**3.6.2 Ferroelectric hysteresis loops**

454 Sintering of Ceramics – New Emerging Techniques

**306**

**Raman scattering, Ceramics BSTx**

**Intensity (a. u.)**

**3.6 Dielectric and ferroelectric properties** 

**3.6.1 Dielectric constant** 

**300 320 340 360 380 400 420 440**

**Ceramic BST0**

**398 K**

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

**Dielectric constant,** ε

**1 kHz 100 kHz**

**0.1 kHz**

**Temperature (K)**

**Dielectric constant,** ε

**100 kHz 1 kHz**

**0.1 kHz**

 **0.1 kHz 1 kHz 100 kHz** **200 400 600 800 1000 1200**

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

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

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

**300 320 340 360 380 400 420 440**

**Ceramic BST1**

**370 K**

 **0.1 kHz 1 kHz 100 kHz**

**Dielectric constant,** ε

**100 kHz**

**1 kHz**

**306 K 0.1 kHz**

**300 320 340 360 380 400 420 440**

**Ceramic BST3**

 **0.1 kHz 1kHz 100 kHz**

**Temperature (K)**

**Temperature (K)**

**BST2 BST3**

**BST1**

**BST4 BST5**

> 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 ferroelectric domains occur [MERZ, 1954].

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

#### **3.7 Piezoresponse Force Microscopy (PFM)**

#### **3.7.1 Ferroelectric domain observation**

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

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 457

It isimportant to note that Figure 29 represents the ideal case of monocrystal domains ideally oriented, i.e., the direction of the observed polarization vectors are orthogonal. For the real case of a polycrystalline ceramic, the direction of the polarization vector would be random, i.e., a domain can point in any direction in 3D space. Therefore, the signals from piezoresponse measurements in OOP or IP are the projections of these random polarization

Fig. 29. Ferroelectric domains with differents orientations of the polarization vector. (a out-

Fig. 30. Standard terminology for polarization vector orientations relative to the observed surface in piezoresponse force microscopy (PFM). IP refers to in-plane, and OOP is out-of-

**(a (b**

of-plane (OOP) and (b in-plane (IP).

vectors.

plane.

one down (antiparallel ↑↓), separated by domain walls (gray stripe). The adjacent domains are oriented in opposite directions (180°). If these domains are observed from above, we would see that the direction of the domains are perpendicular to the surface, either pointing down into the sample (crosses) or up out of the sample (circles)., Both types are described as out-of-plane (OOP) (Figure 30). Figure 29 (b shows domains oriented at 90º (↑→) relative to one another. If these domains are observed from above, we would see domains in the plane of or parallel to the surface. These dominains are described as in-plane (IP) (Figure 30).

Fig. 28. P-E loops obtained for BST0, BST1, BST2 and BST3.

one down (antiparallel ↑↓), separated by domain walls (gray stripe). The adjacent domains are oriented in opposite directions (180°). If these domains are observed from above, we would see that the direction of the domains are perpendicular to the surface, either pointing down into the sample (crosses) or up out of the sample (circles)., Both types are described as out-of-plane (OOP) (Figure 30). Figure 29 (b shows domains oriented at 90º (↑→) relative to one another. If these domains are observed from above, we would see domains in the plane of or parallel to the surface. These dominains are described as in-plane (IP) (Figure 30).

**-20 -10 0 10 20**

**Electric field (kV/cm)**

**Ceramic BST2** *Pmax = 15.6*

**-20 -10 0 10 20**

**Electric field (kV/cm)**

β

Fig. 28. P-E loops obtained for BST0, BST1, BST2 and BST3.

ψ

**Ec = 1.27**

**Ec = 1.4**

β

ψ **Ec = 2.35**

*Pmax = 15.6*

**Ec = 1.89**

**-15**

**-10**

**-5**

**Polarization (**

μ**C/cm2**

**)**

**0**

**5**

**10**

**15**

**-15**

**-10**

**-5**

**Polarization (**

μ**C/cm2**

**)**

**0**

**5**

β

ψ*Pr = 2.28*

*Pr = 1.94*

**Ceramic BST1** *Pmax = 13*

**10**

**15**

**-10 0 10**

**Electric field (kV/cm)**

*Pmax = 12.6* **Ceramic BST3**

*Pr = 6.35*

**-20 -15 -10 -5 0 5 10 15 20**

**Electric field (kV/cm)**

β

ψ**Ec = 1.70**

**Ec = 1.53**

**Ec = 5.79**

**-15**

**-15**

**-10**

**-5**

**Polarization (**

μ**C/cm2**

**)**

**0**

**5**

**10**

**15**

**-10**

**-5**

**Polarization (**

μ**C/cm2**

**)**

**0**

**5**

β

β

ψ*Pr = 3.53*

*Pr = 2.65*

ψ

**Ceramic BST0**

*Pr = 1.91*

 *Pr = 2.69*

**10**

**15**

It isimportant to note that Figure 29 represents the ideal case of monocrystal domains ideally oriented, i.e., the direction of the observed polarization vectors are orthogonal. For the real case of a polycrystalline ceramic, the direction of the polarization vector would be random, i.e., a domain can point in any direction in 3D space. Therefore, the signals from piezoresponse measurements in OOP or IP are the projections of these random polarization vectors.

Fig. 29. Ferroelectric domains with differents orientations of the polarization vector. (a outof-plane (OOP) and (b in-plane (IP).

Fig. 30. Standard terminology for polarization vector orientations relative to the observed surface in piezoresponse force microscopy (PFM). IP refers to in-plane, and OOP is out-ofplane.

Ba1-XSrXTiO3 Ceramics Synthesized by an Alternative Solid-State Reaction Route 459

kHz. The amplitude and phase piezoresponse images present different characteristics. In the Figure 31b, the piezoresponse amplitude image allows us to visualize domains that leave or enter of the surface (OOP), where the amplitude *A* can be the same for antiparallel dominions (↑↓). Different regions are distinguished by their gray tones, delimited by black contours, which correspond to the ferroelectric domain walls. The domain walls are not observed in the topography, as that would have required etching (chemical attack) [FETEIRA]. Regions that appear as similar shades of gray in the piezoresponse amplitude image (Figure 31b) appear as contrasting bright and dark in the piezoresponse phase image (Figure 31c). This indicates a phase shift of 180 from one

These results show that the R-PFM images of amplitude and phase are not influenced by the topography of the samples. In contrast, standard measurements of piezoresponse force microscopy (PFM) were performed at 20 kHz with an alternating voltage (Vac) of 2-15 V without obtaining a piezoelectric response. A piezoresponse was obtained with contact resonance frequencies (~1350 kHz), with a quality factor Q betwen 50 and 100. Taking into account both the quality factor Q and the piezoresponse signal reported about 190 pm/V and to 419 pm/V [SHAO] for the case of BaTiO3, we can estimate a small piezoelectric

domain to another, but with the same piezoresponse amplitude.

constant of our material is of the order of units or tens of pm/V.

**(a) (b) (c) BST0**

Fig. 31. R-PFM of BST0 at a frequency of 1.350 MHz and an excitation voltage of 2 V.

(a) topography, (b) piezorepsonse amplitude, and (c) piezoresponse phase.

### **3.7.2 Contact Resonance-Enhanced Piezoresponse Force Microscopy (CR-PFM)**

In addition to the conventional PFM technique there is another mode called contact resonance-enhanced PFM or CR-PFM [HARNAGEA]. R-PFM is based on the same principles of operation of as PFM, the only difference being the value of the frequency of the alternating voltage applied to the tip (VAC). For contact resonance frequencies (CR-PFM), the strain amplitude response of the material can be more than one or two orders of magnitude higher than the amplitudes recorded by conventional PFM (quality factor Q) [HARNAGEA]. In other words, R-PFM is more sensitive than PFM and can be applied to materials whose piezoelectric constants (dij) are very small. Table 5 lists some materials and their piezoelectric constant (coefficient) .


Table 5. Piezoelectric constants of different materials.

The piezoelectric constant (d33) indicates how much the material will be deformed (in picometers) for each applied volt (V) applied. or Fmaterials with a low piezoelectric constant, it would be necessary to amplify the piezoresponse signal by applying a high voltage, risking a change in piezoelectric response. In such cases, R-PFM is an alternative to observe ferroelectric domains while still using a low voltage.

#### **3.7.3 Results of R-PFM for BSTx samples**

R-PFM measurements for the BSTx samples were made using the modified conventional method on an atomic force microscope (AFM, Veeco di DimensionTM 3100), usig conductive tips of Cr/Pt (Budget Sensors Tap I300E) with a force constant k = 40 N/m, and a free-resonance frequency was 300 kHz. The samples were polished starting with No. 500 sandpaper down to 0.3 μm alumina. The samples were not attacked by any chemical or mechanochemical process, insuring that topography did not contribute to the piezoresponse signal. AFM images of the contact resonance mode piezoresponse (CR-PFM) for BST0, with a grain size of 1-2 μm, are shown Figure 31. The three images, taken of the same area and at the same time, show (a) the topography, (b) the OOP piezoresponse amplitude, and (c) the OOP piezoresponse phase. Measurements were performed over a 5 x 5 μm area, using an applied voltage was 2V and a contact resonance frequency of 1350

In addition to the conventional PFM technique there is another mode called contact resonance-enhanced PFM or CR-PFM [HARNAGEA]. R-PFM is based on the same principles of operation of as PFM, the only difference being the value of the frequency of the alternating voltage applied to the tip (VAC). For contact resonance frequencies (CR-PFM), the strain amplitude response of the material can be more than one or two orders of magnitude higher than the amplitudes recorded by conventional PFM (quality factor Q) [HARNAGEA]. In other words, R-PFM is more sensitive than PFM and can be applied to materials whose piezoelectric constants (dij) are very small. Table 5 lists some materials and

**Material Piezoelectric coefficient, d33 (pm/V)**

Sr0.61Ba0.39Nb2O6 200

BaTiO3 190

PZT4 291

PZT5a 373

Quartz 3

The piezoelectric constant (d33) indicates how much the material will be deformed (in picometers) for each applied volt (V) applied. or Fmaterials with a low piezoelectric constant, it would be necessary to amplify the piezoresponse signal by applying a high voltage, risking a change in piezoelectric response. In such cases, R-PFM is an alternative to

R-PFM measurements for the BSTx samples were made using the modified conventional method on an atomic force microscope (AFM, Veeco di DimensionTM 3100), usig conductive tips of Cr/Pt (Budget Sensors Tap I300E) with a force constant k = 40 N/m, and a free-resonance frequency was 300 kHz. The samples were polished starting with No. 500 sandpaper down to 0.3 μm alumina. The samples were not attacked by any chemical or mechanochemical process, insuring that topography did not contribute to the piezoresponse signal. AFM images of the contact resonance mode piezoresponse (CR-PFM) for BST0, with a grain size of 1-2 μm, are shown Figure 31. The three images, taken of the same area and at the same time, show (a) the topography, (b) the OOP piezoresponse amplitude, and (c) the OOP piezoresponse phase. Measurements were performed over a 5 x 5 μm area, using an applied voltage was 2V and a contact resonance frequency of 1350

Table 5. Piezoelectric constants of different materials.

**3.7.3 Results of R-PFM for BSTx samples** 

observe ferroelectric domains while still using a low voltage.

**3.7.2 Contact Resonance-Enhanced Piezoresponse Force Microscopy (CR-PFM)** 

their piezoelectric constant (coefficient) .

kHz. The amplitude and phase piezoresponse images present different characteristics. In the Figure 31b, the piezoresponse amplitude image allows us to visualize domains that leave or enter of the surface (OOP), where the amplitude *A* can be the same for antiparallel dominions (↑↓). Different regions are distinguished by their gray tones, delimited by black contours, which correspond to the ferroelectric domain walls. The domain walls are not observed in the topography, as that would have required etching (chemical attack) [FETEIRA]. Regions that appear as similar shades of gray in the piezoresponse amplitude image (Figure 31b) appear as contrasting bright and dark in the piezoresponse phase image (Figure 31c). This indicates a phase shift of 180 from one domain to another, but with the same piezoresponse amplitude.

These results show that the R-PFM images of amplitude and phase are not influenced by the topography of the samples. In contrast, standard measurements of piezoresponse force microscopy (PFM) were performed at 20 kHz with an alternating voltage (Vac) of 2-15 V without obtaining a piezoelectric response. A piezoresponse was obtained with contact resonance frequencies (~1350 kHz), with a quality factor Q betwen 50 and 100. Taking into account both the quality factor Q and the piezoresponse signal reported about 190 pm/V and to 419 pm/V [SHAO] for the case of BaTiO3, we can estimate a small piezoelectric constant of our material is of the order of units or tens of pm/V.

Fig. 31. R-PFM of BST0 at a frequency of 1.350 MHz and an excitation voltage of 2 V. (a) topography, (b) piezorepsonse amplitude, and (c) piezoresponse phase.

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