Energy Trapping Effect Research Articles

High-frequency vibration of beveled crystal plates by using subregional geometric fitting method

The beveling process is an important process in the manufacturing of resonators, which has a significant impact on the frequency stability of resonators. Without understanding the frequency characteristics of the resonator after beveling, it is impossible to accurately design the beveled resonators. Thus, in order to investigate the vibration characteristics of AT-cut beveled resonators, we investigated the high-frequency vibration in this work by using the subregional geometric fitting method (SGFM) based on Mindlin’s plate theory. Quartz crystal plates with nonuniform thicknesses are partitioned into three regions and each region is fitted by using the polynomial functions based on the measured geometric morphology data. The governing equations are obtained based on Mindlin’s two-dimensional theory and the coupled vibrations are further solved using the partial differential equation module of COMSOL. In the numerical calculation, we compare the results obtained by the SGFM with those obtained by the global fitting method and the measured data. The accuracy and effectiveness of the SGFM are also verified. It is found that the frequencies obtained by the SGFM are slightly higher than the frequencies obtained by the global fitting method, and the results of SGFM are closer to the measured results. Meanwhile, as the beveling time increases, the frequency increases and the energy trapping effect becomes more significant. The proposed method can significantly improve the computational efficiency of thickness-shear vibration while ensuring accuracy. It is expected to provide a new geometric fitting method for the analysis of beveled crystal resonators.

Propagation characteristics of circumferential feature guided waves propagation in a revolved topological waveguide

In our previous research, propagation characteristics and combined harmonic generation of feature guided waves (FGWs) in welded joints of plate structure, were analyzed theoretically and observed numerically. Circumferential ultrasonic guided waves find extensive applications in assessing rotating structures, highlighting the importance of investigating the propagation characteristics of circumferential feature guided waves (CFGWs) in such revolved topological waveguides. In this study, propagation characteristics of CFGW in revolved topological waveguides are investigated. Semi-analytical finite element (SAFE) method in conjunction with a perfectly matched layer (PML) within a cylindrical coordinate system is used to explore the modal and dispersion characteristics of CFGWs. Second-harmonic generation (SHG) of CFGWs is further analyzed and discussed both in theoretical and numerical manner. Cumulative SHG of selected CFGW mode pairs, propagation in the welded joint of the revolved topological waveguide, is observed successfully. The obtained results demonstrate that the energy trapping effect of CFGWs in the welded joint of revolved topological waveguide amplifies the generation of cumulative second harmonics, thereby enhancing the measurability of SHG of CFGW. This investigation reveals the potential of damage assessment in revolved topological waveguides by CFGWs.

Energy-Trapping Characteristics of Lateral Field Excited GdCOB Crystal Bulk Acoustic Wave Devices Based on Stepped Electrodes.

In this work, high-frequency forced vibrations of lateral field excitation (LFE) devices with stepped electrodes based on monoclinic crystals GdCOB are modeled, and the influence laws of the device parameters (the step number, size, and thickness of the stepped electrodes) on the energy-trapping effects of the device are revealed. The results show that the step number has a significant effect on the energy-trapping effect of the device: with the increase in the step number, the stronger energy-trapping effect of the device can be obtained; with the increase in the thickness difference of two layers of electrodes, the energy-trapping effect of the device becomes stronger; with the increase in the difference of the electrode radius, the energy-trapping effect of the device is enhanced gradually. The results of this work can provide an important theoretical basis for the design of stepped-electrode LFE resonators and sensors with high-quality factors based on monoclinic crystals.

Investigation of energy trapping effect for nonlinear guided waves in a topographical structure

Cumulative second harmonic generation (SHG), where the amplitude of the generated second harmonic increases with propagation distance, is commonly utilized to enhance the measurability of nonlinear guided waves by providing a sufficient signal-to-noise ratio. Investigating and confirming the cumulative SHG of feature guided waves (FGWs) in topographical waveguides is crucial for accurately assessing material nonlinearity in such structures. This study examines the cumulative SHG of FGWs propagating in a typical topographic structure of a welded joint through both numerical simulations and experimental investigations. A theoretical model is developed using the semi-analytical finite-element (SAFE) method and perfectly matched layer (PML) to analyze the propagation characteristics of FGWs in a welded joint. The numerical and experimental results provide verification of the “trapping effect” of FGWs within the welded joint. Furthermore, the “cumulative effect” of SHG of FGWs is observed. Remarkably, both the experimental and numerical findings demonstrate that cumulative SHG of FGWs can be achieved by employing suitable mode selection and frequency tuning in the topographic structure, which aligns well with the theoretical predictions. This investigation contributes to advancing our understanding of cumulative SHG in FGWs propagated within topographical structures. These findings have practical implications for accurately characterizing material nonlinearity in topographic waveguides.

Pure- and Pseudo-Lateral-Field-Excitation Characteristics of Relaxor Ferroelectric Single Crystal PMN-PT.

The relaxor ferroelectric single crystal (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) has high piezoelectric constants, and thus has a good application prospect in the field of highly sensitive piezoelectric sensors. In this paper, for relaxor ferroelectric single crystal PMN-PT, the bulk acoustic wave characteristics on pure- and pseudo-lateral-field-excitation (pure- and pseudo-LFE) modes are investigated. LFE piezoelectric coupling coefficients and acoustic wave phase velocities for PMN-PT crystals in different cuts and electric field directions are calculated. On this basis, the optimal cuts of pure-LFE and pseudo-LFE modes of relaxor ferroelectric single crystal PMN-PT are obtained, namely, (zxt)45° and (zxtl)90°/90°, respectively. Finally, finite element simulations are carried out to verify the cuts of pure-LFE and pseudo-LFE modes. The simulation results show that the PMN-PT acoustic wave devices in pure-LFE mode have good energy-trapping effects. For PMN-PT acoustic wave devices in pseudo-LFE mode, when the device is in air, no obvious energy-trapping emerges; when the water (as a virtual electrode) is added to the surface of the crystal plate, an obvious resonance peak and the energy-trapping effect appears. Therefore, the PMN-PT pure-LFE device is suitable for gas-phase detections. While the PMN-PT pseudo-LFE device is suitable for liquid-phase detections. The above results verify the correctness of the cuts of the two modes. The research results provide an important basis for the development of highly sensitive LFE piezoelectric sensors based on relaxor ferroelectric single crystal PMN-PT.

Design and Analysis of a Novel Quartz Crystal Microbalance Utilizing Distributed Mass Loading Area for Improved Sensitivity

Quartz crystal microbalance (QCM) operates based on a shift in its resonant frequency due to addition of mass in its mass loading area. QCM has been widely used in detecting microgram level surface mass changes in both liquid and gas phases. The conventional QCM structure possesses a circular electrode configuration, which uniformly disperses the mass loading area across its surface. However, due to the energy trapping effect, the radial distribution of mass sensitivity is found to be unequal and diminished toward the edges of the electrode. In this article, the influence of the energy trapping effect is investigated to identify effective regions on the electrode contributing to the frequency shift. From this analysis, a novel topology is proposed by designing a unique distributed electrode configuration to effectively utilize the energy trapping effect and enhance the device mass sensitivity while utilizing smaller mass loading area. This proposed electrode configuration is contrasted with the conventional circular electrode and ring-dot electrode configurations based on their mass sensitivity and uniformity distribution. The conducted analysis revealed that the novel electrode topology attains a noticeably higher mass sensitivity and a comparable uniformity distribution in contrast to the conventional circular and ring-dot electrode configurations.

Transient energy trapping as a size-conserving surface passivation strategy for producing bright ultrasmall upconversion nanoprobes

Lanthanide-doped upconversion nanoparticles (UCNPs) have been widely exploited as nanoprobes or energy transducers in traditional as well as emerging biological applications, such as bioimaging, photodynamic therapy, optogenetics, gene editing. However, the breadth and depth of their utility in the biomedical areas are still not comparable to conventional luminescent probes, such as fluorescent dyes and semiconductor quantum dots. Their application is largely limited by their large size, typically > 20 nm, to ensure a sufficient luminescence brightness. In order to enhance the brightness of UCNPs without exceeding the critical size limitations for biomedical applications, we employ here a transient energy trapping effect as a nanoprobe surface passivation strategy to prevent deleterious distant energy migration in the host lattice, which is particularly prevalent in ultrasmall UCNPs and leads to luminescence quenching. We demonstrate this strategy by incorporating Tm3+ ions as energy trapping centers near the surface of sub-10 nm NaYF4: Yb, Er UCNPs and obtain an emission enhancement by almost one order of magnitude without any increment on the nanoparticle size. Our work presents a promising strategy for the preparation of ultrasmall and bright upconversion nanoprobes that are less vulnerable to surface quenching and that potentially minimize the interference with the object. This facilitates their biomedical applications as here demonstrated by unprecedented high-quality cell labeling and imaging, featured with very uniform nanoparticle distribution in the outer nuclear region.

Exploration of the Mass Sensitivity of Quartz Crystal Microbalance under Overtone Modes Using Electrodeposition Method.

With the in-depth application of quartz crystal microbalance (QCM) sensors in the fields of science and engineering, there is an urgent need for QCM sensors with high mass sensitivity. The mass sensitivity of a QCM is closely related to its resonance frequency, and the high resonance frequency leads to improve its mass sensitivity. However, the resonance frequency of a QCM resonator cannot be increased all the time due to the fragility of quartz wafer and the limits of energy trapping effect. Few studies are associated with mass sensitivity of a QCM resonator under overtone modes. Herein, we propose to make a QCM resonator work in its n-th overtone (n = 3, 5, 7, 9 in this study) mode to increase its resonance frequency during operating. Thereby, the purpose of improving QCM mass sensitivity is achieved, and the mass sensitivity of a QCM working in the n-th overtone mode can be called as n-th overtone mass sensitivity. Then, the n-th overtone mass sensitivity of a QCM sensor is measured by an electrodeposition method. The experimental results show that the n-th overtone mass sensitivity of a QCM is a bit more than n times that of the fundamental mass sensitivity, and it is consistent with the theoretical calculation results. The application of overtone mass sensitivity will greatly improve the sensitivity of QCM sensors, which is very attractive for the research fields that require QCM sensors with high sensitivity.

Acoustofluidic black holes for multifunctional in-droplet particle manipulation.

Acoustic black holes offer superior capabilities for slowing down and trapping acoustic waves for various applications such as metastructures, energy harvesting, and vibration and noise control. However, no studies have considered the linear and nonlinear effects of acoustic black holes on micro/nanoparticles in fluids. This study presents acoustofluidic black holes (AFBHs) that leverage controlled interactions between AFBH-trapped acoustic wave energy and particles in droplets to enable versatile particle manipulation functionalities, such as translation, concentration, and patterning of particles. We investigated the AFBH-enabled wave energy trapping and wavelength shrinking effects, as well as the trapped wave energy-induced acoustic radiation forces on particles and acoustic streaming in droplets. This study not only fills the gap between the emerging fields of acoustofluidics and acoustic black holes but also leads to a class of AFBH-based in-droplet particle manipulation toolsets with great potential for many applications, such as biosensing, point-of-care testing, and drug screening.

Peculiarities of energy trapping of the UHF elastic waves in diamond-based piezoelectric layered structure. II. Lateral energy flow

Features of an acoustic energy trapping and outflow in a High-overtone Bulk Acoustic Resonator (HBAR) were considered. On the example of a specified resonator based on a piezoelectric layered structure (PLS) as “Al/AlN/Mo/(100) diamond”, the simulation of the propagation of microwave acoustic waves in the range of 10–6000 MHz by Finite Element Method (FEM) in COMSOL Multiphysics has been carried out. It was found that the magnitude of acoustic energy retained in the substrate under the bottom electrode depends substantially on the relation between the HBAR’s antiresonance frequency fa,n and the cut-off frequencies fs,n-k and fs,n-k+1 of the substrate. The term “cut-off frequency” has the meaning of the frequency point when integer value of half-waves fits along the thickness of substrate. Parameter gk,n estimating the degree of the HBAR’s energy trapping has been proposed. If 0.5 < gk,n < 1, then a retention of acoustic energy in the HBAR’s center as a maximal ET-effect at the overtone frequency fa,n should be fulfilled. Increasing the width of the top electrode as well as the HBAR’s aperture should expand the frequency interval in which the retained elastic energy in the vicinity of the HBAR’s center will be greater than the similar outside. It was shown that the area-averaged Umov-Poynting’s power energy flow vector from the HBAR’s center in the lateral directions increases when approaching the Thin Film Piezoelectric Transducer half-wave resonance frequency from below, and then decreases sharply in the point of complete energy trapping. This can be explained by the outflow of acoustic wave energy from the center to the periphery as a consequence of the transformation of an operational longitudinal acoustic mode into waves of Lamb type mainly. Results on the peculiarities of an energy trapping effect will be useful developing the HBARs and HBAR-based acoustic sensors operating at microwave frequencies.

Propagation characteristics of ultrasonic weld-guided waves in Friction stir welding joint of same material

Friction stir welding (FSW) is an important technology for manufacturing large-scale aluminum alloy propellant tank. Due to stress corrosion and cyclic loads, the key FSW joints require online monitoring to ensure the structural integrity and service safety of long-term storage propellant tanks. FSW joints in the propellant tank are regarded as a type of circumferential or longitudinal long and narrow region. In order to detect the flaws with high efficiency and fewer sensors, the propagation characteristics of ultrasonic guided waves in the FSW joint of same material is investigated in this paper. The weld of a FSW joint is characterized by concave cross-sectional shape and different microstructure-mechanical parameters. The micro-structure, micro-hardness, and Young′s modulus of a real FSW joint are analyzed, and a two-dimensional semi-analytical finite-element (SAFE) method is employed to study the effects of different parameters on the modal characteristics of weld-guided waves in the FSW joint. In the studied fundamental modes (symmetric (S0), anti-symmetric (A0), and shear-horizontal (SH0)), an almost non-leaky A0-like weld-guided wave at a certain frequency range from 100 kHz to 210 kHz is discovered in the welded zone of a specific FSW model and shows a potential for long-distance detection. Parametric simulation results show that A0-like, SH0-like and S0-like modes at 120 kHz always exist when the weld width is changed while the moduli of the welded zone and base metal zone are maintained the same. Additionally, the simulations demonstrate that some weld-guided waves only exist if the modulus value of the welded zone is lower than that of the base metal zone when the cross section is geometrically continuous (i.e. the shoulder plunge depth is zero). Comparing with weld-guided waves affected by weld width, the weld-guided waves affected by the modulus change shows less obvious energy leakage during propagation. The experiments are conducted to validate the existence of A0-like weld-guided mode with a primary energy trapping effect.

Giant dielectric constant phenomena in Bi2O3-doped Ba0.8Sr0.2TiO3 ferroelectrics

(1−x)Ba0.8Sr0.2TiO3 -xBi2O3 (x: 0.200–0.275) ceramics were prepared by solid-state reaction. X-ray diffraction showed reduction in lattice constant with increase in Bi2O3 content. The peaks of dielectric permittivity, about 400 000 at 1 kHz, shift to low temperature with the increase in frequency. AC conductivities show the linear frequency dependence of the peaks and semiconductive grains, and DC electric pulse polarisation measurement eliminates deep energy trapping effect on the electric conductivity at room temperature. Double-cation mixture-valence structure of Ti3+/Ti4+ and Ba+/Ba2+ is indicated by X-ray photoelectron spectroscopy. Substitutional disorders of Ti3+/Ti4+ and Ba+/Ba2+ may give rise to induce polaron polarisation for hopping transport. These disorders cause distortion of TiO6 octahedra to increase the polarisation in Bi2O3-Ba0.8Sr0.2TiO3 ceramics, alternatively.

Anisotropic effects on ultrasonic guided waves propagation in composite bends

Ultrasonic guided waves have proven to be attractive to the long-range testing of composite laminates. As complex-shaped composite components are increasingly incorporated in high-performance structures, understanding of both anisotropic and geometric effects on guided waves propagation is needed to evaluate their suitability for the non-destructive testing (NDT) of such complex structures. This paper reports the Semi-Analytical Finite Element (SAFE) simulations revealing the capability of energy confinement carried by two types of guided modes in 90° carbon fiber/epoxy (CF/EP) bends. Existence of the phenomenon is cross-validated by both 3D Finite Element (FE) modeling and experimental measurements. The physics of such energy trapping effect is explained in view of geometric variation and anisotropic properties, and the frequency effect on the extent of energy concentration is discussed. Finally, the feasibility of using such confined guided waves for rapid inspection of bent composite plate structures is also discussed.

A Gaussian-shaped AT-cut quartz crystal resonator

This paper reports the design and fabrication of a Gaussian-shaped AT-cut quartz crystal resonator. The thickness distribution of the resonator was designed following a Gaussian-type function. The distribution was based on the analysis of thickness shearing vibration calculated using finite element analysis for a flat-shaped resonator. The vibration analysis showed improvement of the energy trapping effect, and the vibration at the wafer edge was negligible. For the experimental verification, we attempted to fabricate a Gaussian-shaped resonator using microfabrication technologies. The resonant characteristics were substantially improved by the shaping.

Energy-trapping mode in lateral-field-excited acoustic wave devices

We have analyzed the energy-trapping phenomenon of the thickness-shear vibration in lateral-field-excited (LFE) acoustic wave devices based on elastic wave propagation theory and the cutoff frequency. The standard LFE device does not support the energy-trapping effect, which is significantly different from thickness-field-excited devices. However, energy trapping in LFE devices can be achieved by placing an additional mass-loading layer in the gap region between the two working electrodes. A 5 MHz energy-trapping LFE device is fabricated and tested. The experimental results are in close agreement with the theoretical analysis.

Energy-trapping analysis for the bi-stepped mesa quartz crystal microbalance using thefinite element method

AT-cut quartz crystal plate resonators have been widely used for different frequencyapplications, such as the quartz crystal microbalance (QCM), owing to its highfrequency–temperature stability. In this study, a finite element program basedon two-dimensional Mindlin AT-quartz plate equations for thickness shearing,thickness twist and flexure vibration is written using MATLAB language. Thethickness-shearing mode shape and its overtone of the rectangular AT-cut quartz resonatorare computed using the program. The energy-trapping effects on a conventionalresonator, a single-step-mesa resonator and a stepped bi-mesa structure resonatorare analyzed. The convergence study is presented for a rectangular quartz platewithout electrodes, and the frequency spectrum of the quartz plate around thefundamental TS mode is computed. A factor related to the vibrational energy of thethickness-shearing mode is defined to evaluate the energy-trapping characteristics ofdifferent structure designs. The comparisons between the conventional quartzresonator and mesa-design resonator show that the mesa design can trap thevibration energy within the electrode area more effectively. The computation of theenergy-trapping factor as a function of the dimensions of the mesa depth and bi-mesawidth design are performed. The results show that when the mesa depth of the singlemesa reaches a certain value, further energy-trapping improvement cannot beachieved by increasing the mesa depth. A bi-mesa design can further improve thedecoupling characteristics of the resonator beyond that of the single-mesa resonator.

Finite element analysis of interference for the laterally coupled quartz crystal microbalances

Multi-channel quartz crystal microbalance (MQCM) devices have many promising potential applications as sensors to detect the micromass changes in engineering. The frequency interference between adjacent channels is one of the problems for design of the MQCMs. In this paper, a model of MQCM is constructed by finite element analysis (FEA) code ANSYS. The mass sensitivity of the single resonator with different electrode width is examined numerically. The coupling factor is defined to investigate the frequency interference between the adjacent QCMs. The numerical calculation results show that the coupling factor for the detuned QCM pair in one quartz chip is quite weak due to the energy trapping effect of the electrode layer. For a symmetrical QCM pair, the parallel resonance frequency of TSM is reduced almost linearly proportional to the mass absorption on surface, but the anti-parallel resonance frequency is non-linearly reduced. Based on the FEM modeling, the effects of the design parameters of MQCM, i.e. interval spacing between channels, thickness of electrode, and the effect of the layout of QCM pair on AT-cut quartz plate are investigated.

Frequency responses of spherically contoured rectangular AT-cut quartz crystal resonators fabricated by fixed abrasive method

Frequency responses of spherically contoured rectangular AT-cut quartz crystal resonators fabricated by fixed abrasive method have been analyzed experimentally. Not only the required mode, but also many spurious modes can exist on rectangular AT-cut plates. Empirically, in order to eliminate the spurious modes and to achieve high stable and reliable quartz crystal resonators, quartz crystal blanks have been polished into lens-like shape (spherically contoured shape). The spherically contoured blanks have a drastic effect on the decoupling of modes by restricting the vibrating area of the plate within its central region (energy trapping effect). However, a long process time is necessary to fabricate the quartz blanks into spherically contoured shape. In our previous works, a fixed abrasive method has been introduced as a new rotary barrel finishing method for finishing the spherically contoured blanks. In this paper, the frequency responses and the shape of the spherically contoured resonators fabricated with different process times have been presented and discussed. As a result, resonators with very little spurious at 15 MHz within 2 MHz bandwidth have been successfully fabricated.

Shear-Horizontal-Type Surface Acoustic Waves on Quartz with Ta2O5 Thin Film

The propagation characteristics of two modes of surface acoustic waves (SAWs) on ST quartz with a tantalum pentoxide (Ta2O5) thin film are investigated theoretically and experimentally. One is the pure shear-horizontal (SH)-type SAW and the other is the Love-wave-type SAW converted from the leaky SAW (LSAW). For these SAWs, stronger energy trapping effects on the surface can be expected by loading the substrate with the Ta2O5 thin film, because this film has a relatively high density. In fact, the film thickness of the Ta2O5 film required to obtain the minimum insertion loss and the maximum K2 for the SH-type SAW on ST-90°X quartz is around 0.01 λ, which is approximately one-fourth of that reported for silicon dioxide film. Furthermore, the attenuation of the LSAW on ST-33°X quartz was reduced by loading with the Ta2O5 film because the LSAW becomes the Love-wave-type SAW without attenuation.

Off-centre load-insensitive digital quartz resonator force sensor

A digital output force sensor has been developed utilising a unique elastic structure and an AT-cut quartz crystal resonator (QXR) based on an energy trapping effect as sensing element. The force-sensitive QXR is preloaded into the elastic structure, through which a force proportional to the applied force is exerted on the QXR, and the force measurement is accomplished by measuring frequency changes. The elastic structure consists of several flexible hinges and has the advantages of no mechanical friction and no clearance, and therefore nonelastic effects of the digital force sensor are minimised. The elastic structure is specially configured to avoid measurement error induced by off-centre loads. To compensate the temperature coefficient of sensitivity, a dual-harmonic-mode self-temperature-sensing method is employed to measure the applied force and the in situ temperature simultaneously with the same QXR. A practical design is developed and the dependence of the measurement range on the elastic structure dimensions as well as the changes of the quality factor of QXR before and after preloading are discussed. FEM simulation and experimental results show that the force sensor has good performance and is insensitive to off-centre load. Detailed specifications of the force sensor are given.