Understanding the microscopic origin of the excellent electromechanical response in relaxed ferroelectrics requires an understanding of not only the atomic-scale formation of polar nanodomains (PNDs), but also the arrangement of PNDs over longer distances and the rules of stimulated responses.
In view of this, using X-ray coherent nanodiffraction, Yue Cao and Hao Zheng of Argonne National Laboratory and Lane W. Martin of the University of California, Berkeley, demonstrated that PND is staggered and self-assembled into a unidirectional mesoscopic structure in a relaxed ferroelectric 0.68PbMg1/3Nb2/3O3-0.32PbTiO3 (PMN-0.32PT), which they call a polar laminate. They revealed the highly heterogeneous electric field-driven responses of intra- and inter-layer PNDs and established their correlation with local strain and PND wall properties. This observation highlights the critical role of hierarchical lattice structure in macroscopic material properties and provides guidelines for understanding and designing relaxation bodies as well as various quantum and functional materials. The research results were published in the latest issue of Science under the title "Heterogeneous field response of hierarchical polar laminates in relaxor ferroelectrics". Hao Zheng is also the first author of this article.
【PMN-0.32PT film made of monoclinic crystal PND】PMN-0.32PT belongs to a large family of typical relaxed ferroelectric (1-x)PbMg2/3Nb1/3O3-(x)PbTiO3 (PMN-xPT) and is located near MPB. The authors synthesized PMN-0.32PT films on a SmScO3 (SSO) (110)o substrate ("o" stands for orthorhombic line index) with a bottom electrode of 25 nm Ba0.5Sr0.5RuO3 (BSRO). A second 25nm BSRO layer was then grown in situ on top of the PMN-0.32PT and a circular capacitor structure was fabricated as the top electrode for the electric field drive study (Figure 1A). The average lattice structure of the BSRO/PMN-0.32PT/BSRO/SSO(110)o heterostructure is shown in Figure 1B,C. The diffuse scattering of PMN-0.32PT near the 002pc-Bragg peak is essentially isotropic in the film plane (Figure 1C). The line profiles of the diffuse scattering patterns along the H and K directions are Lorentz lines with a full width at half height (FWHM) of 0.075 nm−1 (Figure 1D) and a correlated length of ~13.4 nm, which can be used as the characteristic size of the PND in the film plane.
Figure 1. PMN-0.32PT thin-film device and experimental setup. [PND self-assembly into a polar laminate] On the length scale of the device (50 μm diameter), the PND is tilted along the finite lattice of [100]pc or [010]pc at 90° (Figures 2A to C), which the authors named Δα or Δβ, respectively. THE AUTHORS SHOW A TYPICAL DISTRIBUTION OF ΔΑ AND ΔΒ EXTRACTED FROM RASTER SCANS WITH A 5 ΜM × 5 ΜM FIELD OF VIEW (FIGURES 2A TO C). The spatial distribution of these parameters exhibits three characteristics that are different from those of standard ferroelectrics: (1) the spatial distribution of c-axis strain is not directly related to the spatial distribution of Δα or Δβ. (2) There is indeed a spatial correlation between the c-axis strain and the relative change of the projected lattice tilt ν=(Δβ,Δα). PNDs self-organize and form mesoscale lattice sequences that are almost parallel to <110>pc. THIS LATTICE ORDER IS UNIDIRECTIONAL, WHICH IS BEST SEEN FROM THE STRIP DISTRIBUTION OF ΔΑ (FIGURE 2B) AND ΔΒ (FIGURE 2C).
Figure 2. Further statistical analysis of the mesoscopic distribution of lattice distortion on the projected lattice tilt ν shows that the polar laminate is derived from the self-organization of PND. The ν distribution from the same field of view (as shown in Figure 2B) is shown in the figure (Figure 3A). It is important to note that most of the lattice deviates from the < 100>pc and instead slopes along the <110>pc (Figure 3C). The authors refer to the unidirectional arrangement of PNDs along <110>pc over a contiguous region as a "polar laminate" (Figure 3D). First, each laminate consists of two types of Mc PNDs that are staggered in a 90° domain wall instead of the more common herringbone domain type. Second, hierarchically, these polar laminates diffuse in PMN-0.32PT and serve as the basic building blocks of the entire material. The two-dimensional (2D) fast Fourier transform (FFT) of the laminate distribution has a characteristic ordered wave vector centered on Q = (0.012, 0.014,0) nm−1 (Figure 3E), corresponding to a length scale of approximately 350 nm for the planar feature of the polar laminate sample. After classification, the authors identified six types of interlayer boundaries. The authors provide histograms of these boundaries from the previously used field of view (Figure 3A-F). The discovery of this polar laminate reveals different types of hierarchical spatial heterogeneity in the relaxer and provides important insights into the interactions between PNDs.
Figure 3. Unidirectional Polar Laminates and Their Relationship with PND【Highly Heterogeneous Electric Field Response of PND】The discovery of polar laminates provides a basis for revealing and understanding the spatial heterogeneous field response of PMN-0.32PT. To do this, the authors performed the operation CND in the following form of a DC electric field sequence: 0 kV⋅cm−1→+540 kV⋅cm−1→−540 kV⋅cm−1→0 kV·cm−1. The authors show the distribution of sum ν = (Δβ, Δα) in the field of view of 2.5 μm × 2.5 μm (Figures 4, A1 and B1). A detailed examination of lattice tilt evolution during field cycling reveals a highly heterogeneous field response. The authors performed one-dimensional strain cleavage and projected lattice tilt from the data (black line, Figure 4, A1 and B1) and stacked them as a function of the field loop into a "waterfall" plot. The strain field response is relatively uniform (Figure 4A2), while the lattice tilt varies unevenly (Figure 4B2). Specifically, some areas of the material remain unchanged throughout the cycle, while others show a strong response to the field. They labeled the two types of regions as fixed (P) and responsive (R) (Figure 4B2).
Figure 4. Evolution of Electric-Driven Polar Laminates [Establishing a Local Connection Between Strain and Electromechanical Response] The authors integrated the absolute variation in the tilt of the projected lattice over the entire field period (Figure 4E), with red and blue corresponding to the regions with the strongest and weakest responses, respectively. They also calculated the absolute value of the strain distribution (Figure 4F) and found that there was a clear negative correlation between the lattice tilt caused by the dynamic field and the static strain distribution, with the least strain in the region where the lattice tilt change was most pronounced. The observed negative correlation demonstrates the spatial heterogeneity of electromechanical responses and reveals the origin of relaxation behavior. 【Conclusions and Opinions】The in-situ CND study revealed the existence of layered polar laminates in PMN-0.32PT and their role in the field-induced relaxation response. Hierarchical self-organization of twin monoclinic PNDs separated by free 90° domain walls of a polar laminate structure. The boundary between the laminated structures consists of alternating 90° and 180° domain walls, resulting in the divergence of the maximum and minimum values of the strain distribution and the local lattice tilt. In-situ nanodiffraction studies further establish a direct relationship between the heterogeneous field response and the detailed structure of the polar laminate. The area inside the laminate structure is most active, while the interstory boundary is spatially fixed due to the presence of a 180° PND wall. The discovery of polar laminates underscores the collaboration of PNDs in facilitating electromechanical responses and establishes a link between nanoscale lattice heterogeneity and macroscopic material properties. Therefore, this observation provides guidelines for the design and optimization of future relaxers. Specifically, the authors show that the size of the polar laminate determines the number and density of intra- and inter-laminar PND walls, which are easier to fix and less responsive to electric fields. Therefore, the macroscopic electric field response must be tailored through strain and defect engineering. For example, the location and density of the high-strain region can be locally adjusted directly to the relaxation material or the underlying substrate by ion implantation or electron beam irradiation. The method developed here, including in-situ CND manipulation and correlation analysis, can be further applied to a wide range of quantum and functional materials. This observation should arouse interest in further understanding the role of spatial inhomogeneity in a wide range of materials.
--Testing Services--
Source: Frontiers of Polymer Science
Disclaimer: It only represents the author's personal point of view, the author's level is limited, if there is anything unscientific, please leave a message below to correct!