**3.1 Fabrication of BSTx powders**

The high energy milling process significantly affects the size and shape of the starting powders, as seen in the SEM micrographs of Figure 3. Figure 4 shows the TEM micrographs of the starting powders after milling for 6 h. A final particle size of less than 50 nm was attained for both extreme concentrations (only BaCO3 and TiO2, and only SrCO3 and TiO2).

Fig. 3. SEM image of starting powders (a) milled for 6 hours, and (b) before milling.

Fig. 4. TEM micrographs of (1-X)BaCO3 + XSrCO3+ TiO2 powder milled for 6 hours, with (a) X = 0.0 and (b) X = 1.0.

conventional attrition, planetarium or automatic-agate milling. The milled powders were compacted using much higher pressure (~1.0 GPa) than applied using the conventional approach (~0.1 GPa). This resulted in uniform green compacts which can conduct an homogeneous chemical reaction. Finally, the thermal treatment induces simultaneous reaction and sintering (reaction-sintering, Figure 1) as opposed to the conventional manufacturing process where the starting powders are milled, thermally-treated to react, a second milling process is performed, and then the twice-milled powders are pressed into

The high energy milling process significantly affects the size and shape of the starting powders, as seen in the SEM micrographs of Figure 3. Figure 4 shows the TEM micrographs of the starting powders after milling for 6 h. A final particle size of less than 50 nm was attained for both extreme concentrations (only BaCO3 and TiO2, and only

compacts. Finally, a second thermal treatment (sintering) densifies the compacts.

Fig. 3. SEM image of starting powders (a) milled for 6 hours, and (b) before milling.

Fig. 4. TEM micrographs of (1-X)BaCO3 + XSrCO3+ TiO2 powder milled for 6 hours, with

**a) b)** 

**a) b)** 

**3. Results and discussion** 

SrCO3 and TiO2).

(a) X = 0.0 and (b) X = 1.0.

**3.1 Fabrication of BSTx powders** 

The x-ray diffraction patterns for the milled BaCO3, TiO2 and SrCO3 powder mixtures are presented in Figure 5. The main BaCO3 peak, located at approximately 2θ = 28° is present up to X = 0.9, and the small peak at approximately 30º belongs to TiO2. As expected, increasing the SrCO3 content increases the height of the SrCO3 peak located at approximately 30º. There is a degree of amorphization due to the creation of defects in the crystal structure. Figure 6 presents the thermogravimetric analyses (TGA) curves for the same collection of samples as analyzed by x-ray diffraction (Figure 5). All the curves are similar in their key characteristics. The weight loss behavior for a single sample, with X = 0.65, is shown in Figure 8. There are four stages of weight loss centered at 403, 773, 973 and 1273 K. In the first stage, from room temperature (RT) up to 403 K, a weight reduction of approximately 1.3% occurs due to evaporation of water from the material surface. In the second stage, from 403 to 773 K, the weight loss of about 5.2% is related to the loss of chemically bound water in the form of OH groups from the BaOH that was formed when BaO combined with water during milling [BALÁZ]. This loss typically occurs between 473 and 873 K [ASIAIE]. The phenomenon of water loss has also been reported to occur in other carbonates between 593 and 723 K [DING]. The third stage, between 773 and 973 K, is not related to any structural modification of the BSTx samples. According to the literature, the decomposition of strontium and barium carbonates to form CO2 occurs at higher temperatures, between 1023 and 1273 K [JUDD, L'VOV, MAITRA]. However, in this case, the generation of CO2 begins as early as at 833 K and runs up to 1273 K. The x-ray difffraction patterns of Figure 7 show the appearance of a peak (2θ ≈ 36°) at 873 K, which corresponds to the formation of the perovskite structure of BaTiO3/SrTiO3. Therefore, the weight loss from 773 to 1323 K can be considered a single stage that varies with Sr content. It is directly related to the CO2 excess from the carbonates used as starting powders (see Equation 1). It is the difference between the weight of the (1-X)BaCO3 + XSrCO3 + TiO2 starting powders and that of the resulting Ba(1-X)SrXTiO3. Table 1 lists the total weight loss, the loss in the different stages, and the weight loss expected from CO2 liberation. For the group of samples as a whole, an approximate 5% weight loss was observed between RT and 773 K, and the weight loss from 773 to 1323 K corresponds closely to the stoichiometric CO2 loss.

Fig. 5. X-ray diffraction patterns for (1-X)BaCO3 + XSrCO3 + TiO2 milled powders.

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 443

The thermogravimetric plots also show a correlation between the Sr content and the temperature at final weight loss (zero slope section). For example, the BST0 sample stops losing weight at around 1193 K but the BST10 (with highest Sr content) at around 1273 K. The temperature at which no more weight loss is observed marks the end of the reaction, as corroborated by the XRD measurements (Figure 7). The thermogravimetric curves can

therefore be used as guides to establish the reaction temperature in the BSTx system.

**% Weight loss from RT to 773 K** 

BST0 20.43 5.56 14.87 15.87 BST1 19.38 4.12 15.26 16.16 BST2 21.02 5.48 15.54 16.47 BST3 21.59 5.61 15.98 16.78 BST4 21.52 5.94 15.58 17.10 BST5 21.39 5.80 15.59 17.44 BST6 21.76 4.85 16.91 17.79 BST7 22.48 5.19 17.29 18.15 BST8 24.29 5.76 18.53 18.53 BST9 23.46 5.42 18.04 18.93 BST10 22.87 4.52 18.35 19.34 Table 1. Thermogravimetric analysis of (1-X)BaCO3 + XSrCO3 + TiO2 powder after high

**30 40 50 60 70 80 90**

**X = 0.0**

**X = 1.0**

**2**θ

Fig. 9. X-ray diffraction patterns of (1-X)BaCO3 + XSrCO3 + TiO2 powder milled and heat

The diffraction patterns for the range of samples after milling and thermal treatment at 1273 K for 1 hour are shown in Figure 9. All the samples present the perovskite-type structure ABO3, indicating the reaction was successfully completed. The formation temperature of the BaTiO3 phase coincides with that reported by L. B. Kong [KONG], where the rutile phase of titanium oxide (TiO2) was used instead of TiO2 anatase phase. The peaks shift to higher angle as the Sr content increases. For example, the most intense BaTiO3 peak in Figure 10

treated at 1273 K for 1 h. The crystal structure is perovskite-type ABO3.

**Powders (1-X)BaCO3 + XSrCO3 + TiO2**

**milling for 6h and heat treatment**

**at 1273 K / 1h**

**% Weight loss from 773 to 1323 K** 

**% Weight loss CO2 stoichiometric** 

**Sample ID % Total** 

energy milling for 6 hours.

**Intensity (a. u.)**

**weight loss**

Fig. 6. Thermogravimetric curves of (1-X)BaCO3 + XSrCO3 + TiO2 milled powders.

Fig. 7. XRD patterns of 0.65BaCO3, 0.35SrCO3 and TiO2 powders milled for 6 hours and subsequently heat treated at different temperatures.

Fig. 8. Thermogravimetric analysis of 0.65BaCO3, 0.35SrCO3 and TiO2 powders milled for 6 hours.

**TGA**

**X = 0**

**1193**

**(220) (211) (210)**

 **+ 0.35SrCO3**

**1273 K 1173 K 1073 K 973 K 873 K**

 **+ TiO2**

**773 K**

**CO2**

**H2O**

**X = 1**

**200 400 600 800 1000 1200 1400**

**(111) (200)**

 **+ XSrCO3**

Fig. 6. Thermogravimetric curves of (1-X)BaCO3 + XSrCO3 + TiO2 milled powders.

**Temperature (K)**

**Milled powders 0.65BaCO3**

**30 40 50 60 70 80**

**6.5 %**

**15.76 % Milled powders** 

 **+ TiO2**

**2**θ

**200 400 600 800 1000 1200 1400**

Fig. 8. Thermogravimetric analysis of 0.65BaCO3, 0.35SrCO3 and TiO2 powders milled for 6

 **+ 0.35SrCO3**

**Temperature (K)**

Fig. 7. XRD patterns of 0.65BaCO3, 0.35SrCO3 and TiO2 powders milled for 6 hours and

**1.3 %**

 **+ TiO2**

**1273**

**Mass**

**Intensity (a. u.)**

subsequently heat treated at different temperatures.

**75**

hours.

**80**

**85**

**0.65BaCO3**

**90**

**Mass (%)**

**95**

**100**

**(100)**

**(1-X)BaCO3**

**milled powders**

**(110)**

The thermogravimetric plots also show a correlation between the Sr content and the temperature at final weight loss (zero slope section). For example, the BST0 sample stops losing weight at around 1193 K but the BST10 (with highest Sr content) at around 1273 K. The temperature at which no more weight loss is observed marks the end of the reaction, as corroborated by the XRD measurements (Figure 7). The thermogravimetric curves can therefore be used as guides to establish the reaction temperature in the BSTx system.


Table 1. Thermogravimetric analysis of (1-X)BaCO3 + XSrCO3 + TiO2 powder after high energy milling for 6 hours.

Fig. 9. X-ray diffraction patterns of (1-X)BaCO3 + XSrCO3 + TiO2 powder milled and heat treated at 1273 K for 1 h. The crystal structure is perovskite-type ABO3.

The diffraction patterns for the range of samples after milling and thermal treatment at 1273 K for 1 hour are shown in Figure 9. All the samples present the perovskite-type structure ABO3, indicating the reaction was successfully completed. The formation temperature of the BaTiO3 phase coincides with that reported by L. B. Kong [KONG], where the rutile phase of titanium oxide (TiO2) was used instead of TiO2 anatase phase. The peaks shift to higher angle as the Sr content increases. For example, the most intense BaTiO3 peak in Figure 10

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 445

where *d* and *d0* are the initial and final grain diameters, respectively, *k* is a constant, and *t* is the processing time. Sintering temperatures for the conventional route of ceramic preparation are reported to be between 1623 and 1703 K [ZHONG, WODECKADUS, TERANISHI]. The x-ray diffraction patterns of the thermally treated BSTx ceramics (Figure 11) clearly show the perovskite-type structure. As in the case of the powders, the peaks shift to higher angle as the Sr content increases. From Figure 12 it can be seen that the strongest peak shifts linearly (~0.1º) for each 0.1 increase in X (Sr content), and thus can be used to determine the sample composition (stoichiometry). Figure 13 plots the peak position as a function of the Sr content. All the thermally treated BSTx ceramics have the correct stoichiometry and present the perovskite-type structure ABO3. However, the structure can be either tetragonal or cubic at room temperature depending on the processing conditions. For the BaTiO3 the relative position of the (002) and (200) peaks determine the tetragonality of the phase, i.e., the ratio of the lattice parameters c/a. Such peaks appear at approximately

**30 40 50 60 70 80 90 100**

**Ceramics of BSTx System Sintered at different temperatures**

**2**θ

**37.61**

Fig. 11. X-ray diffraction patterns of BSTx ceramics system sintered from 1523 to 1573 K for 2h.

**37.23**

**37.41**

**36.5 37.0 37.5 38.0**

Fig. 12. Main XRD peaks of BSTx ceramic system sintered from 1523 to 1573 K of the figure 11.

**2**θ

2θ = 53°.

**Intensity (a. u.)**

**Intensity (a. u.)**

**36.81**

**BaTiO3**

**BSTx Ceramics sintered from 1523 to 1573 K** 

**37.02**

( )1/2 1/2 d d 2k t − = 0 (2)

**X = 0.9 X = 0.7 X = 0.6**

**X = 1.0**

**X = 0.8**

**X = 0.0 X = 0.1**

**SrTiO3**

**37.81**

**X = 0.2 X = 0.3 X = 0.4 X = 0.5**

shifts from 36.79° for the BaTiO3 (BST0) to 37.77° for SrTiO3 (BST10). This shift corresponds to a reduction in unit cell size, consistent with the difference between the ionic radii of Ba2+ (1.34 Å) and Sr2+ (1.12 Å). The ABO3 perovskite structure refers to the relative position of the Ba2+, Sr2+ and Ti4+ ions with respect to oxygen (O2-). The structure can present as different phases, depending on the material and temperature. For the BSTx system it may be cubic or tetragonal at room temperature, depending on the strontium content. In this case, we observed the cubic phase after 1 hour of heat treatment at 1273 K (Figure 9). The relationship between the cubic and tetragonal phase and the volume of the unit cell will be discussed in more detail when disucssing compaction.

Fig. 10. Expanded view of the primary peak in Figure 9, showing the shift in peak position with increasing Sr content from X = 0 (BaTiO3) to X = 1 (SrTiO3).

#### **3.2 Sintering**

During conventional manufacture (solid-state reaction) the starting oxide powders are first milled and calcined. The reacted powders (having the desired stoichiometry) are milled once again to reduce the particle size. They are then compacted into disks or other shapes (green ceramic) and finally, thermally treated to sinter the compact. At the sintering temperature, the ceramic particles coalesce with each other to form grains, the material shrinks and the pores are eliminated [KINGERY]. The alternative manufacturing route of the present work is more straightforward. The starting powders are milled only once to homogeneize and reduce the particle size before being compacted into disks or other shapes. The green ceramics are thermally treated at the reaction temperature (1273 K) to obtain the perovskite-type structure ABO3. A second heating step is subsequently applied to sinter the ceramic (Figure 1). In this way, dense ceramics (>90% of the theoretical density) are obtained. The sintering temperatures of the samples with intermediate stoichiometry varied between 1523 K for pure BaTiO3 and 1573 K for pure SrTiO3. The temperatures were empirically determined. Such reduced sintering temperatures can only be applied to powders with particle size smaller than 50 nm, which is uniquely attained in our alternative route, thanks to the high energy milling. Whenever the BaTiO3 samples were sintered at temperatures higher than 1523 K, severe strain was observed as the melting temperature of the material (1898 K [PRADEEP]) was approached. Ceramic shrinkage, or pore reduction, is directly related to the initial particle size, as shown in Equation 2 [KINGERY]:

shifts from 36.79° for the BaTiO3 (BST0) to 37.77° for SrTiO3 (BST10). This shift corresponds to a reduction in unit cell size, consistent with the difference between the ionic radii of Ba2+ (1.34 Å) and Sr2+ (1.12 Å). The ABO3 perovskite structure refers to the relative position of the Ba2+, Sr2+ and Ti4+ ions with respect to oxygen (O2-). The structure can present as different phases, depending on the material and temperature. For the BSTx system it may be cubic or tetragonal at room temperature, depending on the strontium content. In this case, we observed the cubic phase after 1 hour of heat treatment at 1273 K (Figure 9). The relationship between the cubic and tetragonal phase and the volume of the unit cell will be discussed in

**36.5 37.0 37.5 38.0**

Fig. 10. Expanded view of the primary peak in Figure 9, showing the shift in peak position

During conventional manufacture (solid-state reaction) the starting oxide powders are first milled and calcined. The reacted powders (having the desired stoichiometry) are milled once again to reduce the particle size. They are then compacted into disks or other shapes (green ceramic) and finally, thermally treated to sinter the compact. At the sintering temperature, the ceramic particles coalesce with each other to form grains, the material shrinks and the pores are eliminated [KINGERY]. The alternative manufacturing route of the present work is more straightforward. The starting powders are milled only once to homogeneize and reduce the particle size before being compacted into disks or other shapes. The green ceramics are thermally treated at the reaction temperature (1273 K) to obtain the perovskite-type structure ABO3. A second heating step is subsequently applied to sinter the ceramic (Figure 1). In this way, dense ceramics (>90% of the theoretical density) are obtained. The sintering temperatures of the samples with intermediate stoichiometry varied between 1523 K for pure BaTiO3 and 1573 K for pure SrTiO3. The temperatures were empirically determined. Such reduced sintering temperatures can only be applied to powders with particle size smaller than 50 nm, which is uniquely attained in our alternative route, thanks to the high energy milling. Whenever the BaTiO3 samples were sintered at temperatures higher than 1523 K, severe strain was observed as the melting temperature of the material (1898 K [PRADEEP]) was approached. Ceramic shrinkage, or pore reduction, is

directly related to the initial particle size, as shown in Equation 2 [KINGERY]:

**2**θ

**5 6 7 8 1 2 3**

**9 SrTiO3 <sup>4</sup>**

**37.77** 

more detail when disucssing compaction.

**3.2 Sintering** 

**Intensity (a. u.)**

**36.79**

with increasing Sr content from X = 0 (BaTiO3) to X = 1 (SrTiO3).

**BaTiO3**

$$\mathbf{d} - \mathbf{d}\_0 = \left(2\mathbf{k}\right)^{1/2} \mathbf{t}^{1/2} \tag{2}$$

where *d* and *d0* are the initial and final grain diameters, respectively, *k* is a constant, and *t* is the processing time. Sintering temperatures for the conventional route of ceramic preparation are reported to be between 1623 and 1703 K [ZHONG, WODECKADUS, TERANISHI]. The x-ray diffraction patterns of the thermally treated BSTx ceramics (Figure 11) clearly show the perovskite-type structure. As in the case of the powders, the peaks shift to higher angle as the Sr content increases. From Figure 12 it can be seen that the strongest peak shifts linearly (~0.1º) for each 0.1 increase in X (Sr content), and thus can be used to determine the sample composition (stoichiometry). Figure 13 plots the peak position as a function of the Sr content. All the thermally treated BSTx ceramics have the correct stoichiometry and present the perovskite-type structure ABO3. However, the structure can be either tetragonal or cubic at room temperature depending on the processing conditions. For the BaTiO3 the relative position of the (002) and (200) peaks determine the tetragonality of the phase, i.e., the ratio of the lattice parameters c/a. Such peaks appear at approximately 2θ = 53°.

Fig. 11. X-ray diffraction patterns of BSTx ceramics system sintered from 1523 to 1573 K for 2h.

Fig. 12. Main XRD peaks of BSTx ceramic system sintered from 1523 to 1573 K of the figure 11.

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 447

52.694 704 0.485 a = 3.9953

53.227 1265 0.543 c = 4.0311

52.942 388 0.520 a = 3.9844

53.368 1190 0.487 c = 4.0114

53.124 490 0.446 a = 3.9785

53.459 1185 0.477 c = 3.9979

53.611 1764 0.360 c = 3.9737 **BST4** 53.725 10 0.146 a = 3.9611 1

Table 2. Unit cell parameters and fitting parameters of peaks around 53° in 2θ.

**BSTX Ceramic System** 

**3.90 3.92 3.94 3.96 3.98 4.00 4.02 4.04**

Fig. 15. Lattice parameter as a function of Sr content.

**0**

**20**

**40**

**60**

**Theoretical density (%)**

**80**

**100**

**Lattice parameter (**

Å**)**

**Peak width** 

53.457 1327 0.335 a = 3.9684 1.0014

**0 1 2 3 4 5 6 7 8 9 10**

**BSTx Ceramic, x**

**BSTX Ceramic System**

**0 10 20 30 40 50 60 70 80 90 100**

**% Sr in BSTX ceramic system**

Fig. 16. Percentage of theoretical density of sintered compacts as a function of Sr content.

**Lattice parameter of unit cell** 

 **Parameter c Parameter a** **Tetragonality c/a** 

1.0089

1.0067

1.0048

**Maximun intensity of the peak** 

**Ceramic Sample** 

**BST0** 

**BST1** 

**BST2** 

**BST3** 

**Position in 2θ**

Fig. 13. Main diffraction peak position (Figure 12) as a function of stoichiometric composition.

Fig. 14. Separation (or lack therof) of the (002) and (200) reflections of sintered ceramics BST0, BST1, BST2 and BST3 providing a measure of the c/a ration.

The phase is cubic and paralectric if the c/a ratio = 1. In such a case there is only a single peak near 2θ = 53°. If c/a > 1 the phase is tetragonal and ferroelectric. In such case there is a double peak. Figure 14 shows the BST0, BST1 and BST2 samples have a double peak, while sample BST3 apparently has only a single peak. Rietveld refinement (using Maud Program) was performed on the diffraction patterns of Figure 11 in order to determine the unit cell lattice parameters. The results, presented in Figure 15, show a gradual decrease in lattice parameters with increasing Sr content. This is due to the substitution of strontium Sr2+ ions (with ionic radius of 1.12 Å) for barium Ba2+ ions (with ionic radius of 1.34 Å). The tetragonality (c/a) decreases also from 1.008 (BST0) to 1.0014 (BST3) while for BST4 to BST10 it has value of 1. Differential scanning calorimetry (DSC), Raman spectroscopy, as well as the ferroelectric and dielectric measurements confirmed this phase transition, and are presented below, along with the cubic-to-tetragonal phase transition temperature (Curie temperature).

**BST4**

**BST2**

Fig. 13. Main diffraction peak position (Figure 12) as a function of stoichiometric

**BSTx Ceramics**

BST0, BST1, BST2 and BST3 providing a measure of the c/a ration.

**BST0 or BaTiO3**

**0 1 2 3 4 5 6 7 8 9 10**

**BSTx**

**52.0 52.5 53.0 53.5 54.0 54.5**

**2**θ

The phase is cubic and paralectric if the c/a ratio = 1. In such a case there is only a single peak near 2θ = 53°. If c/a > 1 the phase is tetragonal and ferroelectric. In such case there is a double peak. Figure 14 shows the BST0, BST1 and BST2 samples have a double peak, while sample BST3 apparently has only a single peak. Rietveld refinement (using Maud Program) was performed on the diffraction patterns of Figure 11 in order to determine the unit cell lattice parameters. The results, presented in Figure 15, show a gradual decrease in lattice parameters with increasing Sr content. This is due to the substitution of strontium Sr2+ ions (with ionic radius of 1.12 Å) for barium Ba2+ ions (with ionic radius of 1.34 Å). The tetragonality (c/a) decreases also from 1.008 (BST0) to 1.0014 (BST3) while for BST4 to BST10 it has value of 1. Differential scanning calorimetry (DSC), Raman spectroscopy, as well as the ferroelectric and dielectric measurements confirmed this phase transition, and are presented below, along with the cubic-to-tetragonal phase transition temperature (Curie

**(0 0 2) (2 0 0)**

Fig. 14. Separation (or lack therof) of the (002) and (200) reflections of sintered ceramics

**BST3 BST2**

**BST1**

**BST0**

**BST6**

**BST10 or SrTiO3**

**BST8**

**36.8**

**37.0**

**37.2**

**Main peak in 2**θ

**Intensity (a. u.)**

composition.

temperature).

**37.4**

**37.6**

**37.8**


Table 2. Unit cell parameters and fitting parameters of peaks around 53° in 2θ.

Fig. 15. Lattice parameter as a function of Sr content.

Fig. 16. Percentage of theoretical density of sintered compacts as a function of Sr content.

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 449

respectively. Generally speaking, the conventional route for fabrication of mixed oxide ceramics leads to grains larger than 1 μm, in most cases on the order of several microns [LIN, LIOU, LU]. Smaller grains are only attained with nanopowders and special sintering processes such as spark plasma sintering (SPS) [DENG] or hot pressing [XIAO]. Other methods for inhibiting grain growth include the incorporation of 1 wt% of Na, Mn or Mg

**a a' b b'**

**c c' d d'**

sintered at 1573 K, (d) BST10 sintered at 1573 K.

fitting the experimental data (Figure 20):

**3.4 Curie temperature (Tc) via differential scanning calorimetry** 

Fig. 17. SEM micrographs of transversely fractured BST0, BST4, BST8 and BST10 samples at two magnifications: (a) BST0 sintered at 1523 K, (b) BST4 sintered at 1543 K, (c) BST8

DSC measurements were conducted from 203 to 423 K in a nitrogen atmosphere with a heating rate of 20°C/min. Figure 19 presents the DSC curves for samples BST0 to BST3. The cubic to tetragonal phase transition (Curie temperature, Tc) is an endothermic event. Tc decreases with increasing content of Sr in the samples, i.e., as the Sr2+ ions replace Ba2+ ions.

The linear dependence between the Tc and at.% Sr is described by Equation 4, the result of

Tc 128.4871 31.469\*X = − (4)

This behavior was previously reported by Rupprecht and Bell [RUPPRECHET].

ions [LIOU].

#### **3.3 Density**

With the actual volume of the unit cell and considering the number of barium, strontium, titanium and oxygen atoms composing the ABO3 unit cell, the theoretical density can be calculated using:

$$\text{Theoretical Density} = \frac{\text{Unit cell mass}}{\text{Unit cell volume}} \tag{3}$$

The unit cell volume (a2 × c) was calculated using the results of the Rietveld analysis. The mass of the unit cell is calculated considering 3 oxygen, 1 titanium, (x) strontium and (1-x) barium atoms. The bulk density of the samples was determined by the Archimedes method. Figure 16 plots the bulk density as percentage of the theoretical density. All samples have bulk densities higher than 90% of theoretical, proving that the alternative fabrication route can attain a high densification of the ceramics. The density caluclation and measurment results are presented in Table 3.


Table 3. Theoretical and bulk (measured) Densities of BSTx ceramic system.

SEM micrographs of transversely fractured sections from the BST0, BST4, BST8 and BST10 samples are shown in Figure 17. The BST0 (BaTiO3) and BST10 (SrTiO3) ceramics have a uniform compact morphology, present no cracks and have low porosity. The grain boundaries are not observable. Samples BST0 and BST10 have a bulk density of 98.52% and 99.21% of the theoretical, respectively. Even with the lower-than-conventional sintering temperatures, it is possible that the observed morphology resulted from liquid phase formation due to the small particle size [KINGERY, BARSOUM, BARRY]. Grain size distributions for BST0 and BST10 are shown in Figure 18. For the BST0 sample, grain sizes between 1 and 3.5 μm (2 μm average) were measured, while for the BST10 sample, sizes ranged ranged from 1 μm to 2.6 μm (1.4 μm average). The BST4 and BST8 samples, consisting of a barium-strontium solid solution (Ba,Sr)TiO3, have a distinctly smaller grain size, with distributions of 0.2 to 1.3 μm (650 nm average) and 0.3 to 0.9 μm (550 nm average),

With the actual volume of the unit cell and considering the number of barium, strontium, titanium and oxygen atoms composing the ABO3 unit cell, the theoretical density can be

The unit cell volume (a2 × c) was calculated using the results of the Rietveld analysis. The mass of the unit cell is calculated considering 3 oxygen, 1 titanium, (x) strontium and (1-x) barium atoms. The bulk density of the samples was determined by the Archimedes method. Figure 16 plots the bulk density as percentage of the theoretical density. All samples have bulk densities higher than 90% of theoretical, proving that the alternative fabrication route can attain a high densification of the ceramics. The density caluclation and measurment

> **Theoretical density (g m-3)**

**BST0** 64.349 6.016 5.928 98.526 **BST1** 63.684 5.950 5.630 94.632 **BST2** 63.283 5.857 5.486 93.661 **BST3** 62.675 5.782 5.430 93.910 **BST4** 62.152 5.698 5.513 96.758 **BST5** 61.839 5.593 5.246 93.798 **BST6** 61.377 5.501 5.191 94.364 **BST7** 60.905 5.408 5.191 95.986 **BST8** 60.393 5.317 4.883 91.838 **BST9** 59.934 5.220 4.755 91.080 **BST10** 59.514 5.118 5.078 99.217

Table 3. Theoretical and bulk (measured) Densities of BSTx ceramic system.

SEM micrographs of transversely fractured sections from the BST0, BST4, BST8 and BST10 samples are shown in Figure 17. The BST0 (BaTiO3) and BST10 (SrTiO3) ceramics have a uniform compact morphology, present no cracks and have low porosity. The grain boundaries are not observable. Samples BST0 and BST10 have a bulk density of 98.52% and 99.21% of the theoretical, respectively. Even with the lower-than-conventional sintering temperatures, it is possible that the observed morphology resulted from liquid phase formation due to the small particle size [KINGERY, BARSOUM, BARRY]. Grain size distributions for BST0 and BST10 are shown in Figure 18. For the BST0 sample, grain sizes between 1 and 3.5 μm (2 μm average) were measured, while for the BST10 sample, sizes ranged ranged from 1 μm to 2.6 μm (1.4 μm average). The BST4 and BST8 samples, consisting of a barium-strontium solid solution (Ba,Sr)TiO3, have a distinctly smaller grain size, with distributions of 0.2 to 1.3 μm (650 nm average) and 0.3 to 0.9 μm (550 nm average),

Unit cell mass Theoretical Density Unit cell volume <sup>=</sup> (3)

**Bulk density (g m-3)** 

**% Theoretical density** 

**3.3 Density** 

calculated using:

**BSTx Sample** 

results are presented in Table 3.

**Unit cell volume (Å3)** 

respectively. Generally speaking, the conventional route for fabrication of mixed oxide ceramics leads to grains larger than 1 μm, in most cases on the order of several microns [LIN, LIOU, LU]. Smaller grains are only attained with nanopowders and special sintering processes such as spark plasma sintering (SPS) [DENG] or hot pressing [XIAO]. Other methods for inhibiting grain growth include the incorporation of 1 wt% of Na, Mn or Mg ions [LIOU].

Fig. 17. SEM micrographs of transversely fractured BST0, BST4, BST8 and BST10 samples at two magnifications: (a) BST0 sintered at 1523 K, (b) BST4 sintered at 1543 K, (c) BST8 sintered at 1573 K, (d) BST10 sintered at 1573 K.
