Scanning Transmission Electron Microscopy Images Research Articles

Level set simulation of focused ion beam sputtering of a multilayer substrate.

The evolution of a multilayer sample surface during focused ion beam processing was simulated using the level set method and experimentally studied by milling a silicon dioxide layer covering a crystalline silicon substrate. The simulation took into account the redeposition of atoms simultaneously sputtered from both layers of the sample as well as the influence of backscattered ions on the milling process. Monte Carlo simulations were applied to produce tabulated data on the angular distributions of sputtered atoms and backscattered ions. Two sets of test structures including narrow trenches and rectangular boxes with different aspect ratios were experimentally prepared, and their cross sections were visualized in scanning transmission electron microscopy images. The superimposition of the calculated structure profiles onto the images showed a satisfactory agreement between simulation and experimental results. In the case of boxes that were prepared with an asymmetric cross section, the simulation can accurately predict the depth and shape of the structures, but there is some inaccuracy in reproducing the form of the left sidewall of the structure with a large amount of the redeposited material. To further validate the developed simulation approach and gain a better understanding of the sputtering process, the distribution of oxygen atoms in the redeposited layer derived from the numerical data was compared with the corresponding elemental map acquired by energy-dispersive X-ray microanalysis.

Atomic modulation and phase engineering of MoS2 for boosting N2 reduction

Electrochemical nitrogen reduction reaction (ENRR) has emerged as a potential alternative to the conventional Haber-Bosch process for ammonia production. However, ENRR technology is still restricted by the limited Faradaic efficiency due to the hard-to-break N-N triple bond. Herein, inspired by the biomimetic catalyst, we developed a Fe-modulated MoS2 catalyst (named Fe@MoS2) as an efficient ENRR catalyst. Raman spectra, coupled with the X-ray absorption spectroscopy, demonstrate the introduction of Fe into the MoS2 lattice and achieve partial 2H to 1T phase conversion. The presence of S-vacancies on MoS2 substrates was observed on scanning transmission electron microscopy images. Operando infrared absorption spectroscopy confirms that the constructed catalytic site significantly reduces barriers to nitrogen activation. The synthesized Fe@MoS2, with its superior geometric and electronic structures, exhibits a remarkable Faradaic efficiency of 19.7 ± 5.5% at -0.2 V vs. Reversible Hydrogen Electrode and a high yield rate of 20.2 ± 5.3 μg h-1 mg-1 at -0.8 V vs. Reversible Hydrogen Electrode. Therefore, this work provides a fresh direction for designing novel catalysts, eventually boosting the nitrogen reduction reaction kinetics and accelerating the ENRR application.

Moiré fringe imaging of heterostructures by scanning transmission electron microscopy

A heterostructured crystalline bilayer specimen is known to produce moiré fringes (MFs) in the conventional transmission electron microscopy (TEM). However, the understanding of how these patterns form in scanning transmission electron microscopy (STEM) remains limited. Here, we extended the double-scattering model to establish the imaging theory of MFs in STEM for a bilayer sample and applied this theory to successfully explain both experimental and simulated STEM images of a perovskite PbZrO3/SrTiO3 system. Our findings demonstrated that the wave vectors of electrons exiting from Layer-1 and their relative positions with the atomic columns of Layer-2 should be taken into account. The atomic column misalignment leads to a faster reduction in the intensity of the secondary scattering beam compared to the single scattering beam as the scattering angle increases. Consequently, the intensity distribution of MFs in the bright field (BF)-STEM can be still described as the product of two single atomic images. However, in high angle annular dark field (HAADF)-STEM, it is approximately described as the superposition of the two images. Our work not only fills a knowledge gap of MFs in incoherent imaging, but also emphasizes the importance of the coherent scattering restricted by the real space when analyzing the HAADF-STEM imaging.

Thermodynamics of Ga2O3 Heteroepitaxy and Material Growth Via Metal Organic Chemical Vapor Deposition.

Heteroepitaxy of gallium oxide (Ga2O3) is gaining popularity to address the absence of p-type doping, limited thermal conductivity of Ga2O3 epilayers, and toward realizing high-quality p-n heterojunction. During the growth of β-Ga2O3 on 4H-SiC (0001) substrates using metal-organic chemical vapor deposition, we observed formation of incomplete, misoriented particles when the layer was grown at a temperature between 650 °C and 750 °C. We propose a thermodynamic model for Ga2O3 heteroepitaxy on foreign substrates which shows that the energy cost of growing β-Ga2O3 on 4H-SiC is slightly lower as compared to sapphire substrates, suggesting similar high-temperature growth as sapphire, typically in the range of 850 °C-950 °C, that can be used for the growth of β-Ga2O3 on SiC. A two-step modified growth method was developed where the nucleation layer was grown at 750 °C followed by a buffer layer grown at various temperatures from 920 °C to 950 °C. 2θ-ω scan of X-ray diffraction (XRD) and transmission electron microscope images confirm the β-polymorph of Ga2O3 with dominant peaks in the (-201) direction. The buffer layer grown at 950 °C using a "ramp-growth" technique exhibits root-mean-square surface roughness of 3 nm and full width of half maxima of XRD rocking curve as low as 0.79°, comparable to the most mature β-Ga2O3 heteroepitaxy on sapphire, as predicted by the thermodynamic model. Finally, the interface energy of an average Ga2O3 island grown on 4H-SiC is calculated to be 0.2 J/m2 from the cross-section scanning transmission electron microscope image, following the Wulff-Kaishew theorem of the equilibrium island shape.

Protocrystallinity of Monodispersed Ultra-Small Templated Mesoporous Silica Nanoparticles.

Monodisperse and semi-faceted ultra-small templated mesoporous silica nanoparticles (US-MSNs) of 20-25 nm were synthesized using short-time hydrolysis of tetraethoxysilane (TEOS) at room temperature, followed by a dilution for nucleation quenching. According to dynamic light scattering (DLS), a two-step pH adjustment was necessary for growth termination and colloidal stabilization. The pore size was controlled by cetyltrimethylammonium bromide (CTAB), and a tiny amount of neutral surfactant F127 was added to minimize the coalescence between US-MSNs and to favor the transition towards internal ordering. Flocculation eventually occurred, allowing us to harvest a powder by centrifugation (~60% silica yield after one month). Scanning transmission electron microscopy (STEM) and 3D high-resolution transmission electron microscopy (3D HR-TEM) images revealed that the US-MSNs are partially ordered. The 2D FT transform images provide evidence for the coexistence of four-, five-, and sixfold patterns characterizing an "on-the-edge" crystallization step between amorphous raspberry and hexagonal pore array morphologies, typical of a protocrystalline state. Calcination preserved this state and yielded a powder characterized by packing, developing a hierarchical porosity centered at 3.9 ± 0.2 (internal pores) and 68 ± 7 nm (packing voids) of high potential for support for separation and catalysis.

Black Ultrathin Single-Crystalline Flakes of CuVP2S6 and CuCrP2S6 for Near-Infrared-Driven Photocatalytic Hydrogen Evolution.

The development of new near-infrared-responsive photocatalysts is a fascinating and challenging approach to acquire high photocatalytic hydrogen evolution (PHE) performance. Herein, near-infrared-responsive black CuVP2S6 and CuCrP2S6 flakes, as well as CuInP2S6 flakes, are designed and constructed for PHE. Atom-resolved scanning transmission electron microscopy images and X-ray absorption fine structure evidence the formation of ultrathin single-crystalline sheet-like structure of CuVP2S6 and CuCrP2S6. The synthetic CuVP2S6 and CuCrP2S6, with a narrow bandgap of ≈1.0eV, shows the high light-absorption edge exceeding 1100nm. Moreover, through the femtosecond-resolved transient absorption spectroscopy, CuCrP2S6 displays the efficient charge transfer and long charge lifetime (18318.1ps), which is nearly 3 and 29 times longer than that of CuVP2S6 and CuInP2S6, respectively. In addition, CuCrP2S6, with the appropriate d-band and p-band, is thermodynamically favorable for the H+ adsorption and H2 desorption by contrast with CuVP2S6 and CuInP2S6. As a result, CuCrP2S6 exhibits high PHE rates of 9.12 and 0.66mmol h-1 g-1 under simulated sunlight and near-infrared light irradiation, respectively, far exceeding other layered metal phospho-sulfides. This work offers a distinctive perspective for the development of new near-infrared-responsive photocatalysts.

ZnS@Fe2O3 core–shell nanorod arrays for supercapattery applications; theoretical evaluation of faradic and non-faradic behavior using Dunn’s model

Supercapattery has emerged as an ideal energy storage device that has the features of both batteries and supercapacitors. In this work, ZnS@Fe2O3 core–shell nanorod arrays supported on Ti foil have been prepared by the cost-effective, efficient, and facile two-step hydrothermal method and investigated for high performance supercapattery applications. The X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) confirm the successful synthesis of the material, while the scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images clearly show the successful deposition of the Fe2O3 shell over the ZnS core. Electrochemical characterizations including cyclic voltammetry, galvanostatic charge discharge and electrochemical impedence spectroscopy have been employed to investigate the electroactive nature of the materials. It is found that the ZnS@Fe2O3 exhibits excellent specific capacitance of 681 Fg−1 at 1 Ag−1 current density within the potential window of −0.2 to 0.75 V while demonstrating a significant capacitance retention of 85 % and 95 % coulombic efficiency over 2000 cycles. The contribution of faradic and non-faradic processes during electrochemical reactions is evaluated using Dunn’s model. The diffusion controlled mechanism is greater than the surface controlled mechanism in the synthesized material, which depicts the battery grade nature. Interestingly, the electrode was able to exhibit an excellent energy density of 86 Whkg−1 and a maximum power density of 4232 Wkg−1, which is significantly higher than the previously reported ZnS based and Fe2O3 based composites. A Supercapattery device has been assembled using ZnS@Fe2O3 as anode and reduced grapheme oxide (rGO) as cathode, which demonstrate a specific capacitance of 165 Fg−1 at 1 Ag−1 current density, exhibiting 66 Whkg−1 at power density of 3895 Wkg−1 with excellent retention in specific capacitance and coulombic efficiency at 15 Ag−1 after 3000 cycles.

In2O3-ZnO nanoporous photocatalyst modified with CuOx cocatalyst for enhanced photocatalytic bacterial inactivation and dye degradation

In this study, CuOx surface passivated In2O3 loaded porous ZnO, (CuOx/In2O3(x%)-ZnO)), were synthesized utilizing a solvothermally produced organic–inorganic ZnS(en)0.5 hybrid material. The high-resolution scanning electron microscopy (HR-SEM) and transmission electron microscopy (TEM) images of the CuOx/In2O3(2.5%)-ZnO nanocomposite reveal a macrosheet-shaped morphology comprising nanosized grains. The photocatalytic behavior of all the synthesized CuOx/In2O3(x = 0,1,2.5, and 5%)-ZnO nanocomposites were examined against aqueous dye solutions of orange II, and bisphenol A, E. coli bacteria under one sun illumination. The CuOx/In2O3(2.5%)-ZnO nanocomposite exhibits enhanced photoactivity for cationic dyes (eosin Y) than that for anionic (orange II). The results indicate that cationic dyes undergo photocatalytic degradation, whereas the anionic dyes adsorb on the CuOx/In2O3(2.5%)-ZnO nanocomposite surface, reducing the removal of organic pollutants. The optimal nanocomposites, CuOx/In2O3(2.5%)-ZnO photocatalyst exhibit maximum photodegradation performance of 99%, 94%, 27% for orange II dye, eosin dye, BPA, and 98% for E. coli inactivation within 180 min, respectively. The CuOx/In2O3(2.5%)-ZnO nanocomposite was successfully demonstrated to be an effective photocatalyst and excellent antibacterial agent. Finally, the charge transfer mechanism during photocatalytic organic decomposition and bacterial inactivation was studied.

New Poisson denoising method for pulse-count STEM imaging

With the recent progress in the development of detectors in electron microscopy, it has become possible to directly count the number of electrons per pixel, even with a scintillator-type detector, by incorporating a pulse-counting module. To optimize a denoising method for electron counting imaging, in this study, we propose a Poisson denoising method for atomic-resolution scanning transmission electron microscopy images. Our method is based on the Markov random field model and Bayesian inference, and we can reduce the electron dose by a factor of about 15 times or further below. Moreover, we showed that the method of reconstruction from multiple images without integrating them performs better than that from an integrated image.

Application of the polyhedral template matching method for characterization of 2D atomic resolution electron microscopy images

High-throughput image segmentation of atomic resolution electron microscopy data poses an ongoing challenge for materials characterization. In this paper, we investigate the application of the polyhedral template matching (PTM) method, a technique widely employed for visualizing three-dimensional (3D) atomistic simulations, to the analysis of two-dimensional (2D) atomic resolution electron microscopy images. This technique is complementary with other atomic resolution data reduction techniques, such as the centrosymmetry parameter, that use the measured atomic peak positions as the starting input. Furthermore, since the template matching process also gives a measure of the local rotation, the method can be used to segment images based on local orientation. We begin by presenting a 2D implementation of the PTM method, suitable for atomic resolution images. We then demonstrate the technique's application to atomic resolution scanning transmission electron microscopy images from close-packed metals, providing examples of the analysis of twins and other grain boundaries in FCC gold and martensite phases in 304 L austenitic stainless steel. Finally, we discuss factors, such as positional errors in the image peak locations, that can affect the accuracy and sensitivity of the structural determinations.

Kobellite homologues from the Boliden Au–Cu–(As) deposit, Sweden: jigsaw patterning via nanoscale intergrowths in chessboard structures

Abstract Sulfosalt assemblages in a specimen from the Boliden Au–Cu–(As) deposit in northern Sweden, comprise micrometre to nanometre scale intergrowths of Se-rich izoklakeite and tintinaite with average formulae and calculated homologue number (N) given as: (Cu1.88Fe0.18)2.06(Pb22.92Ag1.47Cd0.01Zn0.01)24.41(Sb13.12Bi8.69)21.8(S50.19Se6.43Te0.12)56.73,N = 3.83, and (Cu1.31Fe0.74)2.05(Pb10.58Ag0.18Cd0.05Zn0.02)10.83(Sb10.2Bi5.23)15.43(S32.22Se2.46)34.7, N = 2.05, respectively. Tintinaite coexists with (Bi, Se)-rich jamesonite. High-angle annular dark field scanning transmission electron microscopy (HAADF STEM) imaging reveals chessboard structures comprising PbS and SnS modules with the number of atoms in the octahedral (M) sites counted as: n1 = 18 and n2 = 8 for tintinaite and n1 = 30 and n2 = 16 for izoklakeite. The homologue number can be calculated using the formula: N = (n1/6)–1 and N = n2/4 for PbS and SnS modules giving NTti = 2 and NIz = 4. A new N = 3 homologue, defined by n = 12 and n = 24 SnS and PbS modules, respectively, is identified as single or double units within areas with intergrowths between kobellite and izoklakeite. HAADF STEM imaging also reveals features attributable to lone electron pair micelles within the Sb-rich kobellite homologues. Atomic-resolution EDS STEM chemical mapping of Pb–Bi–Sb-sulfosalts shows a correlation with crystal structural modularity. The maps also highlight sites in the SnS modules of tintinaite in which Sb > Bi. Coherent nanoscale intergrowths between tintinaite and izoklakeite define jigsaw patterns evolving from chessboard structures and are considered to have formed during co-crystallisation of the two phases. Displacement textures and crosscutting veinlets (a few nm in width) are interpreted as evidence for superimposed syn-metamorphic deformation and are associated with the redistribution of Bi and Se. Imaging and mapping using HAADF STEM techniques is well suited to characterisation of Pb–Sb–Bi-sulfosalt phases, offering largely untapped potential to unravel the evolution of chessboard structures with applications across mineralogy but also extending into allied fields.

Ferroelectric behavior arising from polar topologies in epitaxially strained SrTiO3-δ ultrathin films

In this work, we show that epitaxially strained SrTiO3-δ thin films, grown by ion-beam sputtering onto (001)Nb:SrTiO3 substrates, exhibit a ferroelectric behavior. At the atomic-scale, through high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images, it was possible to identify the presence of polar nanoregions with non-trivial polar topological structures in the SrTiO3-δ film, which are induced through oxygen vacancies. To further confirm the presence of strained regions with a polar structure, Raman spectroscopy and high-resolution X-ray diffraction were employed and it was possible to confirm the presence of a tetragonal structure in the SrTiO3-δ film, with a tetragonality ratio (c/a) of 1.005. Scanning probe microscopy and macroscopic polarization-electric field hysteresis loops show ferroelectric behavior with maximum polarization of ∼1.5 μC/cm2, remnant polarization of ∼0.4 μC/cm2 and coercive field of ∼0.3 MV/cm. This work opens a window for exploring novel polar topological effects in sub-10 nm thin film materials for non-volatile memory application.

Investigation of the thermal decomposition of Pu(IV) oxalate: a transmission electron microscopy study

The degradation of the internal structure of plutonium (IV) oxalate during calcination was investigated with Transmission Electron Microscopy (TEM), electron diffraction, Electron Energy-Loss Spectroscopy (EELS), and 4D Scanning TEM (STEM). TEM lift-outs were prepared from samples that had been calcined at 300°C, 450°C, 650°C and 950°C. The resulting phase at all calcination temperatures was identified as PuO2 with electron diffraction. The grain size range was obtained with high-resolution TEM. In addition, 4D STEM images were analyzed to provide grain size distributions. In the 300°C calcined sample, the grains were <10 nm in diameter, at 650°C, the grains ranged from 10 to 20 nm, and by 950°C, the grains were 95–175 nm across. Using the Kolmogorov-Smirnov (K-S) two sample test, it was shown that morphological measurements obtained from 4D-STEM provided statistically significant distributions to distinguish samples at the different calcination conditions. Using STEM-EELS, carbon was shown to be present in the low temperature calcined samples associated with oxalate but had formed carbon (possibly graphite) deposits in the 950°C calcined sample. This work highlights the new methods of STEM-EELS and 4D-STEM for studying the internal structure of special nuclear materials (SNM).

Oxidation behavior and atomic structural transition of size-selected coalescence-resistant tantalum nanoclusters

Herein a series of size-selected Ta N (N = 147, 309, 561, 923, 1415, 2057, 6525, 10 000, 20 000) clusters are generated using a gas-phase condensation cluster beam source equipped with a lateral time-of-flight mass-selector. Aberration-corrected scanning transmission electron microscopy (AC-STEM) imaging reveals good thermal stability of Ta N clusters in this study. The oxidation-induced amorphization is observed from AC-STEM imaging and further demonstrated through x-ray photoelectron spectroscopy and energy-dispersive spectroscopy. The oxidized Ta predominantly exists in the +5 oxidation state and the maximum spontaneous oxidation depth of the Ta cluster is observed to be 5 nm under prolonged atmosphere exposure. Furthermore, the size-dependent sintering and crystallization processes of oxidized Ta N clusters are observed with an in situ heating technique, and eventually, ordered structures are restored. As the temperature reaches 1300 °C, a fraction of oxidized Ta309 clusters exhibit decahedral and icosahedral structures. However, the five-fold symmetry structures are absent in larger clusters, instead, these clusters exhibit ordered structures resembling those of the crystalline Ta2O5 films. Notably, the sintering and crystallization process occurs at temperatures significantly lower than the melting point of Ta and Ta2O5, and the ordered structures resulting from annealing remain well-preserved after six months of exposure to ambient conditions.

Polar Bloch points in strained ferroelectric films

Topological domain structures have drawn great attention as they have potential applications in future electronic devices. As an important concept linking the quantum and classical magnetism, a magnetic Bloch point, predicted in 1960s but not observed directly so far, is a singular point around which magnetization vectors orient to nearly all directions. Here we show polar Bloch points in tensile-strained ultrathin ferroelectric PbTiO3 films, which are alternatively visualized by phase-field simulations and aberration-corrected scanning transmission electron microscopic imaging. The phase-field simulations indicate local steady-state negative capacitance around the Bloch points. The observation of polar Bloch points and their emergent properties consequently implies novel applications in future integrated circuits and low power electronic devices.

Crystal structures of two new high-pressure oxynitrides with composition SnGe4N4O4, from single-crystal electron diffraction.

SnGe4N4O4 was synthesized at high pressure (16 and 20 GPa) and high temperature (1200 and 1500°C) in a large-volume press. Powder X-ray diffraction experiments using synchrotron radiation indicate that the derived samples are mixtures of known and unknown phases. However, the powder X-ray diffraction patterns are not sufficient for structural characterization. Transmission electron microscopy studies reveal crystals of several hundreds of nanometres in size with different chemical composition. Among them, crystals of a previously unknown phase with stoichiometry SnGe4N4O4 were detected and investigated using automated diffraction tomography (ADT), a three-dimensional electron diffraction method. Via ADT, the crystal structure could be determined from single nanocrystals in space group P63mc, exhibiting a nolanite-type structure. This was confirmed by density functional theory calculations and atomic resolution scanning transmission electron microscopy images. In one of the syntheses runs a rhombohedral 6R polytype of SnGe4N4O4 could be found together with the nolanite-type SnGe4N4O4. The structure of this polymorph was solved as well using ADT.

Bayesian inference of atomic column positions in scanning transmission electron microscopy images

Abstract Atomic-resolution scanning transmission electron microscopy combined with 2D Gaussian fitting enables the accurate and precise identification of atomic column positions within a few picometers. The measurement performance significantly depends on the signal-to-noise ratio of the atomic columns. In areas with low signal-to-noise ratios, such as near surfaces, the measurement performance was lower than that of the bulk. However, previous studies evaluated the accuracy and precision only in bulk areas, underscoring the need for a method that quantitatively evaluates the accuracy and precision of each atomic column position with various signal-to-noise ratios. This study introduced Bayesian inference to assess the accuracy and precision of determining individual atomic column positions under various signals. We applied this method to simulated and experimental images and demonstrated its effectiveness in identifying statistically significant displacements, particularly near surfaces with signal degradation. The use of vector maps and kernel density estimate plots obtained from Bayesian inference provided a probabilistic understanding of the atom displacement. Therefore, this study highlighted the potential benefits of Bayesian inference in high-resolution imaging to reveal material properties.

DFT-Assisted Investigation of the Electric Field and Charge Density Distribution of Pristine and Defective 2D WSe2 by Differential Phase Contrast Imaging.

Most properties of solid materials are defined by their internal electric field and charge density distributions which so far are difficult to measure with high spatial resolution. Especially for 2D materials, the atomic electric fields influence the optoelectronic properties. In this study, the atomic-scale electric field and charge density distribution of WSe2 bi- and trilayers are revealed using an emerging microscopy technique, differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). For pristine material, a higher positive charge density located at the selenium atomic columns compared to the tungsten atomic columns is obtained and tentatively explained by a coherent scattering effect. Furthermore, the change in the electric field distribution induced by a missing selenium atomic column is investigated. A characteristic electric field distribution in the vicinity of the defect with locally reduced magnitudes compared to the pristine lattice is observed. This effect is accompanied by a considerable inward relaxation of the surrounding lattice, which according to first principles DFT calculation is fully compatible with a missing column of Se atoms. This shows that DPC imaging, as an electric field sensitive technique, provides additional and remarkable information to the otherwise only structural analysis obtained with conventional STEM imaging.

An advanced fast method for the evaluation of multiple immunolabelling using gold nanoparticles based on low-energy STEM

We present a powerful method for the simultaneous detection of Au nanoparticles located on both sides of ultrathin sections. The method employs a high-resolution scanning electron microscope (HRSEM) operating in scanning transmission electron microscopy (STEM) mode in combination with the detection of backscattered electrons (BSE). The images are recorded simultaneously during STEM and BSE imaging at the precisely selected accelerating voltage. Under proper imaging conditions, the positions of Au nanoparticles on the top or bottom sides can be clearly differentiated, hence showing this method to be suitable for multiple immunolabelling using Au nanoparticles (NPs) as markers. The difference between the upper and lower Au NPs is so large that it is possible to apply common software tools (such as ImageJ) to enable their automatic differentiation. The effects of the section thickness, detector settings and accelerating voltage on the resulting image are shown. Our experimental results correspond to the results modelled in silico by Monte Carlo (MC) simulations.

Disruption of polar order in lead zirconate titanate by composition-modulated artificial superlattice

Lead zirconate titanate (Pb (Zrx, Ti1−x)O3: PZT) is a well-known ferroelectric compound, in which long-range polar order is usually developed. In the present study, it was clarified by distortion-corrected atomic-scale scanning transmission electron microscopy imaging that long-range polar order is disrupted in PZT by utilizing composition-modulated superlattice. Shape of unit cell was unusual both in the Pb(Zr0.65Ti0.35)O3 (PZT65) and Pb(Zr0.30Ti0.70)O3 (PZT30) layers, which was due to mutual in-plane lattice constraint. By taking account of this, first-principles calculations clarified that multiple directions can be energetically favorable for lead-ion displacement, which explains a reason why long-range polar order was disrupted.