Thermodynamic properties and application of CBH model in the ac conductivity of LiNi1.5P2O7 ceramic

The LiNi_1.5P₂O₇ compound was prepared by the solid-state reaction method at 923 K and characterized through XRD and Raman spectroscopy techniques. The impedance spectroscopy measurements were performed in the frequency and the temperature range (300 Hz–5 MHz) and (633–729 K), respectively. The ac conductivity for grain contribution is interpreted using the universal Jonscher’s power low. The exponent n decreases with increasing temperature which reveals that the conduction inside the studied material is insured by the correlated barrier hopping (CBH) model. The parameters of CBH model were determined showing that the ac conduction is realised by single-polaron hopping mechanism. Thermodynamic parameters such as the free energy for dipole relaxation ΔF, the enthalpy ΔH, and the change in entropy ΔS have been calculated.     

Study of complex impedance spectroscopic properties of the KFeP2O7 compound

The KFeP₂O₇ compound was prepared by the conventional solid-state reaction. The sample was characterized by X-ray powder diffraction. The AC electrical conductivity and the dielectric relaxation properties of this compound have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 200 Hz–5 MHz and 553–699 K, respectively. Both impedance and modulus analysis exhibit the grain and grain boundary contribution to the electrical response of the sample. The temperature dependence of the bulk and grain boundary conductivity were found to obey the Arrhenius law with activation energies Eg?=?0.94 (3)?eV and Egb?=?0.89 (1)?eV. The grain-and-grain boundary conductivities at 573 K are 1.07?×?10^?4 and 1.16?×?10^?5 (Ω^?1 cm^?1). The scaling behavior of the imaginary part of the complex impedance suggests that the relaxation describes the same mechanism at various temperatures. The near value of the activation energies obtained from the equivalent circuit, conductivity data, and analysis of M″ confirms that the transport is through ion hopping mechanism.     

Conductivity behavior of the new pyrophosphate NaNi<Subscript>1.5</Subscript>P<Subscript>2</Subscript>O<Subscript>7</Subscript>

NaNi_1.5P₂O₇ compound was obtained by the classic ceramic method at high temperature and was characterized by XRD. It was found to crystallize in the triclinic symmetry with the P-1 space group. The electrical conductivity and modulus characteristics of the system have been investigated in the temperature and the frequency range 586–723 K and 200 Hz–1 MHz, respectively, by means of impedance spectroscopy. The ac conductivity for grain contribution was interpreted using the universal Jonscher’s power law. The exponent s decreased with increasing temperature revealing that the conduction inside the studied material is insured by the correlated barrier hopping (CBH) model. The conduction mechanism was explained with the help of Elliot’s theory, and the Elliot’s parameters were determined. Thermodynamic parameters such as the free energy for dipole relaxation ΔG, the enthalpy ΔH, and the change in entropy ΔS have been calculated.     

Electrical properties and conduction mechanism in the sodium nickel diphosphate

The Na_3.6Ni_2.2(P₂O₇)₂ compound was obtained by the conventional solid-state reaction. The sample was characterized by X-ray powder diffraction and vibrational and impedance spectroscopy. The AC electrical conductivity and the dielectric relaxation properties of this compound have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 209 kHz–1 MHz and 564–729 K, respectively. Dielectric data were analyzed using complex electrical modulus M* at various temperatures. The peak positions ω _m of M″ spectra shift toward higher frequencies with increase in temperature. The AC conductivity data fulfill the power law. Application of the correlated barrier hopping model revealed that the ionic conduction takes place by single-polaron and bipolaron hopping processes.     

NMR study and electrical properties investigation of Zn<Subscript>2</Subscript>P<Subscript>2</Subscript>O<Subscript>7</Subscript>

The α-Zn₂P₂O₇ compound was obtained by conventional solid-state reaction. The sample was characterized by X-ray powder diffraction, solid state ³¹P NMR MAS, and electrical impedance spectroscopy. The solid state ³¹P MAS NMR, performed at 121.49 MHz, shows three isotropic resonances at −21.1, −18.8, and −15.8 ppm, confirming the non-equivalency of the three PO₄ groups in the α-Zn₂P₂O₇ form. They are characterized by different chemical shift tensor parameters with the local geometrical features of the tetrahedra. Electrical impedance measurements of β-Zn₂P₂O₇, form stable for temperature greater than 403 K, were performed as a function of both temperature and frequency. The electrical conduction and dielectric relaxation have been studied. The AC conductivity obeys the universal power law. The approximation type correlated barrier hopping model explains the universal behavior of the n exponent. The impedance plane plot shows semicircle arcs at different temperatures, and an electrical equivalent circuit has been proposed to explain the impedance results. The circuits consist of the parallel combination of bulk resistance R _p and constant phase elements CPE. The simulated spectra show a good correlation with the experimental data.     

Electrical conductivity and dielectric relaxation behavior of AgFeP2O7 compound

In the present study, AgFeP₂O₇ was prepared by a solid-state reaction method. Rietveld refinement of the X-ray diffraction pattern suggests the formation of the single phase desired compound with monoclinic structure at room temperature. Not only were the impedance spectroscopy measurements of our compound carried out from 209 Hz to 5 MHz over the temperature range of 553 K–698 K but its AC conductivity as well as the dielectric relaxation were evaluated. Impedance measurements show AgFeP₂O₇ an ionic conductor being the conductivity 1.04?×?10^–?5(Ω^–?1cm^–?1) at 573 K. The conductivity and modulus formalisms provide nearly the same activation energies for electrical relaxation of mobile ions revealing that transport properties in this material appear to be due to an ionic hopping mechanism dominated by the motion of the Ag⁺ ions along tunnels presented in the structure of the investigated material.     

AC conductivity and mechanism of conduction study of lithium barium pyrophosphate Li<Subscript>2</Subscript>BaP<Subscript>2</Subscript>O<Subscript>7</Subscript> using impedance spectroscopy

The Li₂BaP₂O₇ compound has been obtained by the conventional solid-state reaction and characterized by X-ray powder diffraction. The title material crystallizes in the monoclinic system with C2/c space group. Electrical properties of the compound have been studied using complex impedance spectroscopy in the frequency range 200 Hz–5 MHz and temperature range 589–724 K. Temperature dependence of the DC conductivity and modulus was found to obey the Arrhenius law. The obtained values of activation energy are different which confirms that transport in the titled compound is not due to a simple hopping mechanism. AC conductivity measured follows the power-law dependence σ _AC?～?ω ^s typical for charge transport. Therefore, the experimental results are analyzed with various theoretical models. Temperature dependence of the power law exponent s strongly suggests that tunneling of large polarons is the dominant transport process.     

Electrical properties and conductivity mechanism of LiCuFe2(VO4)3

This paper reports conduction mechanism in LiCuFe₂(VO₄)₃ over a wide range of temperatures (300 to 712 K) and frequencies (209 Hz to 5 MHz). The DC conductivity of the material is thermally activated with activation energy about 0.66 eV. In LiCuFe₂(VO₄)₃, the electrical conductivity is probably due to the hopping of alkali lithium ion along the channel [001]. Temperature dependence of AC conductivity is studied at different frequencies. Frequency exponent s is found to decrease with increase in temperature. The results have been explained on the basis of correlated barrier hopping (CBH) model. Numerical calculations agree well with experimental results. The results show that the frequency and temperature-dependent behavior of AC conductivity of the studied materials are predominantly due to single polaron hopping.     

Synthesis,refinement of the structure,and AC conductivity behavior of sodium lithium orthonavadates

The Na _x Li_1-x CdVO₄ (x = 0.5, 1) orthovanadates were prepared using a solid-state reaction method. The x-ray diffraction patterns (XRDP) of both materials reveal the formation of the Na₂CrO₄ structure. Vibrational study confirms the existence of [VO₄]^3? group. Electrical measurements of our compounds have been investigated using complex impedance spectroscopy (CIS) in the frequency and temperature range 209 Hz–1 MHz and 589–703 K, respectively. Nyquist plots reveal the presence of tow contributions, an equivalent circuit was proposed. DC conductivity shows electrical conduction in the material as a thermally activated process. The AC conductivity is explained using the non-overlapping small polaron tunneling (NSPT) conduction mechanism. A relationship between crystal structure and ionic conductivity was established and discussed.     

AC conductivity and dielectric behavior of low-temperature phase of α-AgCuPO<Subscript>4</Subscript>

The copper monophosphate compound, α-AgCuPO₄, was prepared by the conventional solid-state reaction. The purity of the compound was checked by X-ray diffraction technique (XRD). Detailed dielectric and electrical properties of the compound were analyzed as a function of frequency (209 Hz–1 MHz) and temperature (343–514 K). The AC conductivity has been fitted and studied using Jonscher’s equation, whose exponent n varied with the temperature, showing that the overlapping large polaron tunneling model (OLPT) is the appropriate model to describe the electrical conduction mechanism.     

Ac conductivity study of lithium and potassium diphosphate LiK3P2O7 using impedance spectroscopy

In this work, a LiK₃P₂O₇ ceramic material was prepared by the solid-state reaction method and identified by X-ray diffractometry. The dielectric properties, impedance characteristics, and modulus were studied over a range of frequency (200 Hz to 5 MHz) and temperature (615–708 K). The frequency and temperature dependence of dielectric permittivity, dielectric loss, and electric modulus is studied. The frequency analysis of modulus properties showed a distribution of relaxation times. Conductivity plots against frequency at a higher frequency suggested the response obeying the universal power law. The temperature behavior of the frequency exponents shows that the correlated barrier hopping CBH model is well adapted to this material. The activation energy associated with the impedance relaxation and the electric modulus spectra is close to the activation energy for dc conductivity indicating the similar nature of relaxation and conductivity. Thermodynamic parameters such as free energy of activation, enthalpy, and entropy have been calculated.     

AC conduction mechanism of the zinc potassium diphosphate

Zinc potassium pyrophosphate K₂ZnP₂O₇ was synthesized using the conventional solid-state reaction. X-ray powder diffraction analysis proves the formation of a pure phase which crystallizes in the tetragonal system. The electrical conductivity and modulus characteristics of the system have been investigated in the temperature and the frequency range 614–718 K and 200 Hz–1 MHz, respectively, by means of impedance spectroscopy. The alternating current (AC) conductivity for grain contribution follows the universal Jonscher’s power law. The frequency exponent s is temperature independent and equal to 0.8. The QMT model was proposed to be the most suitable model to characterize the electrical conduction mechanism in the titled sample. Dielectric data were analyzed using complex electrical modulus M* at various temperatures. The bulk relaxation time was found from the peaks position of the above spectra and the thermodynamic parameters were also found using the Eyring theory.     

AC and DC conductivity study of LiH<Subscript>2</Subscript>PO<Subscript>4</Subscript> compound using impedance spectroscopy

The lithium dihydrogen phosphate LiH₂PO₄ has been investigated by X-ray powder diffraction, scanning electron microscopy (SEM), and electrical impedance spectroscopy. The Rietveld refinements based on the XRD patterns show that the compound is crystallized in the orthorhombic system with Pna2₁ space group, and the refined unit cell parameters are a = 6.2428 Å, b = 7.6445 Å, and c = 6.873 Å. The electrical properties were studied using complex impedance spectroscopy as a function of frequency (10⁴–10⁷ Hz) at various temperatures (300–400 K). The Nyquist plots are well fitted to an equivalent circuit consisting of a series of combination of grains and inhomogeneous electrode surface effect. The frequency dependence of the conductivity is interpreted in terms of Jonscher’s law. Moreover, the near value of the activation energies obtained from the equivalent circuit and analysis of M″ confirms that the transport is through ion hopping mechanism dominated by the motion of the proton in the structure of the investigated material.     

Electrical characterization of porous La-doped BaSnO<Subscript>3</Subscript> using impedance spectroscopy

A few compositions in the system Ba_1???x La _x SnO₃ (x?=?0.00, 0.01, 0.05, and 0.10) have been synthesized via the solid state ceramic route. The synthesized powders have been characterized using X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray analysis, Raman spectroscopy, Fourier transformation infrared, thermogravimetrical analysis, and differential thermal analysis techniques. The powder X-ray diffraction pattern of the samples confirms the formation of a single-phase solid solution only up to 0.50?≤?x. It was found that all the samples have a cubic crystal structure. The electrical properties of La-modified BaSnO₃ were studied using ac impedance spectroscopy technique over a wide range of temperatures (50–650 °C) in the frequency range of 10 Hz–13 MHz. The complex impedance plots above 300 °C show that total impedance is due to the contributions of grain and grain boundaries. The resistance of these contributions has been determined. Variation of these resistances with temperature shows the presence of two different regions with different slopes. The nature of the variation of conductivity of the grain and grain boundaries is different in different regions. Based on the value of activation energy, it is proposed that conduction via hopping of doubly ionized oxygen vacancies (V_O ^??) is taking place in the temperature region of 300–450 °C, whereas in the temperature region of 450–650 °C, it is due to proton, i.e., OH^? ions, hopping.     

Crystal structure,NMR spectroscopy,electrical properties of catena-poly[(bis-glycinium-k 2 O:O)-di-μ-thiocyanate- k 2 N:S; k 2 S:N -cadmium (II)]

The crystal structure, the ¹¹¹Cd and ¹³C NMR spectroscopy, and the complex impedance have been carried out on a new polymeric hybrid compound: [Cd(NH₃CH₂COO)₂(SCN)₂] _n . Crystal structure shows that in the title compound the cadmium atoms have a 2N2S2O-hexa-coordination sphere, exhibiting pseudo-octahedral geometry. The cadmium atoms are bridged by two thiocyanate ions generating 1D polymeric chains. ¹¹¹Cd and ¹³C MAS NMR spectroscopy show multiplets that result from ¹¹¹Cd, ¹⁴N and ¹³C, ¹⁴N spin–spin coupling, respectively. The AC impedance measurements were performed as a function of both frequency and temperature. The AC and DC electrical conduction have been studied. The activation energy associated with the bulk resistance determined from equivalent circuit was found close to that of the activation energy obtained from DC conductivity. The conduction mechanisms are attributed to the correlated barrier hopping model.     

Electrical conductivity and dielectric relaxation studies of a polymeric hybrid compound: ([C2H10N2]CdCl2(SCN)2)n

Electrical conductivity and dielectric measurements of ([C₂H₁₀N₂]CdCl₂(SCN)₂)_n were carried out from 200 Hz–5 MHz over a temperature range of 307–352 K. The frequency dependence of electrical data have been analyzed in two frameworks: the electrical modulus formalism with the Kohlrausch-Williams-Watts (KWW) stretched exponential function and the electrical conductivity by using the Jonscher’s power law σ′_Tot(ω,T) = σ_DC(T) + A(T)ω^s(T) in the frequency domain. The conduction mechanism is attributed to the nonoverlapping small polaron tunneling (NSPT) model. Furthermore, the dielectric data have also been analyzed in modulus and polarizability formalisms. The close values of activation energies obtained from the conductivity, the relaxation process, the electric modulus, and the complex polarizability data confirm that the transport is through ion-hopping mechanism.     

Li<Superscript>+</Superscript> ion conductivity and transport properties of LiYP<Subscript>2</Subscript>O<Subscript>7</Subscript> compound

A lithium yttrium diphosphate LiYP₂O₇ was prepared by a solid-state reaction method. Rietveld refinement of the X-ray diffraction pattern suggests the formation of the single phase desired compound with monoclinic structure at room temperature. The infrared and Raman spectrum of this compound was interpreted on the basis of P₂O₇ ^4? vibrations. The AC conductivity was measured in the frequency range from 100 to 10⁶ Hz and temperatures between 473 and 673 K using impedance spectroscopy technique. The obtained results were analyzed by fitting the experimental data to the equivalent circuit model. The Cole–Cole diagram determined complex impedance for different temperatures. The angular frequency dependence of the AC conductivity is found to obey Jonscher’s relation. The temperature dependence of σ _AC could be described in terms of Arrhenius relation with two activation energies, 0.87 eV in region I and 1.36 eV in region II. The study of temperature variation of the exponent(s) reveals two conduction models: the AC conduction dependence upon temperature is governed by the correlated barrier hopping (CBH) model in region I (T < 540 K) and non-overlapping small polaron tunneling (NSPT) model in region II (T > 540 K). The near value of activation energies obtained from the equivalent circuit and DC conductivity confirms that the transport is through ion hopping mechanism dominated by the motion of the Li⁺ ion in the structure of the investigated material.     

Crystal structure,NMR study,dielectric relaxation and AC conductivity of a new compound [Cd3(SCN)2Br6(C2H9N2)2]n

The crystal structure, the ¹³C NMR spectroscopy and the complex impedance have been carried out on [Cd₃(SCN)₂Br₆(C₂H₉N₂)₂]_n. Crystal structure shows a 2D polymeric network built up of two crystallographically independent cadmium atoms with two different octahedral coordinations. This compound exhibits a phase transition at (T=355±2 K) which has been characterized by differential scanning calorimetry (DSC), X-rays powder diffraction, AC conductivity and dielectric measurements. Examination of ¹³C CP/MAS line shapes shows indirect spin–spin coupling (¹⁴N and ¹³C) with a dipolar coupling constant of 1339 Hz. The AC conductivity of this compound has been carried out in the temperature range 325–376 K and the frequency range from 10⁻² Hz to 10 MHz. The impedance data were well fitted to two equivalent electrical circuits. The results of the modulus study reveal the presence of two distinct relaxation processes. One, at low frequency side, is thermally activated due to the ionic conduction of the crystal and the other, at higher frequency side, gradually disappears when temperature reaches 355 K which is attributed to the localized dipoles in the crystal. Moreover, the temperature dependence of DC-conductivity in both phases follows the Arrhenius law and the frequency dependence of σ(ω,T) follows Jonscher's universal law. The near values of activation energies obtained from the conductivity data and impedance confirm that the transport is through the ion hopping mechanism.     

Dielectric study on Zn1−x Mg x O ceramic materials prepared by the solid-state route

The present work investigates the structural and dielectric properties of Zn_1?x Mg _x O composites prepared by the standard sintering method at 1200 °C during 24 h and doped with different weight percentages of MgO (x = 0–40 %). For this purpose, the scanning electron microscopy (SEM) was used to study the effect of the magnesium’s proportion on the morphology and crystallinity of the obtained samples. The SEM observations have shown rougher surfaces of the samples covered by grains having prismatic shapes and different sizes. The dielectric properties of the ceramics were investigated by spectroscopic impedance at different temperatures and frequencies, thus showing a frequency-dependent dispersion of the permittivity constants and dielectric losses. From these measurements, the relaxation processes were identified and their activation energies extracted. Dielectric responses were correlated with the microstructure and chemical composition of the ZnMgO composites. The mechanisms of ac conductivity are controlled by the polaron hopping and the electron tunneling models. Concerning the tunneling model, two types corresponding to the overlapping large polaron tunneling model for the composites Zn_0.9Mg_0.1O and Zn_0.8Mg_0.2O and the small polaron tunneling model for the composites Zn_0.64Mg_0.36O (in the frequency range 1.7 × 10⁴ Hz–1 MHz) and Zn_0.6Mg_0.4O were observed. Besides, one type of hopping model corresponding to the correlated barrier hopping for the composites ZnO and Zn_0.64Mg_0.36O (in the frequency range 6 × 10²–1.7 × 10⁴ Hz) was noted.     

Formation of fast ion-conducting materials in BiI3–Ag2CrO4 binary system

Fast ionic solid specimens of a new binary system namely (BiI₃) _x –(Ag₂CrO₄)_100?x , where x?=?10, 20, 30, 40, 50, 60, 70, 80, and 90 mol%, were synthesized by melt quenching method. Detailed structural, thermal, and electrical transport properties evaluated by means of X-ray diffraction analysis, Fourier transform infrared spectroscopic investigations, and differential scanning calorimetry in conjunction with complex impedance analysis carried out over the frequency range 1 MHz–20 Hz and in the temperature region 298–430 K indicated the composite nature of such superionic solids consisting of glassy and crystalline phases and possessing electrical conductivities of the order 10^?6–10^?3 Scm^?1 at 298 K. The best conducting composition of the present binary system has been identified as the specimen containing 30 mol% BiI₃ and exhibiting a room-temperature electrical conductivity of 7.1?×?10^?3 Scm^?1 with an activation energy of 0.12 eV for silver ionic transport as confirmed by Wagner's polarization and E.M.F. techniques.