detector displaying the electric field vector 𝑬, scattered beam at an angle 𝟐𝜽, and
sample orientation 𝝎. Modified from Refs.
147,3814.2.2
Microstructural Characterization
4.2.2.1 Scanning and Transmission Electron Microscopy
Sintered samples were polished with diamond paste (DP-Paste, Struers GmbH, Germany) of 15 μm, 6 μm, 3 μm, 1 μm, and ¼ μm (polishing discs MD Dur/Nap, Struers GmbH, Germany). SEM imaging was performed using a JSM 7600F (JEOL Ltd., Japan). Images were taken with the back scattered electron (BSE) mode at low acceleration voltages. Orientational contrast imaging was optimized at 8 kV to enhance material (Z) and grain contrasts. Experiments were performed together with Mrs. Kunz. Mean grain size was determined by considering approximately 200 grains from several micrographs. The linear interception method with a numerical multiplication factor of 1.56 was applied for the grain size calculation by assuming isometric grain shape.382 Moreover, the core-shell microstructure of BNT-ST was quantified by a density of cores. The density of cores was defined as
57
the numbers of cores divided by area. Several images, taken from different positions of the sample surface, were analyzed representing a total of ~ 2500 μm2. Energy-dispersive X-ray spectroscopy (EDS) was used to estimate the statistical composition of cores and shells. For this purpose a NCA Energy 350 EDS (Oxford Instruments plc, United Kingdom) was employed with an incident beam of 15 kV to collect spectra in the energy range between 0.50 keV and 9 keV.
TEM samples were ultrasonically cut from disc samples (Figure 4.2 (a)) into smaller discs of 3 mm in diameter by an ultrasonic cutter (Gatan 601, Gatan Inc., United States). A semiautomatic machine was used for grinding the samples between 100 μm and 200 μm with same experimental conditions as described in the previous paragraph (Allied Multiprep Polishing System, Allied High Tech Products Inc., United States). Polished samples were dimpled to a final thickness between 10 μm and 20 µm in a dimple grinder (Gatan 656, Gatan Inc., United States).Samples were annealed at 400 °C for 2 h to minimize residual stresses possibly introduced during machining. Subsequently, samples were perforated on both sides by Ar ion milling using a Dual Ion Mill unit (Gatan 600, Gatan Inc., United States). Initially milling was performed at 5 kV and 16° incidence angle, followed by 4 kV and 12° incidence angle. Prior to characterization, samples were coated with carbon in order to minimize charging under the incident electron beam. Experiments were carried out using a 2100F TEM (JEOL Ltd., Japan) operated at 200 kV and a Be double-tilt holder (EM-31640, Gatan Inc., United States). For EDS mapping in scanning transmission electron microscopy (STEM) mode, the second smallest condenser aperture C2 and an electron probe size of 1 nm with a camera length of 0.80 m were employed. The specimen was tilted by an angle of 10° to maximize the X-ray collection of the detector in the energy range from 0 keV to 20 keV. In situ hot-stage experiments were performed with a double-tilt heating holder (Gatan 652, Gatan Inc., United States) equipped with a SmartSet Hot-Stage Controller (Gatan 901, Gatan Inc., United States). The bright field (BF) and dark field (DF) micrographs and selected area diffraction (SAED) patterns were recorded at 165 °C, 245 °C, and 345 °C with an uncertainty of ± 20 °C. To assure isothermal conditions, temperature was held for 30 min prior to each measurement. Experiments were performed by M. Sc. Scherrer and Dr. Molina-Luna.
4.2.2.2 Density
The Archimedes method was employed for density measurements of 2 to 3 sintered samples of each composition. Initially as-sintered disc samples (Figure 4.2 (a)) were dried for 24 h at 100 °C. Thereafter, their dry weight (DW) was measured (BA110S Basic, Sartorius AG, Germany). Samples were put in distilled water and into a vacuum chamber (RD8, Vacuubrand GmbH, Germany) at a pressure of 50 mbar for 1 h. The samples were weighed in water (saturated weight in water (SWW)) and dried with a clean paper. Subsequently, they were weighed again (saturated weight in air (SWA)). The absolute density of each sample (𝛿𝑠) was calculated taking into account the
Archimedes principle (Equation 4.1) and the density of the water at the measurement temperature.
𝛿𝑠 =
𝛿𝐻2𝑂 ∙ 𝐷𝑊
𝑆𝑊𝐴 − 𝑆𝑊𝑊
58
The theoretical density 𝛿𝑡 of the samples was calculated by considering the mass and volume of
unit cells. Assumption of pseudocubic lattice parameters was performed, as described in Section 4.2.1.1. The relative density 𝛿𝑟 was calculated with Equation 4.2.
𝛿𝑟 =
𝛿𝑠
𝛿𝑡
Equation 4.2.
Results of the Archimedes method were contrasted with analysis of the surface area of micrographs. BSE micrographs of the polished surfaces described in Section 4.2.2.1 were transformed to binary colors with GIMP software (GNU Image Manipulation Software version 2.8.10, United States). Afterwards, binary images were analyzed with the ImageJ software (National Institutes of Health version 1.48v) to obtain the fraction of porosity and material. A total area of ~2500 μm2
was analyzed in several images at different position of the sample surface to obtain representative results. The ratio between porosity and material was considered as the 𝛿𝑟. Both
analyses gave comparable values within measurement errors.
4.3
Thermal Analysis
In order to investigate the calcination process of BNT-ST a homogenized stoichiometric mixture of the chemical reagents was loaded into a thermogravimetric (TGA)/differential thermal analysis (DTA) STA 449C analyzer (Jupiter, Netzsch-Gerätebau GmbH, Germany). The device is coupled to a Fourier transform infrared spectrometer (FT-IR) (Tensor 27, Bruker Optik GmbH, Germany). Powder was heated in air up to 1000 °C (heating rate 5 °C/min). The spectrometer was used to analyze the outgassing species. The IR spectra were recorded during the heating process. The detected IR bands for the outgassing species were integrated and plotted versus temperature. Experiments were performed by Dipl.-Ing. Fasel.
4.4
Electrical Characterization
Poling and large signal characterization methods throughout this section were performed in silicon oil (AK 35 for room temperature and AK 200 for high temperatures, Wacker Chemie AG, Germany) to avoid electric breakdown of air, which is around 3 kV/mm.383
59
4.4.1
Temperature- and Frequency-Dependent Dielectric Properties
Temperature- and frequency-dependent real 𝜀𝑟´ and imaginary 𝜀𝑟´´ relative permittivity values were
obtained on poled and unpoled samples. The dielectric properties of BZT-BCT were measured in the temperature range from - 100 °C to 120 °C with a heating rate of 2 °C/min and in the frequency range from 100 Hz to 10 kHz. An Impedance analyzer Alpha-A equipped with a cryostat (Novocontrol Technologies GmbH & Co. KG, Germany) was employed for the measurements. For the BNT-ST high temperature dielectric properties were tested to evaluate the presence of dielectric relaxations prototypical of relaxors. For this purpose 𝜀𝑟´ and 𝜀𝑟´´ values were measured in
the temperature range from 25 °C to 500 °C with a heating rate of 2 °C/min and in the frequency range from 1 kHz up to 1 MHz. A Precision LCR Meter 4192A (Hewlett Packard Corp., United States) was used for the measurements. In order to depict dielectric relaxations, low temperature frequency-dependent real 𝜀𝑟´ and imaginary 𝜀𝑟´´ relative permittivity were measured with a cooling
rate of 1 °C/min and in the frequency range from 10 mHz to 1 MHz (Impedance analyzer Alpha-A equipped with a cryostat, Novocontrol Technologies GmbH & Co. KG, Germany). The temperature range selected for BZT-BCT was between - 100 °C to 120 °C, whereas for BNT-ST was from 300 °C to - 150 °C. The amplitude of the probing ac electric signal was 0.002 kV/mm peak to peak for all experiments.
4.4.2
Small Signal Properties
Prior to zero bias-field small signal measurements, all BZT-BCT samples were poled for 10 min at room temperature with an electric field of 4 kV/mm (HCN35-35000, Fug GmbH, Germany). Poling conditions were selected based on results from Wu et al.314 Moreover, 𝑑33 was always tested in a
commercial Berlincourt meter (YE2730, Sinocera Inc., China) before performing further measurements in other setups.
The incipient piezoelectric BNT-0.25ST features an almost negligible 𝑑33 ~ 10 pC/N. Therefore,
most of the small signal investigations were performed solely on the BZT-BCT, with the exception of bias-field-dependent measurements that were also done in BNT-0.25ST.
4.4.2.1 Temperature-Dependent Quasi-Static Characterization
In situ 𝑑33 of BZT-BCT as a function of temperature was measured using a custom-designed device,
which consists of a furnace controlled by two thermocouples and a laser vibrometer (sensor head OFV-505 and front-end VDD-E-600, Polytec GmbH, Germany). A pinhole was made in the middle of a thermally insulating alumina covering lid, thereby allowing the laser to pass through. Further details on the device are presented elsewhere.384 All compositions were measured in the temperature range from 25 °C to 105 °C with a heating rate of 2 °C/min in 5 °C steps. A sinusoidal wave of 0.01 kV/mm amplitude and a frequency of 10 kHz was chosen as input voltage (function generator HM8131-2, Hameg GmbH, Germany).
60 4.4.2.2 Electric Field- and Temperature-Dependent Quasi-Static Characterization
Electric field-dependent characterization was performed in BZT-BCT and BNT-ST in their respective operational ranges. A sinusoidal waveform of 1 kHz and 0.02 kV/mm modulated a triangular base waveform of 3 kV/mm and 4 kV/mm with a frequency of 0.05 Hz for the BZT-BCT and BNT-ST, respectively. The waveforms used as input signals are represented in Figure 4.4.