Mechanisms of Electro-Mechanical Coupling in Polycrystalline Piezoelectric Ceramic Materials

MECHANISMS OF ELECTRO-MECHANICAL COUPLING IN POLYCRYSTALLINE PIEZOELECTRIC CERAMIC MATERIALS

A Thesis By Mohammad Jahangir Hossain

Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy

School of Materials Science and Engineering Faculty of Science University of New South Wales

April 2016 PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet

Surname or Family name: Hossain

First name: Mohammad Jahangir Other name/s:

Abbreviation for degree as given in the University calendar: PhD

School: School of Materials Science and Engineering Faculty: Science

Title: Mechanisms of electro-mechanical coupling in polycrystalline piezoelectric ceramic materials

Abstract 350 words maximum: (PLEASE TYPE) Piezoelectric ceramics have extensive applications in electronic industries as sensor and actuator device materials. Most of the currently used piezoelectric ceramics in these electronic devices are based on PbZrxTi1-xO3 (PZT). Due to international consent towards removing toxic substances from the electronic and electrical equipment and biological harmful effects of Pb to the environment, it is necessary to find lead-free compositions with comparable properties to those of PZT. Promising lead-free piezoceramics are mainly based on solid solutions incorporating either Bi1/2Na1/2TiO3 (BNT) or NaxK1-xNbO3. Although lead-free compositions of piezoelectric materials have been reported with enhanced properties, no single lead-free piezoelectric material has been identified for the replacement of PZT over the wide operating conditions that it is currently used for. To improve the electro-mechanical properties of these materials further will require deep knowledge about the underlying structural origin of electric-field-induced strains. A sample cell has been developed, capable of measuring the structural variations of piezoceramics under applied electric field using low-energy X-ray scattering techniques, while simultaneously collecting macroscopic strain data using a linear displacement sensor. The results show that the macroscopic strain measured using the cell can be directly correlated with the microscopic response of the material obtained from diffraction data.

The electro-mechanical coupling mechanisms in PZT and BNT-6.25BaTiO3 (BNT-6.25BT) have been studied using in situ low- energy (12.4 keV) and in situ high-energy (73 keV) synchrotron XRD. The results show that for both systems the intrinsic lattice strains and extrinsic non-180 domain switching strains are larger at the surface than in the bulk. The structure property relationships in a series of (100-x)BNT-xBT (BNT-xBT) solid solutions with the BT content ranging from 5 mol% to 8 mol% in 0.25 mol% steps have been studied using in situ high-energy synchrotron XRD under unipolar stress and bipolar electric field. During application of both stress and electric field, lower BT content samples (x < 5.75) tended to transform to rhombohedral symmetry, while higher BT content (x > 7) tended to go tetragonal. Compositions between these tended to transform to mixed phase symmetry. The results show that the stress and electric-field-induced phase transformation mechanisms are highly analogous.

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Date ……………………….……………...... Table of contents

Table of contents ...... i

Abstract ...... v

List of publication and presentation ...... viii

Acknowledgements ...... ix

List of figures ...... x

List of tables ...... xv

1 Introduction ...... 1

2 Literature review ...... 7

2.1 Fundamental of electro-mechanical coupling ...... 7

2.1.1 Dielectrics and polarisation mechanisms ...... 7

2.1.2 Piezoelectricity ...... 9

2.1.3 Ferroelectricity ...... 11

2.1.4 Relaxor ferroelectricity ...... 16

2.2 Lead-free piezoelectric ceramics ...... 18

2.2.1 Bismuth sodium titanate ...... 18

2.2.2 Barium titanate ...... 20

2.2.3 BNT-BT solid solution ...... 20

2.3 Diffraction methods for studying piezoelectric ceramics ...... 21

2.3.1 Considerations for in situ measurements ...... 24

3 Experimental procedure ...... 26 i

3.1 Fabrication method of ceramic materials ...... 26

3.1.1 Sample preparation for low-energy XRD ...... 27

3.1.2 Sample preparation for high-energy XRD under electric field ...... 29

3.1.3 Sample preparation for high-energy XRD under stress ...... 30

3.2 Experimental methods ...... 32

3.2.1 Macroscopic property measurements ...... 32

3.2.2 In situ low-energy XRD ...... 32

3.2.3 In situ high-energy XRD ...... 35

3.2.4 Data analysis ...... 38

4 Development of a cell for in situ electric-field-dependent structural characterisation and macroscopic strain measurements ...... 41

4.1 Introduction ...... 41

4.2 Experimental procedure ...... 44

4.2.1 Sample cell design...... 44

4.2.2 Sample preparation...... 47

4.2.3 In situ experiment ...... 47

4.2.4 Calibration of strain sensor ...... 48

4.3 Results and Discussion ...... 54

4.3.1 Further considerations ...... 56

4.4 Conclusions ...... 57

5 The effect of inter-granular constraints on the response of polycrystalline piezoelectric ceramics ...... 58 ii

5.1 Introduction ...... 59

5.2 Experimental procedure ...... 65

5.3 Results and discussion ...... 68

5.4 Conclusions ...... 74

6 Structure-property relationships in BNT-xBT system during the application of a mechanical stress ...... 75

6.1 Introduction ...... 76

6.2 Experimental procedure ...... 78

6.3 Results and discussion ...... 79

6.4 Conclusions ...... 88

7 Structure-property relationships in BNT-xBT system during the application of an electric field ...... 89

7.1 Introduction ...... 89

7.2 Experimental procedure ...... 91

7.3 Results and discussion ...... 92

7.4 Conclusions ...... 102

8 General discussion ...... 103

8.1 Development of a sample cell to analyse the structural origin of strains in

piezoelectric materials ...... 103

8.2 The inter-granular effects on the materials response under an electric field .. 106

8.3 The effects of structural changes on variations of piezoelectric properties ... 107

9 Conclusions ...... 111

iii

10 Future work ...... 115

11 References ...... 117

Abstract

In this thesis a sample cell has been developed which is capable of measuring the structural variations of piezoelectric ceramic materials using low-energy X-ray scattering techniques in reflection geometry during the application of an electric field, while simultaneously collecting macroscopic strain data using a linear displacement sensor. The results show that the macroscopic strain measured using the cell can be directly correlated with the microscopic response of the material obtained from diffraction data.

The electro-mechanical coupling mechanisms in polycrystalline ferroelectric materials including a soft PZT and a lead-free 0.9375(Bi1/2Na1/2)TiO3-0.0625BaTiO3 (BNT-

6.25BT) have been contrasted using surface sensitive in situ low-energy (12.4 keV) and bulk sensitive in situ high-energy (73 keV) synchrotron XRD during the application of electric fields. The results allow a direct comparison of the microscopic responses between the bulk grains constrained in three dimensions and the surface grains which have one dimension of mechanical freedom. It is shown that for both PZT and BNT-

6.25BT the intrinsic lattice strains and extrinsic non-180° domain switching strains are larger at the surface than those in the bulk of the samples. The property difference is believed to result from the fact that surface grains are not constrained in three dimensions and consequently domain reorientation and lattice expansion in surface grains along the field direction occur more freely. The magnitude of the property difference between the surface and bulk is higher for PZT than for BNT-6.25BT due to the magnitude of anisotropy in the strain mechanism. The comparison of the results from different methods reveals that the grain-to-grain interactions have a significant influence on the electric-field-induced electro-mechanical responses in bulk

v polycrystalline ferroelectrics.

The structure-property relationships in a series of BNT-BT solid solutions with the BT content ranging from 5 mol% to 8 mol% in 0.25 mol% steps were also studied using in situ high-energy synchrotron XRD. This fine compositional deference helps to make a comprehensive picture of field-induced phases particularly in the “pseudo-cubic” region of the phase diagram. Unipolar stress cycling with a maximum stress of approximately

600 MPa and bipolar electric-field cycling with a maximum field of 5 kV/mm were applied in two separate experiments. In the as-processed state, BNT-5BT exhibited rhombohedral crystallographic symmetry, while the rest of BNT-xBT compositions

(5.25 ≤ x ≤ 8) exhibited the pseudo-cubic symmetry. During the application of stress and electric field in two separate experiments, lower BT content samples (x = 5.25 and

5.5) tended to transform to rhombohedral symmetry, while the compositions with higher

BT contents (7 ≤ x ≤ 8) tended to transform to tetragonal symmetry. Compositions between these (5.5 < x <7) tended to transform to mixed tetragonal-rhombohedral phase symmetry. The results show that the stress and electric-field-induced phase transformation mechanisms are highly analogous.

Based on the results of the surface and bulk response, and the compositional dependent studies, it is suggested that the best piezoelectric performance in a polycrystalline BNT- xBT material occurs when the magnitude of anisotropy of the response mechanism is minimum. In this case, compositions which transform to a mixed phase structure are likely to have superior piezoelectric performance, as all grains in the system strain with a similar magnitude along the applied field direction. This study of field-induced strain generation mechanisms in polycrystalline piezoelectric ceramics has identified an

vi important structural aspect which may be utilised to improve the piezoelectric properties in future developed systems.

vii

List of publication and presentation

Journal publications: i. M. J. Hossain, L. Wang, Z. Wang, N. H. Khansur, M. Hinterstein, J. A. Kimpton, and J. E. Daniels, “A sample cell for in situ electric-field-dependent structural characterisation and macroscopic strain measurements”, Journal of Synchrotron Radiation (2016, 23, doi:10.1107/S1600577516005075).

ii. M. J. Hossain, Z. Wang, N. H. Khansur, J. A. Kimpton, J. Oddershede and J. E. Daniels, “The effect of inter-granular constraints on the response of polycrystalline piezoelectric ceramics”, Applied Physics Letters (Under review).

Conference presentations: i. M. J. Hossain, N. H. Khansur, P. Tung and J. E. Daniels, Stress and electric-field dependence of the induced phase symmetry in BNT-xBT, 40th Annual Condensed Matter and Materials Meeting 2016, Wagga Wagga, Australia.

ii. M. J. Hossain, L. Wang, Z. Wang, N. H. Khansur, M. Hinterstein, J. A. Kimpton, and J. E. Daniels, Development of cell for in situ electric-field- dependent structural and macroscopic strain measurements, AOFSRR/User Meeting 2015, Melbourne, Australia.

iii. M. J. Hossain, L. Wang, Z. Wang, N. H. Khansur, M. Hinterstein, J. A. Kimpton, and J. E. Daniels, Inter-granular effects on the properties of polycrystalline piezoceramics, AMF-AMEC-2014, Shanghai, China.

viii

Acknowledgements

I would like to thank my supervisor John E. Daniels for guiding and providing me all the opportunities, support, advice and inspiration to complete this work.

I want to thank my all group members, especially Zhiyang Wang, Neamul H. Khansur,

Lijun Wang, and Patrick Tung for their help and useful suggestions and discussions. I would like express my gratitude to Manuel Hinterstein.

I would further like to thank my collaborators Jette Oddershede of Denmark Technical

University and Justin A. Kimpton at Australian Synchrotron.

I would like to acknowledge the provision of experimental beamtime by Australian

Synchrotron, Australia and European Synchrotron Radiation Facility (ESRF), France.

I want to express my gratitude to my parents and family for providing opportunity and continuous support throughout my PhD.

Finally, I would like to acknowledge financial support by the Australian Research

Council (ARC) through Discovery Projects DP120103968 and DP130100415.

List of figures

Figure 2-1 Illustration of different types of microscopic polarisation mechanisms. (a) electronic, (b) ionic, (c) orientation and (d) space charge (after Ref. [30, 31]) ...... 9

Figure 2-2 Classification of materials on the basis of crystal system ...... 10

Figure 2-3 Behaviour of piezoelectric material under (a) applied mechanical stress

(direct piezoelectricity) and (b) applied electric field (converse piezoelectricity). The dotted line and solid line indicates the initial and final position, respectively...... 10

Figure 2-4 Illustration of polarisation and strain generation during the application of an electric field cycling (after Ref. [31, 33]). The parameters can be defined as: Epol = a threshold value for poling field, Pmax = polarisation value achieved at the maximum electric field, Prem = polarisation value measured at the remnant state (after removal of electric field), Smax = strain value achieved at the maximum electric field, Srem = strain measured at the remnant state, Susable = Smax - Srem = usable strain measured from the difference between maximum strain and remnant strain...... 12

Figure 2-5 Crystallographic representation of strain generation mechanisms in piezoelectric ceramics as an example of PZT, (a) at initial state and (b) at applied electric field (after Ref. [37])...... 15

Figure 2-6 Comparison of ferroelectrics (FE) and relaxor ferroelectrics (RF) in terms of

(a) relative permittivity as a function of temperature, (b) polarisation and, (c) strain as a function of applied electric field (after Ref. [39])...... 17

Figure 2-7 Material responses during the application of a field in piezoelectric materials.

Lattice strain can be calculated from the changes in the peak positions (∆2θ). Relative changes in peak intensities highlight the domain texture. Field induced phase transformation can be analysed by observing development and/or loss of additional peaks during the application of a field...... 22

Figure 3-1 Flow diagram of sample preparation steps...... 26

Figure 3-2 Pictures of (a) bottom and (b) top surface electrodes ...... 28

Figure 3-3 XRD patterns of BNT-xBT compositions for the as synthesised state...... 31

Figure 3-4 Schematic diagram of experimental setup for macroscopic strain and polarisation measurements (after Ref. [93])...... 32

Figure 3-5 (a) Schematic diagram of the experimental setup with the sample cell used at the Powder Diffraction beamline of the Australian Synchrotron and (b) a picture showing the sample cell mounted at the beamline. A linear displacement sensor (LDS) was used in the cell to measure the macroscopic strain of the sample in situ simultaneously to the diffraction experiment during the application of a cyclic triangular electric field produced by a function generator. Data acquisition system monitored and recorded the measured output of the displacement sensor and output voltage of HV power supply...... 34

Figure 3-6 Schematic diagram of in situ high-energy X-ray scattering experimental setup. Unipolar compressive stress was applied perpendicular direction to the X-ray beam direction...... 36

Figure 3-7 Schematic diagram of in situ high-energy X-ray scattering experimental setups using electric field. A bipolar triangular waveform electric field was applied perpendicular to the incident beam direction...... 37

Figure 3-8 The fit of (200) type peaks in tetragonal phase piezoelectric ceramics ...... 39

Figure 4-1 Photograph and schematic drawing of in situ sample cell showing its major components. Lid (1), spring (2), spring stage (3), inner insulating wall (4), base plate

(5), displacement sensor bracket (6), displacement sensor (7), linear stage (8), sample mount (9), HV connector (10), outer wall (11)...... 45

Figure 4-2 Standard reflective sensitivity curve at near side (curve is provided by the

PHILTEC Company [106])...... 50

Figure 4-3 Measured sensor output voltage (V) as a function of the gap between the displacement sensor and the target surface. Red points indicate the measured data and the blue line is the fitted line with a linear approximation. Estimated errors are within the size of the markers...... 51

Figure 4-4 Comparison of the displacement as a function of electric field curves for

PZT measured using a calibrated macroscopic strain measurement system (TF

Analyser) (red line) and the cell equipped with the displacement sensor (blue line). .... 52

Figure 4-5 (a) comparison of macroscopic strain curves for PZT measured using a standard strain measurement system (purple line-markers) and the developed sample cell (black line-markers) and (b) corresponding in situ X-ray diffraction patterns at three electric field states; Initial (E0), maximum (Emax) of magnitude of 2 kV/mm and remnant

(Erem) state. Estimated errors are within the size of the markers...... 53

Figure 4-6 Comparison between the macroscopic strain (red line and markers) measured using a linear displacement sensor and a lattice strain (200) (blue line and markers) calculated from X-ray diffraction patterns for BNT-5BT. Data acquisition times for the diffraction data were 45 s per data point. Induced lateral strain (111) of gold electrode

(green line and markers). The lattice strain was calculated from diffraction peak position shifts during application of the electric-field and the macroscopic strains were calculated from the change in the sample dimension parallel to the electric-field direction. The lattice strain is approximately 50% of the macroscopic strain at any given field above 1.35 kV/mm. Estimated errors are within the size of the markers...... 55

Figure 5-1 Crystallographic representation of strain generation as a function of electric field in the case of (a) mon-domain single crystal, (b) poly-domain single crystal and (c) polycrystalline ceramic materials...... 64

xii

Figure 5-2 SEM image for BNT-6.25BT ...... 67

Figure 5-3 Diffraction patterns near the (111) and (200) reflections of soft PZT (left panel) and BNT-6.25BT (right panel) measured using surface sensitive low-energy (red) and bulk sensitive high-energy XRD (blue) at initial zero, E0 (top), and maximum electric fields, Emax (bottom). For direct comparison, the data are displayed as a function of the magnitude of scattering vector q, where q = 4휋푠푖푛휃λ. Here, the scattering vector is approximately parallel to the applied electric field direction...... 69

Figure 5-4 (a) lattice strain ε111 and (b) domain texture indicated by of intensity ratio

I002/I200 for PZT, (c) ε111 and (d) ε200 for the pseudo-cubic phase of BNT-6.25BT before transformation, (e) I111I111 and (f) I002/I200 for the induced rhombohedral and tetragonal phases in BNT-6.25BTas a function of applied electric field for the sample surface (red) and bulk (blue)...... 71

Figure 5-5 Schematic diagram showing the condition of grains with constraints at the surface and in the bulk...... 72

Figure 6-1 X-ray diffraction patterns of 111pc and 200pc reflections measured with the scattering vector perpendicular to the stress field direction for (100-x)BNT-xBT (where x= 5 to 8 in steps of 0.25) in the as-processed state (left hand side of the dotted line) and at the 400 MPa stress (right hand side of the dotted line). In the as-processed state,

BNT-5BT is in rhombohedral symmetry while rest of the compositions are in pseudo- cubic state. At the 400 MPa stress; BNT-5BT remains rhombohedral phase (black line),

BNT-5.25BT and BNT-5.5BT transform from a pseudo-cubic to a rhombohedral phase

(blue line), from BNT-5.75BT to BNT-6.75BT transform from a pseudo-cubic to a mixed (rhombohedral and tetragonal) phases (red line) and from BNT-7BT to BNT-

8BT transform from a pseudo-cubic to a tetragonal phase (green line)...... 83

Figure 6-2 (a) phase fractions, (b) relative full width half maxima ∆FWHM and (c)

xiii lattice strains ε are shown as a function of the percentage of BT content in BNT-BT solid solution at stress amplitude of 400 MPa...... 85

Figure 6-3 (a) lattice strains, ε111 and (b) ε200, and (c) relative full width half maximum,

∆FWHM111 and (d) ∆FWHM200 are shown as a function of applied stress for BNT-

5.5BT, BNT-6.5BT and BNT-7.75BT...... 87

Figure 6-4 Domain texture (MRD) of the 002pc reflection for the tetragonal phase and the 111pc reflection for the rhombohedral phase at 540 MPa stress. α is the angle between the scattering vector direction and applied stress field direction. The dotted line indicates the domain texture (MRD) value at initial state...... 87

Figure 7-1 (a) polarisation and (b) macroscopic strain as a function of electric field and the BT content in BNT-xBT...... 95

Figure 7-2 The 111pc and 200pc reflections as a function of the BT content in BNT-xBT system in the as-processed state (E0) (left panel) and at 5 kV/mm (Emax) (right panel). 96

Figure 7-3 Diffraction patterns with scattering vectors at various angles to the applied electric filed (5kV/mm). For (a) BNT-5.75BT, (b) BNT-6.25BT and (c) BNT-8BT..... 98

Figure 7-4 Comparison between measured and fitted selected regions of diffraction patterns near 111pc and 200pc reflections for BNT-6.25BT at 5kV/mm ...... 99

Figure 7-5 The domain texture (MRD) of (a) the 111pc reflection for the rhombohedral phase and (b) the 002pc reflection for the tetragonal phase at 5kV/mm for BNT-6.25BT.

The dotted line indicates the domain texture value at initial state...... 100

xiv

List of tables

Table 2-1 Properties of BNT (Ref. [55]) ...... 19

Table 3-1 Chemicals used for sample preparation ...... 29

Table 4-1 Measured sensor output, sample displacement and distance between target and sensor tip as a function of applied electric field for PZT...... 49

Table 6-1 Symmetry of BNT-xBT at initial and at 400 MPa ...... 81

Table 6-2 Phase fractions as a function BT content in BNT-xBT system ...... 82

Table 7-1 Symmetry of BNT-xBT at initial state and at 5 kV/mm ...... 94

Table 7-2 The refined unit-cell parameters of poled BNT-6.25BT (5kV/mm) using the

P4mm + R3c model ...... 99

Table 7-3 Field induced microscopic stain contributions to the macroscopic strain for

BNT-6.25BT at 5 kV/mm: Lattice strain (SL) and Domain switching strain (SD) ...... 102

1 Introduction

Piezoelectricity was discovered in 1880 and its name originates from the Greek word

"piezo" meaning pressure electricity. Piezoelectric materials generate an electrical charge in response to an applied mechanical stress (the direct effect) and experience a mechanical strain in the presence of an electric field (the converse effect). The direct piezoelectric effect is used in sensor applications and the converse piezoelectric effect is used in actuator devices.

Piezoelectric materials are increasingly playing an important role as sensors and actuators in smart devices. Some examples include, nano-positioning elements in photolithography, acoustic resonators in ultrasound imaging medical diagnostics, piezoelectric motors, inkjet printer heads, voltage transformers, energy harvesting devices and numerous sensors in modern automobiles [1-4]. In 2015 piezoelectric materials have been used in aircraft design with shape changing wings [5]. Using this technology, it may be possible to make future aircraft lighter, more efficient and quieter.

As applications of these materials increase, the value of the associated industry also increases. In 2015 the industry value of piezoelectric actuators alone was in excess of

US$20 billion [6].

Many natural and synthetic piezoelectric materials exist. Natural piezoelectric materials include crystalline materials such as Rochelle salt and quartz. Other organic substances such as silk and bone also display a piezoelectric response [7, 8]. Synthetic piezoelectric materials can be produced in the form of single crystal or polycrystalline ceramic and also include polymer materials such as polyvinylidene fluoride (PVDF) [9]. The use of

1 piezoelectric ceramics has many advantages from the perspective of cost and ease of manufacture.

The most commonly used piezoelectric ceramic is lead zirconate titanate Pb(TixZr1-x)O3

(PZT). From many years, these lead-based ceramics have been used in devices requiring piezoelectric components because of its exceptional electro-mechanical properties over broad environmental conditions, ease of processing and cost-effectiveness [1, 10, 11].

Due to international concern to remove toxic substances from every day devices, the

European Union passed the Waste Electrical and Electronic Equipment (WEEE) and

Restriction of the use of certain Hazardous Substances in electrical and electronic equipment (RoHS) in 2003 [12, 13]. China has implemented a set of legislations on lead containing materials by the Ministry of Industry and Information Technology of the

People’s Republic of China [6]. Japan has also imposed some restriction on lead based materials using in electrical and electronic devices [14]. Due to these legislative requirements driven by the known biological harmful effects of Pb to the environment, it is necessary to develop lead-free piezoelectric materials with comparable properties to

PZT.

Over the past years many researchers have studied lead-free piezoelectric materials, attempting to enhance their properties, including the piezoelectric constant, coercive field, Curie temperature and electromechanical coupling factor. Although promising piezoelectric materials have been developed, no single lead-free piezoelectric material has been identified for the replacement of PZT over the wide operating conditions that it is currently used for. A review of the existing lead-free piezoelectric materials is provided in Section 2.2. To further improve the electro-mechanical properties of these

2 lead-free materials will require deep knowledge about the underlying structural origin of electric-field-induced strain generation. The field-induced macroscopic strain in piezoelectric materials has been shown to originate from at least three possible contributions: (i) intrinsic piezoelectric lattice strain, (ii) extrinsic electric-field-induced non-180° domain wall motion, and (iii) induced phase transformations [15-17].

Piezoelectric lattice strain is generated due to local atomic displacements within the unit cell under an external field. Additionally, lattice strain can originate from the compliance of the polycrystalline materials with other strain mechanisms in surrounding grains [18, 19]. These other strain mechanisms are generally considered extrinsic, and are the result of non-180° domain wall motion and/or crystallographic phase transformations where a spontaneous strain component is reoriented under field.

The above mentioned structural contributions to the macroscopic strain in polycrystalline piezoelectric materials under mechanical, electrical or magnetic fields are more complex than in a single crystal or statistical average of single crystal behaviour over all orientation space. Considering only the converse piezoelectric response, a mono-domain single crystal will respond to an external electric field by a lattice strain associated with the intrinsic piezoelectric effect only. In the case of a poly- domain single crystal, the response will come from both electric-field-induced lattice strain and extrinsic strain associated with non-180° domain wall motion. Electric fields may also induce phase transformations within crystalline materials. The magnitude of macroscopic strain in a single crystal material that undergoes non-180° domain wall motion or a phase transformation is related to the volume of material that reorients or transforms, and the magnitude of the spontaneous strain along the measurement direction. The mechanisms which couple these strains between individual grains within

3 the polycrystalline state are still not fully understood.

X-ray and neutron diffraction techniques are very useful tools to observe these underlying electro-mechanical coupling mechanisms in piezoelectric materials. Using these techniques, we can identify the structural symmetry, crystallographic and domain texture, and intrinsic lattice strain. The intrinsic strain component can be calculated from diffraction peak position shifts while extrinsic strain caused by non-180° domain wall motion or phase transformations is quantified from diffraction peak splitting, broadening and relative intensity changes of symmetry dependent reflections during the application of a field.

When studying functional materials, observing the structural changes during the actuation process is necessary for gaining a complete picture of the structure-property relationship as certain mechanisms may be meta-stable during actuation. In the past, research in the field of functional materials has benefitted from the development of bulk sensitive in situ high-energy (> 60 keV) X-ray scattering in transmission geometry [19-

21], and in situ neutron scattering [22-25]. These probes can transmit through mm sized samples. In situ low-energy studies in reflection geometry using laboratory-based X-ray instruments, and synchrotron X-ray sources have also been previously used [26-29].

Low energy X-rays can penetrate only a few 10’s of micrometres into the material and therefore only provides information from the surface grains, while high-energy X-rays probe the bulk of the sample. Contrasting the results of in situ measurements using both methods provides information regarding the constraints from the neighbourhood grains and its potential influence on bulk properties.

The aim of this research is to understand the electro-mechanical coupling mechanisms at microscopic length scales in polycrystalline piezoelectric ceramic materials, and to identify the structural origin that leads to improved properties at morphotropic phase boundary (MPB) compositions.

This thesis consists of the following components:

 Chapter 2 presents a literature review outlining electro-mechanical coupling

mechanisms in polycrystalline piezoelectric ceramic materials, characterisation

methods to identify the structural origin of the generated strain during the

application of external field and, the structure-property relationships in existing

lead-free systems.

 Chapter 3 presents the ceramic sample preparation process.

 Chapter 4 shows the development of a sample cell for in situ electric-field-

dependent structural characterisation and macroscopic strain measurements. The

sample cell design, calibration, demonstration and capabilities are discussed.

 Chapter 5 presents a study of X-ray diffraction measurements collected from the

surface and the bulk of selected samples to compare piezoelectric properties at

the surface and in the bulk. The underlying electro-mechanical coupling

mechanisms in polycrystalline piezoelectric ceramic materials in different

constraint conditions are also discussed.

 Chapter 6 presents a study of the compositional dependence of stress-induced

phase transitions in BNT-xBT system (where x = 5 to 8 in steps of 0.25) using in

situ high-energy XRD. The structure-property relationships are measured,

compared and discussed a function of BT content.

 Chapter 7 presents a study of the electric-field-induced structural changes in

BNT-xBT system. The structural changes are measured, compare and discussed

as a function of BT content. The stress and electric-field dependent structural

changes in the same composition of BNT-xBT system are also compared and

discussed.

 Chapter 8 presents a general discussion of the overall findings of this study.

 Chapter 9 outlines the conclusions of this study.

 Chapter 10 presents the recommendations for further work in this field.

2 Literature review

In this chapter, a review focusing on several aspects of typical piezoelectric materials is presented, including the composition, structure, piezoelectric properties, fabrication, and characterisation techniques. The aim of this chapter is:

 To summarize the most important fundamental concepts required for the

description and understanding of the electro-mechanical coupling mechanisms

in piezoelectric ceramics as discussed in the present work, and

 To present an overview of preceding work on lead-free piezoelectric materials,

and thereby identify the gaps in research that lead to the objectives of the

present study.

The first part of this chapter discusses the basics of electro-mechanical coupling phenomena in piezoelectric materials and the remaining part elucidates the structure- property relationships in these materials and methods used to characterise these relationships.

2.1 Fundamental of electro-mechanical coupling

The electro-mechanical coupling mechanisms are correlated with the crystal structure and polarizability of the materials. The following Sections will outline these phenomena in dielectrics.

2.1.1 Dielectrics and polarisation mechanisms

The following terms and descriptions of dielectrics are based on the text books of Waser et al. [30].

All the electrical insulator materials are dielectrics. During the application of an electric field, polarisation (P) arises from the dipole moment by rearranging the charge distribution. Ceramic materials are generally insulators and polarisation can be induced by the influence of an electric field. In the case of a perfect dielectric, the total polarisation at an external electric field (E) is as follows,

푃 = 휀0 ∙ 휒 ∙ 퐸 (2.1)

Where ε0 is the permittivity of the vacuum, χ is the dielectric susceptibility.

Polarisation and the dielectric displacement (D) are interrelated by,

퐷 = 휀0 ∙ 퐸 + 푃 (2.2)

Furthermore, the dielectric susceptibility can be expressed by the relative dielectric constant 휀푟,

휒 = 휀푟 − 1 (2.3)

Primarily there are four types of polarisation mechanisms involved in dielectrics, including electronic (displacement of negatively charge electron shell against positively charge core), ionic (displacement of the positive and negative sublattices in ionic crystals), orientation (alignment of dipoles along field direction) and space charge

(spatial inhomogeneity of charge carrier densities), as illustrated in Figure 2-1.

The average dipole moment (푃푎푣) of the dielectric is proportional to the applied electric field as follows,

′ 푃푎푣 = 훼 ∙ 퐸 (2.4)

Where α is the polarizability and 퐸′ is the local electric vector.

Figure 2-1 Illustration of different types of microscopic polarisation mechanisms. (a) electronic, (b) ionic, (c) orientation and (d) space charge (after Ref. [30, 31])

2.1.2 Piezoelectricity

Piezoelectricity was discovered by Jacques and Pierre Curie in 1880 [32]. Among 32 crystal classes material 20 crystal classes materials shows piezoelectric properties.

Classification on the basis of crystal classes is shown in Figure 2-2.

Figure 2-2 Classification of materials on the basis of crystal system

The piezoelectric effect is characterized by the coupling between electrical and mechanical energy. Electric charge generates during the application of a stress (direct piezoelectric effect) and strain generates at the application of an electric field (converge piezoelectric effect) which is schematically shown in Figure 2-3.

Figure 2-3 Behaviour of piezoelectric material under (a) applied mechanical stress

(direct piezoelectricity) and (b) applied electric field (converse piezoelectricity). The dotted line and solid line indicates the initial and final position, respectively.

The response of piezoelectric material during the application of a stress is described by,

Di = dijk σjk (2.5) and during the application of an electric field is given by,

εjk = dijk Ei (2.6)

Where,

D = dielectric displacement d = piezoelectric coefficient

σ = stress = applied load / area

ε = strain = change of length / initial length

E = applied electric field

2.1.3 Ferroelectricity

Ferroelectric materials poses spontaneous polarisation which can be switched by the application of a sufficiently large external fields. The spontaneous polarisation is a result of the positioning of the cations and anions, which intrinsically exists within a material in the absence of the application of an external field.

The ferroelectric materials associated with the current project have the ABO3 perovskite crystal structure. Generally, spontaneous polarisation is due to the B site atomic displacement. During heating, ferroelectric materials exhibit phase transformations from a polar to a non-polar state at temperatures above a critical temperature (the Curie temperature, Tc).

The characteristics of polarisation and/or strain (from Figure 2-4) can be described as follows:

At point A: Initial state, the net macroscopic polarisation is zero due to random orientation of domains.

From point A to B: During the application of an electric field (positive bias), at small values of electric field polarisation increases linearly. The electric field is not strong enough to cause domain wall motion so that here only have intrinsic lattice strain comes from lattice distortion. At or above certain electric field amplitude (Coercive field, Ec) domain wall motion and crystal expansion occurs simultaneously and polarisation increases non-linearly.

12 electric field), Smax = strain value achieved at the maximum electric field, Srem = strain measured at the remnant state, Susable = Smax - Srem = usable strain measured from the difference between maximum strain and remnant strain.

From point B to C: As the electric field is further increased, polarisation increases from point B to point C. At point C, maximum possible alignment for domains is achieved and this polarisation is called saturation polarisation (Ps) and from point A to point C is called poling.

From point C to D: During decreasing the electric field, polarisation decreases and reaches remnant state (Prem) at zero electric field.

From point D to E: With further decrease of the applied electric field (negative bias) a polarisation reversal occurs and at certain negative electric field (-Ec) amplitude the net polarisation becomes zero.

From point E to F: With further increase the negative electric field again a saturation region achieved at point F like state of C but opposite orientation of domains.

From above discussion, there are two types of strains generated during the application of an applied field in the piezoelectric ceramic materials which can be classified as intrinsic and extrinsic strains [15-17]. Generally, intrinsic strain is shown as lattice strain which is generated due to local atomic displacements within the unit cell.

However, it has been shown that the lattice strain can also originate from the compliance of the polycrystalline materials with other strain mechanisms in surrounding grains [18, 19]. Extrinsic strain generates due to non-180° domain switching, and/or induced phase transformations.

Strain generation mechanisms in piezoelectric ceramics are shown in Figure 2-5. In the as-processed state, the domains align randomly in the piezoelectric ceramics. Under the application of an electric field, domains start to reorient along the electric field direction and crystalline unit cell elongates towards the field direction.

Domain wall motion depends on a number of factors including:

 Non-180° domain wall motion depends on composition and the type of dopant.

The addition of donor type dopants decreases oxygen vacancy and therefore,

promotes non-180° domain wall motion. On the other hand, the addition of

acceptor type dopants increases the oxygen vacancies which inhibit the non-

180° domain wall motion [34]. Oxygen vacancy increases local energy

distortion which increases required energy to move the domain walls. In the

case of PZT, it was shown that the addition of La (donor type dopant) increases

piezoelectric coefficient (d33) while the doping with Fe (acceptor type dopant)

2+ 3+ decreases d33 [35]. Substitution of Pb with La decreases the oxygen

vacancies which cause enhances domain wall motion. On the other hand

substitution of Zr4+/Ti4+ with Fe3+ increases the oxygen vacancies which cause a

decrease in the domain wall motion.

 Domain wall motion also depends on the existing phases in the materials and

size of the domains. Non-180° domain wall motion is higher in rhombohedral

phase than in tetragonal phase because residual stress is higher in tetragonal

phase compared to rhombohedral phase [36]. Non-180° domain wall motion is

higher in the bigger domains than in smaller ones [36].

Figure 2-5 Crystallographic representation of strain generation mechanisms in piezoelectric ceramics as an example of PZT, (a) at initial state and (b) at applied electric field (after Ref. [37]).

Generally nonlinear electro-mechanical responses in ferroelectric ceramics are observed above the coercive field. However, Hall et al. has reported nonlinear electro-mechanical response under subcoercive electric field or mechanical stress [36]. The main reason for getting nonlinearities at subcoercive field is overcoming the local energy barrier by non-

180° domain walls. All kinds of defects and residual stress in the materials act like energy barrier.

Modes of coupling between applied fields and resultant strains are different in polycrystalline ceramics than in the single crystal due to the effect of constraints of the neighbourhood grains. The constraint of the polycrystalline materials is one of the limiting factors in material performance. Understanding of the underlying electro- mechanical coupling mechanisms in polycrystalline piezoelectric ceramics is still not complete. 15

2.1.4 Relaxor ferroelectricity

The phenomenon of relaxor ferroelectricity is closely related to conventional ferroelectricity. Relaxor ferroelectrics (RF) also exhibit strong piezoelectric coupling and large field-induced strain like ferroelectrics (FE). Generally, relaxor ferroelectricity arises from compositional disorder [38]. The inherent differences between FE and RF in several aspects are summarised in Figure 2-6.

The first difference can be described by the dielectric permittivity behaviour as a function of temperature (see Figure 2-6(a)). Conventional ferroelectrics exhibit sharp maximum amplitude of relative permittivity at Curie temperature (Tc) while relaxor ferroelectrics have a broad dielectric maximum and a significant frequency dispersion of the relative permittivity. The magnitude of the relative permittivity decreases and the maximum temperature (Tm) of the dielectric constant increases with increasing frequency. Polarisation and strain as a function of applied electric field of these two systems show distinct behaviour (Figure 2-6 (b) and (c)). Conventional FE show wide rectangular shaped P-E hysteresis loops with a large remnant polarisation whereas, RF exhibit a slim P-E loops with negligible remnant polarisation. Strain vs electric field curve shows a butterfly shape for FE while a sprout shape for RF. Additionally, FE have a significant remnant strain while RF shows no remnant strain.

Figure 2-6 Comparison of ferroelectrics (FE) and relaxor ferroelectrics (RF) in terms of

(a) relative permittivity as a function of temperature, (b) polarisation and, (c) strain as a function of applied electric field (after Ref. [39]).

Relaxor ferroelectrics are typically characterised by a pseudo-cubic average structure and strong structural disorder [40, 41]. This disorder generally arises from chemical disorder and the majority of the relaxor ferroelectrics are compositionally disordered on one or more atomic sites. Due to this disorder, polar nanoregions (PNRs) (clusters) with diameter of approximately 10 nm to 100 nm are formed in the materials [30]. Because of these PNRs, many relaxor ferroelectrics have transformed to long-range order ferroelectrics under applied external fields [42]. Surprisingly, this metastable phase

(PNRs) exists for a large temperature range; therefore, RF can be used in wide operational temperature range.

However, a comprehensive understanding of the coupling mechanisms behind relaxor ferroelectricity is still lacking [40, 41, 43-46]. Many models have been proposed to describe the mechanisms of relaxor ferroelectricity [40, 43, 47-51]. Bokov and Ye

17 provided a comprehensive overview on these models [41]. Despite these models and experimental results, there is still controversy on the origin of order-disorder transition and the existence of PNRs in relaxor ferroelectrics.

2.2 Lead-free piezoelectric ceramics

This section presents a brief overview of some common lead-free piezoelectric ceramic materials; in particular the compositions are of most interest to the current thesis. For a detailed review of other promising lead-free compositions one can refer to Ref. [52].

The most interested (on the basis of this work) lead-free piezoelectric systems are,

 Bismuth sodium titanate, Bi1/2Na1/2TiO3 (BNT)

 Barium titanate, BaTiO3 (BT)

 Solid solution of BNT-BT

2.2.1 Bismuth sodium titanate

Bismuth sodium titanate Bi1/2Na1/2TiO3 (BNT) was discovered by Smolenskii et al. in

1961 [53]. BNT is one of the promising lead-free piezoelectric ceramic materials and the base compound for a large family of BNT-derived lead-free piezoelectric ceramics.

Generally, BNT is hard to pole mainly due to the evaporation of bismuth during the sintering which lead to an increased oxygen vacancy density and consequently elevated conductivity [54]. Dense BNT ceramics can be obtained using conventional or hot- pressing sintering process with properly excessive addition of Bi2O3. The electro- mechanical properties of BNT are summarised in Table 2-1.

Table 2-1 Properties of BNT (Ref. [55])

Parameter Value

Coupling factor 푘33 0.459

Relative Intensity εr, 33 583

Piezoelectric constant 푑33 (pC∕N) 72.9

E -12 2 8.32 Elastic compliance 푆33 (10 m ∕N) D -12 2 6.57 Elastic compliance 푆33 (10 m ∕N)

Takenaka et al. reported, a coercive field Ec of 7.3 kV/mm and a remnant polarisation

2 푃rem of 38 µC/cm for pure BNT ceramics [56]. Later others reports are in good agreement with these values [57, 58]. The reported maximum strain is only 0.09% during the unipolar electric field cycling at a maximum amplitude of 7 kV/mm [59].

The Curie temperature of pure BNT ceramic is 310 °C [60]. Main drawbacks of pure

BNT are high coercive field, high electrical conductivity and low depolarisation temperature of 187 °C [61].

There have been some debates on the crystal structure of BNT at room temperature. In the first paper by Smolenskii et al., the room temperature crystal structure of BNT was reported to be cubic perovskite with a lattice parameter of 3.88 Å determined using X- ray diffraction [53]. Jones and Thomas observed a rhombohedral crystallographic phase with R3c space group which exhibit three different phases at different temperatures using neutron diffraction [62]. In other words, BNT undergoes a sequence of phase transition from high temperature cubic (푃푚3푚) phase to a tetragonal (P4mm) phase at

540 °C, and tetragonal phase to rhombohedral (R3c) phase between 200 °C and 300 °C.

Recently Aksel et al. showed that the room temperature crystal structure of BNT is 19 monoclinic (Cc) rather than rhombohedral (R3c) using high resolution XRD [63]. An electron diffraction study by Dorcet et al. [64] and a neutron diffraction study by Liu et al. [65] reported that the room temperature crystal structure is not pure rhombohedral.

These differences are mainly due to the complex crystal structure of the BNT resulting from the chemical ordering of the Bi/Na cations, displacements of cations and the local and average structure difference [66-68].

2.2.2 Barium titanate

Barium titanate (BT) is one of the perovskite type ceramics which was discovered in

1941 [69]. BT has very high electro-mechanical coupling factor 1400 and its piezoelectric constant is 140 pC/N [60]. Because of its low Curie temperature it cannot be used above 120 °C [70]. However many studies have been done to increase its Curie temperature but still not observed [6, 71].

2.2.3 BNT-BT solid solution

The first investigation of (100-x)BNT-xBT (BNT-xBT) (where x = 0 to 30) was reported by Takenaka et al. [72]. They reported a morphotropic phase boundary (MPB) between x=6 and x=7 by measuring dielectric and piezoelectric properties. They observed rhombohedral and tetragonal phase coexistence at the MPB using XRD analysis. A phase diagram of the BNT-xBT system has also been proposed involving ferroelectric, antiferroelectric and paraelectric phases. However, Ranjan and Dviwedi

[73] as well as Garg et al. [74] reported a composition dependent rhombohedral to nearly cubic structural phase transition for BNT-6BT. Simons et al. [16] using in situ neutron diffraction, Daniels et al. [75] and Khansur et al. [76] using in situ X-ray

20 diffraction and, Hinterstein et al. [77] by using transmission electron microscopy

(TEM), neutron and X-ray diffraction showed that near the MPB compositions of BNT- xBT system undergo pseudo-cubic to tetragonal or mixed phase of tetragonal and rhombohedral symmetry during the application of an electric field.

Jo et al. reported a phase evolution in BNT-xBT (0 ≤ x ≤ 15) compositions for both unpoled and poled state [78]. They observed that range of compositions from BNT-6BT to BNT-11BT transform from rhombohedral to rhombohedral and tetragonal mixed phase symmetry. The Maximum piezoelectric property was reported for BNT-7BT which is similar to the study with Takenaka et al. [72]. Later, Ma et al. reported a modified MPB with phase diagram for this materials system using in situ TEM [79].

The solid solution of BNT-xBT based system has attracted wide research interest in the scientific community as a potential high-strain lead-free piezoelectric material [6, 80-

83]. The improved piezoelectric properties of this material system are of great interest and knowledge of the coupling mechanisms in this system will help to further improve the electro-mechanical properties of lead-free piezoelectric compositions for future applications.

2.3 Diffraction methods for studying piezoelectric ceramics

X-ray diffraction (XRD) methods are very powerful experimental techniques to observe underlying electro-mechanical coupling mechanisms in piezoelectric materials.

Crystallographic structure, phase evolution, lattice strain and domain texture can be studied using this technique. This is a non-destructive characterisation method and can be used to study single crystals, bulk polycrystals and thin films. 21

Figure 2-7 Material responses during the application of a field in piezoelectric materials.

Figure 2-7 shows the effect of an applied filed on XRD patterns of a piezoelectric material. The field induced intrinsic lattice strain resulting from the distortion of the unit cell can be examined from diffraction peak position shifts (∆2θ) while the domain texture can be analysed from relative peak intensity changes. Phase transformation can also be analysed from the observation of the changes or evolution in the diffraction patterns.

The above mentioned field-induced changes can be observed using ex situ XRD measurements. In ex situ technique, XRD data are collected from the sample in the as- processed state and after electrical poling state and, a comparison of these data provides the information about the structural changes and property. Ex situ measurements cannot 22 provide the information at the intermediate steps during the application of field. Some fraction of the structural processes in piezoelectric materials can be time-dependent and reversible during actuation [20, 22, 23, 84-86]. Thus, to allow a complete understanding of the structural mechanisms in piezoelectric materials it is necessary to measure diffraction patterns during the application of a field. In other words in situ measurements of piezoelectric materials under field are necessary to observe the structural changes in real environments.

In situ low-energy (< 30 keV) X-ray studies using laboratory-based X-ray instruments and synchrotron X-ray sources in reflection geometry have been conducted previously to observe the coupling mechanisms in piezoelectric materials [26-29, 87]. Low-energy

X-rays penetrate only a few micrometres into the material from the surface, therefore only provide information from the surface grains. In our experimental setups the

Powder Diffraction beamline of the Australian Synchrotron is used. A linear Mythen detector [88, 89] is used to collect the diffraction data. Low-energy diffraction measurements which are restricted to reflection geometry can provide useful insight into the magnitude of the lattice strain for certain crystallographic orientations which lie parallel to the applied field directions; however they do not provide full access to all scattering vector orientations relative to an applied field vector.

The advantages of current XRD measurements using low-energy synchrotron X-rays and a Mythen detector are:

 Penetration depth is low that allows probes from the surface of materials

 High energy resolution, E = 4  10-4 keV

 High intrinsic angular resolution 0.004°

 Large angular 2θ coverage 120°

 Low readout time 250 µs

 Simple experimental setups for in situ measurements

In situ high-energy (> 60 keV) X-ray scattering measurements in transmission geometry have also been used to observe the coupling mechanisms in piezoelectric materials [15,

19-21, 78, 90, 91]. The incident high-energy beam can transmit through millimetre sized samples providing information from the bulk of the sample. In these experimental setups two-dimensional large area detectors are used to collect the diffraction images

[92]. The combination of high energy X-rays and a large area detector facilitates recording a large number of entire Debye-Scherrer rings in a comparatively small 2θ range.

The advantages of using high-energy X-rays combining with a large area detector are:

 Large penetration depth into the materials providing information from the bulk

 Full strain and texture information can be collected rapidly

 The experimental geometry allows for complex sample environments which can

be transmitted by the beam

 Simple experimental setup for in situ measurements

 Large numbers of Debye-Scherrer rings can be collected simultaneously

2.3.1 Considerations for in situ measurements

During the in situ diffraction measurements it is required to have rapid data collection to

24 avoid creep effects and electrical breakdown of the samples. We have performed laboratory based measurements in order to test our collection strategies. For the lab X- ray instrument used, it takes 40 minutes to collect the full diffraction pattern which is not suitable for detailed in situ field dependent measurements. Additionally, we would ideally like the data collection time of high and low-energy XRD to be approximately the same in order for meaningful comparison between bulk and surface property.

Therefore in situ low-energy and high-energy synchrotron XRD measurements have been done under electric field to compare the surface and bulk properties and identify the mechanism differences at the surface and in the bulk for same samples. In situ high- energy synchrotron XRD measurements have been done under stress and electric field for same samples to observe the structure-property relationships during the application of a field.

3 Experimental procedure

3.1 Fabrication method of ceramic materials

Processing methods for the ceramics consists of powder preparation, green compact, sintering and machining. The solid state synthesis route was used to prepare all ceramic samples in this work. Sample preparation steps are schematically shown in Figure 3-1.

Figure 3-1 Flow diagram of sample preparation steps.

Some details of the sample preparation are:

 Powder preparation: The oxide powders including bismuth (iii) oxide (Bi2O3),

titanium (iv) oxide (TiO2), barium carbonate (BaCO3) and sodium carbonate

(Na2CO3) were mixed according to stoichiometric ratios of the target

compositions. The details of used chemicals are listed in Table 3-1. Planetary

ball milling was carried out with 5 mm diameter ZrO2 ball (2/3 volume fraction

of container) in 100% ethanol media for 72 h to mix properly. It is also 26

confirmed that Zr contamination from ball milling does not develop secondary

phases. The resulting slurry and zirconia balls were separated and then the slurry

was placed inside an oven at 100 °C to dry. After drying, calcination was carried

out to remove organics, water and volatiles. During calcination, the temperature

ramps were 5 °C/min for all the stages. In the first stage, holding time was 5 min

at 100 °C to remove moisture from the powder, in the second stage, holding time

was 2h at 700 °C to decompose carbonate and finally in the third stage, holding

time was 3 h at 800 °C to complete phase formations and then cooled to room

temperature at 5 °C/min. The calcined powder was ball milled using 5 mm

diameter ZrO2 ball in 100% ethanol media for 72 h and then slurry was dried in

the oven at 100 °C and subsequently crushed to a finer powder using mortar and

pestle.

 Green compact: 3-4 g ceramic powder was put into 10 mm diameter dye and

pressed at 15 kN force using uniaxial pressing for 10 s and, then pressed by cold

isostatic press (CIP) at 300 Mpa for 30 s.

 Sintering: 10 mm diameter BNT-BT green samples were put on the lid and

covered with alumina crucible. Samples were sintered at 1130 °C for 3 h in an

air atmosphere. Temperature was increased from room temperature to 1130 °C

at a ramp rate of 5 °C/min, and then held at this temperature for 3 h followed by

cooling to the room temperature at a rate of 5 °C/min. The final diameter of the

sintered samples was approximately 8 mm.

3.1.1 Sample preparation for low-energy XRD

 Polishing and grinding: One of the parallel sides of the disc shaped samples was

polished using polishing paper from P180 to P4000 (2.5 µm) and then using 1 µm 27

diamond slurry. The other side of the sample was polished using polishing paper up

to P1200 (15.3 µm). After polishing, samples were cleaned by ultrasonic cleaning

in ethanol solution for around 5-10 min at room temperature. Then washed using

water and dried.

 Annealing: All the samples were put on a hot plate for annealing at a temperature of

400 °C for 30 min in air and subsequently cooled down to room temperature with

the samples on the hot plate.

 Electroding: One of the parallel surfaces of the sample disc was sputtered (high

voltage 500 V, current 40 mA with a duration 110 s. in argon gas atmosphere) with

a gold film with a thickness of approximately 45 nm in order to allow the

penetration of the low-energy X-ray (~ 10 keV) beam into the sample surface. The

other side of the sample was covered with the silver paste as an electrode. Electrode

(silver paste) was painted such that it covered the sample up to approximately 1

mm from the periphery of the sample to avoid current leakage or sample arcing at

the edges during electrical loading. A picture of surface electrode is shown in

Figure 3-2.

Figure 3-2 Pictures of (a) bottom and (b) top surface electrodes

Table 3-1 Chemicals used for sample preparation

Chemicals Purity (%) *CAS# Company

Bi2O3 99.8 1304-76-3 Aldrich

BaCO3 99.98 513-77-9 Aldrich

Na2CO3 99.5 497-19-8 Sigma-Aldrich

TiO2 99.7 1317-70-0 Aldrich

*Chemical Abstracts Service, a division of the American Chemical Society. Provides unique numerical identifier for chemical elements

3.1.2 Sample preparation for high-energy XRD under electric field

The following steps were taken to prepare the samples for high-energy XRD;

 Cutting: Disc shaped samples were mounted on ceramic bar with glue and cut

into a bar with dimensions of 1 × 1 × 6 mm3 using a high-speed diamond saw at

4000 rpm and 0.025 mm/s stroke.

 Removing glue: Samples were put into the chloroform solution around 6 h to

remove the glue from samples.

 Grinding and polishing: parallel surfaces 1 × 6 mm2 of the samples were

polished using polishing paper from P180 to P4000 (2.5µm).

 Cleaning: Samples were cleaned using ultrasonic bath with ethanol solution for

5-10 min and then were washed by water and dried.

 Electroding: Two parallel surfaces of 1 × 6 mm2 were electroded using silver

paste.

3.1.3 Sample preparation for high-energy XRD under stress

 Cutting: Disc shaped samples were mounted on ceramic bar with glue and cut

into a cube with dimensions of 1 × 1 × 1 mm3 using diamond saw at 4000 rpm

and 0.025 mm/s stroke.

 Removing glue: Samples were put into the chloroform around 6 hour to remove

the glue from samples.

 Grinding and polishing: Two parallel surfaces of the samples were polished

using polishing paper from P180 to P4000 (2.5 µm).

 Cleaning: Samples were cleaned by ultrasonic bath with ethanol solution for 5-

10 min and then were washed by water and dried.

In order to confirm the quality of the processed materials full XRD patterns have been collected in the as synthesised state (before application of field), and are shown in

Figure 3-3. All samples were confirmed to be phase pure perovskites. It is also confirmed that Zr contamination from ball milling does not develop secondary phases.

Figure 3-3 XRD patterns of BNT-xBT compositions for the as synthesised state.

3.2 Experimental methods

3.2.1 Macroscopic property measurements

The macroscopic piezoelectric properties of the samples were measured using a standard macroscopic strain measurement system (TF Analyzer 2000 system; aixACCT

Systems GmbH, Aachen, Germany). The experimental setup is schematically shown in

Figure 3-4. The major parts of this experimental setup are high voltage amplifier, function generator, oscilloscope, and strain sensor.

Figure 3-4 Schematic diagram of experimental setup for macroscopic strain and polarisation measurements (after Ref. [93])

Using this experimental setup mainly polarisation vs. applied electric field, macroscopic strain vs. electric field were measured to know the coercive field and macroscopic behaviour of produced ceramics samples for the in situ measurements.

3.2.2 In situ low-energy XRD

Low-energy (< 30 keV) X-rays penetrate only a few micrometres into the material therefore provide information from the surface grains. In situ low-energy X-ray scattering experiments were carried out at the Powder Diffraction beamline of the

Australian Synchrotron [94] using a monochromatic beam of energy 12.4 keV

(wavelength approximately 1 Å). The wavelength was determined by the Rietveld refinement of data from a diluted LaB6 660b Standard Reference Material (NIST, USA) collected in Debye-Scherrer geometry using the software package Topas V4.2. An X- ray beam of resolution E = 4  10-4 keV was selected by a Si (111) flat crystal pair monochromator. A one dimensional silicon microstrip-based detector Mythen [88, 89] was used to collect the diffraction patterns with intrinsic angular resolution of 0.004°, covering a 2 range of 80° and readout time of 250 µs. The experimental setup is shown schematically in

Figure 3-5 (a) and the picture of the experimental setup with sample cell is shown in

Figure 3-5 (b). The electric field was generated using a function generator (Agilent

33220A) and input to the HV power supply (Trek 10/10B-HS). The data acquisition system recorded the measured output of the displacement sensor and output voltage of the HV power supply. XRD data were collected in reflection geometry using the

Mythen detector during the application of bi-polar electric fields with the samples mounted in a specially developed cell (the details of the sample cell will be discussed in

Chapter 4).

In our experimental setup as shown in

Figure 3-5(b), the electric field direction was always perpendicular to the sample surface. In this geometry of the measurement, the incident angle of X-ray beam is adjusted by tilting the sample stage to make it equal to half of the Bragg angle of the recorded characteristic reflections. During the measurements the electric field vector was aligned approximately perpendicular to the 111 or 200 lattice planes. Therefore the diffraction information was collected along the electric field direction.

3.2.3 In situ high-energy XRD

High-energy (> 60 keV) X-rays can transmit through millimetre sized samples and provide information from the bulk of a material. In situ high energy X-ray scattering experiments were carried out at the ID15 beamline of the European Synchrotron

Radiation Facility (ESRF), France. Mechanical stress and electric field were applied in two different experimental setups. The details of the measurements and data analysis are described in the following sections.

3.2.3.1 In situ high-energy XRD measurements under stress

A schematic of the experimental setup is shown in Figure 3-6. An X-ray beam with energy of 73 keV (wavelength λ=0.171 Å) and dimensions 200×200 μm2 was used.

Samples were placed in specifically designed in situ sample cell where compressive stress can be applied perpendicular to the X-ray beam direction [95]. A unipolar triangular compressive stress field waveform with a maximum amplitude of approximately 600 MPa was applied to the sample perpendicular to the incident beam direction. Simultaneously X-ray diffraction images were collected using Pixium 4700

35 large area detector [92]. Full orientation dependent data with respect to scattering vector

(q) angle to the applied electric field vector (E) can be rapidly collected in a single diffraction image using this large area detector.

Figure 3-6 Schematic diagram of in situ high-energy X-ray scattering experimental setup. Unipolar compressive stress was applied perpendicular direction to the X-ray beam direction.

3.2.3.2 In situ high-energy XRD measurements under electric field

The experimental setup is shown schematically in Figure 3-7. An X-ray beam energy of

73 keV (wavelength λ=0.171 Å) and dimensions of 200×200μm2 was used. Samples were placed in a specifically designed sample cell where the electric field was applied perpendicular to the X-ray beam direction [20]. A bipolar triangular electric field waveform cycle was applied to the sample within the sample cell while the diffraction images were collected in the transmission scattering direction using a Pixium 4700 large area detector [92].

3.2.3.3 Data Processing

3.2.3.3.1 Low-energy XRD

One dimensional intensity vs 2θ diffraction patterns for each field step were obtained from the measurement. These diffraction patterns were analysed to get the information for each field step.

3.2.3.3.2 High-energy XRD

Using the software package FIT2D [96], instrumental parameters; sample to detector distance, detector tilts and beam centre were calibrated using diffraction patterns of standard Ceria powder (NIST standard-CeO2) using the identical experimental setup.

The information from calibrated data was used for integrating the diffraction images. 37

The two dimensional detector images were radially segmented into 36 parts with a 10° interval azimuthally and integrated using FIT2D to obtain one dimensional 36 diffraction patterns for specific orientation with a 10° increment. In other words, for each field step we got 36 diffraction patterns. These one dimensional intensity vs 2θ diffraction patterns were analysed to get information for each field step as well as for all direction.

3.2.4 Data analysis

In order to measure the structural changes in piezoelectric materials during the application of fields, the peak intensities and the 2θ positions of the hkl reflections were determined. Peak fitting procedures have been used to quantify field-induced lattice strain and domain texture from the diffraction data. In the case of tetragonal or rhombohedral phase, the field-induced domain texture can be quantified by fitting 200 or 111 type reflections, respectively. Figure 3-8 shows the example fitting of 200 type reflections for a tetragonal phase materials.

The diffraction patterns were fit individually with suitable peak profile shape functions using software package Igor Pro 6.37 to find the diffraction peak intensities, peak positions, peak areas and widths as a function of an applied field and orientations.

Different types of peak profile shape functions were used to fit the different hkl reflections. Peak shapes were different as a function of field as well as scattering vector direction with the field direction. Details about the used peak profile shape functions to the fit the diffraction peaks will be discussed separately in Chapter 4, Chapter 5,

Chapter 6, and Chapter 7.

Figure 3-8 The fit of (200) type peaks in tetragonal phase piezoelectric ceramics

Fitted peak positions were used in the following equation to calculate the microscopic lattice strains,

휀ℎ푘푙 = ∆휃 cot 휃 (3.1)

Where,  hkl is the lattice strain of the hkl plane, ∆θ is the difference of brag peak positions in the initial state and after the application of a field. θ is the brag peak position at the applied field stage.

Peak intensity and widths were used to calculate relative peak intensity ratio and full width half maxima (FWHM), respectively, as a function field amplitude to quantify the extrinsic non-180° domain wall motion and/or phase transformation (Chapter 5, Chapter

6 and Chapter 7).

The phase fractions and multiples of random distribution (MRD) of the reflections were determined by combined texture Rietveld refinements with the weighted strain orientation distribution function (WSODF) strain model [97] and Exponential Harmonic texture model [98] using the program “Materials Analysis Using Diffraction ” (MAUD)

[99] to describe the structure changes as a function of field and scattering vector to the applied field direction (Chapter 6 and Chapter 7).

4 Development of a cell for in situ electric-field-dependent structural

characterisation and macroscopic strain measurements

A manuscript based on the results presented in this Chapter has been published in the

Journal of Synchrotron Radiation (2016, 23, doi:10.1107/S1600577516005075).

Abstract

When studying electro-mechanical materials, observing the structural changes during the actuation process is necessary for gaining a complete picture of the structure- property relationship as certain mechanisms may be meta-stable during actuation. In situ diffraction methods offer a powerful and direct means of quantifying the structural contributions to the macroscopic strain of these materials. Here, we demonstrated a sample cell capable of measuring the structural variations of electro-mechanical materials under applied electric field using low-energy X-ray scattering techniques in reflection geometry, while simultaneously collecting macroscopic strain data using a linear displacement sensor. The results show that the macroscopic strain measured using the cell can be directly correlated with the microscopic response of the material obtained from diffraction data. The capabilities of the cell have been successfully demonstrated at the Powder Diffraction beamline of the Australian Synchrotron, and the potential implementation of this cell with laboratory X-ray diffraction instrumentation is also discussed.

4.1 Introduction

The structural origin of macroscopic piezoelectricity has been the topic of intense investigation over many decades. The electric-field-induced macroscopic strain in

41 piezoelectric materials has been shown to originate from three possible contributions: (i) intrinsic piezoelectric lattice strain, (ii) extrinsic non-180° domain switching, and (iii) induced phase transformations [15-17]. X-ray diffraction (XRD) analysis is a very useful tool to observe each of these underlying electro-mechanical coupling mechanisms in piezoelectric materials. The intrinsic strain component can be calculated from diffraction peak position shifts and the extrinsic strain caused by non-180o domain wall motion or phase transformations is quantified from diffraction peak relative intensity changes and splitting and/or broadening of symmetry dependent reflections.

Some fraction of these structural processes can be time-dependent as well as reversible during actuation [20, 22, 23, 84-86]. Thus, to have a full understanding of the functional mechanisms in these materials it is necessary to measure diffraction patterns during the application of a field.

In the past, research on functional materials has benefitted from the development of bulk sensitive in situ high-energy (> 60 keV) X-ray scattering in transmission geometry

[20], and in situ neutron scattering [22-25, 100]. These probes provide several experimental advantages; 1) mm sized samples can be used in conjunction with complex sample environments with little absorption, 2) sample displacements during actuation have negligible impact on the results observed, and 3) using large area detectors, full strain and texture information can be collected rapidly. However, each of these methods has disadvantages. For high-energy synchrotron X-rays; 1) access to these sources is limited due to the small number of synchrotron beamlines optimised in this energy band, and 2) optical setups at these beamlines are often optimised for rapid data acquisition, not high resolution, which causes difficulties in observing very subtle structural changes under field. For neutrons, the sample size required for reasonable

42 acquisition times is large (normally in cm3 scale), creating difficulties in the material fabrication and increased probability of sample failure under high electric fields.

Conventional structural characterisation of piezoceramics using low-energy X-ray sources has potential advantages, but presents challenges for in situ sample cell design.

At lower X-ray energies, diffraction studies of polycrystalline piezoelectric materials are restricted to reflection geometry due to the generally high absorption coefficients of the materials of interest.

In situ studies in reflection geometry using laboratory-based X-ray instruments, and synchrotron X-ray sources have been conducted previously [26-29, 101-104]. In these scattering experiments, care must be taken to ensure that the sample surface displacement induced by the field is not influencing the measured strain values. If an applied electric field causes the sample surface to displace relative to the X-ray source and detector positions, a pseudo-strain will result, which needs to be carefully accounted for when interpreting the data. Pramanick and Jones [105] reported a sample surface movement of 4 µm for a 1mm thick sample during the application of an electric field. Therefore due to this surface movement they found an 18% error in the measured lattice strains, much larger than the typical angular resolution of a powder diffraction instrument.

An additional difficulty for all in situ diffraction measurements is that the structural strain mechanisms of piezoelectric materials are often correlated to the measured macroscopic strain collected ex situ. Thus, correlating the underlying mechanism to the macroscopic response directly is difficult to achieve. This can be overcome by incorporating a strain sensor into the in situ measurement cell.

Here, we demonstrate an in situ electric field sample cell that can overcome these primary difficulties by having a fixed position of the scattering surface in addition to an in situ macroscopic strain sensor. The applicability of this newly developed cell has been demonstrated by the electric-field-dependent measurements of commercial soft

PbZrxTi1−xO3 (PZT) and lead-free 0.95(Bi1/2Na1/2)TiO3-0.05BaTiO3 (BNT-5BT) ceramics at the Powder Diffraction beamline of the Australian Synchrotron [94].

Several other samples were measured using this cell, however, BNT-5BT sample is chosen to demonstrate the sample cell. Results show that the developed sample cell offers a new capability to directly correlate the microscopic structural changes observed by XRD with the macroscopic response of electro-mechanical materials under the applied electric field.

4.2 Experimental procedure

4.2.1 Sample cell design

Design considerations for the development of an in situ sample cell for the application of electric fields to ceramic materials in reflection geometry XRD are;

 X-ray scattering surface of sample needs to be static with respect to the X-

ray source and detector positions during the application of electric fields

 The total thickness of the cell must be kept small for versatility to mount on

different X-ray diffraction instruments

 minimum shadowing of the detector arc

 isolation of high voltage (HV) for safety of users and avoiding equipment

damage

 built-in strain sensor enabling the concurrent macroscopic strain

measurement in the diffraction experiment

Figure 4-1 Photograph and schematic drawing of in situ sample cell showing its major components. Lid (1), spring (2), spring stage (3), inner insulating wall (4), base plate

(5), displacement sensor bracket (6), displacement sensor (7), linear stage (8), sample mount (9), HV connector (10), outer wall (11).

An initial prototype cell was fabricated in order to test the ability of the design to hold the target electrical voltages and allow the scattering of x-rays from the surface. Once confirmed, the resulting sample cell design which satisfies the above criteria is shown in

Figure 4-1. The sample stage is connected to the HV amplifier via the HV connector.

The outer wall is connected to the ground and the inner insulation (Machinable Glass

Ceramic, Macor) is sufficiently dimensioned to guarantee no electrical breakdown occurs. The high-voltage wire is connected to a spring through the spring stage, which presses the sample against the lid, maintaining electrical connection to the HV amplifier and thus sustaining the electric field at all times during the measurements with the application of electric fields. It should be noted that the spring will apply some force on the sample during the measurements. This design allows the sample to freely expand without moving with respect to the incident beam or detector. At the same time, the integrated displacement sensor monitors the electric-field-induced macroscopic strain, which can later be directly correlated to the structural measurements. The conical opening angle of the lid with an angular range from 10° to 170° allows observations over a broad range of sample orientations, facilitating the alignment of the electric field direction with respect to the incident beam at the desired angle. At 44 mm in height and base plate dimensions of 80 mm × 90 mm and a total weight of 0.63 kg, the sample stage offers a high versatility for a broad range of synchrotron as well as laboratory X- ray instruments.

The strain sensor used is a fiber optical displacement sensor (type D, reflectance dependent, Model D12-C6ET3T5, Serial Nos. 2719, Philtec, Inc.). The displacement sensor operates in reflection mode with the back surface of the sample stage. During the actuation process the sample expands or contracts and thus the distance between the sensor tip and the back surface of the sample stage will change, resulting in a measurable strain value. This strain sensor can be used to measure the macroscopic strain up to frequencies of 20 kHz; however, the cell spring assembly will have limitations estimated to be in the 100’s of Hz.

4.2.2 Sample preparation

Two types of samples including a soft PZT ceramic (PIC151) and a rhombohedral

BNT-5BT lead-free material were used to demonstrate the capabilities of the sample cell. The PZT ceramic sample is commercially available (PI ceramics, Lederhose,

Germany) and the BNT-5BT sample was prepared by a solid state synthesis route. The details of the synthesis route can be found in the Section 3.1. The top surface of the samples was sputtered with a gold thin film with a thickness of approximately 45 nm. It is thick enough to ensure electric contact and thin enough for ensuring a good penetration of the X-ray beam (~12 keV energy used here) into the sample. The bottom surface of the samples was coated with a silver paint electrode. The details of the sample preparation can be found in Section 3.1.1.

4.2.3 In situ experiment

In situ X-ray scattering experiments were carried out at the Powder Diffraction

beamline of the Australian Synchrotron. A monochromatic X-ray beam energy of

approximately 12.4 keV (wavelength 0.1 nm) was used. A one dimensional silicon

microstrip-based detector Mythen [88, 89] was used to collect the diffraction patterns.

The details of the experimental setup can be found in the Section 3.2.2. XRD data were

collected in reflection geometry using the Mythen detector during the application of

unipolar electric fields with maximum field amplitude of 4.5 kV/mm in steps of 0.45

kV/mm. The diffraction data were acquired in a snapshot mode at each field step. In our

setup as shown in

Figure 3-5(b), the electric field direction is always perpendicular to the sample surface.

In this geometry of the measurement, the incident angle of X-ray beam is adjusted by tilting the sample stage to make it equal to half of the Bragg angle of the recorded 47 characteristic reflections. During the measurements the electric field vector was aligned approximately perpendicular to the 111 or 200 lattice planes. In the case of PZT, the incident X-ray beam angle was 13.3° while for BNT-5BT was 13.75°.

Pseudo-Voight profile shape functions were used to fit individual peaks to extract diffraction peak position, area and width using the software Igor Pro 6.37. Fitted peak positions were used to calculate the material lattice strain. A detail of the lattice strain calculation is discussed in Section 3.2.4.

4.2.4 Calibration of strain sensor

A soft PZT material (PIC151) was used to calibrate the displacement sensor. The reproducible strain response of PIC151 was used to correlate the measured voltages with a macroscopic displacement of the reflective strain sensor target surface. A unipolar triangular electric field waveform with a maximum field amplitude of 2 kV/mm and a frequency of 1 Hz was applied. The macroscopic displacement-electric field curves were recorded using a calibrated macroscopic strain measurement system

(TF Analyzer 2000 system; aixACCT Systems GmbH, Aachen, Germany). The samples were then mounted in the in situ X-ray cell and the distance between the sensor and the target surface was adjusted to set the initial output gain voltage in the centre of the output range of the strain sensor. Electric fields were applied to the sample and the sensor output voltage was recorded simultaneously. Relative movements between the displacement sensor and the target surface were then calculated from the calibrated material strain behaviour. The measured output of the sensor and the displacement of the sample during the application of electric field are shown in the Table 4-1. The initial distance (75 μm shown in Table 4-1) between the target surface and the sensor tip, is 48 assumed from the standard reflectivity curve shown in Figure 4-2. The displacement of the sample was calculated from the displacement vs electric field curve measured using a calibrated macroscopic strain measurement system.

Table 4-1 Measured sensor output, sample displacement and distance between target and sensor tip as a function of applied electric field for PZT.

Electric field Sensor output Sample Distance between the target

(kV/mm) (V) displacement (nm) and tip of sensor (μm)

0 2.4682 0 75 0.5 2.4660 372.23 75 - 0.37223 = 74.63 1 2.4510 757.63 74.24 1.5 2.4330 1158.5 73.84 2 2.4143 1506.5 73.49

The measured voltage as a function of the gap between the displacement sensor and target surface is shown in Figure 4-3. The gap means the distance between the sensor tip and the target surface (the target surface is the bottom surface of the sample mount shown in Figure 4-1). A displacement sensor sensitivity of 0.036975 V/µm was calculated from the slope of this curve.

The calculation procedure of reflective sensitivity is as follows:

From Figure 4-3,

푌 = 푚푥 + 푐 (4.1)

[Where, m is slop of the curve and c is a constant]

= 0.036975푥 + 0.2987

So that,

The slope, 푚 = Sensitivity = 0.036975 V/μm

Such a calibration is required prior to each experimental session, as the reflectivity of the target surface is sensitive to the local environment.

Figure 4-2 Standard reflective sensitivity curve at near side (curve is provided by the

PHILTEC Company [106]).

To confirm the calculated reflectivity is correct, the displacement of the sample as a function of electric field was calculated using calculated reflectivity of 0.036975 V/µm and compared with the displacement measured using a calibrated macroscopic strain measurement system. The displacement vs applied electric field curves from two measurements show excellent consistency, as shown in Figure 4-4.

Displacement and macroscopic strain calculation from output gain voltage of displacement sensor for PZT as follows:

From Sensor data,

Voltage difference = voltage at initial – voltage at highest field (4.2)

= 2.8125 – 2.6497

= 0.1628 V

Displacement = voltage difference ∕ slop of the curve (4.3)

= 0.1628 ∕ 0.036975

= 4.4034 µm

Strain = (displacement ∕ thickness) × 100 (4.4)

= (4.4034 ∕ 1074) × 100

= 0.41% 51

Figure 4-4 Comparison of the displacement as a function of electric field curves for

PZT measured using a calibrated macroscopic strain measurement system (TF

Analyser) (red line) and the cell equipped with the displacement sensor (blue line).

A comparison of the electric-field-induced macroscopic strain response in PZT measured using a calibrated strain measurement system and the cell’s displacement sensor during an in situ diffraction experiment is shown in Figure 4-5. The macroscopic strain was calculated using Equation 4.2 to Equation 4.4. It can be observed from this figure that the macroscopic strain measured using the cell is in qualitative agreement with that measured using a standard macroscopic strain measurement system. This difference observed here (Figure 4-5(a)) is likely due to the difference in cycling conditions for the two experiments. The calibration curve was measured using a continuous triangular waveform at 1 Hz, whereas the strain data collected from the sample cell were acquired with step-wise field application at a frequency of 0.0011 Hz.

Corresponding diffraction patterns at initial state (E0), maximum electric field state

(Emax, 2 kV/mm), and remnant sate (Erem) are shown in Figure 4-5(b). In the case of

PZT, the (111) peak is convoluted with the (111) peak of the gold and cannot be

52 separated. For BNT-5BT which is not shown in this figure, the gold peak position was completely separate, where the (111) peak position of gold was at 2θ of 24.545° and the sample was 2θ of 25.691°.

(Erem) state. Estimated errors are within the size of the markers.

4.3 Results and Discussion

Electric-field-induced lattice strain (200) calculated from in situ X-ray diffraction patterns and simultaneously measured macroscopic strain using the displacement sensor for BNT-5BT is shown in Figure 4-6. The lattice strain is approximately 50% of the macroscopic strain at any given field above 1.35 kV/mm. This is consistent with previous measurements on related materials [18, 23, 24, 107], which show in tetragonal and rhombohedral PZT’s that the lattice strain is 60% of the measured macroscopic strain during actuation.

Piezoelectric lattice strain is generated due to local atomic displacements within the unit cell under an external field. Additionally, lattice strain can originate from the compliance of the polycrystalline material with other strain mechanisms in surrounding grains [18, 19]. The other strain mechanisms are generally extrinsic, and are the result of non-180° domain wall motion and/or crystallographic phase transformations [17].

Macroscopic strain is generated from the combination of total lattice strain and total extrinsic strains generated during the application of an electric field.

One of the crucial features of this cell which allows for accurate in situ strain measurements is that the surface of the sample remains static during electric-field application. Any movement of the upper surface of the sample will affect the peak position in the diffraction pattern; and consequently the calculated lattice strain may be misleading. Here, we have ensured stable conditions by mechanically fixing the diffracting surface of the sample. Therefore, there will be no parasitic movement of the diffracting surface of the sample during the application of an electric field which will affect the strain calculation. 54

Induced lateral strain of gold on BNT-5BT surface is also shown in Figure 4-6. An additional outcome of this constraint is that the gold electrode peaks from the surface could be used to measure the macroscopic d31 piezoelectric coefficient of the sample.

This is achievable because as the sample expands in the longitudinal direction, it

55 contracts in the perpendicular direction. This contraction induces a biaxial stress in the gold electrode which results in a positive lattice strain of the film in the field direction.

This response, in the future, could be calibrated for the electrode material, film thickness and diffraction peak used, such that both macroscopic longitudinal d33 and transverse d31 measurements are made in situ with the collection of diffraction data from the sample material.

4.3.1 Further considerations

 This sample cell can be used in laboratory based X-ray instruments as well as

lower energy synchrotron sources, where scattering in reflection geometry is

used. However, the rate of data acquisition and applied electric-field frequency

for respective compositions need to be considered for the given instrumentation.

For example, the lower intensities of laboratory-based X-ray instruments, where

even rapid data collections are on the order of 10’s of seconds, will prevent

experiments where the structural feature of interest changes more rapidly than

this. Example of situations where this may be useful is in the domain and

transformation dynamics at field strengths close to the coercive field, where

timescales of minutes to hours are of interest.

 Careful calibration (Figure 4-3 and Figure 4-5) of the displacement sensor with

respect to the reflective target surface and corresponding calibration with the

measured values of a standard material is crucial. Any error in the calibration

will propagate to the measured strain, yielding erroneous strain results. The error

from the calibration will equally reflect in the measured macroscopic strain. For

example, if a 1% error exists in the calibration then a 1% error will be in the

measured macroscopic strain values also. By direct comparison of the 56

macroscopic strain from the demonstrated cell with that of a calibrated

instrument, the error in the calibration is of the order of 1%. Relative to the error

in the measured lattice strains (Figure 4-6), this error is approximately the same

order of magnitude.

 The maximum electrical load of the sample cell is limited by the electrical

feedthroughs. Those currently used are capable of 10 kV. However, the real

electrical limitation generally arises from the electric field magnitude over the

sample thickness (dielectric strength of the material). In previous experiments,

the maximum field strength achieved on a range of samples was approximately

5 kV/mm for samples with silicone grease applied to the outer edges.

 Temperature is one of the key factors which changes the phase symmetry and

functional properties of electro-mechanical materials [108]. Therefore,

temperature-dependent property measurements are very important for these

materials. Future cell development will concentrate on the addition of a variable

temperature option for high or low temperature measurements.

4.4 Conclusions

An electric-field sample cell equipped with a macroscopic displacement sensor has been successfully developed and demonstrated to enable the in situ structure and macroscopic strain measurements of piezoelectric materials during the application of electric fields.

This cell will provide a method to directly probe structure-property relationships in electrically active functional materials and assist in the development of future piezoelectric materials with improved properties.

5 The effect of inter-granular constraints on the response of

polycrystalline piezoelectric ceramics

Abstract

The electro-mechanical coupling mechanisms in polycrystalline ferroelectric materials including a soft PbZrxTi1-xO3 (PZT) and lead-free 0.9375(Bi1/2Na1/2)TiO3-0.0625BaTiO3

(BNT-6.25BT) have been studied using surface sensitive in situ low-energy (12.4 keV) and bulk sensitive in situ high-energy (73 keV) synchrotron X-ray diffraction. The results show that for tetragonal PZT at maximum electric field of 2.8 kV/mm, the electric-field-induced lattice strain (ε111) and non-180° domain texture as indicated by the intensity ratio (I002/I200) are 20% and 16% higher at the surface than in the bulk, respectively. In the case of BNT-6.25BT, which is pseudo-cubic at 2 kV/mm ε111 and

ε200 are 15% and 20% higher at the surface, while in the mixed tetragonal and

rhombohedral phase at 5 kV/mm, I111⁄I111 and I002/I200 are 12% and 10% higher at the surface than the bulk, respectively. The observed difference in the intrinsic and extrinsic contributions to the electro-mechanical response is believed to result from the fact that surface grains are not constrained in three dimensions and consequently the domain reorientation and lattice expansion in surface grains along the field direction are promoted due to less constraint from neighboring grains. It is suggested that the magnitude of property difference between surface and bulk is higher for the PZT than for BNT-6.25BT due to the level of anisotropy in the strain mechanism. The comparison of the results from different methods reveals that the grain-to-grain interactions have a significant influence on the electric-field-induced electro-mechanical responses in bulk polycrystalline ferroelectrics.

5.1 Introduction

The electric-field-induced macroscopic strain in piezoelectric materials has been shown to originate from at least three structural contributions: (i) intrinsic piezoelectric lattice strain resulting from the distortion of the unit cell by a coupling of the external field with ionic species in the structure, (ii) extrinsic electric-field-induced non-180° domain wall motion in systems accompanied by spontaneous strain and polarisation and (iii) induced phase transformations [15-17]. The above mentioned structural contributions to the macroscopic strain in polycrystalline piezoelectric materials under a mechanical stress or electrical field are more complex than in single crystals due to the coupling of strain between neighbouring or clusters of grains. The exact mechanisms, which couple these strains between individual grains within the polycrystalline state, are still unknown. However, it has been shown that the lattice strain can originate from the compliance of the polycrystalline materials with other strain mechanisms in adjacent grains [18, 19]. The magnitude of this compliance or intergranular coupling effect as well as its influence on the macroscopic strain properties is not completely understood.

It has also been demonstrated that the magnitude of the electric-field-induced strain response in these materials is highly heterogeneous at the grain scale [113], adding further evidence to the importance of the coupling of properties between grains.

Strain generation mechanisms in different constrain conditions are discussed as follows:

Firstly considering mono-domain single crystal, at the initial state there is zero strain

(Figure 5-1(a), at point A). When an electric field is applied along the spontaneous polarisation direction, the crystal expands and the intrinsic strain increases linearly with increasing the amplitude of electric field to the maximum value at point C. During decreasing the amplitude of the electric field, the strain decreases up to point A and

59 again the strain becomes zero. During further decrease the electric field (negative bias, antiparallel to the spontaneous polarisation direction), crystal size decreases and negative strain increases up to point D. At point D, the applied electric field is enough to change the spontaneous polarisation direction toward the electric field direction.

After switching, polarisation direction becomes parallel to electric field direction and strain again becomes positive at point E. Then crystal size and positive strain increases with increasing the electric field amplitude up to point F. Again strain is decreasing with decreasing electric field and again reach zero at point A. In mono-domain single crystal there is only intrinsic strain which induced from lattice distortion.

In the case of poly-domain single crystal (Figure 5-1(b)), strain mechanisms are nearly same as in the mono-domain single crystal. The main difference is that poly-domain single crystal has extrinsic strain components induced by ferroelectric 90° domain switching during the application of an electric field. At initial state (point A) the strain is zero. During the application of an electric field along the spontaneous polarisation direction, macroscopic strain increases with increasing the amplitude of electric field due to lattice distortion and 90° domain wall motion and reaches maximum at point C.

After this point, strain mechanisms are same as described above for mono-domain single crystal. Mono-domain single crystal exhibits only intrinsic strain while poly- domain single crystal exhibits both intrinsic and extrinsic strains.

In the case of polycrystalline ceramics (Figure 5-1(c)) at the initial state (point A), the macroscopic strain is zero due to the random orientations of domains. During the application of an electric field, the macroscopic strain increases with increasing the amplitude of the electric field because of the intrinsic lattice strain induced from lattice

60 distortion and the extrinsic strain induced from non-180° domain wall motion. The lattice distortion and non-180° domain wall motion are influenced by the constraints from neighbourhood grains. Volume of the domains which polarisation direction parallel to the electric field direction, increases with increasing electric field amplitude and highest at point B but still there has some remaining 90° domain due to the constraints. Strain decreases with decreasing the electric field amplitude from point B to

C. At point C, has remnant strain at zero electric field. During further decrease the electric field (negative bias), the strain decreases and maximum at point D. At point D, field amplitude is enough to switch the polarisation direction toward the field direction.

After switching, strain again becomes positive and during further decreasing the electric field, strain increases and reaches highest at point E.

Polycrystalline ceramics consist of interconnected grains with different crystallographic orientations. It is well known that physical properties of crystalline piezoelectric materials are strongly anisotropic. The application of an electric field along unique directions of single crystal piezoelectrics can result in drastically different measured strains [114-116]. The total material response in the polycrystalline state therefore can be considered as a combination of the response of the individual grains with applied fields along unique crystallographic directions. However, the effects of inter-granular constraints must also be considered. In polycrystalline piezoceramics, the crystalline lattice properties effect the motion of intra-grain structural defects such as domain walls causing deformation of the surrounding grains [15, 117, 118]. The intergranular elastic strain accommodation in these materials affects the macroscopic strain. At the grain boundary, the domains orient head-to-tail (positive pole to negative pole) configuration to minimise the systems total free energy. Some domain alignments are in head-to-head

61 or tail-to-tail configuration which increases the elastic and/or electrostatic energy at the grain boundary. These energy barriers act as pinning centers to reduce the domain wall motion as well as piezoelectric response near the grain boundary. Previously reported that head-to-head domain configuration creates lower energy state compare to tail-to-tail configuration. However both of these configurations reduce the domain motion as well as reduce the field-induced structural changes [119]. These constraints of the polycrystalline matrix are one of the limiting factors in material performance.

X-ray diffraction (XRD) is a powerful tool to observe underlying electro-mechanical coupling mechanisms in piezoelectric materials. The intrinsic lattice strain component can be calculated from diffraction peak position shifts while the extrinsic strain caused by non-180° domain wall motion and/or phase transformations is quantified from diffraction peak relative intensity changes and splitting of symmetry dependent reflections during the application of an electric field.

In this study, the constraints of the polycrystalline state on electro-mechanical response are directly probed in PZT and 0.9375(Bi1/2Na1/2)TiO3-0.0625BaTiO3 (BNT-6.25BT) using surface sensitive in situ low-energy and bulk sensitive in situ high-energy synchrotron XRD. The measurements of BNT-6.25BT were successful in both low and high-energy XRD experiments. Low energy X-rays penetrate only a few micrometres into the material therefore only provide information from the surface grains, while high- energy X-rays probe grains primarily from the bulk of the sample. The results show that for both PZT and BNT-6.25BT the intrinsic lattice strains and extrinsic non-180° domain switching strains are larger at the surface than in the bulk of the samples. The observed difference in intrinsic and extrinsic responses from two measurements is presumably related to the distinct inter-granular constraint conditions experienced by surface and bulk grains and the anisotropy of the strain mechanism in the different materials.

5.2 Experimental procedure

Commercial soft PZT (PIC151, PI ceramics, Lederhose, Germany) and BNT-6.25BT were used. Disc shaped samples of BNT-6.25BT were prepared by the solid state synthesis route. Details of the synthesis route can be found in Section 3.1. The same batches of ceramic samples were used for high-energy XRD to allow a direct comparison between the surface and the bulk properties. The details of the sample preparation for low-energy and high energy XRD experiments are discussed in Section

3.1.1 and Section 3.1.2, respectively. The thickness of the samples which used for the high energy experiments were 1 mm.

Two kinds of X-ray scattering experiments, surface sensitive in situ low-energy and bulk sensitive in situ high-energy have been used to collect XRD patterns from the surface and the bulk of the samples, respectively. The details of the experimental setups for surface sensitive in situ low-energy and bulk sensitive in situ high-energy X-ray scattering experiments can be found in Section 3.2.2 and in Section 3.2.3.2, respectively.

Surface sensitive X-ray scattering experiments were carried out at the powder

diffraction beamline of the Australian Synchrotron [94]. A monochromatic X-ray beam

of energy 12.4 keV (λ = 1 Å) was used. XRD data were collected in reflection geometry

using a Mythen detector [89] with the samples mounted in a specially developed cell

(discussed in Chapter 4) during the application of unipolar triangular waveform electric

fields with maximum field amplitude of 2.8 kV/mm in 0.28 kV/mm steps for PZT and 5

kV/mm in 0.5 kV/mm steps for BNT-6.25BT. In this experimental setup (

Figure 3-5(b)) the electric field vector was aligned perpendicular to the characteristic

111 or 200 crystallographic planes. In this experimental geometry, the incident angle of

X-ray beam is adjusted by tilting the sample stage to make it equal to half of the Bragg angle of the recorded characteristic reflections. In the case of PZT, the incident X-ray beam angle was 13.3° while for BNT-6.25BT was 13.75°. The attenuation depth of low- energy X-rays into the surface for this geometry was calculated to be 7.98 µm for BNT-

6.25BT and 5.4 µm for PZT. The attenuation depth was calculated using a fixed x-ray incident angle of 14°, density for PIC151 7.8 g/cm3 and density for BNT-6.25BT 5.6 g/cm3. Errors on these calculated values are of the order of 1%, as they are propagated from the error in the density measurement only. The approximate average grain size of

PZT and BNT-6.25BT was 5 µm and 1.7 µm respectively, meaning that the probed surface layer had a thickness of approximately 1-2 grains for PZT and 4-5 grains for

BNT-6.25BT, however in both cases, scattered intensity is dominated by grains that intersect the surface. The average grain size of BNT-6.25BT sample and PZT were estimated from the SEM image shown in Figure 5-2 and the Ref. of [120], respectively.

Figure 5-2 SEM image for BNT-6.25BT

Bulk sensitive X-ray scattering experiments were carried out at the beamline ID15 of the European Synchrotron Radiation Facility (ESRF). An X-ray beam of energy 73 keV

(λ = 0.171 Å) and dimensions 200 × 200 μm2 was used. Samples were placed in specifically designed in situ sample cell where the electric field was applied perpendicular to the incident X-ray beam direction [20]. Identical electric field cycles used in low-energy XRD experiments were applied to the samples within the cell while the diffraction images were collected in transmission geometry using a Pixium 4700 large area detector [92]. Diffraction images were radially integrated into 36 angular segments of 10° widths using the software package FIT2D [96]. In the following analysis only the integrated data with the scattering vectors parallel to the direction of the applied electric field was analyzed.

The diffraction peaks were fit individually with suitable pseudo-Voigt profile shape 67 functions [121] to obtain diffraction peak position, area and width as a function of applied electric field. Fitted peak positions were used to calculate the microscopic intrinsic lattice strain as a function of electric fields [122]. A detail of the lattice strain calculation can be found in Section 3.2.4. Peak intensity ratios were calculated from fitted diffraction peak areas for symmetry dependent reflections to obtain a quantitative measure of the non-180° domain wall motion and/or any phase transformation behavior as a function of electric field.

5.3 Results and discussion

A comparison between surface sensitive low-energy and bulk sensitive high-energy

XRD patterns for (111) and (200) crystallographic planes of PZT and BNT-6.25BT is shown in Figure 5-3. The resolution of low-energy XRD is higher than high-energy

XRD because of the optical setups of the different beamlines. The high-energy beamline used is optimised for rapid data acquisition, not high resolution, while the low energy beamline used is optimised for high resolution, not rapid acquisition time. Low and high energy data are necessary to draw conclusions on a sample’s performance in the context of this chapter because it specifically aimed to isolate the response from surface and bulk independently. In the case of PZT, the crystallographic phase was tetragonal in the initial state and remained tetragonal up to the maximum electric field amplitude of 2.8 kV/mm. At the surface, asymmetry at left hand side of peak (111) arises due to convolution of (111) gold peak. For BNT-6.25BT, on the other hand, the crystallographic structure was pseudo-cubic from 0 to 2 kV/mm, then transformed to tetragonal and rhombohedral two phase mixture at 2.5 kV/mm and remained mixed phases up to the maximum electric field amplitude of 5 kV/mm.

4휋푠𝑖푛휃 of the magnitude of scattering vector q, where q = . Here, the scattering vector is λ approximately parallel to the applied electric field direction.

A comparison between electric-field-induced structural variations as a function of applied field collected from the surface and the bulk is shown in Figure 5-4. In the case of the PZT sample, the electric-field-induced both intrinsic lattice strain and non-180° ferroelectric domain switching were observed over the full field range measured, consistent with earlier results from tetragonal PZT [107, 118]. For BNT-6.25BT, the initial structure is pseudo-cubic. On the application of the electric field, only lattice expansion occurs and is observed as a shift in the peak positions up to a critical field strength of around 2.5 kV/mm. Here, the material transforms to tetragonal and 69 rhombohedral two phase mixture, also consistent with earlier results [123]. From this point, it is no longer possible to calculate lattice strains as the diffraction peaks have split on the induced phase transformation; however, intensity ratios were calculated from the symmetry dependent reflection to quantify the non-180° domain wall motion.

The magnitudes of the material response, including lattice strain, and induced domain texture are consistently higher at the surface than within the bulk for both materials. In particular, for PZT at the maximum electric field, the electric-field-induced lattice strain

(ε111) and non-180° domain texture as indicated by the intensity ratio (I002/I200) are 20% and 16% higher at the surface than the bulk, respectively. For BNT-6.25BT, at 2kV/mm the lattice strain ε111 and ε200 are 15% and 20% higher at the surface than the bulk. At 5 kV/mm the domain textures in the mixed phase state as measured by the intensity ratios of I111⁄I111 and I002/I200 are 12% and 10% higher at the surface than the bulk.

In order to explain these results, the difference in the constraint conditions of the probed grains of two measurements is considered. At the surface, the grains are less constrained by their neighbor grains than the bulk grains. This is shown schematically in Figure 5-5.

The surface sensitive measurement performed here isolates scattering information from the top 1-2 and 4-5 grain layers for PZT and BNT-6.25BT, respectively, thus approximately 30-50% and 15-20% for PZT and BNT-6.25BT, respectively of the observed electro-mechanical responses are contributed by the grains with a constraint- free boundary at the sample surface. Despite the grain size difference between PZT and

BNT-6.25BT, we can assume that the strain gradient from surface to the bulk is almost same for these two materials, meaning surface effects extend several microns into the material irrespective of grain size. 70

Figure 5-4 (a) lattice strain ε111 and (b) domain texture indicated by of intensity ratio

I002/I200 for PZT, (c) ε111 and (d) ε200 for the pseudo-cubic phase of BNT-6.25BT before

transformation, (e) I111⁄I111 and (f) I002/I200 for the induced rhombohedral and tetragonal phases in BNT-6.25BTas a function of applied electric field for the sample surface (red) and bulk (blue).

The data in Figure 5-4 shows that the magnitude of difference between surface and bulk is higher for the PZT than for BNT-6.25BT. The intensity ratio I002/I200 difference between the surface and bulk of PZT at 2.8 kV/mm is 38% higher than for BNT-6.25BT 71 at 5 kV/mm. To rationalize this it must be recalled that the strain generation mechanisms in PZT and BNT-6.25BT are different. In PZT, the strain originates from the crystal lattice distortion of the intrinsic piezoelectric effect and non-180° domain switching which gives rise to a ferroelastic strain. In the case of BNT-6.25BT, a crystallographic phase transformation to tetragonal and rhombohedral two phase mixture also contributes to the macroscopic strain in addition to these mechanisms.

Figure 5-5 Schematic diagram showing the condition of grains with constraints at the surface and in the bulk.

The magnitude of intergranular stresses developed in polycrystalline piezoceramics experiencing a field-induced macroscopic strain is related to the degree of crystallographic anisotropy of this strain response. That is to say, if only a single crystallographic axis experiences a large field-induced strain, large intergranular 72 stresses will be created in the polycrystalline structure where those “high response” grains are likely to be surrounded by many “low response” grains. Whereas materials which experience more isotropic field induced strain along various grain orientations less intergranular stress is generated, as all grains in the system will strain approximately equally.

Here, the general observation of the surface grains having a larger response than bulk grains may be expected due to their free boundary condition. The difference in magnitude between the surface and bulk response in the two materials can then be explained by the anisotropy of their response mechanisms. In the case of tetragonal

PZT, grains that experience the highest strain are those preferentially aligned with their unit cell c-axis along the external field. These grains will undergo large amounts of non-

180° domain switching, generating a large ferroelastic strain. It is not clear if the observed (111) lattice strain in PZT is intrinsic piezoelectric lattice strain, or a compliant elastic strain due to this non-180° domain switching strain [15]. The fact that the remnant ε111 is qualitatively the same observed in the surface and bulk measurements, gives weight to the argument that (111) lattice strains observed in polycrystalline PZT are likely compliant elastic strains, as if this was not the case, the remnant state for the surface strains would be expected to be significantly smaller than in the bulk.

In the case of the BNT-6.25BT at 2.5 kV/mm, the pseudo-cubic phase has transformed into tetragonal and rhombohedral two phase mixture. This phase transformation generates a transformation strain in both tetragonal <001> and rhombohedral <111> crystallographic directions, thus the response is more isotropic than the case of

73 tetragonal PZT. We believe that this isotropic response is the reason why the difference between the bulk and surface in BNT-6.25BT is less than that for PZT, where the response is confirmed to be highly anisotropic along the [001] grain orientations [115].

When there is more uniform material response between the surface and the bulk during the application of electric field, the intergranular stress effect will be less pronounced in the bulk. The resultant less intergranular stress will probably increase the fracture toughness; reduce the fatigue by which materials life time will increase.

5.4 Conclusions

The electro-mechanical coupling mechanisms in polycrystalline PZT and lead-free

BNT-6.25BT have been observed using surface sensitive low-energy and bulk sensitive high-energy synchrotron XRD. Higher magnitudes of both lattice strain and non-180° domain switching are observed at the surface compared with the bulk for both materials.

It is speculated that the strain mechanisms can occur more easily at the surface than in the bulk because the grains at the surface are less constrained by neighboring grains.

The experimental results indicate that the difference in the electro-mechanical response from the sample surface and bulk is less when the strain mechanism is more isotropic, for instance when the material undergoes a field-induced phase transformation to a mixed-phase state as for BNT-6.25BT.

6 Structure-property relationships in BNT-xBT system during the

application of a mechanical stress

Abstract

The solid solution system (100-x)Bi1/2Na1/2TiO3-xBaTiO3 (BNT-xBT) has attracted wide research interest in the scientific community as a potential high-strain lead-free piezoelectric material. The structure-property relationships in a series of BNT-xBT solid solutions with the BT content ranging from 5 mol% to 8 mol% in 0.25 mol% steps have been studied using in situ high-energy synchrotron X-ray diffraction (XRD) under unipolar stress cycling at room temperature. The series of BNT-xBT solid solutions with fine compositional variation helps to make a comprehensive picture of field induced phases particularly in the “pseudo-cubic” region. A total of 13 compositions were produced with 0.25 mol. % BT difference in each composition. In the as-processed state, BNT-5BT exhibited rhombohedral crystallographic symmetry, while the rest of the BNT-xBT compositions (x = 5.25 to 8) exhibited a region of pseudo-cubic symmetry. During the application of a stress, lower BT content (x = 5.25 and 5.5) samples tended to transform to rhombohedral symmetry, while higher BT content (x ≥

7) tended to go tetragonal. Compositions between these (5.5 < x < 7) undergo a transformation to a mixed rhombohedral and tetragonal phase symmetries. The fine compositional sampling in this work shows that the stress induced phase transition has unique behavior in various regions of the pseudo-cubic compositions. The results show that the stress-induced phase transformation mechanisms are highly analogous to the electric-field-induced phase transformations in this material system as presented in

Chapter 7.

6.1 Introduction

Among the emerging lead-free piezoelectric systems, barium titanate BaTiO3 (BT) and bismuth sodium titanate Bi1/2Na1/2TiO3 (BNT) based materials have been observed as promising lead-free piezoelectric materials [72, 109-111]. Despite several promising findings in recent years, no single lead-free compound has been identified to replace lead-containing materials across the whole diverse range of applications.

Although pure BNT ceramic material presents some promising piezoelectric properties

[124], it suffers from a large coercive field (Ec = 73 kV/cm) at room temperature [72] which limits its usefulness in the transducer devices. The lower Curie temperature (Tc =

120 °C) of pure barium titanate (BT) limits the high temperature applications. Solid solutions of BNT-xBT near the morphotropic phase boundary (MPB) at BT concentrations of 6-7 mol% have shown improved piezoelectric properties [72, 78]. The region of the phase diagram separates the rhombohedral BNT and tetragonal BT in a similar way to the PZT system. Initial investigations of BNT-xBT have been shown that there was a ferroelectric (FE) to anti-FE (AFE) phase transition in the temperature range of 150 °C ≤ T ≤ 120 °C, for compositions containing less than 10BT [72]. Later measurements showed that the existence of a rhombohedral (R3c) to tetragonal (P4bm) phase transition below the Curie temperature [62]. Several studies reported that the field-induced phase transformation plays a critical role for the observed macroscopic properties in this material system. [16, 75, 76, 78, 112, 125, 126]. Daniels et al. showed that the electric-field-induced strain in BNT-7BT to be the result of induced phase transformation from pseudo-cubic to tetragonal symmetry [75]. Simons et al.[16] also reported that the enhanced strain observed in BNT-6BT due to the electric-field-induced phase transformation. A considerable amount of research has been conducted under

76 electric field in the BNT-xBT system [72, 78, 112, 127]. However, under mechanical stress only few selected compositions have been investigated. Stress-induced phase transformations also contribute to the strain response in these materials [91, 125, 128], therefore, they need to be understood to best take advantage of these mechanisms.

In situ X-ray diffraction methods are a powerful and direct means of quantifying the structural contributions to the strain generation mechanisms in these materials. The intrinsic strain component induced from the lattice distortion can be calculated from diffraction peak position shifts and the extrinsic strain caused by non-180° domain wall motion and/or phase transformations is quantified from diffraction peak relative intensity changes and splitting and/or broadening of symmetry dependent reflections during the application of a stress.

Here, we report the compositional dependence of stress-induced phase transitions in a series of BNT-xBT system (where x = 5 to 8 in steps of 0.25) studied using high-energy

(73 keV) XRD under uniaxial compressive stress at room temperature. Results show that in the as-processed state, BNT-5BT is in rhombohedral phase symmetry and all other compositions are in pseudo-cubic phase. At 400 MPa stress, lower BT content compositions (BNT-5.25BT and BNT-5.5BT) transform from pseudo-cubic to rhombohedral phase, higher BT content samples (BNT-7BT to BNT-8BT) transform from pseudo-cubic to tetragonal phase and, compositions between these (BNT-5.75BT to BNT-6.75BT) transform from pseudo-cubic to mixed (rhombohedral and tetragonal) phases. The fine compositional sampling in this work shows that the stress induced phase transition has unique behavior in various regions of the pseudo-cubic compositions. The transition sequence is analogous to that observed under applied

77 electric-field.

6.2 Experimental procedure

The details of the ceramic synthesis route and the sample preparation for this experiment can be found in Section 3.1 and Section 3.1.3, respectively.

In situ high energy X-ray scattering experiments were carried out at the ID15 beamline of the European Synchrotron Radiation Facility (ESRF), France. A monochromatic X- ray beam with energy of 73 keV (wavelength λ = 0.171 Å) and dimensions of 200 × 200

μm2 was used. A unipolar triangular stress field waveform with maximum amplitude of approximately 600 MPa was applied to the sample perpendicular to the incident beam direction. Simultaneously X-ray diffraction images were collected using Pixium 4700 large area detector [92]. The details of the experimental setups and measurements are discussed in Section 3.2.3.1.

The details of the data processing are discussed in Section 3.2.3.3.2. To find the diffraction peak positions, areas and widths as a function of the applied stress, the extracted diffraction patterns were fit individually with pseudo-Voigt functions using the software package Igor Pro 6.37. Fitted peak positions and widths were used to calculate the intrinsic lattice strain and full width half maxima (FWHM) as a function of stress amplitude. The phase fractions and domain texture measured in multiples of a random distribution (MRD) of the reflections were determined by combined texture

Rietveld refinements incorporating the weighted strain orientation distribution function

(WSODF) strain model [97] and Exponential Harmonic texture model [98] in the analysis using the program “Materials Analysis Using Diffraction” (MAUD) [99] to 78 describe the structural changes as a function of stress field and scattering vector to the applied field direction. The details of the structural refinements of in situ diffraction data using MAUD can be found elsewhere [17]. The structural models, including a cubic Pm3m phase symmetry, a rhombohedral R3c phase symmetry and a tetragonal

P4mm phase symmetry were used in the refinements. Initially, different structural models including R3c, R3c + P4mm, R3m + P4mm were considered. Based on the goodness of fit parameter, Rwp, which describes the weighted discrepancy between the measured and calculated intensities, the two-phase R3c + P4mm model gave the best quality fit for two phase mixture. The details of the data analysis can be found in

Section 3.2.4.

6.3 Results and discussion

In the following, the subscript pc denotes the pseudo-cubic perovskite unit cell while R denotes the rhombohedral indexing and T for tetragonal indexing. Selected regions of

XRD patterns near 111pc and 200pc reflections with the scattering vector perpendicular to the applied stress field direction of BNT-xBT compositions in the as-processed state and at 400 MPa stress conditions are shown in Figure 6-1. The asymmetry in the 111pc reflection and single 200pc reflection signifies that the BNT-5BT composition is of rhombohedral symmetry in the as-processed state. However, the rest of the compositions with increasing BT content seem to exhibit symmetric single 111pc and

200pc reflections. Thus, it is reasonable to state that with increasing the BT content, the rhombohedral distortion of the unit cell is suppressed. As there is no observable asymmetry or peak splitting exists, compositions other than BNT-5BT can be termed as pseudo-cubic in the as-processed state. Application of a stress induces different behaviour in the composition range studied here. At 400 MPa, the BNT-5BT shows 79 change in 111푝푐/111푝푐 relative peak intensity without any splitting or asymmetry in the

200pc reflection. This indicates that the BNT-5BT exhibits ferroelastic domain switching without any stress-induced phase transformation. Despite them being in the similar pseudo-cubic state in the as-processed state, compositions from BNT-5.25 to BNT-8BT transform to lower symmetry state under maximum stress. Three different regions in the pseudo-cubic composition range can be visualised as a function of applied stress field.

BNT-5.25BT and BNT-5.5BT undergoes stress-induced pseudocubic to rhombohedral

R3c phase that is signified by the broadening and asymmetry of 111pc reflection with single symmetric 200pc reflection. Compositions in the range of 5.75BT and 6.75BT seem to transform from pseudocubic to mixed phase (rhombohedral and tetragonal) symmetry by broadening and asymmetry of both 111pc and 200pc reflections. From

BNT-7BT to BNT-8BT undergoes stress-induced pseudocubic to tetragonal P4mm phase by peak broadening and asymmetry of 200pc reflection and, single symmetric

111pc reflection. The symmetry of the BNT-xBT compositions at initial state and at 400

MPa is listed in Table 6-1. The full XRD patterns shown in Figure 3-3 have been analysed using the Rietveld refinement software MAUD to identify the most likely phase symmetries in the samples.

Since some material compositions transformed into single phase and some of the compositions transformed into two phases with significant peak overlapping during the phase transformation at the measured stress field, simple reflection profile analysis of

111R or 200T for the whole data sets is not feasible. The phase fractions and the domain texture quantified in units of multiples of a random distribution (MRD) values were calculated using the Rietveld refinement software MAUD. The Exponential Harmonic model was incorporated in the analysis to quantify the domain texture induced by ferroelastic domain switching while the WSODF model was used for the lattice strain

80 calculation caused by lattice distortion during the application of stress. The Exponential

Harmonic texture model yields the orientation distribution function (ODF) for the phase constitutions. Since in these material systems, the most important mechanisms for field induced changes in the ODF are domain switching and phase transformation, the strongest texture effects can be observed at the MRD of the reflections that are related to the direction of the polarisation. Lattice strains, ε, and relative full width half maxima

∆FWHM were calculated from fitted peak positions and areas using software Igor Pro

6.37.

Table 6-1 Symmetry of BNT-xBT at initial and at 400 MPa

Sample At initial At 400 MPa

BNT-5BT Rhombohedral (R) R

BNT-5.25BT Pseudo-cubic (pc) R

BNT-5.5BT pc R

BNT-5.75BT pc R + Tetragonal (T)

BNT-6BT pc R + T

BNT-6.25BT pc R + T

BNT-6.5BT pc R + T

BNT-6.75BT pc R + T

BNT-7BT pc T

BNT-7.25BT pc T

BNT-7.5BT pc T

BNT-7.75BT pc T

BNT-8BT pc T

The phase fractions of rhombohedral R3c and tetragonal P4mm, relative full width half maxima and lattice strains as a function of BT content in BNT-xBT at 400 MPa stress are shown in Figure 6-2. The phase fraction was obtained from the Rietveld refinement of the full patterns of in situ diffraction data using MAUD. The errors of these phase fraction are smaller than the markers. The phase fractions for each composition are shown in Table 6-2. Figure 6-2(a) clearly reveals that, at the 400 MPa stress field, rhombohedral phase decreases and tetragonal phase increases when BT content above

5.5 mol%. In addition, compositions from BNT-5.75BT to BNT-6.75BT exhibit the rhombohedral-tetragonal mixed phases. FWHM of the 111pc reflection decreases and

200pc increases with increasing the amount of BT that correlates with the decreasing and increasing phase fraction of rhombohedral and tetragonal phase, respectively.

Table 6-2 Phase fractions as a function BT content in BNT-xBT system

Composition 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 8

(BNT-xBT) x mole (%)

R3c (%) 100 100 100 60 45 49 20 17 - -

P4mm (%) - - - 40 55 51 80 83 100 100

Figure 6-1 X-ray diffraction patterns of 111pc and 200pc reflections measured with the scattering vector perpendicular to the stress field direction for (100-x)BNT-xBT (where x= 5 to 8 in steps of 0.25) in the as-processed state (left hand side of the dotted line) and 83 at the 400 MPa stress (right hand side of the dotted line). In the as-processed state,

BNT-5BT is in rhombohedral symmetry while rest of the compositions are in pseudo- cubic state. At the 400 MPa stress; BNT-5BT remains rhombohedral phase (black line),

BNT-5.25BT and BNT-5.5BT transform from a pseudo-cubic to a rhombohedral phase

(blue line), from BNT-5.75BT to BNT-6.75BT transform from a pseudo-cubic to a mixed (rhombohedral and tetragonal) phases (red line) and from BNT-7BT to BNT-

8BT transform from a pseudo-cubic to a tetragonal phase (green line).

Figure 6-3 shows the calculated lattice strain and relative full width half maximum for 3 selected compositions, namely BNT-5.5BT (100/0), BNT-6.5BT (20/80) and BNT-

7.75BT (0/100), where numbers in the parenthesis indicate the rhombohedral and tetragonal phase fractions, at an applied stress of 540 MPa. During the experiment the maximum stress field for all the compositions was not same. Therefore 400 MPa stress field (on the rising stress part of the cycle) is chosen to make a comparison between all the compositions and 540 MPa is used to compare between these selected three compositions. At 540 MPa stress lattice strain, ε111 and relative full width half maximum, ∆FWHM111 are higher for BNT-5.5BT due to pure rhombohedral phase transformation while ε200 and ∆FWHM200 are higher for BNT-7.75BT due to pure tetragonal phase transformation. Coercive field (Ec critical field for domain switching and/or phase transformation) is lower for the pseudo-cubic to rhombohedral phase transformation than for the pseudo-cubic to tetragonal phase transformation. This results show consistency with previous results for similar type of materials observed by Hall

[36]. They showed non-180° domain wall motion is easier in the rhombohedral phase than in tetragonal phase for PZT, because field-induced residual stress is lower in

84 rhombohedral phase compared to tetragonal. During the application of field, freedom of domain switching directions in rhombohedral phase materials are 8 along <111> which is higher than in tetragonal which 6 along <001>.

Figure 6-2 (a) phase fractions, (b) relative full width half maxima ∆FWHM and (c) lattice strains ε are shown as a function of the percentage of BT content in BNT-BT solid solution at stress amplitude of 400 MPa.

Figure 6-3 (a) lattice strains, ε111 and (b) ε200, and (c) relative full width half maximum,

∆FWHM111 and (d) ∆FWHM200 are shown as a function of applied stress for BNT-

5.5BT, BNT-6.5BT and BNT-7.75BT.

Variation in field induced ferroelastic domain texture for three different compositions are shown in Figure 6-4. The change in domain texture (MRD) values as a function of angle to the applied field signifies the change in domain texture at maximum stress field. The ferroelastic domain texture decreases along the stress field direction while increases in the perpendicular direction. The change in texture has also been observed under field for other piezoelectric materials [17, 129-132]. The difference in domain texture under electric and stress field lies in the direction of the applied field, i.e., ferroelastic domain texture increases perpendicular to the stress field while ferroelectric domain texture increases parallel to the electric field direction. Under compressive stress, the longer axis of the unit cell aligns in the perpendicular direction.

Figure 6-4 Domain texture (MRD) of the 002pc reflection for the tetragonal phase and

87 the 111pc reflection for the rhombohedral phase at 540 MPa stress. α is the angle between the scattering vector direction and applied stress field direction. The dotted line indicates the domain texture (MRD) value at initial state.

6.4 Conclusions

Stress-induced strain mechanisms in a series of BNT-xBT under uniaxial stress have been studied using in situ high energy XRD. At an applied stress field, lower BT (x <

5.75) content transform from pseudo-cubic to rhombohedral phase, higher BT (x > 6.75) content transform from pseudo-cubic to tetragonal phase and, compositions between these transform to a mixed phase of this. The stress induced strain in lower (x < 5.75) and higher (x > 7) BT content ceramics is generated mostly by the lattice distortion and ferroelastic domain switching, whereas for the in-between compositions, in addition to the lattice distortion and domain switching, phase transformation also contributes to the macroscopic stress-strain behavior.

7 Structure-property relationships in BNT-xBT system during the

application of an electric field

Abstract

The correlation between the electric-field-induced structural changes to the piezoelectric response of lead-free (100-x)Bi1/2Na1/2TiO3-xBaTiO3 (BNT-xBT) (where x= 5, 5.75 to 8 in 0.25 steps) polycrystalline piezoelectric ceramics have been studied using high- energy synchrotron X-ray diffraction under an electric field cycling with a maximum field amplitude of 5 kV/mm. It was found that in the as-processed state, the crystallographic structure of BNT-5BT is rhombohedral symmetry and the rest of the

BNT-xBT compositions investigated here exhibit a pseudo-cubic symmetry. At 5 kV/mm, BNT-5BT remains in rhombohedral symmetry, BNT-5.75BT undergoes a pseudo-cubic to a rhombohedral phase transformation while higher BT content (BNT-

7BT to BNT-8BT) samples tend to transform from a pseudo-cubic to a tetragonal symmetry. Compositions between these (from BNT-6BT to BNT-6.75BT) transform to a mixed (rhombohedral and tetragonal) phase symmetry.

7.1 Introduction

Among other lead-free piezoelectric ceramics, bismuth sodium titanate Bi1/2Na1/2TiO3

(BNT) based materials have been reported with high electro-mechanical properties [6,

71]. Solid solutions of BNT with BaTiO3 (BT) are considered as an attractive system due to showing excellent piezoelectric properties near the morphotropic phase boundary

(MPB) compositions [78, 81]. Takenaka et al. [72] reported an MPB between BNT-6BT and BNT-7BT by measuring dielectric properties and structural measurements.

According to XRD analysis, they observed rhombohedral and tetragonal phase

89 coexistence at the MPB. However, Ranjan and Dviwedi [73] reported a composition dependent rhombohedral to nearly cubic structural phase transition for BNT-6BT.

Simons et al. [16] using in situ neutron diffraction, Daniels et al. [75] and Khansur et al.

[76] using in situ XRD and, Hinterstein et al. [77] by using transmission electron microscopy (TEM), neutron and X-ray diffraction showed that near the MPB compositions of BNT-xBT system undergo phase transformations from a pseudo-cubic to a tetragonal or a mixed phase tetragonal and rhombohedral symmetry during the application of an electric field. Jo et al. reported a phase evolution in BNT-xBT (0 ≤ x

≤ 15) compositions at unpoled and poled state [78]. They observed a range of compositions, from BNT-6BT to BNT-11BT transform from a pseudo-cubic to a mixed phase symmetry. They reported maximum piezoelectric properties for BNT-7BT which is similar to the study of Takenaka et al. [72]. Later Ma et al. also reported a modified

MPB with phase diagram for this materials system using in situ TEM [79]. The solid solution of BNT-xBT based system has attracted wide research interest in the scientific community as a potential high-strain lead-free piezoelectric material [6, 80-83]. A comprehensive study of microscopic origin of electric-field-induced strain in these material system are a great interest to gain further knowledge to improve the electro- mechanical properties of lead-free piezoelectric compositions for future applications.

Here, we report the electric-field-induced phase transformations in BNT-xBT system

(where x = 5, 5.75 to 8 in 0.25 steps) have been studied using in situ high-energy synchrotron X-ray diffraction (XRD). The result shows that lower BT (x = 5.75) content sample transform from a pseudo-cubic to a rhombohedral symmetry while higher BT content (7 ≤ x ≤ 8) compositions transform to a tetragonal symmetry. Compositions between these transform to rhombohedral and tetragonal two phase mixture.

7.2 Experimental procedure

The details of the ceramic synthesis route and the sample preparation for this experiment are discussed in Section 3.1 and Section 3.1.2, respectively.

Macroscopic piezoelectric properties including polarisation and strain were measured using a standard macroscopic strain measurement system (TF Analyzer 2000 system; aixACCT Systems GmbH, Aachen, Germany). The details of this experimental procedure can be found in Section 3.2.1. A unipolar triangular waveform electric field with maximum amplitude of 5 kV/mm was applied.

For in situ high-energy XRD, an X-ray beam energy of 73 keV (wavelength λ=0.171 Å) and dimensions of 200 × 200 μm2 was used. A triangular waveform electric fields with maximum amplitude of 5 kV/mm was applied to the sample while the diffraction images were collected using a Pixium 4700 large area detector [92]. The details of the experimental setups can be found in Section 3.2.3.2.

The details of the data processing are discussed in Section 3.2.3.3.2. The phase fractions and domain texture measured in multiples of a random distribution (MRD) of the reflections were determined by combined texture Rietveld refinements with the weighted strain orientation distribution function (WSODF) strain model [97] and E-

WIMV texture model [98] using the program “Materials Analysis Using Diffraction ”

(MAUD) [99] to describe the structural changes as a function of electric-field and scattering vector angle to the applied field direction. The details of the structural refinements of diffraction data using MAUD can be found in Ref. [17]. For BNT- 91

6.25BT, the structural models including a rhombohedral R3c phase symmetry and a tetragonal P4mm phase symmetry were used in the refinements. Initially, different structural models including R3c, R3c + P4mm, R3m + P4mm were considered. Based on the goodness of fit parameter, Rwp, which describes the weighted discrepancy between the measured and calculated intensities, the two-phase R3c + P4mm model gave the best quality fit. The details of the data analysis can be found in Section 3.2.4.

7.3 Results and discussion

Polarisation and macroscopic strain data as a function of electric field amplitude and the percentage of BT content in BNT-xBT are shown in

Figure 7-1. Polarisation and macroscopic strain are highest for BNT-6.25BT with a coercive field of 2.2 kV/mm.

In the following, the subscript pc denotes the pseudo-cubic perovskite unit cell while R denotes the rhombohedral indexing and T for tetragonal indexing. Figure 7-2 shows the

XRD patterns for 111pc and 200pc reflections with the scattering vector parallel to the applied electric field direction as a function of %BT content in the BNT-xBT system, at the initial sate (E0) and the maximum electric field (Emax = 5 kV/mm) state. It should be noted that BNT-5.25BT and BNT-5.5BT are not shown here because the ceramics failed under high electric fields and data could not be obtained. At the initial state, the asymmetry in the 111pc reflection and single symmetric 200pc reflection of BNT-5BT indicates that it exhibits rhombohedral symmetry. The rest of the compositions (5.75 ≤ x ≤ 8) have nearly symmetric single 111pc and 200pc reflections. Therefore it can be said that in the as-processed state, these compositions are in a pseudo-cubic state and the

92 rhombohedral distortion of unit cell is suppressed with increasing the percentage of BT.

The different types of structural changes are induced during the application of an electric field in the composition range studied here. At 5 kV/mm electric field, the BNT-

5BT shows the relative intensity (I111⁄I111) change and peak splitting in the 111pc reflection, without any significant change in the 200pc reflection. This conforms that

BNT-5BT remains in rhombohedral symmetry without any phase transformation.

Despite having the same phase symmetry in the as-processed state, three types of phase transformation behaviour are observed for the compositions from BNT-5.75BT to BNT-

8BT. In the case of BNT-5.75BT, the initial 111pc reflection splits into doublet under the application of electric field while the 200pc reflection remains singlet and symmetric which indicates that a pseudo-cubic to a rhombohedral phase transformation occurs.

Peak shape asymmetry in the 111pc reflection and splitting in the 200pc reflection are observed in the range of compositions from BNT-6BT to BNT-6.75BT indicating these compositions transform from a pseudo-cubic to rhombohedral and tetragonal two phase mixture. Compositions from BNT-7BT to BNT-8BT show the peak slitting in the 200pc reflection without any observable change in the 111pc reflection. This indicates that these compositions transform from a pseudo-cubic to a tetragonal symmetry. The symmetry of BNT-xBT compositions at initial state and at 5 kV/mm is listed in Table

7-1. The full XRD patterns shown in Figure 3-3 have been analysed using the Rietveld refinement software MAUD to identify the most likely phase symmetries in the samples.

Figure 7-3 shows the for 111pc and 200pc reflections as a function of angle (α) between the scattering vector direction and the applied field direction, for BNT-5.75BT

(rhombohedral phase), BNT-8BT (tetragonal phase) and BNT-6.25BT (rhombohedral and tetragonal two phase mixture) at 5 kV/mm. In the case of BNT-5.75BT, I111⁄I111 reflections change their relative intensity as a function of α without any noticeable change in the 200pc reflection. Parallel to the electric field direction (α = 0) the intensity ratio I111⁄I111 is highest and decreases with increasing α. For BNT-6.25 BT, the

I111⁄I111 and I002/I200 ratios are highest along the electric field direction and both of them decrease with increasing α. In the case of BNT-8BT, only 200pc reflection changes relative intensity ratio as a function of α without any significant change in the 111pc reflection. The I002/I200 ratio is highest along α=0 and decreases with increasing α.

Table 7-1 Symmetry of BNT-xBT at initial state and at 5 kV/mm

Sample At initial At 5 kV/mm

BNT-5BT Rhombohedral (R) R

BNT-5.75BT Pseudo-cubic (pc) R

BNT-6BT pc R + Tetragonal (T)

BNT-6.25BT pc R + T

BNT-6.5BT pc R + T

BNT-6.75BT pc R + T

BNT-7BT pc T

BNT-7.25BT pc T

BNT-7.5BT pc T

BNT-7.75BT pc T

BNT-8BT pc T

Figure 7-1 (a) polarisation and (b) macroscopic strain as a function of electric field and the BT content in BNT-xBT.

Figure 7-2 The 111pc and 200pc reflections as a function of the BT content in BNT-xBT system in the as-processed state (E0) (left panel) and at 5 kV/mm (Emax) (right panel).

Since BNT-6.25BT transforms from single pseudo-cubic phase to two phases with rhombohedral and tetragonal symmetry at 5 kV/mm, simple reflection profile analysis of 111R or 200T is not feasible. The phase fractions, the domain texture values and total macroscopic strain were calculated using the Rietveld refinement software MAUD. The

E-WIMV model was used to calculate the quantitative amount of texture caused from non-180° domain switching and phase transformation and, WSODF model was used for strain calculation caused from lattice distortion during the application of an electric field.

MAUD fitting of the 111pc and 200pc reflections for BNT-6.25BT at 5 kV/mm using

P4mm and R3c two-phase model is shown in Figure 7-4. The reflections and texture are well fitted with measured data. The results of the structure models from the refinement for poled BNT-6.25BT at 5 kV/mm are listed in Table 7-2.

Lattice distortion, ζ was calculated using following equations:

For the tetragonal phase,

푐푇 휁푇 = − 1 (7.1) 푎푇

For the rhombohedral phase,

푐퐻 휁푅 = − 1 (7.2) √6푎퐻

Figure 7-3 Diffraction patterns with scattering vectors at various angles to the applied electric filed (5kV/mm). For (a) BNT-5.75BT, (b) BNT-6.25BT and (c) BNT-8BT.

Figure 7-4 Comparison between measured and fitted selected regions of diffraction patterns near 111pc and 200pc reflections for BNT-6.25BT at 5kV/mm

Table 7-2 The refined unit-cell parameters of poled BNT-6.25BT (5kV/mm) using the

P4mm + R3c model

Structures

5kV/mm P4mm R3c (represented in hexagonal axes) a (Å) 3.88750(5) 5.50111(3) c (Å) 3.93165(4) 13.57737(9)

훇 (%) 1.136(3) 0.76(3)

Phase fraction (%) 28.1(0) 71.9(2)

Rwp (%) 8.848

Rp (%) 6.661

Figure 7-5 shows the domain texture (MRD [132]) for the polar axes as a function of α for the rhombohedral and the tetragonal phases in the applied field state of 5 kV/mm for

BNT-6.25BT. α describes the angle with respect to the electric field vector. It is obvious that both the tetragonal 002pc MRD and rhombohedral 111pc MRD reach its maximum at α = 0, i.e. along the field direction.

Figure 7-5 The domain texture (MRD) of (a) the 111pc reflection for the rhombohedral phase and (b) the 002pc reflection for the tetragonal phase at 5kV/mm for BNT-6.25BT.

The dotted line indicates the domain texture value at initial state.

The phase fractions have to be taken into account to calculate the strain contributions from the individual phases to the macroscopic strain. For BNT-6.25BT, the calculated rhombohedral and tetragonal phase fractions are 71.9% and 28.1%, respectively (see

Table 7-2) at an applied electric field amplitude of 5 kV/mm while 48% and 52% was observed at the applied mechanical stress field amplitude of 400 MPa (Chapter 6). The 100 values of rhombohedral lattice strain SL, R, tetragonal lattice strain SL, T, rhombohedral domain strain SD, R and tetragonal domain strain SD, T consider the pure phase alone. The strain values have to be weighted with the phase fractions because BNT-6.25BT exhibits an electric field induced rhombohedral and tetragonal mixed phase at 5 kV/mm.

The total lattice strain is therefor,

푆퐿 = 푉푅 × 푆퐿,푅 + 푉푇 × 푆퐿,푇 (7.3)

And the total domain strain is,

푆퐷 = 푉푅 × 푆퐷,푅 + 푉푇 × 푆퐷,푇 (7.4)

Where 푉푅 and 푉푇 are the rhombohedral and tetragonal phase fractions, respectively.

The domain switching strain can be calculated using the following equation [133],

1 휋/2 푆 = 휁 ∫ [Δ푀푅퐷 (훼) ∙ 푐표푠2 훼] (sin 훼)푑훼 (7.5) 퐷 2휋 훼=0 ℎ푘푙

Where ζ is the lattice distortions, ΔMRD is the difference between the domain texture magnitude of the polar axis from a random distribution and α is the angle between scattering vector and the electric field vector.

Table 7-3 summarises the strain values obtained for rhombohedral and tetragonal phases. The combined macroscopic strain at 5 kV/mm of BNT-6.25BT is 0.456%. This strain is almost consistent with the macroscopic strain value of 0.5% measured using calibrated TF analyser. The difference is 0.044%.

101

Table 7-3 Field induced microscopic stain contributions to the macroscopic strain for

BNT-6.25BT at 5 kV/mm: Lattice strain (SL) and Domain switching strain (SD)

Strain 5 kV/mm

Lattice strain (SL) Domain strain (SD)

P4mm 0.007% 0.435%

R3c 0.140% 0.321%

Phase weighted 0.103% 0.353%

Total strain 0.456%

7.4 Conclusions

The electric-field-induced strain mechanisms in BNT-xBT system has been studied using high energy synchrotron XRD under an electric field cycling with maximum amplitude of 5 kV/mm. At 5 kV/mm, lower BT content (BNT-5.75BT) transform from a pseudo-cubic to a rhombohedral symmetry while higher BT content (BNT-7BT to

BNT-8BT) transform from a pseudo-cubic to a tetragonal symmetry. The compositions between these (BNT-6BT to BNT-6.75BT) tend to transform to rhombohedral and tetragonal two phase mixture. With increasing the percentage of BT in BNT-xBT, rhombohedral distortion decreases and tetragonal distortion increases. Phase transformation under electric field is highly analogous under mechanical stress field.

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8 General discussion

In this thesis, the electro-mechanical coupling mechanisms in polycrystalline piezoelectric ceramic materials have been studied using X-ray diffraction techniques during the application of stress and electric field. A detail understanding of the strain generation mechanisms is requisite to improve the electro-mechanical properties of piezoelectric materials. These findings may help to design piezoelectric materials with improved properties for future applications.

In this Chapter, the outcomes of this research are reviewed to develop a more fundamental understanding of electro-mechanical coupling mechanisms in polycrystalline piezoelectric ceramics during the application of stress and electric field.

Development of a sample cell to analyse these coupling mechanisms at in situ state, the effects of inter-granular constraints on materials responses under an electric field and the structure-property relationships in BNT-xBT system during the application of a field

(stress and electric field) are separately discussed in Section 8.1, Section 8.2 and

Section 8.3, respectively.

8.1 Development of a sample cell to analyse the structural origin of strains

in piezoelectric materials

To improve the electro-mechanical properties of piezoelectric materials, it is very important to have complete information about the structural mechanisms that generate strains during the application of an electric field. The electric-field-induced macroscopic strain in these materials have been shown to originate from at least three possible contributions: (i) intrinsic lattice strain resulting from the distortion of the unit cell, (ii)

103 extrinsic non-180° domain switching, and (iii) induced phase transformations [15-17].

X-ray diffraction techniques are very useful tools to analyse these structural mechanisms. The electric-field-induced structural changes can be observed using ex situ

XRD measurements (i.e., by recording diffraction data on an as-processed sample and after applying an external field). However, ex situ measurements cannot provide information at the intermediate steps of the applied field. To observe structural changes or dynamics of domain wall motion, it is important to collect information at transient states because some fraction of structural mechanisms may be time-dependent and reversible during the application of an electric field [20, 22, 23, 84-86]. Therefore, it is necessary to collect diffraction data during the application of an electric field for complete understanding of the underlying electro-mechanical coupling mechanisms in these materials. In other words, in situ XRD measurements are essential to gain a complete picture of the strain generation mechanisms in piezoelectric materials.

Previously, In situ low-energy (< 30 keV) XRD techniques including synchrotron X- ray sources and laboratory-based X-ray instruments have been used to observe the structural changes during the application of external electric fields [26-29, 101-104,

134]. One of the main problems in these scattering experiments is the movement of the diffracting surface of the sample during the actuation process. If the diffracting sample surface moves relative to the X-ray source and/or detector position during the application of an electric field, it will affect the peak positions in the diffraction patterns and result a pseudo-strain which needs to be carefully accounted during the interpretation of the diffraction data. Pramanick & Jones observed an 18% error in the measured lattice strains from the diffraction patterns due to 4 µm sample surface displacement of 1mm thickness sample during the application of an electric field [105].

104

Furthermore, usually the structural mechanisms of piezoelectric materials observed by diffraction methods are correlated to the macroscopic strain measured ex situ. Up to date, it is still a challenge to directly correlate the underlying structural mechanisms to the macroscopic response of these materials due to the lack of useful sample cells for in situ field-dependent experiments using low-energy XRD.

A sample cell has been developed (Chapter 4) that can overcome these above mentioned problems by having a fixed diffracting surface of the sample as well as an built-in linear displacement sensor. The stable conditions of the scattering surface of the sample during the application of an electric field are ensured by mechanically fixing the diffracting surface. The conical shape of the lid with an angular range from 10° to 170° allows observations over a broad range of sample orientations, facilitating the alignment of the electric field direction with respect to the incident beam at the desired angle. The sample stage can be used in a broad range of synchrotron as well as laboratory X-ray instruments due to low profile with 44 mm in height, base plate dimensions of 80 mm ×

90 mm and a total weight of 0.63 kg.

This sample cell is capable to measure the structural changes of piezoelectric ceramics during the application of an electric field using X-ray scattering techniques in reflection geometry, while simultaneously collecting macroscopic strain data using a linear displacement sensor. The capabilities of the sample cell have been successfully demonstrated at the Powder Diffraction beamline of the Australian Synchrotron. The results show that the measured macroscopic strain using the cell can be directly correlated with the structural changes of the material obtained from diffraction data.

This cell will provide a method to directly analyse the structure-property relationships

105 in piezoelectric materials and assist to develop piezoelectric materials with improved properties.

8.2 The inter-granular effects on the materials response under an electric

field

Piezoelectric ceramic materials play an important role in smart functional devices as sensors and actuators. The uses of these materials are increasing day by day. To improve the electro-mechanical properties of these materials will require deep knowledge about the underlying structural origin of electric-field-induced strains. The structural contributions to the macroscopic strain in polycrystalline piezoelectric materials under an electrical field are more complex than in single crystals due to the coupling of strain between neighbouring grains. It has been reported that the lattice strain in polycrystalline piezoelectric ceramics can also originate from the compliance of surrounding grains [18, 19]. Therefore it is necessary to understand the effect of these compliances on the resulting macroscopic piezoelectric properties.

Surface sensitive low-energy (12.4 keV) and bulk sensitive high-energy (73 keV) X-ray diffraction techniques have been used to analyse the inter-granular constraint effects on the material responses in PZT and BNT-6.25BT under the application of an electric field (Chapter 5). The above mentioned (Chapter 4) sample cell has been used to measure electromechanical response from the surface in low-energy XRD experiments.

Low-energy X-rays can penetrate around 10-12 micrometres into the materials studied here so that provide information from the surface grains while high-energy X-rays provide information from the bulk. Contrasting the results of these methods provide information on the potential constraints from grain neighbourhoods and its potential 106 influence on the bulk properties. For both PZT and BNT-6.25BT, the observed intrinsic lattice strains and extrinsic non-180° domain switching are higher at the surface than in the bulk of the samples. This property difference is believed to result from the fact that surface grains are not constrained in three dimensions and are therefore free to expand in the electric field direction with less restriction. The grains are in less constrained state by their neighbour grain boundaries at the surface than in the bulk (see Figure 5-5).

Additionally, it was observed from the results that the piezoelectric property differences between the surface and the bulk are less when phase transformations occur due to the magnitude of anisotropy in the strain generation mechanism. The magnitude of intergranular stresses that develop in a polycrystalline material experiencing a field- induced macroscopic strain will be related to the degree of crystallographic anisotropy of that response. Large intergranular stresses generate in the random polycrystalline structure when only a single crystallographic axis experiences large electric-field- induced strains where “high response” grains are surrounded by many “low response” grains. On the other hand materials poses less intergranular stress when they experience electric-field-induced strains more isotropic with grain orientations where all the grains in the material have approximately equal response under an electric field.

8.3 The effects of structural changes on variations of piezoelectric

properties

(100-x)BNT-xBT (BNT-xBT) system has attracted wide research interest as a potential high-strain lead-free piezoelectric ceramic material. Although the promising piezoelectric properties of BNT-xBT system were reported [72], the microscopic structural origin of field-induced strains is still not clear [16, 75-77, 112, 135, 136]. The 107 identification of the effects of structural changes to the field-induced strains is very difficult in this material system due to complex crystallographic structure of the parent

BNT material [53, 62-65]. Therefore the phase identity in BNT-xBT system is very complicated and due to this at least six different phase diagrams have been proposed for this material system [72, 127, 137-140]. Relaxor like behaviour of BNT-xBT system has been reported by Jo et al. [108, 141]. Denis et al. has also reported that the origin of field-induced piezoelectric properties in BNT-based material system may be related to the breaking of Bi-O hybridisation [142]. Consequently it is reasonable to suggest that the room temperature crystallographic structure of compositions close to the MPB in

BNT-xBT system is pseudo-cubic having a long range cubic symmetry with short range rhombohedral and tetragonal symmetry. This pseudo-cubic symmetry undergoes a field- induced phase transformation to a long range lower symmetry [75, 91, 135]. Thus field- induced irreversible phase transformation and domain texture is the major contributor to the field-induced macroscopic strain measured in the MPB compositions of the BNT- xBT system. [16, 75, 76, 78, 112, 125, 126]. This phase transformation can be reversible at elevated temperatures and/or by adding dopants [80].

Near the MPB compositions in the BNT-xBT system have shown improved piezoelectric properties [72, 78]. An electric-field-induced strain of 0.45 % at 8 kV/mm in KNN doped BNT-6BT system was reported by Zhang et al. [81]. Similar to the PZT system, the MPB of BNT-xBT separates a rhombohedral (R3c) and tetragonal (P4mm) ferroelectric phase.

There still debate about the field-induced phases near the MPB compositions in BNT- xBT. Initial investigations of BNT-xBT have shown that there was a ferroelectric (FE)

108 to anti-FE (AFE) phase transition in the temperature range of 150 °C ≤ T ≤ 120 °C, and compositions which contains less than 10BT [72]. Later measurements showed the existence of a rhombohedral (R3c) to tetragonal (P4bm) phase transition below Curie temperature [62]. Tekenaka et al. observed rhombohedral and tetragonal phase coexistence at MPB [72]. Ranjan a and Dviwedi [73] as well as Garg et al. [74] observed a field-induced phase transformation from rhombohedral to nearly cubic structural phase for BNT-6BT. Later, Daniels et al. [75] and Khansur et al. [76] using in situ X-ray diffraction, Simons et al. [16] using in situ neutron diffraction and,

Hinterstein et al. [77] by using transmission electron microscopy (TEM), neutron and

X-ray diffraction showed that the MPB compositions of BNT-xBT system undergo a pseudo-cubic to tetragonal or mixed phase tetragonal and rhombohedral symmetry during the application of an electric field. Jo et al. [78] reported that compositions between BNT-6BT to BNT-11BT transform from a rhombohedral to a mixed phase symmetry under the electric field of 6 kV/mm.

Although a considerable amount of research has been conducted under electric field in the BNT-xBT system [72, 78, 112, 127], a comprehensive study of the microscopic origin of strains under an electric field is still lacking. However, under stress only a few selected compositions have been investigated [91, 125, 128]. In the real environment, many piezoelectric materials are used under high stresses or pre-stress conditions.

Therefore, it is necessary to understand the coupling mechanisms under applied stress to improve the properties of piezoelectric materials. Comparison between stress and electric-field-induced strain generation mechanisms is also lacking.

The effects of structural changes on variations of piezoelectric properties in the BNT-

109 xBT system (where x = 5 to 8 in 0.25 steps) have been studied using high-energy XRD methods during the application of stress (Chapter 6) and electric field (Chapter 7). This very fine compositional variation helps to make a comprehensive picture of field induced phases particularly in the “pseudo-cubic” region. Under both stress and electric field, the results show that the lower BT content (x = 5.25 to 5.5) BNT-xBT compositions transform from a pseudo-cubic to a rhombohedral symmetry while higher

BT content (x = 7 to 8) compositions tend to transform from a pseudo-cubic to a tetragonal symmetry. Compositions between these (x = 5.75 to 6.75) tend to transform from a pseudo-cubic to rhombohedral and tetragonal two phase mixture. The mixed phase region in the middle shows enhanced piezoelectric properties including lattice stain and domain switching strains.

From the above discussions and based on the results of the surface and bulk response it can be suggest that the field-induced phase change materials can be used to engineer better actuator materials. The results of the studies including the surface and the bulk response as well as the compositions dependent measurements for the solid solution of

BNT-xBT show that compositions which transform to a mixed (rhombohedral + tetragonal) phase during the application of fields have the potential to exhibit higher electro-mechanical properties. During a mixed phase transformation the magnitude of the anisotropy of material responses to the applied field is low and all the grains strain almost equally to the field direction. This also reduces the grain-scale heterogeneity of the response and may improve fatigue and lifetime properties in addition to allowing larger strains.

110

9 Conclusions

The underlying electro-mechanical coupling mechanisms in polycrystalline piezoelectric ceramic materials including PZT and lead-free BNT-BT based compositions have been studied using in situ X-ray diffraction techniques under stress and electric field. The major outcomes of this thesis are; a) development of a sample cell to analyse the effects of in situ electric-field-induced structural mechanisms on piezoelectric properties including macroscopic strain in ferroelectric ceramics using low-energy synchrotron X-ray diffraction in reflection geometry, b) the inter-granular interaction effect on the electro-mechanical coupling in ferroelectric ceramics analysed by in situ electric-field-dependent measurements using surface sensitive low-energy and bulk-sensitive high energy synchrotron XRD, c) structure-property relationships in

(100-x)BNT-xBT compositions studied using in situ high-energy synchrotron XRD under a stress and an electric field. All these investigations add to a body of knowledge which may help in the development of lead-free piezoelectric ceramics with improved properties to replace lead based piezoelectric materials as well as for future applications.

Observation of the structural changes to generate strain during the actuation process in piezoelectric ceramic materials is necessary to gain a complete information of the structure-property relationship due to certain structural mechanisms may be meta-stable during actuation. A sample cell equipped with a displacement sensor has been developed to understand the in situ electric-field-induced structural mechanisms in piezoelectric ceramics using low-energy X-ray scattering techniques. The capabilities of this cell have been successfully demonstrated at the powder diffraction beamline of the

Australia Synchrotron. The cell showed the ability to measure the in situ structure and macroscopic strain of piezoelectric ceramics during the application of electric fields.

111

This cell will provide a method to directly correlate the structure-property relationship in electro-active materials.

The structural mechanisms to generate strains in polycrystalline piezoelectric ceramics under external mechanical or electrical fields are more complicated than that in single crystals due to the grain-to-grain interaction effect between neighbouring or cluster of grains in polycrystalline materials. These constraints of the polycrystalline state on electro-mechanical response were analysed in PZT and BNT-6.25BT using surface sensitive in situ low-energy and bulk sensitive in situ high-energy synchrotron XRD under electric fields. The observed lattice strain and non-180° domain wall motion are higher at the surface than that in the bulk. In the case of PZT at 2 kV/mm, the electric- field-induced lattice strain (ε111) and non-180° domain texture (I002/I200) are 20% and

16% higher at the surface than in the bulk, respectively. For BNT-6.25BT which is pseudo-cubic at 2 kV/mm, ε111 and ε200 are 15% and 20% and, in the mixed tetragonal

and rhombohedral phase at 5 kV/mm, I111⁄I111 and I002/I200 are 12% and 10% higher at the surface than in the bulk, respectively. I002/I200 difference between the surface and the bulk of PZT at 2.8 kV/mm is 38% higher than that for BNT-6.25BT at 5 kV/mm meaning the magnitude of property difference between surface and bulk is less when the phase transformation to a mixed phase system occurs.

The effects of underlying structural changes on variations of piezoelectric properties in

(100-x)BNT-xBT system have been studied under mechanical stress and electric field using high-energy synchrotron XRD. In the as-processed state, BNT-5BT was in a rhombohedral phase and the rest of the compositions (x = 5.25 to 8) were in a pseudo- cubic state. During the application of stress or electric field, BNT-5BT remains in 112 rhombohedral symmetry. Lower BT content samples (BNT-5.25BT and BNT-5.5BT under stress and BNT-5.75BT under electric field) transforms from a pseudo-cubic to a rhombohedral symmetry while higher BT content samples (BNT-7BT to BNT-8BT) under both fields tend to transform to a tetragonal symmetry. The compositions between these tend to transform to a mixed rhombohedral and tetragonal symmetry. The polarisation and macroscopic strain was highest for BNT-6.25BT.

Based on the findings of this work, it can be hypothesised that piezoelectric materials may poses higher electro-mechanical properties when it undergoes to a field-induced transformation to a mixed phase system. During a mixed phase transformation all the grain responses are approximately equal in the direction of the applied field and therefore, the material possesses less intergranular stress. A comprehensive study on the field-induced structural changes to generate strain in potential lead-free piezoelectric materials is lacking.

In this thesis an in situ sample cell has been developed to measure electromechanical properties of piezoelectric materials using low-energy XRD. Electromechanical response from the surface of the sample has been observed using low-energy XRD with this cell and response from the bulk has been measured using high-energy XRD. It is observed that the response from the surface is different from the bulk. From the results of the surface and bulk response and the compositional dependent measurements, it was observed that electromechanical properties of piezoelectric materials are higher when materials transform into rhombohedral and tetragonal two phase mixture during the application of field. Hopefully, the investigations of this thesis will help to design piezoelectric materials with enhanced properties for future applications in smart

113 electronic devises.

114

10 Future work

The following proposed future works may help to further understanding of electro- mechanical coupling mechanisms in piezoelectric materials:

 Development of a sample cell to measure temperature-dependent piezoelectric

properties in situ using low-energy XRD in reflection geometry. Temperature-

dependent property measurements are very important for piezoelectric materials

because variations of temperature change the phase symmetry and functional

properties of these materials. The main challenge is to control the thermal

gradients between the diffracting surface and the bulk. The diffracting surface is

open in air, therefore thermal gradient exhibit between the surface and the bulk.

 Develop a micro-mechanical model to predict the electro-mechanical properties

of piezoelectric ceramic materials. The grain-to-grain interactions need to be

considered.

 Data analysis in Chapter 6 can be extended. Although microscopic strains and

domain texture have been reported for 3 selected compositions (BNT-5.5BT

(rhombohedral), BNT-6.5BT (mixed rhombohedral and tetragonal) and BNT-

7.75BT (tetragonal)), the diffraction data for the rest of the compositions can be

analysed.

 XRD data in Chapter 7 for BNT-xBT compositions can be further analysed

using combined texture/strain structural refinements as a function of electric

field amplitude and the BT content in BNT-xBT system.

 Determine the structure-property relationships in a series of BNT-xBT system at

various temperatures under mechanical stress and electric fields. Temperature is

one of the key factor which changes the crystallographic phase and properties of

these materials. Additionally, these materials are used at various temperatures. 115

Although temperature dependent measurements have been done for some

selective compositions, measurements for a series of BNT-xBT compositions is

still lacking.

 The work in this thesis indicates that when BNT-xBT compositions transform to

a mixed phase state under a field, the likely have lower levels of intergranular

stress. It can be hypothesized from this that these compositions would therefore

have more resistance to electrical fatigue and failure. In order to test this,

comprehensive fatigue measurements of BNT-xBT compositions should be

done.

116

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