Stress-induced cubic-to-hexagonal phase transformation in perovskite

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Stress-induced cubic-to-hexagonal phase transformation in perovskite nano thin films Shi-Gu Cao, Yunsong Li, Hong-Hui Wu, Jie Wang, Baoling Huang, and Tong-Yi Zhang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02570 • Publication Date (Web): 26 Jul 2017 Downloaded from http://pubs.acs.org on July 27, 2017

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Stress-induced cubic-to-hexagonal phase transformation in perovskite nano thin films Shi-Gu Cao1, 2, 4, 5, Yunsong Li2, Hong-Hui Wu2, Jie Wang3, Baoling Huang2, and Tong-Yi Zhang,1 1. Shanghai University Materials Genome Institute and Shanghai Materials Genome Institute, Shanghai University, 99 Shangda Road, Shanghai 200444, China 2. Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China 3. Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, 38 Zheda Road, Hangzhou 310007, China 4. Advanced Manufacturing Laboratory, Hong Kong General Technology Corporation Co. Ltd., Hong Kong SAR, China 5. Applied Mechanics Laboratory, Shenzhen Inequation Technology Co. Ltd., Shenzhen, China

Abstract The strong coupling between crystal structure and mechanical deformation can stabilize lowsymmetry phases from high-symmetry phases or induce novel phase transformation in oxide thin films. Stress-induced structural phase transformation in oxide thin films has drawn more and more attention due to its significant influence on the functionalities of the materials. Here, we discovered experimentally a novel stress-induced cubic-to-hexagonal phase transformation in the perovskite nano thin films of barium titanate (BaTiO3) with a special thermomechanical treatment (TMT), where BaTiO3 nano thin films under various stresses are annealed at temperature of 575 °C. Both high resolution transmission electron microscopy and Raman spectroscopy show a higher density of hexagonal phase in the perovskite thin film under higher tensile stress. Both X-ray photoelectron spectroscopy and electron energy loss spectroscopy does not detect any change in the valance state of Ti atoms, thereby excluding the mechanism of

Corresponding author: [email protected], [email protected]

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oxygen vacancy induced cubic-to-hexagonal (c-to-h) phase transformation. First-principles calculations show that the c-to-h phase transformation can be completed by lattice shear at elevated temperature, which is consistent with the experimental observation. The applied bending plus the residual tensile stress produces shear stress in the nano thin film. The thermal energy at the elevated temperature assists the shear stress to overcome the energy barriers during the c-to-h phase transformation. The stress-induced phase transformation in perovskite nano thin films with TMT provides materials scientists and engineers a novel approach to tailor nano/microstructures and properties of ferroelectric materials.

Keywords: perovskite, ferroelectric thin film, stress induced phase transition, cubic to hexagonal phase transformation, lattice shear

Introduction The mechanical stress may lead to structural phase transition in crystalline materials due to the strong coupling between crystal structure and mechanical deformation, which provides a paradigm to induce novel phase transformations and thus tune the functionalities of the materials by mechanical ways. The stress-induced phase transformation in turn results in the mechanical deformation of unit cells and/or the volume change of materials. For example, the volume expansions of 4% and 3% are found when the tetragonal-to-monoclinic and cubic-to-hexagonal phase transformations take place in ZrO2 and BaTiO3 (BTO), respectively,1,2 which hints thermodynamically that applying tensile stress may cause cubic-to-hexagonal phase transition in BTO. Solid-to-solid phase transitions3,4,5,6,7,8 are related to the lattice deformation and controlled by the driving force and the energy barrier between different phases2, 9. Shear is a major mode of lattice deformation, which is executed by fault/dislocation motion10. Partial dislocation motion may cause twinning in fcc crystals and the phase transformation from face centered cubic (fcc) phase to hexagonal close packed (hcp) phase.11,12 Thus, in addition to tensile stress, shear stress may play an important role in solid-to-solid phase transformation. As a typical perovskite crystalline material, BTO exhibits different structural phases at different temperature seven in the absence of applied stress. At room temperature, BTO shows a stable tetragonal phase (t-phase), while above 120 °C it transforms to the cubic phase (c-phase) (Figure 1a).13 In the c- and t-phases, Ba-O (111) planes follow ABCABC stacking sequence, and 2 ACS Paragon Plus Environment

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Ti (111) planes follow CABCAB sequence (Figure S1a). Hexagonal phase(h-phase) BTO exists at temperatures higher than 1432°C14, which belongs to the P63/mmc space group and has been extensively investigated since 1940s.14,15,16,17,18,19,20,21,22 Compared to c-phase, the Ba-O (111) planes in h-phase follow ABCACB stacking sequence, while Ti (111) planes follow CABBAC sequence (Figure S1g). In a cubic lattice system, the (111) lattice planes can slip along one of three directions, namely, b1, b2 and b3 directions as shown in Figure 1b. If the lattices with the spacing of three Ba-O planes at the (111) direction is grouped as a unit, each unit has three Ba-O planes and three Ti planes (Figure 1c, 1d). A such unit is called a “gliding unit” when each plane 2

>. The unit next to the slip unit in the unit slips along < 112 > direction for a length of 3 < 112

is called “stationary unit”, because the unit keep stationary (Figure 1c, 1d) when the slip unit is slipping. The h-phase is transformed from the c-phase (Figure 1d) by the slipping of one unit in every two units alternatively. The c-to-h phase transformation of BTO is of both academic and industrial interest, e.g. the recent work on h-phase BTO focusing on its microwave properties and potential application 17. Oxygen vacancies promote h-phase BTO formation,15 because oxygen vacancies are able to change Ti4+ to Ti3+ and thus reduce the interaction between Ti and Ti. It is very popular to form h-phase by introducing oxygen vacancies, such as air quenching,16 doping,18 sintering with a low oxygen partial pressure19 or in reducing environment,20,21 incomplete oxidation from metalorganic compounds,22 etc. In addition to oxygen vacancies, stress has the great potential to generate h-phase, especially at elevated temperature, as described above. In martensitic transition, when the cubic parent phase is subjected to an external stress, it transits into hexagonal/twinned martensitic, which has a lower energy than c-phase2. Such transition process is done by lattice slide under the shear stress. For BTO, it is reported that the internal stress can activate the lattice slip if it exceeds the critical shear stress.21,23 The effective stress during hot-pressing sintering can be large enough to overcome the energy barrier and exceeds the critical shear stress required to activate the lattice slide.21,24 As the h-phase can be obtained by the coherent lattice slide of cubic {111} planes, it is possible to activate the slide system by applying an external stress to obtain the h-phase. Here we demonstrate a stress assisted c-to-h phase transition in BTO nano thin films via bending at elevated temperature, where an applied bending plus residual tensile stress generates shear stress in the nanometer-thick films and the shear stress and thermal energy are the driving force of lattice shear. The underlying mechanism on the stress induced c-to-h 3 ACS Paragon Plus Environment

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phase transformation is interpreted from the energy evolution with different phases and fault motions based on first-principles calculations.

Results and Discussion BTO thin films were deposited on Pt (100 nm)/Ti (10 nm)/SiO2/Si substrates using the conventional sol–gel method.17 Figure 2a schematically shows the TMT on the BTO thin films. The estimated shear stresses are 31.3, 112.5, 193.7 MPa in the T, R, and C samples, respectively. The detailed experimental information is given in the Methods section. At room temperature, the c-phase transforms to tetragonal phase (t-phase). Figure 2c-e are transmission electron microscopy (TEM) images, showing that in addition to the large volume fraction of t-phase, there are h-phase plates in the T, R, and C samples and the highest h-phase volume fraction occurs in the C sample. Figure 2b illustrates the Raman spectroscopic results of the TMT treated samples, showing the characteristic vibration modes of both tetragonal and hexagonal phases, which is consistent with the fact that the two phases coexist in the samples. The h-phase shows a peak in Raman shift curve around 630cm-1. The peak area ratio of this peak to the characteristic peak (519 cm-1) of tetragonal phase presents the volume fraction of h-phase/t-(or c-) phase. By comparing this ratio in the inset of Figure 2b, it is clear that C sample has the largest h-phase volume fraction, while the T sample has the lowest. All experimental conditions except of bending are identical for all sample groups, thus the difference is attributed to the bending stress, which is the only different parameter during the designed experiment. High resolution TEM (HRTEM) was used to confirm the existence and the relative density of hexagonal phase. Figure 3a-b shows that hexagonal phase coexists with tetragonal phase in a typical grain. A striking characteristic of the stress induced h-phase is that these h-phase plates are almost associated with twin structures, as shown in Figure 3a-b. Also, most of the twin structures generated in this experiment are more or less accompanied with some h-phase plates. Figure 3b shows a high resolution TEM picture of a zone with t- and h-phase coexisting. The measured (10 1 0) and (0001) lattice spacing of the h-phase are 0.493nm and 1.395nm, respectively, consistent with the reported values in literature15.


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The previous work has proved that twins can be induced by stress at temperature 550 °C25 and the present experiment with TMT at 575 °C indicates that the h-phase plates are commonly found at the twinning sites. This might imply that the stress in TMT is able to produce twins and h-phase. The combined thermomechanical driving force might activate the lattice sliding of {111} planes along directions in the c-phase15,16 to form h-phase. The energy land profile, i.e., the energy variation with the sliding for the c-to-h phase transformation are calculated by ab initio calculations and the result supports this hypothesis, which will be described later. The TEM images in Figure 3 provide the evidence of stress induced c- to h-phase transition, showing the angles of kinks on the grain boundaries (GBs). As is stated in Figure 1, a (111) plane has 3 slipping directions, denoted by b1, b2, b3. If we glide each Ba-O plane and each Ti plane sequentially in on “gliding unit” of c-phase along any of the three directions and keep the “stationary unit” stationary, and arrange the gliding and stationary units alternatively, an h-phase will be constructed (Figure 1d). The gliding motion can be recorded as the shape change of the grain, which is especially prominent at the GB in terms of GB kinks 26, 27. If the gliding motion is along b1 direction, the preexisted (001) straight GB will be transformed to a fold line, with a kink angle of 151°, which is briefly illustrated in Figure 3c and coincident with the TEM observation in Figure 3d. If the gliding motion is along b2 or b3 direction, the preexisted (001) straight GB will be transformed to a fold line, with a kink angle of 145°, which is briefly illustrated in Figure 3e and coincident with the TEM observation in Figure 3f. This observation further support the stress induced cubic-to-hexagonal phase transition via lattice gliding. The valence of Ti atoms is critical to the stress induced BTO h-phase. It is crucial to check (i) whether the related reducing environment is brought into the present experiment, and (ii) whether the valence of the Ti atoms in the present samples is reduced. To reduce the valence of the Ti atoms requires a reducing environment which increases oxygen vacancies.16 It has been reported that re-annealing valence-reduced samples in an oxidative atmosphere brings reoxidation of these reduced samples

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and restore the room-temperature equilibrium t-phase. In

the present experiment, all samples were annealed and cooled down slowly in the air, an oxidative atmosphere, which was supposed not to increase oxygen vacancies and reduce the valence of Ti atoms. Figure 4a shows that X-ray photoelectron spectroscopic (XPS) results of all samples are well fitted with Ti4+ peak (see inset of Figure 4), which indicates that the oxygen vacancies are not influenced by stress applied in this experiment. Although the XPS results 5 ACS Paragon Plus Environment

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confirm that the valence of Ti atoms at macroscopic level unchanged, one may doubt whether the generated h-BTO should be attributed to locally concentrated oxygen vacancies. Here we use electron energy loss spectroscopy (EELS) with atomic resolution to answer this question. Prior reports showed a left shift of EELS peak between Ti on twin boundary and Ti inside matrix, thereby concluding that Ti on the twin boundary has a lower covalent state than that inside the matrix.29 Figure 4b is the EELS spectrum of the h-phase and t-phase which coexist in one grain, no difference is found between them. This might be a strong evidence to show that the observed h-phase is not caused by oxygen vacancies. It is widely accepted that, dielectric properties will degrade greatly with even very small concentration of oxygen vacancies, or in other words, Ti3+ concentration.30 Figure 4c indicates that the dielectric properties do not degrade with the increment of h-phase volume fraction, where the three types of samples exhibit more or less the same behavior of relative permittivity versus electric field. Figure 4d shows also that the three types of samples behave more or less the same in leakage current density versus electric field. These results also support the idea that the valance reduction of Ti atoms does not happen in the samples containing h-phase. Some other report16showed that air quenching BaO-excess laser-sintered BTO could stabilize the h-phase, but the mechanism cannot be applied to the present study, where it took about one day to cool down the samples from 575°C to room temperature16. The experiment results may illustrate that (i) the formation and stabilization of h-phase here should not be attributed to oxygen vacancies and (ii) the increase in h-phase volume fraction in highly stretched samples should not be attributed to increased oxygen vacancies. The c-to-h phase transformation in the present BTO is driven by the combined force of stress and temperature. In order to understand the detailed underlying mechanism on the c-to-h phase transformation, first-principles calculations based on density functional theory have been conducted for the structural and energetic properties of the two phases. By first-principles calculations, the obtained lattice parameters of BTO are a = 3.950Å for cubic phase, and a = 5.657 Å and c = 13.792Å for hexagonal, which are in good agreement with the experimental data15, implying that the computational method may be taken as a reliable base for the subsequent calculations. In order to explore the structure stability of c- and h-phases of BTO, the total energy as a function of cell volume for both phases are calculated and the results are shown in Figure 5a, where the minimum energy of the c-phase is taken as zero. Figure 5a indicates that the minimum energy of 6 ACS Paragon Plus Environment

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the h-phase is higher than that of the c-phase by ca.50.2 meV(f.u.)-1, thereby implying that the Cphase is energetically more stable than the h-phase at temperature 0 K. However, increasing temperature may change the relative stability of these crystal structures. The thermal effect on phase transition is studied by calculating phonon free energies of the two phases. Figure 5b shows that a phase transition from the cubic phase to hexagonal phase takes place at about 1485 K, which is lower than that in experimental with 1705 K,16 but the whole trend is consistent. Furthermore, an applied tensile stress favors the h-phase and will lower the critical temperature for the c-to-h phase transformation, as schematically drawing in Figure 5b. As discussed above on Figure 3, lattice gliding may drive the c-to-h phase transition. Hence, stacking faults formed by shearing successive layers represents a possible pathway for this transition. A calculation model was constructed that three-layer stacking faults on (111) slip planes were glided along < 112 > slip direction to enforce this phase transition, as shown in Figure 5c and Figure S1. The calculated supercell is consisted of 18 (111) layers (3 unit cell) with one formula unit BTO per layer (no free surfaces) to represent bulk material. For BTO, one unit cell consists of 6 (111) layers, and one layer consists two planes, i.e., Ti plane and Ba-O plane. Starting with the perfect cubic …ABC… (111)-layer stacking (Figure 5b), the stacking fault was created by slipping Ti planes and Ba-O planes sequentially in each unit cell along direction through one partial Burgers vector, as shown in Figure S1. When the first layer of Ti plane was slipped, the structure was denoted as 0.5-layer fault, while then denoted as 1-layer fault after the first layer of Ba-O layer was slipped. Similarly, 1.5-, 2-, 2.5-, 3-layer fault were created. As shown in Figure S1b, S2d, and S2f, 0.5-, 1.5-, and 2.5-layer fault consists …AA… configurations of Ti and Ba-O plane in the stacking, however, 1-, 2-, and 3-layer fault only consists …AA… configurations of Ti plane in the stacking (Figure S1c, S1e, and S1g). The generalized planar fault energy (GPFE) can provide a comprehensive description of stacking fault. The fault energy is defined by

γ=

E − E0 A

(1)

where γ is stacking fault energy, E is the total energy of fully relaxed stacking fault structure, E0 is the total energy of perfect cubic structure, and A is the area of the fault plane. The calculated GPFE curve for BTO is shown in Figure 5d, where γ1, γ2 and γ3 are the stacking fault energies, and γ0.5, γ1.5 and γ2.5 denote the unstable stacking fault energies. As shown in Figure 5d, the 7 ACS Paragon Plus Environment

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stacking fault energies of γ1, γ2 and γ3 are 190, 124 and 59 mJ m-2, respectively, which are similar to typical stacking fault energies in metals (20-200 mJ m-2), where γ1> γ2 > γ3 indicates that 3layer fault (hexagonal) is the most stable, namely, the hexagonal phase in BTO may form by stacking faults. Literature claims that internal stress can exceed the critical resolved shear stress to activate the lattice slip in BTO,21,23 our calculation and experimental results are both consistent with it. The unstable stacking fault energy γ0.5, γ1.5 and γ2.5 are 675, 683 and 786 mJ m2

, respectively, which are much higher than corresponding values in metals (100-300 mJ m-2).

The energy barrier, defined by the difference between unstable stacking fault energy and stacking fault energy, γ0.5, γ1.5- γ1 and γ2.5-γ2 are 675, 493 and 562 mJ m-2. The first energy barrier is the highest, indicating once the one-layer fault is formed, it is easy to form three-layer fault (hexagonal phase). The ratios between the valley and barrier, γ1/γ0.5, γ2/γ1.5 and γ3/γ2.5 are 0.28, 0.18 and 0.08, respectively. The smallest value implies the most stable stacking fault, so three-layer fault (hexagonal phase) is the most stable in three stacking fault structures. Therefore, the phase transition from cubic to hexagonal phase in BTO may be achieved by shear. Figure 5d shows that the energy barrier between c- and h-phases of BTO is much larger than the energy difference between the two phases. An applied tensile stress lowers the energy barrier for the c- to h-phase transition, while it enhances the energy barrier for reverse transition from the h-phase back to the c-phase. Under an applied tensile stress, the thermal vibration is able to overcome the stress reduced energy barrier to complete the c- to h-phase transition. After the tensile stress loaded sample cooling down to room temperature, the h-phase survives, similar to that a fast air quenching from high temperature (over 1432 ºC) stabilizes the h- phase at room temperature.16

Conclusion In summary, the stress induced cubic-to-hexagonal phase transformation is observed in BTO nano thin films deposited on a substrate. Both Raman spectroscopy and TEM images confirmed that the higher the tensile stress is, the higher the hexagonal phase volume fraction is. The applied bending stress plus the thermal activation at temperature 575°C is the driving force for the lattice to overcome energy barrier between c-phase and h-phase. The c-to-h phase transformation is completed via lattice slipping under shear stress, where the nanometer 8 ACS Paragon Plus Environment

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thickness of the films makes the shear stress higher if the tensile stress is higher. After cooling down the bent sample from 575 °C to room temperature and then unloading, the c-phase transforms to the t-phase, while the transformed h-phase survives as a metastable state. This is because no enough thermal energy can be provided at room temperature for the h-phase to transform back to the c-phase (or t-phase). First-principles calculations also show that the energy barrier for the c-to-h phase transition by shear (partial dislocation motion) in BTO is comparable to that in FCC metals. Thus, the combined force of stress and temperature is able to drive the cto h-phase transition. This work not only demonstrates a new stress-induced phase transformation in perovskite thin films but also suggests a pathway to tune the nano/microstructures of the materials by thermomechanical treatments.

Methods Sample preparation and characterization. The BTO thin films were deposited and then treated by thermomechanical method (TMT) at 575±1ºC (Figure 2) by using the same experimental procedure as that reported before25. There is a residual tensile biaxial stress of 112.5 MPa in the nano films before the TMT treatment. The bending moments of -0.073, 0, and 0.073 N·M were applied to the T, R and C samples, respectively, and maintained during the TMT treatment, as shown in Figure 2. Under these moments, the bending induced stresses at the film surfaces along the longitudinal direction in the T, R and C samples were calculated to be -81.2, 0, and 81.2 MPa, respectively. Thus, the resultant stresses at the film surfaces along the longitudinal direction in the T, R and C samples were 31.3, 112.5, 193.7 MPa, respectively. Since the films were extremely thin, plane stress condition was approximately applied along the thickness direction of the films. Then, the shear stresses were estimated to be 15.7, 56.3, and 96.9 MPa in the T, R and C samples, respectively. The crystal structures of thin films before and after TMT were characterized by both X-ray diffraction (XRD) and Raman spectroscopy at room temperature. High resolution transmission electron microscopy (HRTEM) was used to confirm the crystal structure at the atomic level. X-ray photoelectron spectroscopy (XPS) was applied to obtain the covalent state of elements at room temperature.

First-principles calculations. The first-principles calculations were performed by using the Density-Functional Theory (DFT) with the exchange-correlation functional treated in the spinpolarized local density approximation (LDA) with the projected augmented wave (PAW) 9 ACS Paragon Plus Environment

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method31 as implemented in the Vienna Ab initio Simulation Package (VASP)32,33,34. Convergence with respect to both energy cutoff and k-point mesh was tested. As a result of the convergence, an energy cutoff of 600 eV was chosen to ensure that the total energies were converged within 0.1 meV (f.u.)-1. The Brillouin zone was sampled with a mesh including the gamma point. A 9×9×3 mesh was selected for structural relaxation by using the Gaussian smearing method35, and a smearing parameter of 0.1 eV was chosen such that the error in the extrapolated energy at 0 K was less than 0.1 meV (f.u.)-1. The valence electrons for Ba, Ti and O atoms were treated with 5s25p66s2, 3s23p63d24s2 and 2s22p4, respectively. Forces on the ions were calculated through the Hellmann-Feynman theorem, allowing a full geometry optimization of the different structures (cubic and hexagonal) and FM magnetic phases of BaTiO3. In order to reveal possible phase transitions, we have investigated free energies of different phases over a wide range of temperature and volume. Phonon calculations were carried out using the PHONOPY package36 with the force-constant matrices calculated from VASP. The transition energy barrier from cubic to hexagonal phase were calculated by using the climbing nudged elastic band (NEB)37 method.

Supporting Information Figure S1. Stacking fault pathway along a (1 1 1) fault plane including 18-layer supercell used for phase transition from cubic to hexagonal phase in BaTiO3.

Acknowledgements This work is financially supported by the research grants (No. 15DZ2260300 and No. 16DZ2260600) from the Science and Technology Commission of Shanghai Municipality. Jie Wang is supported by National Natural Science Foundation of China (Grant No. 11472242 and 11672264).

Author Contributions T.Y.Z. managed the project and guided the research. S.G.C conducted all experiments, and Y.S.L carried out the first-principles calculations. S.G.C., Y.S.L. and T.Y.Z. performed the data analysis. T.Y.Z., S.G.C. conceived the storyline of the paper. All authors contributed to the discussions and wrote the paper.


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Figure 1. (a) Lattice structure of a unit cell of BTO in c-phase. (b) The view of the cubic lattice of BTO. (c) The view of the cubic lattice of BTO. (d) The view of the lattice of BTO with a portion of c-phase transformed to h-phase.(e) A 3D sketch of two face shared oxygen octahedral in a hexagonal phase. (f) A 3D sketch of two vertex shared oxygen octahedral in a cubic phase. Green balls stand for barium atoms, red balls stand for oxygen atoms, and gray balls stand for titanium atoms.


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Figure 2. (a) The schematic of different mechanical-thermal treatments for thin film samples, (b) Raman spectroscopy of BTO thin films with different mechanical-thermal treatments shows different volume fractions of hexagonal phase. The inset shows the area ratio of peak 630 cm-1 over peak 519 cm-1. (c-e) TEM images of sample under different treatment. The sample with the highest tensile stress (C sample) has much more sites of h-phase than the reference sample (R sample), which is attributed to a stress-induced phase transition. By contrast, the sample bent to the opposite direction to reduce the tensile stress during annealing (T sample) has the least hphase sites.


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Figure 3. High resolution TEM images for the crystal structures of a BTO grain that consists of tetragonal and hexagonal phases, note that, for simplicity, we denote the tetragonal lattice as cubic lattice which took place of the tetragonal lattice during lattice gliding at high temperature. (a) A typical twined grain with cubic phase and hexagonal phases. The inset shows a nano-beam diffraction pattern in which both twin structure and hexagonal phase can be well identified. The hexagonal phase can be regarded as well-organized twin sequence with each twin slab containing 3 layers of Ba-O plane. (b) A high resolution TEM image for the part of a typical twined grain with cubic matrix and hexagonal slab. (c) Lattice slipping model along b1 16 ACS Paragon Plus Environment

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direction for a grain boundary of (100) plane where c-phase transforms to h-phase. (d) The TEM image of a BTO grain consisting of c- and h-phases and with the same GB kink angle as (c). (e) Lattice slipping model along b2 direction for a grain boundary of (100) plane where c-phase transforms to h-phase. (f) The TEM image of a BTO grain consisting of c- and h-phases and with the same GB kink angle as (e).


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Figure 4. (a) The X-ray photoelectron spectroscopy (XPS) of different samples shows an obvious change by applied stress in volume fraction of h-phase. The larger the tensile stress during annealing, the larger the h-phase volume fraction is. (b) Electron energy loss spectroscopy (EELS) of hexagonal phase and cubic phase coexisting in a crystal grain, which shows that there is no any covalence difference between Ti atoms in different phases and confirms that the generated hexagonal phase could not be attributed to the covalence change of Ti atoms. (c-d) Dielectric properties of thin films with different treatments. It is found that the dielectric properties do not degrade with an increased volume ratio of h-phase, indicating that the increased h-phase is not induced by an extra amount of oxygen vacancies.


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Figure 5 . (a) The calculated total energy versus volume for cubic and hexagonal phases of BaTiO3. (b) Relative free energy versus temperature for the cubic and hexagonal phases. The total energy at the equilibrium volume and the free energy of the cubic phase are set as the reference energy (i.e., set to zero). All energies are rescaled for one BaTiO3 formula unit (f.u.). The dash line schematically shows that under tensile stress, the relative energy of the cubic phase increased with respect to the hexagonal phase. (c) Stacking fault pathway along a (1 1 1) fault plane including 18-layer supercell used for phase transition from cubic to hexagonal phase in BaTiO3, with blue balls Ba atoms, red balls oxygen atoms, and blue balls Ti atoms. The displacement along each pathway is given by the Burgers vector bs= /3. (d) Generalized planar fault energy for phase transition from cubic to hexagonal phase in BaTiO3.


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Stress-induced cubic-to-hexagonal phase transformation in perovskite

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