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Temperature-Dependent Ferroelastic Switching of Soft Lead Zirconate Titanate
Abstract
The longitudinal strain and polarization of a soft polycrystalline ferroelectric ceramic (lead zirconate titanate, PZT) were measured under uniaxial compressive stress at elevated temperatures utilizing a novel testing fixture. Ferroelectric ceramics have not previously been characterized under these conditions due to experimental complexity. In addition to nonlinear macroscopic constitutive behavior, the linear elastic moduli have been measured throughout the loading cycle, allowing for the determination of the relative contributions from the linear and nonlinear ferroelastic behavior as a function of stress and temperature. Experimental results show a strong temperature dependence of ferroelastic switching. The ferroelastic properties of unpoled and poled materials for temperatures up to the Curie point are contrasted with the spontaneous strain, elucidating the role of tetragonality in ferroelastic switching. When thermal changes are considered, marked changes in the maximum strain are observed.
... When considering the above-mentioned examples of applications, one important point is the temperature sensitivity of the piezoelectric prop-erties. This point is particularly interesting for NKN-based ceramics due to the existence of polymorphic phase boundaries (T PPB ) and how they are utilized to increase the piezoelectric charge coefficient d 33 . From low temperature, undoped (Na 0.5 K 0.5 )NbO 3 transitions from rhombohedral (R, R3c) → orthorhombic (O, Amm2) or monoclinic (M, Pm) → tetragonal (T, P4mm) → cubic (C, Pm3m) at approximately − 123 • C, 200 • C, and 420 • C, respectively [5]. ...
... In addition to changes to the piezoelectric properties via temperature, d 33 values can depend highly on the applied amplitude. The reason is that piezoelectric activity in materials is composed of intrinsic and extrinsic contributions [13]. ...
... To study the ferroelastic properties, the stress-strain behavior was evaluated through uniaxial compression testing with a setup described in detail in a previous study [33]. A preload of − 4 MPa was first applied, followed by a uniaxial compressive stress that reached a maximum of − 350 MPa. ...
... The intermediate length scale between unit cell and grains is nano-sized defects, such as dislocations, ferroelectric domains (also known as polarization vectors), and polar nano regions (PNR) (of sub-nm size), thought to have a pronounced influence on the mechanical properties of PEM, as indicated by past and recent studies. While ferroelectric domains alone contribute to the dielectric and piezoelectric properties, dislocation-ferroelectric domain interactions control the mechanical properties of PEM, 7,8,13,[15][16][17][18]23,26,[29][30][31][32] and recent studies have shown that the mechanical properties can also be tailored by taming a systematic network of dislocations 23,26 and ferroelectric domains. 5,22,24,25,27,28,32 However, the defect-based multifunctionality in PEM is still in the nascent stage [29][30][31] and is also a timely topic. ...
... The main function of these PEM devices is to initiate the detonation upon impact, timely closer and opening of valve, and extraction of underwater acoustic signals (response), respectively. Conventional PEM such as BT and PZT, as well as advanced Ba(Zr x Ti 1Àx )O 3 À (Ba y Ca 1Ày )TiO 3 (BZT-BCT) and potassium sodium niobate (KNN)-based Pb-free ceramics have been successfully tested for the above applications and previously several studies have reported their mechanical properties via bulk deformation testing that includes uniaxial compression (both room and controlled temperature environments), 6,7,9,10,12,18,19,20 R-curve behavior, 12,17,19,20 and macro-scale indentation experiments. 6,[33][34][35][36] The R-curve (sometimes also referred to as the tearing resistance curve), a curve representing a change in the fracture resistance with respect to crack extension is of paramount importance in fracture mechanics, particularly in ceramics as a high magnitude of stress field is induced at the growing crack tip. ...
... Following this, the pioneer works of Webber, Rödel, and co-workers 17,19,81 cover the profound discussion on the compressive strength and R-curve behavior during temperature-controlled uniaxial compression testing of PZT-S (mainly La-doped). The novel test setup developed by Webber, Rödel, and co-workers 17,19,81 is shown in Fig. 11(a). They mainly argued that the R-curve behavior in PZT could be primarily attributed to non-180°domain switching at the crack tip. ...
Piezoelectric Materials (PEM) find a wide spectrum of applications that include but are not limited to, sensors, actuators, semiconductors, memory devices and energy harvesting systems due to their outstanding electromechanical and polarization characteristics. Notably, these PEMs can be employed across several length scales (both intrinsic and extrinsic) ranging from meso- (bulk ceramics) to nano- (thin films) during their applications. Over the years, progress in probing individual electrical and mechanical properties of PEM has been notable. However, proportional review articles providing the mechanical characterization of PEM are relatively few. The present article aims to give a tutorial on the mechanical testing of PEMs, ranging from the conventional bulk deformation experiments to the most recent small-scale testing techniques from a materials science perspective. The advent of nanotechnology has led materials scientists to develop in-situ testing techniques to probe the real-time electromechanical behavior of PEMs. Therefore, this article presents a systematic outlook on ex-situ and in-situ deformation experiments in mechanical and electromechanical environments, related mechanical behavior and ferroelectric/elastic distortion during deformation. The first part provides significant insights into the multifunctionality of PEM and various contributing microstructural length scales, followed by a motivation to characterize the mechanical properties from the application's point of view. In the midst, the mechanical behavior of PEM and related mechanical characterization techniques (from meso-to-nanoscale) are highlighted. The last part summarizes current challenges, future perspectives, and important observations.
... I hereby certify that the work which is being presented in the thesis entitled "Role of xvi In piezoceramics, the region of directionally aligned dipoles along distinct polarization directions is known as "ferroelectric domains". The previous and recent studies [Mehta and Virkar, 1990, Haertling, 1999and Wang et al., 2021 on the H of piezoceramics despite the few studies which were focused towards understanding the fracture response (R-curve behaviour) [Mehta andVirkar, 1990 andWebber et al., 2009]. ...
... During loading and unloading cycles of indentation, state of stresses continuously changes around and underneath the indentation zone which is expected to influence the texture of ferroelectric domains. The elastic strain energy associated with the highly ordered ferroelectric domains in AP samples is likely to be accommodated by 90° switching of ferroelectric domains in the elastic-plastic zone of the indentation which is in agreement with the literature studies on poled PZT [Mehta and Virkar, 1990, Webber et al., 2009, Seo et al., 2013 (determined indirectly from the concomitant changes in remanent strain, values). This implies that majority of the switched ferroelectric domains cannot reorient themselves upon unloading thereby leading to irreversible depolarization Zeng, 2008, 2010]. ...
... The indentation and fracture studies on PZT and Pb-free piezoceramics also show that a decrease in leads to an increase in H and decrease in [Mehta and Virkar, 1990, Webber et al., 2009, Seo et al., 2013, Vögler et al., 2015, Wang et al., 2021. (Table 3.3). ...
... The applied load was controlled by a load cell and the displacement was measured with a custom-built linear variable differential transformer system. 35 Cylindrical samples with a height of 6.00 mm (±0.01 mm) and a diameter of 5.80 mm (±0.01 mm) were loaded from an initial preload of −5 MPa to a maximum load of −500 MPa and unloaded to preload. The loading rate of 5 MPa/s was used during the measurements. ...
... The grain-size dependent mechanical behavior of PZT is shown in Fig. 13, displaying a ferroelastic response consistent with previous reports. 35 Interestingly, ferroelastic parameters, that is, coercive stress, σ c , and remanent strain, ε r , determined from the stress-strain measurements, show variation with grain size. Similar to the coercive electric field (E c ), the coercive stress was also found to be influenced by the variation in grain size, that is, σ c increases with decreasing grain size. ...
... The degree of back-switching, η b , can be estimated by the parameter 1-(ε r /ε i ), where ε r is the remanent strain and ε i is the x axis intersection of a linear fit of the linear region in the unloading curve. 35 During unloading, the stress-strain loop shows nonlinearity due to domain back-switching at low-stress levels. In addition to the vacancy mediated domain pinning mechanism, the backswitching of non-180°domains is related to the intergranular residual mechanical and electrical fields in the polycrystal. ...
The ferroelectric, ferroelastic, and dielectric properties as well as the crystal structure were investigated for polycrystalline donor doped lead zirconate titanate (PZT) with grain sizes ranging from 0.25 to 5 μm, which were prepared using a novel zirconium titanium hydrate precursor (ZTH) with a specific surface area of 310 m²/g. Piezoforce microscopy was used to investigate the change in the domain structure, revealing a change in the domain configuration from a complex 3D structure to a simple lamellar domain formation at a 1 μm grain size that corresponded to a rapidly increasing internal mechanical stress observed with in situ synchrotron x-ray experiments. The correlation between the change in domain configuration, increasing internal stresses, effects of poling on the crystal structure, and the macroscopic ferroelectric and ferroelastic properties are discussed in detail, allowing a deeper understanding of size effects in polycrystalline donor doped PZT ceramics.
... Ferroelasticity is a phenomenon which is strongly dependent on temperature as described by Webber et al. [33]. They have tested samples under uniaxial compression at temperatures ranging from 25 to 300°C and have found that maximum and remnant strains in the samples decrease at high temperatures. ...
... This enhanced activity of the dipoles also causes their increased interactions and random orientations. Random orientations of the electric dipoles thereby decrease the net effective polarization which results in low surface charge density and hence leads to the low value of 3 pC/N for d 33 . This drastic change in d 33 is thus due to the thermal depoling and not due to the mechanical loading [33]. ...
... Random orientations of the electric dipoles thereby decrease the net effective polarization which results in low surface charge density and hence leads to the low value of 3 pC/N for d 33 . This drastic change in d 33 is thus due to the thermal depoling and not due to the mechanical loading [33]. Thus, activation of non-ferroelastic domains at high temperatures results in random orientation of the domains which causes depoling in the sample. ...
A comparative study of electromagnetic radiation (EMR) detection from Soft
PZT (SP 5A) and Hard (SP 4) PZT under impact at high temperatures has been
presented. EMR is detected by applying impact load on the samples at temperatures varying from 288 to 514 K. With increase in temperature, thermal
energy increases imparting molecular vibrations which reduce the net effective
polarization and this in turn results in the low amplitude of EMR signals. EMR
voltage amplitude and EMR energy release rate show an overall decreasing
pattern with increase in temperature. Experiments conducted on samples poled
at different d.c. poling fields exhibit strong dependence of EMR signals on d.c.
poling field. EMR voltage amplitude is found to increase with increase in the
strength of d.c. poling field. This study pertaining to the effect of poling as well
as high temperatures on the EMR signal variation will be an aid towards the
development of wireless sensing technique.
... In our freestanding BiFeO 3 membranes, there is no substrate clamping effect; therefore, it is reasonable to expect much more elastic and flexible behavior in them from enhanced ferroelastic domain switching and improved strain tolerance, which is the same as we have demonstrated in our study. In addition, elastic properties, such as Young's modulus, are sensitive to both the phase and domain states, which means that they vary with the applied mechanical strain/stress (35). Hence, a full stressstrain curve is needed in the future to determine the true mechanical properties of the freestanding BiFeO 3 membranes. ...
... We also notice some amount of residual strain that reaches ~1% after the application of the maximum bending strain (Fig. 3E), and it mainly originates from ferroelastic domain switching of rhombohedral BiFeO 3 , as we demonstrated in Fig. 4E. Mechanical stressinduced irreversible ferroelastic domain switching is widely observed in a variety of ferroelectric/ferroelastic materials after releasing the applied stress (35). Here, the residual strain in freestanding BiFeO 3 membranes is about two times larger than that observed in conventional bulk ferroelectric/ferroelastic materials (35). ...
... Mechanical stressinduced irreversible ferroelastic domain switching is widely observed in a variety of ferroelectric/ferroelastic materials after releasing the applied stress (35). Here, the residual strain in freestanding BiFeO 3 membranes is about two times larger than that observed in conventional bulk ferroelectric/ferroelastic materials (35). Rhombohedral BiFeO 3 could probably tolerate a large spontaneous strain of about 7% in a single-domain state because it could maintain a large c/a ratio of about 1.07 (taking rhombohedral as pseudocubic for simplicity) (18). ...
The integration of ferroic oxide thin films into advanced flexible electronics will bring multifunctionality beyond organic and metallic materials. However, it is challenging to achieve high flexibility in single-crystalline ferroic oxides that is considerable to organic or metallic materials. Here, we demonstrate the superior flexibility of freestanding single-crystalline BiFeO 3 membranes, which are typical multiferroic materials with multifunctionality. They can endure cyclic 180° folding and have good recoverability, with the maximum bending strain up to 5.42% during in situ bending under scanning electron microscopy, far beyond their bulk counterparts. Such superior elasticity mainly originates from reversible rhombohedral-tetragonal phase transition, as revealed by phase-field simulations. This study suggests a general fundamental mechanism for a variety of ferroic oxides to achieve high flexibility and to work as smart materials in flexible electronics.
... Zhou and Kamlah [17] focused on the experimental investigation of time-dependent effects of piezoceramic material at room temperature and found the material exhibited the greatest timedependent effects at a stress level near the coercive stress. Webber et al. [18] indicated that the nonlinear strain can be attributed to the domain wall motion and accompanying misfit strains surrounding switching domain. Furthermore, Pojprapai et al. [19] theoretically proposed a rheological model representing time-dependent deformation and separated the steady-state creep strain from transient creep strain macroscopically under the square wave cyclic loading. ...
... Ferroelastic behavior can be separated into linear and nonlinear material response, as quantified in the following equation [18]: ...
... Webber et al. [18] separated the linear and nonlinear strain from the total and demonstrated that the nonlinear strain comprised approximately one-half of the total strain at maximum stress. ...
In this paper, the electromechanical behavior of lead zirconate-titanate ceramics (P51) has been characterized and modeled. The variation of the energy dissipation and peak electrical displacement of the P51 ceramic has been investigated in details. The total strain of P51 under cyclical loading consists of elastic deformation (εije), immediate ferroelectric domain switching deformation (εijd), and time-dependent deformation (εijc). Thus, an expression for the energy dissipation of P51 can be theoretically derived. In addition, a practical method for calculating the dissipated energy has been proposed by integrating the curve of a hysteresis loop. The experimental results show that the peak electrical displacement and dissipated energy both decrease monotonously with the increase of the number of cycles. Furthermore, ferroelectric 90° domain switching was observed by X-ray diffraction (XRD) and the percentage of domain switching has been calculated by the variation of the peak intensity ratio of (002) to (200) at about 45 degrees. Then, grain debonding, crack, and crush were found around voids inside the specimen by using scanning electron microscope (SEM). It is indicated that switching of more capable-switch domains stimulates larger dissipated energy and a bigger peak electrical displacement at the initial cyclic loading. Finally, an exponential functional model has been proposed to simulate the peak evolution of electrical displacement based on the energy dissipation of P51 ceramics under cyclical load.
... Additionally, the temperature-dependent ferroelastic behavior is also critical for the basic understanding of the origin of their functional properties. Improved understanding of the ferroelastic response as a function of oxygen deficiency, internal stresses, and temperature is important for enhancing LSCF-based SOFCs and OTMs as well as other applications that use electroactive materials with ferroelastic behavior, such as piezoelectric actuators and sensors [53,54] . These applications often operate with varying oxygen partial pressures, which can influence the mechanical properties. ...
... A load cell controlled the applied load and the displacement was measured with a custom-built LVDT (linear variable differential transformer) system. Details of the setup can be found elsewhere [53] . Uniaxial compressive tests were carried out in a temperature range from − 150 °C to 150 °C with temperature steps of 25 °C. ...
... Upon further increase of stress, ferroelastic domains can switch and the strain deviates from linearity. The critical coercive stress c required for ferroelastic switching is typically defined as the inflection point during loading [53] . Eventually, this nonlinear switching effect saturates due to the finite number of switchable domains, whereupon the material response becomes again linear [14] . ...
The macroscopic ferroelastic behavior of polycrystalline (La 0.6 Sr 0.4 ) 0.95 Co 0.2 Fe 0.8 O 3−δ and its dependence on annealing conditions was investigated over a temperature range from −150 °C to 150 °C. A temperature- and defect concentration-dependent variation of the ferroelastic behavior was attributed to internal stresses, oxygen deficiency, and a corresponding change of the crystal structure. In particular, there was an observed decrease in remanent strain and the formation of a closed ferroelastic hysteresis loop at temperatures below approximately 0 °C for samples annealed in air, which was suppressed through the reduction in oxygen vacancies by annealing the samples in oxygen. The macroscopic mechanical behavior as a function of annealing conditions is discussed with respect to the crystal structure and oxygen deficiency determined by means of x-ray and neutron diffraction.
... The setup details can be referred from earlier work. 15 The temperature-dependent permittivity of AgNbO 3 is shown in Fig. 1(a). Compared to heating cycle, permittivity is higher in the cooling cycle due to thermal hysteresis, 2,16 consistent with previous studies. ...
... 2,20 The stress-strain curve of AgNbO 3 at room temperature (M I phase) showed nonlinear behavior and strain hysteresis, indicating its ferroelastic nature [see Fig. 1(b)]. Critical parameters, including coercive stress r c (the stress with the highest domain-switching rate), maximum strain S M , remnant strain S R , and back-switching strain g (S M -S el R , as the intergranular stress overcomes external stress during unloading), 15 are indicated in Fig. 1(b). Note that the ferroelasticity of AgNbO 3 remains but differs in hightemperature paraelectric states, due to changes in domain wall motion, as reported in previous work. ...
Antiferroelectric AgNbO 3 ceramic is investigated with a focus on the effects of uniaxial compressive stress on dielectric response and phase transitions as well as its frequency-dependent ferroelastic behavior. The application of uniaxial compressive stress leads to diffused phase transitions, higher phase transition temperatures, and increased permittivity parallel to the stress application direction for low-temperature phase regions (M I , M IIa ). The stress-dependent permittivity response at different phase regions reveals the influence of stress on domain wall motion and phase changes. Additionally, loading rate-dependent stress–strain measurements demonstrate easier ferroelastic domain switching under a lower loading frequency, where the coercive stress increases with frequency initially while getting saturated above 5 mHz. This study reveals the impact of external stress, which can alter the dielectric response and affect domain wall movement at different extents depending on the loading frequency and shift phase boundaries of AgNbO 3 , implying positive prospects of property engineering of energy storage materials by stress application.
... Similar effects have been observed in other ferroelectric and ferroelastic materials, which was attributed to the reduced spontaneous strain of the unit cell with increasing temperature. 58,59 Interestingly, around 300°C, i.e., at the R-T phase transition, 60,61 the coercive stress values display a Bi content independent anomaly, whereby the coercive stress increases from approximately −50 to −100 MPa, followed by a decreasing trend with further increasing temperature. This same anomaly is not observed in the remanent strain, where a saturation above 275°C is observed up to 400°C, indicating that stress-induced hysteretic processes are retained. ...
... The variation in mechanical properties showed an overall decrease in the coercive stress with increasing temperature that can be attributed to a decreasing energy barrier for domain switching due to the increased thermal energy and the reduced crystal structure distortion [ Fig. 10(d)]. 59,78 In the vicinity of the coexisting range of rhombohedral and tetragonal phases, an increase in the coercive stress can be due to the interaction of the two phases, which was observed previously in lead-free perovskite ferroelectric materials, e.g., by means of an increased coercive field. 79 Martin et al. 80 showed a reversible transition in the orthorhombictetragonal phase transition region in (Na 0.5 K 0.5 )NbO 3 -based materials and a related increase in the coercive stress. ...
Na1/2Bi1/2TiO3 (NBT) with varying Bi content has gained significant interest as a potential new material for solid-oxide fuel cells and oxygen separation membranes because of its excellent oxygen-ion conductivity. In this work, the effect of varying Bi content in NBT ceramics of compositions Na1/2BixTiO2.25+1.5x, where x = 0.485–0.510, on the temperature-dependent mechanical and dielectric properties and the crystal structure has been investigated, as these applications expose the components to high thermal and mechanical fields. The effects of Bi variation on phase compositions and structural transitions were systematically investigated by scanning electron microscopy-energy dispersive x-ray analyses and neutron diffraction at room temperature, in situ high-temperature x-ray diffraction, dielectric permittivity, and mechanical measurements. In-depth analysis of the temperature-dependent data shows that the Bi content of the samples does not alter the average crystal structure of the NBT; however, the temperature-dependent behavior of the latter depend on variations in Bi content and the associated oxygen vacancy concentration. This change in phase transition temperature displays a good correlation with the temperature-dependent ferroelastic response and with the Bi content.
... Instead, ferroelastic measurements under uniaxial stress were performed using a screw-driven load frame (Z010, Zwick GmbH & Co. KG, Ulm, Germany). 29 The samples were ground to round cylindrical form with a diameter of ∼3 mm and a thickness of 3−4 mm using water-cooled machining on a lathe. They were then prestressed at −5 MPa to ensure smooth contact and subjected to a loading rate of 1 MPa/s. ...
... The potential of this material is exemplified by the fact that the total strain of compositions with x = 0.7 and 0.8 is about −1.0% (Figure 6b), which is about double that for unpoled high-strain commercial PZT at the same applied stress. 29 The large P S of the LiNbO 3 phase leads to such high switching strains. The coexistence of the tetragonal phase with the rhombohedral phase and hence the presence of the morphotropic phase boundary might also explain the maximized domain switching. ...
... Therefore, the stress-strain behavior of KNN-BLT-6BZ was characterized using two techniques: uniaxial compression and four-point bending. Details about the equipment and experimental procedure can be found elsewhere [35,36]. For the former, experiments were conducted at 20 C, 100 C, 180 C, and 350 C, in accordance with the temperature at which the fracture toughness was obtained. ...
... The strain measured at zero stress is defined as the remanent strain ε r . Significant recovery of the plastic deformation was observed during unloading in KNN-BLT-6BZ, with a degree higher than PZT [35,37,39], but smaller than BiFeO 3 ePbTiO 3 [40]. As the unit cell distortion decreases with increasing temperature, a higher propensity for domain switching at 100 C and 180 C is indicated. ...
The fracture toughness of unpoled and electrically poled lead-free KNN-based piezoelectric ceramics with the composition of 0.92KNN-0.02Bi0.5Li0.5TiO3-0.06BaZrO3 was investigated. Results reveal that at room temperature, the intrinsic fracture toughness (KI0) of the unpoled samples, evaluated by the near-tip crack opening displacement (COD) technique, is the lowest with a value of 0.70 MPa⋅m0.5; the long (through-thickness) crack fracture toughness (KIvnb), obtained by the single edge V-notch beam (SEVNB) technique, is the highest, with a value of 0.95 MPa⋅m0.5; intermediate short surface crack fracture toughness (KIsc) of 0.86 MPa⋅m0.5 was determined by the surface crack in flexure (SCF) technique. These results were rationalized by the toughening behavior of the material combined with the crack geometry-dependent stress intensity evolution during crack propagation. With increasing temperature, KIvnb and KIsc decrease, and become nearly identical at 350 °C, suggesting an absence of toughening. For electrically poled samples, their room temperature fracture toughness was characterized by both SCF and SEVNB techniques, with values of 0.88 MPa⋅m0.5 and 0.99 MPa⋅m0.5, respectively, slightly larger than the values measured for unpoled samples. Nonlinear electric field-strain and stress-strain analysis of the material was also employed during electric field loading, mechanical compression and four-point bending in order to quantify crack tip shielding by domain switching and the actual stress at the point of instable crack propagation.
... For example, in perovskite ferroelectrics, trivalent ions Ce 3+ , La 3+ , Nd 3+ , and Bi 3+ were used to replace divalent ions Pb 2+ , or Sb 5+ , Ta 5+ , Nb 5+ were used to replace tetravalent ions Ti 4+ . [55,56] This doping process destroyed the electrical neutrality of the protocell. Lead vacancies might appear in some PbTiO 3 cells to maintain the system's local electrical neutrality. ...
Ferroelectric (FE) materials, including BiFeO3, P(VDF‐TrFE), and CuInP2S6, are a type of dielectric material with a unique, spontaneous electric polarization that can be reversed by applying an external electric field. The combination of FE and low‐dimensional materials produces synergies, sparking significant research interest in solar cells, photodetectors (PDs), nonvolatile memory, and so on. The fundamental aspects of FE materials, including the origin of FE polarization, extrinsic FE materials, and FE polarization quantification are first discussed. Next, the state‐of‐the‐art of FE‐based optoelectronic devices is focused. How FE materials affect the energy band of channel materials and how device structures influence PD performance are also summarized. Finally, the future directions of this rapidly growing field are discussed. For the development of ferroelectric (FE)‐based optoelectronic devices, a better understanding of the fundamental properties of FE materials, quantification of FE polarization, and interface study of heterostructures between FE/low‐dimensional (LD) materials are of great importance. This review summarizes recent developments and challenges in FE‐enhanced LD optoelectronic devices.
... Before collecting the AE signals during the ferroelectric switching, we have preapplied an AC electric field of 16 kV/cm to the same sample for several cycles to check the electrical contact. This step ensures a starting point of the poled state for the AE measurement, and it is important for the later comparison since the unpoled/poled state will affect the ferroelastic switching response [35,36]. The maximum applied electric field of 16 kV/mm is much higher than the coercive fields of both the ceramic and single crystal samples (see hysteresis loop of the single crystal sample and the ceramic compared in the Supplemental Material [34]). ...
Ferroic switching of 90 ° domains in BaTiO3 can be simultaneously ferroelectric and ferroelastic. Although the general features of their respective ferroelectric and ferroelastic hysteresis loops are similar, the dynamic properties are not. Switching proceeds via avalanches, where changes of the domain structure trigger further nanostructural changes until the avalanches expire and the sample remains in a metastable state. Avalanches are characterized by energy singularities (energy “jerks”), which are power law distributed with an energy exponent ε. Using acoustic emission spectroscopy, we find that the energy exponent in ceramics during ferroelectric switching is near the mean field value ɛ∼1.3, whereas stress driven ferroelastic switching is characterized by ɛ∼1.8. This value is much larger than the field integrated mean field value ɛ∼1.66, which was found for ferroelectric switching of single crystals. Thus, BaTiO3 displays three separate dynamical processes for microstructural changes under electric and mechanical stress fields.
... On the contrary, research on PIN-PMN-PT thin films has been rare. Compared to bulk films, thin films are grown on a substrate, which impose a strain constraint due to a substrate lattice mismatch [9,[20][21][22][23]. It is known that the misfit strain can, in general, influence the phase structures and electromechanical properties in thin films [24]. ...
xPb(In1/2Nb1/2)O3-(1−x−y)Pb(Mg1/3Nb2/3)O3−yPbTiO3 (PIN–PMN–PT) bulks possess excellent electromechanical coupling and dielectric properties, but the corresponding epitaxial PIN–PMN–PT thin films have not yet been explored. This paper adopts a nonlinear thermodynamics analysis to investigate the influences of misfit strains on the phase structures, electromechanical properties, and electrocaloric responses in epitaxial PIN–PMN–PT thin films. The misfit strain–temperature phase diagram was constructed. The results reveal that the PIN–PMN–PT thin films may exist in tetragonal c-, orthorhombic aa-, monoclinic M-, and paraelectric PE phases. It is also found that the c-M and aa-PE phase boundaries exhibit a superior dielectric constant ε11 which reached 1.979 × 106 with um = −0.494%, as well as the c-M phase boundary showing a large piezoelectric response d15 which reached 1.64 × 105 pm/V. In comparison, the c-PE and M-aa phase boundaries exhibit a superior dielectric constant ε33 over 1 × 105 around um = 0.316% and the piezoelectric response d33 reached 7235 pm/V. The large electrocaloric responses appear near the paraelectric- ferroelectric phase boundary. These insights offer a guidance for experiments in epitaxial PIN–PMN–PT thin films.
... The PZT-52 sample had defects such as porosity and impurities due to sintering [36]. The nonlinear contribution below the Curie temperature was primarily due to the motion of the domain walls and their interactions with defects [37]. The ferroelectric domain configurations and defect vacancies can be controlled by the addition of aliovalent dopants in PZT-52, which causes a respective increase in the polarization and d33 values [38]. ...
The manipulator is the key component of the micromanipulator. Using the axial expansion and contraction properties, the piezoelectric tube can drive the manipulator to achieve micro-motion positioning. It is widely used in scanning probe microscopy, fiber stretching and beam scanning. The piezoceramic tube actuator used to have continuous electrodes inside and outside. It is polarized along the radial direction. There are relatively high polarization voltages, but poor axial mechanical properties. A new tubular actuator is presented in this paper by combining interdigitated electrodes and piezoceramic tubes. The preparation, polarization and mesoscopic mechanical properties were investigated. Using Lead Zirconate Titanate (PZT-52) as a substrate, the preparation process of interdigitated electrodes by screen printing was studied. For initial polarization voltage determination, the local characteristic model of the actuator was extracted and the electric field was analyzed by a finite element method. By measuring the actuator’s axial displacement, we measured the actuator’s polarization effect. Various voltages, times and temperatures were evaluated to determine how polarization affects the actuator’s displacement. Optimal polarization conditions are 800 V, 60 min and 150 °C, with a maximum displacement of 0.88 μm generated by a PZT-52 tube actuator with interdigitated electrodes. PZT-52 tube actuators with a continuous electrode cannot be polarized under these conditions. The maximum displacement is 0.47 μm after polarization at 4 kV. Based on the results, the new actuator has a more convenient polarization process and a greater axial displacement from an application standpoint. It provides technical guidance for the preparation and polarization of the piezoceramic tube actuator. There is potential for piezoelectric tubular actuators to be used in a broader range of applications.
... To characterize the ferroelastic response, the stress-strain behavior was measured during uniaxial compressive stress loading with a 30 kN screw-type load frame (5967, Instron) equipped with a custom displacement sensor based on a linear variable differential transformer, described in detail elsewhere [47] . In order to measure the stress-dependent permittivity during mechanical loading, an LCR-meter (4980Al, Keysight) was electrically connected to the sample, where 1 kHz, 10 kHz, 100 kHz, and 1 MHz were used as measurement frequencies. ...
In this study, in situ stress-dependent Raman and Brillouin spectroscopy has been performed on polycrystalline 0.93(Na1/2Bi1/2)TiO3-0.07BaTiO3 (NBT-7BT). Brillouin scattering revealed stress-dependent changes in the elastic properties around the onset stress as well as the appearance of a transversal acoustic wave mode at elevated stress levels, which is understood to be due to the formation of long-range order. These data were compared with additional Raman scattering measurements, ex situ x-ray diffraction, and macroscopic stress-strain behavior, which revealed analogous changes in the apparent crystallographic structure and ferroelectric order in the vicinity of the onset and coercive stresses.
... Temperature-dependent ferroelastic measurements [ Fig. 2(b)e(f) taken in FAU, Germany] with a compressive load up to 5 MPa were conducted in a screw-driven load frame (Instron 5657, 30 kN) equipped with a thermal chamber (TK 26.600.LN2, Fresenberger) capable of adjusting the temperature from À150 C to 600 C. Cooling was achieved through liquid nitrogen. During testing, the sample was contacted by two tungsten carbide loading dies connected to alumina cylinders that extended into the thermal chamber; additional information on the experimental arrangement can be found elsewhere [37]. The mechanical load was applied with a linear rate of 0.5 MPa/s during loading and unloading for two cycles. ...
Multiferroics have received considerable interest over the last decade due to the fascinating fundamental phenomena and potential use in various applications, such as low-power electronics and spintronics. Among those, investigations have focused on the coexistence of ferroelectric and ferromagnetic materials. Here, we report the rare case that the para-to ferroelastic ordering transition in antiferromagnet Mn2V2O7 occurred at TS = 260 ∼ 280 K, verified by temperature-dependent magnetization measurements, dielectric, differential scanning calorimetry, and macroscopic strain-stress hysteresis loops. Furthermore, this transition was accompanied by a structural transition from the high-temperature C2/m monoclinic phase (β-phase) to a low-temperature P 1¯ triclinic phase (α-phase), as identified by temperature-dependent X-ray diffraction. Consequently, TS can be successfully increased by Co- and Ni-doping and decreased by Ca-doping. Thus, the phase diagram was established for the structural stability of (Mn1-xAx)2V2O7 (A=Co, Ni, and Ca). In addition, the physical and chemical pressure effects were applied on (Mn1-xCax)2V2O7 to correlate the ferroelastic (TS) and antiferromagnetic (TN) orderings. Consequently, the magnetoelastic coupling was revealed, and a unique multiferroic material (Mn2V2O7) with a ferroelastic and antiferromagnetic ordering was obtained.
... The obtained results are illustrated in Fig. 1 . The polarized PZT exhibits the typical mechanical behavior of a ferroelastic material [68][69][70] . As can be seen in Fig. 1 , the stress-strain curves show a visible non-linearity in loading part, which is due to non-180 °ferroelastic domains switching. ...
In this study the behavior of a soft PZT ceramic subjected to compressive cyclic loadings is investigated with the aim of providing an insight into different dissipative processes which affect the ferroelastic cyclic behavior of the material. Two quantitative imaging techniques, infrared (IR) thermography and digital image correlation (DIC), are employed to measure superficial temperature and in-plane displacement of the sample under mechanical cyclic loadings. Thermal and strain responses are further deduced from these measurements. This allows to quantify the energy dissipated by the material during applied mechanical loadings. Self-heating (SH) and DIC measurements reveal that, even in the piezoelectric regime, the level of dissipation is significant. This suggests that PZT ceramic response under cyclic compression is significantly influenced by domain switching mechanisms. The two imaging techniques are shown to be efficient tools to identify domain wall activity in ferroelectric ceramics and can be advantageously substituted for polarization measurements when polarization variations are too small to be detected. It is also shown that, due to the initial compressive stress experienced by all specimens, the domain wall activity under cyclic uniaxial compressive stress is almost independent of the initial polarization state of the material.
... Mechanical measurements were performed with cylindrical samples with dimensions of 6 mm in height and 5:8 mm in diameter. The stressstrain behavior of unpoled NBT-6BT and NBT-6BT-4KNN was measured during uniaxial compressive stress loading with an experimental setup previously described detailed in Webber et al. (2009). A preload of À3:8 MPa was used to ensure mechanical contact, followed by an increase in the compressive stress to À500 MPa and subsequent unloading. ...
A fully electromechanically coupled, three dimensional phenomenological constitutive model for relaxor ferroelectric materials was developed for the use in a finite-element-method (FEM) solution procedure. This macroscopic model was used to simulate the macroscopic electromechanical response of lead-free ergodic [Formula: see text] and non-ergodic [Formula: see text] relaxor materials. The presented constitutive model is capable of accounting for the observed pinched hysteretic response as well as non-deviatoric polarization induced strain and internal order transitions. Time integration of the history dependent internal variables is done with a predictor-corrector integration scheme. The adaptability of the constitutive model regarding the pinching of the hystereses is shown. Simulations are compared to experimental observations.
... Additionally, an enhancement of maximum and remanent polarization was also evident. It should be mentioned here that the threshold mechanical field (σ pol ), required to switch/reorient ferroelastic domains, is much lower for PIC151 than that of the NBT-7BT, that is, σ pol for PIC 151 and NBT-7BT is 51 [98] and 275 MPa, [80] respectively. Importantly, the NBT-7BT with AD Cu electrode shows similar enhancement in electromechanical response without requiring any externally applied mechanical field. ...
Na1/2Bi1/2TiO3‐based relaxor ferroelectrics are extensively investigated for use in transduction applications because of their relatively large electromechanical properties. Integration of these materials into devices, however, requires better temperature stability in addition to electromechanical properties. This work demonstrates a novel approach to enhance the temperature stability of the long‐range ferroelectric order as well as to enhance electromechanical properties in a non‐ergodic relaxor 0.93(Na1/2Bi1/2)TiO3‐0.07BaTiO3 (NBT‐7BT) without changing the chemical composition through, for example, chemical substitutions or second phase particles. The approach involves the room temperature deposition of copper electrodes directly on the relaxor ceramic substrate using the aerosol deposition (AD) method. The collision of solid‐state particles with the substrate surface during AD results in large impact and residual stresses, inherent to the AD process, which are shown with piezo‐response force microscopy to induce long‐range ferroelectric domain ordering in non‐ergodic relaxor NBT‐7BT. Using Raman spectroscopy, the magnitude and depth profile of the stress‐induced transformation are determined. It is demonstrated that deposition‐induced stresses significantly increase the temperature stability of the electromechanical properties, where long‐range ferroelectric ordering is observed up to 150 °C, which is approximately 41 °C higher than NBT‐7BT samples without the AD processed electrode. Moreover, the AD treatment also facilitates ferroelectric domain switching at a lower electric field, enabling maximum polarization at a relatively lower field and an enhancement in the piezoelectric response. It is shown that the deposition‐induced stress is responsible for such an enhancement. Importantly, this impact‐stress‐driven tailoring of electromechanical properties can potentially be utilized for other functional ceramic materials as well, where internal residual stress can result in enhanced functional properties. The deposition‐induced stresses and the related deformation of the substrate inherent to the aerosol deposition are employed to enhance the electromechanical properties of lead‐free relaxors. Complementary measurements demonstrated the advantages of deposition stress. The utilization of deposition‐induced stress is a promising approach to tune functional properties.
... [15] This is particularly critical, as many applications apply elevated electrical, thermal, and mechanical fields to the electroactive materials during operation. In addition to possible component failure due to reduced mechanical strength, external fields are known to change the large-signal [16][17][18] and small-signal [19][20][21] electromechanical response and can induce structural phase transitions, either stabilizing the high-temperature paraelectric phase or low-temperature ferroelectric phase depending on the stress state, i.e., uniaxial, [22] biaxial, [23] or hydrostatic. [24] For example, underwater sound projectors apply uniaxial compressive stresses up to 63 MPa, [25] whereas hydrophones mechanically load the piezoelectric ceramic in hydrostatic compression up to several MPa. ...
The small‐signal direct piezoelectric coefficient and dielectric permittivity are characterized as a function of temperature from 25 to 450 °C and uniaxial compressive stress up to 80 MPa in porous Pb(Zr,Ti)O3 (PZT; 10, 20, 30, 40, and 50 vol% porosity). Results show retention of piezoelectric response throughout the temperature range with increasing porosity up to 30 vol%, above which a subsequent decrease is observed. Similarly, increasing porosity did not result in a significant change of the depolarization temperature, although a slight increase in the Curie point is observed with increasing porosity. Macroscopic experimental results are discussed together with microcomputed tomography, which shows the 3D pore structure. These results are important for sensing applications that operate at elevated temperatures and apply compressive stress to the electroactive element.
... Furthermore, large-area ferroelastic switching under small stimuli can also be vital for magnetoelectric coupling in multiferroics, which are being considered for low-power electric field-controlled spintronics [8][9][10] . Large-area ferroelastic switching in ferroelectrics, however, has typically only been observed in bulk materials [11][12][13] . In fact, it is generally thought that ferroelastic switching is quenched in ferroelectric epitaxial thin films due to substrate constraints [14][15][16] . ...
Ferroelastic switching in ferroelectric/multiferroic oxides plays a crucial role in determining their dielectric, piezoelectric, and magnetoelectric properties. In thin films of these materials, however, substrate clamping is generally thought to limit the electric-field- or mechanical-force-driven responses to the local scale. Here, we report mechanical-force-induced large-area, non-local, collective ferroelastic domain switching in PbTiO3 epitaxial thin films by tuning the misfit-strain to be near a phase boundary wherein c/a and a1/a2 nanodomains coexist. Phenomenological models suggest that the collective, c-a-c-a ferroelastic switching arises from the small potential barrier between the degenerate domain structures, and the large anisotropy of a and c domains, which collectively generates much larger response and large-area domain propagation. Large-area, non-local response under small stimuli, unlike traditional local response to external field, provides an opportunity of unique response to local stimuli, which has potential for use in high-sensitivity pressure sensors and switches. Clamping effects in ferroelestastic thin films limits their usefulness for applications such as sensitive mechanical sensors. Here, the authors report on non-local mechanical force induced switching in PbTiO3 thin films by tuning the material to a state of nearly energetically degenerate co-existing domains.
... The stress-strain response of unpoled relaxor NBT-6BT has established a transformation from a relaxor state with polar nanoregions in a cubic matrix to a ferroelectric state with domain structure [21]. The mechanical response of poled NBT-6BT involves domain wall movement quantified by a coercive stress (related to a yield stress in metals) leading to higher remanent strains after the loading cycle [22]. ...
The stress-strain response of composites constituting relaxor 0.94Na1/2Bi1/2TiO3–0.06BaTiO3 matrix phase with ZnO inclusions is investigated. The ZnO inclusions are found to increase the transformation stress (unpoled) for the relaxor-ferroelectric transformation and the coercive stress (poled) for domain switching. The plastic and remanent strain decreases with increasing volume fraction of the hard ZnO inclusions. This mechanical hardening mechanism is contrasted quantitatively to electromechanical hardening by comparing the transformation stress and coercive stress to the poling field and coercive field respectively, as well as the corresponding plastic strain from mechanical loading to the total strain quantified by electric field loading.
... Mechanical creep on bulk piezoceramics has been studied by researchers in the past (Fett and Thun, 1998;Guillon et al., 2004;Ji and Kim, 2013;Lynch, 1996; Pramanik and Arockiarajan, 2018a; Webber et al., 2009;Zhou and Kamlah, 2006). Influence of mechanical compressive pre-stress on the electromechanical response of ferroelectric polycrystals has been studied (Srivastava and Weng, 2007). ...
1-3 piezocomposites are often subjected to mechanical pre-stress under elevated temperatures in naval and offshore applications, actuators, and so on, where the presence of the ductile epoxy matrix causes considerable creep in the system. This deteriorates the system efficiency and its overall performance. To address this issue, experiments are performed to capture the electromechanical response for thermo-mechanical creep of 1-3 piezocomposites for different fiber volume fractions under various thermal loads, wherein mechanical depolarization is observed. The piezo-coupling coefficient is observed to degrade. Higher thermal loads resulted in an increase in creep strain coupled with a decrease in creep polarization. A Kelvin–Voigt fractal derivative viscoelastic model is used to capture the creep strain. The creep strain is decomposed into ferroelastic and anelastic parts. The evolution of creep polarization is obtained using the ferroelastic component of the creep strain. The model predictions are found to be in agreement with the experimental observations.
... To characterize the ferroelastic as well as creep behavior, the stress-strain curves were recorded during uniaxial compressive stress loading with an experimental setup described in detail elsewhere. 27 For all measurements, a preload of À4 MPa was applied before loading the sample with a uniaxial compressive stress. For ferroelastic measurements, the maximum applied stress was À500 MPa, whereas the maximum bias stress for creep experiments ranged between À50 and À500 MPa. ...
In this work, the creep behavior of (Na1/2Bi1/2)TiO3-0.07BaTiO3 was characterized as a function of bias stress up to −500 MPa, revealing the time-dependence of the stress-induced relaxor-to-ferroelectric long-range order transformation. Creep strain was observed across a range of applied compressive stress levels, in particular at stresses approximately 50% above the critical coercive stress, indicating the significant time-dependence of the transformation on the long-range ferroelectric order. The macroscopic behavior is discussed in conjunction with ex situ piezoresponse force microscopy measurements that directly show the formation of ferroelectric domains in mechanically loaded relaxor ferroelectrics.
Compared to a quasistatic environment, the electromechanical response of piezoelectric ceramics exhibits a considerably nonlinear behavior when subjected to impact. If the effect of ambient temperature is further considered, then the situation becomes more unpredictable. The thermal, mechanical, and electrical properties of soft-doped piezoelectric ceramics (PZT-5H) under compression and impact conditions were analyzed in the temperature range of −60°C to 200°C (below Curie temperature). The experimental results indicate that the fracture strength of PZT-5H has an extreme value near room temperature. The dynamic piezoelectric coefficient is strongly temperature dependent and has a maximum value near 100°C because of the “electric devil’s staircase effect” between polarization and domain switching threshold. These temperature-dependent data will enable the accurate prediction of the dynamic performance of devices by computer simulation.
In this study, stress-dependent impedance spectra were characterized as a function of uniaxial compressive stress up to –300 MPa for Zr-doped (Na 0.55 K 0.45 )(Nb 1-x/125 Zr x/100 )O 3-δ (x =5, 10 mol%). This allowed for the evaluation of the stress-induced changes in the grain and grain boundary capacitance. The grain capacitance from equivalent circuit fitting exhibited decreasing behavior with increasing uniaxial compressive stress increased, which is attributed to hindered domain wall movement reducing the extrinsic contributions. Interestingly, NKNZ10 showed a more significant degradation in grain capacitance than NKNZ5. One possible explanation is the difference in oxygen vacancies, and by extension defect dipoles, when introducing Zr into the lattice. As such, this study reveals the amplifying effect of oxygen vacancies on the mechanical suppression of domain wall movement.
In this paper, micro indentation studies were carried out on the samples made of partially coated Barium titanate thin film deposited over the silicon substrate using pulsed laser deposition technique. Direct and indirect indentation was carried out on the coating to estimate the fracture toughness of Barium titanate thin film. Fracture toughness estimation in the direct and indirect indentation methods is through the stress-based and energy-based approaches, respectively. Fracture toughness estimate through direct indentation resulted in a 30% overestimate. Detailed finite element models were developed for both direct and indirect indentation. Cohesive surfaces were incorporated in the numerical models to capture the indentation radial cracks accurately. Unlike the direct method, in the indirect method, indentation was carried out on the substrate at an offset distance from the coating on the partially coated sample. Through experiments and numerical simulations, it was found that offset distance (7-27 μm) in the indirect method has low sensitivity on the estimation of fracture toughness of Barium titanate for the load levels of 0.98 to 2.94 Newton. Thereby making the indirect method easier and more appropriate for fracture toughness estimation.
The macroscopic ferroelastic response of polycrystalline AgNbO3 was investigated under the uniaxial compressive stress of up to -300 MPa from -150°C to 450°C, covering weak ferroelectric, antiferroelectric, and paraelectric phase regions. It is found that AgNbO3 exhibits ferroelasticity in the weak ferroelectric (M1), antiferroelectric (M2, M3), as well as the paraelectric regions (O and T), i.e. displaying ferroelastic hysteresis and remnant strain. The changes in mechanical parameters such as coercive stress, back switching strain, and remnant strain values reflect the specific crystal symmetry features at different phase regions together with the influence of temperature on domain wall motion. With stress removed and cooled down to room temperature, X-ray diffraction showed that the sample (at M1 state) exhibited different degrees of remnant domain textures and lattice strains, depending on its phase state when being compressed. Additionally, in situ stress and temperature-dependent Raman spectroscopy measurements revealed that uniaxial compressive stress could induce changes in NbO6 octahedra and cation displacement, especially for high-temperature phases. Overall, the ferroelasticity, effects of stress on the structure and phase transitions offer opportunities for property engineering of AgNbO3 in capacitor applications.
Bending strength of commercially relevant lead‐free piezoceramics – 0.935Na0.5Bi0.5TiO3‐0.065BaTiO3 (NBT‐6.5BT) with and without acceptor Zn‐doping and 0.92(K0.5Na0.5)NbO3‐0.02(Bi0.5Li0.5)TiO3‐xBaZrO3; x = 0.06, 0.07 (KNN‐BZ100x) have been quantified using 4‐point bending tests and contrasted to that of commercial lead zirconate titanate (PZT, PIC151). The compressive and tensile strength probed using additional strain gauges under 4‐point bending indicate negligible non‐linear deformation, in stark contrast to that of commercial PIC151. The bending strength of KNN‐BZ100x is about 100 MPa, comparable to PIC151, while that of NBT‐6.5BT‐based materials is about twice that of PIC151 at ∼160 MPa. These results are rationalized based on the intrinsic characteristics of the lead‐free piezoceramics in terms of fracture toughness, coercive stress, and Young's modulus. Weibull statistics indicate a higher fracture probability for KNN‐based materials, with NBT‐6.5BT‐based materials featuring Weibull modulus twice that of KNN‐based materials.
Piezoelectric materials have more and more applications in modern smart fuzes due to their multiple uses such as energy storage and sensing. The electrical output characteristics of piezoelectric ceramics under high temperature and high overload environments are critical to the reliability of the device. In this paper, the mechanical and electrical response of pre‐polarized doped lead zirconate titanate (PZT‐5H) under impact at room temperature to 250°C, ie above the Curie temperature, was investigated through split‐Hopkinson pressure bar experiment with an additional electrical output measurement system. The depolarization effect caused by temperature and mechanical load was analyzed. A thermoviscoelastic constitutive model considering temperature and the strain rate was built based on the experimental data. The model can successfully predict the mechanical and electrical response of PZT‐5H under impact at different temperatures. The discharge characteristics of PZT‐5H under impact in the cooling stage after high‐temperature depolarization were also investigated, and the apparent flexoelectric coefficient of the PZT after complete depolarization was calculated. The research results show that the dynamic piezoelectric coefficient of PZT‐5H has a nonlinear relationship with temperature. During the high‐temperature cooling process, PZT has a shock induced polarization under impact, and the output voltage is less than the polarized piezoelectric ceramic but higher than the flexural polarization at the same temperature. After complete depolarization, the apparent flexoelectric coefficient of PZT‐5H is 127 μC/m. This article is protected by copyright. All rights reserved
Re-analyzing the measured data of Mun et al. (J Kor Ceram Soc 57(6):684–691, 2020) gives a modified set of fitting equations on the evolutions of remnant state variables and linear material properties during compressive stress-induced domain switching in ferroelectric ceramics. Then a poled PZT ceramic specimen is subject to large compressive stress at five different loading rates. We apply the modified set of fitting equations to the responses of the ceramic specimen and calculate the evolutions of remnant state variables during domain switching. Normalizing the remnant state variables by the relative or absolute maximum values of corresponding variables at the end of loading provides a revealing insight into the process of domain switching in the materials. Finally, the loading rate independence of the relationships between relatively normalized remnant polarization and strains may lead us to a useful modeling clue for a construction of macroscopic switching equations of ferroelectric ceramics.
The indentation response of polycrystalline soft doped-lead zirconate titanate (PZT) with varying ferroelectric domain configurations is investigated using nano and micro indentation. The as-poled (AP) PZT samples are selectively annealed at below and above the Curie temperature, Tc, to obtain different ferroelectric domain configurations. In the fully depoled state (with completely random ferroelectric domain configurations), PZT exhibit higher hardness, H (~ 40%) as compared to AP PZT (where ferroelectric domains are highly ordered). Severe cracking is observed at the imprint corners at high indentation loads and ferroelectric domain configurations are visualized in the vicinity and ahead of the indentation crack using piezoresponse force microscopy. The domains remain fully plastic in the regions from where the crack has propagated and just ahead of the crack, while farther from the indentation crack, they are elastic. The indentation fracture toughness, K_IC^i values computed from the cracks emanated from imprint corners indicate that ferroelectric domain configurations also influence toughening behaviour of PZT. The results are rationalized using remnant strain, ε_r and converse piezocharge coefficient, d_33^* measured around the indentation crack. This work highlights the new pathways to tailor strength and toughness of PZTs.
The mechanical behavior of 3 mol% Y2O3-ZrO2 ceramic and 21 wt.% Al2O3-3 mol% Y2O3-ZrO2 ceramic composite with submicron grain size was studied. Mechanical properties, such as hardness, Young's modulus, four-point bending strength, and fracture toughness of both materials were measured. Linear stress-strain deformation behavior of both 3 mol% Y2O3-ZrO2 and 21 wt.% Al2O3-3 mol% Y2O3-ZrO2 was observed in flexure, both at room temperature and at 400 °C. A small deviation from linear elastic deformation was detected in 21 wt.% Al2O3-3 mol% Y2O3-ZrO2 ceramic composite when loaded above a stress of 1500 MPa. Therefore, it was concluded that only elastic deformation occurred at low stresses upon loading, which exclude the presence of domain switching in zirconia upon bending under the loading conditions of this study.
Present work shows waste energy (thermal/mechanical) harvesting and storage capacity in bulk lead-free ferroelectric 0.6Ba(Zr0.2Ti0.8)O3-0.4(Ba0.7Ca0.3)TiO3 (0.6BZT-0.4BCT) ceramics. The thermal energy harvesting is obtained by employing the Olsen cycle under different stress biasing, whereas mechanical energy harvesting calculated using the thermo-mechanical cycle at various temperature biasing. To estimate the energy harvesting polarization-electric field loops were measured as a function of stress and temperatures. The maximum thermal energy harvesting is obtained equal to 158 kJ/m3 when the Olsen cycle operated as 25-81 °C (at contact stress of 5 MPa) and 0.25-2 kV/mm. On the other hand, maximum mechanical energy harvesting is calculated as 158 kJ/m3 when the cycle operated as 5-160 MPa (at a constant temperature of 25 °C) and 0.25-2 kV/mm. It is found that the stress and temperature biasing are not beneficial for thermal and mechanical energy harvesting. Further, a hybrid cycle, where both stress and temperature are varied, is also studied to obtain enhanced energy harvesting. The improved energy conversion potential is found as 221 kJ/m3 when the cycle operated as 25-81 °C, 5-160 MPa and 0.25-2 kV/mm. The energy storage density varies from 43 to 66 kJ/m3 (increase in temperature: 25-81 °C) and 43 to 80 kJ/m3 (increase in stress: 5 to 160 MPa). Also, the pre-stress can be easily implemented on the materials, which improve energy storage density almost 100% by domain pining and ferroelastic switching. The results show that stress confinement can be an effective way to enhance energy storage.
The nanomechanical properties of polycrystalline “hard” and “soft” lead zirconate
titanate (PZT) (abbreviated as PZT-H and PZT-S, respectively) are measured on samples
having different ferroelectric domain configurations. The ferroelectric domain configurations are varied by selectively annealing the as poled samples below and above the curie temperature, Tc. The ferroelectric domain configurations characterized using piezoresponse force microscopy reveal that the degree of randomization of ferroelectric domains increases with increasing annealing temperature. Nanoindentation experiments reveal that the above Tc annealed samples exhibit the highest hardness, H among all the samples. All the samples, exhibit strong indentation size effect where H decreases with increasing in indentation load. The possible reasons for enhancement in H in annealed samples is attributed to the differences in ferroelectric domain configurations, defect dipoles, and oxygen vacancies. The results provide insights about designing piezoelectric materials with good combination of mechanical and piezoelectric properties.
Piezoelectric actuators are essential for numerous electromechanical applications, because of their advantages of high resolution, large generated forces, no friction, low heat dissipation and fast response. The design of the next-generation piezoelectric actuators is desired to meet the complex needs of advanced machines and instruments, where the high-performance and stable output under the combined thermal and mechanical loads are expected. However, simultaneously achieving high-performance and good temperature stability of piezoelectric actuators is a challenge, which hinders the use temperature range in practical applications. Here, in the studied Sm-doped Pb(Mg1/3Nb2/3)O3-PbZrO3-PbTiO3 system, the high piezoelectric strain coefficient d33* = 870 pm/V with superior temperature stability (below 7% variation over the temperature of 20°C to 280°C), together with negligible property degradation up to 10⁶ cycles was successfully achieved. The outstanding blocking stress of 37.2 MPa and mechanical work of 6.4 kJ/m³ were obtained under the driving electric field of 15 kV/cm. This work provides a paradigm to achieve high piezoelectric strain properties with good temperature stability, where the studied materials are expected to greatly benefit the development of high temperature piezoelectric actuator applications.
Despite the importance of (Na1/2Bi1/2)TiO3 as an end member in lead-free ferroelectrics and as an oxide ion conductor, the relaxor/ferroelectric nature remains unclear. In order to understand the relaxor-like behavior, frequency-dependent macroscopic mechanical measurements of polycrystalline (Na1/2Bi1/2)TiO3 were performed as a function of poling state, revealing the role of a potential field-induced long-range ferroelectric order on the nonlinear hysteretic stress-strain behavior. The mechanical measurements showed an increase in remanent strain and decrease in coercive stress with electrical poling, consistent with previous studies of relaxors. Electrical poling and mechanical texturing were found to influence the frequency dispersion of the relative permittivity, highlighting the potentially relaxor-like response. Further, the relative permittivity showed a directional dependence with respect to the previously applied electrical and mechanical fields. These data are discussed in conjunction with ex situ stress- and electric-field-dependent piezoresponse force microscopy measurements that revealed a clear ferroelectric domain switching through the application of a sufficiently high electric field, but no change of the domain configuration for uniaxial compressive stresses up to −750 MPa. The in situ stress-dependent crystal structure, which was characterized using synchrotron x-ray diffraction, however, indicates stress-induced ferroelastic domain switching as the primary hysteretic process.
Lead-free (Li,Na,K)NbO3-based multilayered piezoceramics were prepared, and their large-signal piezoelectric properties, under combined electrical and mechanical loadings, were characterized from 25 °C to 100 °C. Under zero stress, the multilayer exhibited a high large-signal piezoelectric constant d 33 ∗ ( = S max / E max ) ≈ 350 pm/V with an applied unipolar field of 6 kV/mm. The stress-dependent d 33 ∗, with a unipolar field of 6 kV/mm, featured a pronounced sensitivity to the electric field with an evolving peak at −80 MPa, which was not observed at 100 °C. The disappearance of the evolving peak with increasing temperature suggests a strong influence of the crystallographic phase on the electromechanical properties of (Li,Na,K)NbO3-based multilayers. Further investigations of the stress–strain loop and stress–polarization change revealed that the field-dependent peak below 100 °C was due to the non-180° domain orientation induced by the combined electric field and compressive stress.
The fracture behavior of unpoled and electrically poled Ka0.5Na0.5NbO3 (KNN)- and Na1/2Bi1/2TiO3 (NBT)- based lead-free piezoceramics were characterized using the Vicker's indentation technique and compared with soft Pb(Zr,Ti)O3 piezoceramics. In the unpoled state, NBT-based piezoceramics demonstrate the largest fracture toughness in comparison with KNN-based and soft PZT piezoceramics due to its large intrinsic fracture toughness, which is in accordance with the previous reports. In the electrically poled state, KNN- and NBT- based piezoceramics exhibit large fracture toughness along the poling direction as opposed to perpendicular to the poling direction, with aspect ratios of 1.2 and 1.1, significantly smaller than that for PZT (1.8). The variations of the remanent strain and the process zone, which are related to the texture and the material properties during crack propagation were used to rationalize the results.
In this study, Vickers indentation was utilized to characterize the crack propagation anisotropy of Nb/Ce co-doped Pb(Zr0.52Ti0.48)O3 (ab. PZT-NC) ceramics in different media environments and under varying temperatures. Three-point bending associated with Weibull statistics was used to further evaluate the fracture properties. The results demonstrate that PZT-NC ceramics have the best fracture toughness in silicone oil and the worst in air. The fracture toughness and flexural strength of poled PZT-NC ceramics have significant anisotropy due to ferroelastic toughening (Ksh) with crack propagation. Parallel to the poling direction, the fracture toughness and reliability of the flexural strength of poled PZT-NC ceramics are higher. As the temperature increases (from 25 °C to 205 °C), the fracture toughness of PZT-NC ceramics dramatically decreases, which is attributed to the decrease in ferroelastic switching (Ksh).
Two series of compressive stress cycles are applied to a commercial poled ferroelectric cube specimen at room temperature \(\,20\,{^\circ }{\text{C}}\): one is big stress cycles of increasing magnitude and the other small stress cycles of constant magnitude. The former is applied at five different rates to induce domain switching, and the latter at the fastest loading rate possible to estimate the evolutions of linear material properties during switching. From measured data, we find that the relationships among remnant polarization, longitudinal remnant strain, and transverse remnant strain are equal and the same independent of loading rates. The dependence of piezoelectric coefficient, elastic compliance coefficients, and Poisson’s ratio on remnant state variables is also the same independent of loading rate. These observations lead to conclude that switching processes by compressive stress are loading rate independent, which would be useful in developing constitutive equations for nonlinear behavior of ferroelectric ceramics.
Ferroelectric ceramics are of interest for engineering applications because of their electro-mechanical coupling and the unique ability to permanently alter their atomic-level dipole structure (i.e., their polarization) and to induce large-strain actuation through applied electric fields. Although the underlying multiscale coupling mechanisms have been investigated by modeling strategies reaching from the atomic level across the polycrystalline mesoscale to the macroscopic device level, most prior work has neglected the important influence of temperature on the ferroelectric behavior. Here, we present a phase-field (diffuse-interface) constitutive model for ferroelectric ceramics, which is extended to account for the effects of finite temperature by considering thermal lattice vibrations based on statistical mechanics and by modifying the underlying Landau-Devonshire potential to depend on temperature. Results indicate that the chosen interpolation of the Landau energy coefficients is a suitable approach for predicting the temperature-dependent spontaneous polarization accurately over a broad temperature range. Lowering the energy barrier at finite temperature by the aforementioned methods also leads to better agreement with measurements of the bipolar hysteresis. Based on a numerical implementation via FFT spectral homogenization, we present simulation results of single- and polycrystals, which highlight the effect of temperature on the ferroelectric switching kinetics. We observe that thermal fluctuations (at the phase-field level realized by a thermalized stochastic noise term in the Allen-Cahn evolution equation) promote the nucleation of needle-like domains in regions of high heterogeneity or stress concentration such as grain boundaries. This, in turn, leads to a faster polarization reversal at low electric fields and a simulated domain pattern evolution comparable to experimental observations, stemming from the competition between nucleation and growth of domains. We discuss the development, implementation, validation, and application of the temperature-dependent phase-field framework for ferroelectric ceramics with a focus on tetragonal lead zirconate titanate (PZT), which we demonstrate to admit reasonable model predictions and comparison with experiments.
We report an experimental approach, designed based on the recent findings that domain switching in ferroelectric ceramics can be separated into three regimes during antiparallel electric field loading, to investigate the influence of domain switching process on the electrical fatigue behavior of ferroelectrics. Uniaxial compressive stress (-2 MPã -100 MPa) and thermal loading (20 °C–150 °C) were used to tune the domain switching process. Under the same loading condition, the bipolar electrical fatigue behavior of soft lead zirconate titanate ceramics was systematically characterized. The amplitude and frequency of the applied electric field are 2 kV/mm and 10 Hz, respectively. By analyzing the evolution of the domain switching process, combined with the measured polarization and strain response, as well as the cracks observed on the surface of the specimen, it is found that the fatigue of ferroelectric ceramics was mainly related to the domain switching process near the coercive electric field: the regime 2 defined in this paper. The underlying mechanism was further discussed by considering the interplay between the domain switching process with the main factors affecting the electrical fatigue of ferroelectrics, namely defect redistribution, charge carrier injection, and crack initiation.
A multiphase field theory and corresponding finite element simulations are developed to describe ferroelastic domain switching in bulk polydomain tetragonal zirconia (t′-zirconia). We consider the ferroelastic switching as mechanical twinning in our model which differs from the Landau-Devinshire theory used in ferroelectric thin films. The approach is advanced in several directions: the thermodynamic potential is developed, introducing interface tension at the domain wall with a multiphase field framework; the ferroelastic features, such as spontaneous strain, coercive stress and hysteresis loop, are explicitly derived from the potential; and a penalizing term in interface energy is introduced to constrain the switching paths between different domains for correctly describing the hysteresis. The phase field model is applied towards prediction of switching rules among three domains of an externally stressed t′-zirconia. Numerical simulations demonstrate fair agreement between phase field solutions and experimental observations that the two sets of domains grow at the expense of the third set upon application of uniaxial compression. The simulations also reproduced a phenomenon that the domain switching occurs and develops inside the colony domain pattern, i.e., the switching rules are dominated by the applied stress tensor and the pre-existing domain patterns of materials. The developed approach can be extended to study the domain switching of any pure ferroelastic material or ferroelectrics subjected to applied stress in the absence of an electric field.
Despite considerable research interest in developing piezoelectric materials, little work has focused on the fundamental design of these materials from the ground up. Herein, we present a general, versatile method for producing tunable, flexible piezoelectric energy harvesters (PEHs) with excellent piezoelectric response. Using a poly(dimethylsiloxane) (PDMS) foam derived from a sugar template, we separate the electrical and mechanical properties of the PEH, thereby allowing us to optimize them separately. The electrical properties were tuned by varying the poling field, the polar dopant, and the dopant concentration. The mechanical properties were tuned by varying foam preparation and thus the compressive modulus. Through the careful tuning of these properties, we are able to achieve a maximum piezoelectric response of 153 pC/N—considerably higher than most other reported flexible PEHs. Combined with our previous work, we demonstrate that doping polymer foams with polar dopants is a highly general strategy and has the potential to lead to materials with considerably higher piezoelectric responses.
The poling behavior of a lead-zirconate-titanate piezoelectric ceramic is investigated by measurements of the ferroelectric hysteresis, the longitudinal piezoelectric coefficient, and field-cooling poling experiments. At high temperatures, the decrease in the coercive field facilitates poling at lower electric fields, resulting in higher values of the longitudinal piezoelectric coefficient. However, there exists a threshold field of about 150 V/mm, below which fully poled samples cannot be obtained even when field cooling from temperatures above the transition. Further, a temperature regime below the Curie temperature is observed, where a polarization under field can be measured, but a remanent polarization is not stable. The results are discussed with respect to the phase transition behavior.
Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs electric field curves and the corresponding electric displacement vs electric field loops [1]. It is also the source of a stress—strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress [2, 3]. In this work, ceramic lead lanthanum zirconate titanate (PLZT) is polarized by loading with a strong electric field. The resulting strain and polarization hysteresis loops are recorded. The polarized sample is then loaded with compressive stress parallel to the polarization and the stress vs strain curve is recorded. The experimental results are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The observed strain and electric displacement hysteresis loops and the nonlinear stress—strain curve for the polycrystalline ceramic are reproduced by the simulation.
In situ uniaxial compression experiments on Pb(Zr,Ti)O3 or PZT-based polycrystalline electroceramics were conducted using time-of-flight neutron diffraction. Elastic lattice strain and texture evolution were observed in PZT’s near the edge of the morphotropic phase boundary (with tetragonal and rhombohedral phases present). Multiphase Rietveld analysis yielded anisotropic lattice strain evolution curves in directions parallel and perpendicular to the loading axis for both phases. A quantitative analysis of the domain switching under applied stress was possible through application of a March–Dollase model for texture.
Part I Capacitative Applications BackgroundDielectric StrengthThermal Shock ResistanceCapacitorsPart II Principal Ceramic Types and Applications Low-permittivity Ceramic Dielectrics and InsulatorsMedium-permittivity CeramicsHigh-permittivity CeramicsProblemsBibliography Background
Dielectric StrengthThermal Shock ResistanceCapacitors Low-permittivity Ceramic Dielectrics and InsulatorsMedium-permittivity CeramicsHigh-permittivity CeramicsProblemsBibliography
To increase the reliability of multilayer actuators, calculation of the mechanical stress inside the device during operation is important. This paper shows that the small-signal value of the elastic constant s is not sufficient to describe the complicated behavior of lead zirconate titanate (PZT) ceramics. Therefore, compressive strain and depolarization have been measured as a function of large-signal stress applied parallel to the poling direction. The nonlinear dependence of the strain and depolarization can clearly be explained by domain processes. Soft and hard PZT ceramics have been investigated. In hard PZT, domain switching appears at higher stresses than in soft PZT. Moreover, in hard PZT, the domains partly switch back during unloading. The critical stress (coercive stress) necessary for a domain-switching process shows a dependence on the Zr:Ti ratio that is quite similar to the dependence of the electric coercive field. The influence of an electric field applied parallel to the poling direction and superimposed on the compression experiment also has been examined. The coercive stress depends linearly on the electric field. The linear coefficient of this relation is given by the ratio of depolarization to compressive strain caused by domain switching.
Modern piezoelectric transducers normally have complicated structures and work under severe loading conditions. Due to their inherent domain-switching processes, the real response of piezoceramics under large-signal loading is dominated by a significantly non-linear behavior that is to be considered in reliability assessment and devices design. This paper presents systematic measurements of the non-linear depolarization and strain behavior of soft lead zirconate titanate piezoceramics over a wide range of compression loads and bias electric fields. An attempt has been made to explain the experimental findings by simultaneously taking into account the contributions of dielec-tric response, elastic deformation, irreversible domain switching, and piezoeffects.
The effect of prestress on the nonlinear dielectric (polarization) and piezoelectric (strain) response of lead zirconate–lead titanate (PZT–5H) piezoelectric ceramic is studied. The response to bipolar (−2/+2 MV/m) and unipolar (0/+2 MV/m, −0.4/+2 MV/m) electric field under constant prestress (up to 175 MPa) is experimentally evaluated. In the bipolar regime, prestress mainly influences the first non-180° process. In the unipolar regime, the dielectric and piezoelectric response achieve maximum values near 50–60 MPa because the prestress increases the number of available non-180° domains. A detailed description of the effect of the prestress on electro–mechanical response is provided in terms of non-180° domain wall motion. Based on rule of mixtures formulation, an analytical model is developed to estimate the optimum prestress value for the unipolar electric loading condition. It is found that the dielectric and piezoelectric response of the material is proportional to the volume fraction of the non-180° domains and the difference in domain wall pressure created by mechanical and electrical loads.
Measurements of changes in permittivity, tanδ, and d ∂∂ as function of compressive stress parallel to the polar axis are presented for lead zirconate—lead titanatetransducerceramics. The “hard” ceramics (PZT‐4 and PZT‐8) suitable for high‐power application show large changes of properties for stresses to 20 kpsi, but have good recovery on release of stress. The “soft” donor‐doped ceramics (PZT‐5A and PZT‐5H) suitable for detector applications show serious degradation with successive stress cycles. However, for peak stress below about 10 kpsi, their variation of properties and hysteresis within any cycle are less than those of the hard ceramics.Permittivity and tanδ of all these ceramics increase with increase of acelectric field. For the soft ceramics, the tanδ increase is great enough to eliminate their consideration for uses where efficiency or cool operation are necessary. High acelectric fieldcombined with compressive stress reduces these detrimental increases for the soft ceramics and increases them for the hard ceramics. Nevertheless, the hard ceramics remain far superior for high‐power high stress uses, with PZT‐8 being superior to PZT‐4.
The domain-switching behavior of lead zirconate titanate (PZT) during mechanical cyclic loading between 10 and 150 MPa was investigated by in situ time-of-flight neutron diffraction. The domain-switching behavior was represented by a change of the pole density distribution during cycling. With increasing number of cycles, domain switching becomes saturated, correlating with a decrease in the rate of remnant strain accumulation in the stress-strain curve. Moreover, a relationship was demonstrated between the macroscopic strain and that developed from ferroelastic domain switching. The contribution of ferroelastic strain to the macroscopic strain was calculated from an orientation average of the domain switching distributions and the c/a ratio. The results show that nearly 80% of macroscopic strain arises from ferroelastic domain switching during mechanical cyclic loading.
A micro-electro-mechanical model of the behavior of piezoelectric ceramics including thermal effects is presented and compared to experimental data. Results include analytical and numerical investigations of the behavior of piezoelectric ceramics. The model is based on physical mechanisms and includes elastic, dielectric, and piezoelectric anisotropy. Moreover, the model is based on an internal energy approach so that work-energy relations may be directly applied. Results from the model give insight into material behavior.
Stresses suffered by lead zirconate titanate (PZT) components in actuators are the origin of the gradual degradation of the microstructure and piezoelectric capability that limits their lifetime. The stress–strain behavior of a PZT ceramic has been studied in compressive uniaxial cyclic loading using a constant loading rate, in order to determine the operating stresses that cause structural damage associated to the exhaustion of twinning. Domain switching strain curves have been calculated considering that stress-induced switching of 90° domains is the mechanism responsible of non-linear stress–strain behavior. Each load–unload cycle caused a permanent strain in the PZT. Successive cycles produced incremental increases in stress-induced permanent strain, up to a maximum value or ‘saturated cyclic permanent strain’, attributed to irreversible stress-induced domain switching. The dependence of the saturated permanent strain with the maximum cyclic load showed a characteristic non-linear behavior, with a steep slope at a stress level σI, that we called the ‘critical stress for irreversible domain switching’. Below σI, the majority of domain switching is reversible. We have called σR to the stress at which the increase in reversible domain switching is more pronounced. At stresses between σR and σI high reversible strains can be reached without resulting in permanent stress-induced depoling and thus without the exhaustion of available twinning during subsequent load cycles. At maximum cyclic stresses higher than σI, irreversible domain switching accounts for the majority of strain and increase rapidly toward values close to the maximum 90° domain switching strain available. The number of cycles to failure also had a strong dependence with the maximum cyclic stress. Cyclic stresses above the critical stress caused a rapid accumulation of permanent strains, so the saturated value is reached after a few cycles, resulting in early catastrophic failure, because of the exhaustion of reversible domain switching.
Ferroelastic domain switching in a soft lead zirconate titanate (PZT) ceramic is measured by neutron diffraction on the texture diffractometer HIPPO with mechanical compression applied in situ. Complete orientation distribution functions are measured by time-of-flight neutron diffraction and represented as pole figures and inverse pole figures at compressive stresses in 50MPa increments up to a maximum of 200MPa. Significant domain switching hysteresis was observed in parallel to the macroscopic strain hysteresis. The contribution of ferroelastic domain switching to the measured macroscopic strain is calculated directly from the 00l pole figure. Subtraction of this contribution from the measured macroscopic strain yields the bulk-averaged lattice strain. After unloading, the macroscopic strain of 0.30% consists of 0.22% ferroelastic domain switching and 0.08% crystallographic lattice strain.
Diffracted intensities from axially symmetric flat-plate or capillary specimens, composed of effectively rod- or disk-shaped crystallites, can be corrected for preferred orientation with a single pole-density profile. A convenient procedure is to approximate this profile with a function whose variable parameters are fit during least-squares structure refinement. Several functions have previously been suggested but without theoretical justification. The present study reviews the derivation of this method and examines its assumptions and applications. The several proposed functions are compared with each other and with the March function which describes the pole-density distribution produced by rigid-body rotation of inequant crystallites (i.e. crystallites with unequal sides) upon axially symmetric volume-conserving compression or expansion. For its basis, ease of use, single variable parameter, direct interpretability and good refinement test results, the March distribution is proposed as an advantageous pole-density profile function for general use.
This paper introduces saturated domain switching textures of three different ferroelastic ceramic crystal systems. The accompanying extrinsic domain switching strain is calculated exclusively using a volume-weighted integral of a single pole figure. In ceramics which are also ferroelectric, the electromechanical response is defined by the domain switching textures, strains, and strain asymmetry, which are found to be functions of the number and directions of possible ferroelastic structural distortions.
The effect of bias electric field on the nonlinear stress–strain response of a lead zirconate–lead titanate piezoelectric ceramic is studied. The material is subjected to various compressive stress amplitudes (25–300 MPa) under constant electric field (from −0.5 to 2.0 MV/m) along the original poling direction. Application of a positive electric-field bias results in closed stress–strain hysteresis loops absorbing significant amounts of mechanical energy. Increasing the positive electric field increases the specific damping and decreases the elastic modulus. The trend is reversed when the electric field becomes sufficiently high to inhibit the domain-wall motion by the mechanical stresses. Measured specific damping values vary from 0.18 to 0.46 depending on the stress amplitude and bias electric field. The corresponding secant modulus varies from 79 to 24 GPa. The coercive stress is found to approach zero as the negative electric-field bias approaches the coercive field value. The coercive stress increases with increasing positive electric field as expected from the balance of mechanical and electrical energies. The physics of the observed phenomena is explained in terms of non-180° domain-wall motion. © 2002 American Institute of Physics.
The domain structure of ferroelectric ceramics can be altered by the process of electrical poling. This paper develops quantitative approaches for reflection geometry and spherical harmonic texture analysis, both of which describe these changes at angles parallel to and tilted from the poling axis. The x-ray-diffraction approach uses the relative intensity ratio of ferroelectric poles in poled and unpoled lead zirconate titanate to calculate a domain switching fraction (η) or a multiple of a random distribution, which are shown to be linearly related. An x-ray area detector diffractometer was used for these measurements, although the technique applies to any x-ray reflection geometry. The neutron-diffraction approach employs a Rietveld refinement with a spherical harmonic texture model. Both approaches calculate similar domain textures for two poling fields and the small differences between the approaches can be attributed to surface domain texture. This paper shows that the March–Dollase pole distribution function can inadequately describe domain textures.
Piezoelectric actuators are at an important stage of their development into a large component market. This market pull is for dynamically driven actuators for Diesel injector valves in automobiles. Cost, yield, and reliability are important concerns for the automobile industry. A number of these concerns relate back to basic material science issues in the manufacture of the piezoelectric actuators. This paper discusses material development of the piezoelectric ceramic and new opportunities for higher temperature materials. An important consideration in developing low-fire ceramics is the flux selection for a given system, and these must be selected to limit electrode-ceramic interface reactions in both Ag/Pd and copper-metallized electrode actuators.
Young's moduli were measured in compression tests using partial unloading. Three different poling states (unpoled, parallel, and normally poled with respect to the load direction) were investigated. The Young's modulus was found to be variable during the mechanical tests and increased up to about 130-150 GPa. A simple description of the possible effects on Young's modulus is presented.
The performance and expected lifetime of piezoelectric ceramic components are ultimately defined by bulk material fatigue processes. In this work, strain accumulation of a ferroelectric/ferroelastic ceramic lead zirconate titanate is characterized under mechanical cycling using four-point bend bar geometry. Strain accumulation occurs at a higher rate than in creep alone, indicating that the processes are fatigue related, and it is confirmed by X-ray diffraction that the accumulated strain is contributed under both cyclic tensile and compressive stress by domain switching. The relative ranking of measured mechanical strains is nearly the same as the theoretical saturated domain-switching strains.
Ferroelectric ceramics used in advanced actuator systems may be subject to high stresses and large deformations that may lead to nonlinearity and performance degradation. A preliminary experimental investigation has been undertaken to study the relevant mechanical responses. For this purpose, polarization and strain are measured continuously on a compression cuboid. Severe nonlinear and hysteretic behavior is observed in several cases. An attempt has been made to establish constitutive laws, applicable to this nonlinear deformation, which may be used for design purposes.
To increase the reliability of multilayer actuators, calculation of the mechanical stress inside the device during operation is important. This paper shows that the small-signal value of the elastic constant s is not sufficient to describe the complicated behavior of lead zirconate titanate (PZT) ceramics. Therefore, compressive strain and depolarization have been measured as a function of large-signal stress applied parallel to the poling direction. The nonlinear dependence of the strain and depolarization can clearly be explained by domain processes. Soft and hard PZT ceramics have been investigated. In hard PZT, domain switching appears at higher stresses than in soft PZT. Moreover, in hard PZT, the domains partly switch back during unloading. The critical stress (coercive stress) necessary for a domain-switching process shows a dependence on the Zr:Ti ratio that is quite similar to the dependence of the electric coercive field. The influence of an electric field applied parallel to the poling direction and superimposed on the compression experiment also has been examined. The coercive stress depends linearly on the electric field. The linear coefficient of this relation is given by the ratio of depolarization to compressive strain caused by domain switching.
In many polycrystalline piezoelectric ceramics, domain switching during the poling process leads to the development of a macroscopic polarization and piezoelectric behavior. Traditionally, poling involves the application of electric fields across two parallel electrodes. In the present work, a radial mechanical compressive stress is applied transverse to the electric field, increasing the potential for domain alignment during poling by taking advantage of ferroelasticity. Experiments demonstrate that poling of lead zirconate titanate using a combination of an electric field and a transverse mechanical compressive stress increases the d33 coefficient from 435 to 489 pC/N. Using neutron diffraction and pole figure inversion methods, the degree of non-180° domain switching is described using pole density distributions of the tetragonal c-axis (002). The degree of 002 domain alignment parallel to the electric field after the electromechanical poling process increases from 1.30 multiples of a random distribution (mrd) to >1.40 mrd at stresses exceeding 40 MPa.
A systematic investigation of the stress-dependent (σ) electromechanical properties of various ferroelectric ceramics and single crystals has been performed. Studies have been carried out on “hard” and “soft” piezoelectrics, electrostrictive ceramics, and various orientations of (1−x)Pb(Mg1/3Nb2/3)O3–(x) PbTiO3 PMN–x%PT single crystals. The large signal piezoelectric constant, acoustic power density, and coupling coefficient have been determined by calculation. The results are compared, in order to develop an understanding of the relative merits of the different types of active acoustic materials.
8/65/35 PLZT is characterized under stress and electric field loading above the coercive field. Strain—electric-field and electric-displacement—electric-field hysteresis loops are measured at various compressive stress levels showing the effect of stress on the electro-mechanical coupling. Stress—strain curves are run at zero electric field, showing that depolarization begins at as little as 5 MPa. The limitations of linear constitutive modeling and the limitations of this composition of PLZT as an actuator material are examined. The “yield” or ferroelastic switching stress is suggested as a good criteria for assessing the capability of actuator ceramics. This parameter is an indication of the actuation limitations of the material. An equivalence of the slopes of the strain—electric-field curve at several compressive stress levels and the electric-displacement—stress curve at the same stress level is observed. This suggests that the conjugacy of the piezoelectric coefficients may hold during path dependent polarization switching.
Pb(Mg1/3Nb2/3)O3–0.32(PbTiO3), PMN–0.32PT, single crystals have been characterized under combined stress and electric field loading [McLaughlin EA, Liu T, Lynch CS. Relaxor ferroelectric PMN–32%PT crystals under stress and electric field loading: I-32 mode measurements. Acta Mater 2004;52:3849, McLaughlin EA, Liu T, Lynch CS. Relaxor ferroelectric PMN–32%PT crystals under stress, electric field and temperature loading: II-33-mode measurements. Acta Mater 2005;53:4001]
[1],
[2] and [3]. This approach is extended to PMN–0.26PT single crystals to explore the effect of composition on field driven phase transformations and to PMN–0.32PT ceramic specimens to compare with polycrystalline behavior. Electric displacement and strain were measured as a function of combinations of stress and both unipolar and bipolar electric fields. The single-crystal results indicate that compositions further from the morphotropic phase boundary require higher driving forces for field induced phase transformations. Evidence of these transformations is not apparent in the results from the ceramic specimens.
Samples of the polycrystalline ferroelectric ceramic PZT-5H were poled by applying an electric field at room temperature. Subsequently, an electric field was applied to the samples at a range of angles to the poling direction. The measured non-linear responses in electric displacement are used to construct “yield surfaces” in electric field space corresponding to the onset of ferroelectric switching. The results are compared with predictions from three models: (i) a previous self-consistent polycrystal calculation with rate-independent, non-hardening crystal plasticity; (ii) a simplified crystal plasticity model with viscoplastic (rate-dependent) behaviour and a sufficient number of transformation systems to reproduce the polycrystalline behaviour; (iii) a phenomenological model based on rate-independent flow theory, using kinematic hardening and a quadratic yield surface in electric field and stress space. The experiments suggest that the self-consistent crystal plasticity formulation is most able to reproduce the multi-axial electrical response and yield surface of the polycrystal. The phenomenological model is able to reproduce the uniaxial response accurately, but gives relatively poor performance for multi-axial loading paths, in its present form. A tolerable compromise in multi-axial modelling is the simplified crystal plasticity approach. This is able to reproduce multi-axial constitutive behaviour with reasonable accuracy, whilst offering computational simplicity and speed similar to that of the phenomenological model.
The mechanical stressing of PZT produces irreversible deformation by the irreversible switching of 90° domains. This leads to highly anisotropic deformation behaviour for poled materials. The threshold stresses required to produce this switching are relatively small, <10 MPa. The strains that can be achieved, ∼1%, are relatively large for ceramic materials. The domain switching is a thermally activated process, so that the deformation behaviour is strain rate dependent. The cyclic stressing of PZT produces significant incremental increases in the irreversible strain. This behaviour is the basis of electromechanical fatigue effects that cause the degradation of piezoelectric materials.
Polarization and strain hysteresis curves of lead zirconate titanate (PZT) multilayer actuators were obtained for both bipolar and unipolar electrical loading as a function of applied uniaxial compressive stress. These large-signal dielectric and piezoelectric properties are correlated with the corresponding small-signal properties of longitudinal piezoelectric coefficient d33 and longitudinal dielectric permittivity ε33. A complete comparison is afforded by obtaining the small-signal properties as functions of both applied DC electrical field and uniaxial compressive stress. Results are presented in terms of guidelines for optimal performance of multilayer actuators, but also in terms of a qualitative description correlating the hysteresis of the piezoelectric coefficient with the macroscopic strain.
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