An Unconventional Transient Phase with Cycloidal Order of Polarization in Energy‐Storage Antiferroelectric PbZrO3

Antiferroelectric‐based dielectric capacitors are receiving tremendous attention for their outstanding energy‐storage performance and extraordinary flexibility in collecting pulsed powers. Nevertheless, the in situ atomic‐scale structural‐evolution pathway, inherently coupling to the energy storage process, has not been elucidated for the ultimate mechanistic understanding so far. Here, time‐ and atomic‐resolution structural phase evolution in antiferroelectric PbZrO3 during storage of energy from the electron‐beam illumination is reported. By employing state‐of‐the‐art negative‐spherical‐aberration imaging technique, the quantitative transmission electron microscopy study presented herein clarifies that the hierarchical evolution of polar oxygen octahedra associated with the unit‐cell volume change and polarization rotation accounts for the stepwise antiferroelectric‐to‐ferroelectric phase transition. In particular, an unconventional ferroelectric category—the ferrodistortive phase characteristic of a unique cycloidal polarization order—is established during the dynamic structure investigation. Through clarifying the atomic‐scale phase transformation pathway, findings of this work unveil a new territory to explore novel ferrodistortive phases in energy‐storage materials with the nonpolar‐to‐polar phase transitions.

Antiferroelectric-based dielectric capacitors are receiving tremendous attention for their outstanding energy-storage performance and extraordinary flexibility in collecting pulsed powers. Nevertheless, the in situ atomic-scale structuralevolution pathway, inherently coupling to the energy storage process, has not been elucidated for the ultimate mechanistic understanding so far. Here, timeand atomic-resolution structural phase evolution in anti ferroelectric PbZrO 3 during storage of energy from the electron-beam illumination is reported. By employing state-of-the-art negative-spherical-aberration imaging technique, the quantitative transmission electron microscopy study presented herein clarifies that the hierarchical evolution of polar oxygen octahedra associated with the unit-cell volume change and polarization rotation accounts for the stepwise antiferroelectric-to-ferroelectric phase transition. In particular, an unconventional ferroelectric category-the ferrodistortive phase characteristic of a unique cycloidal polarization order-is established during the dynamic structure investigation. Through clarifying the atomic-scale phase transformation pathway, findings of this work unveil a new territory to explore novel ferrodistortive phases in energy-storage materials with the nonpolar-to-polar phase transitions.
critical components for many electrical power systems, e.g., portable/wearable electronics and collection of fluctuating energy sources. With adoption of different design strategies, e.g., polymorphic nanodomain, [3] chemical doping [4] and structure sandwiching, [5] the recoverable energy density has been improved from ≈5 to over 150 J cm −3 in the past decade. [5,6] Among the dielectrics, antiferroelectric-based capacitors serve as an important group of energy-storage materials, where the energy density stored through the antiferroelectric-ferroelectric (AFE-FE) phase transition can be expressed as U e = E P d ∫ with respect to the applied electric field E and the induced polarization P (Figure 1a). [7] Nevertheless, with regard to the concrete structural evolution, [8,9] the ultimate mechanistic understanding has never been elucidated so far from experiments. This seriously hinders the development of new materials for energy storage and conversion. Exploring the emergence of a net polarization from the nonpolar matrix plays a key role in understanding the energystorage process. Compared with other characterization techniques, in situ transmission electron microscopy (TEM) holds the promise of exposing the atomic-scale structural information. However, such a dynamic study is also challenged by a number of practical difficulties. i) A strong electric field is required to activate the phase transition, which is up to ≈220 kV cm −1 for pure PbZrO 3 . [10] Being close to the strength of dielectric breakdown, the field may directly destroy the specimen. ii) It has been reported by in situ selected-area electron diffraction (SAED) and X-ray diffraction studies that the AFE-FE transition completes instantly at the critical switching field. [11][12][13] This implies that possible intermediate phases are simply concealed during the transition process. iii) Nucleation of the FE phase, reverse piezoelectric effect and domain reorientation [14] under electric field set obstacles to acquire atomically resolved structural data. iv) To accurately analyze the structural change, tracking the evolution of intricate structural order parameters, e.g., the cationic displacement order and antiferrodistortive (AFD) oxygen octahedra, [9,15,16] poses a high demand on the detection technique and quality of the collected data.
As a prototypical energy-storage material, PbZrO 3 undergoes an AFE-paraelectric (PE) phase transition at T C ≈ 506 K, [17] around which an FE rhomhohedral (FE R ) phase appears in a narrow (≈20 K) temperature window. [18][19][20] With small amount of chemical doping, additional structural phases can be introduced into the phase diagram, e.g., AFE tetragonal phase in PbZr 1−x Ti x O 3 (PZT, x = 0.03) and (Pb 1−y Sr y )ZrO 3 (0 < y < 0.27). [21,22] The existence of FE monoclinic (FE M ) phases in the phase diagram of PZT (0 ≤ x ≤ 1) further complicates the phase constituents of PbZrO 3 near the transition temperature. [23][24][25] As T C is approached from the PE side, the PbZrO 3 also exhibits complex structural features, e.g., an incipient FE state arising from competition of polar clusters with elastic anomalies, [26] and covalent bonding of disordered Pb with neighboring oxygen. [27,28] The complexity of structural polymorphs highlights the necessity of clarifying the phase-change route for understanding the energy-storage process.
Here, we employ the illumination electron beam, as an external driving force, [29][30][31] to consecutively excite and characterize the phase transitions of PbZrO 3 crystal in an aberration-corrected TEM. By using the negative spherical-aberration imaging (NCSI) technique, [32,33] we simultaneously resolve the evolution of oxygen octahedra and cationic displacement order at seconds-level time and atomic resolution. Our simulation-based quantitative study reveals that the AFD-ferrodistortive (FD) transition of oxygen octahedra breaks the spatial inversion symmetry, and creates a novel cycloidal polarization order in the "AFE" orthorhombic lattice. Associated with successive volume change and polarization rotation, the FE-FD phase further transforms to a FE M phase and then to the FE R phase. Our time-and atomic-resolution TEM study provides a novel insight to understand the phase-transition pathway in PbZrO 3 -based energy-storage materials.
The AFE orthorhombic phase of PbZrO 3 has lattice parameters of a O = √2a p , b O = 2√2a p , and c O = 2c p (a p , b p , and c p are pseudocubic cell parameters). [34] Apart from the characteristic antiparallel Pb displacements in pairs along the   (Figure 2a). Referring to the oxygen atoms locating at the neutral sites (red solid lines), horizontal chains of oxygen atoms displacing along the y direction clearly manifest the AFD order of the AFE phase. While in the intermediate phase, the oxygen atoms originally locating at the neutral sites also exhibit buckling behaviors on every other row. Analogously, vertical chains of oxygen atoms displacing along the x direction also show distinct behaviors between these two phases. Nevertheless, the characteristic antiparallel Pb displacements are maintained throughout the entire region and their unit-cell sizes appear to be the same.
Specifically, the displacement behaviors of oxygen are indexed by symbols of +, −, and 0 along the orthogonal x/[100] O and y/[010] O directions. Along the y direction, it is seen that the displacement sequences are changed from (+, 0, −, 0) and (−, 0, +, 0) in the AFE phase to (+, 0, −, +) and (−, 0, +, −) in the intermediate phase, which give rise to the FD y component. At the orthorhombic unit-cell scale, the net displacement of oxygen is separately created along the odd-and even-column (Oo and Oe) atoms, but the alternation in direction cancels each other out (y-direction black arrows in Figure 2a). Along the x direction, the alteration of (−, 0, +, 0) in the AFE phase to (−, 0, +, +) in the intermediate phase results in an overall net displacement of oxygen atoms, which gives rise to the FD x component. This indicates a clear AFD-FD transition of oxygen octahedra during the phase transition and a net polarization is expected to develop along this direction in the intermediate phase.
Based on the 2D Gaussian fitting to intensity peaks of oxygen columns, the displacement behavior of oxygen in image #7 is calculated and mapped over an area of ≈9 × 9 nm 2 ( Figure S1, Supporting information). Along the x direction, it is seen that the FD x component prevails but mixes with the AFD x component (Figure 2b). Meanwhile, a reversal of net oxygen displacement seems to occur in the upper-right corner region without destroying the antiparallel Pb order. Along the y direction, a complex texturing of the FD y with the AFD y component is also discernible from regions marked by white solid lines (Figure 2c). Comparison of the x-and y-component maps suggests that the AFD x -FD x transition initiates the AFE-FE phase transition. Furthermore, it is noticed that the net displacements of oxygen may also occur along the y direction inside the intermediate phase ( Figure S2, Supporting information).
To quantify structural details of the intermediate phase, iterative image simulations associated with comparison to the experimental image were performed on a local region of image #7 with a uniform FD x and FD y distribution (Figure 3a,b). Relative to the centrosymmetric atomic sites in the cubic phase (see the Experimental Section), the atomic displacements in the experimental image are extracted by averaging along x and plotted along the y direction, and are taken as targets for the image simulation. It is seen that the antiparallel displacement of Pb atoms, with a magnitude of ≈25 pm, is well retained along the x direction, and the small displacement along the y direction is well within the measurement error (Figure 3c,d). With reservation of antiparallel Zr displacement in pairs along the x direction, the displacement along the y direction is increased from 1 to ≈8 pm (Figure 3e,f).
Pertinent to the AFE-FE transition, the critical atomic displacements occur to the oxygen atoms. Compared with the AFD x component, every other two rows of oxygen atoms, originally locating at the neutral positions, clearly displace toward the positive the x direction, e.g., the Oe-x atoms (Figure 3g  the atoms responsible for the FD order exhibit an opposite displacement feature along the y direction ( Figure S4, Supporting information).
With respect to the AFE-AFD phase, an ideal unit cell of the FD phase is illustrated along the [001] O direction, where the FD oxygen displacements are highlighted by blue arrows (Figure 4a). In terms of the displacements of Pb, Zr, and O atoms, the spontaneous polarization (P S ) of the FD phase is calculated along the x and y directions based on a sliding unit cell. [15] It is seen that both P SX and P SY exhibit sinusoidal wave profiles and their mean values are 〈P SX 〉 = −2.8 µC cm −2 and 〈P SY 〉 ≈ 0 (Figure 4b and Experimental Section). This demonstrates that breaking of spatial inversion symmetry by the AFD-FD transition allows emergence of P S in the intermediate phase. Specifically, it is found that tails of the 2D polarization vectors, composed of the fitted sinusoidal profiles, can be nicely approximated by a curtate cycloid, which has a periodicity of 4b O along the y direction (Figure 4c; Figure S5, Supporting  The yellow arrows and dashed rectangles mark the antiparallel Pb displacements and the unit cell, respectively. c-h) Atomic displacements of Pb, Zr, and Oe (even-column oxygen) of the FE-FD phase, plotted as a function of distance along the y direction (solid squares), and compared with that of the AFE-AFD phase (empty circles), respectively. The Oo (odd-column oxygen) displacement is presented in Figure S4 of the Supporting Information. The pink solid lines in (g,h) highlight the FD oxygen displacements against the originally centrosymmetric positions (cyan solid lines). Information). When structural defects appear, e.g., the translational boundaries, [35,36] the commensurate relation of polarization with lattice will be broken in periodicity.
With further electron-beam irradiation, the FE-FD phase transforms completely into the FE pseudocubic phase, in which the oxygen octahedra are free of tilting or rotation (Figure 4d). The atomically resolved TEM image (#9) shows that both O-Zr/O-O and O-Pb-O columns form zigzag chains along the b p axis. Based on the available imaging conditions, our quantitative image simulation reveals that the FE phase adopts a monoclinic symmetry. Referring to center of the unit cell, the Zr atom and oxygen octahedron displace opposite to each other by 7.9 and −12.1 pm along the a p direction. Meanwhile, the Zr atom shift by ≈7 pm from the oxygen octahedral center along the b p direction. Different from the monoclinic PbZr 1−x Ti x O 3 (x ≈ 0.5), [23] the monoclinic PbZrO 3 resembles the rhombohedral BaTiO 3 [37] in structure and has a polarization of P SX = 31.1 µC cm −2 and P SY = 5.8 µC cm −2 ( Figure S6, Supporting information). The net polarization P S = 31.7 µC cm −2 is about half of the FE R phase (55 µC cm −2 ) of PbZrO 3 obtained by firstprinciples calculations. [38] Its rotatable polarization orientation is illustrated in Figure S7 of the Supporting information.
In the ordinary FE phase zone (Figure 1c-e), we have observed the increase of lattice parameters and expansion of unit-cell volume at t > 60 s. The atomic-resolution TEM images (#13 and #14 in Figure S8 in the Supporting Information) indicate that this is ascribed to a first-order FE M -FE R phase transition. [39] In the virgin FE state of PbZrO 3 , the FE R phase with a larger volume than the coexisting FE M phase at nanoscale further supports the transition tendency ( Figure S9, Supporting Information). These results therefore conclude a hierarchical evolution of cationic and oxygen octahedral polarity in PbZrO 3 (Figure 5a-d). It is noticed that the time-dependent change of volume and polarization, including emergence, enhancement and rotation of P S , [40] well corresponds to the macroscopic change of polarization and strain measured under application of electric field ( Figure S10, Supporting information).
By combining the ground-state energy of different structural phases [41] with our experimental observations, it is interesting to note that the high-energy-state monoclinic phase appears prior to the low-energy-state rhombohedral phase (Figure 5e). Nevertheless, such a phase-transition route nicely follows a monotonic increase of the polarization, where the P S ranges from ≈38 to 55 µC cm −2 for the FE R phase. [38,42] This implies that the energy is stored in a very complicated manner. Referring to the AFE orthorhombic phase, the 0.04-0.21 eV energy gap with the FE M and FE R phase indicates that about 10-57 J cm −3 is stored during the phase transition, which well agrees with the first-principles calculated value of ≈19 J cm −3 at 900 kV cm −1 in PbZrO 3 . [4] Clearly, the transfer and storage of electron-beam energy is realized through the complex electron-specimen interactions and the excited phase transitions. [29] Regarding the driving force for the dynamic transition, the following experimental facts indicate that this is governed by the charging effect, rather than the heating effect. i) As frequently seen in our experiments, the charging effect leads to a random motion of the specimen. As a function of irradiation time, the unit-cell volume of AFE PbZrO 3 continuously decreases ( Figure S11, Supporting Information). This is opposite to the heating effect that leads to expansion of the unit-cell volume. [43] ii) On being heated to ≈T C , the characteristic Pb displacements along [100] O direction are reduced to ≈17 pm. However, such a reduction in magnitude was not observed in the AFE-AFD and FE-FD phase of , and tetragonal (tetra) phases calculated by using different functionals, [41] i.e., the Ceperley-Alder-Perdew-Zunger (CA-PZ), Perdew-Wang (PW), and Perdew-Burke-Ernzerhoff (PBE), respectively. The phase-transition pathway (orange, green, and blue) and the monotonic increase of polarization (red) are denoted by dashed lines with arrows. PbZrO 3 . In addition, a reversed evolution sequence indicates that the AFE phase of PbZrO 3 stems from a "commensurate" FE-FD phase, rather than an "incommensurate" phase. [44] This is also supported by observation of modulated phases near the FE-AFE phase boundary in Sm-doped BiFeO 3 . [45] In summary, our time-and atomic-resolution quantitative electron microscopy study provides an unprecedented insight to comprehend the AFE-FE phase transitions in energystorage PbZrO 3 and derived compounds. [14] More intriguingly, our results establish an unconventional FE category-the FD phase, which is characteristic of a cycloidal polarization order and is distinct from the ordinary FEs and ZnSnO 3 -like oxides. [46,47] Analogous to various noncollinear spin structures in magnets, [48] a noncollinear polarization order was reported for the first time in the unconventional FE materials. Our findings offer a plethora of opportunities to explore novel polarization orders in many different kinds of dielectric materials. [49] It is also believed that our results may boost the study of energystorage nonpolar materials at multiple scales in the future.

Experimental Section
Sample Preparation: The PbZrO 3 single crystals were grown by flux method with the PbO-B 2 O 3 mixture (soaking at 1050 K) used as a solvent. Details about the cooling procedures and removal of the residuals were presented elsewhere. [15] The lamella specimens were prepared using an FEI Helios Nanolab 400s focused ion beam system. To remove the contamination and the damaged layers, plasma cleaning and NanoMill Model 1040 system operated at 500 V were used to clean and mill the lamella samples. The lamella samples were heated above T C and then cooled at ≈9 K min −1 to recover the AFE orthorhombic phase from the FE phase at the thin edges. [50,51] Electron Microscopy Imaging Experiments: The diffraction contrast analysis and SAED experiments were carried out on an FEI Tecnai F20 microscope. The atomic resolution TEM study was performed on an FEI Titan 80-300 microscope, which is equipped with a Cs corrector for the objective lens and is operated at an accelerating voltage of 300 kV. The available point resolution was better than 80 pm and a dose rate of the electron beam was ≈1.3 × 10 6 e nm −2 s −1 . A 2k × 2k Gatan UltraScan 1000 CCD camera was used for the image acquisition and each frame exposure time was 0.8 s. It is noted that the energy transferred from the electron beam to the atom is inversely proportional to the atomic number. [52] After the 60 s irradiation, the lattice parameters were found to increase again with time. Apart from the FEM-FER transition, oxygen vacancies were also found in some local areas of the atomic-resolution images.
Image and Polarization Quantification: After filtering the image in a proper way, [32] quantitative measurements of atomic column positions were carried out by fitting the column intensities with 2D Gaussian peaks on the basis of maximum likelihood estimation. [53] Structure modeling, high-resolution image simulation and SAED simulation were carried out using CrystalKit-MacTempas software package. The imaging parameters used in image simulation are C S = −12 µm, A1 = 2.5 nm, A2 = 30 nm, and B2 = 30 nm. With the structural models that lead to the best matching of the simulated images with the experimental ones, the polarization is calculated in terms of the formula where δ i is atomic displacement with respect to the ideal position in the cubic phase and * Z i is the effective charge for the element. The Born charges [41] are Z* Pb = 3.56, Z* Zr = 4.91, and Z* O = −2.82 for the FD phase and Z* Pb = 3.73, Z* Zr = 4.71, and Z* O = −2.81 for the monoclinic phase.
Definition of Lattice Coordinate Origin: Considering the fact that most atomic columns in the FE-FD phase have displacements with respect to their ideal positions in the cubic phase, it is not wise to measure the relative displacements between different column types from the experimental image. Since the antiparallel Pb atoms, with equal magnitudes, undergo the identical shift behaviors in the AFD and FD phases (Figure 2a), the centrosymmetric lattice origin is defined as follows: 1) With the calculated mean lattice parameter, a O , the displacements of Pb along the [100] O direction is averaged with respect to the image coordinate origin. 2) The obtained Pb-displacement profile is linearly fitted and subtracted to fulfill the equal but opposite Pb displacements with respect to their ideal positions in the cubic phase. The linear background is taken as a reference for quantifying the net displacements of Zr and oxygen columns from the experimental image. Similar method is applied to quantify the atom-column displacements along the [010] O direction. For the FE monoclinic phase (image #9), the relative atom-column displacements are calculated by taking the Pb and oxygen columns as references. [53]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.