Impedance Formalism Research Articles

Comprehensive characterization of thermophysical properties in solids using thermal impedance

Thermal impedance Zth(iω) is a way of defining the thermophysical characteristics and behavior of thermal systems. Existing photoacoustic and photothermal approaches based on thermal impedance formalism merely allows a partial thermal characterization of the materials (generally, either thermal diffusivity or thermal effusivity). In this work, a new approach based on the thermal impedance concept in terms of its characteristic thermal time constant is developed from thermal quadrupoles formalism. The approach outlined in this contribution presents a set of analytical equations in which through a single measurement of thermal impedance is sufficient to obtain a comprehensive characterization of the thermophysical properties of solid materials in a simple way.

Microstructure And Dielectric Relaxation Of BT And ST Doped Ba(Fe0.5Nb0.5)O3 ceramics For Sensor Applications

Recently a new wave of interest has risen on complex perovskite structure due to their wide use in fabrication of multilayer ceramic capacitors, electrostrictive actuators, and electromechanical transducers. The polycrystalline ceramics of Ba(Fe0.5Nb0.5)O3 (BFN) and its solid solutions 0.89Ba(Fe0.5Nb0.5)O3-0.11BaTiO3 (BFN-BT11) and 0.89Ba(Fe0.5Nb0.5)O3-0.11SrTiO3 (BFN-ST11) were fabricated by a solid-state reaction Method. Processing parameters such as calcination temperature, sintering temperature and sintering durations were optimized to get best dielectric properties. It was found that the above ceramics sintered at 1250°C for 6 hours exhibited maximum density and uniform microstructure. X-ray diffraction studies of the compound showed the formation of single-phase monoclinic crystal structure at room temperature. Surface morphology of the compounds was studied by Scanning electron microscope (SEM). The effects of BaTiO3 and SrTiO3 substitution on the structure and on the electrical and ferroelectric properties of Ba(Fe0.5Nb0.5)O3 samples have been studied by performing x-ray diffraction and dielectric measurements. The electrical properties of the samples were investigated in a frequency range of 100 Hz - 1 MHz and temperature range of 30-350 °C using complex impedance spectroscopic technique. The frequency-dependent electrical data are also analyzed in the framework of conductivity and impedance formalisms.

DIELECTRIC RESPONSE AND IMPEDANCE SPECTROSCOPY OF (Na0.5Bi0.5)0.95Ba0.05Zr0.04Ti0.96O3 FERROELECTRIC CERAMIC

A new lead-free ferroelectric relaxor ceramic was prepared by conventional solid-state synthesis by modifying A-site and B-site in (Na0.5Bi0.5)TiO3 system, i.e., (Na0.5Bi0.5)0.95Ba0.05Zr0.04Ti0.96O3 (0.05BNBZT). X-ray diffraction studies reveal a single phase rhombohedral structure. Crystallite size and strain analysis has been done by Debye–Scherrer and Williamson–Hall technique. The tolerance factor is 0.81, indicating a stable Perovskite structure of the material. Scanning electron micrograph of the material shows a distribution of grains, average grain size is 1.41 μm. Dielectric response of (Na0.5Bi0.5)0.95Ba0.05 Zr0.04Ti0.96O3 , ferroelectric ceramic has been studied as a function of frequency over a wide range of temperatures. The studied ceramic exhibited maximum frequency dispersion in both real and imaginary part of dielectric susceptibility at and around the dielectric transition temperature (Tm). The frequency dependence of transition temperature, Tm (temperature of the maximum of dielectric constant) was studied in terms of Vogel–Fulcher relation. The dielectric relaxation of (Na0.5Bi0.5)0.95Ba0.05Zr0.04Ti0.96O3 ceramic was studied at different temperatures using the complex impedance (Z*) and electrical modulus (M*) formalism. Impedance measurements were made on over a wide range of temperatures (300–600°C) and frequencies (45 Hz–5 MHz) which show the presence of both grain and grain boundary effects in the material. The Impedance spectroscopy is shown to be an efficient method capable of detecting the contributions of the resistances of grain boundaries (at higher temperature), in addition to granular contribution (at all temperatures), which influences the device properties of a material. The electric modulus (M*) formalism used in the analysis enabled us to distinguish and separate the relaxation processes. Conductivity studies in the material obey the Jonscher's power law in frequency (45 Hz–5 MHz) and temperature (30–600°C). These results give evidence that the lead-free ferroelectric ceramics is extensively may be used for device and electronic applications, when compared with lead-based materials.

Dielectric and magnetic study of BaTi0.5Mn0.5O3 ceramics, synthesized by solid state sintering, mechanical alloying and chemical routes

A comparative study of the surface morphology, dielectric and magnetic properties of the BaTi0.5Mn0.5O3 (BTMO) ceramics has been carried out by synthesizing the samples in different routes. BTMO samples have shown single phased 12R type hexagonal structure with R3¯m space group. Interfacial effects on the dielectric properties of the samples have been understood by Cole–Cole plots in complex impedance and modulus formalism. It has been found that huge dielectric constant (103–106) at lower frequencies is largely contributed by the heterogeneous electronic microstructure at the interfaces of grains. Modulus formalism has identified the effects of both grain and grain boundary microstructure on the dielectric properties, particularly in chemical routed samples. The order of grain boundary resistivity suggests the semiconductor/insulator class of the material. The grain boundary resistivity of the mechanical alloyed samples is remarkably lower than the solid state and chemical routed samples. Some of the samples have exhibited signature of weak ferromagnetism at room temperature.

Synthesis and Electrical Properties of Well-Ordered Layered α-MoO3 Nanosheets

Abstractα-MoO3ordered nanosheets have been synthesized under hydrothermal conditions using commercial MoO3and hydroquinone as structuring agent. X-ray diffraction (XRD), scanning electron microscope (SEM) and transmission electron microscopy (TEM) were used to analyse the obtained material. The conductivity mechanism of the Molybdenum ordered nanosheets has been investigated using combined complex impedance and modulus formalism.The temperature dependence of the conductivity, which was between 473 and 573 K, is very close to the Arrhenius’ law, with an activation energy of 0.76 eV. However, the conductivity of the material increases with temperature. It shows a typical negative temperature coefficient resistance (NTCR) similar to that of a semiconductor. The dielectric properties of the MoO3compound have been studied in the temperature range of 473–573 K as well as the frequency range of 10 Hz to 13 MHz. The ac-conductivity for high frequency σac(ω) obeys the universal power law.

Frequency Methods Applied to the Characterization of the Thermophysical Properties of a Granular Material with a Cylindrical Probe

In many fields, such as in the agri-food industry or in the building industry, it is important to be able to monitor the thermophysical properties of granular materials. Regular thermal probes allow for the determination of one or several thermophysical factors. The success of the method used depends in part on the nature of the signal sent, on the type of physical model applied and eventually on the type of probe used and its implantation in the material. Although efficacious for most applications, regular thermal probes do present some limitations. It is the case, for example, when one has to know precisely the thermal contact resistance or the nature of the signal sent. In this article is presented a characterization method based on thermal impedance formalism. This method allows for the determination of the thermal conductivity, the thermal diffusivity, and the contact thermal resistance in one single test. The application of this method requires the use of a specific probe developed to enable measurement of heat flux and temperature at the interface of the probe and the studied material. Its practical application is presented for dry sand.

Structural and electrical properties of Gd(Ni 1/2Zr 1/2)O 3

The Gd(Ni 1/2Zr 1/2)O 3 (GNZ) ceramic is synthesized by the solid-state reaction technique. The X-ray diffraction pattern of the sample shows monoclinic phase at room temperature. The dielectric dispersion of the material is investigated in the temperature range from 303 K to 673 K and in the frequency range from 100 Hz to 1 MHz. The relaxation peak is observed in the frequency dependence of the loss tangent. The relaxation time at different temperatures is found to obey Arrhenius law having activation energy of 1.1 eV which indicates the hopping of ions at the lattice site and may be responsible for the dielectric relaxation of GNZ. The scaling behaviour of loss tangent suggests that the relaxation mechanism is temperature independent. The frequency dependent conductivity spectra follow the power law. In the impedance formalism, the Cole–Cole model is used to study the relaxation mechanism of GNZ.

Electrical and electromechanical studies in ferroelectric Gd3+modified lead potassium niobate ceramics

The change in dielectric constant relaxation time over temperature (35–590 °C) and frequency (45 Hz–5 MHz) in ceramics of Pb 0.77 K 0.115 Gd 0.115 Nb 2 O 6 (PKGN, T c = 340 °c) has been studied. Powder X-ray diffraction revealed the single-phase formation with orthorhombic crystal structure. The P-E hysteresis loop parameters are P s = 21.77 μ C/cm 2 , P r = 17.09 μ C/cm 2 , E c = 11.86 kV/cm; the piezoelectric constants, K p = 31.7%, K t = 47%, d 33 = 115 × 10 −12 C/N, d 31 = −41 × 10 −12 C/N, are determined in the material and some transducer applications are discussed. Cole-Cole (Z ll vs. Z l ) plots showed a non-Debye type relaxation. Conductivity obeyed Jonscher’s universal power law, σ = σ 0 + A ω n . The theoretical values of e l and σ are computed using the parameters ‘ A ( T )’ and ‘ n ( T )’ (0 1) and are well fitted with the experimental data. The hopping ion frequency ( ω p ) and charge carrier concentration ( K l ) have been analyzed using Almond-West formalism. The dielectric relaxation processes are associated with localized oxygen vacancies conduction at high frequency region. A long-range conductivity by Gd 3+ ions is found to be predominant at low frequency region. The activation energies from impedance and modulus formalisms revealed the ionic type conduction in PKGN.

Magnetization Dynamics of Amorphous Ribbons and Wires Studied by Inductance Spectroscopy.

Inductance spectroscopy is a particular formulation variant of the well known complex impedance formalism typically used for the electric characterization of dielectric, ferroelectric, and piezoelectric materials. It has been successfully exploited as a versatile tool for characterization of the magnetization dynamics in amorphous ribbons and wires by means of simple experiments involving coils for sample holding and impedance analyzer equipment. This technique affords the resolution of the magnetization processes in soft magnetic materials, in terms of reversible deformation of pinned domain walls, domain wall displacements and spin rotation, for which characteristic parameters such as the alloy initial permeability and the relaxation frequencies, indicating the dispersion of each process, can be defined. Additionally, these parameters can be correlated with chemical composition variation, size effects and induced anisotropies, leading to a more physical insight for the understanding of the frequency dependent magnetic response of amorphous alloys, which is of prime interest for the development of novel applications in the field of telecommunication and sensing technologies. In this work, a brief overview, together with recent progress on the magnetization dynamics of amorphous ribbons, wires, microwires and biphase wires, is presented and discussed for the intermediate frequency interval between 10 Hz and 13 MHz.

Electrical Properties of Rare Earth Double Perovskite Sr2CeSbO6

The double perovskite oxide strontium cerium antimonate, Sr2CeSbO6 (SCS) is synthesised by solid state reaction technique. Thermal behaviour of SCS are investigated using thermogravimetric analyser and differential scanning calorimeter in the temperature range from 303 to 1500 K. Dielectric relaxation spectroscopy is used to investigate the frequency dependent dielectric relaxation in SCS in the frequency range from 100 Hz to 1 MHz and in the temperature range from 303 to 703 K. The frequency dependent electrical data are analysed by impedance formalism. The relaxation mechanism of the sample is modelled by Davidson-Cole equation (modified Debye equation). The frequencies corresponding to the maxima of imaginary part of impedance at the various temperatures are found to obey the Arrhenius law with activation energy ∼ 0.15 eV. The scaling behaviour of imaginary part of impedance suggests that the relaxation describes the same mechanism at various temperatures.

Dielectric Properties of Reduced Heterogeneous Silica–Titania Glasses

We have studied the frequency and temperature dependences of the dielectric properties of a heterogeneous silica–titania (SiO2–TiO2) glass by ac impedance spectroscopy measurements in the temperature range 25–700°C and the frequency range 40–107 Hz. The heterogeneous glass was prepared by the controlled heat treatment of a homogenous SiO2–TiO2 glass, containing ∼7.5 wt% TiO2, in a reducing atmosphere to create a microstructure consisting of many discrete particles of the rutile/anatase TiO2 phase dispersed in a homogeneous SiO2‐rich glassy matrix. Unlike the homogeneous SiO2–TiO2 glass, which exhibited only one electrical/dielectric dispersion, presumably due to ion hopping, the heterogeneous glass material exhibited two distinct electrical responses in the impedance formalism. We attributed these contributions to the two‐phase microstructure and explained the dielectric behavior in terms of the Maxwell–Wagner relaxation arising at the interfaces between the TiO2 crystals and the SiO2‐rich matrix phase.

Dielectric properties of high permittivity ceramics based on Dy2/3CuTa4O12

Abstract The paper reports on the dielectric properties of Dy 2/3 CuTa 4 O 12 ceramic—a new material exhibiting very high permittivity exceeding 10 4 at low frequencies and broad steps in the permittivity versus temperature plots. Impedance spectroscopy studies performed in a frequency range 10 Hz to 2 MHz and within a temperature range from −160 to 650 °C revealed two distinct contributions in impedance and electric modulus formalisms, which were attributed to semiconducting grains and more resistive grain boundaries. Two plateaus of about 40,000 and 50 were found in the real part of the permittivity versus frequency plots. Resistances and capacitances of grains, estimated on the basis of the impedance data, are 1.5–2 orders and about 400 times, respectively, lower than those of grain boundaries. The influence of sintering temperature within a range 1180–1250 °C on the dielectric properties and the microstructure of the ceramics was also investigated. The permittivity values were found to increase significantly with increasing sintering temperature. The observed high dielectric constant behavior was explained in terms of Maxwell–Wagner polarization related to internal (grain boundary) barrier layer capacitance effects.

Impedance spectroscopy, electronic structure and X-ray photoelectron spectroscopy studies of Pb(Fe 1/2Nb 1/2)O 3

Impedance spectroscopy is used to study the electrical behaviour of lead iron niobate, Pb(Fe 1/2Nb 1/2)O 3 (PFN) in the frequency range from 100 Hz to 1 MHz and in the temperature range from 203 to 363 K. The frequency-dependent electrical data are analyzed by impedance and conductivity formalisms. The complex impedance plane plot shows that the relaxation (conduction) mechanism in PFN is purely a bulk effect arising from the semiconductive grains. The relaxation mechanism of the sample in the framework of electric modulus formalism is modelled by Davidson–Cole equation. The scaling behaviour of imaginary electric modulus suggests that the relaxation describes the same mechanism at various temperatures. We have studied the electronic structure of the PFN using X-ray photoemission spectroscopy (XPS). The density of states (DOS) obtained from the first principles full potential linearized augmented plane wave calculation of PFN shows a direct energy gap ∼0.43 eV. The XPS spectrum is compared with the calculated DOS spectra. It has been observed that the electrical properties of PFN are dominated by the interaction between transition metal and oxygen ions as its valence band consists mainly of the oxygen p-states hybridized with the iron d-states.

Relaxation studies of spray deposited Bi2Co0.1V0.9O5.35 solid electrolyte thin films on stainless steel substrate

The room temperature-stabilized γ-phase ion conducting Bi2Co0.1V0.9O5.35 thin film was deposited by spray pyrolysis on stainless steel substrate. The intra-grain and grain interior charge transfer was confirmed in these films with impedance spectroscopic measurements done from 1 Hz to 10 MHz in the temperature range 550 K to 741 K. Impedance data further revealed non-Debye kind of relaxation dispersion in the film. The relaxation frequency ranges from 10 to 100 Hz, which predicts long range jumping of the oxygen ions with chemical diffusivity. The Arrhenius plots for relaxation frequency and grain boundary conductivity were found to have same activation energy revealing grain boundary dominant conduction. The effect of polycrystallinity on relaxation dispersion is investigated for the first time on Bi2Co0.1V0.9O5.35 thin films using impedance formalism.

Sintering and dielectric properties of Cu 2Ta 4O 12 ceramics

In this work, Cu 2Ta 4O 12 ceramic was investigated as a promising, lead-free, nonferroelectric material with high dielectric permittivity. The results of impedance spectroscopy studies carried out at frequencies 10 Hz to 2 MHz over a wide temperature range from −55 to 700 °C were analyzed in the impedance, dielectric permittivity and electric modulus formalisms. In complex impedance plots two distinct arcs were distinguished, ascribed to the semiconducting grains and to the insulating grain boundaries. Cu 2Ta 4O 12 ceramic was found to exhibit a high dielectric permittivity exceeding 10,000 at low frequencies in the temperature range 150–740 °C. High permittivity of this material was attributed to the formation of internal (grain boundary) barrier layer capacitors. The influence of sintering conditions on microstructure, composition and dielectric properties of Cu 2Ta 4O 12 ceramics was also studied.

Nitrogen-doped ultrananocrystalline carbon: Response to small amplitude AC signals

The response to small amplitude AC signals of nanometer-sized carbon films with nitrogen added in the gas is analyzed in a wide frequency range. Measurements have also been developed at temperatures between 300 and 600 K. Domains of sp 3-coordinated carbon embedded into a connective tissue have been evidenced in SEM micrograph and confirmed by photocurrent yield measurements. Samples with nitrogen added in gas showed a sharp peak at 3.9 eV associated to a defective band close to the conduction band. Small quantities of nitrogen added in the gas appear able to relax the connective tissue, but no drastic change in surface morphology occurs upon low (5%) nitrogen addition. Admittance and impedance formalisms have been used to evidence the involvement of grain boundaries in transport by tunneling and hopping among defects at Fermi level, as well as to evidence a transport mechanism with activation energy of 0.21 eV which takes place mainly in a defective band formed below the conduction band when nitrogen is added.

Ion transport studies in CuI-doped silver borovanadate glassy system

In the present report, ionic transport properties and microstructural investigations of superionic materials in a cost-effective glassy system xCuI–(100 − x)[2Ag 2O–0.7V 2O 5–0.3B 2O 3], where x = 30, 40, 45, 50 and 60, have been described. The temperature dependent electrical conductivity studies were carried out by ac impedance analysis. The microstructure of the materials studied by SEM indicated the presence of dispersed CuO and AgI micro-crystals in the silver oxysalt glass matrix. High room temperature electrical conductivity of 3.58 × 10 −3 S cm −1 and low activation energy of 0.24 eV were obtained for the best conducting composition. The ac impedance data were analyzed using impedance and modulus formalisms. These materials show extremely high t i value of 0.999 and the ionic conductivity is apparently due to Ag + ions only. The use of two glass formers helped to form materials with higher T g, higher thermal stability and better ionic transport properties.

Effect of simultaneous substitution of Li+ and Ti4+ in ceramics of Pb2KNb5O15 on structure, dielectric, modulus, impedance and conductivity properties

AbstractLead potassium lithium titanium niobate, Pb0.8K0.2Li0.2Ti0.25Nb1.8O6 (PKLTN) is prepared through a solid‐state reaction route. The XRD analysis at room temperature indexed as single phase with orthorhombic tungsten bronze (TB) with completely filled (A6C4B10O30‐type) structure. Partial substitution of Ti4+ in Nb5+ increased the B sites ordering, and is associated in charge compensation, creating oxygen vacancies entering in the crystal structure described by Kroger–Vink notation. Simultaneous substitution of Li+ and Ti4+ in Pb2KNb5O15 (PKN) resulted in an increase in the lattice parameters (a = 18.0131 Å, b = 18.1520 Å and c = 3.9376 Å) and a decreased TC to 445 °C. Space‐charge polarization, relaxation phenomenon and conduction mechanism due to charge carriers have been analyzed using dielectric, impedance and modulus characterization. Cole–Cole plots showed non‐Debye (polydispersive) type relaxation. DC conductivity activation energies calculated from Rb, MII peak frequencies and thermal behavior of AC and DC conductivity at 1 kHz in the ferro region are comparable to 0.32 eV, reveals the ionic conduction mechanism in PKLTN. Conduction via a hopping mechanism has been established from Jonscher's power law, σ (ω) = σDC + Aωn. The stretched exponential parameter, β is a measure of the distribution of relaxation times and was computed as a function of temperature (360–595 °C) using an impedance formalism, and has a minimum value of 0.74 at TC. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modulus spectroscopy of lead potassium titanium niobate (Pb0.95K0.1Ti0.25Nb1.8O6) ceramics

The modulus Spectroscopy of Lead Potassium Titanium Niobate (Pb0.95K0.1Ti0.25Nb1.8O6, PKTN) Ceramics was investigated in the frequency range from 45 Hz to 5 MHz and the temperature, from 30 to 600 °C. XRD analysis in PKTN indicated a orthorhombic structure with lattice parameters a = 18.0809 A, b = 18.1909 A and c = 3.6002 A. The dielectric anomaly with a peak was observed at 510 °C. Variation of eI and eII with frequency at different temperatures exhibit high values, which reflects the effect of space charge polarization and/or conduction ion motion. The electrical relaxation in ionically conducting PKTN ceramic analyzed in terms of Impedance and Modulus formalism. The Cole–Cole plots of impedance were drawn at different temperatures. The dielectric modulus, which describes the dielectric relaxation behaviour is fitted to the Kohlrausch exponential function. Near the phase transition temperature, a stretched exponential parameter β indicating the degree of distribution of the relaxation time has a small value. From the AC conductivity measurements the activation energy near phase transition temperature (T C°C) has been found to different from that of the above and below T C. The temperature dependence of electrical modulus has been studied and results are discussed.

Effect of Processing Conditions on Electrical and Magnetic Properties of Pb(Zr, Ti)O3 CoFe2O4 Multilayers Thin Films

The multilayers of ferroelectric (FE) Pb(Zr, Ti)O3 (PZT) and ferromagnetic (FM) CoFe2O4 (CFO) thin films with 3, 5, and 9 layers having configurations PZT/CFO (PC) and CFO/PZT (CP) were fabricated by pulsed laser deposition technique. We have investigated the effect of inter-diffusion at the interface of multilayers (MLs) and reversing the order of FE and FM layers in the multilayers configuration on the electrical/magnetic properties. The TEM of the films showed that the layer structure was not maintained and the inter-diffusion of the CFO into PZT and vice verse were observed at the interface of MLs. Both the PC and CP configurations of multilayer films exhibited pseudo FE hysteresis loop and proper FM hysteresis loops at room temperature. Reversing the multilayer configuration from CP to PC resulted in increasing the pseudo remanent polarization, however this behavior was not observed in magnetic properties. The frequency and temperature dependences of the impedance and modulus spectroscopy of the multilayer PC and CP films were studied in the ranges of 102 to 106 Hz and 200 to 650 K respectively. The electrical response of all multilayer films investigated could be resolved into two contributions. We attributed these to the grain and grain boundary effects in impedance and modulus formalism. We found that the difference between the grain and grain boundary capacitive effect decreased due to increase of the number of layers.