We present a critical review that encompasses the fundamentals and state-of-the-art knowledge of barium titanate-based piezoelectrics. First, the essential crystallography, thermodynamic relations, and concepts necessary to understand piezoelectricity and ferroelectricity in barium titanate are discussed. Strategies to optimize piezoelectric properties through microstructure control and chemical modification are also introduced. Thereafter, we systematically review the synthesis, microstructure, and phase diagrams of barium titanate-based piezoelectrics and provide a detailed compilation of their functional and mechanical properties. The most salient materials treated include the (Ba,Ca)(Zr,Ti)O3, (Ba,Ca)(Sn,Ti)O3, and (Ba,Ca)(Hf,Ti)O3 solid solution systems. The technological relevance of barium titanate-based piezoelectrics is also discussed and some potential market indicators are outlined. Finally, perspectives on productive lines of future research and promising areas for the applications of these materials are presented.

Lead zirconate-titanate [Pb(Zr,Ti)O3 (PZT)] is the most widely used piezoceramic material for electromechanical device applications. The toxicity and environmental impacts of lead have been known since the ancient times,1 and many lead-free piezoelectrics were investigated over the past 50 years.2 However, it was not until 2002 that directives regulating the use of Pb and other toxic elements in commercial products were introduced in the European Union.3,4 These regulations have stimulated renewed interest in lead-free piezoelectrics. In 2004, Saito et al.5 reported alkaline-niobate-based lead-free piezoelectrics with properties comparable with those found in PZT. This report triggered an exponential increase in the number of both basic and applied research investigations related to lead-free piezoelectrics. The expanding research community soon revisited the pioneering work performed by Takenaka et al.6 in 1991 which had reported on alkaline-bismuth-titanate-based piezoelectrics. Thereafter, research efforts focused on strategies to improve the piezoelectric properties of these materials. These strategies have included searching for systems with morphotropic or polymorphic phase boundaries, microstructure optimization, and texturing. (Section IV provides details on different strategies to improve piezoelectric properties.)

BaTiO3 (BT) was the first polycrystalline ceramic material ever discovered that exhibited ferroelectricity. During the 1950s, it was considered a serious candidate for piezoelectric transducer applications7 and the basic phenomenological theory for the monodomain, monocrystalline state was developed (see Sec. III for details).8,9 However, PZT,2 which possesses better piezoelectric properties and a higher Curie temperature TC, was discovered soon after. This development diminished the interest in BT for piezoelectric applications.10 It was not until 2009 that Liu and Ren11 reconsidered the potential of BT-based materials for piezoelectric applications. The outstanding piezoelectric properties found in Ca- and Zr-modified BT resulted in an even greater volume of work related to lead-free piezoelectrics (see Sec. V A for details). The discovery of other BT-based piezoelectrics with outstanding piezoelectric properties followed, albeit restricted to a limited temperature range (see Sec. V for details).

As of 2017, after 16 years of continuous worldwide research effort, the development of lead-free piezoelectrics is entering into a mature stage.12 Nonetheless, several challenges remain. To date, no material encompasses the set of functional properties of PZT which are required for the broad range of piezoelectric applications in which it is implemented. Alkaline-niobate-based compositions possess piezoelectric properties that are generally lower than PZT, although the temperature stability of the piezoelectric properties is the best among lead-free materials.13,14 Furthermore, the processing of materials within this family is still a major concern, due to a narrow sintering window in terms of temperature and dwell time, the high volatilization of alkalies, and early activation of surface diffusion that reduces the driving force for densification, among other factors.15 Alkaline-bismuth-titanate-based materials, on the other hand, feature only moderate small signal piezoelectric properties with acceptable temperature stability. Thus, they have been thoroughly investigated for applications working in the large signal off-resonance regime due to their giant strain. Early works demonstrate, however, that the giant strain typically occurs at too high electric field for commercial applications.16,17 In contrast, BT-based materials have attracted attention due to their large small signal piezoelectric properties, although the stability of these properties is quite limited in temperature. To date, chemically modified and/or microstructurally engineered BT-based materials have resulted in a maximum TC ∼ 160 °C.18–21 

Consequently, a lead-free piezoelectric capable of replacing PZT in all commercial applications is still far from reality. However, the continuous research and development efforts have led to the commercialization of devices based on lead-free piezoelectrics and several prototypes have been tested.12,22 Innovations based on lead-free piezoelectrics could position technology startups strategically or could assist manufacturers in diversifying their product portfolios.

From a scientific point of view, BT-based materials are a very interesting research platform since their phase diagrams involve phase transitions at relatively low temperature, making them attractive for probing mechanisms of enhanced piezoelectricity. These mechanisms include tricritical behavior, property divergence near interferroelectric phase boundaries, property enhancements due to polarization rotation and/or extension, among others. In addition, BT-based materials are quite versatile for fundamental studies since their functional properties are sensitive both to microstructure and chemical modifications. Despite their inherent advantages, the low temperature stability of piezoelectric properties in BT-based materials limits their technological implementation. Section VI discusses specific examples of the current technological relevance of BT-based piezoelectrics. Prototype piezodevices based on the family of BT materials include loud-speakers,23 biocompatible nanogenerators,24,25 self-powered fluid velocity sensors,26 and intravascular ultrasonic transducers,27 to name the most prominent examples.

Here, we review the current understanding of piezoelectricity in BT-based materials. We first briefly present the history and technological potential of BT-based materials. This is followed by an introduction to the fundamental concepts related to ferroelectricity and piezoelectricity. The most widely used approaches to engineer and optimize piezoelectric properties are then introduced. Chemical modifications are highlighted because binary and ternary solid solutions with different types of phase transitions constitute the most commonly used approach to tune the piezoelectric properties of BT-based materials. Subsequently, we assess the current state of understanding of the (Ba,Ca)(Zr,Ti)O3, (Ba,Ca)(Sn,Ti)O3, and (Ba,Ca)(Hf,Ti)O3 systems. Detailed information on the synthesis, microstructure, phase diagrams, electromechanical and mechanical properties, reliability, and doping strategies is compiled. The technological relevance of BT-based piezoelectrics is assessed in terms of market potential. Furthermore, novel fields of application, as well as insights into toxicity and biocompatibility of this family of materials, are presented. Finally, potential lines of future research are suggested.

This section briefly outlines some of the key historical events leading up to the present day understanding of BT materials, with a focus on those discoveries connected with its use in piezoelectric applications. The current technological potential of BT-based materials for piezoelectric applications is also summarized. Readers interested in a more comprehensive background are referred to several excellent books and review articles describing the history of BT, as well as the broader fields ferroelectricity and piezoelectricity.2,10,28–36

Three key discoveries gave birth to the fields of ferroelectricity and piezoelectricity in polycrystalline ceramic materials. The first was the finding of an extremely high relative permittivity in BT, which was more than ten times higher than that of other oxide compounds, such as TiO2. The second was the recognition that the high relative permittivity was connected with the underlying phenomenon of ferroelectricity. The third was the discovery of the poling process for polycrystalline materials, which could produce a high remanent polarization, and continues to be of paramount importance for the application of ferroelectric ceramics as piezoelectric sensors, actuators, and transducers.2 

The early history of BT is somewhat clouded by the fact that its discovery in 1941 took place during the second world war.37 Due to issues with the supply of Mica, the most widely used dielectric at that time, BT soon became an important strategic material for various military technologies.36 This scenario led to the independent discovery of BT in the United States,38,39 United Kingdom,37 Russia,40 and Japan41 in the search for new dielectric materials that involved the modification of TiO2 with BaO. It is widely reported that the unusually high dielectric properties of BT were associated with ferroelectricity by von Hippel et al.42 in the United States, and by Wul and Goldman43 in Russia, although according to Fousek,31 the first claim that BT was ferroelectric was made by Vul and Vereschtschagin.44 BT constituted the first demonstration of ferroelectricity in a simple ternary oxide compound. This was not thought possible at that time. Ferroelectricity was believed to exist only in potassium dihydrogen phosphate and related hydrogen bonded crystals displaying ferroelectric phase transitions of the order disorder type. Barium titanate differed from these materials in that the crystal structure is considerably simpler, and the phase transition at the Curie point is one of the displace type. After these concepts were understood and several new ferroelectrics discovered, a classification based on their type of phase transitions became possible.45 

Upon termination of the second world war, the phase transitions and physical properties of BT became topics of intensive investigation.42,46,47 Some of the most important scientific advances came from crystallographic investigations. Megaw,48 Kay and Voudsen49 in the United Kingdom, as well as Miyake and Ueda50 in Japan, provided the first detailed understanding of the crystal structure and changes in symmetry on cooling through the phase transitions. Blattner et al.51 produced the first BT single crystals in Switzerland in 1947 via ternary melts. This method was improved by Matthias in the United States (formerly in Switzerland), after moving to the Laboratory for Insulation Research at M. I. T., which was led by von Hippel. During the 1940s, von Hippel and co-workers advanced the field of ferroelectricity by providing a thorough understanding of the ferroelectric switching, domain structure, and crystal structure evolution of BT.47 

Another major breakthrough that occurred during this early period was the discovery of the poling process. At the time, it was not yet recognized that the polarization direction in a randomly oriented ferroelectric ceramic could, in fact, be reoriented. Hence, the understanding of the poling process was a major breakthrough. This also enabled the implementation of polycrystalline ceramics into piezoelectric applications, as they were mechanically more robust and less expensive than single crystals. This process was first reported by Gray52 with the purpose to produce transducers. Following this discovery, several authors pushed forward the understanding of the poling process, electrostriction, and piezoelectricity in BT.53–56 Forsbergh also investigated the evolution of domains under mechanical strain and electric fields.57 Between 1947 and 1950, the first commercial products based on BT became available, which included phonograph pickups, transducers for ultrasonic generation, accelerometers, by-pass capacitors, and filter capacitors.2,7,58,59

During the same period, theoretical approaches were put forward in an effort to explain the experimental observations.60 Between 1949 and 1951, Devonshire developed the first phenomenological theory to reconcile relationships between the structural, dielectric, electromechanical, and thermal properties of BT (and generally of ferroelectrics).8,9 The Devonshire theory was a particular form of the statistical thermodynamic theories of phase transitions put forward by Ginzburg, Landau, and Lifshitz.61,62 Later on, in 1954, Remeika produced larger and higher quality single crystals.63 This allowed further detailed characterization to be performed and correlated with the existing theoretical descriptions.64 For instance, the seminal work of Merz65 on nucleation and growth of ferroelectric domains was performed with Remeika's single crystals. Miller and Weinreich66 extended these concepts. Together these early studies formed the basis for our current understanding of polarization dynamics.

The late 1940s and early 1950s witnessed a large proliferation of new perovskite-structured ferroelectric materials, which was accompanied by a continuous improvement in dielectric and piezoelectric properties.29 Some studies focused on the phase diagram and synthesis optimization of polycrystalline BT,67,68 whereas others expanded the scope of research to encompass more complex BT-based solid solutions.69–71 McQuarrie and Behnke69 were the first to synthesize the quaternary system between BaTiO3, BaZrO3, CaTiO3, and CaZrO3 with the objective to investigate its structural and dielectric properties. During this same era and with similar purposes, the quaternary system between BaTiO3, BaSnO3, SrSnO3, and CaSnO3 was investigated by Coffeen.70 Even with the development of these complex solid solutions, the poor temperature stability of the piezoelectric properties was not improved.

Between 1949 and 1954, a major breakthrough in the field of ferroelectrics and piezoelectrics occurred. In 1949, Waku and Hori discovered that PbTiO3 and PbZrO3 form a solid solution, PZT.72 The PZT system attracted the attention of Japanese scientists because of the variation in crystal structure with the Zr/Ti ratio and the apparent pseudo-cubic degeneration of the tetragonal and rhombohedral phases when approaching the composition Pb(Zr0.55Ti0.45)O3.73–76 It was not until 1954 though, that Jaffe et al.77 recognized that PZT solid solutions featured outstanding electromechanical properties with a maximum response near the Pb(Zr0.55Ti0.45)O3 composition. Moreover, this composition offered stable properties up to temperatures of 200 °C. This was attributed to the high Curie temperatures that characterize PZT solid solutions, which were found to lie between 220 °C and 490 °C, depending on the Zr/Ti ratio.77 Soon after, Jaffe filed a patent that recognized the potential of PZT for transducers.78 Jaffe also introduced the concept of a morphotropic phase boundary to the piezoelectric community79 (discussed in Sec. IV B 2 a) and recognized its potential for a broad range of electromechanical devices.80 This shifted the interest of the scientific community and industry towards this family of materials for piezoelectric applications. In the following decades, the interest in BT-based materials was mostly focused on their dielectric properties and their use in capacitor applications.

During the 1960s and 1970s, new solid state physics concepts arose to explain ferroelectricity in perovskite oxides, including lattice dynamical approaches and the soft mode theory.31,33,81 During the 1970s through 1990s, there was a diversification of the ferroelectrics community working in PZT and BT-based materials, which was marked by the appearance of new fields associated with electro-optics and thermistors. In fact, BT-based materials have been indispensable in the understanding and technological applications of thermistors due to their positive temperature coefficient of resistance (PTCR).33 

During the 1980s and 1990s, the integration of ferroelectrics and miniaturization of devices began.33 In part due to these technological drivers, the basic knowledge of piezoelectric materials continued to evolve. BT single crystals and ceramics proved themselves highly pertinent as model materials for research on strain mechanisms82–85 as well as domain structure and microstructure engineering.86–96 This trend, together with the governmental regulations targeting environmentally friendly piezoelectrics, was probably the impetus for research on (Ba,Ca)(Zr,Ti)O3 for piezoelectric applications.11,97 Clearly, the work by Liu and Ren11 reignited the interest of scientists and some industries in this system (see Sec. VI for further details), which had been lost to a great extent since 1954.

It is important to note, however, that the technological utility of these materials as piezoelectrics is rather limited owing to their restricted temperature operational range. Thus, to date, this family of materials does not constitute an all-encompassing solution for lead-containing piezoelectrics. To highlight this fact, Table I provides well-established and impending piezoelectric applications, together with our view of the realistic potential of BT-based piezoelectrics for each technology. The reader interested in comparing the evolution of the technological applications based on piezoelectrics in the last 25 years may compare this table with Table 2 of Ref. 31. As it will become apparent throughout Secs. V and VI, however, there is still need for further research to make technology transfer of BT-based materials into industry a reality.

TABLE I.

Current and future applications of piezoelectric materials, their critical figures of merit, and perspectives on the potential of BT-based materials for each type of application. Reprinted with permission from J. Rödel et al., J. Eur. Ceram. Soc. 35, 1659–1681 (2015). Copyright 2015 Elsevier. k: electromechanical coupling coefficient, Qm: mechanical quality factor, d: piezoelectric strain coefficient, g: piezoelectric voltage coefficient, Fr-TC: temperature coefficient of resonance frequency, xmax/Emax: normalized strain, vmax: vibration velocity.

Temperature rangeResonant or non-resonantApplications well-established impendingFigures of meritPotential of BT-based materials
well-establishedimpending
Special use TC > 500 °C Resonant  Aerospace, aircraft, nuclear power plant or geothermal power plant sensors k2·Qm, d·g Very low 
SMD piezoelectric Sounders TC > 250 °C Resonant Filter  k, FrTC Low 
Oscillator  Qm, FrTC 
Gyro sensor  k2·Qm 
Non-resonant Acceleration sensor and HDD shock sensor  d·g 
Automotive TC = –40–125 °C Resonant Knocking sensor and back sonar Energy harvesting (TPMS) k2·Qm Moderate 
Non-resonant Knocking sensor Energy harvesting (TPMS) d·g Moderate 
Fuel injection  xmax/Emax Low 
Consumer TC = –20–80 °C Resonant Fish sonar, flow meter, and medical probe Energy harvesting (Burglar alarm), ultrasonic transducer (data entry device), and non-destructive testing k2·Qm Very High 
Ultrasonic cleaner, ultrasonic machining tool, camera lens autofocus (motor), power window (motor), backlight inverter, and high-voltage supply transformer Wind blower and air ionizer k2·Qm, vmax High 
 Micro-mass sensor Qm High 
Non-resonant Microphone Energy harvesting (Burglar alarm) d·g High 
Stove burner, lighter, buzzer, and vibration damping (sports gear)  d High 
Ink jet, loud speaker, and camera lens module HDD tracking and pump xmax/Emax Moderate 
Temperature rangeResonant or non-resonantApplications well-established impendingFigures of meritPotential of BT-based materials
well-establishedimpending
Special use TC > 500 °C Resonant  Aerospace, aircraft, nuclear power plant or geothermal power plant sensors k2·Qm, d·g Very low 
SMD piezoelectric Sounders TC > 250 °C Resonant Filter  k, FrTC Low 
Oscillator  Qm, FrTC 
Gyro sensor  k2·Qm 
Non-resonant Acceleration sensor and HDD shock sensor  d·g 
Automotive TC = –40–125 °C Resonant Knocking sensor and back sonar Energy harvesting (TPMS) k2·Qm Moderate 
Non-resonant Knocking sensor Energy harvesting (TPMS) d·g Moderate 
Fuel injection  xmax/Emax Low 
Consumer TC = –20–80 °C Resonant Fish sonar, flow meter, and medical probe Energy harvesting (Burglar alarm), ultrasonic transducer (data entry device), and non-destructive testing k2·Qm Very High 
Ultrasonic cleaner, ultrasonic machining tool, camera lens autofocus (motor), power window (motor), backlight inverter, and high-voltage supply transformer Wind blower and air ionizer k2·Qm, vmax High 
 Micro-mass sensor Qm High 
Non-resonant Microphone Energy harvesting (Burglar alarm) d·g High 
Stove burner, lighter, buzzer, and vibration damping (sports gear)  d High 
Ink jet, loud speaker, and camera lens module HDD tracking and pump xmax/Emax Moderate 

The piezoelectric effect represents a linear coupling between electrical and mechanical fields. When a piezoelectric material is subjected to external mechanical stress, electric charge is generated on the surface. The polarity of the generated surface charge depends on the direction of the applied stress, i.e., compressive or tensile. The conversion of mechanical to electrical energy is known as the direct piezoelectric effect. If, on the other hand, an external electrical field is applied to the piezoelectric material, the material dimensions are changed. Depending on the direction of the field, the material either contracts or expands. This property is known as the converse piezoelectric effect. Piezoelectricity is exhibited by crystals belonging to 20 of the 32 crystal classes.

Polar dielectrics, also referred to as pyroelectrics, belong to one of the ten crystal classes in which there exists a polar axis with a direction that is fixed by symmetry. The direction of the polar axis cannot change, for example, with temperature or pressure, unless the symmetry changes. A change in temperature, however, modifies the magnitude of the polarization. The relation between the changes in temperature and polarization is known as the pyroelectric effect.

Ferroelectrics are polar materials that possess at least two equilibrium orientations of spontaneous polarization in the absence of an electric field. Under the application of an electric field, the direction of the polarization vector can be reoriented. Hence, ferroelectric materials are both piezoelectric and pyroelectric and exhibit nonlinear phenomena associated with polarization reversal. The linear and nonlinear material responses of polar dielectrics and ferroelectrics are treated in Sec. III C. Most ferroelectric materials undergo a displacive structural phase transition from a high temperature prototype phase (often centrosymmetric) into one or more ferroelectric phases of lower symmetry. Barium titanate belongs to the family of perovskite materials with general formula ABO3. In the schematic in Fig. 1, Ba2+ is located on the A-site at the corners of the cubic unit cell, while Ti4+ occupies the B-site in the cell center. The O2– anions are located at the face centers of the unit cell and constitute BO6 octahedra.98,99 From a crystallographic point of view, the appearance of spontaneous polarization in barium titanate is related to a shift of the Ti4+ and O2– ions relative to the Ba2+ ion at the origin. The resulting electric dipole moment is known as the spontaneous polarization, Ps. The appearance of spontaneous polarization is accompanied by changes in the dimensions of the unit cell. The strain relative to the cubic prototype due to these dimensional changes is termed the spontaneous strain, xs.

FIG. 1.

Changes in primite-cell lattice parameters and anomalies in relative permittivity (εr=ε/ε0) during the sequence of phase transitions in BaTiO3. The right side of the figure illustrates the crystal structure of the cubic prototype phase and the unit cell distortions in each of the ferroelectric phases of BaTiO3. Note that the cell-doubled orthorhombic structure is represented as a primitive pseudo-monoclinic cell for ease of comparison with the tetragonal and rhombodedral phases. From F. Jona and G. Shirane, Ferroelectric Crystals. Copyright 1962 Dover Publications, Inc. Reprinted with permission from Dover Publications, Inc.99 

FIG. 1.

Changes in primite-cell lattice parameters and anomalies in relative permittivity (εr=ε/ε0) during the sequence of phase transitions in BaTiO3. The right side of the figure illustrates the crystal structure of the cubic prototype phase and the unit cell distortions in each of the ferroelectric phases of BaTiO3. Note that the cell-doubled orthorhombic structure is represented as a primitive pseudo-monoclinic cell for ease of comparison with the tetragonal and rhombodedral phases. From F. Jona and G. Shirane, Ferroelectric Crystals. Copyright 1962 Dover Publications, Inc. Reprinted with permission from Dover Publications, Inc.99 

Close modal

The cubic phase of barium titanate belongs to the centrosymmetric crystal class m3¯m. As such, it is both paraelectric and non-piezoelectric. The order parameter for the transition from the cubic prototype phase into the lower symmetry ferroelectric phases is the spontaneous polarization and is related to the amplitude of a transverse optic soft mode that condenses at the Curie temperature, TC. The Curie principle asserts that the “proper” ferroelectric phase(s) that may appear in the crystal are those that are subgroups of the prototype phase. Thus, they must contain all symmetry elements common to the symmetry group of the prototype and the symmetry group of the order parameter. The spontaneous polarization is a polar vector quantity and its symmetry group is m. Shuvalov100 demonstrated that the cubic m3¯m prototype phase of the perovskite crystals allows seven proper ferroelectric phases, one of tetragonal (4mm), one of rhombohedral (3m), one of orthorhombic (mm2), three of monoclinic (m), and one of triclinic (1) symmetry.

When cooled at ambient pressure, barium titanate undergoes a sequence of first-order phase transitions: cubic (Pm3¯m)131°C tetragonal (P4mm) 0°C orthorhombic (Amm2) ¯90°C rhombohedral (R3m).99 These transitions correspond to the appearance of spontaneous polarization directed parallel to the edge (tetragonal) of the pseudocubic unit cell of the perovskite structure, and its subsequent re-orientation along a face diagonal (orthorhombic) and body diagonal (rhombohedral). The transitions between phases are accompanied by strong dielectric softening, as indicated by three distinct maxima in the relative permittivity (Fig. 1). These phase transitions are also accompanied by distinct anomalies in thermal, mechanical, and piezoelectric properties, which are exploited in device applications.

As the transition between the cubic and tetragonal structure at TC involves the appearance of spontaneous polarization, it is a paraelectric–ferroelectric transition. In barium titanate, this transition is of first-order. Above the Curie temperature, the dielectric susceptibility (η) follows the Curie-Weiss law:

ηεε0=CTθ,
(1)

where C is the Curie constant, θ is the Curie-Weiss temperature, ε is the real part of dielectric permittivity, and εo is the permittivity of free-space.98 In contrast, the lower temperature transitions involve a re-orientation of the polarization direction and are often referred to as inter-ferroelectric transitions. From group theoretical analyses of the relations between phases at the tetragonal ↔ orthorhombic and orthorhombic ↔ rhombohedral transitions, these transitions are also of first-order.

The starting point for understanding the constitutive behavior of polar dielectrics is a form of the general field response theory constructed in the approximation of linear thermodynamics. It is assumed that the equilibrium state of the crystal is described by a set of three intensive thermodynamic variables comprising temperature (T), stress tensor (X, note that bold letters indicate tensors), and electric field vector (E), and their proper conjugate extensive variables of entropy (S), strain tensor (x), and dielectric displacement vector (D). According to the first law of thermodynamics the reversible change of the internal energy, dU, is given by

dU=Q+W,
(2)

where, from the second law of thermodynamics, the heat absorbed by the crystal is Q=TdS. The work, W, done on the crystal consists of both mechanical and dielectric contributions

W=Xdx+EdD,
(3)

and so the differential form of the internal energy becomes

dU(S,X,D)=TdS+Xijdxij+EidDi,
(4)

wherein the range of letter indices is i,j =1, 2, and 3. Since three independent variables can be chosen in eight different ways from among the pairs of conjugate variables, there are seven thermodynamic functions in addition to Eq. (4), each of which can serve as an equation of state. In most cases, however, it is convenient to express Eq. (4) in a form where the independent variables are those under experimental control. Using the auxiliary function of enthalpy, H=U+W, the differential form of the free energy, G=HTS, is obtained in terms of the independent variables of temperature, stress, and electric field98,101

dG(T,X,E)=SdTxijdXijDidEi.
(5)

As Eq. (5) is an exact differential, it follows that the entropy, strain, and dielectric displacement are given by

S=GTX,E;xij=GXijT,E;Di=GEiX,T,
(6)

where the subscripts indicate those variables held constant. The second-order partial derivatives of Eq. (5) with respect to temperature, stress, and electric field give the principal material property coefficients of heat capacity (CX,E), elastic compliance (sijklE,T), and dielectric permittivity (εijX,T), respectively. It is clear from Eq. (6) that these are

CX,ET=2GT2X,E=STX,E,
(7)
εijX,T=2GEiEjX,T=DiEjX,T,
(8)
sijklE,T=2GXijXklE,T=xijXklE,T.
(9)

The second-order cross-partial derivatives of Eq. (5) describe coupled effects in the crystal. Because the order of differentiation can be reversed, the same numerical values of property coefficients are obtained for direct and converse effects. For example, the electrocaloric effect and the converse effect of pyroelectricity are described by the same property coefficient, piX,

piX=2GTEiX=SEiX,T=DiTX,E.
(10)

Similarly, the piezocaloric effect and the converse effect of thermal expansion are described by the same property coefficient, αijE,

αijE=2GXijTE=SXijE,T=xijTX,E,
(11)

while direct and converse piezoelectric effects are described by dijkT

dijkT=2GXjkEiT=DiXjkE,T=xjkEiX,T.
(12)

Naturally, under appropriate conditions all of the effects in Eqs. (7)–(12) can contribute to the entropy, strain, or dielectric displacement. Integrating these relations over small changes in temperature, stress, or electric field from an initial isothermal, stress-free, and zero-field state leads to a set of linear relations

ΔS=CX,ETΔT+αijT,EXij+piT,XEi,
(13)
xij=αijX,EΔT+sijklT,EXkl+dkijT,XEk,
(14)
Di=piX,EΔT+dijkT,EXjk+εijT,XEj.
(15)

Equations (13)–(15) describe the linear calorimetric, mechanical, and dielectric equations of state of the material. The relations are generally valid for linear polar dielectrics. They also hold for nonlinear dielectrics, such as ferroelectric materials as treated in Sec. III C, provided that the changes in independent variables are sufficiently small. However, some of the most important characteristics of ferroelectrics, such as strong electrostrictive coupling between spontaneous polarization and mechanical strain, and hysteresis in the polarization–electric field response, are inherently nonlinear. To account for these nonlinear phenomena, higher-order terms must be included in the equation of state. Higher-order terms also provide a description of possible divergences in material response, as observed in the proximity of paraelectric–ferroelectric and inter-ferroelectric transitions.

The phenomenological theory of barium titanate was developed in the classic work of Devonshire.8,9 It provided the first unified description of the observed changes in crystal form and of the variations of the thermal, dielectric, mechanical, and piezoelectric properties on cooling through the sequence of phase transitions. The phenomenological theory assumes that the observed divergences in material responses originate in the nonlinear behavior of the dielectric response. It is further assumed that there exists a spontaneous strain due to electrostriction and that the stress-induced strain can be described in the linear approximation of Hooke's law. Coupling of the dielectric nonlinearities to mechanical and thermal properties automatically gives rise to associated anomalies in other responses. Taking into account the multicomponent nature of the order parameter, i.e., the polarization vector P, allows the full matrix of tensor components describing the intrinsic properties of the monodomain, monocrystalline state to be determined in each of the ferroelectric phases.

It is usually convenient to express the free energy by choosing temperature, dielectric displacement, and stress as the independent variables. The dielectric displacement includes the free-space polarization, Di=ε0Ei+Pi, but for most ferroelectric materials the free-space polarization can be neglected in comparison to material polarization, and, hence, DiPi. With these considerations in mind, the non-equilibrium free energy can be written as the sum of three parts

ΔG1=G1T,P,XG0T=GL(T,P)+GCP,X+GE(X),
(16)

wherein G0T is the reference energy of the cubic prototype phase. The first term on the right hand side of Eq. (16), GL(T,P), is a 2‐4-6 Landau polynomial describing the phase transitions among paraelectric and ferroelectric phases. The second term, GC(P,X), is the lowest-order (linear-quadratic) electrostrictive coupling energy. The third term, GE(X), is the elastic energy. The non-zero terms in the Landau polynomial, GL(T,P), are determined by the symmetry of the cubic (m3¯m) prototype phase, and the polynomial adopts the following form:

GL(T,P)=12χ0TθP12+P22+P32+14ξ1(T)P14+P24+P34+12ξ2(T)P12P22+P22P32+P32P12+16ζ1(T)P16+P26+P36+12ζ2(T)P14P22+P32+P24P32+P12+P34P12+P22+12ζ3(T)P12P22P32.
(17)

In accordance with the Curie-Weiss law [Eq. (1)], the coefficient of the quadratic term, χ0=1/ε0C, is the dielectric stiffness and the coefficients of the quartic and sextic terms, ξi(T) and ζi(T), are higher-order dielectric stiffnesses. The higher-order dielectric stiffnesses are, in principle, also analytical functions of temperature, and in accordance with the Landau theory102 are given by equations of the form

ξi(T)=ξiθ+ξ1Tθ+12ξiTθ2+.
(18)

As Tθ, the Landau polynomial becomes asymptotically accurate, and it is evident that near the Curie temperature the higher-order terms can be treated as constants, ξiξiθ and ζiζiθ. A general observation for ferroelectric perovskite crystals is that the range of validity of the Landau theory is wider than expected given the assumptions inherent to its formulation, such that the theoretical predictions can often be extrapolated with reasonable accuracy to temperatures well below the Curie temperature.103 

The electrostrictive strain associated with the distortion of the cubic prototype phase is assumed to be of the same order of smallness as the square of the spontaneous polarization

xij=QijklPkPl,
(19)

where Qijkl are the electrostrictive coefficients of the cubic phase in polarization notation. The electrostriction tensor is symmetrical with respect to any permutations ij, kl, and (ij)(kl) and there are three non-zero components in cubic crystals (in Voigt notation: Q11, Q12, and Q44). We note here that the existence of a converse electrostriction remains a controversial subject with authors disagreeing on its existence.104,105 The discussion of this phenomenon is outside the scope of this review.

The coupling energy, GC(P,X), is the product of an applied stress and the electrostrictive strain, and using Voigt notation, it follows from Eq. (19) that this is

GCP,X=Q11X1P12+X2P22+X3P32Q12X1P22+P32+X2P32+P12+X3P12+P22Q44X4P2P3+X5P1P3+X6P1P2.
(20)

In the approximation of Hooke's law, the stress-induced mechanical strain is

xij=sijklPXkl,
(21)

where sijklP are the elastic compliances of the cubic phase (in Voigt notation s11P, s12P, and s44P) at constant polarization. The elastic energy, GE(X), is the product of applied stress and induced mechanical strain, and again using Voigt notation, it follows from Eq. (21) that this is

GEX=12s11PX12+X22+X32s12PX1X2+X2X3+X3X112s44PX42+X52+X62.
(22)

Substituting Eqs. (17), (18), (20), and (22) into Eq. (16) gives the elastic Gibbs free energy, ΔG1, which describes the nonlinear coupling between the thermal, dielectric, and mechanical responses of the crystal.

For barium titanate, the Landau polynomial [Eq. (17)] has four solutions of interest, which depend on the non-zero components of the polarization vector, P={P1,P2,P3}. There is one trivial solution corresponding to the paraelectric cubic phase

P1=P2=P3=0,
(23)

and three others corresponding to differing directions of polarization of modulus, P=P,

P=P3,P1=P2=0,
(24)
P/2=P1=P20,P3=0,
(25)
P/3=P1=P2=P30,
(26)

or the equivalent solutions obtained by interchanging P1, P2, and P3. Inserting Eqs. (24)–(26) into the elastic free energy gives the non-equilibrium free energies of the tetragonal, orthorhombic, and rhombohedral phases, respectively. After applying these solutions to the elastic free energy [Eq. (16)], quantities of interest in each of the ferroelectric phases are computed by taking first and second partial derivatives with respect to temperature, polarization, and/or stress.

The first partial derivatives with respect to each of these variables give the electric field components, entropy, and mechanical strain components, respectively. Taking conditions of constant temperature and stress, these are

Ei=ΔG1Pi;SP=ΔG1TP;xiP=ΔG1XiP.
(27)

Putting the electric field components equal to zero

ΔG1P1=0,ΔG1P2=0,ΔG1P3=0,
(28)

yields the equilibrium values, P0,i determining the equilibrium spontaneous polarization Ps,α=P0 in each of the ferroelectric phases. The second partial derivatives give the material property coefficients. Taking these derivatives again with respect to temperature, polarization, and stress provides the excess heat capacity (ΔCP), the dielectric stiffnesses (χij), and the elastic compliances (sijP)

χij=2ΔG1PiPj;ΔCPT=2ΔG1T2P;sijP=2ΔG1XiXjP.
(29)

The dielectric stiffnesses are converted from absolute to relative values by multiplying by the permittivity of free-space, ε0. The relative dielectric susceptibility coefficients (ηij) are given by

ηij=Aij/Δ,
(30)

where Aij and Δ are the cofactor and determinant of χij matrix, respectively. As with the linear thermodynamic theory, second-order cross-partial derivatives give other properties of interest. In particular, the piezoelectric charge coefficients (dij) are given by

dij=bkjηik,
(31)

wherein bij=2ΔG/PiXj. Using Maxwell relations, it can also be shown6 that the elastic compliances at constant electric field are

sijE=sijP+bmidmj.
(32)

Equation (16) together with Eqs. (24)–(32) are sufficient to describe the equilibrium free energies in each of the ferroelectric phases and the corresponding matrices of thermal, mechanical, dielectric, and piezoelectric property coefficients.9 

As a parameterized phenomenological theory, suitable experimental data must be available to determine the Curie and Curie-Weiss temperatures (TC, θ), dielectric stiffness (χ0), higher-order stiffnesses (ξi, ζi), the electrostrictive coefficients (Qij), and the elastic compliances (sijP). If a suitable set of coefficients is available from experiments, the intrinsic properties of the monodomain state can be self-consistently determined, as depicted in Fig. 2.

FIG. 2.

Representative predictions of the Devonshire theory (a) spontaneous polarization, (b) dielectric susceptibility, (c) piezoelectric charge coefficients, and (d) elastic compliances for a mechanically free, monodomain single crystal of barium titanate at zero electric field.

FIG. 2.

Representative predictions of the Devonshire theory (a) spontaneous polarization, (b) dielectric susceptibility, (c) piezoelectric charge coefficients, and (d) elastic compliances for a mechanically free, monodomain single crystal of barium titanate at zero electric field.

Close modal

The phenomenological theory as summarized above is a useful tool for experimentalists because it provides a relatively simple framework within which the various physical properties of ferroelectric materials can be correlated. For example, the extrema in dielectric and piezoelectric coefficients near phase transitions, as illustrated in Fig. 2, have been described in terms of polarization rotation and extension mechanisms. These two terms emphasize the relative importance of the divergence in transverse or longitudinal dielectric susceptibility, respectively, on approaching either a paraelectric to ferroelectric or an inter-ferroelectric phase transition.106,107 In addition, physical properties of a particular crystal as measured subject to one set of experimental conditions can be predicted under a different set of conditions, the latter being difficult to access in the laboratory. Alternatively, the physical properties of a given crystal as measured by different experimental methods can be compared with the theoretical predictions and so checked against one another for consistency. In those instances, where discrepancies between theory and experiment are observed, it is often possible to trace the differences in the quality of the specimens, to errors in the measurements, or to the occurrence of other physical phenomena in the crystal that were not anticipated at the outset of the experiments. In the latter case, embellishments to the low-order phenomenological theory described above may be required. Following this approach, a self-consistent set of physical properties characterizing the monodomain, single crystalline state can be established. For high-quality crystals for which reliable information is available, polycrystalline-averaging, such as the Voigt-Reuss-Hill method, may be used to estimate the properties of corresponding randomly oriented ceramic material.101 

In the absence of external stimuli, such as an electric field or mechanical stress, the spontaneous polarization will be oriented along a family of crystallographic directions with the lowest free energy. For example, in the tetragonal (P4mm) phase of BT, the spontaneous polarization vector may be parallel to any of the six equivalent ⟨100⟩ directions. The regions of the ferroelectric where the polarization is uniformly oriented are called ferroelectric domains and the boundary between two domains is termed a domain wall.

The formation of domains in ferroelectric crystals is a consequence of the reduction in the elastic and electrostatic energies.101,108,109 The walls separating domains with parallel but opposite polarization directions are called 180° domain walls, whereas the walls separating domains with polar vectors oriented at a given angle to one another are described as non-180° domain walls. For example, in the tetragonal phase of BT, both 90° and 180° domains contribute to the reduction of the energy due to depolarizing electric fields, but only 90° domains contribute to the minimization of elastic energy. The permitted domains for orthorhombic (Amm2) symmetry are 60°, 90°, 120°, and 180°, while for the rhombohedral (R3m) symmetry, the allowed domains are 71°, 109°, and 180°.110 

In the virgin state, a ferroelectric material exhibits a random polydomain configuration. This leads to a macroscopic polarization equal to zero. Figure 3(a) represents schematically the virgin state of a ferroelectric material. At low electric fields, the relation between strain and polarization is nearly linear

Pi=ε0εijEj,
(33)

where the linear increase with electric field is due to the intrinsic material response described above. Upon application of a sufficiently large external stimulus, such as an electric field or mechanical stress, domain walls can be displaced leading to domain switching. Domain switching is an extrinsic process, in the sense that it occurs on a length scale larger than that of a unit cell. The polarization loop, which arises as a consequence of switching, is the fingerprint of a ferroelectric material and involves the nonlinear increase of polarization with electric field (Fig. 3).111 As discussed above, the angles between the polarization vectors of neighboring domains are restricted by crystal symmetry. Only an electric field can reorient 180° domain walls and no strain is generally associated with this type of domain switching (although higher order strain contributions were actually proven112). The non-180° domain walls, on the other hand, can be reoriented either by an electric field or a mechanical stress. This type of reorientation is generally termed ferroelastic switching and significantly contributes to the macroscopic strain of ferroelectrics.

FIG. 3.

Polarization–electric field hysteresis loop of ferroelectric crystal with remanent polarization Pr and coercive field Ec where the polarization is set back to zero. (a), (b), (c), (d), and (e) represent different polarization configurations under an applied electric field. The strain-electric field butterfly loop is also shown.

FIG. 3.

Polarization–electric field hysteresis loop of ferroelectric crystal with remanent polarization Pr and coercive field Ec where the polarization is set back to zero. (a), (b), (c), (d), and (e) represent different polarization configurations under an applied electric field. The strain-electric field butterfly loop is also shown.

Close modal

Domain walls can be displaced reversibly or irreversibly. Reversible domain wall displacements refer to domain wall motion around a local energy minimum, while irreversible domain wall displacement arises from jumps of domain walls between local energy minima separated from one another by a potential barrier.113 At very high electric fields, the domain walls oriented along the field direction reach a saturation state, thereby restoring a linear change in polarization with electric field. The saturation state is characterized by a substantial change in the domain configuration as compared with the virgin state [Fig. 3(b)]. Once the linear increase in polarization sets in, a saturation of polarization, Psat, is reached. The spontaneous polarization Ps of the material may be estimated by extrapolating the linear polarization region near the saturation polarization down to zero electric field along the saturation polarization tangent.

When the field is reduced, some domain walls will back-switch. Hence, at zero electric field, a non-zero macroscopic polarization, or remanent polarization Pr, is observed [Fig. 3(c)]. To bring the polarization back to zero an electric field must be applied in the opposite direction. The field at which the polarization regains a value of zero is called the coercive field Ec. The polarization state at the coercive field is again random and has no net polarization [Fig. 3(d)]. The observed hysteresis in the PE curve is thus a consequence of reversible and irreversible displacement of domain walls (i.e., switching). Switching is accompanied by energy dissipation in the material and produces undesired thermal losses.112,114 The mechanisms of polarization switching have been studied in many different ferroelectric materials.65,115

The re-orientation of spontaneous polarization and domain switching are accompanied by a mechanical strain. As a result, if the electric field is cycled, a strain-electric field hysteresis loop is also obtained, which resembles the shape of a butterfly (Fig. 3). At any given electric field strength, at which the strain-field response deviates from linearity, an engineering large signal piezoelectric coefficient, also referred to as normalized strain, can be defined as

dij*=xijEj.
(34)

Most of the strain developed in ferroelectrics under an electric field and far away from phase transitions arises from (i) the intrinsic converse piezoelectric effect, (ii) intrinsic electrostriction, and (iii) the extrinsic reversible and irreversible displacement of non-180° domain walls. Due to the importance of intrinsic and extrinsic effects these contributions are described in more detail in Sec. III E.

Several investigations in barium titanate, and related materials such as PZT, indicate that domain wall movement, among other extrinsic contributions, can be the major factor determining the dielectric and piezoelectric properties.116–118 The extrinsic contributions are highly dependent on the crystal symmetry, defects, external stimuli, boundary conditions, and temperature. They can be strongly reduced under measurement conditions involving high dc electric fields where domain switching is saturated, high-frequency ac electric fields where domain wall motion cannot follow the alternating field, and/or at cryogenic temperatures where domain wall motion is thermally frozen. These conditions are often used to experimentally discriminate between intrinsic and extrinsic contributions. A common approach to estimate the irreversible domain wall displacement in ferroelectrics is provided by the Rayleigh model.82,84,119 The Rayleigh model can be applied in low field conditions, where the density and structure of the domain walls remain mostly unchanged as the field is cycled.82,119 This model relies on the assumption that the nonlinear behavior is a consequence of irreversible domain wall displacements.84,119 The piezoelectric response as a function of electric field amplitude can be described by

dE0=dint+αE0,
(35)

where dint represents the initial piezoelectric response as consequence of reversible domain wall displacement and intrinsic piezoelectricity, α is the Rayleigh coefficient, and E0 is the amplitude of the applied alternating field. Similarly, the piezoelectric terms in Eq. (35) can also be replaced by the corresponding relative permittivity terms. The field-dependent component αE0 represents the hysteretic contribution of irreversible domain wall displacements into a new equilibrium positions when the applied electric field is sufficiently large to overcome the potential barrier between two equilibrium positions. The origin of the hysteresis (energy loss) is the pinning and unpinning processes of the domain walls during field cycling while the domain wall is displaced from one equilibrium position to another.83,119,120 The Rayleigh model has also certain limitations. It cannot describe, for instance, the domain wall displacement of hard PZT. In such cases, or at electric fields higher than the Rayleigh regime, higher-order terms can be generally used to described the domain wall displacement.83,119 Irreversible domain wall displacement strongly depends on the domain structure architecture and domain wall mobility. The most important variables controlling domain wall mobility are the crystal symmetry and concomitant spontaneous strain as well as pinning centers and microstructure.84 Pinning centers alter domain wall mobility dramatically and are a result of defects such as vacancies, interstitials, among others.121,122

The measurement of recoil curves and bias-field-dependent small signal properties are alternative approaches to estimating extrinsic properties.123–125 A recoil curve is a subloop at a given electric field and polarization state. In this method, it is assumed that the extrinsic irreversible contributions can be estimated by the remaining polarization upon electric field removal. The extrinsic reversible contribution is calculated as the difference between the total polarization and remaining polarization. For the correct estimation of reversible and irreversible processes, the recoil curve should be obtained at sufficiently low electric field to assure that irreversible processes remain constant. Probing the extrinsic contributions via recoil curves near the coercive field is not reliable. This is because an electric field of a low magnitude such as the one used during the recoil loop is high enough to produce irreversible domain wall displacements near the coercive field.124 

Bias-field-dependent small signal properties are measured by superimposing a sinusoidal ac electric field in the kHz range to a base waveform in the Hz range. For a proper estimation, the amplitude of the modulating wave should be as low as possible so that domain walls are only displaced reversibly. The base waveform should be ideally as large as required to achieve the saturation of the material. This ensures that the intrinsic contributions are properly estimated upon saturation of switching. The measured property with zero bias-field is comprised of intrinsic and irreversible extrinsic contributions, under the assumption that reversible switching is considerably reduced at zero bias-field. This measurement has to be interpreted pointwise since the measured reversible domain wall motion will be a function of the domain configuration imposed by the base waveform. In other words, it provides information on the reversible domain wall movement at a given irreversible domain state defined by the base waveform. Bias-field dependent capacitance measurements provide information on both 180° and non-180° switching processes, whereas bias-field-dependent measurements of d33 provide information only on non-180° switching processes.124,125 The latter considers that 180° domain wall displacements do not contribute to the strain of the material at low electric field.126 

1. Grain and domain size

Microstructural engineering is an effective strategy to tune functional properties. Grain size has a profound effect on the dielectric and piezoelectric properties of ferroelectrics.127–134 Grain size can be tailored by modification of powder particle size and/or the sintering process. Another related approach to optimize properties is by engineering the domain configuration. Domain engineering is a method to produce a stable and desirable domain size in order to maximize the piezoelectric and dielectric properties.135 It has been applied to single crystals94,136 but has not been widely used to tailor properties in polycrystalline materials. Both approaches, however, share similarities since the grain size and domain size in polycrystalline materials are related.

An optimized grain size generally results in increased small signal and large signal electromechanical properties, increased relative permittivity, decreased Curie temperature, and decreased coercive field as compared with the material with non-optimized grain size.127,128,132 The optimal grain size results in a maximized density of domain walls that are capable of switching with minimal back switching.117,130–132 Grains that are too large often reduce piezoelectric and dielectric properties as a consequence of excessive back switching.131 In contrast, grains that are too small generally lead to suppression of ferroelectricity due to reduced lattice distortion.137–139 At very small grain sizes, domains may also become unstable, since the spontaneous polarization is compensated by charges at grain boundaries and/or by polarization gradients.139 Thus, depending on the material, there is a threshold grain size at which ferroelectricity ceases.

Increasing grain size in BT yields an enlargement of domain size [Fig. 4(a)] and reduction of the piezoelectricity [Fig. 4(b)]. A strong increase in functional properties in BT occurs at grain sizes between 1 μm and 2.3 μm and domain sizes below 100 nm.90,117,129,132 In contrast, a critical grain size between 10 nm and 100 nm induces a paraelectric state in BT at room temperature.137–139 Several studies of BT have determined that a fine domain structure through engineered synthesis routes can greatly enhance its piezoelectric and dielectric properties.86,88–91 For BT at room temperature, d33 values between 350 pC/N and 500 pC/N and d31=−185 pC/N were achieved.86,89,90,129,140,141 Thus, the properties of engineered BT can be comparable with the most widely investigated solid solutions that will be treated later on.

FIG. 4.

(a) Relationship between domain size and grain size for BT polycrystalline materials adapted from Ref. 142. (b) d31 and k31 as a function of domain size for [111]c-poled BT single crystals taken from Ref. 94.

FIG. 4.

(a) Relationship between domain size and grain size for BT polycrystalline materials adapted from Ref. 142. (b) d31 and k31 as a function of domain size for [111]c-poled BT single crystals taken from Ref. 94.

Close modal

2. Texturing

Texturing is also an effective way to enhance piezoelectric and dielectric properties, as well as to improve their temperature stability.5,143–146 In contrast to other approaches, it does not lower the temperature range at which the ferroelectric state remains stable.147 Templated grain growth and reactive templated grain growth are the most commonly used texturing techniques.148 In lead-free ferroelectrics possessing the perovskite structure, orientation degrees up to 90% were achieved in various systems. A high degree of grain orientation produces enhancements of d33 between 1.4 and 2.1 times with respect to the random polycrystalline material.148 The maximum piezoelectric and dielectric properties achievable in textured polycrystalline materials are limited by the properties of the corresponding single crystal.149 This is schematically represented in Fig. 5.

FIG. 5.

Schematic representation of the piezoelectric coefficient d33 as a function of texturing degree.

FIG. 5.

Schematic representation of the piezoelectric coefficient d33 as a function of texturing degree.

Close modal

BT materials with [001], [110], and [111] texture feature improved electromechanical properties compared with random polycrystalline materials.95,150,151 Vriami et al.151 used [001]-oriented BT plate-like particles synthesized via the molten salt method to improve piezoelectricity. With an optimum incorporation of 1 wt. % templates, they achieved a 97% textured material and a d33 = 274 pC/N. Note, however, that leakage current increased substantially with template addition.151 Kobayashi et al.150 synthesized [111]-textured BT via electrophoretic deposition under a magnetic field of 12 T. They claimed 100% texture, which led to an enhancement of 30% in d33* and reduced the strain hysteresis. Texturing is also applicable in materials with engineered grain and domain sizes, although it increases the processing complexity and costs.152 Wada et al.92,95,96 indicated that [110]-textured BT, with an average grain size of 75 μm and average domain size of 800 nm, has a d33 of 788 pC/N, clearly highlighting the potential of this approach. Texturing maximizes the piezoelectric and dielectric properties since it increases the fraction of domains oriented along the electric field.147,148

3. Composite and core-shell approach

One of the recent strategies to improve the properties of alkaline-niobate- and alkaline-bismuth-titanate-based piezoelectrics involves the design of heterostructure composite153–157 and core-shell materials.17,158 The development of BT-based core-shell bulk materials has been widely used to improve dielectric properties for capacitor applications.17,159 Nonetheless, to date, this microstructural engineering approach remains in its infancy to tailor piezoelectric properties.17 The core-shell microstructures in bulk materials are generally a consequence of partial homogenization as a result of limited diffusion160–162 or formation of a liquid phase with an excess of solute that precipitates or crystallizes upon cooling.163–165 

The main research in alkaline-bismuth-titanate-based materials is directed towards their application in off-resonance actuators working at high electric fields.16,17 In this context, the large signal strain has been attributed to an electric field-induced phase transition.16 Composites were designed to aid this electric field-induced phase transition due to the different polarity of the chosen ferroelectric constituents.153–155 Recently, alkaline-bismuth-titanate-based composites also were tested for temperature-stable small signal piezoelectric applications. In this case, a semiconductor was selected as seed material. It was proposed that the free charges of the semiconductor agglomerate at grain boundaries, thereby stabilizing the domains of the matrix. This results in considerably improved stability of the piezoelectric properties.156,157

The core-shell approach was also successful in obtaining promising alkaline-niobate-158 and alkaline-bismuth-titanate-based17,166 piezoelectrics suitable for off-resonance actuators working at high electric fields. Tuning the core-shell microstructure, grain size, and density was used to increase the large signal strain output and reduce the electric field required to induce the high strain.160 It was also proven that the mechanisms of core-shell materials can be quite complex167 and that the electrical charges at the interface between core and shell have an important role in determining the piezoelectric properties.168 To date, no core-shell materials were specifically developed for small signal piezoelectric applications. Neither have BT-based core-shell materials been engineered for piezoelectric properties. Therefore, the potential of core-shell piezoelectrics remains largely unexplored.

Owing to their simplicity, chemical modifications constitute the most common approach for tuning dielectric and electromechanical properties of ferroelectrics. In ferroelectrics, the term doping typically refers to ion substitutions made at concentrations lower than 3 to 5 at. %. Despite the low concentration, dopants can alter properties significantly. Chemical modification typically refers to substitutions greater than 5 at. % and extending well into the chemical mixing regime to form solid solutions.10 Modifiers are used to raise or lower the Curie temperature and/or to alter the nature and sequence of phase transitions from the high temperature prototype phase. Both dopants and modifiers are discussed in detail below.

1. Doped BaTiO3 for piezoelectric applications

In perovskites, doping generally involves the replacement of either the A- or B-site cations. Although the dopant concentration may be very low, they can considerably alter the functional properties by modifying the extrinsic contributions.121,169 Isovalent or aliovalent dopants can be added prior to calcination to modify properties or also as a sintering aid to facilitate the densification process. The dopants used for a particular ferroelectric are selected based on properties to be controlled for a target application.

Aliovalent dopants can have a lower or higher oxidation number as compared to the lattice site, referred to as acceptor or donor doping, respectively. Acceptor doping is compensated by an increase in the concentration of oxygen vacancies and/or electron holes. This can lead to the formation of complex defect dipoles between dopant ions and oxygen vacancies that locally modify the elastic and electrostatic fields. These complex defects serve as pinning centers, which hinder domain wall motion and lead to ferroelectric hardening. Hardening is reflected in pinched ferroelectric hysteresis loops and development of an internal bias-field. It is also accompanied by a reduction of the dielectric and piezoelectric response as well as a decrease in the dissipation factor.

Acceptor-doped ferroelectrics with charge-compensating oxygen vacancies form the technological basis for hard piezoceramics.170,171 It is well documented that domain configurations, switching processes and thus electromechanical properties are highly dependent on the defect dipoles and their alignment along the spontaneous polarization direction of ferroelectric phases.172,173 This phenomenon has been termed a symmetry-conforming short-range ordered (SC-SRO) configuration of point defects.174 The SC-SRO model indicates that, at equilibrium, the local symmetry surrounding point defects will conform to the symmetry as the host crystal. In the case of ferroelectrics, the local symmetry is that of the defect dipoles, which align along the spontaneous polarization direction.174 Since the ferroelastic switching responsible for the strain does not involve diffusion of ions, symmetry conforming defect dipoles act as a restoring force for reversible domain switching and concomitant strain. This strain mechanism has been used to describe the recoverable strain of several doped single crystals174,175 and ceramics.176–178 It is worth noting though that this mechanism is based on a balance between kinetics (ion migration) and thermodynamics.179 Therefore, the effectiveness of this mechanism to produce a restoring force after cycling, different temperatures, and frequencies should be assessed for each specific case. Some studies have indeed established certain stability of the reversible strain180–182 but more work in this area is required.

Replacing the A- or B- site cations with a donor dopant is compensated by free electrons, a decrease in oxygen vacancies, and/or formation of cation vacancies. Donor doping leads to ferroelectric softening, resulting in a high remanent polarization, high dielectric loss, as well as an increase in dielectric and piezoelectric properties. These features are ascribed most commonly to an increased mobility of domain walls.2,183

Doping can be used as an effective strategy to tune several functional properties. A good example for aliovalent doping can be found for semiconductors based on barium titanate, which exhibit a PTCR. In PTCR materials, the electrical conductivity abruptly changes from a conductive to a non-conductive state when the temperature is raised, and the change in conductivity can be used in sensors, self-regulating heaters, overcurrent protection, and time delay circuitry. In barium titanate, the PTCR behavior is achieved by introducing donor dopants, such as Y3+ or La3+. These A-site donor dopants, or B-site donor dopants such as Nb5+ and Ta5+, may also be used to suppress the magnitude of the relative permittivity at TC for high temperature dielectrics, although they may need to be compensated with acceptor dopants to avoid semiconducting properties.2,10

A summary of recent works that realized promising doped BT-based materials with d33 values above 200 pC/N is given in Table II. Table II include the Curie temperature (TC), relative permittivity (ε), piezoelectric strain coefficient (d33), planar electromechanical coupling coefficient (kp), and mechanical quality factor (Qm). For comparison purposes, we note here that pure BT (with no specific engineering approaches) typically features a TC∼130 °C, room temperature εr∼1700, d33∼190 pC/N, and kp∼0.35.2 Note that all dopants presented in Table II were added before calcination, i.e., not as sintering aids. Li+ is a classical dopant used to lower the sintering temperature and promote densification through liquid phase sintering. Kimura et al.184 demonstrated that Li-doped BT nanopowders obtained by a solvothermal method can be sintered successfully at 1100 °C, which is between 200 °C and 250 °C lower than the sintering temperature generally employed for BT.2 The samples featured a d33=260 pC/N and a TC=130 °C. Yang et al.185 demonstrated the possibility to sinter LiF-doped BT at 1100 °C leading to an optimum d33 = 270 pC/N for 0.04 at. % LiF. Zhu et al.186 revealed that 0.04 at. % LiF doped BT with an excess of 0.025 at. % Ba features a d33=340 pC/N, while keeping the same sintering temperature of 1100 °C. Nonetheless, in both studies, the Curie temperature was decreased to below 95 °C. If 0.02 at. %, Ca2+ excess is added instead of Ba2+ excess to 0.04 at. % LiF-doped BT, an even higher d33 = 361 pC/N is obtained. Concomitantly, a lower TC=70 °C is also obtained. Co-doping BT with 0.04 at. % Sn4+ and 0.002 at. % Y3+ leads to promising properties with a high d33=454 pC/N and a moderate TC=84.7 °C. Nonetheless, the sintering temperature of 1420 °C was relatively high.187 Doping with A(Cu1/3Nb2/3)O3 (A = Ca2+, Sr2+, Ba2+) revealed that this combination of cations lowers TC considerably and does not increase d33 above 350 pC/N.188 

TABLE II.

Piezoelectric and dielectric properties at room temperature of doped BT with d33 values above 200 pC/N.

CompositionDopantContentOptimal contentTC (°C)εrd33 (pC/N)kpQmReferences
Li-doped BaTiO3 Li+ 0–0.06 at. 0.03 at. 130 1744 260 0.4 357 184  
Ba1+xTiO3-0.04LiF LiF 0–0.04 mol. 0.025 mol. 95 1600 340 — — 186  
BaTiO3-xLiF LiF 0–0.06 mol. 0.04 mol. 73 2857 270 0.5 — 185  
(Ba0.94Cax)Ti0.94Oδ -0.04LiF LiF and Ca2+ 0–0.05 mol. 0.02 mol. 70 2150 361 0.4 374 189  
Ba(Ti0.96Sn0.04)O3-xY2O3 Sn4+ and Y3+ 0–0.004 at. 0.002 at. 84.7 3000 454 0.5 — 187  
(1-x)BaTiO3-xCa(Cu1/3Nb2/3)O3 Ca(Cu1/3Nb2/3)O3 0–0.035 mol. 0.03 mol. 52 4000 260 0.3 — 188  
(1-x)BaTiO3-xSr(Cu1/3Nb2/3)O3 Sr(Cu1/3Nb2/3)O3 0–0.035 mol. 0.015 mol. 97 2700 333 0.5 — 188  
(1-x)BaTiO3-xBa(Cu1/3Nb2/3)O3 Ba(Cu1/3Nb2/3)O3 0–0.035 mol. 0.025 mol. 96 2000 333 0.4 — 188  
CompositionDopantContentOptimal contentTC (°C)εrd33 (pC/N)kpQmReferences
Li-doped BaTiO3 Li+ 0–0.06 at. 0.03 at. 130 1744 260 0.4 357 184  
Ba1+xTiO3-0.04LiF LiF 0–0.04 mol. 0.025 mol. 95 1600 340 — — 186  
BaTiO3-xLiF LiF 0–0.06 mol. 0.04 mol. 73 2857 270 0.5 — 185  
(Ba0.94Cax)Ti0.94Oδ -0.04LiF LiF and Ca2+ 0–0.05 mol. 0.02 mol. 70 2150 361 0.4 374 189  
Ba(Ti0.96Sn0.04)O3-xY2O3 Sn4+ and Y3+ 0–0.004 at. 0.002 at. 84.7 3000 454 0.5 — 187  
(1-x)BaTiO3-xCa(Cu1/3Nb2/3)O3 Ca(Cu1/3Nb2/3)O3 0–0.035 mol. 0.03 mol. 52 4000 260 0.3 — 188  
(1-x)BaTiO3-xSr(Cu1/3Nb2/3)O3 Sr(Cu1/3Nb2/3)O3 0–0.035 mol. 0.015 mol. 97 2700 333 0.5 — 188  
(1-x)BaTiO3-xBa(Cu1/3Nb2/3)O3 Ba(Cu1/3Nb2/3)O3 0–0.035 mol. 0.025 mol. 96 2000 333 0.4 — 188  

2. Binary BaTiO3-based solid solutions

The perovskite crystal structure admits a wide range of isomorphous ion substitutions. In fact, there are numerous binary ferroelectric systems showing complete solubility across the sub-solidus phase diagram. Typical examples of A-site modifiers in barium titanate include Sr2+, Ca2+, Bi3+, and Cu2+.10,190 Typical isovalent B-site modifications to improve barium titanate piezoelectric properties include Zr4+, Hf4+, and Sn4+.2,191–198 More details about the effect of these modifiers on the pseudo-binary phase diagrams, synthesis, and piezoelectric properties are given below.

a. Fundamentals of pseudo-binary phase diagrams

The technologically most relevant solid solution systems are those that have compounds of different symmetry located as opposing end members. In such systems, a change in composition leads to a change in Curie temperature and often to a change in the order of the paraelectric to ferroelectric transitions from first-order to second-order, or in some cases, to diffuse and/or relaxor ferroelectric behavior. The phase diagrams of these systems are usually constructed under the assumption that atomic diffusion providing equilibration of the system is thermally frozen such that single-phase regions of differing symmetry are separated by line boundaries. These boundaries may be crossed either by an isothermal change in composition or by a change in temperature at a fixed composition. It is typically the extrema in physical properties occurring near the phase boundary lines that are utilized in device applications. The physical phenomena underlying the disparate phase change characteristics displayed near transition lines in solid solution systems thus remain of intense interest.

Despite the fact that most research since 1950s has utilized the property softening associated with these transitions to enhance piezoelectric properties,7 we note that there does not seem to be a consensus as to whether the phase transitions occurring at the boundary lines should be more properly regarded as polymorphic or morphotropic.199 For example, Goldschmidt200 proposed a distinction between systems that feature compositionally driven polymorphs from those in which the transition between polymorphs occurs as a consequence of changes in temperature or pressure. The transition line in materials with compositionally driven polymorphs was termed a morphotropic phase boundary (MPB), whereas the transition line occurring as a result of changes in other thermodynamic variables was termed a polymorphic phase boundary (PPB). However, in the ferroelectrics literature, the term morphotropic is usually reserved for systems that display nearly temperature-independent (e.g., vertical) boundary lines in the composition-temperature plane.79 The archetypal example of such a system is PZT. Though widely used, this definition is somewhat arbitrary, since even in lead-based systems the MPB is not strictly vertical, and depending on the particular system, displays varying degrees of inclination and curvature. Nonetheless, we will adopt this convention here. We will refer to an MPB only to denote a nearly vertical phase boundary and use the term PPB to denote a phase boundary showing substantial inclination and/or curvature. We note the latter type of phase boundary is more typical of the BT-based solid solutions, as discussed below in more detail.

Four representative pseudo-binary phase diagrams for barium titanate-based solid solutions are illustrated in Fig. 6, which introduces a nomenclature to differentiate among the various topologies of phase diagrams in BT systems that are referred later in the text. Note that we will refer to many phase diagrams in this and subsequent sections as “pseudo-binary,” “pseudo-ternary,” and so on. The term “pseudo” is used to indicate that the end members on the phase diagram of interest are not the individual components of the system. As an example, the 50 mol. % isopleth in the three-component system BaO-SrO-TiO2 may be referred to as pseudo-binary system comprising the oxide compounds BaTiO3 and SrTiO3 as end members. The solid solution between barium titanate and strontium titanate (BSrT) is represented by the phase diagram of Fig. 6(a).201 Both the line of paraelectric–ferroelectric transitions and the lines of the inter-ferroelectric transitions shift to lower temperatures with increasing strontium concentration, and thus BSrT solid solution is described here as having a phase diagram of the “shifting” type. The second phase diagram in Fig. 6(b) is representative of the solid solution between barium titanate and barium zirconate (BZT).193,194 Note, however, that this type of phase diagram is also displayed by solid solutions between barium titanate and barium hafnate (BHT),194,198 as well as between barium titanate and barium stanate (BSnT).196 The B-site cations Zr4+, Hf4+, and Sn4+ have similar effects as modifiers, albeit Sn4+ generally modifies the phase boundaries more strongly than Zr4+ and Hf4+.202 With sufficiently high B-site dopant concentration, these systems exhibit relaxor features, which were attributed to local chemical heterogeneity in BSnT.203 The line of paraelectric–ferroelectric transitions decreases with zirconium (hafnium, tin) concentration, but the lines of the inter-ferroelectric transition increase, such that stability fields of the four phases (cubic-tetragonal-orthorhombic-rhombohedral) converge on approaching the line of Curie points. The BZT (BHT, BSnT) solid solution may, therefore, be described as having a phase diagram of the “pinching” type. The third phase diagram in Fig. 6(c) is representative of the solid solution between barium titanate and calcium titanate (BCT).190 The line of paraelectric–ferroelectric transitions decreases slightly with calcium concentration, but the stability fields of the orthorhombic and rhombohedral phases vanish, at the expense of the tetragonal phase, at comparatively low substitution levels. The BCT solid solution may, therefore, be described as having a phase diagram of the “disappearing phase” type. A very similar phase diagram, except with an increase in Curie temperature, occurs in the solid solution between barium titanate and lead titanate.204 It is evident that other pseudo-binary systems can be formed by choosing appropriate isopleths within the solid solution fields of the pseudo-ternary or pseudo-quaternary systems comprising the four end-member compounds (barium titanate, barium zirconate, strontium titanate, and calcium titanate) just considered. For example, by choosing such an isopleth in the pseudo-ternary diagram formed by barium titanate, barium zirconate, and calcium titanate, the phase diagram depicted in Fig. 6(d) is obtained, which is a schematic representation of the BZT-BCT pseudo-binary phase diagram. Section V A 2 a discusses the details of this phase diagram.

FIG. 6.

Diffusionless pseudo-binary phase diagrams of barium titanate-based solid solutions: (a) barium titanate-strontium titanate,201 (b) barium titanate-barium zirconate,193,194 (c) barium titanate-calcium titanate,190 and (d) BZT-BCT. The occurrence of a tricritical point (Ttcp) and quantum saturation (QS) effects are indicated on (a).

FIG. 6.

Diffusionless pseudo-binary phase diagrams of barium titanate-based solid solutions: (a) barium titanate-strontium titanate,201 (b) barium titanate-barium zirconate,193,194 (c) barium titanate-calcium titanate,190 and (d) BZT-BCT. The occurrence of a tricritical point (Ttcp) and quantum saturation (QS) effects are indicated on (a).

Close modal

Because of the similarity of the diagram in Fig. 6(d) with the so-called morphotropic systems, such as lead zirconate titanate (PZT), lead magnesium niobate-lead titanate (PMN-PT), or lead zinc niobate-lead titanate (PZN-PT), this diagram was first regarded as a morphotropic system.11 However, this similarity is evident only in a portion of the diagram above room temperature. A careful comparison of the diagrams in Figs. 6(a), 6(b), and 6(d) reveals that the phase diagram of BZT-BCT is not topologically distinct from those of other binary solid solutions. In fact, the phase diagrams of BZT (BHT, BSnT) and BZT-BCT are both diagrams of the pinching type, differing only in the slopes of the interferroelectric transition lines. Further, as discussed above, since a morphotropic transition should occur only in systems for which the inter-ferroelectric transition lines are nearly vertical, all of the transitions between phases indicated on the diagrams in Fig. 6 should be regarded as polymorphic based on the nomenclature proposed by Goldschmidt200 and Jaffe.7 

The different phase diagrams in Fig. 6 can be rationalized by considering how the various solutes (Sr2+, Ca2+, Zr4+, Hf4+, and Sn4+) interact with the host barium titanate. The first, and perhaps most important, of these interactions is the modification of the paraelectric–ferroelectric phase transition temperature. It has been argued that the variation of the transition temperature with solute concentration can be divided into four regimes.205 In the first regime, the solute concentration is very low, and the solute atoms are widely separated, such that the distortion fields around the solute atoms do not interact. In this regime, the transition temperature is essentially insensitive to the presence of the solute. In the second regime, at somewhat higher solute concentrations, the distortion fields still do not overlap, but can couple indirectly by interactions through the structure of the host crystal. In this regime, the transition temperature changes linearly with solute concentration. In the third regime, as the solute concentration is further increased, the distortion fields begin to overlap more significantly, producing conjugated fields and a more dramatic change in transition temperature. In the fourth regime, at even higher solute concentrations, the average distance between solute atoms becomes comparable with the interatomic separation distance in the host crystal, and a homogenous field develops. In this fourth regime, the transition temperature is again linearly proportional to concentration, but with a proportionality constant that is different from that in the second regime. The net result is that the variation of the paraelectric–ferroelectric transition temperature is linear with concentration in the chemical mixing regime, but weakens at low solute concentrations, resulting in a plateau effect.205 Such an effect is evident in the phase diagram of BZT depicted in Fig. 6(b). The concentration range of this effect, in turn, depends on the type of solute (isovalent or aliovalent) and the corresponding nature and strength of the defect field. It is typically in the range of a few mole percent but may be much less. Thus, such an effect may be present in the other diagrams provided in Fig. 6. However, it may not be visible on the scale of the figure or transition temperatures may not have been measured at sufficiently low solute concentrations.

The linear dependence of a transition temperature on solute concentration in the chemical mixing regime can be described by adding to the Landau polynomial of Eq. (17), the Gibbs free energy of the solute interaction

GS(x,P)=ϑ1x(P12+P22+P32)+ϑ2x(P14+P24+P34)+ϑ3x(P12P22+P22P32+P12P32),
(36)

where ϑi are the interaction coefficients. Eq. (17) then becomes

GL(T,x,P)=GL(T,P)+GS(x,P),
(37)

and considering only the lead terms, this reduces to

GL(T,x,P)=χ0(Tθ+λ1x)2(P12+P22+P32)+ξ10(1+λ2x)4(P14+P24+P34)+ξ20(1+λ3x)2(P12P22+P22P32+P12P32)+,
(38)

wherein λ1=2ϑ1/χ0, and the ξi0=ξi(θ) with λ2=4ϑ2/ξ10 and λ3=2ϑ3/ξ20. Comparing Eqs. (17) and (38), it is seen that the Curie-Weiss temperature is a linear function of composition

θ(x)=θ(0)λ1x,
(39)

where θ(0) is the Curie-Weiss temperature in pure barium titanate (x =0) and decreases with solute concentration for λ1> 0. Similarly, the quartic terms in Eq. (38) also take on a dependence on solute concentration

ξ1(θ,x)=ξ10(1+λ2x),
(40)
ξ2(θ,x)=ξ20(1+λ3x).
(41)

A point on the composition-temperature diagram where the transition between paraelectric and ferroelectric phases passes over from first-order to second-order is known as a tricritical point (TCP) and occurs when the sum of the quartic terms in Eq. (38) are equal to zero. Thus, following Eqs. (40) and (41), the Gibbs free energy of the solute interaction also provides for the possibility of such a point. For example, a TCP has been reported in the BSrT system,206 with the location indicated in Fig. 6(a).

If, on the other hand, the solute concentration is sufficiently high as to reduce the paraelectric–ferroelectric transition temperature to values approaching absolute zero, the simple predictions in the mean-field approximation of the Landau theory no longer apply. Near absolute zero, quantum mechanical effects play a significant role, and the dependence of the transition temperature on composition strengthens. This phenomenon is known as the quantum saturation (QS) effect.207 It has been shown that for this situation, the free energy in Eq. (38) is modified to

GL(T,x,P)=χ02(θScothθSTθScothθSθ+λ1x)(P12+P22+P32)+ξ10(1+λ2x)4(P14+P24+P34)+ξ20(1+λ3x)2(P12P22+P22P32+P12P32)+,
(42)

where θS is the saturation temperature below which quantum effects become important. The steepening of the paraelectric to ferroelectric transition temperature versus composition curve due to quantum saturation effects is also observed in the BSrT system [Fig. 6(a)]. A quite similar situation occurs when barium titanate is placed under hydrostatic pressure.208,209

With reference to the phase diagrams displayed in Fig. 6, attention has thus far been focused on phenomena that occur close to the lines of the paraelectric–ferroelectric transitions, namely, the expected variation of the paraelectric–ferroelectric transition temperature with solute concentration and the possible occurrence of a TCP. To describe the different topologies of these diagrams, it is now necessary to account for the inter-ferroelectric transitions, and hence to consider explicitly the solutions to the Landau polynomial given by Eqs. (24)–(26), which correspond to the tetragonal, orthorhombic, and rhombohedral phases, respectively. Writing the Landau polynomial of Eq. (17) in terms of the modulus of polarization, P, the non-equilibrium free energy for each of these phases is

GL,T(T,P)=12χ0(Tθ)P2+14ξ1P4+16ζ1P6,
(43)
GL,O(T,P)=12χ0(Tθ)P2+18(ξ1+ξ2)P4+124(ζ1+3ζ2)P6,
(44)
GL,R(T,P)=12χ0(Tθ)P2+112(ξ1+2ξ2)P4+154(ζ1+6ζ2+ζ3)P6,
(45)

wherein it is understood that, as discussed above, the Curie-Weiss temperature is a function of composition and that the dielectric and higher-order stiffness coefficients may also depend on composition and/or temperature. Inspection of Eqs. (43)–(45) reveals that the topology of the energy surface, and hence the transitions between ferroelectric phases, as well as the anisotropy in dielectric, piezoelectric, and elastic properties, are controlled by the differences between higher-order dielectric stiffness coefficients. After minimizing the free energies of Eqs. (43)–(45) with respect to P, the free energies are equal if it turns out that ξ1=ξ2, ζ1=ζ2, and ζ3=2ζ2. It is thus convenient to rewrite the free energy in terms of three parameters, B2=ξ1ξ2, C2=ζ1ζ2, and C3=ζ32ζ2, which describe the anisotropy of the energy surface. As such, the composition and/or temperature dependences of these terms primarily control the phase diagram.

The analysis of differing types of phase diagrams becomes more transparent if Eqs. (43)–(45) are expressed in a simple general form, taking the polarization vector P to be nP, where n is unit vector in the direction of polarization and P =|P| is its absolute value210,211

G(T,x,n,P)=12A(T,x,n)P2+14B(T,x,n)P4+16C(T,x,n)P6,
(46)

with

A(T,x,n)=A0(x)[Tθ(x)](n12+n22+n32),
(47)
B(T,x,n)=B1(x)(n12+n22+n32)2+B2(T,x)(n14+n24+n34),
(48)
C(T,x,n)=C1(x)(n12+n22+n32)3+C2(T,x)(n16+n26+n36)+C3(T,x)(n12n22n32),
(49)

wherein the three invariants of the form (n12+n22+n32)m=1 and are therefore isotropic. It is thus evident from Eqs. (47)–(49) that the inter-ferroelectric transitions will be dictated by the three anisotropy parameters, B2(T,x), C2(T,x), and C3(T,x). After inserting Eqs. (47)–(49) into Eq. (46) and minimizing the free energy with respect to n and P, the equilibrium free energies of the tetragonal, orthorhombic, and rhombohedral phases are obtained. Assuming that the Landau polynomial is asymptotically accurate on approaching the line of Curie points, the polarization becomes small, and the sextic contributions can be neglected. The lead anisotropic term B2(T,x) then plays a dominant role. Under these conditions, the paraelectric–ferroelectric transition will be of the type cubic to tetragonal if B2(T,x)<0 and of the type cubic to rhombohedral if B2(T,x)>0; the truncated Landau polynomial cannot produce a stable minimum for the orthorhombic phase at small values of P.212 

The phase diagrams represented by BSrT, BZT (BHT, BSnT), and BZT-BCT all display a convergence region. Taking B2(T,x) to be a linear function of composition and temperature, as in the low-order approximation described above, then gives an equation for a line in the phase diagram along which the anisotropy of the energy surface is dramatically reduced

B2(T,x)=B0[(λ(xxCP)+ξ(TTCP)]0,
(50)

or simply,

TTCPλξ(xxCP).
(51)

As the temperature is lowered from the convergence point (xCP, TCP), the polarization increases, and so the sextic terms in Eq. (49) begin to play a more important role. It is therefore expected that the inter-ferroelectric transitions between tetragonal, orthorhombic, and rhombohedral phases occur in the region of the phase diagram around the line in Eq. (51). The particular topology of the phase diagram will then depend on the variation of the sextic terms, C2(T,x) and C3(T,x), with composition and temperature. In fact, the topologies of the shifting, pinching, and polymorphic phase diagrams (Fig. 6) can all be adequately reproduced by simply changing the slope of the line, λ/ξ along which the lead contribution to the anisotropy of the energy surface is reduced.213–215 This reduction leads to a rotational instability of the polarization, which has important consequences for the domain structure and electromechanical properties. For example, as can be appreciated from Fig. 2, near the tetragonal-orthorhombic phase boundary, the rotational instability is reflected in a divergence of the transverse dielectric susceptibility and a strong softening of the shear compliance. The implications of such instabilities for the conformal miniaturization of the domain structure to nanoscale dimensions were pointed out216 and have been recently reviewed.217 Gao et al.218 confirmed experimentally the miniaturization of the domain structure near phase boundaries in BaSn0.105Ti0.895O3. Convergent beam electron diffraction revealed that the nanometer-sized domains feature different local symmetries.

In addition, the simple low-order theory described above also accounts for the possibility of one or more TCPs. As noted above, a tricritical transition occurs when the entire quartic contribution in Eq. (48) to the free energy vanishes

min[B(T,x,n)]=0.
(52)

The variation of the difference between Curie and Curie-Weiss temperatures can then be easily determined from the standard thermodynamic relation for first-order transitions

Δ(x)=TC(x)θ(x)=316[B(T,x,n)]2A0(x)C(T,x,n).
(53)

Since, to a first approximation, θ(x) and all the Landau coefficients may be taken as linear functions of x, it is apparent that the value of Δ(x) varies as x2. Hence, the temperature difference Δ(x), which is a measure of the first-order character of the transition, becomes vanishingly small, asymptotically approaching zero as (xxcr) → 0.

The application of the simple analysis above is complicated in real systems by two main factors. First, the type of solute also plays an important role in determining whether the phase transitions are sharp or diffuse. The influence of differing types of solutes has been divided into three main classes: (i) solutes that cannot generate electric fields locally, but modify the transition temperature, (ii) solutes that generate random local electric fields that interact with the host crystal and (iii) solutes that are thermally frozen in non-equilibrium configurations and which persist below the transition temperature.219 Although the isovalent ion substitutions (Sr2+, Ca2+, Zr4+, Hf4+, and Sn4+) may be expected to act as solutes of type (i), it is well-known that perovskite crystals contain rather high densities of defects in the form of uncompensated oxygen vacancies, thereby generating random fields normally attributed to solutes of type (ii). Further, depending on the thermal process history, compositional heterogeneities corresponding to solutes of type (iii) may not always be eliminated. A second complicating factor concerns two-phase coexistence. The inter-ferroelectric boundary lines drawn in Fig. 6 describe two phases in equilibrium at the same composition under the condition that atomic diffusion is thermally frozen. Under these conditions, there always exists a metastable two-phase coexistence region adjacent to the boundary line, as the transitions between the ferroelectric phases are all of first-order. However, if atomic diffusion providing equilibration of the system is not thermally frozen, then the free energy of mixing must be explicitly taken into account. For example, if the enthalpy of mixing is positive, a miscibility gap may exist, leading to rather more extensive two-phase fields along the boundary lines.220 Either of these two factors can produce strong smearing of the phase transitions, making the accurate determination of transition temperatures, phase convergence, and TCPs—i.e., compared with the corresponding homogeneous system—experimentally quite difficult. Many of the controversies in the literature concerning the phase diagrams in Fig. 6 are likely to have their origins in measurement uncertainties or errors in analysis arising from smearing of the phase transitions due to defects or phase coexistence.

b. Synthesis

The synthesis parameters and formation mechanisms of BT-based materials generally follow similar trends. BaTiO3 powder is produced by the solid state reaction between BaCO3 and TiO2 in the temperature range between 800 °C and 1300 °C.221,222 The reaction consists of several stages, whereby the Ba2+ and O2– ions first diffuse into TiO2 and the perovskite BaTiO3 phase is formed. The product, however, hinders further diffusion of Ba2+, which results in the formation of the intermediate Ba2TiO4 phase. Finally, in the case of a stoichiometric starting mixture, this intermediate phase reacts with remaining TiO2 to form the BaTiO3 phase.

The formation of solid solution compositions can be more complex. As an example, let us consider the synthesis and formation mechanism of BZT. Bera et al.223 investigated the formation mechanism of BaTi0.60Zr0.40O3 produced via the solid state route from BaCO3 (D50=2.09 μm), TiO2 (D50=0.35 μm), and ZrO2 (D50=10.27 μm) powders. From differential scanning calorimetry and thermal gravimetric analysis, they observe that BaCO3 begins to decompose at 556 °C, although the most significant decomposition occurs at 979 °C. X-ray diffraction indicates that BT starts to form at 700 °C and BaZrO3 (BZ) begins to form at 800 °C. In contrast to BT, formation of intermediary phases was not detected by the authors. Note that this is a similar temperature range, between 600 °C and 700 °C, reported for the formation of BaSnO3.224 BZT forms due to interdiffusion between BT and BZ that begins at 1300 °C, but secondary phases can be still resolved even at 1600 °C.223 Cation diffusion has been recognized as the limiting step in the synthesis of BZT223 and in similar systems such as BaSnO3.224 Thus, solid solutions of BT-based piezoelectrics have been generally calcined at temperatures between 1100 °C and 1300 °C to form a perovskite phase. Generally, sintering between 1400 °C and 1560 °C under atmospheric conditions has been performed.191–197,201 Under these conditions, secondary phases may remain.223 

c. Piezoelectric properties

Kalyani et al.191 investigated the effect of the electric field magnitude on the poling behavior of BaZr0.02Ti0.98O3. A maximized d33 value of 357 pC/N was obtained when the material was subjected to a poling field of 1.7 kV/mm. For electric fields lower than 1.7 kV/mm, BaZr0.02Ti0.98O3 features coexistence of tetragonal and orthorhombic phases. For poling fields larger than 1.7 kV/mm, the electric field stabilized a single rhombohedral phase thereby diminishing the piezoelectric properties.

Yao et al.201 considered the relationship between the phase diagram and the d33 activity in the BSnT, as displayed in a contour plot in Fig. 7. Near the convergence region at 11 mol. % Sn4+ and 40 °C, an extremely large d33=697 pC/N was found. So far, this is the largest d33 value reported for a binary BT-based system. The high temperature variations of d33 values with variation of composition and temperature in BSnT are clearly highlighted in this figure.

FIG. 7.

Contour plot of d33 as a function of temperature and composition for BaTiO3-xBaSnO3. Reprinted with permission from Yao et al. Europhys. Lett. 98, 27008 (2012). Copyright 2012 IOP Science.

FIG. 7.

Contour plot of d33 as a function of temperature and composition for BaTiO3-xBaSnO3. Reprinted with permission from Yao et al. Europhys. Lett. 98, 27008 (2012). Copyright 2012 IOP Science.

Close modal

Figure 8 shows the variation of (a) TC and (b) d33 as a function of Zr4+, Sn4+, and Hf4+ content at room temperature with data adapted from several works.191,193,195–197,201 With increasing modifier content, TC is clearly reduced in all systems. It is observed that Zr4+ and Hf4+ affect TC quite similarly, whereas Sn4+ decreases TC more strongly. The d33 values are similarly modified with Zr4+ and Hf4+ modification below 4 at. %. For higher modifier content, Zr4+ induces much higher d33 values. Sn4+ generally leads to the highest d33 values with a maximum value of 425 pC/N at 4 at. % Sn4+.

FIG. 8.

Variation of (a) TC and (b) d33 as a function of modifier content at room temperature. Zr4+, Sn4+, and Hf4+ modifier contents are depicted. Data were obtained from Refs. 191, 193, 195–197, and 201.

FIG. 8.

Variation of (a) TC and (b) d33 as a function of modifier content at room temperature. Zr4+, Sn4+, and Hf4+ modifier contents are depicted. Data were obtained from Refs. 191, 193, 195–197, and 201.

Close modal

The effect of texturing on piezoelectric properties was investigated in detail for different BCT compositions.225,226 [100] texturing enhanced the electromechanical properties, whereas [111] texturing decreases properties.225,226 Haugen et al.225 synthesized textured Ba0.92Ca0.08TiO3 via templated grain growth. They achieved a texturing degree of 98% producing an enhancement of 30% in d33* as compared with the untextured material. Schultheiß et al.226 demonstrated for Ba0.85Ca0.15TiO3 that enhancing the degree of texturing has a major effect on the electromechanical properties. Variation of the texturing degree from 26% up to 83% resulted in a linear enhancement of 20% in TC, 20% reduction in coercive field, and 19% increase in d33*.226 Similar improvements in the piezoelectric properties were reported for textured BZT.227,228

CuO-doping improved the piezoelectric properties of BaZrxTi1-xO3 and BaSnxTi1-xO3.229,230 Zheng et al.229 reduced the sintering temperature of BaTi0.9625Zr0.0375O3 from 1450 °C to 1300 °C with 1 mol. % CuO and attained a d33 = 300 pC/N and d31 = −120 pC/N. These values were 15% and 30% higher than the d33 and d31 values obtained for the undoped BaTi0.9625Zr0.0375O3, respectively. The temperature stability of the piezoelectric properties was also improved as compared with the undoped material.229 Zhao et al.230 revealed that doping of Ba(Ti0.90Sn0.10)O3 with 1 mol. % CuO leads to a high d33=650 pC/N at room temperature for samples sintered at 1450 °C. This enhancement was not observed for samples sintered at lower temperature, indicating that apart from the dopant, enhancement of the properties should be related to increased density. This was attributed to the stabilization of rhombohedral, orthorhombic, and tetragonal phases at room temperature.230 

Many BT-based materials with high piezoelectricity have been discovered in recent years. Among them, the (Ba,Ca)(Zr,Ti)O3, (Ba,Ca)(Sn,Ti)O3, and (Ba,Ca)(Hf,Ti)O3 systems have been the most widely investigated solid solutions. Therefore, this section describes in detail their synthesis, phase diagrams, microstructure, and functional properties.

Barium titanate modified with both Ca2+ and Zr4+ was first investigated by McQuarrie and Behnke69 in 1954, as it was considered a relevant system for capacitor applications at the time, and during subsequent decades (see more details in Sec. II).231–233 Any BT-based material modified with Ca2+ and Zr4+ can be represented within a pseudo-quaternary system consisting of BaTiO3 (BT), BaZrO3 (BZ), CaTiO3 (CT), and CaZrO3 (CZ). From now on, any composition in this system will be termed (Ba,Ca)(Zr,Ti)O3 (BCZT). Any composition in the quaternary space can be identified by giving the ratio between Ba2+ and Ca2+ for the A-site and Ti4+ and Zr4+ for the B-site.69 To facilitate visualization, we will neglect the CZ component and consider the system as pseudo-ternary with end members being BT, BZ, and CT. We note that almost simultaneously (and independently) with this manuscript, a review treating (Ba,Ca)(Zr,Ti)O3 was published.234 We refer the readers also to this publication for further insights.

It was not until 2009, following the work of Liu and Ren11 that BT-based materials modified with Ca2+ and Zr4+ caught the attention of the piezoelectrics community. Interestingly, other works investigated the piezoelectricity of this quaternary system before this work but failed to obtain technologically appealing properties.97 The attention of the community focused on the work of Liu and Ren11 due to the finding of outstanding electromechanical properties such as d33 > 500 pC/N and d33* > 1000 pm/V at 0.5 kV/mm in the compositional range between (Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (BZT-40BCT) and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT). From now on the abbreviation BZT-BCT will be used to distinguish the isopleth proposed by Liu and Ren from other compositions in the ternary systems.11 In other words, the reader should bear in mind that BCZT is used as a nomenclature for any other composition which is not contained within this BZT-BCT isopleth. Despite the large electromechanical properties of BZT-BCT, the operational range of compositions along this isopleth is limited to 90 °C. This is discouraging for a broad range of applications and has created skepticism in the community with respect to the technological applicability of BT-based piezoelectrics. Further details on this issue are discussed in Sec. VI. In Subsections V A 1 and V A 2, we review the state-of-the-art knowledge on BCZT thin and thick films, single crystals, and bulk polycrystalline ceramics for piezoelectric applications. A few works also treated the BCZT in the form of nanomaterials,235–238 but they will not be discussed here in too much detail.

1. Single crystals and thin films

There have been several attempts to synthesize BZT-BCT single crystals by the spontaneous nucleation, Czochralski, and the top-seeded solution growth methods.239–242 Electron probe microscopy analysis indicated that it is challenging to maintain the desired stoichiometry in the BZT-BCT single crystals as a result of TiO2 volatilization.239,242 All compositions synthesized so far reveal relaxor features and high dielectric losses.239,240,242 Veber et al.242 attributed these features to an excess of Zr4+. They also characterized the dynamic piezoelectric properties along the [001]pc (where “pc” denotes pseudocubic) direction for (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT). A piezoelectric coefficient d31=−93 pC/N and coupling coefficient k31=0.18 were found.242 Future works should improve the volatilization and segregation issues during synthesis in order to improve the single crystal's quality and thus performance.239,242

BCZT thin films for piezoelectric applications have been synthesized by sol-gel,243–249 radiofrequency (RF) magnetron sputtering,250,251 and pulsed laser deposition (PLD).252–257 Further details related to the processing and functional properties of the thin films are provided in Table III.

TABLE III.

Methods used to process BCZT thin films and their functional properties. SC: Single Crystal.

CompositionMethodSubstrateTC (°C)d33 (pm/V)References
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) Sol-gel Pt/Ti/SiO2/Si  72 243  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Si/SiO2/Ti/Ir  141 244  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Pt/Si  28 245  
Ba0.92Ca0.08Ti0.95Zr0.05O3 Sol-gel Pt/Ti/SiO2/Si 75 50 246  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel (100)-Si  85 247  
(Ba0.835Ca0.165)(Zr0.09Ti0.91)O3 (BZT-55BCT) Sol-gel Pt(111)/Ti/SiO2/Si  132 248  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Pt(111)/Ti/SiO2/Si  114 248  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Pt/Ti/SiO2/Si   249  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) RF magnetron sputtering Pt(111)/Ti/SiO2/Si  122 250  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) RF magnetron sputtering La0.7Sr0.3MnO3/(111)-SrTiO3 SC  100 251  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD SrRuO3/(001)-SrTiO3 SC  96 252  
(1-x)Ba(Zr0.2Ti0.8)O3–x(Ba0.7Ca0.3)TiO3 (downgraded multilayers x=0.3 to x=0.7) PLD SrRuO3/(001)-SrTiO3 SC  103 253  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD SrRuO3/(001)-SrTiO3 SC  100 254  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD (001)-SrTiO3 60  255  
Ba0.97Ca0.03Ti0.9625Zr0.0375O3 PLD IrO2/SiO2/Si 69 32 256  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD Pt/TiO2/SiO2/Si  80 257  
CompositionMethodSubstrateTC (°C)d33 (pm/V)References
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) Sol-gel Pt/Ti/SiO2/Si  72 243  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Si/SiO2/Ti/Ir  141 244  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Pt/Si  28 245  
Ba0.92Ca0.08Ti0.95Zr0.05O3 Sol-gel Pt/Ti/SiO2/Si 75 50 246  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel (100)-Si  85 247  
(Ba0.835Ca0.165)(Zr0.09Ti0.91)O3 (BZT-55BCT) Sol-gel Pt(111)/Ti/SiO2/Si  132 248  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Pt(111)/Ti/SiO2/Si  114 248  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sol-gel Pt/Ti/SiO2/Si   249  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) RF magnetron sputtering Pt(111)/Ti/SiO2/Si  122 250  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) RF magnetron sputtering La0.7Sr0.3MnO3/(111)-SrTiO3 SC  100 251  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD SrRuO3/(001)-SrTiO3 SC  96 252  
(1-x)Ba(Zr0.2Ti0.8)O3–x(Ba0.7Ca0.3)TiO3 (downgraded multilayers x=0.3 to x=0.7) PLD SrRuO3/(001)-SrTiO3 SC  103 253  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD SrRuO3/(001)-SrTiO3 SC  100 254  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD (001)-SrTiO3 60  255  
Ba0.97Ca0.03Ti0.9625Zr0.0375O3 PLD IrO2/SiO2/Si 69 32 256  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) PLD Pt/TiO2/SiO2/Si  80 257  

Table III emphasizes that still a limited amount of work exists on BCZT thin films, which concentrates mostly in the BZT-BCT isopleth. Even for BZT-50BCT, properties vary considerably depending on processing route and deposition conditions. One important result is an enhancement of almost 100 °C in TC for BZT-50BCT through stabilization of the ferroelectric phase due to in-plane stresses imposed by the substrate.255 This points to a strategy that can be used to overcome the low operational temperature of BT-based materials. Indeed, a large enhancement of TC with strain has been demonstrated for BT-based nanocomposite thin films too.258 

Due to the limited work on single crystals and thin films related to piezoelectric applications, Secs. V A 2 aV A 2 d mostly deal with results in bulk materials and thick films unless stated otherwise.

2. Polycrystalline bulk materials and thick films

a. Synthesis

Wet chemical and solid state synthesis have been used to produce bulk BZT-BCT. Only a few works achieved promising piezoelectric properties utilizing wet chemical synthesis routes, such as sol-gel259 and oxalate precursor methods.260 Table IV introduces the most common synthesis conditions used to produce BCZT by wet chemical and solid state methods. An advantage of the wet chemical methods over solid state synthesis is that they allow better mixing and shorter diffusion distances thereby reducing the calcination temperature by at least 300 °C. Another advantage is that wet chemical routes generally result in a better homogeneity of the powders. Most likely due to the complexity, lack of promising piezoelectric properties, and problems with the scalability of wet chemical methods, most works have so far focused on the solid state route.

TABLE IV.

Some of the processing parameters for BZT-BCT reported in the literature.

CommentsCalcinationSinteringReferences
Temperature (°C)Time (h)AtmosphereTemperature (°C)Time (h)Atmosphere
Sol-Gel 700 Air 1450 Air 259  
Oxalate precursor 800 Air 1200–1500 10 Air 260  
Solid state 1100 Air 1300–1525 Air 267  
Solid state 1150 Air 1500 Air 268  
Hot-pressing/post-annealing 1150 Air 1000/1500 1/6 40 MPa and argon/air 268  
Solid state 1200 Air 1200-1400 Air/nitrogen (pO2 = 5 × 102 Pa) 97  
Solid state 1200 Air 1500 1–6 Air 269 and 270  
Solid state 1200 Air 1500 2–6 Air 271  
Solid state 1250 2-3 Air 1300-1400 2–3 Air 272  
Solid state 1300 2–5 Air 1400–1500 3–6 Air 273 and 274  
Solid state 1300 Air 1550 Air 275 and 276  
Spark plasma sintering/post-annealing 1300 Air 1050–1300/900 0.05/10 Argon and 50 MPa/air 277  
Spark plasma sintering/post-annealing 1350 Air 1450/800 0.05/20 10−2 Pa vacuum and 40 MPa/Air 278  
Spark plasma sintering/post-annealing 1350 15 Oxygen 1300/900-1000 0.16/12 Vacuum and 90 MPa/oxygen 279  
Solid state. BaZrO3 was used as raw material 1350 2–4 Air 1450–1500 Air 11, 27, and 280–294  
Solid state 1350 15 Oxygen 1400–1450 Oxygen 295 and 296  
Solid state 1350 Air 1500 Air 297  
Solid state 1350/1350a 6/6 Air 1500 10 Air 298  
Solid state 1000/1400a 4/4 Air 1350 Air 299  
CommentsCalcinationSinteringReferences
Temperature (°C)Time (h)AtmosphereTemperature (°C)Time (h)Atmosphere
Sol-Gel 700 Air 1450 Air 259  
Oxalate precursor 800 Air 1200–1500 10 Air 260  
Solid state 1100 Air 1300–1525 Air 267  
Solid state 1150 Air 1500 Air 268  
Hot-pressing/post-annealing 1150 Air 1000/1500 1/6 40 MPa and argon/air 268  
Solid state 1200 Air 1200-1400 Air/nitrogen (pO2 = 5 × 102 Pa) 97  
Solid state 1200 Air 1500 1–6 Air 269 and 270  
Solid state 1200 Air 1500 2–6 Air 271  
Solid state 1250 2-3 Air 1300-1400 2–3 Air 272  
Solid state 1300 2–5 Air 1400–1500 3–6 Air 273 and 274  
Solid state 1300 Air 1550 Air 275 and 276  
Spark plasma sintering/post-annealing 1300 Air 1050–1300/900 0.05/10 Argon and 50 MPa/air 277  
Spark plasma sintering/post-annealing 1350 Air 1450/800 0.05/20 10−2 Pa vacuum and 40 MPa/Air 278  
Spark plasma sintering/post-annealing 1350 15 Oxygen 1300/900-1000 0.16/12 Vacuum and 90 MPa/oxygen 279  
Solid state. BaZrO3 was used as raw material 1350 2–4 Air 1450–1500 Air 11, 27, and 280–294  
Solid state 1350 15 Oxygen 1400–1450 Oxygen 295 and 296  
Solid state 1350 Air 1500 Air 297  
Solid state 1350/1350a 6/6 Air 1500 10 Air 298  
Solid state 1000/1400a 4/4 Air 1350 Air 299  
a

Two calcination steps with intermediate milling.

Solid state synthesis of bulk BCZT has been performed following the conditions for BT.221 The A/B stoichiometry should be strictly controlled since it can easily result in secondary phases along grain boundaries and triple points junctions that affect functional properties.261 Chao et al.262 demonstrated that using anatase or rutile TiO2 as raw powders modifies the microstructure and electromechanical properties of BZT-50BCT to a great extent, despite the fact that TiO2 transforms from anatase to rutile at 915 °C during the synthesis. Using rutile increases the grain size, the magnitude of d33 by 43%, and the remanent polarization by 26%. Modification of the TiO2 raw powder has little to no effect on the TC and coercive field.262 Liu and Ren11 have been among the few authors using BaZrO3 as raw material to synthesize BZT-BCT. Thus, this could be a reason why Liu and Ren reported a d33 value for BZT-50BCT that is comparably higher than the mean d33 value reported in the literature (Table VI). A recent work investigated this synthesis route and concluded that homogenization is more challenging when using BZT as raw powder.263 

TABLE VI.

Electromechanical properties at room temperature in the BCZT pseudo-ternary system. The letters in the column “source/s of variation in properties” indicate the most probable variable that leads to variation in properties. Namely, (a) variation in the processing conditions and microstructures, (b) discrepancies among reported values due to uncertainties in measurements, characterization technique and/or conditions, and (c) variation in the poling conditions.

CompositionTC (°C)εrd33 (pC/N)kpQmd33* (pm/V)aGrain size (μm)ReferencesSource/s of variation in properties
(Ba0.95Ca0.05) TiO3 130 1030 175 0.267    344   
(Ba0.95Ca0.05)(Zr0.01Ti0.99)O3  1270 200 0.29    344   
(Ba0.98Ca0.02)(Zr0.05Ti0.95)O3 106 2160 210 0.322 122   345   
(Ba0.95Ca0.05)(Zr0.02Ti0.98)O3  1440 229 0.327    344   
(Ba0.95Ca0.05)(Zr0.03Ti0.97)O3  1580 283 0.341    344   
(Ba0.96Ca0.04)(Zr0.05Ti0.95)O3 102 1680 240 0.426 127   345   
(Ba0.95Ca0.05)(Zr0.04Ti0.96)O3 120 2070 338 0.36    344   
Ba(Zr0.10Ti0.90)O3 82.7 1680 182 0.294    328   
(Ba0.95Ca0.05)(Zr0.05Ti0.95)O3  1550 305 0.267    344   
(Ba0.94Ca0.06)(Zr0.05Ti0.95)O3 105 2650 341 0.448 132   345   
(Ba0.95Ca0.05)(Zr0.07Ti0.93)O3 105 1480 283 0.249    344   
(Ba0.97Ca0.03)(Zr0.10Ti0.90)O3 83.5 1700 236 0.382    328   
(Ba0.92Ca0.08)(Zr0.05Ti0.95)O3 110 2610 360 0.486 136   345   
(Ba0.92Ca0.08)(Zr0.055Ti0.945)O3 107  323   537 17 343   
(Ba0.95Ca0.05)(Zr0.10Ti0.90)O3 82.9 1745 ± 2% 249 ± 0.2% 0.32 ± 26%    328 and 344  
(Ba0.90Ca0.10)(Zr0.05Ti0.95)O3 102 2619 328 0.447 149   345   
(Ba0.85Ca0.15)TiO3 130 ± 2% 773 ± 32% 94 ± 28% 0.21 ± 39% 160  11 269 and 328  b and c 
(Ba0.94Ca0.06)(Zr0.105Ti0.895)O3 92.4  430  430   273   
(Ba0.90Ca0.10)(Zr0.067Ti0.933)O3 103  381   683 25 343   
(Ba0.95Ca0.05)(Zr0.12Ti0.88)O3 85 1930 264 0.207    344   
(Ba0.93Ca0.07)(Zr0.10Ti0.90)O3 82.3 2470 384 0.512    328   
(Ba0.92Ca0.08)(Zr0.09Ti0.91)O3 101  403     273   
(Ba0.88Ca0.12)(Zr0.05Ti0.95)O3 — — 291 0.431 212   345   
(Ba0.91Ca0.09)(Zr0.0825Ti0.9175)O3 105  373     273   
(Ba0.894Ca0.106)(Zr0.0705Ti0.9295)O3 114 2252 414       
(Ba0.85Ca0.15)(Zr0.03Ti0.97)O3 130  200 317  258 10.9 320   
(Ba0.95Ca0.05)(Zr0.15Ti0.85)O3 54 2840 182 0.164    344   
(Ba0.90Ca0.10)(Zr0.10Ti0.90)O3 82.4 2730 429 0.522    328   
(Ba0.88Ca0.12)(Zr0.08Ti0.92)O3 98.4  312   710 16 343   
(Ba0.85Ca0.15)(Zr0.05Ti0.95)O3 118 ± 7% 1367 ± 25% 204 ± 33% 0.33 ± 37% 255 ± 45% 383 12 ± 3% 269, 320, 328, and 345  b and c 
(Ba0.875Ca0.125)(Zr0.10Ti0.90)O3 84.6 2940 459 0.541    328   
(Ba0.85Ca0.15)(Zr0.075Ti0.925)O3 105 2350 237 29 132  17 269   
(Ba0.91Ca0.09)(Zr0.14Ti0.86)O3 (BZT-30BCT) 61 2772 195 ± 36%   680 71 ± 61% 318 and 320  a and b 
(Ba0.86Ca0.14)(Zr0.09Ti0.91)O3 88.3  417   713 32 343   
(Ba0.85Ca0.15)(Zr0.08Ti0.92)O3 101 ± 6% 2620 ± 13% 320 ± 10% 0.45 ± 4%  463 14.8 320 and 328  
(Ba0.904Ca0.096)(Zr0.136Ti0.864)O3 (BZT-32BCT) 62.3 2301 ± 5% 211 ± 19%  105 648 20 318 and 319  
(Ba0.895Ca0.105)(Zr0.13Ti0.87)O3 (BZT-35BCT) 61.1 2350 ± 8% 230 ± 22%  97 660 36 318 and 319  
(Ba0.889Ca0.111)(Zr0.126Ti0.874)O3 (BZT-37BCT) 65.1 2357 ± 0.3% 231 ± 12%  101 645 28 318 and 319  
(Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) 73 2570    794 31 346   
(Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (BZT-40BCT) 73 ± 16% 2273 ± 10% 243 ± 21%  92 792 ± 7% 26 ± 44% 11, 318–320  a and b 
(Ba0.85Ca0.15)(Zr0.09Ti0.91)O3 100 2710 346 42 114  18 269   
(Ba0.874Ca0.126)(Zr0.116Ti0.884)O3 (BZT-42BCT) 75 2550    854 31 346   
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) 82 ± 7% 2627 ± 12% 353 ± 5%  91 731 ± 6% 36 11, 318, and 319  
(Ba0.85Ca0.15)(Zr0.095Ti0.905)O3 86  458   740 24 343   
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 91 ± 14% 3590 ± 33% 491 ± 33% 0.48 ± 20% 123 ± 71% 1053 ± 10% 21 ± 54% 11, 128, 260, 269, 281, 300, 302, 318–320, 328, and 346  a, b, and c 
(Ba0.825Ca0.175)(Zr0.075Ti0.925)O3 77.2 2520 225 0.36 227 429  324   
(Ba0.8Ca0.2)(Zr0.05Ti0.95)O3 92.7 1450  0.3 ± 6% 350 ± 10% 284  324 and 345  
(Ba0.775Ca0.225)(Zr0.025Ti0.975)O3 99.2 1000 111 0.24 628 204  324   
(Ba0.75Ca0.25)TiO3 96.7 345 95 0.19 732 173  324   
(Ba0.845Ca0.155)(Zr0.10Ti0.90)O3 84  419   740 19 343   
(Ba0.835Ca0.165)(Zr0.09Ti0.91)O3 (BZT-55BCT) 100 2290 380   478  11   
(Ba0.85Ca0.15)(Zr0.11Ti0.89)O3 85 3150 323 0.39 99.4  20 269   
(Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) 97 ± 10% 2175 ± 16% 264 ± 13%  159 365 ± 11% 28 ± 52% 11, 318–320, and 346  a and b 
(Ba0.85Ca0.15)(Zr0.12Ti0.88)O3 68.9 4780 506 0.515    328   
(Ba0.79Ca0.21)(Zr0.06Ti0.94)O3 (BZT-70BCT) 107 1560     22 ± 20% 320  
(Ba0.825Ca0.175)(Zr0.10Ti0.90)O3 80.5 4690 511 0.542    328   
(Ba0.73Ca0.27)(Zr0.02Ti0.98)O3 (BZT-90BCT) 113 702 107 ± 9%    22 ± 27% 320  
(Ba0.85Ca0.15)(Zr0.15Ti0.85)O3 60 ± 14% 4727 ± 54% 221 ± 29% 0.26 ± 49% 123 351 20 ± 12% 269, 320, and 328  b and c 
(Ba0.80Ca0.20)(Zr0.10Ti0.90)O3 84.8 4440 419 0.48    328   
CompositionTC (°C)εrd33 (pC/N)kpQmd33* (pm/V)aGrain size (μm)ReferencesSource/s of variation in properties
(Ba0.95Ca0.05) TiO3 130 1030 175 0.267    344   
(Ba0.95Ca0.05)(Zr0.01Ti0.99)O3  1270 200 0.29    344   
(Ba0.98Ca0.02)(Zr0.05Ti0.95)O3 106 2160 210 0.322 122   345   
(Ba0.95Ca0.05)(Zr0.02Ti0.98)O3  1440 229 0.327    344   
(Ba0.95Ca0.05)(Zr0.03Ti0.97)O3  1580 283 0.341    344   
(Ba0.96Ca0.04)(Zr0.05Ti0.95)O3 102 1680 240 0.426 127   345   
(Ba0.95Ca0.05)(Zr0.04Ti0.96)O3 120 2070 338 0.36    344   
Ba(Zr0.10Ti0.90)O3 82.7 1680 182 0.294    328   
(Ba0.95Ca0.05)(Zr0.05Ti0.95)O3  1550 305 0.267    344   
(Ba0.94Ca0.06)(Zr0.05Ti0.95)O3 105 2650 341 0.448 132   345   
(Ba0.95Ca0.05)(Zr0.07Ti0.93)O3 105 1480 283 0.249    344   
(Ba0.97Ca0.03)(Zr0.10Ti0.90)O3 83.5 1700 236 0.382    328   
(Ba0.92Ca0.08)(Zr0.05Ti0.95)O3 110 2610 360 0.486 136   345   
(Ba0.92Ca0.08)(Zr0.055Ti0.945)O3 107  323   537 17 343   
(Ba0.95Ca0.05)(Zr0.10Ti0.90)O3 82.9 1745 ± 2% 249 ± 0.2% 0.32 ± 26%    328 and 344  
(Ba0.90Ca0.10)(Zr0.05Ti0.95)O3 102 2619 328 0.447 149   345   
(Ba0.85Ca0.15)TiO3 130 ± 2% 773 ± 32% 94 ± 28% 0.21 ± 39% 160  11 269 and 328  b and c 
(Ba0.94Ca0.06)(Zr0.105Ti0.895)O3 92.4  430  430   273   
(Ba0.90Ca0.10)(Zr0.067Ti0.933)O3 103  381   683 25 343   
(Ba0.95Ca0.05)(Zr0.12Ti0.88)O3 85 1930 264 0.207    344   
(Ba0.93Ca0.07)(Zr0.10Ti0.90)O3 82.3 2470 384 0.512    328   
(Ba0.92Ca0.08)(Zr0.09Ti0.91)O3 101  403     273   
(Ba0.88Ca0.12)(Zr0.05Ti0.95)O3 — — 291 0.431 212   345   
(Ba0.91Ca0.09)(Zr0.0825Ti0.9175)O3 105  373     273   
(Ba0.894Ca0.106)(Zr0.0705Ti0.9295)O3 114 2252 414       
(Ba0.85Ca0.15)(Zr0.03Ti0.97)O3 130  200 317  258 10.9 320   
(Ba0.95Ca0.05)(Zr0.15Ti0.85)O3 54 2840 182 0.164    344   
(Ba0.90Ca0.10)(Zr0.10Ti0.90)O3 82.4 2730 429 0.522    328   
(Ba0.88Ca0.12)(Zr0.08Ti0.92)O3 98.4  312   710 16 343   
(Ba0.85Ca0.15)(Zr0.05Ti0.95)O3 118 ± 7% 1367 ± 25% 204 ± 33% 0.33 ± 37% 255 ± 45% 383 12 ± 3% 269, 320, 328, and 345  b and c 
(Ba0.875Ca0.125)(Zr0.10Ti0.90)O3 84.6 2940 459 0.541    328   
(Ba0.85Ca0.15)(Zr0.075Ti0.925)O3 105 2350 237 29 132  17 269   
(Ba0.91Ca0.09)(Zr0.14Ti0.86)O3 (BZT-30BCT) 61 2772 195 ± 36%   680 71 ± 61% 318 and 320  a and b 
(Ba0.86Ca0.14)(Zr0.09Ti0.91)O3 88.3  417   713 32 343   
(Ba0.85Ca0.15)(Zr0.08Ti0.92)O3 101 ± 6% 2620 ± 13% 320 ± 10% 0.45 ± 4%  463 14.8 320 and 328  
(Ba0.904Ca0.096)(Zr0.136Ti0.864)O3 (BZT-32BCT) 62.3 2301 ± 5% 211 ± 19%  105 648 20 318 and 319  
(Ba0.895Ca0.105)(Zr0.13Ti0.87)O3 (BZT-35BCT) 61.1 2350 ± 8% 230 ± 22%  97 660 36 318 and 319  
(Ba0.889Ca0.111)(Zr0.126Ti0.874)O3 (BZT-37BCT) 65.1 2357 ± 0.3% 231 ± 12%  101 645 28 318 and 319  
(Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) 73 2570    794 31 346   
(Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (BZT-40BCT) 73 ± 16% 2273 ± 10% 243 ± 21%  92 792 ± 7% 26 ± 44% 11, 318–320  a and b 
(Ba0.85Ca0.15)(Zr0.09Ti0.91)O3 100 2710 346 42 114  18 269   
(Ba0.874Ca0.126)(Zr0.116Ti0.884)O3 (BZT-42BCT) 75 2550    854 31 346   
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) 82 ± 7% 2627 ± 12% 353 ± 5%  91 731 ± 6% 36 11, 318, and 319  
(Ba0.85Ca0.15)(Zr0.095Ti0.905)O3 86  458   740 24 343   
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 91 ± 14% 3590 ± 33% 491 ± 33% 0.48 ± 20% 123 ± 71% 1053 ± 10% 21 ± 54% 11, 128, 260, 269, 281, 300, 302, 318–320, 328, and 346  a, b, and c 
(Ba0.825Ca0.175)(Zr0.075Ti0.925)O3 77.2 2520 225 0.36 227 429  324   
(Ba0.8Ca0.2)(Zr0.05Ti0.95)O3 92.7 1450  0.3 ± 6% 350 ± 10% 284  324 and 345  
(Ba0.775Ca0.225)(Zr0.025Ti0.975)O3 99.2 1000 111 0.24 628 204  324   
(Ba0.75Ca0.25)TiO3 96.7 345 95 0.19 732 173  324   
(Ba0.845Ca0.155)(Zr0.10Ti0.90)O3 84  419   740 19 343   
(Ba0.835Ca0.165)(Zr0.09Ti0.91)O3 (BZT-55BCT) 100 2290 380   478  11   
(Ba0.85Ca0.15)(Zr0.11Ti0.89)O3 85 3150 323 0.39 99.4  20 269   
(Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) 97 ± 10% 2175 ± 16% 264 ± 13%  159 365 ± 11% 28 ± 52% 11, 318–320, and 346  a and b 
(Ba0.85Ca0.15)(Zr0.12Ti0.88)O3 68.9 4780 506 0.515    328   
(Ba0.79Ca0.21)(Zr0.06Ti0.94)O3 (BZT-70BCT) 107 1560     22 ± 20% 320  
(Ba0.825Ca0.175)(Zr0.10Ti0.90)O3 80.5 4690 511 0.542    328   
(Ba0.73Ca0.27)(Zr0.02Ti0.98)O3 (BZT-90BCT) 113 702 107 ± 9%    22 ± 27% 320  
(Ba0.85Ca0.15)(Zr0.15Ti0.85)O3 60 ± 14% 4727 ± 54% 221 ± 29% 0.26 ± 49% 123 351 20 ± 12% 269, 320, and 328  b and c 
(Ba0.80Ca0.20)(Zr0.10Ti0.90)O3 84.8 4440 419 0.48    328   
a

d33* was calculated at 1 kV/mm.

Mishra et al.264 analyzed the synthesis of BZT-50BCT by differential scanning calorimetry and thermal gravimetric analysis. Between room temperature and 200 °C volatilization of adsorbed water and decomposition of thermally unstable organic compounds was observed. Between 600 °C and 800 °C, a second weight loss was associated with the volatilization of CO and CO2 originating from the decomposition of carbonates. At around 1000 °C, the appearance of an endothermic peak and X-ray diffraction (XRD) analyses indicated the crystallization of BZT-50BCT. Although the weight loss ended above 1000 °C, the presence of secondary phases in the XRD patterns remained up to the calcination temperature of 1300 °C.264 This might be a result of the continuation of the solid state reaction and crystallization processes that, according to Chao et al.,262 remain active even at 1350 °C. More detailed studies indicated that the secondary phases may actually persist even at temperatures above 1350 °C due to a limited solubility of Ca2+ and Zr4+ and/or to kinetically stable intermediary phases.69,265,266

Calcination at 1300 °C for 2 h in air maximizes the electromechanical properties.300 Excessive milling after calcination should be avoided since it can lead to the development of secondary phases.274 Several works indicated that sintering between 1480 °C and 1550 °C with dwell times between 2 h and 5 h constitute the optimum conditions to maximize electromechanical properties.270,300–302 Sun et al.302 demonstrated that the sintering temperature and dwell time have little influence on the TC of BZT-50BCT. Excessive sintering temperature or time can lead to undesired effects such as formation of secondary phases or decrease of density.302 The effect of sintering atmosphere on the piezoelectric properties has barely been investigated in BZT-BCT. Zhang et al.97 determined that a reducing sintering atmosphere composed of N2 (pO2=5 × 102 Pa) did not affect the d33=200 pC/N of (Ba0.95Ca0.05)(Ti0.88Zr0.12)O3 in samples sintered at 1350 °C, although the kp and εr values were reduced.97 

Spark plasma sintering in general increases the density and reduces the grain size considerably, as compared with conventionally sintered materials.277–279 Temperatures between 1050 °C and 1450 °C and dwell times between 3 min and 10 min were used to produce BZT-50BCT.277–279 The optimum spark plasma sintering conditions were obtained at 1250 °C leading to a higher remanent polarization than materials synthesized by the conventional sintering originating.277 Spark plasma sintered compositions also feature a lower relative permittivity and diffuse phase transitions. This was attributed to structural and chemical disorder. The piezoelectric properties of spark plasma sintered materials are considerably inferior to the piezoelectric properties reported for conventionally sintered materials.278,279

Ye et al.268 contrasted the functional properties of conventionally and hot-pressed BZT-50BCT. The conventional sintering procedure was carried out at 1500 °C for 6 h in air. Hot-pressing was done in argon atmosphere and 40 MPa at 1000 °C for 1 h, followed by post-annealing at 1500 °C for 6 h under air. The average grain size of conventionally sintered samples was 10 μm and the relative density was 94.4%, whereas for hot-pressed samples, an average grain size of 20 μm and relative density of 97.5% were reported. Hot-pressed samples also featured a higher TC=76 °C, which was 16 °C higher than the TC values reported for the conventionally sintered samples. A d33=510 pC/N and kp=0.44 were obtained for the hot-pressed samples, which indicated an enhancement of 45% in d33 and of 33% in kp as compared with conventionally processed samples. The improvement of the dielectric and piezoelectric properties was attributed to the enhanced grain size and density of the hot-pressed samples.268 

Kaushal et al.303 investigated the stability of BZT-50BCT untreated and di-hydrogen phosphate surface-treated powders in aqueous suspensions containing 5 wt. % BZT-50BCT by monitoring their pH value for 7 days. The suspensions with surface-treated powders demonstrated little variations in their pH value. This indicated negligible leaching of Ba2+, Ca2+, and Zr4+. This work opened the possibility to fabricate BCZT in aqueous media, which is the basis of colloidal methods such as slip casting, gel casting, tape casting, among others. In a subsequent work, Kaushal et al.299 explored the possibility to produce micron-sized spherical granulates via freeze granulation in surface-treated BZT-50BCT. The green bodies obtained after this procedure featured good sinterability and homogeneity as compared with conventionally processed materials. No piezoelectric properties were reported, albeit the processing affected strongly the dielectric properties of the materials.299 We would like to point out that in both works of Kaushal et al.299,303 the BZT-50BCT was actually obtained by a two-step calcination route with conventional ethanol processing. The challenge of complete aqueous-based processing of BCZT thus remains open.

b. Phase diagram and phase transitions

Figure 9 introduces the pseudo-ternary phase diagram between BZ, BT, and CT, with the dotted line corresponding to the BZT-BCT isopleth. The areas marked with A, B, and C are characterized by materials with small non-cubic distortions and quite different functional properties. The materials in region A, marked in orange, depict the prototypical phase transitions of BT and similar ferroelectric properties. Increasing the Ca2+ content reduces the temperature of the rhombohedral (R) to orthorhombic (O) phase transition considerably. Materials in the region C, marked in light green, display dielectric properties similar to canonical relaxors; i.e., frequency-dependent dielectric anomalies. Materials in region B, marked in purple, feature broader dielectric anomalies as compared with materials in region A. The dielectric anomalies do neither follow the Curie-Weiss law nor do they show frequency-dependent anomalies. The region resulting from the superposition of B and C comprises materials with unique non-canonical relaxor features. The fingerprint of materials within this region is that they transform spontaneously upon decreasing the temperature from a relaxor to a ferroelectric state.304–306 

FIG. 9.

Pseudo-ternary phase diagram of BZ, BT, and CT based on data from Ravez et al.305 and Liu and Ren.11 Shaded areas A, B, and C are characterized by pseudocubic structures. The dotted line indicates the isopleth along which Liu and Ren11 reported large piezoelectric properties. The highlighted shaded area indicates the compositional range between BZT-20BCT and BZT-70BCT, for which the piezoelectric properties are most widely investigated. Region A: materials with properties similar to BT. Region B: broader dielectric anomalies than conventional BT. They do not follow the Curie-Weiss law. Region C: dielectric properties similar to canonical relaxors. Superposition between region B and C: materials with features similar to non-canonical relaxors.

FIG. 9.

Pseudo-ternary phase diagram of BZ, BT, and CT based on data from Ravez et al.305 and Liu and Ren.11 Shaded areas A, B, and C are characterized by pseudocubic structures. The dotted line indicates the isopleth along which Liu and Ren11 reported large piezoelectric properties. The highlighted shaded area indicates the compositional range between BZT-20BCT and BZT-70BCT, for which the piezoelectric properties are most widely investigated. Region A: materials with properties similar to BT. Region B: broader dielectric anomalies than conventional BT. They do not follow the Curie-Weiss law. Region C: dielectric properties similar to canonical relaxors. Superposition between region B and C: materials with features similar to non-canonical relaxors.

Close modal

Several experimental and theoretical works have demonstrated that increasing the Ca2+ and Zr4+ content destabilizes the ferroelectric state of BT.192,307–310 Nonetheless, the origins of the relaxor features in BT-based materials remain controversial. Relaxor features were ascribed to either the difference in polarizability of constituent cations276,308–310 or local chemical heterogeneities.203 

The isopleth corresponding to the BZT-BCT piezoelectrics (white region in Fig. 9) is characterized by materials with a pseudocubic structure and weak to no relaxor features depending on the synthesis conditions and microstructure.128,276,311,312 Detailed XRD experiments revealed that the average atomic structure275,276,292,296 differs substantially from the short-range structure,313 similar to relaxors. Although some works highlighted that the BZT-BCT does not show relaxor features,314 Brajesh et al.276 suggested that BZT-50BCT is a relaxor but with relatively ordered A-site cations. The Burns temperature in BZT-50BCT was determined to be between 200 °C and 230 °C.276,315 The freezing temperature was also calculated to be Tf=92 °C,276 which is quite close to the TC generally reported in other works (Table VI). A relaxor state or at least a precursor polar state with tetragonal symmetry was found by Raman spectroscopy for temperatures above TC between 100 °C and 200 °C.315–317 This was attributed to a high defect concentration or compositional fluctuations.316,317

The phase diagram of the BZT-BCT isopleth has been determined by means of XRD,286,296 dielectric and elastic measurements,11,272,283,284,297,318–321 Raman spectroscopy,316 thermally stimulated depolarization currents,322 and phenomenological calculations.215,319,323 Figure 10 displays the BZT-BCT pseudo-binary phase diagram adapted from data taken from several works.11,286,296,318,321 Similar phase diagrams were reported for other isopleths within the BCZT ternary system.273,324,325 We note that the convergence region features a shadowed area since it has been reported to consist of a single quadruple point or two triple points. In the case of two triple points, the most probable scenario is that at one triple point cubic-tetragonal-rhombohedral phases converge, whereas at the other triple point, rhombohedral-orthorhombic-tetragonal phases converge. This conforms to the thermodynamic considerations previously discussed.

FIG. 10.

Pseudo-binary phase diagram with data taken from Liu and Ren,11 Keeble et al.,296 Ehmke et al.,286 Xue et al.,321 and Acosta et al.318 The shaded areas depict approximate phase stability regions. The blurred shaded area indicates the phase convergence region.296,318 R: rhombohedral, O: orthorhombic, T: tetragonal, and C: cubic phases.

FIG. 10.

Pseudo-binary phase diagram with data taken from Liu and Ren,11 Keeble et al.,296 Ehmke et al.,286 Xue et al.,321 and Acosta et al.318 The shaded areas depict approximate phase stability regions. The blurred shaded area indicates the phase convergence region.296,318 R: rhombohedral, O: orthorhombic, T: tetragonal, and C: cubic phases.

Close modal

Liu and Ren11 proposed the presence of a MPB separating the rhombohedral (R) and tetragonal (T) phases. Due to the tilting of the phase boundary, we call it here a PPB as justified before. The PPB converged into a triple point. Despite the initial structural findings of Liu and Ren,11 there is a recent consensus on the presence of two PPBs in the system,275,276,283,286,292,296,297,314,318,319,321 as found in other similar BT-based materials.326,327 Detailed synchrotron diffraction studies pointed out that the high temperature paraelectric phase has a prototype cubic structure with Pm3¯m symmetry. Upon cooling below the Curie temperature, the cubic phase transforms to a R phase with R3m symmetry for low BCT content or to a T phase with P4mm symmetry for high BCT content.292,296 Some authors resolved the interleaving region between the R and T phases as an orthorhombic (O) phase with Amm2 symmetry,265,283,296,328 whereas others reported a mixture of R and T phases with R3m and P4mm symmetries.286,292,316 Brajesh et al.275,276 suggested the coexistence of the three aforementioned phases near the PPBs. A few reports also suggested the presence of a monoclinic phase at the interleaving region,264,272 although detailed studies have pointed out that this phase is not required to obtain a satisfactory refinement model.275,276

Convergent beam electron studies supported the presence of a mixture of R and T phases.280,329,330 Thus, the apparent observation of an O phase may be a result of the adaptive diffraction of the nanodomains that characterize the compositions near phase boundaries. This suggestion does not explain the observation of an O phase via micro-Raman scattering,331 albeit other micro-Raman study proposed a mixture of R and T phases.316 Some works pointed out that the phase transitions in BZT-BCT occur gradually throughout 10 °C to 30 °C.285,316,331 This may be correlated to the presence of metastable phases as consequence of an electric field or uniaxial stress near PPBs264,275 or could be related to other factors such as those treated in Sec. IV B 2 a.

Further clarification is also required at the convergence region, highlighted in Fig. 10. Initially, Liu and Ren11 suggested the presence of a triple point. In contrast, Keeble et al.296 introduced the terminology “convergence region” to indicate the region where the R, T, interleaving phase/s, and C phases merge into either a triple or a quadruple point that is experimentally very hard to resolve. Phenomenological calculations can reproduce either two triple points215,319 or a quadruple point323 depending on how the free energy in the convergence region is formulated.

Liu and Ren11 indicated that the triple point was also a tricritical point (TCP) as a result of the reduction of the hysteresis in the dielectric properties measured upon heating and cooling. In subsequent works, Gao et al.294,314 estimated the transition enthalpy by integrating raw differential scanning calorimetry powder curves obtained on compositions spanning the convergence region. They asserted that these measurements also indicated a TCP as a result of negligible transition enthalpy and less than 1.5 °C hysteresis in dielectric properties upon heating and cooling around the line of Curie temperatures between (Ba0.91Ca0.09)(Zr0.14Ti0.86)O3 (BZT-30BCT) and (Ba0.895Ca0.105)(Zr0.13Ti0.87)O3 (BZT-35BCT). However, the phase transitions in this region of the phase diagram are strongly smeared, making the relevant transition parameters exceptionally difficult to measure. As discussed above, for a homogeneous crystal, the corresponding parameters would be the difference between Curie and Curie-Weiss temperatures, and the latent heat of transition evaluated at the Curie temperature, neither of which was directly measured. Indeed, it is well established that the proximity to a TCP in situations involving smeared transitions is difficult to unambiguously analyze in the context of the classical Landau theory.332 As a result, the available experimental evidence for the existence of a tricritical point at the triple point must presently be regarded as inconclusive.

Despite experimental errors, some authors indicated that the overall reduction in the first order character of the transition near to the (Ba0.9025Ca0.0975)(Zr0.135Ti0.865)O3 (BZT-32.5BCT) composition and at 60 °C is indicative of a TCP.294,314 It was recently suggested, however, that due to the shift of the maximum d33 values to temperatures higher than the line of Curie temperatures at finite bias-field values, BZT-BCT may actually feature a line of critical points at non-zero electric field rather than a TCP located in the zero-field phase diagram.125 Due to the previously discussed experimental difficulties in determining the locations and order of the phase transitions over such narrow temperature and compositional ranges, we will follow the nomenclature proposed by Keeble et al.296 and refer to this portion of the phase diagram as the convergence region.

c. Microstructure

Investigations performed via high-resolution transmission electron microscopy (TEM), including in situ temperature- and field-dependent studies, revealed that each phase in BZT-BCT is characterized by unique domain morphology.280,282,312,314,329,330,333,334 The rhombohedral (R) phase features wedge-shaped domains, whereas the tetragonal (T) phase is characterized by lamellar domains. The region near the PPBs has hierarchical domain morphology composed of nanometer domains, with sizes between 10 nm and 60 nm. The nanodomains are assembled in micrometer wedge-shaped330 or lamellar-shaped280 domains. It was stated that many of the domains around the PPBs were actually curved and thus domain walls did not correlate with {100} nor {110} family of directions.330 This morphology was attributed to the reduced free energy anisotropy characteristic of the PPBs280,314 or accommodation of non-uniform elastic/electric fields.330 

The hierarchical domain morphology around PPBs is highly susceptible to temperature variations.280,330 Increasing the temperature of BZT-50BCT leads to a gradual disappearance of the nanodomains within the micrometer-sized domains, followed by a gradual transformation into lamellar domains. This change indicates a gradual transition into the T phase.280,330 Cooling down to room temperature resulted in a partial re-development of the original domain morphology, indicating that the phase transformation is accompanied by irreversible switching.330 Cooling down to −180 °C led to the disappearance of nanometer-sized domains and development of micrometer-sized wedge-shaped domains, corresponding to the R phase.280 

Gao et al.294,314 discovered by temperature-dependent in situ TEM curved nanodomains or alternatively “mottled nanodomain patterns” at the convergence region, similar to those observed near PPBs. This characteristic domain morphology was attributed to the decoupling of the polarization direction from the lattice314 or minimization of elastic and electric fields.330 The mean domain width around the convergence region was around 10 nm,294,314 the same as found near PPBs in other works.330 It is important to note, however, that TEM can hardly be used as a statistically representative characterization technique. Thus, the domain width values reported are representative rather than a statistically significant mean. Piezoelectric force microscopy indicated much bigger domain size with mean values around 2 μm,311 which most probably indicates that the nanometer hierarchical domain morphology was not resolved by this technique. Bharathi and Varma260 found a correlation between the domain size and the grain size in BZT-BCT (Fig. 11). Many researchers investigating domains fail to report the grain size, which may be the source of domain size discrepancies in the literature.

FIG. 11.

Domain size as a function of grain size obtained from scanning electron microscopy studies in chemically etched materials. Reprinted with permission from J. Appl. Phys. 116, 164107 (2014). Copyright 2014 AIP Publishing LLC.

FIG. 11.

Domain size as a function of grain size obtained from scanning electron microscopy studies in chemically etched materials. Reprinted with permission from J. Appl. Phys. 116, 164107 (2014). Copyright 2014 AIP Publishing LLC.

Close modal

In situ electric field-dependent TEM studies indicated that the domain morphology is highly susceptible to the electric field. The compositions between (Ba0.91Ca0.09)(Zr0.14Ti0.86)O3 (BZT-30BCT) and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) can develop a monodomain state within grains, indicating a high degree of switching.282,312,333,334 In the case of compositions near the PPBs, the monodomain state was achieved by coalescence of the hierarchical domain structure.282,312,333 For compositions away from PPBs, the initial micrometer size domain morphology underwent a transformation into a hierarchical domain morphology similar to the one found near PPBs or the convergence region. Subsequently, with higher electric field, a monodomain state was also achieved in these compositions. This transformation was found to be reversible and is schematically represented in Fig. 12(a). Some works also pointed out that in some portions of the probed grains, a partial monodomain state surrounded by micrometer size domains may actually persist upon electric field removal.282,312

FIG. 12.

Schematic representation of domain morphology evolution in BZT-BCT during application of an external electric field, where only a tetragonal phase was considered to aid visualization. Representation is based on Refs. 333 and 334.

FIG. 12.

Schematic representation of domain morphology evolution in BZT-BCT during application of an external electric field, where only a tetragonal phase was considered to aid visualization. Representation is based on Refs. 333 and 334.

Close modal

Under sufficiently high magnitude or long period of exposure of applied electric field, the monodomain state evolved into a state with hierarchical domain morphology with the presence of nanometer and micrometer size domains, followed by the disappearance of the nanometer size domains [Fig. 12(b)]. This indicated that the monodomain state was metastable. The changes of domain morphology with electric field were found to be irreversible. Upon removal of the electric field, the micrometer size domain morphology was retained in the samples with no intermediate monodomain or nanodomain state.282,312,333,334 It was also found that compositions in the R phase and near PPBs required an electric field of ∼0.2 kV/mm (varying with composition) to nucleate the monodomain state. This value was found to be one order of magnitude lower than the electric field required to induce the monodomain state in the T phase. The nucleation of the nanometer size domain morphology in between monodomain and micrometer size domain states was ascribed to local strain gradients and strain incompatibility between adjacent grains.333,334 However, a rigorous physical model describing the origins of these observations is lacking.

The grain size of BZT-BCT affects its functional properties considerably. Grain size values between 10 μm and 50 μm are typically reported in the literature.267,271,282,285–291,335,336 The results coincide unambiguously in that the enlargement of grain sizes from around 1 μm to above 20 μm enhances the electromechanical properties.128,260 Hao et al.128 explored the effect of the variation of grain size between 0.4 μm and 32.2 μm on the electromechanical properties of BZT-50BCT, as displayed in Fig. 13. Increasing grain size from 0.4 μm to 20 μm resulted in an enhancement of the saturation polarization of 40% and an enhancement of the strain output of five times at 0.4 kV/mm. Increasing grain size from 20 μm to 32.2 μm led to little variation of polarization and strain. Thickness mode coupling kt, planar coupling coefficient kp, and small signal d33 values increased around five times in magnitude with increasing grain size from 0.4 μm to 20 μm. Thus, small and large signal properties increased in a similar way with increasing grain size.260 

FIG. 13.

Electromechanical properties of BZT-50BCT. The properties displayed are (a) bipolar polarization and (b) bipolar strain as a function of electric field for samples with grain size varying between 0.4 μm and 32.2 μm. (c) kt, kp, d33, and SmEm (d33*) as a function of grain size. Reprinted with permission from Hao et al., J. Am. Ceram. Soc. 95, 1998 (2012). Copyright 2012 John Wiley & Sons, Inc.

FIG. 13.

Electromechanical properties of BZT-50BCT. The properties displayed are (a) bipolar polarization and (b) bipolar strain as a function of electric field for samples with grain size varying between 0.4 μm and 32.2 μm. (c) kt, kp, d33, and SmEm (d33*) as a function of grain size. Reprinted with permission from Hao et al., J. Am. Ceram. Soc. 95, 1998 (2012). Copyright 2012 John Wiley & Sons, Inc.

Close modal

Apart from enhancing the magnitude of electromechanical properties, larger grain size also resulted in lower temperature stability of properties. The variations of properties with increasing grain size were attributed to increased domain switching and reduced residual stress in materials with coarser grain size.128 Grain size also affects dielectric properties. In some works, it was found that BZT-50BCT features a weak dielectric relaxation similar to relaxors, which becomes quite pronounced with decreasing grain size.128,260 Increasing grain size also leads to a decrease in phase transition temperatures between 10 °C and 20 °C as well as a reduction of εr and tan(δ).128,232

Texturing using BT as template particles has also been used to improve the electromechanical properties of BZT-BCT thick films337 and bulk materials.152,268,271,338–340 Research so far has explored textured BZT-BCT along the ⟨001⟩ direction via templated grain growth268,271,337–339 or reactive templated grain growth methods.152,340 Textured materials generally feature a larger average grain size as compared with untextured materials, which is generally attributed to the presence of BT template particles.152,268,271,337–340 The parameters used to optimize the texturing degree were the BT template particle content, sintering temperature, and sintering time. So far, texturing degrees (i.e., Lotgering factors) between 58% and 98% have been reported.152,268,271,337–340 The optimum content of BT template particles to maximize the texturing was found to be between 5 mol. % and 10 mol. %.339,340 Zhao et al.152 indicated that the optimum sintering procedure to maximize the texturing degree up to 95% was 1300 °C for 2 h. They also highlighted that employing pre-reacted BT, BZ, and CT as raw materials, as opposed to carbonates, promotes densification, increases average grain size, increases texture, and improves electromechanical properties. Following this procedure, Zhao et al.152 obtained a d33*=719 pm/V at 3 kV/mm, which was 57% higher than the value of untextured BZT-50BCT. In BZT-50BCT thick films, a texturing degree of 81% resulted in a Pr=15.8 μC/cm2 and a d33*=427 pm/V. Thus, enhancement of 48% in Pr and of 60% in d33* over the values of untextured thick films were achieved.337 

Ye et al.268 considered the effect of texturing and hot-pressing on the microstructure and piezoelectric properties of BZT-50BCT. Conventionally, sintered textured materials featured a texturing degree of 82%, an average grain size of 30 μm, and a relative density of 93.7%. Hot-pressing BZT-50BCT samples with the same content of BT template particles led to a texturing degree of 85%. The higher texturing degree of hot-pressed samples was attributed to the high stresses that impeded the re-orientation of the BT template particles during sintering. Hot-pressing did not increase the grain size of textured samples albeit the relative density was enhanced to 95.7% due to reduction of the porosity. The TC of hot-pressed textured samples was 90 °C, indicating an increase of 12 °C over textured samples produced via conventional sintering. The hot-pressed textured samples presented a d33=580 pC/N and a kp=0.49, which indicated an improvement of 23% in d33 values and of 11% in kp values over conventionally sintered textured samples. The enhancement of dielectric and piezoelectric properties was attributed to the higher density and higher degree of texturing of hot-pressed textured samples over conventionally sintered textured samples.268 

d. Functional and mechanical properties

(i) Poling:

Small and large signal electromechanical properties of BZT-BCT are highly dependent on poling conditions.259,269,285,286,289,293,341 Saturation of the poling degree in BZT-BCT occurs at 4 kV/mm at room temperature.269 The maximum degree of poling retained upon field removal depends on the BZT-BCT composition, with maximum values retained near the O to T phase transition and at the T phase.269,319 In contrast, it was suggested that high temperature field cooling promotes a higher degree of poling in the R phase than in the T phase producing a more pronounced enhancement of the electromechanical properties.289 

Some works pointed out that the optimized poling conditions for BZT-50BCT are 40 °C and electric fields ranging between 0.42 kV/mm and 0.7 kV/mm. This poling procedure resulted in a d33 630 pC/N and a d33* 513 pm/V at 3 kV/mm.259,293 In contrast, Wu et al.269 found that the optimum poling conditions for BZT-50BCT occur at 40 °C and 4 kV/mm. For (Ba0.85Ca0.15)(Zr0.08Ti0.92)O3, the optimum poling conditions were found at 30 °C and 5 kV/mm.320 Optimization of the poling conditions in BZT-50BCT resulted in an enhancement between 21% and 300% in d33.259,269,293 High temperature poling above 70 °C decreased the piezoelectric properties considerably.259,269,293 This may be attributed to the exacerbated degree of back switching found near phase transitions.342 

The poling procedure followed by field cooling led to considerably different findings. Poling at 90 °C with 3 kV/mm and field cooling led to optimized electromechanical properties in BZT-50BCT with a d33*=433 pC/N at 3 kV/mm.285 This indicated an enhancement of 20% in d33* as compared with the poling at 30 °C and 3 kV/mm without field cooling. Similarly, for BZT-60BCT poling at 120 °C with 3 kV/mm followed by field cooling resulted in a d33*=510 pm/V at 3 kV/mm. This indicated an enhancement of 42% in d33* as compared with the poling at 30 °C and 3 kV/mm with no field cooling.341 Other optimized poling conditions for some compositions of the BZT-BCT isopleth are indicated in Table V.

TABLE V.

Optimized poling conditions and electromechanical properties reported for BZT-BCT materials.

CommentsCompositionElectric field (kV/mm)Temperature (°C)Time (min)d33 (pC/N)d33* (pm/V) at 3 kV/mmReferences
Conventional poling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 0.42 40  637 513 259  
Conventional poling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 40 30 423  269  
Conventional poling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 0.7 40 20 630  293  
Poling followed by field cooling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 120 30  510 341  
Poling followed by field cooling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 90 30  433 285  
Poling followed by field cooling (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) 120 30  510 285  
Poling followed by field cooling (Ba0.79Ca0.21)(Zr0.06Ti0.94)O3 (BZT-70BCT) 120 30  379 285  
CommentsCompositionElectric field (kV/mm)Temperature (°C)Time (min)d33 (pC/N)d33* (pm/V) at 3 kV/mmReferences
Conventional poling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 0.42 40  637 513 259  
Conventional poling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 40 30 423  269  
Conventional poling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 0.7 40 20 630  293  
Poling followed by field cooling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 120 30  510 341  
Poling followed by field cooling (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 90 30  433 285  
Poling followed by field cooling (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) 120 30  510 285  
Poling followed by field cooling (Ba0.79Ca0.21)(Zr0.06Ti0.94)O3 (BZT-70BCT) 120 30  379 285  

Increasing the poling electric field or temperature followed by field cooling has an analogous effect. Both types of poling processes led to a gradual enhancement of the asymmetry in dielectric and electromechanical properties as well as the development of polarization offset and of an internal bias-field.285,289,341 These phenomena were more markedly observed in the R phase than near PPBs or in the T phase. The R phase was also characterized by the highest remanent ferroelastic texture.289 It is also worth noting that the remanent ferroelastic texture parallel to the electric field remained unaltered for each specific composition after re-poling.285,289,341 This indicated a high back switching upon electric field removal for all phases either for room temperature or field cooling after poling.

The changes in properties due to poling were attributed to the migration of point defects. The enhanced electromechanical properties obtained after optimum poling conditions were attributed to the facile development of a reversible ferroelastic texture upon field application. It was suggested that the properties of the R phase were affected more strongly by poling due to the lower coercive field, more polarization directions than the T phase, and lower spontaneous strain.285,289,341

(ii) Small and large signal properties:

The most relevant electromechanical properties at room temperature in BCZT are summarized in Table VI. We report a mean value calculated from references reporting each composition and the maximum deviation as a percentage of the mean value. We also speculate on the most probable source of variation in the properties such as different processing conditions and microstructures, discrepancies between measurement techniques and/or experimental conditions, or variation in poling conditions. Immediately after poling and during a period between 24 h to 36 h, relaxation/aging of the piezoelectric and dielectric properties is likely to occur prior to reaching stable properties. The waiting time before properties are measured is generally not reported and could also be a source of discrepancies in the literature. Similar sources of discrepancies among literature values were also highlighted previously.343 

Although the majority of reports focused on the compositions at the BZT-BCT isopleth, several works also investigated other BCZT compositions and also found remarkable electromechanical properties. Another point to highlight is the high discrepancies among the values reported. Let us take BZT-50BCT as an example to elucidate this issue. The TC=91 °C and d33*=1053 have deviations below 15% among works. All other properties have variations ranging between 20% and 54%. The high variations in properties clearly indicate that BCZT is extremely susceptible to raw materials, synthesis and measurement conditions/techniques, microstructure, poling conditions, among others. For the sake of reproducibility, it is crucial to clearly report the experimental procedures. The experimental procedures reported in many research papers are often over-simplified and the importance of some experimental details are sometimes overlooked.

Let us now focus on the general trends found in BCZT. To pursue this, we present the pseudo-ternary phase diagram of BCZT in Fig. 14 superimposed with color coded data markers. The bars next to the phase diagrams correlate the color of the data marker with the magnitude of (a) TC, (b) d33, and (c) d33*. We indicate the BZT-BCT isopleth with a dotted line.

FIG. 14.

Representation of the TC, d33, and d33* values reported in the literature for the BCZT pseudo-ternary diagram. The color code of data markers indicates their magnitude according to the scale bars. The dotted line indicates the BZT-BCT isopleth.

FIG. 14.

Representation of the TC, d33, and d33* values reported in the literature for the BCZT pseudo-ternary diagram. The color code of data markers indicates their magnitude according to the scale bars. The dotted line indicates the BZT-BCT isopleth.

Close modal

Most studies of the piezoelectric properties concentrated on the BT-rich region. The Curie temperature is greatest in the region between 0% and 5% BZ, between 82% and 100% BT, and between 0% and 15% CT. This is expected since Zr4+ is known to suppress TC, whereas Ca2+ does not shift TC but rather reduces the O to T phase transition in BT. The highest TC 130 °C was reported for the (Ba0.85Ca0.15)(Zr0.03Ti0.97)O3, (Ba0.95Ca0.05)TiO3, and (Ba0.85Ca0.15)TiO3.269,320,328,344 The high TC of these compositions is a consequence of the low Zr4+ addition and is accompanied by low piezoelectricity. The compositions with highest d33 and d33* are found in the region between 8% and 12% BZ, between 72% and 80% BT, and between 12% and 17% CT. This compositional region is near or at the BZT-BCT isopleth. We highlight the BZT-50BCT, (Ba0.85Ca0.15)(Zr0.12Ti0.88)O3, and (Ba0.825Ca0.175)(Zr0.10Ti0.90)O3 compositions. They feature a TC > 68 °C, d33 > 500 pC/N, and d33* > 700 pm/V at 1 kV/mm.11,328

We now focus on the BZT-BCT isopleth. Table VII is adapted from Ref. 281 and introduces small signal dynamic piezoelectric properties of BZT-50BCT, BT, and PZT5A (commercial soft PZT) for comparison. The BZT-50BCT presents the highest electromechanical properties. It features a d33 185% higher than BT and 46% higher than soft PZT, as well as a d31 192% higher than BT and 35% higher than soft PZT. It should also be highlighted that PZT5A features the highest coupling coefficients. Liu and Ren11 indicated that the d33* value of BZT-50BCT is 20% higher than in soft PZT (PZT5H) at 0.5 kV/mm. We point out, though, that d33* values are considerably lower at 2 kV/mm, which is the working electric field of soft PZT in actuators. This is a consequence of the lower EC of BZT-50BCT compared with soft PZT.347 

TABLE VII.

Small signal dynamic piezoelectric properties for BZT-50BCT, BT, and soft PZT (PZT5A). Reprinted with permission from J. Appl. Phys. 109, 054110 (2011). Copyright 2011 AIP Publishing LLC.

Materiald33 (pm/V)d31 (pm/V)d15 (pm/V)k33k31k15ktkp
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 546 −231 453 0.65 0.31 0.48 0.42 0.53 
BT 191 −79 270 0.49 0.21 0.48  0.35 
Soft PZT (PZT5A) 374 −171 584 0.7 0.34 0.68 0.49 0.6 
Materiald33 (pm/V)d31 (pm/V)d15 (pm/V)k33k31k15ktkp
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) 546 −231 453 0.65 0.31 0.48 0.42 0.53 
BT 191 −79 270 0.49 0.21 0.48  0.35 
Soft PZT (PZT5A) 374 −171 584 0.7 0.34 0.68 0.49 0.6 

Only a few works reported 31 measurements in BZT-BCT. For BZT-50BCT, d31 values between −200 pC/N and −231 pC/N were reported,281,295 although Wang et al.300 found a considerably lower d31=−74 pC/N. For (Ba0.904Ca0.096)(Zr0.136Ti0.864)O3 (BZT-32BCT), a d31=−120 pC/N was reported.

Figure 15 displays the quasi-static small signal d33 as a function of composition for the BZT-BCT isopleth.283 It is clear that maximized properties are found at the O to T PPB with a d33 = 545 pC/N, followed by local maxima values at the R to O PPB with a d33 = 320 pC/N.

FIG. 15.

Quasi-static small signal d33 as a function of composition for the BZT-xBCT isopleth. Reprinted with permission from Appl. Phys. Lett. 105, 162908 (2014). Copyright 2014 AIP Publishing LLC.

FIG. 15.

Quasi-static small signal d33 as a function of composition for the BZT-xBCT isopleth. Reprinted with permission from Appl. Phys. Lett. 105, 162908 (2014). Copyright 2014 AIP Publishing LLC.

Close modal

Figure 16 presents the large signal unipolar strain of (Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (BZT-40BCT), (Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT), (Ba0.856Ca0.144)(Zr0.104Ti0.896)O3 (BZT-48BCT), and (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT). The measurements were performed in the unpoled and poled state with an electric field of 0.5 kV/mm and a frequency of 0.1 Hz. The calculated d33* values at 0.5 kV/mm are also displayed. All compositions feature higher electromechanical response in the poled state. In contrast to the small signal d33 presented in Fig. 15, the large signal d33* has the highest values near the R to O PPB with a d33*=1230 pm/V (1310 pm/V) in the unpoled (poled) state.

FIG. 16.

Unipolar strain of BZT-40BCT, BZT-45BCT, BZT-48BCT, and BZT-50BCT. The measurements were done at 0.5 kV/mm and 0.1 Hz in the unpoled and poled state. Reprinted with permission from J. Appl. Phys. 111, 124110 (2012). Copyright 2012 AIP Publishing LLC.

FIG. 16.

Unipolar strain of BZT-40BCT, BZT-45BCT, BZT-48BCT, and BZT-50BCT. The measurements were done at 0.5 kV/mm and 0.1 Hz in the unpoled and poled state. Reprinted with permission from J. Appl. Phys. 111, 124110 (2012). Copyright 2012 AIP Publishing LLC.

Close modal

Figure 17 introduces dynamic small signal d33 and kp as well as the quasi-static large signal d33* for the compositions ranging between BZT-32BCT and BZT-60BCT as a function of temperature. Dashed lines indicate phase transitions obtained from dielectric properties.347 From the analysis of the temperature profiles of all curves and literature reports,11,318,319,343,346 it becomes clear that electromechanical properties in 33 mode feature local maxima values around phase transitions. Maximized d31 values and minimized coercive field values were also found near phase transitions.295,342 The functional properties found in the R and O phases are much more susceptible to temperature variations than in the T phase (Fig. 17). The room temperature piezoelectric properties of the R phase after high temperature excursions286 or stress287 deteriorate much more than those in other phases.

FIG. 17.

In situ small signal dynamic piezoelectric properties (a) d33 and (b) k33 as a function of temperature obtained from impedance characterization. Row (c) displays the large signal d33* as a function of temperature. Dashed lines indicate phase transitions obtained from dielectric properties. From Acosta, Strain Mechanisms in Lead-Free Ferroelectrics for Actuators, 1st Edition. Copyright 2016 Springer. Reprinted with permission from Springer.

FIG. 17.

In situ small signal dynamic piezoelectric properties (a) d33 and (b) k33 as a function of temperature obtained from impedance characterization. Row (c) displays the large signal d33* as a function of temperature. Dashed lines indicate phase transitions obtained from dielectric properties. From Acosta, Strain Mechanisms in Lead-Free Ferroelectrics for Actuators, 1st Edition. Copyright 2016 Springer. Reprinted with permission from Springer.

Close modal

The magnitude of d33 varies with measurement technique. For instance, under equal driving voltage, resonance and off-resonance measurements will provide different d33 values.318,319,347 The highest dynamic piezoelectric coefficient 448 pC/N <d33< 592 pC/N value is found at 45 °C for BZT-45BCT. d33 values with magnitudes ∼30% lower than at the O to T PPB are discerned in the convergence region.318,319,347 The T phase in BZT-60BCT a relatively constant 240 pC/N<d33<310 pC/N for temperatures between 25 °C and 95 °C since in this temperature range there are no phase boundaries.318,319,347 A clearly non-zero d33 100 pC/N value persists even at 10 °C above the TC for most compositions. Presence of residual piezoelectricity has been found by many authors,128,293,317–319,347 which can result from persistence of domains330 and/or polar clusters.316,317

The coupling coefficient k33 has values between 0.40 and 0.58 at room temperature, which are relatively high and comparable to PZT [row (b) of Fig. 17].348 BZT-45BCT and BZT-50BCT feature the highest k33=0.58 at room temperature.281 The phase transitions modify the slope of the k33 curves, indicating less susceptibility to phase boundaries than d33 values. Consistent with the d33 curves, residual non-zero k33 values persist above TC. Only local k33 maximum values are observed in the convergence region.

The normalized strain d33* at 3 kV/mm is introduced in row (c) of Fig. 17. There is a weak correlation of d33* temperature profiles as compared with the small signal properties, with much smoother variations around phase transitions. The compositions with R and O phases feature a much more stable large signal response as a function of temperature than the small signal one. In contrast, the d33* is not as stable as the small signal d33 found in the T phase, since it presents a decay of 30% between 25 °C and 95 °C. For all compositions, a d33* 200 pm/V is observed even at 10 °C above TC.

Contour plots of (a) d33 and (b) d33* as a function of temperature and composition are introduced in Fig. 18 to visualize the relationship between the phase diagram and electromechanical properties. The phase transitions obtained from dielectric measurements are superimposed in white.347 Figure 18(a) indicates that the highest d33 is obtained along the O to T PPB,318,319,347 as found in other BT-based materials.326 Local maxima in d33 values also become apparent near the O to R PPB and convergence region. These local maxima values are ∼30% lower than the values at the O to T PPB. Figure 18(b) indicates that high d33* values are found in a broad region around the O phase and at both PPBs. In contrast to the small signal d33 where properties were maximized along the O to T PPB, the highest d33* values were found along both PPBs.318,347

FIG. 18.

Contour plot of (a) d33 and (b) d33* as a function of temperature and composition. The resolution of the contour plots is given by 7 × 16 and 7 × 11 experimental data points, respectively. The values between the measured points were estimated by linear interpolation between data points. Shaded area indicates the convergence region. From Acosta, Strain Mechanisms in Lead-Free Ferroelectrics for Actuators, 1st Edition. Copyright 2016 Springer. Reprinted with permission from Springer.

FIG. 18.

Contour plot of (a) d33 and (b) d33* as a function of temperature and composition. The resolution of the contour plots is given by 7 × 16 and 7 × 11 experimental data points, respectively. The values between the measured points were estimated by linear interpolation between data points. Shaded area indicates the convergence region. From Acosta, Strain Mechanisms in Lead-Free Ferroelectrics for Actuators, 1st Edition. Copyright 2016 Springer. Reprinted with permission from Springer.

Close modal

(iii) Origins of outstanding electromechanical properties:

Figure 19 introduces the most notable experimental observations related to the piezoelectric properties of each of the phases and phase boundaries of BZT-BCT.

FIG. 19.

Most notable experimental observations related to the piezoelectric properties in BZT-BCT.

FIG. 19.

Most notable experimental observations related to the piezoelectric properties in BZT-BCT.

Close modal

Models that consider exclusively the intrinsic contribution to the piezoelectric effect highlighted the importance of the presence of a TCP11,295,314,324 or PPBs,215,319 energy barrier,323,349 and high electrostriction.350 Other models that include extrinsic contributions pointed out factors such as the effect of the remanent polarization and permittivity,283,314,318,319,349 elastic properties,282,283,297,319 and polarization dynamics.322,351,352 Some authors highlighted the extrinsic contributions to the piezoelectric effect are more significant than intrinsic contributions. These works pointed out several important aspects related to the extrinsic contributions such as ferroelastic texturing,286,288,290 hierarchical domain morphology and domain miniaturization,280,282,312,314,330,333,334 the formation of a monodomain state within grains,282,312,333,334 the contribution of domain wall mobility (switching),125,284,286,290,335 and domain wall density.287,291 Some contributions also indicated that there are key structural aspects that should be considered especially around the PPBs. These phenomena include phase coexistence286,317,343 or presence of a low symmetry phase,272,282 relaxor properties,275,276 and electric field-induced phase transformations.275,276,282,333 It is clear that many of these factors are closely related to each other. In fact, many authors investigated more than one factor and their interdependency.

From a structural point of view, it was proposed that on an atomic scale, the polarization and piezoelectricity in BZT-50BCT are determined largely by Ti4+ displacement.275,276 Phase coexistence286,317,343 or presence of a low symmetry phase272,282 as well as reduction of the free energy anisotropy141,186,187,231 with concomitant domain miniaturization314 were proposed to be key aspects leading to enhanced properties in BZT-50BCT. The susceptibility of BZT-BCT to variations in temperature or poling conditions were ascribed to the reduction in anisotropy energy that aids the polarization rotation.295 

Several reports indicated that phase transitions originating in a TCP result in negligible polarization anisotropy that facilitates polarization rotation.63,114,146,151 Liu and Ren11 suggested that there is near degeneration of the free energy surface, which leads to easy polarization rotation that extends to phase boundaries originating from a tricritical point. It was proposed that this contrasts to the case of PPBs that do not originate in a tricritical point since in these cases a larger energy barrier for polarization rotation persists.11 However, a reduction in the anisotropy energy occurs in a broad region enveloping the phase boundaries, even when the triple point is not a TCP.215,319 On the other hand, assuming such a point, Yang et al.323 rationalized the ease of polarization rotation using the energy barrier along the minimum energy pathway on the free energy surface of BZT-BCT. This was done to reconcile the experimentally observed higher d33 at the O to T PPB, rather than at the R to O PPB.318,319 The energy barrier was calculated as the difference between the saddle point on the minimum energy pathway and the energetically degenerate variants connected by the minimum energy pathway. It was proposed that this barrier serves as a better measure of the polarization anisotropy than does the anisotropy energy.323 However, the energy barriers at the R-O and T-O transitions are both very small. The energy barriers are also significantly reduced in the same region of the phase diagram as the anisotropy energy. Thus, the differing thermodynamic descriptions of the phase diagram led to substantially the same conclusion, i.e., a nearly spherical energy surface is an important factor contributing to enhanced piezoelectricity.

Li et al.350 reported high electrostrictive coefficients for BZT-40BCT, BZT-50BCT, and BZT-60BCT with values Q 0.04 m4/C2 between 20 °C and 100 °C. This value is twice as high as the electrostrictive coefficients found in La-doped PZT. A high relative permittivity and remanent polarization were also reported at PPBs.283,319 The elastic properties of BZT-BCT were measured by flexural resonance, dynamic mechanical analysis, and by impedance analysis methods.282,283,297,317,319,321 It was demonstrated that all phase boundaries are clearly discerned by these techniques.297,321 Importantly, the O to T PPB was revealed to be softer than the R to O PPB, thus re-affirming that the highest electromechanical properties are expected at this phase boundary (Figure 19). Thus, in addition to flattening of the energy surface, the shear elastic softening demonstrated at the O to T PPB plays an important role in differentiating the properties at the two PPBs. The importance of elastic properties near phase transitions in reconciling piezoelectric properties has been recently reviewed.353 

The domain miniaturization and hierarchical domain morphology found in the convergence region and near the PPBs in BZT-BCT has generally been recognized as a major extrinsic contributor to piezoelectric properties.280,282,312,314,330,333,334 A high degree of domain switching was corroborated by in situ electric field-dependent TEM282,312,333,334 as well as ferroelastic measurements.288,290 TEM studies also indicated that high domain wall mobility leads to a metastable monodomain state, as described in Sec. V A 2 c.282,312,333,334 It was found that the macroscopic properties such as maximum polarization and strain correlate with the coercive fields and the fields required to trigger the monodomain state. The lowest electric fields were found for the O phase, followed by the R phase. For the T phase, much higher electric fields were required to trigger the monodomain state.333 

Based on local piezoelectric force microscopy measurements, Turygin et al.352 supported the TEM findings of a high degree of switching. Moreover, they indicated that BZT-50BCT features a high domain wall mobility in comparison to BT and La-doped PZT. Thus, it was suggested that high switching dynamics may also contribute to the large piezoelectricity of BZT-50BCT.352 Zhukov et al.322,351 investigated the effect of the polymorphic phase transitions on the polarization dynamics of BZT-BCT. It was found that the polarization dynamics are governed by two distinct time dependencies as a function of electric field. The threshold electric field that determines the change in the mechanism of polarization dynamics varied monotonically between 0.30 kV/mm and 0.72 kV/mm for compositions between (Ba0.91Ca0.09)(Zr0.14Ti0.86)O3 (BZT-30BCT) and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT). These values are near the electric field values required to induce a monodomain state,282,312,333,334 although no correlation between these phenomena has been discussed so far. For the low field region, the time dependence of the polarization followed the non-equilibrium polarization switching model proposed by Vopsaroiu et al.354 At the higher electric field region, the time dependence of the polarization dynamics followed the Merz law65 or alternatively the domain wall creep motion form.355 Analysis of the low field region determined that a broad minimum in the energy barrier for switching coincides with the O phase. Moreover, it was found that the low energy barrier for switching in the O phase has a stronger effect than the reduction in the energy barrier for switching with increasing temperature.148,185

Several reports estimated the intrinsic and extrinsic contributions to the electromechanical properties of BZT-BCT using diffraction techniques,290,335 Rayleigh analysis,284 and bias-field-dependent d33.125 The structural studies were performed in the region where the T phase is stable between (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) and (Ba0.73Ca0.27)(Zr0.02Ti0.98)O3 (BZT-90BCT). Switching was found to be the main source of strain for all the compositions in the T phase.290,335 As the O to T PPB is approached, higher macroscopic strain occurs as a result of higher extrinsic and intrinsic contributions.335 The higher extrinsic contribution was ascribed to the enhanced domain wall motion and alignment under either weak or high electric field.335 It was also observed that the largest intrinsic lattice strain contribution for all compositions originates from non-polar directions.290,335 These reports did not discuss, however, the reversible and irreversible contributions separately.

Figure 20 displays the intrinsic, extrinsic reversible, and extrinsic irreversible contributions for BZT-BCT at room temperature.125,284 Dashed lines indicate phase transitions between R, O and T phases determined elsewhere.318 

FIG. 20.

Intrinsic, reversible extrinsic, and irreversible extrinsic contributions to the piezoelectric effect at room temperature. Data were digitized from Gao et al.284 and Acosta et al.125 Dashed lines indicate phase transitions between R, O and T phases from dielectric properties.318 

FIG. 20.

Intrinsic, reversible extrinsic, and irreversible extrinsic contributions to the piezoelectric effect at room temperature. Data were digitized from Gao et al.284 and Acosta et al.125 Dashed lines indicate phase transitions between R, O and T phases from dielectric properties.318 

Close modal

Figure 20(a) also reveals a good agreement in the intrinsic contribution estimated in both works with variations of less than 10%. Gao et al.284 estimated the intrinsic contribution via the slope of the large signal strain output, whereas Acosta et al.125 obtained it by taking the d33 at 3 kV/mm where most switching processes were considered to be saturated. Far from PPBs, the intrinsic contribution to the piezoelectric effect of the T phase was the highest, followed by the contribution found in the R phase. For BZT-50BCT, high discrepancies between both works are discerned. According to Gao et al.,284 the reversible extrinsic switching corresponded to 48% of the total d33, whereas Acosta et al.125 indicated that it leads to 11%. The relative irreversible extrinsic contribution was estimated to be 53% by Acosta et al.,125 whereas Gao et al.284 indicated that it contributes to 29%. Thus, it becomes clear that the Rayleigh analysis leads to a lower relative estimation of the irreversible extrinsic contribution and higher one of the reversible extrinsic contribution than bias-field experiments. The most probable source of discrepancy is the difference in poling state; i.e., of the irreversible domain state at a given measurement point.

Both reports ascertain that the extrinsic contributions are the major factor contributing to the d33 around PPBs. Acosta et al.125 also investigated the relative contributions to the d33 as a function of temperature. It was found that the R phase has similar fractions of intrinsic and extrinsic contributions (adding both reversible and irreversible). The O phase presented a high irreversible switching contribution between 35% and 55%. This finding was supported by in situ temperature-dependent TEM measurements.330 The T phase featured as much as 70% of extrinsic contributions close to the O to T PPB. Increasing the temperature reduced the overall extrinsic contributions, which was attributed to a temperature hardening effect.125,319 Gao et al.294 revealed that near to the convergence region the intrinsic and extrinsic reversible contributions are maximized, which was attributed to the proximity to a phase transition and domain miniaturization.294 

Electric field-induced phase transformations have been evoked in some works to reconcile the large piezoelectricity of BZT-BCT around PPBs.275,276,282,312,333 Brajesh et al.275,276 proposed that an irreversible electric field-induced phase transformation leads to an increase in the R and O phase fractions at expense of the T phase in BZT-50BCT. These phases remain metastable over a broad temperature range and thus they may contribute to the large piezoelectricity of BZT-50BCT,275,276 as found for BT near room temperature.356 Other reports also speculated that an electric field-induced phase transformation into an O phase may also occur in BZT-50BCT. The field-induced O phase was associated with the monodomain state observed by in situ TEM and also with a steep increase in the elastic compliance at ∼0.3 kV/mm in compositions between (Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (BZT-40BCT) and (Ba0.844Ca0.156)(Zr0.096Ti0.904)O3 (BZT-52BCT).282,333 However, no discernable changes in the selected area electron diffraction patterns were found.282,312,333 Preliminary proof was provided based on a refinement of partial XRD patterns of BZT-50BCT in its virgin state and at 0.6 kV/mm.282 Subsequently, more detailed refinements indicated that there is an irreversible electric field-induced phase transformation, analogous to a stress-induced transformation that increases the fraction of O and R phases at expense of the T phase fraction.275,276 The increment of O phase upon electric field application and its softness were proposed to be a major contributor to the high d33 of BZT-50BCT.275,276,282,333 This model does not reconcile, however, the discovery of the metastable monodomain state for other BZT-BCT compositions far from PPBs.333 It was also speculated that the weak relaxor properties found in BZT-50BCT may contribute to its large piezoelectric activity since polar nanoregions may favor the electric field-induced phase transformation and domain wall motion.275,276

The convergence region is the softest region of the BZT-BCT isopleth, followed closely by the O to T PPB.319,321 Gao et al.314 measured negligible transition enthalpy and less than 1.5 °C hysteresis in dielectric properties near the line of Curie temperatures between (Ba0.91Ca0.09)(Zr0.14Ti0.86)O3 (BZT-30BCT) and (Ba0.895Ca0.105)(Zr0.13Ti0.87)O3 (BZT-35BCT). This suggested a TCP around the convergence region. Other investigations indicated that critical points may occur at non-zero electric field along the line of Curie temperatures of the BZT-BCT isopleth, rather than just at the convergence region. This assumption was based on local maxima values of reversible switching found above TC at finite bias-fields.125 Concomitantly, a concurrence in the zero-field phase diagram between the convergence region and a critical point cannot be obtained. However, as previously discussed, due to the strong smearing of the phase transitions in this region of the phase diagram, these findings cannot be regarded as conclusive.

Based on energetic considerations and the assumption of TCP, the highest d33 and d33* values of the BZT-BCT isopleth a are expected at the convergence region, which is not the case (Fig. 19). Some researchers pointed out that poling degree and elastic properties should also play a significant role in defining the electromechanical properties.314,319,323 Measurements of thermally stimulated depolarization currents indicated a continuous decay of polarization.295,322 Impedance measurements indicated a decay of the poling degree in the R phase with increasing temperature that results in a low poled state in the convergence region.319 These findings corroborate that one of the reasons behind the lower d33 in the convergence region is the temperature induced depolarization314,318,319 that leads to the disappearance of ferroelastic texturing above 70 °C.286 In analogy, we suspect that the high d33 values reported near the convergence region in BSnT (see Fig. 7) are found as consequence of the proximity of the convergence region to room temperature.

The d33* values around the convergence region are considerably lower than around PPBs. This cannot be attributed to an effect of the thermal depolarization since the probing electric field strength is high enough to re-pole BZT-BCT.318 Moreover, switching around the convergence region should be high taking into account the domain size, domain morphology, and the high polarization at 3 kV/mm.314,318 It was speculated that the low d33* value around the convergence region is a result of the small contribution to the strain per switching event.318 This was ascribed to the small non-cubic distortions from the cubic symmetry.296 Tutuncu et al.335 indicated that the strain per switching event is a function of the tetragonality, which was expressed as c/a–1. In other words, lower distortions result in higher switching but with less strain per switching event.

The non-zero d33 found above TC in many compositions may result from the weak relaxor properties described in many reports275,276,315 and/or the presence of a T polar phase between 100 °C and 200 °C.315–317 The non-zero d33* above TC can result from an electric field-induced phase transformation above TC due to the probing electric field, as confirmed for BT.357 

(iv) Mechanical properties:

Mechanical properties in piezoelectrics are important for the design of actuators.358 Moreover, they offer an alternative approach to characterize piezoelectric properties without conductivity issues. The stiffness and ferroelastic switching can influence to a great extent the electromechanical response of a piezoelectric as well as the long-term reliability of a multilayer actuator. Brandt et al. reported the stress-strain curves in the compositional range between (Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT), as displayed in Fig. 21.

FIG. 21.

Stress-strain curves at room temperature for BZT-BCT in the compositional range between (Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT). Reprinted with permission from J. Appl. Phys. 115, 204107 (2014). Copyright 2014 AIP Publishing LLC.

FIG. 21.

Stress-strain curves at room temperature for BZT-BCT in the compositional range between (Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT). Reprinted with permission from J. Appl. Phys. 115, 204107 (2014). Copyright 2014 AIP Publishing LLC.

Close modal

The stress-strain curves indicate an increased remanent strain and decreased back switching with increasing BCT content at room temperature. This was attributed to the increased lattice distortion and enhanced strain per switching event towards the T phase. The Young's modulus had little variation among compositions with values ranging between 165 GPa and 179 GPa. The remanent strain and ferroelastic hysteresis of all compositions decreased with increasing temperature.346 

Ehmke et al.287,291 investigated the effect of uniaxial compressive stress on the small and large signal electromechanical response for (Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (BZT-40BCT), (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT), and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT). All compositions featured a monotonic decrease of the small signal d33 with increasing uniaxial stress. The d33 values were reduced by 50% with loads of (−6.3 ± 2.1) MPa and (−7.0 ± 2.3) MPa for BZT-40BCT and BZT-50BCT, respectively. BZT-60BCT required a much higher load of (−24.3 ± 4.5) MPa to reduce its d33 values by 50%. Unloading the samples (and reloading them to the pre-stress state required for the measurement) resulted in values of (52 ± 12) %, (39 ± 12) %, and (71 ± 9) % of their initial d33 values for BZT-40BCT, BZT-50BCT, and BZT-60BCT, respectively. The BZT-60BCT is the composition with the highest retention of d33 values under uniaxial stress and also it recovers its properties more pronounced upon stress relief. It was proposed that this correlates with its larger coercive stress/field. It was stated that the most relevant mechanism responsible for the decrease in d33 values under stress is the reduction of domain wall density. Because of the d33 recovery upon load relief, it was proposed that changes in domain wall density under small stresses are partially reversible. The sensitivity of the small signal d33 values to external loading can be a problem in applications working in the small signal regime under external loads.

Large signal properties can be enhanced by moderate uniaxial stress loadings (Fig. 22).291,359 The large signal properties under compressive stress can be separated into an electric field-controlled and a stress-controlled regime. In the former, the domains that switched ferroelastically perpendicular to the applied mechanical loading can be switched back by sufficiently high electric field. Within the electric-field-controlled regime, maximized piezoelectric properties are expected since a sufficiently high electric field can realign domains parallel to the electric field. On the other hand, for the stress-controlled regime, the domains remain clamped as a consequence of sufficiently high stress. This situation cannot be reversed with the application of an electric field and results in a diminished strain output.291,359,360 Ehmke et al.291 investigated the large signal d33* as a function of compressive loads for BZT-40BCT, BZT-50BCT, and BZT-60BCT at different electric fields and temperatures. For BZT-40BCT, the highest 1420 pm/V<d33*<1540 pm/V values were found at 0.5 kV/mm for temperatures between 25 °C and 50 °C and for stresses between 8 MPa and 10 MPa. Similar maximum d33* values were reported under the same electric field and stress states for BZT-50BCT at 25 °C. These maxima corresponded to as much as 30% higher d33* values than those obtained without external loading. BZT-60BCT also featured maximized d33*<500 pm/V values but with a lower stress influence.

FIG. 22.

Large signal d33* (Su/Emax, where Sij indicates large signal strain) for (Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (40BCT), (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (50BCT), and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (60BCT) as a function of compressive stress. Unipolar electric field was varied between 0.5 kV/mm, 1 kV/mm, and 2 kV/mm and temperatures between 25 °C, 50 °C, 75 °C, and 100 °C. Reprinted with permission from M. C. Ehmke et al., Acta Mater. 78, 37 (2014). Copyright 2014 Elsevier Ltd.

FIG. 22.

Large signal d33* (Su/Emax, where Sij indicates large signal strain) for (Ba0.88Ca0.12)(Zr0.12Ti0.88)O3 (40BCT), (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (50BCT), and (Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (60BCT) as a function of compressive stress. Unipolar electric field was varied between 0.5 kV/mm, 1 kV/mm, and 2 kV/mm and temperatures between 25 °C, 50 °C, 75 °C, and 100 °C. Reprinted with permission from M. C. Ehmke et al., Acta Mater. 78, 37 (2014). Copyright 2014 Elsevier Ltd.

Close modal

Similar features are found in the large signal d33* curves as a function of stress measured at higher temperatures (Fig. 22). The local maxima d33* values at higher temperatures are generally found at higher stress and electric field, although they remain lower in magnitude than the local maxima d33* values found at room temperature. Humburg et al.359 also reported an enhancement of around 20% in d33* with a stress of 15 MPa at room temperature in (Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT). Weak maxima in d33* values were also found in doped BZT-BCT materials.359 

Generally, piezoelectric properties are tested with negligible external load indicating a free displacement condition that is generally termed the free stroke or free strain (geometry independent). Nonetheless, in commercial applications, the piezoelectric element is exerting a force and thus performing work. The external force required to clamp the piezoelectric is generally termed the blocking force or blocking stress (geometry independent).361 Table VIII introduces the blocking stress and free strain of relevant lead-containing and lead-free piezoelectrics at room temperature together with the method employed for the measurement.

TABLE VIII.

Blocking stress and fracture toughness of piezoelectric materials at room temperature. The method employed for the fracture toughness measurement is also given. CT: compact tension specimen and IN: indentation measurement.

CompositionBlocking stress (MPa)aFracture toughness (MPa m1/2)MethodReferences
PZT −48 1.05 ± 0.3 CT 361 and 362  
(Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) −54 0.67 ± 0.3 CT 346 and 363  
(Ba0.874Ca0.126)(Zr0.116Ti0.884)O3 (BZT-42BCT) −64 — — 346  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) −63 1.3 ± 0.3 IN 346 and 364  
(Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) −38 — — 346  
CompositionBlocking stress (MPa)aFracture toughness (MPa m1/2)MethodReferences
PZT −48 1.05 ± 0.3 CT 361 and 362  
(Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) −54 0.67 ± 0.3 CT 346 and 363  
(Ba0.874Ca0.126)(Zr0.116Ti0.884)O3 (BZT-42BCT) −64 — — 346  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) −63 1.3 ± 0.3 IN 346 and 364  
(Ba0.82Ca0.18)(Zr0.08Ti0.92)O3 (BZT-60BCT) −38 — — 346  
a

Blocking stress values given were determined by the proportional loading method.

Table VIII indicates that the blocking stress of BZT-BCT compositions at room temperature is quite high and comparable or superior to commercial PZT. Brand et al.346 investigated the temperature dependence of the blocking stress. Similarly, as in the temperature profiles of the free strain (Fig. 17), it was found that maximum values of blocking stress occurred around phase transitions. The overall maximum blocking stress of -64 MPa was found for BZT-42BCT at 40 °C.

Multilayer actuators are composed of inactive electrodes and active ferroelectric layers in order to reduce the driving voltage as compared with monolithic actuators. The strain incompatibility between active and inactive layers will promote a substantial crack driving force.365 Hence, data on the effect of residual stress and fracture toughness as a function of poling direction and subcritical crack growth are required. Fracture toughness in BZT-BCT was measured through crack growth in compact tension specimens or through indentation experiments.366,367 Table VIII displays the fracture toughness values reported for (Ba0.8845Ca0.1155)(Zr0.123Ti0.877)O3 (BZT-38.5BCT) and (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT). The fracture toughness values are in a similar range as those found for PZT, although more work is required to establish trends363,364 especially for BZT-50BCT considering the discrepancies that may arise in the calculation of fracture toughness via the Vickers indentation method.368,369 In the work by Vögler et al.363 on BZT-38.5BCT, led grain bridging was considered negligible and the temperature-dependent R-curve behavior was provided. They revealed that the fracture toughness of BZT-38.5BCT decays linearly with increasing temperature, which may reduce the lifetime of multilayers composed of BZT-BCT.363 

(v) Reliability studies:

Zhang et al.336 indicated that poled BZT-50BCT suffers from aging within one month, as evidenced by a reduction in the remanent and maximum polarization values, development of an internal bias-field of 28 V/mm, asymmetry in the bipolar strain loop, and reduction in the small signal relative permittivity as a function of bias-field.336 Su et al.293 found a much more pronounced deterioration of properties in aged samples. 7 days after the poling procedure, aging led to a decay of 25% in d33 and of 30% of kp in dry atmosphere. Under wet conditions, the loss of small signal piezoelectric properties due to aging was slightly exacerbated.293 Increasing the aging temperature leads to a considerably higher reduction of the piezoelectric properties.23 Zhang et al.336 observed that 10 000 bipolar cycles recover properties to a great extent. They propose that aging in BCZT results from the formation of defect dipoles and accumulation of oxygen vacancies at grain boundaries, the latter being the preponderant mechanism.336 

Bipolar fatigue was investigated in (Ba0.92Ca0.08)(Zr0.055Ti0.945)O3 and (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT). Both compositions feature a decrease in the remanent and maximum polarization, broadening of the current peak associated with domain switching, asymmetry of the strain hysteresis, and a decrease in small signal d33 with increasing cycles. (Ba0.92Ca0.08)(Zr0.055Ti0.945)O3 exhibited a 17% higher decrease in remanent polarization as compared with BZT-50BCT after 105 cycles, although its d33 withstood 15% more. The large signal bipolar strain asymmetry was three times higher in (Ba0.92Ca0.08)(Zr0.055Ti0.945)O3 than in BZT-50BCT. The fatigued BZT-50BCT composition was, however, characterized by a large decrease in relative permittivity and a large increase in dielectric losses as a function of bias-field. In contrast, for (Ba0.92Ca0.08)(Zr0.055Ti0.945)O3, bias-field dependent properties became asymmetric with no reduction in magnitude. The surface of the fatigue samples became discolored after electrode removal. (Ba0.92Ca0.08)(Zr0.055Ti0.945)O3 materials were more severely discolored and featured micro-cracking that was not reversed upon annealing. The BZT-50BCT discoloration was partially reversed by annealing, and no micro-cracking was observed.370,371

Unipolar fatigue was also investigated in BZT-50BCT.371 A decrease of 30% of the maximum polarization and of 9% of the maximum strain was observed after 1000 unipolar cycles. Subsequent cycling did not alter the properties further. The bipolar polarization and bipolar strain loops, as well as small signal properties as a function of bias-field, became asymmetric after unipolar cycling. An internal positive bias-field of up to 26 V/mm after 5 × 106 cycles developed. Rojas et al.372 observed a decrease in the remanent polarization between 6% and 12% as well as a decrease in the large signal strain between 2% and 13% after 107 unipolar cycles for BZT-40BCT, BZT-50BCT, and BZT-60BCT. BZT-50BCT showed the greatest degradation in properties, whereas BZT-60BCT was the most resistant composition. Fatigued samples have a reduction in their electromechanical properties owing to a reduction in irreversible domain wall movement since intrinsic contributions remain unaffected.372 The properties of the fatigued samples recovered almost totally after thermal annealing at 400 °C.371,372 It was proposed that charge agglomeration and concomitant domain wall pinning account for the unipolar fatigue of all the materials,371,372 although the orientation of defect dipoles under cycling may also contribute.371 Overall, it can be stated that BCZT seems quite resistant to fatigue. It features high bipolar fatigue resistance as compared with lead-containing and other lead-free materials.370 Its unipolar fatigue resistance remains also high as compared with BNT-based compositions, although the degradation of properties under unipolar cycling is slightly higher than in KNN-based materials and commercial soft PZT.371 

(vi) Doping strategies:

Hansen et al.373 explored the effect of a broad range of processing conditions, acceptor and donor dopants in BCZT. Several heterovalent B-site dopants such as acceptor Mg2+, Al3+, Ga3+, Sc3+, Y3+, and Yb3+ as well as oxygen vacancies reduce the distortions of the unit cells thereby shifting TC to lower temperature. B-site donor dopants, for instance Nb5+, result in a reduction of TC and can lead to semiconducting properties due to free electrons. For both types of dopants, it was proposed that the temperature shift of TC depends on the type of dopant, valence state, and ionic radius. In case of dopants with a variable ground state in different atmospheres, modification of annealing/sintering temperature, time, and atmosphere will modify further the functional properties. The largest reduction of TC will be generally found with acceptor dopants that distort more considerably the local structure and require a higher amount of oxygen vacancies for charge compensation. Co-doping can lead to enhancement of TC as a result of the charge compensation between acceptor and donor dopants, thus rendering less oxygen vacancies.373 

Table IX introduces the most promising doped BCZT piezoelectrics found in the literature. Typically, BZT-BCT samples produced via the conventional solid state route have been sintered between 1300 °C and 1500 °C (Table IV). As observed from Table IX, some dopants and sintering aids contribute significantly to the reduction of the sintering temperature.

TABLE IX.

Electromechanical properties and sintering temperature of the most promising BCZT doped materials.

CompositionDopantContentOptimal contentAddition beforeTs (°C)aTC (°C)εrd33 (pC/N)kpQmd33* (pm/V)bReferences
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Li+ 0.3 wt. % 0.3 wt. % Sintering 1450 80 4394 512 0.45 190  374  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Li+ 0.1–1 wt. % 0.5 wt. % Sintering 1350 74 5289 493 0.47 145 980 375  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Li+/F- 0.02–0.15 mol. % 0.06 mol. % Calcination 1450 93 2775 380 0.4   376  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Cu2+/B3+ 0.004 wt. % + 0.5–2.5 wt. % 1.5 wt. % Sintering 1250 95 3018 462 0.45 147  377  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Si4+ 0.025–0.2 mol. % 0.05 mol. % Calcination 1500 91 4250 500    301  
(Ba0.838Ca0.162)(Zr0.092Ti0.908)O3 (BZT-54BCT) Mn2+ 0–0.01 mol. % 0.006 mol. % Calcination 1480 99 2320 410 0.40 150  378  
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) Fe3+ 1 at. % 1 at. % Calcination 1500 32 7410    490 359  
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) Fe3+/Nb5+ 1 at. % + 1 at. % 1 at. % + 1 at. % Calcination 1500 38 7840    500 359  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Zn2+ 0–0.1 mol. % 0.06 mol. % Calcination 1480 85 3935 521 0.48 139  379  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Ga3+ 0.02–0.40 wt. % 0.08 wt. % Sintering 1350 118 1430 440 0.56 135  380  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Y3+ 0.2–0.8 mol. % 0.2 mol. % Calcination 1500 120 2310 360 0.42   381  
(Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 (BZT-50BCT) Y3+ 0.01–0.04 mol. % 0.02 mol. % Calcination 1400 103 3078 564 0.58   382  
(Ba0.90Ca0.10)(Zr0.07Ti0.93)O3 Y3+ 0.05–0.15 mol. % 0.1 mol. % Sintering 1450 109 2170 363   745 383  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Ce3+ 0.02–0.10 wt. % 0.04 wt. % Sintering 1350 90 4843 600 0.51   384  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Ce3+ 0–0.10 wt. % 0.08 wt. % Sintering 1550 110 2780 673 0.56   385  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Pr3+ 0.02–0.10 wt. % 0.04 wt. % Sintering 1350 103 2110 435    386  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Pr3+ 0–0.01 mol. % 0.002 mol. % Calcination 1400 84 2930 325    387  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Dy3+ 0.2 wt. % 0.2 wt. % Calcination 1500 125 2190 366 0.43   388  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Ho3+ 0–0.6 mol. % 0.2 mol. % Calcination 1450 115 2260 330 0.4   389  
(Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 (BZT-50BCT) Bi3+ 0.05–1 mol. % 0.1 mol. % Sintering 1350 94 3125 325 0.42   390  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sr2+/Sn4+ 1 mol. % + 1 mol. % 1 mol. % + 1 mol. % Calcination 1550 85 3260 514 0.53   391  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Cu2+/W4+ 0.05–1 wt. % 0.10 wt. % Sintering 1350 95 3540 555 0.55 129  392  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Cu2+/W4+ 0–2.4 wt. % 1.2 wt. % Sintering 1220 99 3911 609 0.51  1250 23  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Bi3+/Al3+ 0.3–1.5 mol. % 0.8 mol. % Calcination 1300 72 3370 568 0.54   393  
CompositionDopantContentOptimal contentAddition beforeTs (°C)aTC (°C)εrd33 (pC/N)kpQmd33* (pm/V)bReferences
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Li+ 0.3 wt. % 0.3 wt. % Sintering 1450 80 4394 512 0.45 190  374  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Li+ 0.1–1 wt. % 0.5 wt. % Sintering 1350 74 5289 493 0.47 145 980 375  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Li+/F- 0.02–0.15 mol. % 0.06 mol. % Calcination 1450 93 2775 380 0.4   376  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Cu2+/B3+ 0.004 wt. % + 0.5–2.5 wt. % 1.5 wt. % Sintering 1250 95 3018 462 0.45 147  377  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Si4+ 0.025–0.2 mol. % 0.05 mol. % Calcination 1500 91 4250 500    301  
(Ba0.838Ca0.162)(Zr0.092Ti0.908)O3 (BZT-54BCT) Mn2+ 0–0.01 mol. % 0.006 mol. % Calcination 1480 99 2320 410 0.40 150  378  
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) Fe3+ 1 at. % 1 at. % Calcination 1500 32 7410    490 359  
(Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT) Fe3+/Nb5+ 1 at. % + 1 at. % 1 at. % + 1 at. % Calcination 1500 38 7840    500 359  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Zn2+ 0–0.1 mol. % 0.06 mol. % Calcination 1480 85 3935 521 0.48 139  379  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Ga3+ 0.02–0.40 wt. % 0.08 wt. % Sintering 1350 118 1430 440 0.56 135  380  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Y3+ 0.2–0.8 mol. % 0.2 mol. % Calcination 1500 120 2310 360 0.42   381  
(Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 (BZT-50BCT) Y3+ 0.01–0.04 mol. % 0.02 mol. % Calcination 1400 103 3078 564 0.58   382  
(Ba0.90Ca0.10)(Zr0.07Ti0.93)O3 Y3+ 0.05–0.15 mol. % 0.1 mol. % Sintering 1450 109 2170 363   745 383  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Ce3+ 0.02–0.10 wt. % 0.04 wt. % Sintering 1350 90 4843 600 0.51   384  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Ce3+ 0–0.10 wt. % 0.08 wt. % Sintering 1550 110 2780 673 0.56   385  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Pr3+ 0.02–0.10 wt. % 0.04 wt. % Sintering 1350 103 2110 435    386  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Pr3+ 0–0.01 mol. % 0.002 mol. % Calcination 1400 84 2930 325    387  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Dy3+ 0.2 wt. % 0.2 wt. % Calcination 1500 125 2190 366 0.43   388  
(Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 Ho3+ 0–0.6 mol. % 0.2 mol. % Calcination 1450 115 2260 330 0.4   389  
(Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 (BZT-50BCT) Bi3+ 0.05–1 mol. % 0.1 mol. % Sintering 1350 94 3125 325 0.42   390  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Sr2+/Sn4+ 1 mol. % + 1 mol. % 1 mol. % + 1 mol. % Calcination 1550 85 3260 514 0.53   391  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Cu2+/W4+ 0.05–1 wt. % 0.10 wt. % Sintering 1350 95 3540 555 0.55 129  392  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Cu2+/W4+ 0–2.4 wt. % 1.2 wt. % Sintering 1220 99 3911 609 0.51  1250 23  
(Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 (BZT-50BCT) Bi3+/Al3+ 0.3–1.5 mol. % 0.8 mol. % Calcination 1300 72 3370 568 0.54   393  
a

Ts refers to the sintering temperature of the optimized composition.

b

d33* was calculated at 1 kV/mm.

BZT-50BCT co-doped with 0.004 wt. % CuO and 1.5 wt. % B2O3 was synthesized at 1250 °C rendering quite promising properties such as d33 = 462 pC/N, kp = 0.45, Qm=147, and TC=95 °C.377 Chao et al.23 indicated that adding Ba(Cu,W)O3 as sintering aid to (Ba0.85Ca0.15)(Zr0.10Ti0.90)O3 reduced the sintering temperature to 1220 °C. Importantly, 1.2 wt. % Ba(Cu,W)O3 resulted in quite high electromechanical properties such as a d33=609 pC/N, kp = 0.51, and a d33* = 1250 pm/V at 1 kV/mm. The properties remain quite stable up to ∼90 °C, indicating that this is one of the most promising materials developed so far. A prototype loudspeaker was successfully built with this material. The loudspeaker functionality was demonstrated by driving it between 10 V and 20 V, which led to a relatively constant sound output of 85 dB between 10 kHz and 20 kHz.23 

Dopants can considerably modify the stability regions of the BCZT phases375,382,383 or even lead to relaxor features.390 Figure 23 summarizes the TC values of BZT-50BCT doped materials as a function of dopant concentration. The dashed line indicates the mean TC value calculated from the literature for undoped BZT-50BCT.

FIG. 23.

Variation of TC in BZT-50BCT with dopant concentration in (a) mol. % and (b) wt. %. Data were taken from several papers from the literature for Li+/F-, Si4+, Y3+, Bi3+/Al3+, B3+, Ce3+, Pr3+, and Cu2+/W4+.301,376,377,382,384,386,392,393 Dashed lines indicate the mean TC for BZT-50BCT.

FIG. 23.

Variation of TC in BZT-50BCT with dopant concentration in (a) mol. % and (b) wt. %. Data were taken from several papers from the literature for Li+/F-, Si4+, Y3+, Bi3+/Al3+, B3+, Ce3+, Pr3+, and Cu2+/W4+.301,376,377,382,384,386,392,393 Dashed lines indicate the mean TC for BZT-50BCT.

Close modal

As previously pointed out,373 only a few dopants enhance the TC of BZT-50BCT. Moderate contents of Y3+ and Pr3+ can enhance slightly the TC of BZT-50BCT,382,386 whereas other dopants such as Si4+ and Ce3+ have little effect on TC.301,384 The temperature stability of the piezoelectric properties is one of the main issues that needs to be overcome in BCZT piezoelectrics. Figure 24 introduces the d33 values of doped BZT-50BCT as a function of TC. The dashed lines indicate the mean TC and d33 values for undoped BZT-50BCT. In region D, the most promising dopants can be found such as Ce3+, Y3+, and Pr3+. Region A displays the dopants that generally need to be avoided since they enhance neither the temperature stability nor the d33 values. Region C indicates the dopants that lead to high d33 values at the expense of a reduction in the temperature stability such as Li+ and Zn2+. In contrast, region B comprises doped materials that sacrifice d33 but gain in temperature stability such as Ta5+.

FIG. 24.

d33 as a function of TC in some doped BZT-50BCT materials. Data were taken from the literature for Li+, Li+/F-, B3+, Si4+, Mn2+, Zn2+, Y3+, Ce3+, Pr3+, Sr2+/Sn4+, Cu2+/W4+, and Bi3+/Al3+.301,374,376–379,382,384,386,391–393 Dashed lines indicate the mean TC and d33 of BZT-50BCT obtained from the literature.

FIG. 24.

d33 as a function of TC in some doped BZT-50BCT materials. Data were taken from the literature for Li+, Li+/F-, B3+, Si4+, Mn2+, Zn2+, Y3+, Ce3+, Pr3+, Sr2+/Sn4+, Cu2+/W4+, and Bi3+/Al3+.301,374,376–379,382,384,386,391–393 Dashed lines indicate the mean TC and d33 of BZT-50BCT obtained from the literature.

Close modal

Doping is also a successful strategy to enhance the temperature stability of d33.378,380,385,388,389 Doping with 0.006 mol. % Mn2+ enhanced the temperature stability of d33 up to 80 °C.378 Doping (Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 with 0.08 wt. % Ga led to a d33=440 pC/N that remains quite stable up to 115 °C.380 Li et al.381 revealed that Y3+-doped (Ba0.99Ca0.01)(Zr0.02Ti0.98)O3 has a stable d33=359 pC/N up to 90 °C, although for the case of (Ba0.90Ca0.10)(Zr0.07Ti0.93)O3 the d33*=744 pm/V decayed considerably with small temperature variations.383 For (Ba0.99Ca0.01)(Zr0.02Ti0.98)O3, either 0.2 wt. % Dy3+ or 0.2 mol. % Ho3+ led to high d33 values between 320 pC/N and 370 pC/N that remain stable up to around ∼100 °C.388,389 Doping with Ce3+ the BZT-50BCT led to very good properties. Sintering temperatures between 1350 °C and 1550 °C were reported for these materials and although this is high as compared with other dopants, exceptionally large d33>550 pC/N and kp>0.51 were consistently reported up to temperatures near their TC, which was higher than 89 °C in all studies.384,385 Some dopants also led to a hardening effect, as indicated by an increase in Qm, which is desirable for high power applications. Wu et al.379 indicated that doping BZT-50BCT with 0.1 mol. % Zn leads to a Qm=202 and a concomitant reduction of 24% in d33. The optimized 0.06 mol. % Zn doped BZT-50BCT was found to have a high d33=521 pC/N, kp=0.48, and Qm=139.379 

There has not been much work done on mechanical, ferroelastic, and reliability studies on doped BCZT for piezoelectric applications. Humburg et al.359 considered the ferroelastic properties of 1 mol. % Fe-doped and 1 mol. % Fe/1 mol. % Nb co-doped (Ba0.865Ca0.135)(Zr0.11Ti0.89)O3 (BZT-45BCT). Ferroelectric properties of the doped materials were destabilized as compared with the undoped material. This led to less influence of the uniaxial compressive stress on the electromechanical properties, although qualitatively the same behavior as in undoped BZT-45BCT was observed. Chao et al.23 investigated the aging in BZT-50BCT doped with Ba(Cu0.5W0.5)O3. As with the ferroelastic properties, doping did not improve the aging resistance.23 

In 2011, Li et al.394 and Xue et al.395 recognized the potential of modifying BCT with Sn for piezoelectric applications. This work was preceded by earlier studies related to the dielectric properties of this system for capacitors.70,233 To date, there is a much smaller body of work on this system than on BZT-BCT. Nevertheless, several authors reported remarkably high d33 values between 500 pC/N and 670 pC/N.327,394,395 Zhu et al.396 also revealed a high d33*=990 pm/V at 1 kV/mm (determined from bipolar curves). As a downside, this system is even more susceptible to temperature variations than BZT-BCT. No information related to single crystals for piezoelectric applications was found in the literature and only scarce information exists related to piezoelectric thin films.397 This section is thus focused on bulk materials.

1. Synthesis and microstructure

(Ba1-xCax)(SnyTi1-y)O3 (BCSnT) ceramics were mostly synthesized via the conventional solid state route with similar synthesis parameters as BCZT. Most works have calcined BCSnT at temperatures ranging between 1200 °C and 1350 °C. Sintering was performed between 1450 °C and 1500 °C.202,327,394–396,398–401 The high sintering temperature of this system can be justified taking into account that shrinkage of (Ba0.95Ca0.05)(Sn0.10Ti0.90)O3 begins at 1050 °C,402 which is ∼100 °C higher than the beginning of shrinkage in BT.403 Zhao et al.202 discovered that average grain size reduces drastically from ∼90 μm for (Ba0.94Ca0.06)(Sn0.05Ti0.95)O3 to ∼20 μm for (Ba0.94Ca0.06)(Sn0.15Ti0.85)O3. Zhu et al.400 investigated the (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3 system and reported that increasing the content of BSnT has a similar effect to increasing only Sn4+. Increasing either BSnT or Sn4+ leads to reduced average grain sizes as well as diminished relative density. In contrast, BSnT without Ca2+ features a decrease in grain size with the addition of this cation.398,401 These results highlight that the densification behavior of the BCSnT varies considerably with composition.

2. Phase diagram and phase transitions

Figure 25 displays the pseudo-ternary phase diagram between the end members BaSnO3 (BS), BaTiO3 (BT), and CaTiO3 (CT). Similarly, as with the BZT-BCT, isopleths with promising properties were realized in this system. The (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3 isopleth investigated by Xue et al.,395 the (1-x)BT-x(0.40CT-0.60BS) isopleth investigated isopleth investigated by Zhu et al.,396 and the (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3 isopleth investigated by Zhu et al.400 are the most salient systems. The materials in region A, marked in light blue, feature a tetragonal phase. Due to the Ca2+ content, these materials generally have their orthorhombic to tetragonal phase transition below room temperature and display a temperature insensitive relative permittivity. The materials within region B, marked in purple, have an orthorhombic phase.394,398,401 They feature dielectric properties similar to BT; i.e., a defined phase transition following the Curie-Weiss law.394,398 Zhu et al.396 reported phase coexistence between tetragonal and orthorhombic phases along (1-x)BT-x(0.40CT-0.60BS) isopleth, thus delimiting regions A and B. Materials in region C, marked in light green, are characterized by a rhombohedral phase and may not follow the Curie-Weiss law.395,404 They feature a low TC close or below room temperature. An increase of Sn4+ above 0.19 at. % in BT leads to relaxor properties.404,405 Thus, as with BZT-BCT, weak relaxor features may be also expected especially in regions A and C with high Sn4+ content.

FIG. 25.

Pseudo-ternary phase diagram of BS, BT, and CT based on pseudo-ternary diagram made by Zhu et al.400 The isopleths corresponding to (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3 from Xue et al.,395 (1-x)BT-x(0.40CT-0.60BS) from Zhu et al.,396 and (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3 from Zhu et al.400 are superimposed with dotted lines. Shaded areas A, B, and C are characterized as tetragonal, orthorhombic, and rhombohedral phases, respectively.

FIG. 25.

Pseudo-ternary phase diagram of BS, BT, and CT based on pseudo-ternary diagram made by Zhu et al.400 The isopleths corresponding to (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3 from Xue et al.,395 (1-x)BT-x(0.40CT-0.60BS) from Zhu et al.,396 and (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3 from Zhu et al.400 are superimposed with dotted lines. Shaded areas A, B, and C are characterized as tetragonal, orthorhombic, and rhombohedral phases, respectively.

Close modal

Figure 26 introduces the pseudo-binary phase diagrams proposed for (a) (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3, (b) the (1-x)BT-x(0.40CT-0.60BS), and (c) the (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3.395,396,400 In Figs. 26(b) and 26(c), we present the phase diagrams from high to low x content so that it is comparable with (a) as well as the other phase diagrams in this review. These pseudo-binary phase diagrams correspond to the isopleths superimposed with dotted lines on the pseudo-ternary phase diagram (Fig. 25). On first sight, the three phase diagrams look quite similar and correspond to the pinching-type (Fig. 6). Figure 26(a) resembles the original phase diagram of BZT-BCT reported by Liu and Ren,11 whereas the phase diagrams of the other isopleths are similar to the state-of-the-art phase diagram of BZT-BCT (Fig. 10). Thus, we expect that more detailed crystallographic studies in (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3 may reveal an interleaving phase/s between the rhombohedral and tetragonal phases. All isopleths feature a TC between 25 °C and 120 °C, with clearly lower TC for compositions with high modifier content. Thus, these compositions have a major technological drawback taking into account that even self-heating can depolarize the material during service. This may be an advantage, however, in other applications such as electrocalorics.406,407

FIG. 26.

Pseudo-binary phase diagrams for (a) (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3 investigated by Xue et al.,395 (b) (1-x)BT-x(0.40CT-0.60BS) investigated by Zhu et al.396 (presented from high to low x content for comparison), and (c) (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3 investigated by Zhu et al, (presented from high to low x content for comparison).400 

FIG. 26.

Pseudo-binary phase diagrams for (a) (1-x)Ba(Sn0.12Ti0.88)O3-x(Ba0.70Ca0.30)TiO3 investigated by Xue et al.,395 (b) (1-x)BT-x(0.40CT-0.60BS) investigated by Zhu et al.396 (presented from high to low x content for comparison), and (c) (1-x)(Ba0.90Ca0.10)TiO3-xBa(Sn0.20Ti0.80)O3 investigated by Zhu et al, (presented from high to low x content for comparison).400 

Close modal

The triple points and/or convergence regions are given by the compositions (Ba0.724Ca0.276)(Sn0.0096Ti0.9904)O3 (0.92(Ba0.70Ca0.30)TiO3‐0.08Ba(Sn0.12Ti0.88)O3) in Fig. 26(a), (Ba0.92Ca0.08)(Sn0.12Ti0.88)O3 (0.80BT-0.20(0.40CT-0.60BS)) in Fig. 26(b), and (Ba0.95Ca0.05)(Sn0.10Ti0.90)O3 (0.50(Ba0.90Ca0.10)TiO3‐0.50Ba(Sn0.20Ti0.80)O3) in Fig. 26(c). Their temperatures are ∼47 °C, ∼39 °C, and ∼37 °C for Figs. 26(a)–26(c), respectively. These convergence regions are found between 15 °C and 25 °C lower than the convergence temperature in BZT-BCT. This can be reconciled based on the effect of the modifiers in BT. Ca2+ has generally little effect on TC but decreases the temperature for inter-ferroelectric phase transitions. In contrast, TC is substantially reduced by addition of Sn4+.394,398,400,401,405 This is known since early studies on dielectric properties in the system.233 The decreasing rate of TC as a function of composition x (dTCdx) found was 8.5 °C/mol. % in (Ba0.95Ca0.05)(Ti1-xSnx)O3.327 This value is similar to that found in BaTi1-xSnxO3.405 

3. Electromechanical properties

Table X lists the most salient electromechanical properties found in the ternary system BCSnT. We report the mean values and the maximum deviation found, as described for BCZT. Note that we do not report d33* values here because most studies obtained this parameter from bipolar curves and for electric fields where the material was not saturated. Thus, they may not be representative for applications. More representative d33* values should be generally aimed for, meaning that measurements should be done in poled materials and under a driving unipolar electric field that is sufficiently high to ensure saturation of the material. Table X indicates that the scatter among the piezoelectric properties reported is generally lower than in BCZT with maximum variations in TC values below 20% and for the case of d33 below 21%.

TABLE X.

Piezoelectric and dielectric properties of doped BCSnT at room temperature. The letters in the column “source/s of variation in properties” indicate the most probable variable that leads to variation in properties. Namely, (a) variation in the processing conditions and microstructures, (b) discrepancies among reported values due to uncertainties in measurements, characterization technique and/or characterization conditions, and (c) variation in the poling conditions.

CompositionTC (°C)εrd33 (pC/N)kpQmGrain size (μm)ReferencesSource/s of variation in properties
(Ba0.99Ca0.01)(Sn0.08Ti0.92)O3 58 3747 443 0.41 117 28 401   
(Ba0.99Ca0.01)(Sn0.04Ti0.96)O3 72 ± 11% 4384 ± 7% 354 ± 10% 0.36 ± 14%   394 and 398  
(Ba0.984Ca0.016)(Sn0.024Ti0.976)O3 112 2642 360 0.46 115.2  396   
(Ba0.98Ca0.02)(Sn0.08Ti0.92)O3 60 4000 455 0.43 126 36 401   
(Ba0.98Ca0.02)(Sn0.04Ti0.96)O3 73 ± 7% 5175 ± 8% 435 ± 17% 0.45 ± 8%   394 and 398  
(Ba0.97Ca0.03)(Sn0.08Ti0.92)O3 60 3632 503 0.46 130 37 401   
(Ba0.97Ca0.03)(Sn0.04Ti0.96)O3 70 ± 12% 5570 ± 24% 445 ± 1% 0.45   394 and 398  
(Ba0.968Ca0.032)(Sn0.048Ti0.952)O3 96 2880 441 0.48 119.1  396   
(Ba0.96Ca0.04)(Sn0.12Ti0.88)O3 36 10952 95 0.11 135.9 400   
(Ba0.96Ca0.04)(Sn0.08Ti0.92)O3 61 3906 525 0.48 145 39 401   
(Ba0.96Ca0.04)(Sn0.04Ti0.96)O3 74 ± 13% 426 ± 28% 363 ± 11% 0.39 ± 14%   394 and 398  
(Ba0.952Ca0.048)(Sn0.072Ti0.928)O3 78 3280 520 0.51 72.5  396   
(Ba0.95Ca0.05)(Sn0.10Ti0.90)O3 53 6194 390 0.28 84.6  400   
(Ba0.95Ca0.05)(Sn0.11Ti0.89)O3 45 6100 670 0.45 90  327   
(Ba0.945Ca0.055)(Sn0.09Ti0.91)O3 62 4955 630 0.52 67.9  400   
(Ba0.94Ca0.06)(Sn0.20Ti0.80)O3 −32 4770   202   
(Ba0.94Ca0.06)(Sn0.15Ti0.85)O3 18 15 000 50 0.15  22 202   
(Ba0.94Ca0.06)(Sn0.125Ti0.875)O3 40 13 000 320 0.18   202   
(Ba0.94Ca0.06)(Sn0.11Ti0.89)O3 45 5620 520 0.41   202   
(Ba0.94Ca0.06)(Sn0.10Ti0.90)O3 50 5030 600 0.51  49 202   
(Ba0.94Ca0.06)(Sn0.096Ti0.904)O3 63 4200 478    395   
(Ba0.95Ca0.05)(Sn0.08Ti0.92)O3 62 3968 568 0.48 158 41.3 401   
(Ba0.94Ca0.06)(Sn0.08Ti0.92)O3 68 ± 5% 4000 ± 5% 543 ± 4% 0.48 ± 8% 110 ± 27% 14 400 and 401  
(Ba0.94Ca0.06)(Sn0.075Ti0.925)O3 70 3110 430 0.44   202   
(Ba0.94Ca0.06)(Sn0.05Ti0.95)O3 90 3060 325 0.42  90 202   
(Ba0.936Ca0.064)(Sn0.096Ti0.908)O3 62 5200 570 0.52 71.8  396   
(Ba0.93Ca0.07)(Sn0.06Ti0.94)O3 90 3223 402 0.50 135.2  400   
(Ba0.925Ca0.075)(Sn0.09Ti0.91)O3 69 3240 441    395   
(Ba0.92Ca0.08)(Sn0.12Ti0.88)O3 39 10 100 282 0.22 95.1 6.5 396   
(Ba0.92Ca0.08)(Sn0.04Ti0.96)O3 104 2015 258 0.41 171.2 27 400   
(Ba0.91Ca0.09)(Sn0.084Ti0.916)O3 73 3800 530    395   
(Ba0.90Ca0.10)(Sn0.10Ti0.90)O3 46 ± 16% 8134 ± 10% 452 ± 15% 0.41 ± 11%   408 and 409  a and c 
(Ba0.90Ca0.10)(Sn0.08Ti0.92)O3 66 ± 14% 5500 ± 2% 406 ± 6% 0.42 ± 1%   408 and 409  a and c 
(Ba0.90Ca0.10)(Sn0.06Ti0.94)O3 81 ± 3% 2700 ± 12% 333 ± 21% 0.39 ± 9%