Extreme Room Temperature Compression and Bending in Ferroelectric Oxide Pillars


 Plastic deformation in ceramic materials is normally only observed in nanometre-sized samples. However, we have observed unprecedented levels of plasticity (>50% plastic strain) and excellent elasticity (6% elastic strain) in perovskite oxide Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT), under compression along <100>pc pillars up to 2.1 μm in diameter. The extent of this deformation is much higher than has previously been reported for ceramic materials, and the sample size at which plasticity is observed is almost an order of magnitude larger. Bending tests also revealed over 8% flexural strain. Plastic deformation occurred by slip along {110} <110>. Calculations indicate that the resulting strain gradients will give rise to extreme flexoelectric polarization. First principles models predict that a high concentration of oxygen vacancies (Vo) weaken the covalent/ionic bonds, giving rise to the unexpected plasticity. Mechanical testing on Vo-rich Mn-doped PIN-PMN-PT confirmed this prediction. These findings will facilitate the design of plastic ceramic materials and the development of flexoelectric-based nano-electromechanical systems.

There are some rare exceptions to this rule. Crystals with the rock salt structure show limited plasticity due to their unique structure (slip occurs on {110} planes and along <11 � 0> directions, where it does not bring similarly charged atoms together) 3 . Among perovskite oxides, SrTiO3 (STO) has been reported to display around 7% plastic deformation under uniaxial compression at an extremely low strain rate (10 -4 ) 4 . More recently, good plasticity was reported in semiconductor α-Ag2S and InSe single crystals 5,6 . In α-Ag2S, excellent plasticity was attributed to planes with weak atomic interactions and irregularly distributed sulfur-silver and silver-silver bonds 5 , while in InSe, the plasticity is thought to result from long-range In-Se Coulomb interactions across the van der Waals gap and soft intralayer In-Se bonding 6 . Flash-sintered TiO2 has been compressed to ~10% strain, attributed to a high-density of stacking faults, nanotwins, and dislocations 7 . Plastic deformation observed in nano pillars, nanowires, etc., is mostly attributed to the low chance of smaller samples containing flaws, allowing the materials' intrinsic plasticity to be observed 8, 9, 10, 11, 12, 13, 14 . The existence of deformable ceramics has striking potential, but systems that display this characteristic must be identified and plasticity mechanisms need to be understood in order to guide the design of such materials. Because plastic deformation is not typical of ceramics, the applications have not yet been fully considered. It is expected such properties might enable applications such as sensors or even bendable and foldable electronics 15 where flexible ceramic film capacitors are required 16 .
Excellent elastic properties are especially desirable 17 for functional oxides. A mechanical bending moment enables a dielectric material to polarize, giving rise to flexoelectricity. Flexoelectricity has a strong scaling effect and is therefore significant at micro/nano scales. For this reason, it has the potential to be used for electromechanical actuators and sensors that can be integrated into advanced nano-/micro-electromechanical systems (N/MEMS) 18,19 , meeting the requirement for the millions of micro-and nano-scale sensors to be employed during the expected rapid implementation of the Internet of Things.
Perovskite oxides are of great interest to both geophysics and materials science 20 . In geophysics, a MgSiO3-rich perovskite phase is thought to account for 50 − 90% of the volume of the region of the earth that controls seismic activity 21,22 (i.e. the 670 km seismic discontinuity to the core-mantle boundary 19 ). In the field of materials science, perovskites are of interest because they exhibit useful flexoelectric, dielectric, piezoelectric, ferroelectric, ferromagnetic, multiferroic, superconducting, and photovoltaic properties, as well as colossal magnetoresistance 23 . Pb(In1/2Nb1/2)O3- S3 and S4. Fig. 1a shows an engineering stress-strain curve from a 140 nm diameter pillar. The slope of the curve starts to decrease from ~5% strain. Two short stress plateaus appear when the strain reaches ~15% and ~44% respectively, typical of plastic deformation. The total compression strain of the pillar exceeds 60%, over 50% of which is plastic. This extreme strain far surpasses the expected deformability of ceramic materials 27 and is much higher than has been previously reported in micro/nanopillars 9,10,13     For perovskite oxides, it is generally accepted that, at ambient temperature, the preferred slip system is {110} <11 � 0>, with a<11 � 0> dislocations 19 . This type of dislocation is usually dissociated into two partials due to the high energy of two extra atomic planes. Previous studies on as-grown single/double crystals, polycrystals, or thin films show that a<11 � 0> dislocations are dissociated either in a glide or a climb mode 21,34,35,36,37 . Unexpectedly, we have observed climb-dissociated dislocation core structures, which would normally be expected to form at elevated temperatures because climb is a diffusion-assisted process 38 . Instead, a<110> dislocations formed during room temperature deformation might be expected to dissociate in a slip configuration 38 , as was previously reported for compression-tested KNbO3 39 . We note here that a high density of point defects in the PIN-PMN-PT might enable the diffusion that is required to form climb-dissociated dislocations, leading to much better deformability compared to other perovskites such as STO or KNbO3.
In perovskites oxides, vacancies are far more common than interstitials 20  To trace the possible microscopic origin of the observed extreme plasticity, we conducted first principles atomistic simulations based on density functional theory (DFT). The results are given in Fig. 3. On the basis of a simplified model, PIN-PMN-PT is composed of three sets of subunits, PIN, PMN and PT (Fig. 3a). Atomic-scale Energy-Dispersive X-ray Spectroscopy (EDS) mapping ( Fig. S16) indicates that the cations are uniformly distributed at the atomic level, suggesting a high density of mini-interfaces between the three subunits. Relaxed atomic structure and lattice constants of the bulk and interfaces are shown in Figs. S17 & S18, and Table S1 & S2. Calculated interface formation energies (shown in Fig. S19) suggest that the presence of interfaces promote the concentration of •• but not ′′ . Favourable •• sites in different side-by-side and top-down interface systems are shown in Fig. S20. Interestingly, these calculations show that it is energetically favourable to form oxygen vacancies (but not lead vacancies) at these interfaces to mitigate the large lattice mismatch (Fig. S21). That is, the three subunits that make up the PIN-PMN-PT naturally facilitate a uniformly-distributed high density of •• . As an example, the atomic structure of 1PIN-1PMN-1PT containing one oxygen vacancy is shown in Fig. 3b. To assess the corresponding ductility, we calculated the elastic constants and derived the bulk modulus (B) 43 and the anisotropic shear modulus (G) on the (110) plane along <11 � 0> direction for different single tetragonal crystalline species 44 , as shown in Fig. 3c and Table S3. The Pugh's B/G ratio is widely  Fig. 4a. A lower intensity is observed for the O-k edge fine structure peak B compared to A for all three EELS curves. It is known that the peak at position B being lower than the peak at position A is an indication of oxygen deficiency in perovskite oxides 46,47,48 , suggesting that •• with appreciable concentrations exist in all three samples. Furthermore, the inset image shows that peak B is larger for the Sm-doped sample than the un-doped crystal, indicating a lower •• concentration, and is smaller for the Mn-doped sample, indicating a higher •• fraction.
According to the DFT predictions, the •• -rich (Mn-doped 26  around dislocations is estimated to be about 10 7 µC·cm -2 according to Pf = u × ∇S, where Pf is flexoelectric polarization, u is flexoelectric coefficient, and ΔS is gradient of the horizontal lattice constant along the vertical direction. However, this large calculated polarization is thought to be an over-estimate for two reasons. 1) In the case of such high strain gradients, higher-order coupling terms of flexoelectric polarization and strain gradient, which is nonlinear, should not be neglected, and the magnitude of those terms is still unclear. 2) For smaller samples, permittivity (ɛ) is expected to decrease as a result of a size effect 51 , and the flexoelectric coefficient µ, which is a function of ɛ in a manner of µ = f • ɛ, should also be smaller than the corresponding bulk value (here f is flexo-coupling coefficient, about 10 V for PTO-based relaxor ferroelectrics). However, this extremely large polarization should give rise to a large number of bound charges. To screen these bound charges, free charges will accumulate. Transport properties or even magnetic properties around these dislocations can also be affected due to free charges. For slip bands, where a strain gradient also exists (as shown in Fig. S11e), the situation would be similar. As the strain gradient around a slip band is much smaller than it is around dislocations, the flexoelectric effect will be smaller. The movement of dislocations and the introduced slip bands make a functional region which is potentially applicable for flexoelectric based micro-and nano-scale electronic devices.
In addition to strain gradients around dislocations and slip bands, bending-induced elastic strain gradients are also of great interest for flexoelectricity because of their reversibility. The maximum elastic strain introduced by bending test is calculated to be 6.8% at the root of the cantilever beam, and the width (b) of the cantilever beam is 0.67 µm, which gives rise to a strain gradient of about

Materials:
The experimental work reported in this paper was performed using

Sample preparation:
Micro-pillars preparation for compression, tensile and bending tests: The PIN-PMN-PT single crystal was first cut into slices of 0.5 mm in thickness, then further thinned using tripod polishing to ~ 500 nm at the front edge. Pillars used for in-situ tests were fabricated at the thin edge by using FIB. Columnar pillars with an aspect ratio (height/diameter) of 2:1 ~ 3:1 were prepared for compression tests. The FIB was operated at 30 kV using a current of 1 nA for coarse milling and 5 pA ~ 300 pA for final milling of pillars with diameters ranging from 130 nm ~ 2.1 µm. The pillar taper angles are estimated to be around 3˚. The diameter of the top surface was used for stress calculation, which is the first part of the sample to undergo plastic deformation. Cantilever beams for bending tests were prepared with FIB operating at 30 kV and using a current of 50 pA for final milling. The length, width and depth are 6.5, 0.67 and 0.8 µm, respectively. Dog bone shaped pillars were prepared for tensile tests, and 30 kV, 5 pA were used for final milling.
TEM sample preparation: The deformed pillars were lifted-out using a tungsten manipulator onto a copper base, and then thinned to electron transparency (~ 50 nm) for TEM observation. 10 kV and 10 pA were used for FIB final milling. 5 kV, 10 pA and 2 kV, 10 pA were used for final cleaning of the surface. To protect the pillars from FIB damage, platinum was deposited around the pillars before thinning.
TEM sample preparation for O-K EELS: TEM samples for O-K EELS were prepared by grinding using tripod polisher and ion milling employing a Gatan precision ion polishing system II (PIPS II). 4˚ and 0.5 kV were used for final milling.

In-situ mechanical tests:
In-situ compression experiments were carried out in both a TEM (JEOL JEM 2100) and an SEM (Zeiss Ultra), while in-situ tensile and bending tests were conducted in the SEM. The JEOL JEM 2100 uses a high brightness LaB6 electron source. It is equipped with Xarosa (4 k x 4 k) as well as Veleta Ultrascan (2 k x 2 k) cameras. In the TEM, in-situ compression tests of pillars with diameters around 200 nm were carried out by using a Hysitron PI 95 Picoindenter with a flat diamond tip. As the load applied is limited to 1.5 mN for the PI 95 Picoindenter, the requirement for thin sample in the TEM, we carried out the in-situ compression experiment of the larger pillars by using a Hysitron PI 85L picoindenter inside an SEM, with a specially designed system for applying loads up to 10 mN. This system allows real-time observation of deformation process (i.e. slip band development, slip planes and slip directions). Load was applied to pillars by moving the indenter toward the pillars in the displacement control mode. The displacement rates were 1 nm·s -1 and 2 nm·s -1 for compression of pillars of around 200 nm in diameter and from 500 nm ~ 2.1 µm in diameter, respectively. For the tensile test, a displacement rate of 1 nm·s -1 was used. For the bending test, a higher displacement rate -4 nm·s -1 was used.

Microstructure investigation of the deformed pillars:
A JEOL JEM 2100 TEM and a FEI Themis-Z Double-corrected 60-300 kV S/TEM were used to observe the compressed pillars. High-resolution STEM-HAADF images, EDS element mapping and O-K edge EELS were acquired using the FEI Themis-Z S/TEM. The convergence and collection angle under the STEM-HAADF mode are 17.9 mrad and 50 -200 mrad, respectively.
Strain was analysed using free Geometric Phase Analysis script (by C.T. Koch) 58 . EELS of the O-K edge was acquired under the TEM mode at a collection angle of 100 mrad. Dual-EELS was used and zero peak was corrected for all three samples. The energy resolution is estimated to be 1.0 eV, measured from full width at half maximus of zero loss peak, while an energy dispersion of 0.025 eV/ch was employed. The point resolution of Themis-Z under the STEM mode is around 0.6 Å (operated at 300 kV). It is equipped with X-FEG high-brightness gun, Monochromator, ChemiSTEM (Super-X) EDS detectors as well as a Gatan Quantum ER/965 GIF (<0.14 eV (1s)) with Dual-EELS.
First-principles simulation: DFT calculations were performed using the plane-wave pseudopotential total energy method as implemented in the VASP code 59,60 . Projector augmented wave potentials 61 and the generalized gradient approximation 62 were used for exchangecorrelation. A plane-wave basis set was used with an energy cut off of 500 eV. The summation over the Brillouin zone for the bulk structures was performed on a ~0.06 Å -1 spacing Monkhorst-Pack k-point mesh for all calculations. For all systems, atomic relaxation was allowed until all the forces were less than 0.01 eV/Å. For charge density calculations, Pb-5d, Nb-4p, Mg-2p, Ti-3p and In-4d semi-core states were treated as valence states to ensure high accuracy. Additional computational details can be found in the Supporting Information.