Loss Tangent Measurements Research Articles

Comparisons of the dynamic moduli of various polymers

To fully characterise the elastic properties of a homogeneous, isotropic material, two independent elastic constants are needed, usually the bulk and shear moduli. For the types of polymers used in sonar applications, these moduli are typically both frequency and temperature dependent. Of particular interest is the position (in frequency and temperature) of peak loss tangent, which is related to the glass transition temperature through the free volume concept. Although there exists in the literature a lot of data on the dynamic shear (and Young's) modulus for various polymers, data on dynamic bulk modulus is scarcer, due to the difficulty of the measurement. This paper reviews the current literature on the dynamic moduli of various polymers, with particular regard to the relationship between the peak loss tangents of the bulk and shear moduli. Simple relaxation models are studied to give insight on the factors affecting the peak of the loss tangent and new measurements on a nitrile‐butadiene rubber compound are presented.

A Measurement Process to Characterize Natural and Engineered Low-Loss Uniaxial Dielectric Materials at Microwave Frequencies

We present a measurement method to characterize low-loss engineered materials and natural uniaxial dielectrics. Our approach employs a rectangular cavity coupled with tailored finite-element simulations to accurately determine the permittivity tensors and loss tangents of material assemblies. Although similar approaches for natural crystals have been reported, this is the first time this method is adapted to engineered metamaterials. Loss-tangent measurements with an accuracy of 4-5 significant digits can be achieved by this simple and effective measurement approach. To demonstrate the method, we characterize a layered barium titanate-alumina stack and show that low-loss engineered crystals can be achieved via a proper choice of a bonding agent.

Electrical properties of Ni0.93Co0.02Mn0.05Fe2O4 + BaTiO3 ME composites

Polycrystalline samples of mixed composites of Ni0.93Co0.02Mn0.05Fe2O4 + BaTiO3 were prepared by conventional double sintering ceramic method. The phase analysis was carried out by using X-ray diffraction technique. Variation of dc resistivity and thermo emf was studied as a function of temperature. AC conductivity (σac) was investigated in the frequency range 100 Hz–1 MHz. The loss tangent (tan δ) measurements conclude that the conduction mechanism in these samples is due to small polaron hopping. The magnetoelectric conversion factor, i.e. dc(ME)H was studied as a function of intensity of magnetic field and the maximum value 407 μV/cm/Oe was observed at a field of 0.8 kOe in a composite with 85% BaTiO3 and 15% Ni0.93Co0.02Mn0.05Fe2O4 phase.

Effects of Nano-Structure of Silica on Dynamic Properties of Styrene-Butadiene Rubber

Properties of four materials based on styrene-butadiene rubber (SBR), one without filler and the other three with the same amount but different types of silica fillers, are investigated. The fillers used are Vulkasil S and two new fillers, differing in nano-structures: specific surface area and particle aggregate morphology. All other components in the material formulations are the same as well as the procedures of material preparation. Thermal and thermo-mechanical properties of all four materials are investigated by modulated differential scanning calorimetry (MDSC) and dynamic mechanical analysis (DMA). Morphology of the materials is studied using scanning electron microscopy (SEM). The results for glass transition temperature (Tg ) of gum rubber and three filled rubbers, obtained by MDSC are for all four materials Tg = -50±1 0C, and by DMA loss tangent measurements also for all of them Tg = -29±1 0C. It indicates no significant influence of active silica fillers on the rubber network segment dynamics, in the temperature range close to Tg of SBR. But, at higher temperatures MDSC gives insights into dynamic transitions that are under the influence of filler interactions and sensitive to filler structure. The difference in Tg results obtained for the same material by MDSC and DMA can be understood in terms of different sensitivity of network segment dynamics to conditions provided by those two measuring methods.

Compositional, temperature and frequency dependence of dielectric behaviour of zinc substituted copper- ferri-chromates

The comprehensive study on compositional, temperature and frequency dependent dielectric properties of ZnxCu1−xFeCrO4 (x = 0.0, 0.2, 0.4 and 0.6 ) was carried out by means of a. c. resistivity (ρac), dielectric constant (e′) and loss tangent (tanδ) measurements in the frequency range from 100 Hz to 1 MHz at different temperatures ranging from 40 °C to 500 °C. An abnormal behaviour of e′ as a function of temperature is explained on the basis of contribution of two types of charge carriers in the polarization process. It is found that magnetic ordering does not have marked influence on the dielectric properties. The probable conduction mechanism in the present system is due to electron transition such as Fe2+ $$ \leftrightarrows $$ Fe3+ and Cu2+ $$ \leftrightarrows $$ Cu1+ rather than ionization or polaron hopping mechanism.

Amendment of cavity perturbation technique for loss tangent measurement at microwave frequencies

Theoretically, the quality factor of a metal resonant cavity will be increased after introducing a lossless dielectric sample. However, this increment of quality factor is not put into the consideration of the calculation of loss tangent measurement for the conventional cavity perturbation method, widely used on the measurements of microwave dielectric properties. Therefore, the conventional resonant perturbation formulas for dielectric loss measurement should be amended. This amendment is introduced in this study and the amended formulas for loss tangent measurement are given. With the amended formulas, no standard sample is required for measurement which simplifies the measuring procedure suggested by the previous publication. In addition, the measuring error on loss tangent on the conventional formula is discussed. Experiments have shown the improvement of measurement accuracy by this modification.

Fabry–Perot Open Resonator Technique for Dielectric Permittivity and Loss Tangent Measurements of Yttrium Iron Garnet

This paper presents a Fabry-Perot open resonator system for the precision measurement of real part of permittivity and loss tangent of yttrium iron garnet specimens at 60 GHz. This system allows us to vary the cavity length at 10-nm step size to study the resonance profile of each excited fundamental mode with great stability and reproducibility. The obtained highly symmetrical, fully resolved Gaussian resonance profile results in a significantly high Q factor for the overall system. It enables us to determine the dielectric permittivity and loss tangent of ferrite materials accurately and reliably for the first time. Measurements have been performed on a 99.9% pure yttrium iron garnet and a gadolinium substituted yttrium iron garnet specimen at 60 GHz. A temperature dependence study has also been conducted at a limited temperature range near room temperature

Thin film Ba 0.25Sr 0.75TiO 3 voltage tunable capacitors on fused silica substrates for applications in microwave microelectronics

Thin film Au/Pt/Ba 0.25Sr 0.75TiO 3/Pt/Au/Ti capacitor structures were fabricated on fused silica substrates using pulsed laser deposition of ferroelectric films. Low-field dielectric measurements were performed as a function of frequency in the range 1–25 GHz at different external dc fields up to 360 kV/cm. Resonant microwave power absorption observed at frequencies less than 10 GHz under dc field is due to electrostriction and field induced piezoelectric effects. The effects are simulated using an electroacoustic model of the multilayer capacitor structure. A circuit model is applied to investigate the influence of series resistance and inductance of interconnect/lead strips on capacitor performance. Analysis shows that the measured loss tangent of the capacitor is mainly due to series resistance and frequency dispersion of capacitance is caused by series inductance. The de-embedded value of the loss tangent is 0.005 at 10 GHz. The measured loss tangent is less than 0.02 and tunability is up to 40% in the whole frequency range. These parameters indicate high potential of Ba 0.25Sr 0.75TiO 3 capacitors for applications in voltage controlled devices of microwave microelectronics.

Static and high frequency magnetic and dielectric properties of ferrite-ferroelectric composite materials

A series of sintered composite materials was fabricated from Parascan™ barium strontium titanate (BSTO) and Trans-Tech nickel zinc ferrite powders. The ferrite loading was varied from zero (BSTO only) to 100wt% (ferrite only). X-ray diffraction data show the presence of a third, nonmagnetic phase that sets the ferrite loading at values somewhat lower than the as prepared wt % amounts. The average magnetization is found to scale linearly with the loading. The initial susceptibility, saturation field, and coercive force as obtained from hysteresis loop data show trends consistent with these data. Ferromagnetic resonance linewidth and effective linewidth measurements at 10GHz show reasonable values for the 100wt% samples, but any amount of BSTO causes a severe degradation in both loss parameters. Similarly, it is found that any amount of ferrite causes a rapid drop in the relative dielectric constant that is consistent with standard mixing models. Loss tangent measurements gave modest values in the 0.001–0.005 range at 1MHz and much larger values in the 0.02–0.03 range at 10GHz.

Dielectric characterisation of Barium Fluoride at cryogenic temperatures using TE 011 and quasi TE 0mn mode dielectric resonators

Barium Fluoride (BaF 2), mainly used in optical applications, has similar properties to those of CaF 2 but better stability under environmental conditions. In this paper, we report measurements of loss tangent and the real part of the relative permittivity ε r of single crystal BaF 2 in the temperature range from 14 to 290 K at frequencies of 8, 10.4, 12.1, 17.6, 21.1 and 24.4 GHz. Microwave properties of BaF 2 were determined by measurements of the resonance frequency and the unloaded Q-factor of TE 011 and quasi TE 0mn modes cylindrical cavities containing the sample under test. Two techniques namely Hakki–Coleman Dielectric Resonator and dielectric post resonators have been used for characterizing the dielectric material. Losses due to the uncalibrated cables and adaptors inside the cryocooler are accounted in the calculation of unloaded Q-factor using the Transmission Mode Q-Factor data processing technique. The permittivity of BaF 2 exhibited a 5% increase from 6.9 (14 K) to 7.35 (290 K). The loss tangent increased from 1 × 10 −5 to 1.1 × 10 −4 over the measured temperature range, 14–290 K at a frequency of 10.4 GHz. The measured microwave properties show that BaF 2 can be used in many microwave devices.

Complex Permittivity Measurements of Thin Ferroelectric Films Employing Split Post Dielectric Resonator

Split post dielectric resonator (SPDR) operating at frequency about 19 GHz has been used for measurements of permittivity and dielectric loss tangent of ferroelectric films deposited on low loss dielectric substrates. These properties are evaluated form measured resonant frequencies and Q-factors of SPDR with substrate (with and without deposited film) employing full wave electromagnetic theory. Sensitivity and uncertainty analysis have shown that it is possible to measure real permittivity of ferroelectric films having thickness in the range 200 nm to 2000 nm and permittivity range 100–10000 with uncertainties similar to uncertainties of their thickness. Loss tangent resolution for this technique is about 1 × 10−4 for samples having permittivity about 1000 and thickness of the order of 500 nm.

Cryogenic complex anisotropic permittivity of magnesium fluoride

The complex tensor permittivity of MgF 2 has been measured using whispering gallery mode and quasi TE 0np dielectric post resonator techniques as a function of frequency and temperature. MgF 2 exhibits uniaxial anisotropy. At room temperature permittivity component parallel to the anisotropy axis is 4.77 ± 0.2% and the component perpendicular to anisotropy axis is 5.49 ± 0.2%. Dielectric loss tangent component perpendicular to anisotropy axis is approximately 4 × 10 −5 and dielectric loss tangent component parallel to anisotropy axis is approximately 7 × 10 −5 at 39 GHz and room temperature. Losses at room temperature increase quasi-linearly with frequency. At the temperature of 15 K measured loss tangent values for both the components of the dielectric loss tangent were about 1 × 10 −6 at 39 GHz. The RF and microwave losses of magnesium fluoride (MgF 2) crystal are low as compared with other commonly used Fluorides. MgF 2 is hygroscopic and dielectric losses of this material vary with the contents of water.

Influence of frequency and prestrain on the mechanical efficiency of dielectric electroactive polymer actuators

The effect of frequency and bidirectional static prestrain on the results of dynamic mechanical measurements of loss tangent for acrylic elastomer films is investigated. These prestrained elastomer films are used in electroactive polymer actuators, sometimes referred to as artificial muscles, where the loss tangent determines the mechanical efficiency of the actuator. It is found that mechanical efficiency of the actuator increases with increased bidirectional prestrain, and decreases with increased frequency.

Dielectric behavior of three phase polyimide percolative nanocomposites

AbstractThree phase ceramic–metal–plastic (cermetplas) percolative nanocomposite films were prepared using polyimide, as the matrix to prepare the composite films. Silver nanoparticles with a mean particle size of about 41 nm were prepared and used as the metal phase. Nanocomposites of barium titanate (BaTiO3) particles in polyimide matrix, with silver as metallic inclusion, were formulated using effective medium theory and percolation theory. The concentration and frequency dependence of dielectric permittivity (ε) and loss tangent (tan δ) measurements were reported and discussed for cermetplas below the percolation threshold. Experimental results for cermetplas show that a ε of above 500 can be achieved below the percolation. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci, 2006

Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique

The anisotropic loss tangent has been determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. The Q-factors of quasi-TE and quasi-TM modes were measured precisely in four cylindrical sapphire resonators at room temperature, from which was determined a maximum attainable Q-factor of (2.1 +/- 0.2) x 10(5) at 9 GHz in a quasi-TM mode. Sapphire dielectric material from three different manufacturers was compared over the 270-345 K temperature range and the 5-16 GHz frequency range.

Tunable high-quality-factor interdigitated (Ba, Sr)TiO 3 capacitors fabricated on low-cost substrates with copper metallization

Interdigitated capacitors containing the field-tunable ferroelectric Ba 0.75Sr 0.25TiO 3, polycrystalline alumina substrates, and copper metallization have been fabricated. Dielectric layers were prepared by magnetron sputtering, while the Cu metallization was evaporated. The dielectric tunability of the Ba 0.75Sr 0.25TiO 3 was 40% at an applied electric field of 12 V/μm. This corresponds to a 3-μm electrode gap width and a 35 V dc bias. Low-frequency (1 MHz) loss tangent measurements indicate a dielectric Q (quality factor) of ∼100 while microwave measurements reveal a zero bias device Q of ∼30 at 26 GHz. These values are comparable or superior to numerous reports of barium strontium titanate interdigitated capacitors prepared using single crystalline substrates and noble metallization. As such, this technology is significantly less expensive and more amenable to large-volume manufacturing.

Structural and dielectric properties of strain-controlled epitaxial SrTiO3 thin films by two-step growth technique

Structural and dielectric properties of epitaxial SrTiO3 (STO) thin films on LaAlO3 substrates fabricated by a two-step growth technique using pulsed laser deposition were investigated by in situ and ex situ observations in terms of strain relaxation from the lattice mismatch between the film and the substrate. In a first step, a very thin STO layer of less than 10nm was deposited at low temperature. The main part of the film was deposited in a second step at high temperature, as commonly used for epitaxial growth. In situ reflection high-energy electron diffraction observations showed that almost full strain relaxation was realized before the deposition of the second layer, whereas the normally grown film was not fully relaxed even when the film thickness exceeded 300nm. The relaxation process of the two-step-grown film took place through the crystallization of the first layer with substantial misfit dislocation formation, which is therefore fundamentally different from that of the normally grown film. Since the normally grown film possesses compressive strain due to less strain relaxation, the two-step-grown film showed larger permittivity and larger tuning compared to the normally grown film. The estimation of the extrinsic loss contribution from the measured loss tangent implied that the two-step growth technique could suppress the extrinsic loss due to a redistribution of defects in the film. The first layer leads to two effects: (i) strain relaxation and (ii) lower loss of the film.

Complex permittivity measurements of low-loss microwave ceramics employing higher order quasi TE0np modes excited in a cylindrical dielectric sample

Higher order quasi TE0np modes have been used for precise measurements of permittivity and dielectric loss tangent of low-loss dielectric ceramics versus frequency in the microwave frequency range. It has been shown that, using this technique, dielectrics having arbitrary permittivity value and dielectric loss tangent values in the range 10−6–10−2 can be measured with relative uncertainties below 0.5% for real permittivity and below 5% for dielectric losses. Several dielectric materials have been measured including single- crystal quartz, single-crystal sapphire and the low-loss microwave ceramics BMT, BZT and BZNT.

Dielectric properties of AlN x thin films prepared by RF magnetron sputtering of Al using a N 2/Ar sputtering gas mixture

Aluminium nitride is a low conductivity material which has applications as a dielectric and passivation layer in microelectronics. Normally, this material is prepared using chemical vapour deposition or molecular beam epitaxy, but following earlier work in which it has been demonstrated that silicon nitride may be successfully prepared by RF magnetron sputtering, we have investigated the electrical properties of aluminium nitride prepared by this technique. Al–AlN x –Al sandwich structure films were prepared by using a pure Al target with a sputtering gas mixture of N 2/Ar in the ratio 3:7 (partial pressures 0.40 Pa nitrogen and 0.93 Pa argon) using an RF discharge power of 180 W. Initial measurements indicated that the relative permittivity was approximately 9.1 and that the capacitance was independent of applied DC voltage, demonstrating that the contacts did not form Schottky barriers. The AC conductivity σ was observed to follow an expression σ= Aω s , where A is a constant, ω is the angular frequency and s is an index. Values of s were found to be in the range 0.62–1.31, increasing with increasing frequency in the range 100 Hz–20 kHz and decreasing with increasing temperature in the range 161–373 K. This type of behaviour was consistent with a carrier-hopping process having a density of localised states value N∼6×10 27 m −3. Low-temperature activation energies were in the range 0.001–0.008 eV, further indicating the presence of a carrier hopping process. The capacitance showed a decrease with increasing frequency and an increase with increasing temperature, tending towards a constant value at higher frequencies and lower temperatures. Measurements of loss tangent as functions of frequency and temperature showed a minimum in its frequency dependence, which appeared to shift to higher frequencies with increasing temperature. These measurements are in accordance with the model of Goswami and Goswami for samples with ohmic contacts, and are representative of results obtained on other insulating films, including nitrides.

Growing of crystalline zones in EPDM irradiated with a low neutron flux

The effects of low neutron flux irradiation on commercial ethylene–propylene–diene-monomer (EPDM) filled with ceramic particles were studied. This material is used as housing in non-ceramic outdoor electrical insulators. Mechanical dynamical analysis (loss tangent and modulus measurements), swelling test, infrared absorption and X-ray diffraction were employed as experimental techniques. It was found out that the low flux neutron irradiation promotes the growing of crystalline zones in the EPDM, which leads to an increase of the elastic modulus and a maximum in the loss tangent at around 310 K.