Fingerprints of relaxor ferroelectrics: Characteristic hierarchical domain configurations and quantitative performances

Highlights

• Relation between domains and in-situ quantitative intrinsic properties is revealed.

• Domain configurations of PMN-PT single crystals show strong composition dependence.

• Polygonal lamellar domains in the MPB composition own better performances.

• The original local d₃₃ of polygonal domains is 14 pm V⁻¹.

• Polygonal domains have low coercive voltage and high effective Young's modulus.

Abstract

Ferroelectrics’ structure-property relationships are of guiding significance in high-performance material designing and usually clarified from the aspect of symmetries, which is arduous and costly. On the principle of convenience, here, the concept that domains can provide a brandnew nondestructive and fast way for this relationship clarification is demonstrated. Utilizing scanning probe microscopy, quantitative original local elastic/piezoelectric/ferroelectric performances of various characteristic domain configurations are directly investigated in relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ single crystals. Among them, the polygonal lamellar domains with coexistence of straight c, a and c/a walls in the at-morphotropic phase boundary composition, own high surface effective Young's modulus (average values close to 160 GPa), strong original average local piezoresponse (8.5 pm) and effective longitudinal piezoelectric response (d₃₃, 14 pm V⁻¹), together with ease of electrical switching. Low free energy barrier and strong piezoelectric anisotropy contribute intrinsically to these better functionalities. Higher and easier domain wall motion, larger ratio of c⁺/c⁻ domains, and larger depolarization and elastic energies stemmed from larger domain width/size act as extrinsic factors. These results help to understand relaxor ferroelectrics comprehensively and provide a reference of domain-based structure selection for better material design.

Introduction

Ferroelectrics have a wide application in industry as actuators, transducers, memories, and ultrasonic/optical-electric/energy harvesting devices [1,2], because of their excellent dielectric/piezoelectric/photoelectric performances. Among them, relaxor ferroelectrics, e.g., (1-x%)Pb(Mg_1/3Nb_2/3)O₃-x%PbTiO₃ (PMN-x%PT), attract much more attention than others by virtue of ultrahigh electromechanical and optoelectric [3] capabilities. For instance, the macroscopic longitudinal piezoelectric response (d₃₃) of PMN-PT single crystals (e.g., > 2500 pC N⁻¹) around morphotropic phase boundary (MPB) is four times larger than that of the best doped PbZr_0.48Ti_0.52O₃ ceramics in value of ~500 pC N⁻¹ [4,5]. Debate on the origin of these attracting performances in relaxor-PT based solid solutions has never stopped over the past two decades, due to the complexity in distinguishing symmetries accurately via combination of various diffraction techniques [6], [7], [8], [9], such as reciprocal space map, synchrotron radiation, neutron diffuse scattering and Raman scattering. Moreover, these revelation is arduous, time-consuming and costly.

Apart from the atomic arrangement related symmetries, domains are crucial to ferroelectrics’ basic structure-property relationship understanding and performance tailoring. Domains, i.e., areas having the same polarization direction, are one of the essential, distinct but vital microstructures in ferroelectrics. Domain formation bounds up with structural symmetries resulted from atoms’ arrangement, long range order (LRO) and vibration. With the capability to be easily reconfigured by external electric or elastic field, domains can affect ferroelectrics’ functionalities notably, especially for nanomaterials. For instance, polar nanoregions (PNRs) [4,10], one unique kind of microstructures in relaxor ferroelectrics, may formed due to pinning by local strong enough random field [6]. They can facilitate polarization rotation thanks to their ease of switching abilities by external stimuli, and thus contribute largely (e.g., 50%−80%) to the aforementioned novel longitudinal and shear electromechanical properties [4,10]. Despite the fact that ferroelectric domains with longer range ordered are still different from PNRs in short range order (SRO), these inspiring findings highlight the significance of microstructures to properties. Besides, domains and domain walls are found to have intriguing phenomena basically different from their parent materials like wall conductivity [11] and vortex domains [12], triggering evolution on applications in nanoelectronic devices. Furthermore, macroscopic performances (e.g., di-, piezo-, opto- and pyro-electric performances) of relaxor ferroelectrics can be greatly further enhanced and tailored via domain engineering [3,5,13], through manipulation of domain patterns, width or sizes, amount and motion of domain walls.

Various kinds of microscopies make it convenient to visualize domain patterns, including polarized optical microscopy (POM) [14,15], transmission electron microscopy [16,17], scanning electron microscopy [18], piezoresponse force microscopy (PFM) [6,19,20]. Quite plenty of works have reported domain configurations in relaxor-PT solid solutions, however, several key issues on structure-property relationship clarification from the aspect of domains are not stated clearly. Firstly, the lateral component of polarization vector affects in-plane electromechanical capabilities greatly but is seldom characterized. Moreover, for the previous out-of-plane domain configuration observation, uniform conclusion can hardly be drawn due to the divergences in the reported case-by-case specimens, aside from the complexity in domains themselves originated from doping of relaxors (e.g., PMN) into ferroelectrics (e.g., PT). For instance, multiple states coexisted complex domains at MPB in the (001) PMN-PT single crystals at room temperature via POM were observed [14]. But elsewhere, in the near-MPB-composition of PMN-PT by the same technique, fine crosshatched domains in rhombohedral (R) symmetry were found [21]. In contrast, by PFM, a domain hierarchy on length scales from 40 nm to 0.1 mm presents in PMN-PT single crystals [15]. Nanodomains with opposite polarization orientation embedded on the micro-sized domains can be seen [15], indicating the coexistence of polar clusters within ferroelectric domains [6]. Secondly, despite its indispensable significance in clarifying the domain structure-property relationships, direct evidence between these configurations and in-situ properties of domains has seldom been provided in the simple binary [17,22] relaxor-PT systems, ascribed to difficulties in combination of the conventional macroscopic property detection techniques with the aforementioned microscopies. Not to mention those complex cases in the ternary [23], [24], [25] and even quaternary [26] systems. Without better solutions and direct experimental proofs, domain patterns are usually merely thought and believed to be related and contribute to relaxor ferroelectrics’ macroscopic capabilities, acquired from macroscopic permittivity-temperature relationships, hysteresis [polarization versus electric field (P-E)] loops and strain-electric field curves [7,27]. To be more rigorous, direct dielectric/ferroelectric/elastic domain properties contributing to macro-performances are needed urgently. Thirdly, comprehensive and direct relationships between configurations and in-situ original properties of domains in relaxor ferroelectrics are far in lack, especially experimentally. The recent rapid development of scanning probe microscopy (SPM) facilitates the possibility of visualizing domain configurations and characterizing their local multifunctionality conveniently on mesoscale. However, quantitative performances by nondestructive and fast testing methods in relaxor ferroelectrics still remain unknown. For instance, in the rare reported studies for elastic property characterization, the commonly used nano-indentation [28], force curve and three-point bending [29] methods have slow test rate and sampling heterogeneity. More importantly, the excessive applied forces by these means result in damage to specimens’ surfaces such as protrusion [28], dent, or even cracks [29], which are not desirable and should be avoided especially for nanomaterials/devices. On the other hand, for piezoelectric/ferroelectric performance measurement, the reported after-normalization [22,30] piezoresponses without cantilever calibration are incomparable from case to case, making it confusing to distinguish the best corresponding material. Without cantilever calibration of inverse optical lever sensitivity and spring constant, the detected responses usually include a tip-sample-dependent equipment magnification and thus cannot reflect the intrinsic properties of the materials themselves. This magnification is quite common in commercial PFM utilizing a piezo ceramic to generate cantilever's vibration, and should be eliminated in quantitative analyses.

In this work, we clarify relationships between various typical vertical and lateral domain configurations and their original in-situ quantitative local elastic/piezoelectric/ferroelectric performances, in the simple binary relaxor ferroelectric PMN-x%PT single crystals mainly by SPM. Direct evidence of better domain properties in the at-MPB composition is given. Great variation in local effective piezoresponse and effective d₃₃ values without/with cantilever calibration is revealed. Extrinsic and intrinsic factors are discussed for explanation of these performance differences. These investigations help draw a round picture of domain structures in the relaxor ferroelectric, provide a domain perspective for structure-property relationship clarifying and offer a reference of domain-based structure selection for better material design.