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

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

The linear dependence between the Tc and at.% Sr is described by Equation 4, the result of fitting the experimental data (Figure 20):

$$\mathbf{Tc} = 128.4871 - 31.469^{\circ}\mathbf{X} \tag{4}$$

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 451

 **Tc**

 **Linear fit Tc**

**0 10 20 30 40 50**

**Sr (atomic %)**

**Sample ID Calculated Tc (K) Experimental Tc (K)**  BST0 401.48 399.80 BST1 370.02 371.36 BST2 338.55 340.96 BST3 307.08 306.62 BST4 275.61 273.0 BST5 244.15 241.65

Table 4. Experimental Curie temperatures (via DSC), and those calculated using Equation 4. Tc for samples BST6 – BST10 were not experimentally determined due to exceeding the

Figure 21 shows the Raman scattering spectrum (radiation wavelength = 514.5 nm) for BaTiO3 (BST0) with perovskite-type structure ABO3 and tetragonal phase at room temperature. Raman active phonons for the P4/mmm tetragonal symmetry are represented by 3A1 + B1 + 4E. Long-range electrostatic forces induce a splitting in the transverse and longitudinal phonons, resulting in a split of the Raman active phonons represented by 3 [A1 (TO) + A1 (LO)] + B1 + 4 [E (TO) + E (LO)] [SHIRATORI]. Raman shift bands are reported at 250, 520 and 720 cm-1 with a sharp peak at around 306 cm-1 [DIDOMENICO, ROUSSEAU,

**Curie Temperature (K)**

**Y = A + B \* X** ------------------------------ **A 401.4871 B -3.1468** ------------------------------

Fig. 20. Linear fit of the Curie temperature (Tc) from the DSC curves.

BST6\* 212.68 BST7\* 181.21 BST8\* 149.74 BST9\* 118.27 BST10\* 86.80

temperature range of the differential scanning calorimeter.

**3.5 Curie temperature (Tc) via Raman spectroscopy** 

BASKARA].

Fig. 18. Grain size distribution of (a) BST0, (b) BST10, (c) BST4 and (d) BST8 ceramic samples.

where Tc is the Curie temperature and x is the Sr content in at.%. Table 4 presents the Curie temperatures of samples BST0 to BST3 determined by Equation 4. The equation was extrapolated to the composition of samples BST4 to BST10. The determined Curie temperatures resulted not so different from those reported in the literature, for example, the BST35 system (35 mol% of Sr) has an approximate Tc of 292 K [ALI] compared to 291.35 K determined with Equation 4. The BST3 system was reported to have a Tc of 306~307 K [PITICESCU], compared to 307.08 K calculated with Equation 4. The Ba60Sr40TiO3 system (BST4) has a Tc of 272 K (274.15 K) [FETEIRA], compared to our calculation of 276.6 K.

Fig. 19. Differential scanning calorimetry curves of the BST0, BST1, BST2 and BST3 samples.

Fig. 18. Grain size distribution of (a) BST0, (b) BST10, (c) BST4 and (d) BST8 ceramic samples.

**Exo**

**Energy**

**Endo**

**Ceramic BST3**

**Ceramic BST2**

**Ceramic BST1**

where Tc is the Curie temperature and x is the Sr content in at.%. Table 4 presents the Curie temperatures of samples BST0 to BST3 determined by Equation 4. The equation was extrapolated to the composition of samples BST4 to BST10. The determined Curie temperatures resulted not so different from those reported in the literature, for example, the BST35 system (35 mol% of Sr) has an approximate Tc of 292 K [ALI] compared to 291.35 K determined with Equation 4. The BST3 system was reported to have a Tc of 306~307 K [PITICESCU], compared to 307.08 K calculated with Equation 4. The Ba60Sr40TiO3 system (BST4) has a Tc of 272 K (274.15 K) [FETEIRA], compared to our calculation of 276.6 K.

**180 210 240 270 300 330 360 390 420 450**

**Temperature (K)**

Fig. 19. Differential scanning calorimetry curves of the BST0, BST1, BST2 and BST3 samples.

**Ceramic BST0**

**306.6 K**

**DSC of BSTx Ceramic System**

**340.9 K**

**371.3 K**

**398.8 K**

Fig. 20. Linear fit of the Curie temperature (Tc) from the DSC curves.


Table 4. Experimental Curie temperatures (via DSC), and those calculated using Equation 4. Tc for samples BST6 – BST10 were not experimentally determined due to exceeding the temperature range of the differential scanning calorimeter.

#### **3.5 Curie temperature (Tc) via Raman spectroscopy**

Figure 21 shows the Raman scattering spectrum (radiation wavelength = 514.5 nm) for BaTiO3 (BST0) with perovskite-type structure ABO3 and tetragonal phase at room temperature. Raman active phonons for the P4/mmm tetragonal symmetry are represented by 3A1 + B1 + 4E. Long-range electrostatic forces induce a splitting in the transverse and longitudinal phonons, resulting in a split of the Raman active phonons represented by 3 [A1 (TO) + A1 (LO)] + B1 + 4 [E (TO) + E (LO)] [SHIRATORI]. Raman shift bands are reported at 250, 520 and 720 cm-1 with a sharp peak at around 306 cm-1 [DIDOMENICO, ROUSSEAU, BASKARA].

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 453

**519**

**306 Raman scattering, Ceramic BST0**

**720**

**200 400 600 800 1000**

**Raman shift, (cm-1)**

**Raman scattering, Ceramic BST1 <sup>306</sup>**

**0 200 400 600 800 1000 1200**

**0 200 400 600 800 1000 1200**

**Raman shift, (cm-1)**

**Raman shift, (cm-1)**

**Raman scattering, Ceramic BST2**

**250**

Fig. 23. Raman scattering spectra at different temperatures for BST0.

Fig. 24. Raman scattering spectra at different temperatures for BST1.

Fig. 25. Raman scattering spectra at different temperatures for BST2.

**306**

**Intensity (a. u.)**

**Intensity (a. u.)**

**Intensity (a. u.)**

**323 K**

**R. T.**

**383 K 373 K 363 K 353 K 343 K 333 K 323 K**

**363 K**

**353 K 343 K 333 K**

**323 K**

**373 K**

**393 K**

**403 K 400 K**

Fig. 21. Raman scattering spectra for BST0.

The shoulder at around 180 cm-1 in bulk BaTiO3 is attributed to the coupling of the three disharmonic phonons A1 (TO) [VENKATESWARAN, FREY]. Figure 23 shows the Raman scattering spectra of the BST0 sample at different temperatures. The 250, 520 and 720 cm-1 bands as well as the 306 cm-1 peak decrease gradually as the temperature increases. At 403 K, the sharp 306 cm-1 peak disappears, indicating the transition from cubic to tetragonal phase (Tc). The transition temperature was previously reported by C. H. Perry [PERRY]. Thus, the sharp peak around 306 cm-1 indicates whether the BSTx system is in the tetragonal or cubic phase. The relative intensity of the 306 cm-1 peak as a function of temperature for BST0 is presented in Figure 22. Figures 24 and 25 show the temperature-dependent Raman scattering spectra for BST1 and BST2, respectively. The cubic to tetragonal phase transition is observed in the range from 363 to 373 K for BST1 and 333 to 343 K for BST2. Both ranges match those determined by DSC. Figure 26 shows the Raman scattering spectra for BST1 to BST5 at room temperature. Samples BST4 and BST5 do not present the sharp peak at 306 cm-1, i.e., they have a stable cubic phase and a tetragonality of 1 (c/a = 1). These results are consistent the XRD and DSC results presented earlier.

Fig. 22. Realtive peak intensity for the 306 cm-1 Raman reflection (from Figure 21) as a function of temperature for BST0.

**B1, E(TO + LO)**

**A1(TO),E(TO),E(LO),A1(LO) Raman scattering**

**E(TO), A1(TO)**

**A1(TO)**

**Intensity (a. u.)**

Fig. 21. Raman scattering spectra for BST0.

consistent the XRD and DSC results presented earlier.

**0.0**

**0.2**

**0.4**

**0.6**

**Relative Intensity, peak 306 cm-1**

function of temperature for BST0.

**0.8**

**1.0**

**200 400 600 800 1000**

**Raman shift, (cm-1**

The shoulder at around 180 cm-1 in bulk BaTiO3 is attributed to the coupling of the three disharmonic phonons A1 (TO) [VENKATESWARAN, FREY]. Figure 23 shows the Raman scattering spectra of the BST0 sample at different temperatures. The 250, 520 and 720 cm-1 bands as well as the 306 cm-1 peak decrease gradually as the temperature increases. At 403 K, the sharp 306 cm-1 peak disappears, indicating the transition from cubic to tetragonal phase (Tc). The transition temperature was previously reported by C. H. Perry [PERRY]. Thus, the sharp peak around 306 cm-1 indicates whether the BSTx system is in the tetragonal or cubic phase. The relative intensity of the 306 cm-1 peak as a function of temperature for BST0 is presented in Figure 22. Figures 24 and 25 show the temperature-dependent Raman scattering spectra for BST1 and BST2, respectively. The cubic to tetragonal phase transition is observed in the range from 363 to 373 K for BST1 and 333 to 343 K for BST2. Both ranges match those determined by DSC. Figure 26 shows the Raman scattering spectra for BST1 to BST5 at room temperature. Samples BST4 and BST5 do not present the sharp peak at 306 cm-1, i.e., they have a stable cubic phase and a tetragonality of 1 (c/a = 1). These results are

**280 300 320 340 360 380 400**

Fig. 22. Realtive peak intensity for the 306 cm-1 Raman reflection (from Figure 21) as a

**Temperature (K)**

 **Raman, Ceramic BST0**

**E(LO), A1(LO)**

**Ceramic BST0**

**)**

Fig. 23. Raman scattering spectra at different temperatures for BST0.

Fig. 24. Raman scattering spectra at different temperatures for BST1.

Fig. 25. Raman scattering spectra at different temperatures for BST2.

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 455

ferroelectric material with such a behavior is Pb(Mg1/3Nb2/3)O3 [KOVALA]. The determined Tc's agree well with those obtained by DSC and Raman. The dielectric constant peak values are 3.179, 6.540 and 4.432 for BST0, BST1 and BST3 ceramics respectively, 2 to 3 orders of magnitude larger than those of other materials conventionally used in capacitors or CMOS

All of the BSTx samples showed a maximum in the dielectric constant at Tc. Above this temperature, the dielectric behavior obeys the Curie-Weiss law and has the form [BURFOOT]:

When an external electric field *E* is applied to a dielectric material, it produces a *P* vs. *E* curve. In the case of ferroelectric materials there is a delay in the *P* response to the *E* stimulus, i.e., hysteresis. A freshly manufactured ferroelectric has a zero spontaneous net polarization (*Ps=0*). When an external electric field is applied, nucleation and growth of the

The shape of the ferroelectric curve P = f(E) depends on both time and temperature. In the present work, ferroelectric measurements were performed at room temperature (~298 K) at a fixed frequency of 100 Hz using a comercial Sawyer-Tower circuit (ferroelectric RADIANT Test System) [SAWYER and TOWER]. Figure 28 presents the hysteresis loops for BST0, BST1, BST2 and BST3. The **P**-**E** urves exhibit the typical behavior of polycrystalline ferroelectric ceramics [MERZ, 1953]. The remanent polarization (Pr) is low compared to that of BaTiO3 single crystals (>20 μC/cm2 [SRIVASTAVA]), but higher than that of nanocrystalline BaTiO3 (Pr < 1 μC/cm2 [BUSCAGLIA]). It is comparable to that of BaTiO3

Ferroelectric materials are composed of ferroelectric domains, which can be observed by polarized light microscopy [RUPPRECHT, ARLT], scanning electron microscopy [CHOU, ROUSSEAU] and transmission electron microscopy [FREY, GANPULE]. To be detected by these techniques, some sort of chemical attack is necessary to reveal the ferroelectric domains, as they demonstrate a preferential rate of erosion [FETEIRA, LAURELL]. Furthermore, these techniques do not directly indicate the direction of polarization (direction of the domain); they only discriminate one domain from another. Piezoresponse force microscopy (PFM) does not suffer from these shortcomings [RABE], allowing visualization of ferroelectric domains with sizes on the order of 1 μm [SAURENBACH, WITTBORN], accurate detection of the polarization direction [ENG 1998, CHO**]** and reconstruction of the three-dimensional orientation of the domains [ENG, 1999]. Figure 29 is a diagram of oriented domains in ferroelectric grains. Figure 29 (a shows a domain up and

ε

0 C

is the dielectric constant (material permittivity), *C* is the Curie-Weiss constant, *T* is

T T <sup>=</sup> <sup>−</sup> (5)

(complementary metal oxide semiconductor) devices [ROBERTO, WILK].

the temperature of the material and *T0* is the Curie-Weiss temperature.

**3.6.2 Ferroelectric hysteresis loops** 

ferroelectric domains occur [MERZ, 1954].

ceramics with grain sizes of around 1 μm [TAKEUCHI].

**3.7 Piezoresponse Force Microscopy (PFM)** 

**3.7.1 Ferroelectric domain observation** 

where ε

Fig. 26. Raman scattering spectra at room temperature for BST1, BST2, BST3, BST4 and BST5.

#### **3.6 Dielectric and ferroelectric properties**

#### **3.6.1 Dielectric constant**

When a polycrystalline ferroelectric ceramic is cooled below its Curie temperature, some of its properties undergo strong changes. For example, the dielectric constant (ε) shows a maximum at Tc for BST0, BST1 and BST3 at 0.1, 1.0, and 100 kHz (Figure 27), a typical ferroelectric behavior of perovskite-type materials [MILLAR, STANFORD]. A widening of the peak at Tc has been reported to occur with decreasing grain size [KINOSHITA, SAKABE]. The dielectric constant has a magnitude larger than 1000 within most of the measured temperature interval, and it decreases at higher frequencies. This effect has been observed in BaTiO3 ceramics containing Zr [DEB] and in those containing Na and Bi (BTNx) [GAO]. The dielectric constant has polar and ionic parts, therefore, the dielectric dispersion can be attributed to the dipoles ceasing to contribute to the dielectric constant as the frequency increases [MERZ, 1954]. The dielectric relaxation effect occurs at frequencies where the electric dipoles can no longer follow the oscillation of the applied electric field. The relaxation frequency can be determined by a drop in the real part of ε and a maximum in the imaginary part [RAVEZ]. Although there is dielectric relaxation in the BSTx samples, the material does not present typical reflexor behavior. That is, there is no change in the position of Tc when the frequency changes. Another

Fig. 27. Dielectric constant curves for (a) BST0, (b) BST1 and (c) BST3.

ferroelectric material with such a behavior is Pb(Mg1/3Nb2/3)O3 [KOVALA]. The determined Tc's agree well with those obtained by DSC and Raman. The dielectric constant peak values are 3.179, 6.540 and 4.432 for BST0, BST1 and BST3 ceramics respectively, 2 to 3 orders of magnitude larger than those of other materials conventionally used in capacitors or CMOS (complementary metal oxide semiconductor) devices [ROBERTO, WILK].

All of the BSTx samples showed a maximum in the dielectric constant at Tc. Above this temperature, the dielectric behavior obeys the Curie-Weiss law and has the form [BURFOOT]:

$$\mathbf{c} = \frac{\mathbf{C}}{\mathbf{T} - \mathbf{T}\_0} \tag{5}$$

where ε is the dielectric constant (material permittivity), *C* is the Curie-Weiss constant, *T* is the temperature of the material and *T0* is the Curie-Weiss temperature.
