# Rejuvenation of giant electrostrain in doped barium titanate single crystals

E. A. Patterson, P. Finkel, M. G. Cain, P. Thompson, C. Lucas, M. Staruch

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E. A. Patterson, P. Finkel, M. G. Cain, P. Thompson, C. Lucas, et al. Rejuvenation of giant electrostrain in doped barium titanate single crystals. APL Materials, 2023, 11 (4), pp.041109. 10.1063/5.0142103. [hal-05094709](https://hal.science/hal-05094709v1)

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# Rejuvenation of giant electrostrain in doped barium titanate single crystals

E. A. Patterson ; P. Finkel ; M. G. Cain ; P. Thompson ; C. Lucas ; M. Staruch

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APL Mater. 11, 041109 (2023)

https://doi.org/10.1063/5.0142103

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# Rejuvenation of giant electrostrain in doped barium titanate single crystals

Cite as: APL Mater. 11, 041109 (2023); doi: 10.1063/5.0142103

Submitted: 11 January 2023 • Accepted: 10 March 2023 •

Published Online: 3 April 2023

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E. A. Patterson,<fnref n="1" /> ID P. Finkel,<fnref n="1" /> ID M. G. Cain,<fnref n="2" /> ID P. Thompson,<fnref n="3" /> ID C. Lucas,<fnref n="3" /> ID and M. Staruch<fnref n="1" />, a ID

## AFFILIATIONS

## ABSTRACT

Engineering materials through the introduction of point defects has resulted in significant advances in semiconductor processing and, more recently, the observation of novel phenomena such as large reconfigurable strains in ferroelectrics as a result of defect dipole complexes. Up to 0.8% strain has been demonstrated in BaTiO₃ crystals dilutely doped with iron. However, the defect dipole pinning sites and the corresponding achievable strains are found to degrade as the crystal is electrically cycled as part of the measurement process. The strain degradation rate is dependent on the applied field values but shows an exponential change in materials properties regardless of the electric field. This behavior, plus a change in impedance with number of times cycled, suggests these changes are due to electric field induced oxygen migration—similar to the cause of the resistance degradation effect. Despite this, effective piezoelectric coefficients of over 4700 pm/V were recorded with 1.5 kV/cm fields, one of the largest values for a lead-free piezoelectric material thus far. In addition, the defect dipole-aligned state and the high strains can be repeatably recovered by a subsequent heat treatment step after cycling. Potential paths to exploiting the defect dipole induced effects and large piezoelectric coefficient in these dilutely doped systems are proposed.

© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0142103

## INTRODUCTION

Defects exist in all materials, with some number of defects always being thermodynamically favorable, no matter what processing steps are taken<fnref n="1" />⁻<fnref n="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

<footnote n="1">¹ U.S. Naval Research Laboratory, Washington, District of Columbia 20375, USA</footnote>

<footnote n="2">²Electrosciences Ltd., Farnham, Surrey GU9 9QT, United Kingdom</footnote>

<footnote n="3">³Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 3BX, United Kingdom and XMaS Beamline, European Synchrotron Radiation Facility, Grenoble F-38043, France</footnote>

<footnote>a) Author to whom correspondence should be addressed: margo.staruch@nrl.navy.mil</footnote>
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 (Fe'ₜᵢ - V'₀)⁻ 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.

## EXPERIMENTAL METHODS

(001) oriented 0.5 mol % Fe doped BaTiO₃ (BaTi₀.₉₉₅Fe₀.₀₀₅O₃, 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.

## RESULTS AND ANALYSIS

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

<figure><img src="image_10.png" /><figcaption>FIG. 1. Bulk strain along the poling direction for BTFO crystals showing multiple measurements with (a) 25 kV/cm and (b) 5 kV/cm applied electric field. (c) Unipolar measurements showing similar reduction in strain with continued cycling at 10 kV/cm as full bipolar measurements at various fields.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>FIG. 4. (a)–(d) The (020) pseudocubic reciprocal space map for the BTFO crystal at various temperatures (160, 255, 340, and 450 K, respectively). (e) The lattice parameter *a* vs temperature for decreasing (red, filled symbols) and increasing (purple, open symbols) temperature sweeps.</figcaption></figure>

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 $BaTiO_3$^{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 $Ti^{4+}$ sites.

DISCUSSION

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 crystals35,36 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 electro strains. 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
<figure><img src="image_12.png" /><figcaption>**FIG. 5.** Strain vs electric field as the field is cycled at 1.5 kV/cm for up to 500 cycles, showing little change in strain values for sub-coercive field switching. The value of effective $d_{33}$ as calculated from the slope of these curves (dashed line) is found to be 4700 pm/V.</figcaption></figure>

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.

## SUMMARY

The polarization and strain have been recorded for many cycles for a 0.5% Fe-doped $BaTiO_3$ 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.

## SUPPLEMENTARY MATERIAL

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

## ACKNOWLEDGMENTS

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.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

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).

## DATA AVAILABILITY

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

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