Piezoelectricity usually accompanies with flexoelectricity in polar materials which is the linear response of polarization to a strain gradient. Therefore, it is hard to eliminate piezoelectric effect in determination of pure flexoelectric response. In this work, we propose an analytical method to characterize the flexoelectric coefficient quantitatively at nanoscale in piezoelectric materials by screening piezoelectricity. Our results show that the flexoelectricity reduces the nanopillar stiffness while the piezoelectricity enhances it. With careful design of the shape of the nanopillars and measuring their stiffness difference, the flexoelectric coefficient can be obtained with the piezoelectric contribution eliminated completely. This approach avoids the measurement of electrical properties with dynamic load, which helps to reduce the challenge of flexoelectric measurement at nanoscale. Our work will be beneficial to quantitative characterization of flexoelectric properties and design of flexoelectric devices at nanoscale.
The origin of "giant" flexoelectricity, orders of magnitude larger than theoretically predicted, yet frequently observed, is under intense scrutiny. There is mounting evidence correlating giant flexoelectric-like effects with parasitic piezoelectricity, but it is not clear how piezoelectricity (polarization generated by strain) manages to imitate flexoelectricity (polarization generated by strain gradient) in typical beam-bending experiments, since in a bent beam the net strain is zero. In addition, and contrary to flexoelectricity, piezoelectricity changes sign under space inversion, and this…
This note corrects some errors in a previously published paper: Size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect[PHYSICAL REVIEW B 77, 125424 (2008)]. The comlete published paper is also included in this note.
It has been well known that flexoelectricity can be exploited to generate an analogous piezoelectric response in non-piezoelectric materials. For the direct flexoelectric effect, the induced electric polarization is linearly proportional to the applied strain gradient. Therefore, it is logical to expect that such a piezoelectric response would be enhanced in the materials with reduced dimensions. In this paper, we will report our experimental observation of such a gradient scaling phenomenon of piezoelectricity in non-piezoelectric polyvinylidene fluoride (PVDF) films.
Flexoelectricity is defined as the coupling between strain gradient and polarization, which is expected to be remarkable at nanoscale. However, measuring the flexoelectricity at nanoscale is challenging. In the present work, an analytical method for measuring the flexoelectric coupling coefficient based on nanocompression technique is proposed. It is found that the flexoelectricity can induce stiffness softening of dielectric nano-cone-frustum. This phenomenon becomes more significant when the sample size decreases or the half cone angle increases. This method avoids measuring the electric pol…
Large bending of materials can occur at the nanoscale in response to an electric polarization, what is called the flexoelectric effect, but to date this has not been observed directly. We report the direct observation of large flexoelectric bending in [110] oriented DyScO3 inside an electron microscope. We corroborate these observations with independent ex-situ measurements of the flexoelectric coefficient with a three-point bending setup. The relevant flexocoupling voltage was measured to be -42(2) V, which is higher than expected based upon current flexoelectric models.
SrTiO3 ceramics are investigated by piezoresponse force microscopy. Piezoelectric contrast is observed on polished surfaces in both vertical and lateral regimes and depends on the grain orientation varying in both sign (polarization direction) and amplitude. The observed contrast is attested to the surface piezoelectricity due to flexoelectric effect (strain gradient-induced polarization) caused by the surface relaxation. The estimated flexoelectric coefficient is approximately one order of magnitude smaller as compared to those recently measured in SrTiO3 single crystals. The observed enhance…
Flexoelectricity is a form of electromechanical coupling that has recently emerged because, unlike piezoelectricity, it is theoretically possible in any dielectric material. Two-dimensional (2D) materials have also garnered significant interest because of their unusual electromechanical properties and high flexibility, but the intrinsic flexoelectric properties of these materials remain unresolved. In this work, using atomistic modeling accounting for charge-dipole interactions, we report the intrinsic flexoelectric constants for a range of two-dimensional materials, including graphene allotro…
A centrosymmetric stress cannot induce a polar response in centric materials, piezoelectricity is, for example, possible only in non-centrosymmetric structures. An exception is meta-materials with shape asymmetry, which may be polarized by stress even when the material is centric. In this case the mechanism is flexoelectricity, which relates polarization to a strain gradient. The flexoelectric response scales inversely with size, thus a large effect is expected in nanoscale materials. Recent experiments in polycrystalline, centrosymmetric perovskites [e.g., (Ba,Sr)TiO3] have indicated values o…
The origin of the functional properties of complex oxide superlattices can be resolved using time-resolved synchrotron x-ray diffraction into contributions from the component layers making up the repeating unit. The CaTiO3 layers of a CaTiO3/BaTiO3 superlattice have a piezoelectric response to an applied electric field, consistent with a large continuous polarization throughout the superlattice. The overall piezoelectric coefficient at large strains, 54 pm/V, agrees with first-principles predictions in which a tetragonal symmetry is imposed on the superlattice by the SrTiO3 substrate.
Upon application of a uniform strain, internal sub-lattice shifts within the unit cell of a non-centrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric…
Due to their combination of mechanical stiffness and flexibility, two-dimensional (2D) materials have received significant interest as potential electromechanical materials. Flexoelectricity is an electromechanical coupling between strain gradient and polarization. Unlike piezoelectricity, which exists only in non-centrosymmetric materials, flexoelectricity theoretically exists in all dielectric materials. However, most work on the electromechanical energy conversion potential of 2D materials has focused on their piezoelectric, and not flexoelectric behavior and properties. In the present work…
Chemical vapor deposition has been most recently employed to fabricate centimeter-scale high-quality single-layer MoSi2N4 (Science; 2020;369; 670). Motivated by this exciting experimental advance, herein we conduct extensive first-principles based simulations to explore the stability, mechanical properties, lattice thermal conductivity, piezoelectric and flexoelectric response, and photocatalytic and electronic features of MA2Z4 (M = Cr, Mo, W; A = Si, Ge; Z = N, P) monolayers. The considered nanosheets are found to exhibit dynamical stability and remarkably high mechanical properties. Moreove…
Compound phases often display properties that are symmetry-forbidden relative to their nominal, average crystallographic symmetry, even if extrinsic reasons (defects, strain, imperfections) are not apparent. Here, we investigate macroscopic inversion symmetry breaking in nominally centrosymmetric materials and measure Resonant Piezoelectric Spectroscopy (RPS) and Resonant Ultrasound Spectroscopy (RUS) in 15 compounds, 18 samples, and 21 different phases, including unpoled ferroelectrics, paraelectrics, relaxors, ferroelastics, incipient ferroelectrics, and isotropic materials with low defect c…
Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, the electromechanical response for a finite sample is "symmetric". "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consi…
Piezoelectricity is inherent only in noncentrosymmetric materials, but a piezoelectric response can also be obtained in centrosymmetric crystals if subjected to inhomogeneous deformation. This phenomenon, known as flexoelectricity, affects the functional properties of insulators, particularly thin films of high permittivity materials. We have measured strain-gradient-induced polarization in single crystals of paraelectric SrTiO$_3$ as a function of temperature and orientation down to and below the 105 K phase transition. Estimates were obtained for all the components of the flexoelectric tenso…
Flexoelectricity has garnered much attention owing to its ability to bring electromechanical functionality to non-piezoelectric materials and its nanoscale significance. In order to move towards a more complete understanding of this phenomenon and improve the efficacy of flexoelectric-based devices, it is necessary to quantify microstructural contributions to flexoelectricity. Here we characterize the flexoelectric response of bulk centrosymmetric LaAlO$_3$ crystals with different twin boundary microstructures. We show that twin boundary flexoelectric contributions are comparable to intrinsic …
The triboelectric effect, charge transfer during sliding, is well established but the thermodynamic driver is not well understood. We hypothesize here that flexoelectric potential differences induced by inhomogeneous strains at nanoscale asperities drive tribocharge separation. Modelling single asperity elastic contacts suggests that nanoscale flexoelectric potential differences of $\pm$1-10 V or larger arise during indentation and pull-off. This hypothesis agrees with several experimental observations, including bipolar charging during stick-slip, inhomogeneous tribocharge patterns, charging …
Oxygen vacancies, especially their distribution, are directly coupled to the electromagnetic properties of oxides and related emergent functionalities that have implication in device applications. Here using a homoepitaxial strontium titanate thin film, we demonstrate a controlled manipulation of the oxygen vacancy distribution using the mechanical force from a scanning probe microscope tip. By combining Kelvin probe force microscopy imaging and phase-field simulations, we show that oxygen vacancies can move under a stress-gradient-induced depolarisation field. When tailored, this nanoscale fl…
Flexoelectricity is a universal electromechanical coupling effect whereby all dielectric materials polarize in response to strain gradients. In particular, nanoscale flexoelectricity promises exotic phenomena and functions, but reliable characterization methods are required to unlock its potential. Here, we report anomalous mechanical control of quantum tunnelling that allows for characterizing nanoscale flexoelectricity. By applying strain gradients with an atomic force microscope tip, we systematically polarize an ultrathin film of otherwise nonpolar SrTiO$_{3}$, and simultaneously measure t…
We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wavevector q around the Gamma (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q…
Abstract: In this paper we show that experimentally realizable apparently piezoelectric thin-film super-lattices can be created from non-piezoelectric materials provided an odd-order (e.g. trilayer) stacking sequence is used. The size-dependent mechanism of flexoelectricity, which couples gradients of strain to polarization, allows such a possibility. We present closed-form analytical expressions for the response of various thin-film and super-lattice configurations. We also clarify some of the subtleties that arise in considering interface boundary conditions in the theory of flexoelectricity…
Dielectric nano-swithes made of the materials that exhibit piezoelectric and/or flexoelectric properties with significant electro-mechanical coupling are considered. In this case, a nonuniform strain field may locally break inversion symmetry and induce polarization even in nonpiezoelectrics. At reducing dimensions to the nanoscale, the flexoelectric effect demonstrates the nonlocality of the dielectric materials and plays more significant role than piezoelectric effect. The flexoelectric effect is included into consideration via additional term coupling strain gradient and polarization in the…
We report on nanoscale strain gradients in ferroelectric HoMnO3 epitaxial thin films, resulting in a giant flexoelectric effect. Using grazing-incidence in-plane X-ray diffraction, we measured strain gradients in the films, which were 6 or 7 orders of magnitude larger than typical values reported for bulk oxides. The combination of transmission electron microscopy, electrical measurements, and electrostatic calculations showed that flexoelectricity provides a means of tuning the physical properties of ferroelectric epitaxial thin films, such as domain configurations and hysteresis curves.
Piezoelectric nanowires are promising materials for sensing, actuation and energy harvesting, due to their enhanced properties at the nanoscale. However, quantitative characterization of piezoelectricity in nanomaterials is challenging due to practical limitations and the onset of additional electromechanical phenomena, such as the triboelectric and piezotronic effects. Here, we present an open-circuit conductive atomic force microscopy (cAFM) methodology for quantitative extraction of the axial piezoelectric coefficients of nanowires. We show, both theoretically and experimentally, that the s…
Motived by experimentally synthesized $\mathrm{MoSi_2N_4}$ (\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020})), the intrinsic piezoelectricity in monolayer $\mathrm{XSi_2N_4}$ (X=Ti, Zr, Hf, Cr, Mo and W) are studied by density functional theory (DFT). Among the six monolayers, the $\mathrm{CrSi_2N_4}$ has the best piezoelectric strain coefficient $d_{11}$ of 1.24 pm/V, and the second is 1.15 pm/V for $\mathrm{MoSi_2N_4}$. Taking $\mathrm{MoSi_2N_4}$ as a example, strain engineering is applied to improve $d_{11}$. It is found that tensile biaxial strain can enhance $d_{11}$ of $\mat…
Flexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the response of electrical polarization to mechanical strain gradients while not restricted to the symmetry of materials. However, large elastic deformation in most solids is usually difficult to achieve and the strain gradient at minuscule is challenging to control. Here we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~ 1.2 nm-1) within 3 ~ 4 unit-cells, and thus obtain atomic-scale flexoelectric polarization up to ~ 38 μC/cm2 at a 24 LaAlO3 grai…
Low-dimensional (LD) transition metal dichalcogenides (TMDs) in the form of nanoflakes, which consist of one or several layers, are the subject of intensive fundamental and applied research. Due to the size-induced transition from a bulk to nanoscale, they can be both nonpolar, piezoelectric or even ferroelectric. Also, in terms of electronic properties, they can be direct-band semiconductors, semi-metals or even metals. The tuning of the electronic properties in the LD-TMDs are commonly related with applied strains and strain gradients, which can affect strongly their polar properties via the…
Piezoelectric semiconductor III-Nitride nanostructures have received increasing interest as an alternative material for energy harvesters, sensors, and self-sustainable electronics, demanding well-clarification of their piezoelectric behavior. Despite the feasibility of piezoresponse force microscopy (PFM) to resolve piezo-responses at the nanoscale, several difficulties arise when the measurements are performed on low piezo-coefficient materials due to various artifacts. This work shows that semi-quantitative PFM on low piezo-coefficient III-Nitrides can be achieved in high-aspect-ratio nanos…
Nanoscale enables a broad range of electromechanical coupling mechanisms that are forbidden or negligible in the materials. We conduct a theoretical study of the electromechanical response of thin paraelectric films with mobile vacancies (or ions) paradigmatic for capacitor-type measurements in X-ray scattering, piezoresponse force microscopy (PFM), and electrochemical strain microscopy (ESM). Using quantum paraelectric SrTiO3 film as a model material with well known electromechanical, electronic and electrochemical properties, we evaluate the contributions of electrostriction, Maxwell stress,…
Ferroelectric oxides have attracted much attention due to their wide range of applications, especially in electronic devices such as nonvolatile memories and tunnel junctions. As a result, the monolithic integration of these materials into silicon technology and its nanostructuration to develop alternative cost-effective processes are among the central points in current technology. In this work, we used a chemical route to obtain nanowire thin films of a novel Sr1+δMn8O16 (SMO) hollandite-type manganese oxide on silicon. Scanning transmission electron microscopy combined with crystallographic …
Piezoresponse force microscopy (PFM) is a powerful tool widely used to characterize piezoelectricity and ferroelectricity at the nanoscale. However, it is necessary to distinguish microscopic mechanisms between piezoelectricity and non-piezoelectric contributions measured by PFM. In this work, we systematically investigate the first and second harmonic apparent piezoresponses of silicon wafer in both vertical and lateral modes, and we show that it exhibits apparent electromechanical response that is quadratic to the applied electric field, possibly arising from ionic electrochemical dipoles in…
A nanometric needle sensor mounted in an Atomic Force Microscopy allows systematic picometer-range distance measurements. This force sensing device is used in Piezoresponse Force Microscopy (PFM) as a distance sensor, by employing the cantilever spring constant as the conversion factor opening a pathway to explore the piezoelectric effect at the nanoscale. The force-distance equivalence is achieved if the force sensor does not disturb the system to study, solely. In this manuscript we report a systematic study in which different Lead Zirconate Titanate (PZT) materials, having different d33 val…
