Fatigue-free dielectric and piezoelectric response in single-crystal BaTiO₃ tuned by dislocation imprint

Manipulating the mobility of domain walls is central to the macroscopic response of ferroic materials.^1,2 Point defect (0D) doping,^3,4 domain-wall (2D) engineering,^5,6 and insertion of precipitates or secondary phase (3D) particles^7,8 are state-of-the-art approaches to control the motion of ferroic domain walls. In particular, due to the intrinsically strong coupling between lattice and charge degrees of freedom in ferroelectrics,⁹ the introduction of dislocations and their associated elastic strain fields allows localized strain engineering and offers a new design route to tailor ferroelectric properties.^10–12 There are some excellent examples demonstrating the utilization of misfit dislocations for the enhancement of ferroelectric properties of epitaxial thin films (e.g., remanent polarization was improved by at least 250% in strained BaTiO₃ thin films¹² and room-temperature ferroelectricity was reported in paraelectric SrTiO₃¹²). However, dislocations are often blamed for the degradation of ferroelectric films.^13–17 For instance, dielectric and piezoelectric responses^13,14 and phase transition temperatures¹⁶ are significantly degraded by misfit dislocations, due to the formation of an interfacial ferroelectric dead layer or near-surface eigenstrain relaxation. Even a single dislocation located in the substrate can suppress the local spontaneous polarization of the ferroelectric PbZr_0.2Ti_0.8O₃ layer by up to 48%.¹⁸ While the control and manipulation of pinning–depinning dynamics caused by extended dislocations play a key role in enhancing properties,^19,20 there is very little knowledge about how to eliminate or at least minimize the dislocation-related degradation of ferroelectrics.

Recently, we demonstrated that mechanically imprinted {101}⟨101⟩ dislocation networks in bulk single-crystal BaTiO₃ allow access to a 19-fold increase in electromechanical response, whereas the interaction between dislocations and domain walls provides macroscopic restoring force as well as local domain wall pinning for functional harvesting.²¹ Also, we are able to directly control anisotropic electromechanical properties by taking full use of dislocation–domain wall interactions based on domain-wall pinning force anisotropy.²² In bulk ferroelectrics, this dislocation-based anisotropy offers a route to maximize domain wall pinning and stabilize domain-wall variants. Rather unexpectedly, near-surface eigenstrain relaxation and the formation of an interfacial dead layer in thin-film ferroelectrics can be automatically avoided since the mechanical dislocation imprint induces dislocations into the volume instead of locating near the interface dislocation structure.

In this Letter, by introducing {100}⟨100⟩ dislocation fields into a model system of bulk single-crystal BaTiO₃ using high-temperature plastic deformation, we found that large-signal piezoelectric strain coefficient and dielectric permittivity were largely enhanced, whereby dislocation structures embedded in engineered domain walls played a crucial role in nonlinear macroscopic response. Moreover, we observed these enhanced dielectric and piezoelectric responses without any degradation by performing unipolar electrical fatigue measurements up to a large amount of cycles. Our results demonstrate that dislocations in bulk ferroelectric ceramics are highly underestimated, forcing us to rethink the role of dislocations in ferroelectrics.

In contrast to metals, only limited sets of slip systems can be activated in ferroelectric oxide ceramics.^23,24 For example, KNbO₃ single crystals can be plastically deformed by uniaxial compression at room temperature,^25,26 while both {110}⟨110⟩ and {100}⟨100⟩ slip systems of BaTiO₃ can be thermally activated in compression at elevated temperature only.^21,22 Single crystals are an ideal platform to investigate the dislocation-tuned functionality owing to their easier orientation-controlled deformation and less complex microstructure as compared to polycrystalline materials. To this end, uniaxial compression of [110]-oriented BaTiO₃ single crystals along the [110] crystallographic orientation was conducted at 1150 °C with a loading rate of 0.2 N/s using a load frame (Z010, Zwick/Roell) equipped with a HTM Reetz furnace and a linear variable differential transducer system for precise displacement measurement. Under these conditions, high-temperature {100}⟨100⟩ slip systems are preferred to be activated since they have a maximized Schmid factor of 0.5.²⁷ Detailed high-temperature deformation procedures can be found elsewhere in previous publications.^22,24 In this work, a pronounced yield point at ∼60 MPa and a textbook plastic deformation behavior were recorded [see Fig. 1(a)]. A noticeable feature of the stress–strain curve is the pattern of stress “plateaus” or extended plastic region, which benefits to introduce aligned dislocations, as schematically presented in Fig. 1(b). Previously, dislocations oriented along the [001] direction (i.e., [001] line vector) were confirmed by extensive transmission electron microscopy experiments.²² 

After deformation, the average domain size decreased from ∼80 to ∼30 μm, as displayed in Fig. S1. To study the influence of dislocations on electrical properties, we sliced the original specimen with a diamond wire saw and extracted thin slabs [see red box in Figs. 1(b) and S2] from the deformed sample and sputtered gold electrodes on two large (110) surfaces. The [110]-orientated samples were confirmed using the Laue backreflection (1001 Model, Huber, Rimsting) with an orientation accuracy of ±0.5°. In this case, the applied electric field is perpendicular to the dislocation line vector or parallel to the deformation direction of [110], see the inset of Fig. 1(c). Room-temperature polarization–electric field (P–E) hysteresis loops were quantified at 1 Hz using a TF 2000E system (aixACCT Systems Inc.). Macroscopic polarization loops highlighted the remarkable impact of mechanically imprinted dislocations on large-signal properties. Apparently, the coercive field of the deformed sample was increased when compared to the reference sample. Concurrently, remanent and spontaneous polarizations cannot reach the values of the reference sample, indicating the degradation of ferroelectric properties via domain wall pinning.²¹ Concurrently, a twofold increase in domain back-switching [see Fig. 1(c)] was observed when compared with the reference sample, indicating a strong macroscopic restoring force.²¹ After deformation, the unipolar strain decreased notably (Fig. S3) and bipolar strain exhibited asymmetric response due to the presence of dislocations (Fig. S4). For the extracted samples with a coordinate system of X:[$1¯$10]; Y: [001]; Z:[110], out-of-plane domains refer to a₁ (polarization vectors parallel to [100]) and a₂ (polarization vectors parallel to [010]), in-plane domains are defined as c (polarization vectors parallel to [001]), as highlighted in Fig. S2. Based on ¹³⁷Ba nuclear magnetic resonance (NMR) data published in Ref. 22, the plastically deformed sample in the poled state had out-of-plane a₁ and a₂ domain variants only, while the poled reference sample ensured 4.4% c-domains.²² Note that direct current (DC) poling along the [110] direction with a field of 10 kV/cm was performed at room temperature for 30 min. Macroscopically, the increased domain population of out-of-plane a-domains in the poled sample caused a slight enhancement of the dielectric permittivity after deformation [see Fig. 2(a) at a field of 1 V/mm], due to anisotropy of the dielectric tensor of BaTiO₃ with ε_a > ε_c.²⁸ 

Application of large-signal sub-coercive alternating current (AC) fields (approximately 40% of the coercive field) manipulates the mobility of ferroelectric and/or ferroelastic domain walls though dislocation-induced domain-wall pinning and depinning phenomena. To simultaneously quantify the sub-coercive field dependence of converse piezoelectric coefficient (d₃₃^*) and dielectric permittivity (ε₃₃), we combined two lock-in amplifiers (SR830, Stanford Research System) and a high voltage amplifier (PZD700A M/S, Trek Inc.) with a high-speed laser vibrometer (Polytec GmbH). As compared to the poled reference sample, in addition to the clear suppression of macroscopic polarizations, deformed samples in the poled state afford a two-stage piece-wise (almost) linear AC field dependence of d₃₃^* and ε₃₃ in the sub-coercive field regime, as featured in Fig. 2(a). Below a pinning field of 16 V/mm, both values remain constant and rise strongly beyond it. Note that, the extrinsic contribution to piezoelectric response in BaTiO₃ is dominated by the interaction between dislocations and 90° ferroelastic domain walls, while dislocations interacting with both 90° and 180° domain walls contribute to dielectric response.^29,30

To disentangle these contributions, a₁ and a₂ domain variants were engineered by DC-poling along the [110] direction, as schematically depicted in Fig. S5. In this case, we expect the dislocation–domain wall configuration with maximized domain wall pinning to mitigate the degradation of d₃₃^* because imprinted dislocations are perfectly aligned on slip planes and all a₁–a₂ 90° domain walls are parallel to the dislocation lines (see Fig. S6). 180° domain walls could be parallel to dislocations and develop a configuration with domain walls intersecting dislocation lines. We compared both the d₃₃^* and ε₃₃ values of the deformed sample at a range of AC fields with magnitudes between 1 and 50 V/mm. The d₃₃^* was increased by 660%, and the ε₃₃ was enhanced by 1260% at the highest applied AC field of 50 V/mm. This revealed that the interaction between 180° domain walls and dislocations played an important role in the dielectric enhancement. The enhancement of dielectric and piezoelectric properties is a clear signature of dislocation-induced domain-wall pinning and depinning phenomena.²¹ Note that the dielectric loss [see Fig. S7(a)] significantly increased once the field exceeded the pinning field, indicating a sign of strong dislocation–domain wall interactions.

The best way to evaluate the dislocation-related degradation is to conduct fatigue measurements at given fields with cycle numbers up to millions. As expected, we observed fatigue-free dielectric and piezoelectric responses under AC field either below or above the pinning field (16 V/mm), as plotted in Figs. 2(b) and 2(c). When the AC field is lower than the pinning field, both d₃₃^* and ε₃₃ are stable, indicating that domain walls are efficiently pinned by dislocations. When the AC field is higher than the pinning field, both d₃₃^* and ε₃₃ at 40 and 50 V/mm increase at the beginning and then become stable. We observed similar changes in dielectric loss [Fig. S7(b)] for the deformed sample under AC fields, whereas the loss varies with applied AC field, as expected. Therefore, the changes observed in both sub-coercive field parameters reveal rather a training effect based on more complete poling. Specifically, there is no reduction in properties observed (Ref. 31 review on fatigue). The property reduction has been described as due to motion of charge carriers to grain boundaries under the driving force of the depolarization field present at grain boundaries for the case of polycrystalline ferroelectrics.³² For the case of bulk ferroelectric single crystals, electric fatigue has been suggested to be related to the occurrence of microcracking, which accompanied large strain misfit.³³ Generally, d₃₃^*, electrostrictive coefficient Q, dielectric permittivity ε₃₃, and polarization P follow the equation: d₃₃^* ∝ Qε₀ε₃₃P,³⁴ where ε₀ is the vacuum permittivity. In this work, d₃₃^* and ε₃₃ have a linear relationship with increasing the AC cycles, as highlighted in Fig. 2(d). From a mechanic point of view, dielectric permittivity and piezoelectric response are mainly related to dislocation–domain wall interactions.

We propose a simple scenario to relate the existence of dislocation structures and the fatigue-free dielectric and piezoelectric responses. Unlike the chemical doping with homogeneous distribution of pinning centers (e.g., oxygen vacancies),^4,35 dislocation-based pinning sites imhomogeneously distribute on activated slip planes [see schematic in Fig. 3(a)]. In our case of dislocation imprint, the estimated dislocation density is about 2 × 10¹²/m²,²² corresponding to an average spacing of 500 nm. DC-poling along the [110] direction favors a₁–a₂ domains and the walls are locally pinned, allowing only relatively short motion of domain walls. In ferroelectrics, the domain configurations are governed by the system energetics.^36,37 Above the domain wall pinning field, the domain wall can overcome the local pinning potential. It means that domain walls at glide planes with low dislocation density are irreversibly unpinned. The pinning of one wall under an AC field, thus, imposes an effective pressure on walls within a given interaction volume and, hence, increases the probability of their simultaneous displacements, leading to a domino effect.³⁸ Therefore, active pinning and depinning events ensure the system to reach a new equilibrium state [see schematic in Fig. 3(b)] and simultaneously improve the dielectric and piezoelectric responses. This equilibrium state can be rationalized by domain wall variants pinned by dislocations with high dislocation density, which is accompanied by a relatively long motion of the domain walls, unless all domain walls reversibly move, as featured in Fig. 3(c). The measured displacement of the deformed sample with a thickness of about 0.9 mm is 95 nm. Considering the average domain size of ∼30 μm (see Fig. S1), one could estimate 30 domain walls that exist in the thickness direction. The overall displacement is overwhelmingly by domain wall movement and not by lattice extension. Let us assume that all domain walls are coordinately moving in one direction, then we could estimate, each domain wall is moving about 3 nm, thereby contributing to the whole displacement of the sample during one cycle. The estimated distance of domain wall motion is in good agreement with previous phase-field simulation on a BaTiO₃ single crystal where a single domain wall moves several nanometers.³⁹ The reversible domain wall motion results in dielectric and piezoelectric response without degradation even if the AC fields run up to 68 × 10⁶ cycles (see Fig. S8). In this work, the dielectric and piezoelectric nonlinearity is linked to the dynamic pinning–depinning between domain walls and dislocations, reminiscent of dynamic heterogeneity in the interaction between defect dipoles and domain switching.^4,35 This fatigue-free behavior is rooted in a complex potential energy landscape [Fig. 3(d)] where irreversible and reversible domain wall motions depend on energy wells. Further work is required to provide direct evidence for the nanoscale bending of the domain walls between pinning sites. It has been demonstrated that defect-chemistry-induced pinning sites do not trigger electrical fatigue when the defect dipoles are stable under AC poling.^40,41 In this work, these mechanically introduced dislocations are not necessarily electrically charged so that they will benefit fatigue resistance in the same manner as point defect-induced pinning sites.

In summary, we developed a strategy to eliminate the dislocation-induced degradation in a ferroelectric model system of bulk single-crystal BaTiO₃, whereby well-directed dislocation networks from the {100}⟨001⟩ slip systems were imposed into volume by high-temperature plastic deformation. The underlying mechanism responsible for the fatigue-free dielectric and piezoelectric response is the interplay of the dislocations with ferroelectric domains, which is done by tailoring the dislocation–domain wall configuration and microstructure, thus providing a paradigm for the design of ferroelectrics via dislocation technology. Considering the high dielectric and piezoelectric response and good fatigue resistance, deformed BaTiO₃ is expected to be a great potential for high-displacement piezoelectric actuator applications.

See the supplementary material for optical images, schematics for domain variants and dislocation domain wall configurations, and electrical properties.

This work was financially supported by the German Research Foundation (DFG) through Project No. 414179371 and the seed fund from the Research Field “Matter and Materials” at TU Darmstadt (Grant No. 40101529). F.Z. thanks for support from the Alexander von Humboldt (AvH) Foundation for the fellowship with Award No. 1203828. Open access funding enabled and organized by Projekt DEAL.