Piezoelectric Tensor Research Articles

Low-temperature piezoresponse force microscopy on barium titanate

Piezoresponse force microscopy (PFM) is a well-established method to study ferroelectric domains on the nanometer length scale. Here, we apply low-temperature PFM and Kelvin probe force microscopy (KPFM) to investigate the domain configuration of (111)-oriented barium titanate in the temperature range from 150 K to 290 K. We are able to identify all three ferroelectric phases and domain orientations from the combined PFM, KPFM, and topographic data. Ferroelectric phase transitions manifest in changes of the piezoelectric tensor elements as well as in variations of the spatial domain arrangement. A complete reordering of domains occurs exclusively upon the rhombohedral-to-orthorhombic phase transition during heating.

Low-temperature phase transition in γ-glycine single crystal. Pyroelectric, piezoelectric, dielectric and elastic properties

Temperature changes in the pyroelectric, piezoelectric, elastic and dielectric properties of γ-glycine crystals were studied in the range 100 ÷ 385 K. The pyroelectric coefficient increases monotonically in this temperature range and its value at RT was compared with that of other crystals having glycine molecules. A big maximum in the d14 component of piezoelectric tensor compared by maximum in attenuation of the resonant face-shear mode were observed at 189 K. The components of the elastic stiffness tensor and other components of the piezoelectric tensor show anomalies at this temperature. The components of electromechanical coupling coefficient determined indicate that γ-glycine is a weak piezoelectric. The real and imaginary part of the dielectric constant measured in the direction perpendicular to the trigonal axis show the relaxation anomalies much before 198 K and the activation energies were calculated. These anomalies were interpreted as a result of changes in the NH3+ vibrations through electron-phonon coupling of the so called “dynamical transition”. The anomalies of dielectric constant ε*11 and piezoelectric tensor component d14 taking place at 335 K are associated with an increase in ac conductivity caused by charge transfer of protons.

Spontaneous piezoelectric effect as order parameter in (NH4)2CuBr4·2H2O crystal

Temperature change of piezoelectric properties of (NH4)2CuBr4·2H2O crystal in the low-temperature ferroelastoelectric phase is studied. The macroscopic order parameter is proved to be the h36 component of the spontaneous piezoelectric tensor. The critical exponent related with the phase transition is α=0.60±0.05.

Shear Piezoelectricity in Poly(vinylidenefluoride-co-trifluoroethylene): Full Piezotensor Coefficients by Molecular Modeling, Biaxial Transverse Response, and Use in Suspended Energy-Harvesting Nanostructures.

The intrinsic flexible character of polymeric materials causes remarkable strain deformations along directions perpendicular to the applied stress. The biaxial response in the shear piezoelectricity of polyvinylidenefluoride copolymers is analyzed and their full piezoelectric tensors are provided. The microscopic shear is exploited in single suspended nanowires bent by localized loading to couple flexural deformation and transverse piezoelectric response.

First-Principles Study of Properties of Strained PbTiO3/KTaO3 Superlattice**Supported by the National Natural Science Foundation of China under Grant Nos 11372085 and 10902029, and the Shenzhen Science and Technology Project under Grant No JCYJ20150625142543461.

The impacts of strain and polar discontinuities on the performance of superlattices have attracted widespread attention. Using first-principles calculation, we study the polarization and piezoelectricity of PbTiO3/KTaO3 (PTO/KTO) superlattices with strain and polar discontinuities. The strain caused by lattice mismatch between the superlattice and the substrate induces lattice distortion, the displacement of each atom and dynamical charge transfer between the Ti atom or Ta atom and the O atoms in the PTO/KTO superlattice. With more compressive or less tensile strain, the polarization value increases linearly, piezoelectric tensor e31 (e32) increases while e33 and e25 (e16) increase negatively. Polarity discontinuity caused by the interfacial charge will produce large irreversible polarization. Proved by Γ-point phonons of PTO/KTO superlattices of different strain values, the polar discontinuity and the piezoelectric properties are just weakly dependent on temperature as found in PTO/KTO superlattices.

The internal-strain tensor of crystals for nuclear-relaxed elastic and piezoelectric constants: on the full exploitation of its symmetry features.

Symmetry features of the internal-strain tensor of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the quantum-mechanical evaluation of the internal-strain tensor of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain tensor is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric tensors of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients.

Direct Piezoelectric Tensor of 3D Periodic Systems through a Coupled Perturbed Hartree–Fock/Kohn–Sham Method

Abstract A quasi-analytical theoretical method is devised, and implemented in the Crystal program, for calculation of the direct “proper” piezoelectric tensor of periodic systems including both the clamped-nuclei electronic and nuclear relaxation contributions. It is based on using the analytical Coupled-Perturbed-Hartree–Fock/Kohn–Sham (CPHF/KS) procedure to obtain dipole derivatives with respect to lattice deformations as well as internal coordinates. The sole numerical step required involves building the Hessian matrix through differentiation of analytical energy gradients. Two prototypical piezoelectric, non-ferroelectric, crystals, namely ZnO and α-quartz, are used to demonstrate the accuracy and computational efficiency of our new scheme, which significantly improves upon the commonly used numerical Berry phase approach.

Enhanced piezoelectricity and modified dielectric screening of two-dimensional group-IV monochalcogenides

We use first-principles calculations to investigate the lattice properties of group-IV monochalcogenides. These include static dielectric permittivity, elastic and piezoelectric tensors. For the monolayer, it is found that the static permittivity, besides acquiring a dependence on the interlayer distance, is comparatively higher than in the 3D system. In contrast, it is found that elastic properties are little changed by the lower dimensionality. Poisson ratios relating in-plane deformations are close to zero, and the existence of a negative Poisson ratio is also predicted for the GeS compound. Finally, the monolayer shows piezoelectricity, with piezoelectric constants higher than those recently predicted to occur in other 2D systems, such as hexagonal BN and transition-metal dichalcogenide monolayers.

Growth of AgGaGe3−xSnxSe8 single crystals with light-operated piezoelectricity

We present a growth and photoinduced piezeoelctricity for novel chalcogenide single crystalline alloys – AgGaGe3−xSnxSe8. The titled crystals possess promising laser-operated piezoelectric properties. A specific procedure of Bridgman–Stockbarger method synthesis is described. The effective piezoelectric tensor coefficient deff is reduced by 74% upon illumination with a 400mW 532nm continuous wave laser. The relaxation of the piezoelectricity after switching off of the laser is explored. A principal role of Sn ions is demonstrated.

Ab Initio Prediction of Piezoelectricity in Two-Dimensional Materials.

Two-dimensional (2D) materials present many unique materials concepts, including material properties that sometimes differ dramatically from those of their bulk counterparts. One of these properties, piezoelectricity, is important for micro- and nanoelectromechanical systems applications. Using symmetry analysis, we determine the independent piezoelectric coefficients for four groups of predicted and synthesized 2D materials. We calculate with density-functional perturbation theory the stiffness and piezoelectric tensors of these materials. We determine the in-plane piezoelectric coefficient d11 for 37 materials within the families of 2D metal dichalcogenides, metal oxides, and III-V semiconductor materials. A majority of the structures, including CrSe2, CrTe2, CaO, CdO, ZnO, and InN, have d11 coefficients greater than 5 pm/V, a typical value for bulk piezoelectric materials. Our symmetry analysis shows that buckled 2D materials exhibit an out-of-plane coefficient d31. We find that d31 for 8 III-V semiconductors ranges from 0.02 to 0.6 pm/V. From statistical analysis, we identify correlations between the piezoelectric coefficients and the electronic and structural properties of the 2D materials that elucidate the origin of the piezoelectricity. Among the 37 2D materials, CdO, ZnO, and CrTe2 stand out for their combination of large piezoelectric coefficient and low formation energy and are recommended for experimental exploration.

Studying the Polarization Switching in Polycrystalline BiFeO3 Films by 2D Piezoresponse Force Microscopy.

For rhombohedral multiferroelectrics, non-180° ferroelectric domain switching may induce ferroelastic and/or (anti-)ferromagnetic effect. So the determination and control of ferroelectric domain switching angles is crucial for nonvolatile information storage and exchange-coupled magnetoelectric devices. We try to study the intrinsic characters of polarization switching in BiFeO3 by introducing a special data processing method to determine the switching angle from 2D PFM (Piezoresponse Force Microscopy) images of randomly oriented samples. The response surface of BiFeO3 is first plotted using the piezoelectric tensor got from first principles calculations. Then from the normalized 2D PFM signals before and after switching, the switching angles of randomly oriented BiFeO3 grains can be determined through numerical calculations. In the polycrystalline BiFeO3 films, up to 34% of all switched area is that with original out-of-plane (OP) polarization parallel to the poling field. 71° polarization switching is more favorable, with the area percentages of 71°, 109° and 180° domain switching being about 42%, 29% and 29%, respectively. Our analysis further reveals that IP stress and charge migration have comparable effect on switching, and they are sensitive to the geometric arrangements. This work helps exploring a route to control polarization switching in BiFeO3, so as to realize desirable magnetoelectric coupling.

Laser-induced piezoelectricity in AgGaGe3–xSixSe8chalcogenide single crystals

Photoinduced changes of piezoelectric coefficients for novel chalcogenide AgGaGe 3– x Si x Se 8 ( x = 0.15, 0.3, 0.6, 0.9) single crystals are discovered. The measurements were performed during illumination by cw 532 nm laser (above energy band gap) with power about 400 mW. The relaxation after switching off of the laser beam was studied. Additional temperature dependences of piezoelectric diagonal tensor components were recorded to separate the thermal effect with respect to pure electronic contribution to the photoinduced piezoelectricity. In addition to the photoinduced piezoelectric effect FTIR spectra are studied in order to explore the influence of the thermal contribution. The photoinduced changes with taking into account of temperature contribution have achieved magnitude equal to approximately 50–60% for all the studied samples and the changes were found to be completely reversible. The possible mechanisms for the observed effects are discussed and additional quantum chemical DFT simulations for the principal structural fragments were performed.

Structure, elastic and piezoelectric properties of A3BO7 (A = Ga, Al; B = P, As) compounds: A DFT study

A first-principles study of the structure, elastic and piezoelectric properties of A3BO7 (A=Ga, Al; B=P, As) using the density functional perturbation theory (DFPT) has been performed. The structure-properties relation was established. We found that the piezoelectric constant is highly sensitive to the distortion of crystal structures. The larger A–O–B bridging angle θ is, the smaller piezoelectric stress coefficient e15 will be. The obtained piezoelectric tensor d15 of Ga3AsO7 is −23.9pC/N, which is more than ten times larger than the d11 of SiO2. The new finding will be useful in the applications of Ga3AsO7 in the piezoelectric devices with high Curie temperature.

Finite element analysis of the macro fiber composite actuator: macroscopic elastic and piezoelectric properties and active control thereof by means of negative capacitance shunt circuit

The finite element method (FEM) model of a piezoelectric macro fiber composite (MFC) is presented. Using a specially developed numerical model, the complete set of macroscopic values of elastic compliance and piezoelectric tensors is computed. These values are useful in numerical FEM simulations of more complex systems such as noise and vibration suppression devices or active acoustic metamaterials, where the MFC actuator can be approximated by a plate-like uniform piezoelectric material. Using this approach, a great reduction of the FEM model complexity can be achieved. The computed numerical macroscopic values of the MFC actuator are compared with MFC manufacturerʼs data and with data obtained using different computational methods. A demonstration of active tuning of effective elastic constants of the piezoelectric MFC actuator by means of a shunt electric circuit is presented. The effective material constants are computed using the FEM model developed. The effect of the shunt circuit capacitance on the effective anisotropic Youngʼs moduli is analyzed in detail. A method for finding the proper shunt circuit adjustment that yields the maximum values of the MFC actuator Youngʼs modulus is shown. Possible applications to noise and vibration suppression are discussed.

Complete electroelastic set for the (YXt)-45° cut of a KNbO3 single crystal

A complete and consistent set (elastic, dielectric, and piezoelectric tensors) of a commercial lead-free (YXt)-45° cut KNbO3 single crystal is reported. These data were obtained using several samples and the resonance-antiresonance method. Particular attention was paid to the consistency of this delivered database. A genetic algorithm with an appropriate criterion was used. Electromechanical characterization revealed a high thickness coupling factor of approximately 60%. These properties make this single crystal a good candidate for several applications such as medical imaging. This complete set provides a basis for simulation designs of such devices integrating this piezoelectric lead-free material, especially for ultrasonic transducers.

Ferroelastoelectric phase transition in (NH4)2CuCl4·2H2O single crystal

The (NH4)2CuCl4·2H2O crystal exhibits anomalous thermal, piezoelectric, dielectric and elastic properties in the vicinity of the ferroelastoelectric phase transition at TC = 200 K. Macroscopic order parameter is the h36 component of the spontaneous piezoelectric tensor connecting polarisation P3 and strain η6. The temperature change in h36 component was proportional to (TC − T)α, where α = 0.58 ± 0.05. Close to TC changes in dielectric permittivity were negligible. High value of ac conductivity in the high-temperature phase results from protons jumping between disordered ions NH4+ and between molecules of crystallisation water. Only longitudinal ultrasonic waves exhibited an abrupt change upon the phase transition. The relaxation time of the order parameter was determined from anomalous changes in attenuation of the longitudinal waves.

Piezoelectric molecular dynamics model for boron nitride nanotubes

A classical molecular dynamics model with an incorporated strain-dependent dipole potential energy term is introduced to represent the piezoelectric properties of boron nitride nanotubes (BNNTs). The model allows for an analytical expression of the piezoelectric tensor of hexagonal BN monolayers in terms of the properties of the interatomic potential and two fitting parameters. The deformation-induced polarization predicted by this model is verified against the results of previously published electronic structure (ab-initio and tight-binding) calculations. The model works well for BNNTs over the full range of chiral angles from φ=0° (zig-zag tubes) to φ=30° (armchair tubes) and under loading in both tensile and twist modes. The presented model can be a foundation for atomic-level modeling of the electroactive properties of large systems of BNNTs and BNNT composites, as well as a base for analytical studies.

Polarization in dielectrics modeled as micromorphic continua

On the basis of an extension of the micromorphic continuum theory accounting for electromagneto-elastic coupling in a consistent way, we develop a continuum formulation of polarization in dielectrics. The introduction of dielectric multipoles by means of the microdisplacement and the exploitation of their linearized evolution equations allows to achieve a representation of the polarization in terms of macroscopic and microscopic strain measures and in particular of the microrotation tensor. The microdeformation is then expressed by means of the macroscopic strain and the dependence of polarization from the gradients of the mechanical displacement is explicitly written, up to the third order in multipoles. Piezoelectric and flexoelectric tensors are thus obtained, and it is shown that they uniquely depend on electric quadrupoles and octupoles. We also discuss the reduction in the present model to micropolar continua, giving a representation of the flexoelectric tensor for isotropic micropolar dielectrics.

Piezoelectric, elastic, structural and dielectric properties of the Si1−xGexO2 solid solution: a theoretical study

We apply first principles quantum mechanical techniques to the study of the solid solution Si1−xGexO2 of α-quartz where silicon atoms are progressively substituted with germanium atoms, to different extents, as a function of the substitutional fraction x. For the first time, the whole range of the substitution (x = 0.0, 0.1, 0., 0.5, 0., 0.8, 1.0), including pure end-members α-SiO2 and α-GeO2, is explored. An elongated supercell (doubled along the c crystallographic axis) is built with respect to the unit cell of pure α-quartz and a set of 13 symmetry-independent configurations is considered. Their structural, energetic, dielectric, elastic and piezoelectric properties are computed and analyzed. All the calculations are performed using the CRYSTAL14 program with a Gaussian-type function basis set with pseudopotentials, and the hybrid functional PBE0; all geometries are fully optimized at this level of theory. In particular, for each configuration, fourth-rank elastic and compliance tensors and third-rank direct and converse piezoelectric tensors are computed. It has already been shown that the structural distortion of the solid solution increases, almost linearly, as the substitutional fraction x increases. The piezoelectric properties of the Si1−xGexO2 solid solution are found to increase with x, with a similar quasi-linear behavior. The electromechanical coupling coefficients are enhanced as well and the linear trend recently predicted by Ranieri et al (2011 Inorg. Chem. 50 4632) can be confirmed from first principles calculations. These doped crystals do represent good candidates for technological applications requiring high piezoelectric coupling and high thermal stability.

A general closed-form solution for the overall response of piezoelectric composites with periodic and random particulate microstructures

In this paper, we make use of a new iterative homogenization technique in finite electroelastostatics (Lopez-Pamies, 2014) to derive a closed-form solution for the overall response of two-phase piezoelectric composites with particulate microstructures. The calculations amount to solving a system of Riccati differential equations for the effective elastic, dielectric, and piezoelectric tensors of the composites, where the volume fraction of the inclusions plays the role of independent variable. The solution is valid for any choice of piezoelectric behaviors for the underlying matrix and inclusions, and any choice of the one- and two-point correlation functions describing the microstructure. In addition to discussing the key theoretical and practical features of the solution, its descriptive and predictive capabilities are illustrated via comparisons with a broad range of experimental data and full-field simulations (available from the literature) for composites with periodic and random distributions of inclusions of various shapes.