Frequency-temperature Behavior Research Articles

The study of electronic structure and magnetic properties of ferromagnetic Kondo-lattice CePd2P2 from the first-principles

The electronic structure of ferromagnetic CePd2P2 Kondo lattice crystallizing in the tetragonal ThCr2Si2-type structure is investigated by means of the Density Functional Theory (DFT) and Time-Depedent DFT (TDDFT) methods. The calculated electronic properties from DFT are presented and compared to those of the non-magnetic LaPd2P2 compound. The differences in the FS topologies upon changing magnetic states (paramagnetic → ferromagnetic) is also examined. Including the relativistic effects of without or with spin-orbit coupling, and Hubbard corrections in the calculations, ferromagnetic ground state with an ordered magnetic moment of ∼ 0.8-0.9 μB is corroborated. Meaningful changes in the magnetic moment and electronic properties of CePd2P2 are discussed in terms of effects brought by the Coulomb interaction (U), and the Hund coupling (J). In particular, the reduction in magnetic moment and simultaneously enhancement of DOS at the Fermi energy due to decreasing J are in quantitative concordance with the Kondo lattice characteristic. Furthermore, dynamical model used in TDDFT calculations exhibits that 4 f electrons in CePd2P2 tend to be delocalized. The frequency-temperature behavior of response function allows to estimate the Kondo temperature to amount 19 K.

A Dual Resonance Frequency-Selective Surface Temperature Sensor With Linear Frequency–Temperature Behavior

Metamaterial temperature sensors are receiving increasing attention due to the wireless and passive operation. Unfortunately, the frequency response of most metamaterials sensors to temperature is nonlinear, which increases the complexity of signal processing. A dual resonance frequency selective surface (FSS) temperature sensor with linear frequency-temperature characteristic is proposed in this work. The dual frequency resonance of the sensor is realized by introducing the circular slot unit cell into the substrate integrated waveguide (SIW) structure. The linear relationship between the temperature and the difference in the two resonance frequencies can be achieved at specific condition. The proposed sensor was fabricated and measured from room temperature to 120 °C. Measured resonance frequency of the sensor decreases from 12.658 GHz to 12.57 GHz in SIW cavity resonance mode and from 13.787 GHz to 13.727 GHz in circular slot resonance mode. The experiment result shows that wireless temperature sensing is feasible and that the difference in resonance frequency has a good linear relationship with temperature. The sensitivity of the sensor is 0.309 MHz/°C. This design method can be extended to a wider temperature range and the sensor can be potentially applied in temperature sensing in industrial systems.

A langasite surface acoustic wave wide-range temperature sensor with excellent linearity and high sensitivity

Langasite (LGS) surface acoustic wave (SAW) temperature sensors have a large second order temperature coefficient of frequency, which leads to their non-linear and non-monotonic responses in a wide temperature range and possibly makes the measured temperatures non-unique for a specific sensor response. Here, we propose a high-temperature Pt/LGS SAW sensor with linear frequency–temperature behavior in a wide temperature range, which was fabricated on a LGS (0°, 138.5°, 72°) substrate. The sensor has a single acoustic mode, but dual resonances with similar second- and third-order temperature sensitivities that were utilized for achieving a linear frequency–temperature response by a method of difference. A linear relationship between the measured sensor output (Δfm21) and temperature was obtained in the range of −60 °C to 700 °C, consistent with the theoretical analysis. The sensor has a high sensitivity of −167 ppm/K for the whole temperature range. All the results demonstrated exciting prospects of the sensor for wide temperature monitoring in harsh environments.

Geometric Nonlinear Model for Prediction of Frequency-Temperature Behavior of SAW Devices for Nanosensor Applications.

Surface acoustic wave (SAW)-based sensors have become highly valued for their use as nanosensors in industrial applications. Accurate prediction of the thermal stability is a key problem for sensor design. In this work, a numerical tool based on the finite element method combined with piezoelectric Lagrangian equations has been developed to accurately predict the thermal sensitivity characteristics of surface acoustic wave devices. Theoretical analysis for the geometric nonlinearity contributing to the frequency–temperature characteristic and material constants’ dependency on temperature were taken into consideration. The thermomechanical equilibrium equation built on the three-dimensional finite element method (3D-FEM) mesh node took mesh movement into account because thermal expansion was employed. The frequency–temperature characteristics of different SAW modes, including Rayleigh waves and leaky waves excited on a piezoelectric substrate of quartz or lithium tantalate, respectively, were calculated. The theoretical accuracy of the proposed numerical tool was verified by experiments.

A novel design method for SAW temperature sensor with monotonic and linear frequency-temperature behavior in wide temperature range

In this work, a novel method was proposed to achieve linear temperature dependent frequency in SAW temperature sensors. The designed SAW temperature sensor can operate in a wide temperature range without the limitation originated from the large second-order frequency-temperature coefficient of traditional SAW resonators. An SAW temperature sensor which consists of two SAW resonators was designed with the proposed method. The frequency characteristics of the SAW resonators were measured from room temperature up to 600 °C. The resonance frequency shows good linearity as the function of the temperature. This novel design method can be widely applied in the SAW temperature sensors based on the piezoelectric substrates with large second-order frequency-temperature coefficient.

Examinations of vibration frequency and mode shape variations of quartz crystal plates in a thermal field with strain and kinetic energies

The frequency-temperature behavior has long been analyzed to ensure the smoothness of functioning frequency of a quartz crystal resonator during the temperature variation and maintain its operations in a stable state. It has been proven that vibrations of quartz crystal plates in the thickness-shear mode can be well described by the theory of incremental thermal field in conjunction with the Mindlin plate equations, demonstrating the possibility that vibration frequencies and mode shapes can also be well predicted with the temperature as a targeted variable. By studying the vibrations with temperature changes in a given range, the frequencies and vibration modes can be calculated as a function of temperature, then they can be used in the calculations of both strain and kinetic energies for vibration mode identification or characterization based on energy proportion and changes. The trends of changes of vibration frequency, amplitudes, and energy with temperature variation make it possible for characterization the variations of vibrations and particularly the weakening or enhancement of the dominance of specific vibration modes. With such relations between vibration properties and temperature known, possible analytical tools can be developed to aid the optimal design by avoiding significant mode changes or occurrences of mode conversion.

LiTaO3/Silicon Composite Wafers for the Fabrication of Low Loss Low TCF High Coupling Resonators for Filter Applications

SAW devices are widely used for radio-frequency (RF) telecommunication filtering and the number of SAW filters, resonators or duplexers is still increasing in RF stage of cellular phones. Therefore, a strong effort is still dedicated to reduce as much as possible their sensitivity to environmental parameter and more specifically to temperature. Bounding processes have been developed at FEMTO-ST and CEA-LETI using either Au/Au or direct bonding techniques for the fabrication of composite wafers combining materials with very different thermoelastic properties, yielding innovative solutions for about-zero temperature coefficient of frequency (TCF) bulk acoustic wave devices. In the present work, this approach has been applied to (YXl)/42∘ lithium tantalate plates, bounded onto (100) silicon wafers and thinned down to 25μm. The leading idea already explored by other groups as mentioned in introduction consists in impeding the thermal expansion of the piezoelectric material using silicon limited expansion. 2GHz resonators have been built on such plates and tested electrically and thermally, first by tip probing. A dramatic reduction of the TCF is observed for all the tested devices, allowing to reduce the thermal drift of the resonators down to a few ppm.K-1 within the standard temperature range. We then propose an analysis of the frequency-temperature behavior of the device to improve the resonator design to use these wafers for industrial applications.

Experimental and theoretical investigations of some useful langasite cuts for high-temperature SAW applications

Passive high-temperature sensors are a most promising area of use for SAW devices. Langasite (La3Ga5SiO14; LGS) has been identified as promising piezoelectric material to meet high-temperature SAW challenges. Because it is necessary to know the material behavior for an accurate device design, the frequency¿temperature behavior of Rayleigh SAW (R-SAW) and shear-horizontal SAW (SH-SAW) LGS cuts is investigated on delay line and resonator test structures up to 700°C by RF characterization. In the range of the 434-MHz ISM band, the (0°, 22°, 90°) SH-SAW cut shows thermal behavior similar to the (0°, 138.5°, 26.7°) R-SAW cut. Associated with the (0°, 22°, 31°) cut, in which SAWs present mixed types of polarization, the (0°, 22°, 90°) SH-SAW orientation might allow differential measurements on a single substrate. In the temperature range of 400 to 500°C, delay line test devices using the SH-SAW cut show a considerable drop of signal. Theoretical analysis indicates that this newly described behavior might be a result of anisotropy effects in this cut, occurring in case of any slight misorientation of electrode alignment.

Low Frequency and Low Temperature Behavior of Si, Solar Cell by AC Impedance Measurements

In this work, the DC measurements and AC measurements (impedance spectra) have been used to characteristic the Si-module solar cell 6×6 (36 cells), 3.8V and 85mA. From the I-V characteristics under dark conditions for different temperatures (300 - 350K) and by using the ARREHENIUS diagrams defined by Ln(I)=f(1/T) v=const, we have obtained the barrier height ψ(eV), ideal factor A, and the reverse saturation current Io(μA) eV, 2.83 and 0.831 The AC measurement impedance [X(ω)=f(R(ω))] has been employed to measure the parameters of the Si- module solar cell such as: heterogeneity factor, β, DC resistance Rdc, the bulk resistance Rb, activation energy E (eV), donor density Nd (cm-3), and density states Ns (cm-2). The solar cell module was exposed to thermal stress within the range (300 - 350°K), the diagram of complex impedance in the dark, was obtained. This plot gives arcs of a semicircle, their centers lie below the real axis R(ω),corresponding to the appearance of the depression angle (θ≠0), which represents,β(β=2θπ) which is in good agreement with the Cole-Cole diagram. It is noted that,, increases with temperature. The intersection of the circle arcs from the right with x axis (i.e. at very low frequency) gives Rdc the intersection from the left gives Rb, of the sample (2.77KΩ)(i.e. at very high frequency). By using ARREHENIUS diagrams defined by Ln(f)=f(1/T), we have obtained the parameters E (eV), Nd (cm-3), and Ns (cm-2), which equal to 0.354eV, 1.38×1013cm-3 and 6.93×109cm-2 respectively.

Conceptual Design of a High-Q, 3.4-GHz Thin Film Quartz Resonator

Theoretical analyses and designs of high-Q, quartz thin film resonators are presented. The resonators operate at an ultra-high frequency of 3.4 GHz for application to high-frequency timing devices such as cesium chip-scale atomic clocks. The frequency spectra for the 3.4-GHz thin film quartz resonators, which serve as design aids in selecting the resonator dimensions/configurations for simple electrodes, and ring electrode mesa designs are presented here for the first time. The thin film aluminum electrodes are found to play a major role in the resonators because the electrodes are only one third the thickness and mass of the active areas of the plate resonator. Hence, in addition to the material properties of quartz, the elastic, viscoelastic, and thermal properties of the electrodes are included in the models. The frequency-temperature behavior is obtained for the best resonator designs. To improve the frequency-temperature behavior of the resonators, new quartz cuts are proposed to compensate for the thermal stresses caused by the aluminum electrodes and the mounting supports. Frequency response analyses are performed to determine the Q-factor, motional resistance, capacitance ratio, and other figures of merit. The resonators have Q's of about 3800, resistance of about 1300 to 1400 ohms, and capacitance ratios of 1100 to 2800.

A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory

The frequency–temperature characteristics of quartz crystal resonators, particularly the frequency stability in a specific temperature range in which the vibration modes are strongly coupled, has been an important requirement in most applications. The analytical work on frequency–temperature relations has been done over the last decades in many aspects, ranging from the fundamental theory for the thermal effect on vibrations of elastic solids to simplified plate equations of a few strongly coupled vibration modes. However, it has been clearly observed that due to complications of the resonator structures such as the presence of a mounting structure and electrodes, simple and analytical solutions will not be able to consider all the factors which will have inevitable and noticeable effects. In this paper, we incorporate the frequency–temperature theory for crystal plates based on the incremental thermal field formulation by Lee and Yong into our finite element analysis implementation, which is then used to analyze the free vibrations of crystal plates with the higher-order Mindlin plate theory. The effect of electrodes on the frequency–temperature relation is also considered. The computational results are compared with experimental ones from actual products. The satisfactory agreement demonstrates the precise prediction of the frequency–temperature behavior and practical applications of the finite element analysis in product modeling and development.

Frequency-temperature behavior of langasite rectangular beam resonators vibrating in length extension

This paper shows that first order temperature compensated cut exists in Langasite rectangular cross-section beam vibrating in length extensional mode. Theoretical and experimental investigations of frequency-temperature effects are given.

Modeling of dynamic mechanical properties of vulcanized fluoroelastomer

AbstractThe dynamic mechanical properties of a vulcanized fluoroelastomer (FKM) were studied over a range of temperatures and shear frequencies. Dynamic mechanical analysis and differential scanning calorimetry were used for the purpose of the study. A model was developed in order to describe FKM's viscoelastic behavior at various temperatures. The model was fitted to experimental data using an algorithm, which was developed for this purpose. As a result the FKM discrete relaxation spectrum at two reference temperatures was obtained, as well as the Williams‐Landel‐Ferry (WLF) equation parameters or the activation energy equivalent. Further on, the model was applied on storage modulus and loss tangent values obtained from the experiments, during which the temperature increased linearly. It was observed that the WLF equation fits well with the results during the glass transition, while the Arrhenius‐type relationship predicted too rapid decrease of the storage modulus during the glass transition. The master curves were constructed using the previously calculated WLF parameters and the activation energy equivalent. The developed model may be readily applied for the prediction of the numerous FKM compounds' frequency–temperature behavior using the dynamic mechanical properties obtained from either isothermal or low linear heating rate program measurements. POLYM. ENG. SCI., 47:2085–2094, 2007. © 2007 Society of Plastics Engineers

Effects of Thermal Stresses on the Frequency-Temperature Behavior of Piezoelectric Resonators

The frequency-temperature behavior of a piezoelectric crystal resonator can be predicted quite accurately if the resonator is under a stress-free and steady-state uniform temperature condition. The condition is however seldom achieved practically. Most practical resonators are subjected to thermal stresses. Conventional finite element analytical tools such as ANSYS cannot provide a sufficiently accurate model for the frequency-temperature behavior of piezoelectric quartz resonators. A new dynamic frequency-temperature model which accurately predicted the frequency-temperature behavior of quartz resonators affected by transient and steady state temperature changes was presented. Lagrangean equations for small vibrational (incremental) displacements superposed on initial thermal stresses and strains were employed. The initial thermal stresses and strains were obtained from the uncoupled heat and thermoelastic equations. The constitutive equations for the incremental displacements incorporated the temperature derivatives of the material constants. Numerical results were compared with the experimental results for a 50 MHz AT-cut quartz resonator mounted on a glass package. Good comparisons between the experimental results and numerical results from our new model were found. The differences between the thermal expansion coefficients of glass and quartz gave rise to the thermal stresses that had adverse effects on the frequency stability of resonators. Different optimal crystal cut angles of quartz, and resonator geometry were found to achieve stable frequency-temperature behavior of the resonator in a glass package. The dynamic frequency-temperature model was used in the theoretical analyses and designs of high Q, 3.3 GHz, quartz thin film resonators.

Frequency-temperature behavior of flexural quartz resonators by means of Timoshenko's model

The frequency of a flexural resonator and its frequency-temperature behavior usually are computed by Bernoulli's classical approximation. This approach is valid for beams with a large length-over-thickness-ratio. For shorter beams, the effects of shear stress and rotary inertia may play a significant role for temperature-compensated resonators. These effects have been taken into account for isotropic beams. The aim of this paper is to discuss the extension of the shear coefficient in the case of an anisotropic material and to compute the frequency-temperature characteristic of an (XYt)theta cut resonator when the shear stress and the rotary inertia have been taken into account. Comparisons between the classical approximation and this treatment are given for quartz. Furthermore, the numerical predictions obtained by means of different sets of data available for thermal sensitivities of elastic coefficients are compared.

Influence of Viscosity Loss on Coupled Vibrations of Ultrahigh Frequency AT-Cut Quartz Plates

We numerically analyze the influence of viscosity loss in quartz on the unwanted coupling between fundamental thickness-shear (TS) and spurious modes. Classical mode-matching is used to solve the two-dimensional coupled vibrations in an AT-cut quartz plate with an inverted-mesa shape. Using this technique, we calculate the loci of admittance near the main TS response as a function of the loss factor. The temperature behavior of frequency and conductance is also examined for the main TS resonance. The results reveal that, for two strongly coupled vibrations of TS and spurious modes, two resonances on the real frequency-axis are combined into one with increasing loss, although there are still two resonances in the complex frequency plane. We also find that the conductance–temperature behavior of the main TS response is more sensitive to mode coupling than the frequency–temperature behavior, and it therefore works well as a detector of mode coupling.

Determination of the electromechanical coupling factor of gallium orthophosphate (GaPO/sub 4/) and its influence on resonance-frequency temperature dependencies

The quartz homeotype gallium orthophosphate (GaPO4) is a representative of piezoelectric single crystals of large electromechanical coupling factor. It is known that its coupling factor kappa26 associated with the resonators vibrating in the thickness-shear mode is approximately two times greater than that of quartz. This property increases the spacing between the series and parallel resonance frequencies of resonators, as well as the difference between the resonance frequency temperature dependencies of the fundamental and harmonic resonance frequencies of resonators vibrating in the thickness-shear mode. In this paper, the methods for determination of the coupling factor kappa26 are presented, and the computed values are compared with the measured ones. The influence of the coupling factor to the resonance-frequency temperature dependencies of the fundamental and third harmonics of selected rotated Y-cut GaPO4 resonators vibrating in the thickness-shear mode is presented. The purely elastic case for a laterally unbounded plate, which corresponds closely to the limiting case of high harmonic resonance frequency-temperature behavior was assumed for the calculations. The computed temperature coefficients for the Y-cut orientation and calculated turnover point temperatures TTP for different (YX1) orientations are presented.

Quartz crystal microbalance in elevated temperature viscous liquids: Temperature effect compensation and lubricant degradation monitoring

The quartz crystal microbalance (QCM) was extended to investigate viscous liquids at elevated temperatures in both isothermal and non-isothermal systems. An analysis of the frequency–temperature behavior of the QCM resulted in a new approach to compensate for the effect of the rate of temperature rise on the theoretical QCM temperature coefficients. The temperature-dependent viscosities of a series of liquids were evaluated by measuring the damping voltage of QCM. Thermal degradation experiments on pentaerythritol tetrapelargonate based lubricants demonstrated the potential application of QCM as an in situ sensor to evaluate the thermal stability of lubricants or other viscous fluids. The solid residue deposition rates and liquid phase property changes (i.e., product of density and viscosity) were extensively investigated by monitoring variations in the QCM frequency and damping voltage during the lubricant thermally stressing over a temperature range of 150–220 °C.

Microstructure and magnetic properties of Fe85$minus;xCoxNb5B8P2 high temperature nanocrystalline alloys

A new family of Fe–Co based high temperature nanocrystalline alloy was developed using Fe85−xCoxNb5B8P2 as a precursor amorphous material, which can be cast in air. The nanocrystalline sample presented a flat hysteresis loop with excellent high frequency and high temperature behaviour. The material crystallizes at relative low temperature (400°C), with a relatively low activation energy (2.7 eV) for x=20. The sample annealed at 500°C shows temperature independent soft magnetic properties (Hc around 40 A/m, relative permeability 450 up to 1 MHz) up to the applied annealing temperature.

Microstructure and magnetic properties of Fe85−Co Nb5B8P2 high temperature nanocrystalline alloys

A new family of Fe–Co based high temperature nanocrystalline alloy was developed using Fe 85− x Co x Nb 5 B 8 P 2 as a precursor amorphous material , which can be cast in air. The nanocrystalline sample presented a flat hysteresis loop with excellent high frequency and high temperature behaviour. The material crystallizes at relative low temperature (400°C), with a relatively low activation energy (2.7 eV) for x =20. The sample annealed at 500°C shows temperature independent soft magnetic properties (Hc around 40 A/m, relative permeability 450 up to 1 MHz) up to the applied annealing temperature.