Rejuvenation of giant electrostrain in doped barium titanate single crystals

Defects exist in all materials, with some number of defects always being thermodynamically favorable, no matter what processing steps are taken^1–3 since all processes take place at some finite temperature. Three types of defects have been identified in crystalline materials: point defects (including vacancies, interstitials, and impurities), dislocations, and planar defects such as grain boundaries, twinning, and stacking faults. There have been various efforts by many researchers to harness certain types of defects to improve the material properties of a given system. For example, defects play an essential role in semiconductors with materials being deliberately engineered through the addition of dopants, such as boron or phosphorus, to modify the carrier concentration making silicon either n-type or p-type.⁴ Or, in ferroelectric materials, a small amount of acceptor (lower valence) or donor (higher valence) dopant can modify the dielectric and piezoelectric properties⁵ and even reduce fatigue due to compensation of oxygen vacancies.^5–7 

Recently, there have been several efforts to modify the domain configuration via the introduction of defects that yield a restoring force for a recoverable initial domain configuration that can produce a very high, repeatable piezoelectric response. Of particular interest is revisiting well-known ferroelectric BaTiO₃ (BTO) single crystals, which with certain domain configurations were reported to have ultra-high strain (∼1%).⁸ However, after one cycle, the crystal was de-poled and the strain dropped to zero, which would be of little use for any practical application in transduction. In contrast, Höfling et al. applied a repeated mechanical stress to create dislocations to control the domain structure in (001) BTO single crystals, yielding repeatable high piezoelectric coefficient of 1890 pm/V.⁹ Another approach is to introduce defects by doping, with work showing similar behavior in BTO single crystals doped with a small amount (<2 atm %) of either Fe³⁺ or Mn³⁺ at the Ti⁴⁺ site, with measured electrostrains of up to 0.8% that were repeatable for several cycles.^10,11 The reconfigurability of the domain structure, in this case, was proposed to be due to the alignment of defect dipoles with the ferroelectric dipoles. The defect dipoles are formed during an aging process via oxygen vacancy migration to the most energetically favorable sites—in this case, associated with the more electronegative dopant element. Electron paramagnetic resonance spectroscopy on similar Fe³⁺-doped systems has confirmed the presence of charged (⁠$FeTi′−VO⋅⋅⋅$ defect associates with an anisotropic center that favors orientation along the direction of the c-axis for tetragonal BTO.¹² This trapping of oxygen vacancies by the acceptor dopant during the aging process provides a restoring force for reversible 90° domain switching.^8,13,14

While this large strain and associated constricted hysteresis loop are quite stable in doped (Ba, Sr)TiO₃ ceramics,¹⁵ the 0.8% strain in single crystal Fe-doped BTO was only demonstrated through four electric field cycles, and that work did not investigate any impacts of continued ac fields.¹⁰ However, this is critical to explore because hysteresis relaxation, or a change in the internal bias field and the shape of the hysteresis loop with repeated ac electric field, has also been frequently demonstrated in these doped systems.^16,17 We had previously noted a change in the ferroelectric hysteresis loop and the piezoelectric response depending on sample pre-history¹⁸ but have not fully explored this phenomenon until now. In this paper, we have identified irreversibility in the large electrostrains in doped BaTiO₃ with continued electrical cycling, and seek to understand what role oxygen vacancies are playing in the evolution of the ferroelectricity and piezoelectricity. We also propose a path forward to exploiting these large strains in practical devices.

(001) oriented 0.5 mol % Fe doped BaTiO₃ (BaTi_0.995Fe_0.005O₃, hereafter referred to as BTFO) single crystals were provided by Ceracomp Co. Ltd. and were produced via a solid-state single crystal growth technique. More details can be found in Ref. 19. The as-received samples were then aged at 80 °C for 24 h to allow for diffusion and to obtain the defect dipole aligned state. Ferroelectric and piezoelectric measurements were performed with a Sawyer-Tower system and a linear variable differential transformer (LVDT) for displacement) connected to a lock-in amplifier. Impedance measurements were carried out using an impedance analyzer (Keysight E4990A Impedance Analyzer).

X-ray diffraction measurements were performed on a laboratory microfocus tube source at 8.047 keV, a facility hosted on the XMaS (BM28) beamline. Radiation from this source was collimated using a Montel mirror,²⁰ before passing through a Germanium 〈220〉 channel cut monochromator, to improve the energy resolution. The sample was mounted within an ARS Cryogenics cryofurnace, based on a DE-202 cryocooler with a sapphire thermal switch, to enable measurements at both high and low temperatures, and this cryofurnace was mounted onto a Huber four circle diffractometer. An ESRF Maxipix 2D detector²⁰ was used as a detector. Images from this detector were processed using specialized software written by Electrosciences to enable 3D volumes of reciprocal space to be determined.

After initial aging, the samples demonstrated large strains of 0.6%–0.8%. However, it was immediately noticed that after the measurement cycle, re-measuring the sample resulted in a significantly lower maximum strain value as can be seen in Fig. 1(a). Furthermore, the strain continued to degrade with additional cycles and ultimately reached a value similar to that expected for undoped BaTiO₃ (∼0.05%) after about 100 cycles. This is for the maximum strain values that were achieved with an electric field of 25 kV/cm. By reducing the maximum applied field to 10 or 5 kV/cm, the maximum strain is slightly reduced [Fig. 1(b)] with the strain still reducing with electric field cycling. However, the number of cycles that it takes to match the same reduction observed at a higher field is higher, with 1000 cycles or more needed to achieve the same 0.05% values. Once the sample reaches the level of undoped BTO, the P-E and ε − E loops stabilize. To verify if this was an effect of depoling the sample, we performed unipolar measurements and observed the same strain degradation effects as for the full bipolar loop [see Fig. 1(c)]. This suggests the loss of defect dipole (⁠$FeTi′$ - $VO⋅⋅$⁠)^· complexes with ac electric field cycling. A hysteresis relaxation has previously been observed for acceptor-doped ferroelectrics, but only focused on the impact on the polarization hysteresis loops.^16,17,21 Our results establish that this same phenomenon has a large impact on the strain response as well. Since effective piezoelectricity is highly dependent on domain switching, this also implies a relationship between the defect dipoles and ferroelectric domain configuration that are both changing during this de-aging process. We have also explored the cyclic behavior when driven at electric fields, E, lower than the coercive field (E_C), and although the maximum achievable strain is low as expected there is no change in the ε−E curve for over 1000 cycles.

Because the defect dipole-aligned state is confirmed to have a pinched polarization hysteresis loop, whereas undoped BTO has a conventional PE loop, tracking the increase in the remanent polarization (P_R) is a convenient way to explore the evolution of the strain degradation effect. By plotting P_R vs number of cycles for different maximum electric fields, we can see in Fig. 2 that a logarithmic increase is observed regardless of the electric field when at or above the coercive field. The 1.5 kV/cm field data also represents a sub-coercive field switching process and, therefore, the remanent value was not reached so P_R is instead defined as the maximum value reached, which is why that curve saturates at a value lower than for higher applied voltages. However, consistent with previously observed strains, the critical exponent τ dramatically varies between the different curves. By fitting the data with a simple exponential law (⁠$e−t/τ$⁠), values for τ of 51, 280, and 227 were determined for 25, 10, and 1.5 kV/cm field, respectively. This behavior for the remanent polarization is most likely directly tied to previous modeling that demonstrated aging of a doped sample with applied ac field where the internal bias will decrease with time by an exponential law,²² or in fact that samples can be de-aged with the internal bias decreasing exponentially as modeled by Lohkamper, Neumann, and Arlt.²¹ However, they did not find any change with ac electric field amplitude, which we report here and was also previously reported by Carl and Hardtl where τ changes as 1/E.¹⁶ Although we cannot validate that relationship here, the higher electric field certainly yields a smaller time constant.

This behavior is, therefore, directly in line with earlier works in understanding the de-aging process of doped ferroelectric systems through the application of temperature or ac electric field. There are a number of different mechanisms proposed during the aging process including domain wall effects or the volume effect. Oxygen vacancies are understood to be the more mobile defect and their conductivity is a well-characterized phenomenon in BTO and similar materials.^23–26 It is natural to assume that if thermal aging would result in the formation of the defect complexes and an exponential increase in the internal bias E_i, then the hysteresis relaxation phenomenon and decrease in E_i with an increasing number of cycles would be driven by breaking up the defect complexes and migration of the oxygen vacancies away from the Fe³⁺ ions. This is all consistent with the volume effect previously proposed during aging.¹⁷ 

At elevated temperatures in Fe-doped BaTiO₃, oxygen vacancy mobility with applied electric field results in their migration toward the cathode resulting in a change in conductivity.^27–31 To look to see if a similar phenomenon is occurring at room temperature with ac field cycling, the frequency dependence of impedance was measured after various number of cycles at an intermediate (10 kV/cm) electric field as shown in Fig. 3. A dramatic increase in impedance as a function of applied electric field cycles is observed, with some indication that the material’s resonance behavior is also affected, with a notable shift in frequency up through 500 cycles. The peaks also are suppressed significantly at 1000 cycles, although verification afterward determined the sample was still poled so there may be a shift to frequencies above the measured range. These results suggest a change in the conductivity with continued ac cycling and that the hysteresis relaxation and concomitant decrease in strain are also related to oxygen vacancy migration with an applied electric field that is quenching the defect dipole alignment in the sample and, thus, reducing recoverable non-180° domain switching.

To further investigate this irreversible behavior with aging, XRD (HK) contour plots of the (020) type crystallographic reflection at four different temperatures for the as-received BTFO crystal are shown in Figs. 4(a)–4(d). As the temperature is increased, four distinct phases are observed that are consistent with rhombohedral (R), orthorhombic (O), tetragonal (T), and cubic (C) symmetries. The sequence, including the temperature of the various transitions, is nearly identical to that of undoped BaTiO₃^32,33 as seen clearly in the video with temperature indicator (supplementary material). The expected discontinuities in the value of the lattice parameter a and the hysteresis in the increasing vs decreasing temperature sweeps are also observed. There is a slight difference in the value of lattice parameter, a, once the sample was heated to over 400 K [Fig. 4(e)] that could potentially be attributed to the diffusion of oxygen vacancies and the loss of alignment to the ferroelectric polarization when the sample is heated above T_C. However, this could also be attributed to thermal depoling. Overall, the structure of BTFO seems to be identical to undoped BTO and the thermodynamics and stabilities of the phases are unchanged by this dilute doping. There is, therefore, little evidence of any impact of the doping on the crystal structure due to the expected thermally induced oxygen vacancy migration at elevated temperatures. The iso-symmetric nature of the doped material to the undoped may suggest a rationale for the polarization and strain values gradually returning to the values of an undoped BTO with continued electrical cycling—once the oxygen vacancies are completely unaligned to the ferroelectric dipoles, the dilutely doped material is functionally identical, with a negligible difference in polarization expected for 0.5% Fe substitution at the Ti⁴⁺ sites.

Our results suggest several development pathways or trajectories in the utilization of the defect-dipole effect in doped BTFO for practical devices. The annealing, sintering, and aging conditions (including the atmospheric conditions during each step) are all expected to impact vacancy concentration, ionic mobility, and ultimately the ferroelectric behavior. The first path proposed here is, therefore, to modify the processing conditions and the amount of dopant or even the dopant ion to prevent electric field-induced diffusion in the sample.^30,34 The second pathway that we propose is to use this system only within an application that can operate with a significantly reduced electric field, but with a highly repeatable strain state. As demonstrated in Fig. 5, the strains measured with a 1.5 kV/cm electric field are relatively stable through 500 cycles. Perhaps more importantly, by approximating the strain response as a single linear response, then the doped BTFO crystal shows an effective piezoelectric coefficient (d*₃₃) of up to 4700 pm/V even after 500 cycles. This is an exceptionally high value for any material, comparable with the best values observed in AC-poled relaxor ferroelectric single crystals^35,36 and is one of the highest values reported for any lead-free ferroelectric materials.

Finally, regardless of the pre-history of the sample, by re-ageing the BTFO crystal at 80 °C for at least 24 h, the initial defect dipole state is recovered along with the large electrostrains. This is actually demonstrated by the data in Fig. 2, which was all measured using the same sample that was re-aged after each measurement at the different electric fields, illustrating the recoverable initial state. In addition, the exponential hysteresis relaxation is also repeatable after this re-aging treatment. Based on the number of different remnant polarization values that can be achieved during the ac field cycling process, the authors propose that the electric field-induced migration and subsequent recovery with heating could be exploited in novel ferroelectric memristor elements. Instead of varying resistance though, the remanent polarization itself can be set at a number of different available states by controlling the applied voltage, or the number of times a given voltage is cycled. The read voltage, if low enough, should not impact the state significantly. An element could then be “cleared” through the application of a temperature to re-age the material and obtain the initial zero-remanence state. The stability and time evolution of these intermediate states (that is between the defect dipole aligned condition and the traditional ferroelectric state) remain ongoing research.

The polarization and strain have been recorded for many cycles for a 0.5% Fe-doped BaTiO₃ single crystal. The strain values decrease and the pinched polarization hysteresis loop opens with an increasing number of electric field cycles, for almost all voltages applied. Our data are consistent with an exponential increase in conductivity that suggests significant oxygen ion vacancy mobility in the sample, even at room temperature, which is affecting the defect dipole-driven behavior.

See the supplementary material for a video of the temperature dependence of XRD scans showing the evolution of the peak is available online.

The authors would like to acknowledge funding from the Office of Naval Research through the U.S. Naval Research Laboratory’s Basic Research program and the Office of Naval Research Global, ONRG-NICOP Project No. N62909-18-1-2008 Electrosciences Ltd. This research work was carried out under the framework of the ADVENT project (Grant No. 16ENG06 ADVENT), which was supported by the European Metrology Program for Innovation and Research (EMPIR). The EMPIR initiative was co-funded by the European’s Horizon 2020 research and innovation program and the EMPIR Participating States. XMaS, BM28, was a UK National Research Facility funded by the Engineering and Physical Sciences Research Council (EPSRC), UK.

The authors have no conflicts to disclose.

E. A. Patterson: Formal analysis (equal); Investigation (equal); Methodology (supporting); Writing – original draft (supporting). P. Finkel: Conceptualization (equal); Methodology (equal); Writing – original draft (supporting). M. G. Cain: Formal analysis (equal); Investigation (supporting); Writing – original draft (supporting). P. Thompson: Data curation (supporting); Investigation (supporting); Writing – original draft (supporting). C. Lucas: Formal analysis (supporting); Investigation (supporting); Writing – original draft (supporting). M. Staruch: Conceptualization (equal); Funding acquisition (equal); Investigation (lead); Writing – original draft (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.