Multi-Parameter Characterization of Liquid-to-Ice Phase Transition Using Bulk Acoustic Waves.

The detection of the liquid-to-ice transition is an important challenge for many applications. In this paper, a method for multi-parameter characterization of the liquid-to-ice phase transition is proposed and tested. The method is based on the fundamental properties of bulk acoustic waves (BAWs). BAWs with shear vertical (SV) or shear horizontal (SH) polarization cannot propagate in liquids, only in solids such as ice. BAWs with longitudinal (L) polarization, however, can propagate in both liquids and solids, but with different velocities and attenuations. Velocities and attenuations for L-BAWs and SV-BAWs are measured in ice using parameters such as time delay and wave amplitude at a frequency range of 1-37 MHz. Based on these measurements, relevant parameters for Rayleigh surface acoustic waves and Poisson's modulus for ice are determined. The homogeneity of the ice sample is also detected along its length. A dual sensor has been developed and tested to analyze two-phase transitions in two liquids simultaneously. Distilled water and a 0.9% solution of NaCl in water were used as examples.

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.

Acoustic Waves in Piezoelectric Layered Structure for Selective Detection of Liquid Viscosity.

The acoustic waves of higher orders propagating in a layered structure consisting of a silicon plate coated with piezoelectric ZnO and/or AlN films were used for the development of a sensor with selective sensitivity to liquid viscosity η in the range of 1-1500 cP. In that range, this sensor possessed low sensitivity to liquid conductivity σ and temperature T in the ranges of 0-2 S/m and 0-55 °C, respectively. The amplitude responses insensitive to the temperature instead of the phase were used to provide the necessary selectivity. The sensor was based on a weak piezoactive acoustic wave of higher order. The volume of the probes sufficient for the measurements was about 100 µL. The characteristics of the sensors were optimized by varying the thicknesses of the structure layers, number of layers, wavelength, wave propagation direction, and the order of the acoustic waves. It was shown that in the case of the layered structure, it is possible to obtain practically the same selective sensitivity toward viscosity as for acoustic waves in pure ST, X quartz. The most appropriate waves for this purpose are quasi-longitudinal and Lamb waves of higher order with in-plane polarization. It was found that for various ranges of viscosity η = 1-20 cP, 20-100 cP, and 100-1500 cP, the maximum sensitivity of the appropriate wave is equal to 0.26 dB/cP, 0.087 dB/cP, and 0.013 dB/cP, respectively. The sensitivity of the waves under study toward the electric conductivity of the liquid is much less than the sensitivity to liquid viscosity. These two responses become comparable only for very small η < 2 cP. The waves investigated have shown no temperature responses in contact with air, but in the presence of liquid, they increase depending on liquid properties. The temperature dependence of liquid viscosity is measurable by the same sensors. The results obtained have shown the possibility of designing acoustic liquid viscosity sensors based on multilayered structures. The set of possible acoustic waves in layered structures possesses modified propagation characteristics (various polarization, phase velocities, electromechanical coupling coefficients, and attenuations). It allows choosing an optimal acoustic wave to detect liquid viscosity only.

Surface Roughness Effects on the Vibration Characteristics of AT-Cut Quartz Crystal Plate.

With the miniaturization and high-frequency requirements of quartz crystal sensors, microscopic issues affecting operating performance, e.g., the surface roughness, are receiving more and more attention. In this study, the activity dip caused by surface roughness is revealed, with the physical mechanism clearly demonstrated. Firstly, the surface roughness is considered as a Gaussian distribution, and the mode coupling properties of an AT-cut quartz crystal plate are systematically investigated under different temperature environments with the aid of two-dimensional thermal field equations. The resonant frequency, frequency-temperature curves, and mode shapes of the quartz crystal plate are obtained through the partial differential equation (PDE) module of COMSOL Multiphysics software for free vibration analysis. For forced vibration analysis, the admittance response and phase response curves of quartz crystal plate are calculated via the piezoelectric module. The results from both free and forced vibration analyses demonstrate that surface roughness reduces the resonant frequency of quartz crystal plate. Additionally, mode coupling is more likely to occur in a crystal plate with a surface roughness, leading to activity dip when temperature varies, which decreases the stability of quartz crystal sensors and should be avoided in device fabrication.

Langmuir-Blodgett Films with Immobilized Glucose Oxidase Enzyme Molecules for Acoustic Glucose Sensor Application.

In this work, a sensitive coating based on Langmuir-Blodgett (LB) films containing monolayers of 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) with an immobilized glucose oxidase (GOx) enzyme was created. The immobilization of the enzyme in the LB film occurred during the formation of the monolayer. The effect of the immobilization of GOx enzyme molecules on the surface properties of a Langmuir DPPE monolayer was investigated. The sensory properties of the resulting LB DPPE film with an immobilized GOx enzyme in a glucose solution of various concentrations were studied. It has shown that the immobilization of GOx enzyme molecules into the LB DPPE film leads to a rising LB film conductivity with an increasing glucose concentration. Such an effect made it possible to conclude that acoustic methods can be used to determine the concentration of glucose molecules in an aqueous solution. It was found that for an aqueous glucose solution in the concentration range from 0 to 0.8 mg/mL the phase response of the acoustic mode at a frequency of 42.7 MHz has a linear form, and its maximum change is 55°. The maximum change in the insertion loss for this mode was 18 dB for a glucose concentration in the working solution of 0.4 mg/mL. The range of glucose concentrations measured using this method, from 0 to 0.9 mg/mL, corresponds to the corresponding range in the blood. The possibility of changing the conductivity range of a glucose solution depending on the concentration of the GOx enzyme in the LB film will make it possible to develop glucose sensors for higher concentrations. Such technological sensors would be in demand in the food and pharmaceutical industries. The developed technology can become the basis for creating a new generation of acoustoelectronic biosensors in the case of using other enzymatic reactions.

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.

Features of the Formation of Sensitive Films Based on Mycelium of Higher Fungi for Surface and Plate Acoustic Waves Gas Sensors.

A comparative analysis of the responses of two types of acoustic waves (surface SAW and plate APW) with close frequencies and the same type of waves (SAW) with different frequencies toward various liquid vapors (water, acetone, ethanol) was carried out in this paper. Two types of films based on mycelium of higher fungus Ganoderma lucidum (Curtis) P. Karst (G. lucidum) prepared by various methods were used as sensitive coatings. These films were based on G. lucidum mycelium ethanolic (48% v/v) homogenizate (MEGl) and extract (EGl). A film deposition procedure compatible with acoustic devices technology was developed. Various piezoelectric substrates (YX-LiNbO3, 128 YX-LiNbO3) were used for appropriate acoustic delay lines production. It was found that additional SAW and APW attenuation associated with the appearance of mycelium films on the surface of the acoustic waveguide is two times greater for MEGL than for EGL films in the frequency range of 20-80 MHz The changes in acoustic wave amplitude and phase due to vapor absorption were measured and compared with each other, taking into account the differences in geometry of the samples. It was found that the phase response of the SAW delay lines with EGL films is three times higher than one with the presence of MEGL films for water and ethanol vapors. The films used are demonstrated good reproducibility and long-term stability for at least 2 months. Based on the results obtained, it was concluded that MEGl film is not appropriate for use in high frequency SAW delay lines as a sensitive coating. However, both types of the films (MEGl and EGl) could be used as sensitive coatings for low frequency SAW and APW sensors based on corresponding delay lines. Additionally, it was found that the films used are not sensitive to acetone vapor. As a result of the work carried out, a technique for creating sensitive films based on the mycelium of higher fungi compatible with the planar technology of acoustoelectronic delay lines was developed. The possibility of using such films for the development of gas SAW and APW sensors was shown.

Backward Acoustic Waves in Piezoelectric Plates: Possible Application as Base for Liquid Sensors.

Backward acoustic waves are characterized by oppositely directed phase and group velocities. These waves can exist in isotropic and piezoelectric plates. They can be detected using a set of interdigital transducers with different spatial periods located on the same piezoelectric substrate. In this paper, the effect of a nonviscous and nonconductive liquid on the characteristics of a first-order backward antisymmetric wave in a YX plate of lithium niobate is studied theoretically and experimentally. It is shown that the presence of liquid does not lead to the transformation or disappearance of this wave. It is shown that these waves are close to the cutoff frequency and are characterized by the presence of a point with zero group velocity. The design of a liquid sensor based on these waves is proposed.

Multimode Design and Piezoelectric Substrate Anisotropy Use to Improve Performance of Acoustic Liquid Sensors.

Using acoustic wave modes propagation in piezoelectric plates loaded with conductive liquids, peculiarities of the mode-liquid acoustoelectric interaction are studied. It is found that (i) in contrast to bulk and surface acoustic waves propagating in piezoelectric semiconductors, the acoustoelectric attenuation of the modes is not symmetric in respect to its maximum, (ii) a large increase in attenuation may be accompanied by a small decrease in phase velocity and vice versa, (iii) the peculiarities are valid for "pure" (without beam steering) and "not pure" (with beam steering) modes, as well as for modes of different orders and polarizations, and (iv) conductivity of test liquid increases electromagnetic leakage between input and output transducers, affecting results of the measurements. To decrease the leakage, the liquid should be localized between transducers, outside the zone over them. If so, the mode sensitivity may be as large as 8.6 dB/(S/m) for amplitude and 107°/(S/m) for phase. However, because of comparable cross-sensitivity towards viscosity and dielectric permittivity, modes with selective detection of liquid conductivity are not found.

Radio-Absorbing Materials Based on Polymer Composites and Their Application to Solving the Problems of Electromagnetic Compatibility.

Recently, designers of electronic equipment have paid special attention to the issue of electromagnetic compatibility (EMC) of devices with their own components and assemblies. This is due to the high sensitivity of semiconductor microcircuits to electromagnetic interference. This interference can be caused either by natural phenomena, such as lightning strikes, or by technical processes, such as transients in circuits during fast periodic or random switching. Either way, interference implies a sudden change in voltage or current in a circuit, which is undesirable, whether it propagates along a cable or is transmitted as an electromagnetic wave. The purpose of this article is to review the works devoted to the development, creation, and investigation of modern polymeric nanocomposite materials used for shielding electromagnetic radiation and their effective application for solving problems of electromagnetic compatibility. Additionally, the approach to design EMI shielding complex media with predetermined parameters based on investigation of various properties of possible components is shown. In the review, all polymer composites are classified according to the type of filler. The issues of the interaction of a polymer with conductive fillers, the influence of the concentration of fillers and their location inside the matrix, and the structure of the nanocomposite on the mechanisms of electromagnetic interaction are considered. Particular attention is paid to a new generation of nanocomposite materials with widely adjustable electrical and magnetic properties. A wide class of modern filled polymeric materials with dielectric and magneto-dielectric losses is considered. These materials make it possible to create effective absorbers of electromagnetic waves that provide a low level of reflection coefficient in the microwave range. The model mechanisms for shielding electromagnetic radiation are considered in the paper. A detailed review of the electro-physical properties of polymer nanocomposites is provided. Multilayer electrodynamic media containing combinations of layers of filled polymer composite materials with nanoparticles of different compositions and manufactured using a single technology will make it possible to create electrodynamic media and coatings with the required electro-physical characteristics of absorption, transmission, and reflection. Within the framework of the two-layer coating model, the difference in the effects of the interaction of electromagnetic radiation with conductive layers located on a dielectric and metal substrate is demonstrated. It is shown that in order to achieve optimal (maximum) values of reflection and absorption of electromagnetic radiation in the appropriate frequency range, it is necessary to fit the appropriate layer thicknesses, specific conductivity, and permittivity. Such approach allows designers to create new shielding materials that can effectively vary the shielding, absorbing, and matching characteristics of coatings over a wide frequency band. In general, it can be said that the development of innovative polymer composite materials for shielding electronic devices from electromagnetic interference and excessive electromagnetic background is still an important task. Its solution will ensure the safe and uninterrupted operation of modern digital electronics and can be used for other applications.

High-Frequency Vibration Analysis of Piezoelectric Array Sensor under Lateral-Field-Excitation Based on Crystals with 3 m Point Group.

Based on Mindlin's first-order plate theory, the high-frequency vibrations of piezoelectric bulk acoustic wave array sensors under lateral-field-excitation based on crystals with 3 m point group are analyzed, and the spectral-frequency relationships are solved, based on which, the optimal length-thickness ratio of the piezoelectric crystal plate is determined. Then, the dynamic capacitance diagram is obtained by a forced vibration analysis of the piezoelectric crystal plate. The resonant mode conforming to good energy trapping is further obtained. The frequency interferences between different resonator units are calculated, and the influences of the spacing between two resonant units on the frequency interference with different electrode widths and spacings are analyzed. Finally, the safe spacings between resonator units are obtained. As the electrode spacing value of the left unit increases, the safe spacing d0 between the two resonator units decreases, and the frequency interference curve tends to zero faster. When the electrode spacings of two resonator units are equal, the safe distance is largest, and the frequency interference curve tends to zero slowest. The theoretical results are verified further by finite element method. The analysis model of high frequency vibrations of strongly coupled piezoelectric bulk acoustic array device based on LiTaO3 crystals with 3 m point group proposed in this paper can provide reliable theoretical guidance for size optimization designs of strongly coupled piezoelectric array sensors under lateral-field-excitation.

Genetically Modified Soybean Detection Using a Biosensor Electrode with a Self-Assembled Monolayer of Gold Nanoparticles.

In this study, we proposed a genosensor that can qualitatively and quantitatively detect genetically modified soybeans using a simple electrode with evenly distributed single layer gold nanoparticles. The DNA sensing electrode is made by sputtering a gold film on the substrate, and then sequentially depositing 1,6-hexanedithiol and gold nanoparticles with sulfur groups on the substrate. Then, the complementary to the CaMV 35S promoter (P35S) was used as the capture probe. The target DNA directly extracted from the genetically modified soybeans rather than the synthesized DNA segments was used to construct the detection standard curve. The experimental results showed that our genosensor could directly detect genetically modified genes extracted from soybeans. We obtained two percentage calibration curves. The calibration curve corresponding to the lower percentage range (1-6%) exhibits a sensitivity of 2.36 Ω/% with R2 = 0.9983, while the calibration curve corresponding to the higher percentage range (6-40%) possesses a sensitivity of 0.1 Ω/% with R2 = 0.9928. The limit of detection would be 1%. The recovery rates for the 4% and 5.7% GMS DNA were measured to be 104.1% and 102.49% with RSD at 6.24% and 2.54%. The gold nanoparticle sensing electrode developed in this research is suitable for qualitative and quantitative detection of genetically modified soybeans and can be further applied to the detection of other genetically modified crops in the future.

Selective Detection of Liquid Viscosity Using Acoustic Plate Waves with In-Plane Polarization.

Using plates of weak piezoeletcric crystal (quartz) loaded with various liquids, it is shown that along with common modes, whose sensitivity towards different liquid parameters comparable with each other, there are some uncommon modes, whose amplitude responses towards viscosity η are much larger than towards temperature T and electric conductivity σ. The search of the modes with the selective properties is accomplished by varying plate thickness h, crystal orientation, wave length λ, and mode order n. It is found that all modes possessing the property are characterized by small surface-normal displacement, avoiding wave radiation into adjacent liquid, large in-plane displacements, enhancing viscous coupling the modes and liquids, and small electro-mechanical constant, reducing electro-acoustic interaction. Basing on the modes, the sensor prototypes with selective operation are developed and tested for η from 1 to 1500 cP, σ from 0 to 1.2 S/m, and t from 0 to 55 °C. Because of operation at ultrasonic frequency (tens MHz) the prototypes have different sensitivities in various η-ranges: 0.3 dB/cP for 1−20 cP, 0.12 dB/cP for 20−100 cP, and 0.015 dB/cP for 100−1500 cP. Viscosity responses of the prototypes become comparable with their electric outputs only for η < 2 cP. Temperature responses are almost zero in air, but when plate is coated with liquid they increase depending on liquid properties, allowing measurements of the temperature dependence of the liquid viscosity.

Impact of PN junction inhomogeneity on the piezoelectric fields of acoustic waves in piezo-semiconductive fibers.

Non-uniform mechanical strain can be easily induced at the interface of a piezoelectric semiconductive (PS) PN junction with variable cross sections by using piezoactive acoustic waves, and thus produces a giant piezoelectric field to significantly enhance the piezotronic effect. For revealing the piezotronic performance modulation in the non-uniform PS PN junction, the electromechanical field under a pair of applied end mechanical forces is studied from perspectives of theoretical analysis and numerical simulations. A one-dimensional linearized model for the PS fiber is established, which is applied for the mechanical analysis of a selected profile with the cross section varying in a specific quadratic function. Numerical results indicate that the acoustoelectric fields in the space charge region of the non-uniform PS PN junction are more sensitive to the applied mechanical forces, compared with that of the uniform junction, especially for a heterogeneous PN junction. Furthermore, the current-voltage relations of a necking PS PN junction can be modulated more easily by the end mechanical forces. Both qualitative conclusions and quantitative results can offer guidance for the piezotronic device design.

Langmuir-Blodgett Films of Arachidic and Stearic Acids as Sensitive Coatings for Chloroform HF SAW Sensors.

Properties of the Langmuir-Blodgett (LB) films of arachidic and stearic acids, versus the amount of the films' monolayers were studied and applied for chloroform vapor detection with acoustoelectric high-frequency SAW sensors, based on an AT quartz two-port Rayleigh type SAW resonator (414 MHz) and ST-X quartz SAW delay line (157.5 MHz). Using both devices, it was confirmed that the film with 17 monolayers of stearic acid deposited on the surface of the SAW delay line at a surface pressure of 30 mN/m in the solid phase has the best sensitivity towards chloroform vapors, compared with the same films with other numbers of monolayers. For the SAW resonator sensing using slightly longer arachidic acid molecules, the optimum performance was reached with 17 LB film layers due to a sharper decrease in the Q-factor with mass loading. To understand the background of the result, Atomic Force Microscopy (AFM) in intermittent contact mode was used to study the morphology of the films, depending on the number of monolayers. The presence of the advanced morphology of the film surface with a maximal average roughness (9.3 nm) and surface area (29.7 µm2) was found only for 17-monolayer film. The effects of the chloroform vapors on the amplitude and the phase of the acoustic signal for both SAW devices at 20 °C were measured and compared with those for toluene and ethanol vapors; the largest responses were detected for chloroform vapor. For the film with an optimal number of monolayers, the largest amplitude response was measured for the resonator-based device. Conversely, the largest change in the acoustic phase produced by chloroform adsorption was measured for delay-line configuration. Finally, it was established that the gas responses for both devices coated with the LB films are completely restored 60 s after chamber cleaning with dry air.

Morphology of Mixed Langmuir and Langmuir-Schaefer Monolayers with Covered CdSe/CdS/ZnS Quantum Dots and Arachidic Acid.

The process of formation of a Langmuir-Schaefer (LS) matrix based on a mixed monolayer of arachidic acid (AA) and 8 nm CdSe/CdS/ZnS quantum dots (QDs) stabilized by molecules of trioctylphosphine oxide (TOPO) was investigated. The change in the morphology, monolayer compressibility, and area per elementary cell of the created mixed monolayers, depending on the ratio of the components, was studied. It is shown that the change in the morphology of Langmuir-Blodgett (LB) monolayers begins to occur at a ratio between the number of QDs and AA molecules of 1:24. Dendrimeric structures with a thickness of the order of 30-40 nm appear in the mixed monolayer when LB film deposition was carried out above the collapse surface pressure of a Langmuir film from only TOPO-covered QDs. Information on the dependence of the morphology of such structures on the molar ratio of the components is necessary for the production of ordered 2D nanostructures containing 0D and 1D objects with quantum bonds. Such nanostructures can be used in nanoelectronic and optoelectronic devices as a sensitive sensor element. The obtained results would be relevant for any type of spherical shape nanoparticles.

The Peculiarities of the Acoustic Waves of Zero-Order Focusing in Lithium Niobate Plate.

In this research, beam focusing in lithium niobate plate was studied for fundamental anti-symmetric (A0) and symmetric (S0) Lamb waves, and the shear-horizontal (SH0) wave of zero-order. Using the finite element method, appropriate configuration of the interdigital transducer with arc-like electrodes was modeled accounting for the anisotropy of the slowness curves and dispersion of the modes in the plate. Profiles of the focalized acoustic beams generated by the proposed transducer were theoretically analyzed. Based on the result of the analysis, relevant delay lines were fabricated and transfer functions (insertion loss) of the line were measured for SH0 wave in YX-lithium niobate plate. Using an electron scanning microscope, distribution of the electric fields of the same wave were visualized. The results of this study may be useful for hybrid devices and sensors combining nano and acoustoelectronic principles.

The Experimental Registration of the Evanescent Acoustic Wave in YX LiNbO3 Plate.

Evanescent acoustic waves are characterized by purely imaginary or complex wavenumbers. Earlier, in 2019 by using a three dimensional (3D) finite element method (FEM) the possibility of the excitation and registration of such waves in the piezoelectric plates was theoretically shown. In this paper the set of the acoustically isolated interdigital transducers (IDTs) with the different spatial periods for excitation and registration of the evanescent acoustic wave in Y-cut X-propagation direction of lithium niobate (LiNbO3) plate was specifically calculated and produced. As a result, the possibility to excite and register the evanescent acoustic wave in the piezoelectric plates was experimentally proved for the first time. The evanescent nature of the registered wave has been established. The theoretical results turned out to be in a good agreement with the experimental ones. The influence of an infinitely thin layer with arbitrary conductivity placed on a plate surface was also investigated. It has been shown that the frequency region of an evanescent acoustic wave existence is very sensitive to the changes of the electrical boundary conditions. The results obtained may be used for the development of the method of the analysis of thin films electric properties based on the study of evanescent waves.

An Analysis of the Water-to-Ice Phase Transition Using Acoustic Plate Waves.

It is shown that, in spite of the wave radiation into the adjacent liquid, a large group of Lamb waves are able to propagate along piezoelectric plates (quartz, LiNbO3, LiTaO3) coated with a liquid layer (distilled water H2O). When the layer freezes, most of the group's waves increase their losses, essentially forming an acoustic response towards water-to-ice transformation. Partial contributions to the responses originating from wave propagation, electro-mechanical transduction, and wave scattering were estimated and compared with the coupling constants, and the vertical displacements of the waves were calculated numerically at the water-plate and ice-plate interfaces. The maximum values of the responses (20-30 dB at 10-100 MHz) are attributed to the total water-to-ice transformation. Time variations in the responses at intermediate temperatures were interpreted in terms of a two-phase system containing both water and ice simultaneously. The results of the paper may turn out to be useful for some applications where the control of ice formation is an important problem (aircraft wings, ship bodies, car roads, etc.).

A Theoretical Model for Analyzing the Thickness-Shear Vibration of a Circular Quartz Crystal Plate With Multiple Concentric Ring Electrodes.

A dynamic model to analyze the thickness-shear vibration of a circular quartz crystal plate with multiple concentric ring electrodes on its upper and bottom surfaces is established with the aid of coordinate transformation. The theoretical solution is obtained, which can be written in a superposition form of Mathieu functions and modified Mathieu functions. The convergence of the solution is demonstrated, and the correctness is numerically validated via results from the finite element method (FEM). Subsequently, a systematic investigation is carried out to quantify the effect of the electrode size on the energy trapping phenomenon, i.e., the resonant frequency and mode shape, which reveals that the ring electrode has a great influence on the work performance of resonators. With the increase of the electrode inertia, i.e., the radius and mass ratio, new trapped modes emergence with the vibration mainly focused on the plate with partial electrodes. Besides, owing to the anisotropy, degenerated trapped modes have different resonant frequencies and the frequency discrepancy between them will become smaller for higher modes. Finally, the influence of multiple ring electrodes is investigated, and the qualitative analysis and quantitative results demonstrate that multiple ring electrodes will lead to a more uniform mass sensitivity compared with a single ring electrode. The outcome is widely applicable, which can provide theoretical guidance for the structural design and manufacturing of quartz resonators, as well as a thorough interpretation about the underlying physical mechanism.