix with permittivity    .As a result, the relation between the experimental   and the corrected    is given by ) . (3) Figure 8 presents the dielectric permittivity obtained for the ceramic matrix (   ) using (3) for both samples studied.At low frequencies, the values are strongly dependent on the grain size, with values of 10 3 and 2 × 10 2 measured at 10 Hz for the samples C450 and C600, respectively.Furthermore, sample C450 presents a dielectric profile with a slight shoulder between 10 2 and 10 3 Hz, indicating interfacial polarization of the grain boundaries [9].The low frequency dielectric response of ceramics is attributed to grain boundaries [30] and the dispersion of the permittivity values is explained by the movement of charge carriers [31].In this case, this movement occurs probably in the space charge region at the grain boundaries [32].At higher frequencies ( = 30 kHz), the values presented in Figure 8 are    = 47 for sample C450 and    = 44 for sample C600.These values are in good agreement with [9,17], which have reported   = 38 ( = 5.5 GHz,  = 250 ∘ C) and   = 45 ( = 30 kHz,  = 250 ∘ C) for Bi 12 GeO 20 ceramics produced via solid state route, although no porosity corrections were made in those references.For single crystals, the values reported in literature are   = 44 at  = 1 kHz and  = 25 ∘ C [19,20], which also agree with the values determined in the present work.The low sensitivity of    to the grain size, when measured at high frequencies, was previously mentioned in [28] and indicates that the polarization processes do not depend on the volume fraction of grains and grain boundaries in the sample.

Conclusions
Single phase Bi 12 GeO 20 was successfully produced by the modified Pechini method, with calcinations at 600 ∘ C/1 h or at 550 ∘ C/5 h.For the samples calcined at 450 ∘ C/1 h, single phase was obtained after sintering the ceramic bodies.These fabrication conditions are advantageous if compared to the synthesis parameters used for solid state route, which were 850 ∘ C in [17] and 680 ∘ C/5 h according to [9].The use of low temperatures allowed the control of the final grain size of the sintered ceramics.Electrical and dielectric characterizations of ceramics with grain sizes of 3.4 ± 0.5 m and 5.7 ± 0.8 m were analysed.From the results, it can be concluded that these values are comparable to those ones previously reported for ceramics and single crystals, validating the synthesis method.Additionally, it was observed that the dielectric permittivity measured at high frequencies is insensitive to the grain size, while the AC conductivity presents a noticeable dependency    on the grain size, probably due to the displacement of charge carriers in the space charge regions.

Figure 7 :FrequencyFigure 8 :
Figure 7: Dark conductivity as function of the frequency of the ceramics sintered at 750 ∘ C/1 h, using the powders calcined at (a) 450 ∘ C/1 h and (b) 600 ∘ C/1 h.
(a)and was investigated in order to identify the best calcination temperature to produce Bi 12 GeO 20 .
Figure 2: X-ray diffraction patterns of the Bi 12 GeO 20 powders calcined at temperatures from 400 to 600 ∘ C with calcination times of 1 h or 5 h.