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Keywords = piezoelectric tensor

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15 pages, 36663 KiB  
Article
Self-Sensing of Piezoelectric Micropumps: Gas Bubble Detection by Artificial Intelligence Methods on Limited Embedded Systems
by Kristjan Axelsson, Mohammadhossien Sheikhsarraf, Christoph Kutter and Martin Richter
Sensors 2025, 25(12), 3784; https://doi.org/10.3390/s25123784 - 17 Jun 2025
Viewed by 357
Abstract
Gas bubbles are one of the main disturbances encountered when dispensing drugs of microliter volumes using portable miniaturized systems based on piezoelectric diaphragm micropumps. The presence of a gas bubble in the pump chamber leads to the inaccurate administration of the required dose [...] Read more.
Gas bubbles are one of the main disturbances encountered when dispensing drugs of microliter volumes using portable miniaturized systems based on piezoelectric diaphragm micropumps. The presence of a gas bubble in the pump chamber leads to the inaccurate administration of the required dose due to its impact on the flowrate. This is particularly important for highly concentrated drugs such as insulin. Different types of sensors are used to detect gas bubbles: inline on the fluidic channels or inside the pump chamber itself. These solutions increase the complexity, size, and cost of the microdosing system. To address these problems, a radically new approach is taken by utilizing the sensing capability of the piezoelectric diaphragm during micropump actuation. This work demonstrates the workflow to build a self-sensing micropump based on artificial intelligence methods on an embedded system. This is completed by the implementation of an electronic circuit that amplifies and samples the loading current of the piezoelectric ceramic with a microcontroller STM32G491RE. Training datasets of 11 micropumps are generated at an automated testbench for gas bubble injections. The training and hyper-parameter optimization of artificial intelligence algorithms from the TensorFlow and scikit-learn libraries are conducted using a grid search approach. The classification accuracy is determined by a cross-training routine, and model deployment on STM32G491RE is conducted utilizing the STM32Cube.AI framework. The finally deployed model on the embedded system has a memory footprint of 15.23 kB, a runtime of 182 µs, and detects gas bubbles with an accuracy of 99.41%. Full article
(This article belongs to the Section Physical Sensors)
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33 pages, 669 KiB  
Article
On Anisothermal Electromagnetic Elastic Deformations in Flight in Fair Weather and Lightning Storms
by Luiz M. B. C. Campos and Manuel J. S. Silva
Appl. Sci. 2025, 15(7), 3605; https://doi.org/10.3390/app15073605 - 25 Mar 2025
Viewed by 236
Abstract
The thermomechanical effects on aircraft structures in flight are compared between fair weather and a lightning storm based on a model problem, namely, equations of anisothermal unsteady piezoelectromagnetism are solved in the particular case of a parallel-sided slab assuming (i) steady conditions and [...] Read more.
The thermomechanical effects on aircraft structures in flight are compared between fair weather and a lightning storm based on a model problem, namely, equations of anisothermal unsteady piezoelectromagnetism are solved in the particular case of a parallel-sided slab assuming (i) steady conditions and spatial dependence only on the coordinate orthogonal to the slab; (ii) the displacement vector orthogonal to the slab; (iii) the magnetic field orthogonal to the electric field, with both in the plane parallel to the sides of the slab. The exact analytical solution is obtained in the linear approximation for the displacement vector, electric and magnetic fields and temperature as function of the coordinate normal to the slab, taking into account heating by the Joule effect of Ohmic electric currents and Fourier thermal conduction. These specify the strain and stress tensors, the electric current and the heat flux. The material properties involved include the mass density, dielectric permittivity, magnetic permeability, elastic stiffness tensor, electromagnetic coupling and thermal stress tensors, pyroelectric and pyromagnetic vectors and piezoelectric and piezomagnetic tensors. The analytic results of the theory are simplified assuming (i) isotropic material properties; (ii) a steady state independent of time. The profiles as a function of the coordinate normal to the slab of the electric and magnetic fields, temperature and heat flux and displacement, strain and stress are obtained in these conditions. Full article
(This article belongs to the Special Issue Novel Applications of Electromagnetic Energy Systems)
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16 pages, 323 KiB  
Article
Three-Dimensional and Two-Dimensional Green Tensors of Piezoelectric Quasicrystals
by Markus Lazar and Eleni Agiasofitou
Crystals 2024, 14(10), 835; https://doi.org/10.3390/cryst14100835 - 26 Sep 2024
Cited by 3 | Viewed by 1625
Abstract
In this work, within the framework of the linear piezoelectricity theory of quasicrystals, the three-dimensional and two-dimensional Green tensors for arbitrary piezoelectric quasicrystals are derived. In the piezoelectricity of quasicrystals, where phonon, phason and electric fields exist, we introduce the corresponding multifields by [...] Read more.
In this work, within the framework of the linear piezoelectricity theory of quasicrystals, the three-dimensional and two-dimensional Green tensors for arbitrary piezoelectric quasicrystals are derived. In the piezoelectricity of quasicrystals, where phonon, phason and electric fields exist, we introduce the corresponding multifields by developing a hyperspace notation for piezoelectric quasicrystals. Using Fourier transform and the multifield formalism, the three-dimensional Green tensor for piezoelectric quasicrystals as well as its spatial gradient necessary for applications, are derived. The solutions for the “displacement”, “distortion” and “stress” multifields in the presence of a “force” multifield in a piezoelectric quasicrystal as well as the solution of the generalised Kelvin problem, are given. In addition, the two-dimensional Green tensors of piezoelectric quasicrystals as well as of quasicrystals, are determined. Full article
(This article belongs to the Special Issue Structures, Properties and Applications of Quasicrystals)
12 pages, 2072 KiB  
Article
Piezoelectric Gauge of Small Dynamic Bending Strains
by Nelly Rogacheva, Vladimir Sidorov and Yulia Zheglova
Buildings 2024, 14(8), 2447; https://doi.org/10.3390/buildings14082447 - 8 Aug 2024
Cited by 3 | Viewed by 1017
Abstract
This paper is devoted to a new gauge of small dynamic bending deformations of structures. Unlike previously existing strain gauges that measure elongation or compression at a certain point on the surface of a deformable body, the proposed gauge measures the change in [...] Read more.
This paper is devoted to a new gauge of small dynamic bending deformations of structures. Unlike previously existing strain gauges that measure elongation or compression at a certain point on the surface of a deformable body, the proposed gauge measures the change in curvature at a point on the surface of a deformable body and does not respond to elongation–compression strains. The gauge is a layered bar made of piezoelectric and elastic materials. It functions using the direct piezoelectric effect. In order to competently study the deformed state of a structure at points on a surface, it is necessary to determine all components of the strain tensor. The gauges currently used measure only elongational or compressive strains, which does not provide a complete picture of the strain state. It is very important to complement these deformations with bending strains measured by the new gauge. Full article
(This article belongs to the Special Issue Safety and Optimization of Building Structures—2nd Edition)
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11 pages, 2905 KiB  
Article
Investigation of Piezoelectric Properties of Wurtzite AlN Films under In-Plane Strain: A First-Principles Study
by Guoqiang Qin, Ziyuan Zhao, Ao Wang, Wentao Wang, Shengjian Qin, Hongya Wu, Zhigang Yang, Gang Yu and Guanglei Zhang
Coatings 2024, 14(8), 984; https://doi.org/10.3390/coatings14080984 - 4 Aug 2024
Cited by 1 | Viewed by 3769
Abstract
This research article presents a comprehensive first-principles study on the piezoelectric properties of Wurtzite Aluminum Nitride (AlN) films under in-plane strain conditions. By calculating the piezoelectric tensor coefficients (e33, e31, and e15), we investigate the variation patterns of these constants with respect to [...] Read more.
This research article presents a comprehensive first-principles study on the piezoelectric properties of Wurtzite Aluminum Nitride (AlN) films under in-plane strain conditions. By calculating the piezoelectric tensor coefficients (e33, e31, and e15), we investigate the variation patterns of these constants with respect to in-plane strain. Our results indicate significant changes in the piezoelectric constants within the range of in-plane strain considered, exhibiting a linear trend despite opposite trends for e33 compared to e31 and e15. This study highlights the extreme sensitivity of AlN films’ piezoelectric performance to in-plane strain, suggesting its potential as an effective means for tuning and optimizing the piezoelectric properties of AlN-based devices. Full article
(This article belongs to the Special Issue Recent Progress on Functional Films and Surface Science)
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14 pages, 4280 KiB  
Article
Insights into Antisite Defect Complex Induced High Ferro-Piezoelectric Properties in KNbO3 Perovskite: First-Principles Study
by Bei Li, Yilun Zhang, Meng Wang, Xu Zhang, Xiaofeng Zhang and Kai Liu
Materials 2024, 17(14), 3442; https://doi.org/10.3390/ma17143442 - 11 Jul 2024
Cited by 1 | Viewed by 1410
Abstract
Improving ferro-piezoelectric properties of niobate-based perovskites is highly desirable for developing eco-friendly high-performance sensors and actuators. Although electro-strain coupling is usually obtained by constructing multiphase boundaries via complex chemical compositions, defect engineering can also create opportunities for novel property and functionality advancements. In [...] Read more.
Improving ferro-piezoelectric properties of niobate-based perovskites is highly desirable for developing eco-friendly high-performance sensors and actuators. Although electro-strain coupling is usually obtained by constructing multiphase boundaries via complex chemical compositions, defect engineering can also create opportunities for novel property and functionality advancements. In this work, a representative tetragonal niobate-based perovskite, i.e., KNbO3, is studied by using first-principles calculations. Two intrinsic types of Nb antisite defect complexes are selected to mimic alkali-deficiency induced excess Nb antisites in experiments. The formation energy, electronic profiles, polarization, and piezoelectric constants are systematically analyzed. It is shown that the structural distortion and chemical heterogeneity around the energetically favorable antisite pair defects, i.e., (NbK4·+KNb4), lower the crystal symmetry of KNbO3 from tetragonal to triclinic phase, and facilitate polarization emergence and reorientation to substantially enhance intrinsic ferro-piezoelectricity (i.e., spontaneous polarization Ps of 68.2 μC/cm2 and piezoelectric strain constant d33 of 228.3 pC/N) without complicated doping and alloying. Full article
(This article belongs to the Section Materials Simulation and Design)
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16 pages, 5129 KiB  
Article
Piezoelectric Yield of Single Electrospun Poly(acrylonitrile) Ultrafine Fibers Studied by Piezoresponse Force Microscopy and Numerical Simulations
by Margherita Montorsi, Lorenzo Zavagna, Lorenzo Scarpelli, Bahareh Azimi, Simone Capaccioli, Serena Danti and Massimiliano Labardi
Polymers 2024, 16(10), 1305; https://doi.org/10.3390/polym16101305 - 7 May 2024
Cited by 3 | Viewed by 1285
Abstract
Quantitative converse piezoelectric coefficient (d33) mapping of polymer ultrafine fibers of poly(acrylonitrile) (PAN), as well as of poly(vinylidene fluoride) (PVDF) as a reference material, obtained by rotating electrospinning, was carried out by piezoresponse force microscopy in the constant-excitation frequency-modulation mode [...] Read more.
Quantitative converse piezoelectric coefficient (d33) mapping of polymer ultrafine fibers of poly(acrylonitrile) (PAN), as well as of poly(vinylidene fluoride) (PVDF) as a reference material, obtained by rotating electrospinning, was carried out by piezoresponse force microscopy in the constant-excitation frequency-modulation mode (CE-FM-PFM). PFM mapping of single fibers reveals their piezoelectric activity and provides information on its distribution along the fiber length. Uniform behavior is typically observed on a length scale of a few micrometers. In some cases, variations with sinusoidal dependence along the fiber are reported, compatibly with a possible twisting around the fiber axis. The observed features of the piezoelectric yield have motivated numerical simulations of the surface displacement in a piezoelectric ultrafine fiber concerned by the electric field generated by biasing of the PFM probe. Uniform alignment of the piezoelectric axis along the fiber would comply with the uniform but strongly variable values observed, and sinusoidal variations were occasionally found on the fibers laying on the conductive substrate. Furthermore, in the latter case, numerical simulations show that the piezoelectric tensor’s shear terms should be carefully considered in estimations since they may provide a remarkably different contribution to the overall deformation profile. Full article
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13 pages, 4418 KiB  
Article
Evaluation of a Machine Learning Algorithm to Classify Ultrasonic Transducer Misalignment and Deployment Using TinyML
by Des Brennan and Paul Galvin
Sensors 2024, 24(2), 560; https://doi.org/10.3390/s24020560 - 16 Jan 2024
Cited by 3 | Viewed by 1966
Abstract
The challenge for ultrasonic (US) power transfer systems, in implanted/wearable medical devices, is to determine when misalignment occurs (e.g., due to body motion) and apply directional correction accordingly. In this study, a number of machine learning algorithms were evaluated to classify US transducer [...] Read more.
The challenge for ultrasonic (US) power transfer systems, in implanted/wearable medical devices, is to determine when misalignment occurs (e.g., due to body motion) and apply directional correction accordingly. In this study, a number of machine learning algorithms were evaluated to classify US transducer misalignment, based on data signal transmissions between the transmitter and receiver. Over seven hundred US signals were acquired across a range of transducer misalignments. Signal envelopes and spectrograms were used to train and evaluate machine learning (ML) algorithms, classifying misalignment extent. The algorithms included an autoencoder, convolutional neural network (CNN) and neural network (NN). The best performing algorithm, was deployed onto a TinyML device for evaluation. Such systems exploit low power microcontrollers developed specifically around edge device applications, where algorithms were configured to run on low power, restricted memory systems. TensorFlow Lite and Edge Impulse, were used to deploy trained models onto the edge device, to classify signals according to transducer misalignment extent. TinyML deployment, demonstrated near real-time (<350 ms) signal classification achieving accuracies > 99%. This opens the possibility to apply such ML alignment algorithms to US arrays (capacitive micro-machined ultrasonic transducer (CMUT), piezoelectric micro-machined ultrasonic transducer (PMUT) devices) capable of beam-steering, significantly enhancing power delivery in implanted and body worn systems. Full article
(This article belongs to the Special Issue Energy Harvesting in Environmental Wireless Sensor Networks)
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23 pages, 354 KiB  
Article
On the Constitutive Modelling of Piezoelectric Quasicrystals
by Eleni Agiasofitou and Markus Lazar
Crystals 2023, 13(12), 1652; https://doi.org/10.3390/cryst13121652 - 30 Nov 2023
Cited by 9 | Viewed by 2285
Abstract
Quasicrystals endowed with piezoelectric properties belong nowadays to novel piezoelectric materials. In this work, the basic framework of generalized piezoelectricity theory of quasicrystals is investigated by providing an improvement of the existing constitutive modelling. It is shown, for the first time, that the [...] Read more.
Quasicrystals endowed with piezoelectric properties belong nowadays to novel piezoelectric materials. In this work, the basic framework of generalized piezoelectricity theory of quasicrystals is investigated by providing an improvement of the existing constitutive modelling. It is shown, for the first time, that the tensor of phason piezoelectric moduli is fully asymmetric without any major or minor symmetry, which has important consequences on the constitutive relations as well as on its classification with respect to the crystal systems and Laue classes. The exploration of the tensor of phason piezoelectric moduli has a significant impact on the understanding of the piezoelectric properties of quasicrystals. Using the group representation theory, the classification of the tensor of phason piezoelectric moduli with respect to the crystal systems and Laue classes is given for one-dimensional quasicrystals. The number of independent components of the phason piezoelectric moduli is determined for all 31 point groups of one-dimensional quasicrystals. It is proven that the 10 centrosymmetric crystallographic point groups have no piezoelectric effects and that the remaining 21 non-centrosymmetric crystallographic point groups exhibit piezoelectric effects due to both phonon and phason fields. Moreover, the constitutive relations for one-dimensional hexagonal piezoelectric quasicrystals of Laue class 9 with point group 6 and Laue class 10 with point group 6mm are explicitly derived, showing that the constitutive relations for piezoelectric quasicrystals depend on the considered Laue class as well as on the point group. Comparisons with existing results in the literature and discussion are also given. Full article
(This article belongs to the Special Issue Recent Advances in Quasicrystals)
36 pages, 10264 KiB  
Article
Reflection and Transmission Analysis of Surface Acoustic Wave Devices
by Tai-Ho Yu
Micromachines 2023, 14(10), 1898; https://doi.org/10.3390/mi14101898 - 1 Oct 2023
Cited by 2 | Viewed by 2684
Abstract
This paper presents a study of the propagation of surface acoustic waves in a single and periodic array of metal strip overlays on the surface of layered substrates. Responses of reflected and transmitted surface acoustic waves due to various geometric design parameters of [...] Read more.
This paper presents a study of the propagation of surface acoustic waves in a single and periodic array of metal strip overlays on the surface of layered substrates. Responses of reflected and transmitted surface acoustic waves due to various geometric design parameters of the grating arrays are investigated. An eight-dimensional matrix formulation based on Stroh formalism is adopted to analyze wave propagation in piezoelectric layered media. The dispersion curves for aluminum–zinc oxide films on glass substrates are determined using the surface impedance tensor method. A transfer matrix in terms of the state vectors in cooperation with continuity conditions on the edges of the grating array is used to determine the reflectivity and transmittance of the horizontally propagating surface acoustic waves. The analysis and simulation results show that when the surface acoustic wave is obliquely incident on an array of gratings and the strip width is equal to the gap between strips, the constructive interference of the reflected wave occurs at odd multiples of the strip width to a wavelength ratio of 0.25. When the strip width is unequal to the gap, the constructive interference of the reflected wave is an odd multiple of the strip width to a wavelength ratio of 0.5. An increase in the number of strips concentrates the reflectivity’s extreme frequencies, and an increase in the strip height increases the bandwidth of the extreme frequencies. Both of these increases strengthen the reflected wave’s constructive interferences. Full article
(This article belongs to the Special Issue Recent Advances in SAW Resonators)
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25 pages, 10305 KiB  
Article
Damage Localization on Composite Structures Based on the Delay-and-Sum Algorithm Using Simulation and Experimental Methods
by Cedric Bertolt Nzouatchoua, Mourad Bentahar, Silvio Montresor, Nicolas Colin, Vincent Le Cam, Camille Trottier and Nicolas Terrien
Sensors 2023, 23(9), 4368; https://doi.org/10.3390/s23094368 - 28 Apr 2023
Cited by 8 | Viewed by 2444
Abstract
Damage detection and localization based on ultrasonic guided waves revealed to be promising for structural health monitoring and nondestructive testing. However, the use of a piezoelectric sensor’s network to locate and image damaged areas in composite structures requires a number of precautions including [...] Read more.
Damage detection and localization based on ultrasonic guided waves revealed to be promising for structural health monitoring and nondestructive testing. However, the use of a piezoelectric sensor’s network to locate and image damaged areas in composite structures requires a number of precautions including the consideration of anisotropy and baseline signals. The lack of information related to these two parameters drastically deteriorates the imaging performance of numerous signal processing methods. To avoid such deterioration, the present contribution proposes different methods to build baseline signals in different types of composites. Baseline signals are first constructed from a numerical simulation model using the previously determined elasticity tensor of the structure. Since the latter tensor is not always easy to obtain especially in the case of anisotropic materials, a second PZT network is used in order to obtain signals related to Lamb waves propagating in different directions. Waveforms are then translated according to a simplified theoretical propagation model of Lamb waves in homogeneous structures. The application of the different methods on transversely isotropic, unidirectional and quasi-transversely isotropic composites allows to have satisfactory images that well represent the damaged areas with the help of the delay-and-sum algorithm. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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21 pages, 800 KiB  
Article
Stress–Charge Nonlinear Physical Description and Tensor Symmetries for Piezoelectric Materials
by A. F. Jaramillo-Alvarado, A. Torres Jacome, P. Rosales-Quintero, H. Vazquez-Leal, G. Diaz-Arango, J. Huerta-Chua and J. Martínez-Castillo
Materials 2023, 16(9), 3432; https://doi.org/10.3390/ma16093432 - 28 Apr 2023
Viewed by 1944
Abstract
Nonlinear piezoelectric materials are raised as a great replacement for devices that require low power consumption, high sensitivity, and accurate transduction, fitting with the demanding requirements of new technologies such as the Fifth-Generation of telecommunications (5G), the Internet of Things (IoT), and modern [...] Read more.
Nonlinear piezoelectric materials are raised as a great replacement for devices that require low power consumption, high sensitivity, and accurate transduction, fitting with the demanding requirements of new technologies such as the Fifth-Generation of telecommunications (5G), the Internet of Things (IoT), and modern radio frequency (RF) applications. In this work, the state equations that correctly predict the nonlinear piezoelectric phenomena observed experimentally are presented. Furthermore, we developed a fast methodology to implement the state equations in the main FEM simulation software, allowing an easy design and characterization of this type of device, as the symmetry structures for high-order tensors are shown and explained. The operation regime of each high-order tensor is discussed and connected with the main nonlinear phenomena reported in the literature. Finally, to demonstrate our theoretical deductions, we used the experimental measurements, which presented the nonlinear effects, which were reproduced through simulations, obtaining maximum percent errors for the effective elasticity constants, relative effective permittivity, and resonance frequencies of 0.79%, 2.9%, and 0.3%, respectively, giving a proof of the potential of the nonlinear state equations presented for the unifying of all nonlinear phenomena observed in the piezoelectric devices. Full article
(This article belongs to the Special Issue Piezoelectric Materials and Piezoelectric Robots)
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12 pages, 2695 KiB  
Article
Eshelby Tensors for Two-Dimensional Decagonal Piezoelectric Quasicrystal Composites
by Guangfang Li and Lianhe Li
Crystals 2022, 12(10), 1456; https://doi.org/10.3390/cryst12101456 - 14 Oct 2022
Cited by 3 | Viewed by 2102
Abstract
The Eshelby tensor for two-dimensional (2D) piezoelectric quasicrystal composites (QCs) is considered. The explicit expressions of Eshelby tensors for 2D piezoelectric QCs are given using the Green’s function method and the interior polarization tensor method, respectively. On this basis, numerical examples of the [...] Read more.
The Eshelby tensor for two-dimensional (2D) piezoelectric quasicrystal composites (QCs) is considered. The explicit expressions of Eshelby tensors for 2D piezoelectric QCs are given using the Green’s function method and the interior polarization tensor method, respectively. On this basis, numerical examples of the Eshelby tensor for 2D piezoelectric QCs with ellipsoidal inclusions are discussed in detail. Full article
(This article belongs to the Special Issue Feature Papers in Crystal Engineering in 2022)
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11 pages, 708 KiB  
Article
Mott Insulator Ca2RuO4 under External Electric Field
by Giuseppe Cuono and Carmine Autieri
Materials 2022, 15(19), 6657; https://doi.org/10.3390/ma15196657 - 26 Sep 2022
Cited by 4 | Viewed by 2797
Abstract
We have investigated the structural, electronic and magnetic properties of the Mott insulator Ca2RuO4 under the application of a static external electric field in two regimes: bulk systems at small fields and thin films at large electric fields. Ca2 [...] Read more.
We have investigated the structural, electronic and magnetic properties of the Mott insulator Ca2RuO4 under the application of a static external electric field in two regimes: bulk systems at small fields and thin films at large electric fields. Ca2RuO4 presents S- and L-Pbca phases with short and long c lattice constants and with large and small band gaps, respectively. Using density functional perturbation theory, we have calculated the Born effective charges as response functions. Once we break the inversion symmetry by off-centering the Ru atoms, we calculate the piezoelectric properties of the system that suggest an elongation of the system under an electric field. Finally, we investigated a four-unit cell slab in larger electric fields, and we found insulator–metal transitions induced by the electric field. By looking at the local density of states, we have found that the gap gets closed on surface layers while the rest of the sample is insulating. Correlated to the electric-field-driven gap closure, there is an increase in the lattice constant c. Regarding the magnetic properties, we have identified two phase transitions in the magnetic moments with one surface that gets completely demagnetized at the largest field investigated. In all cases, the static electric field increases the lattice constant c and reduces the band gap of Ca2RuO4, playing a role in the competition between the L-phase and the S-phase. Full article
(This article belongs to the Topic First-Principles Simulation—Nano-Theory)
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13 pages, 342 KiB  
Article
Further Study on C-Eigenvalue Inclusion Intervals for Piezoelectric Tensors
by Gang Wang, Xiaoxuan Yang, Wei Shao and Qiuling Hou
Axioms 2022, 11(6), 250; https://doi.org/10.3390/axioms11060250 - 26 May 2022
Cited by 1 | Viewed by 1889
Abstract
The C-eigenpair of piezoelectric tensors finds applications in the area of the piezoelectric effect and converse piezoelectric effect. In this paper, we provide some characterizations of C-eigenvectors by exploring the structure of piezoelectric tensors, and establish sharp C-eigenvalue inclusion intervals [...] Read more.
The C-eigenpair of piezoelectric tensors finds applications in the area of the piezoelectric effect and converse piezoelectric effect. In this paper, we provide some characterizations of C-eigenvectors by exploring the structure of piezoelectric tensors, and establish sharp C-eigenvalue inclusion intervals via Cauchy–Schwartz inequality. Further, we propose the lower and upper bounds of the largest C-eigenvalue and evaluate the efficiency of the best rank-one approximation of piezoelectric tensors. Numerical examples are proposed to verify the efficiency of the obtained results. Full article
(This article belongs to the Section Algebra and Number Theory)
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