Vogel-Fulcher Law Research Articles

Dielectric response and ac-conductivity studies of Gd<sub>2</sub>O<sub>3</sub>- contained K<sub>0.5</sub>Na<sub>0.5</sub>NbO<sub>3</sub> piezoelectric ceramics

We report the role of Gd2O3 substitution on the dielectric properties of alkali niobate K0.5Na0.5NbO3 (KNN) ceramics. This system exhibits relaxor behaviour for 0.5 wt% of Gd2O3 in KNN matrix and shows enhanced dielectric permittivity (er = 4147 at T = 628 K) and low loss (Tanδ ~ 0.008) at frequency f = 1 MHz. The position of crystallographic phase transitions of Orthorhombic to Tetragonal (T1) and Tetragonal to Cubic (T2) shifts significantly from 480 K to 413 K and 668 K to 582 K, respectively. The temperature and the frequency dependence of the position of maximum dielectric permittivity Tm obeys the Vogel–Fulcher law, with the attempt frequency f0 = 5.32×1011 Hz, freezing temperature Tf = 598 K and activation energy EA= 0.038 eV for KNN + 0.5 wt% Gd2O3. The temperature dependence of AC-conductivity σac (T) analysis in the range 300 K < T < 600 K reveals the existence of variable range hopping of charge carriers with average hopping length RH in the range 7.93-29.24 nm and 5.55-26.41 nm for ξ = 0 and ξ = 0.5, respectively. The diffuseness exponent ‘γ’ (~1.74) estimated from the high temperature slopes of the diffused dielectric permittivity data reveals the weakly coupled relaxor behavior.

Magnetic properties of NiO (nickel oxide) nanoparticles: Blocking temperature and Neel temperature

Crystalline nickel oxide (NiO) nanoparticles dispersed in an amorphous silica matrix have been prepared by a sol–gel combustion synthesis method. The sample was characterized using X-ray powder diffraction, energy-dispersive X-ray spectroscopy, scanning electron microscopy, transmission electron microscopy and superconducting quantum interference device magnetometry. The nanoparticles were spherical with an average size of about 5 nm and narrow particle size distribution. The magnetization measurements revealed two maxima in the zero-field cooled magnetization curve at 5 K and 56 K. An analysis of DC and AC magnetic susceptibility measurements revealed that the higher temperature maximum corresponded to the onset of antiferromagnetic ordering within the particles. The Néel temperature of TN = 56 K is much lower than in bulk NiO. The 5 K maximum corresponded to the particle blocking temperature TB. The frequency dependence of TB was successfully fitted using the Vogel–Fulcher law, indicating the presence of weak inter-particle interactions (C1 = 0.08 and C2 = 0.76). A Curie–Weiss law fit to the magnetic susceptibility above TN revealed antiferromagnetic exchange interactions with a Curie–Weiss temperature of θ = 24 K and an effective magnetic moment of μeff = 2.87 μB per NiO unit. We conclude that these magnetic properties can be attributed to the smallness of the NiO nanoparticles and to crystal lattice defects.

Relaxation dynamics and fragility during liquid–glass transitions of poly(propylene glycol)s

The acoustic and thermal properties of the liquid–glass transitions of propylene glycol and its oligomers, poly (propylene glycol)s, were studied by temperature modulated DSC and Brillouin scattering. The fragility indices were determined from Angell plots using the observed modulation frequency dependence of the complex heat capacity. The variation in the glass transition temperatures is discussed on the basis of the free volume theory. The relaxation time of the structural relaxation obeys the Vogel–Fulcher law, and its high frequency end is in good agreement with the result of the dielectric measurement in the literature. The correlation between the observed thermal expansion coefficients and the glass transition temperature is discussed based on the free volume theory. The sound velocity and attenuation were accurately determined as a function of the temperature by Brillouin scattering by combination with the refractive index measurement. The relaxation dynamics were discussed by considering the relaxation from segmental motions. All of these physical properties were discussed based on the third-order anharmonicity and the Grüneisen parameter.

Dielectric Spectroscopy of Polymer Based PDMS Nanocomposites with ZnO Nanoparticles

Dielectric spectroscopy results of organic polymer Polydimethylsiloxane (PDMS) with different ZnO nanoparticle concentrations are presented in wide temperature range. Dielectric loss was measured as a function of electromagnetic field frequency at various temperatures. Our measurements have shown that the value and position of dielectric loss peak on a temperature scale depends on the concentration of ZnO nanoparticles within PDMS. The temperature behaviour of dielectric losses was compared with temperature dependencies of ultrasonic attenuation in the samples. It is shown that the maximum of dielectric losses in PDMS nanocomposite is described according to the Vogel-Fulcher law and the glass transition increases with ZnO concentration.

Effects of Electron Irradiation on the Dielectric Behavior of Langmuir-Blodgett Terpolymer Films

The dielectric response of the Langmuir-Blodgett poly(vinylidene fluoride-trifluoroethylene-chlorofloroethylene) terpolymer films with various electron irradiation doses was investigated. The dielectric data were analyzed with Vogel-Fulcher law, confirming the relaxor behavior of irradiated samples. Besides, after fitting the data to an empirical law it was proved that the diffuseness of phase transition increased with increasing irradiation dose. Both the Curie temperature and the Curie constant, which were derived from fitting the data to the Curie-Weiss law, were used to calculate a local order parameter within a spin-glass model. It was found that sharper temperature dependence of the local order parameter corresponds to less diffused phase transition.

On the nature of magnetic state in the spinel Co2SnO4

In the spinel Co2SnO4, coexistence of ferrimagnetic ordering below TN ≃ 41 K followed by a spin glass state below TSG ≃ 39 K was proposed recently based on the temperature dependence of magnetization M(T) data. Here new measurements of the temperature dependence of the specific heat CP(T), ac-susceptibilities χ′(T) and χ″(T) measured at frequencies between 0.51 and 1.2 kHz, and the hysteresis loop parameters (coercivity HC(T) and remanence MR(T)) in two differently prepared samples of Co2SnO4 are reported. The presence of the Co2+ and Sn4+ states is confirmed by x-ray photoelectron spectroscopy (XPS) yielding the structure: Co2SnO4 = [Co2+][Co2+Sn4+]O4. The data of CP versus T shows only an inflection near 39 K characteristic of spin–glass ordering. The analysis of the frequency dependence of ac-magnetic susceptibility data near 39 K using the Vogel–Fulcher law and the power-law of the critical slowing-down suggests the presence of spin clusters in the system which is close to a spin–glass state. With a decrease in temperature below 39 K, the temperature dependence of the coercivity HC and remanence MR for the zero-field cooled samples show both HC and MR reaching their peak magnitudes near 25 K, then decreasing with decreasing T and becoming negligible below 15 K. The plot of CP/T versus T also yields a weak inflection near 15 K. This temperature dependence of HC and remanence MR is likely associated with the different magnitudes of the magnetic moments of Co2+ ions on the ‘A’ and ‘B’ sites and their different temperature dependence.

Synthesis, structural characterization and magnetic properties of Fe/Pt core-shell nanoparticles

Structural and magnetic properties of Fe/Pt core-shell nanostructure prepared by a sequential reduction process are reported. Transmission electron microscopy shows nearly spherical particles fitting a lognormal size distribution with Do = 3.0 nm and distribution width λD = 0.31. In x-ray diffraction, Bragg lines only from the Pt shell are clearly identified with line-widths yielding crystallite size = 3.1 nm. Measurements of magnetization M vs. T (2 K–350 K) in magnetic fields up to 90 kOe show a blocking temperature TB = 13 K below which hysteresis loops are observed with coercivity HC increasing with decreasing T reaching HC = 750 Oe at 2 K. Temperature dependence of the ac susceptibilities at frequencies fm = 10 Hz–5 kHz is measured to determine the change in TB with fm using the Vogel-Fulcher law. This analysis shows the presence of significant interparticle interaction, the Neel-Brown relaxation frequency fo = 5.3 × 1010 Hz and anisotropy constant Ka = 3.6 × 106 ergs/cm3. A fit of the M vs. H data up to H = 90 kOe for T &amp;gt; TB to the modified Langevin function taking particle size distribution into account yields magnetic moment per particle consistent with the proposed core-shell structure; Fe core of 2.2 nm diameter and Pt shell of 0.4 nm thickness.

Dielectric Characteristics in BiFeO3-Modified SrTiO3 Incipient Ferroelectric Ceramics

We investigate the dielectric and ferroelectric properties of Sr1−xBixTi1−xFexO3 solid solutions (x = 0, 0.05, 0.1, 0.15 and 0.2) together with their structures. Through the analysis of Rietveld refinement of powder x-ray diffraction, a cubic structure in space group Pm3̄m is determined for all the compositions. An obvious dielectric relaxation peak differing from SrTiO3 is observed in the present ceramics. The peak temperature Tm increases with increasing x, and it approaches room temperature at x = 0.2. The Vogel—Fulcher law and Curie—Weiss law fittings further confirm the relaxor ferroelectricity in the present ceramics.

Spin Dynamics in Hybrid Iron Oxide–Gold Nanostructures

We report a broadband H-1 NMR study of the spin dynamics of coated maghemite and goldmaghemite hybrid nanostructures with two different geometries, namely dimers and coreshells. All the samples have a superparamagnetic behavior, displaying a blocking temperature (T-B similar to 80 K (maghemite), similar to 105 K (dimer), similar to 150 K (coreshell)), and the magnetization reversal time follows the VogelFulcher law. We observed three different anomalies in H-1 NMR T(1)1 versus T that decrease in amplitude when increasing the applied magnetic field. We suggest that the anomalies are related to three distinct system dynamics: molecular rotations of the organic groups (240 < T < 270 K), superparamagnetic spin blockage (100 < T < 150 K), and surfacecore spin dynamics (T < 25 K). By fitting the T(1)1 data with a heuristic model, we achieved a good agreement with magnetic relaxation data and literature values for methyl group rotation frequencies.

Dynamics of nanoscale polarization fluctuations in a uniaxial relaxor.

We have studied neutron diffuse scattering in a Sr(0.61)Ba(0.39)Nb(2)O(6) single crystal by neutron backscattering at sub-μeV energy resolution. We can identify two response components with transverse polarization: an elastic (resolution limited) central peak, which monotonically increases with decreasing temperature, and a quasielastic central peak, having a maximum intensity around the ferroelectric phase transition close to 350 K. In contrast to previous neutron experiments on this and other relaxor materials, we were able to observe a temperature dependence of the characteristic frequency of these fluctuations, obeying the same Vogel-Fulcher law as the dynamic part of the dielectric permittivity of this material. In this way our findings provide a first direct link between the Vogel-Fulcher-type frequency dependence of dielectric permittivity and dynamic nanoscale lattice modulations with a transverse correlation length of about 5-10 unit cells.

The dielectric behavior of Zn1−xNixO/NiO two-phase composites

The effect of nickel content on the dielectric permittivity ‘εr’ and the ac-electrical conductivity of Zn1−xNixO/NiO (0 ≤ x ≤ 0.55) two-phase composites were investigated. The antiferro to the paramagnetic Néel temperature TN (~ 523 K) of the NiO associated with the structural phase transition from the rhombohedral to the cubic phase has been exploited to realize a dielectric anomaly across 523–541 K in the Zn1−xNixO/NiO composite system. Also, a giant dielectric peak across 410 °C in pure NiO was observed together with an anomaly across TN. The formation of tiny polar clusters due to the compositional heterogeneity for the samples with x ≥ 0.16 drove the system to exhibit a weakly coupled relaxor-like behavior with a locally varying maximum temperature of T* (~ 530 K at 106 Hz), obeying the Vogel–Fulcher law and the Uchino–Nomura criteria. The values of the diffuseness-exponent ‘γ’ (1.91) and the shape-parameter ‘δ’ (88 °C) were determined by using the empirical scaling relation (εA/εr = 1 + 0.5 (T − TA)2/ δ2), which is often used to describe relaxor-like behavior. Our results provide strong evidence for the variable-range-hopping of charge carriers between the localized states. The effects of non-ohmic sample-electrode contact impedance and negative-capacitance on the global dielectric behavior of a Zn1−xNixO/NiO composite system are discussed.

Molecular and impedance spectroscopy of Na 2 Mo 2 O 7 ceramics

The fine (i.e. 38 nm) powder of polycrystalline Na2Mo2O7 was prepared by the high-temperature solid-state reaction technique. The formation of the compound in orthorhombic system is confirmed by preliminary structural analysis using X-ray diffraction (XRD) data. Spectroscopic studies of the compound have been carried out by vibration spectroscopy (Raman/FTIR) to understand its molecular structure at microscopic level. The complex impedance spectroscopy (CIS) technique has been used to study the electrical properties of the material as a function of frequency (102–106 Hz) at different temperatures (23–450∘C), and also to investigate the fundamental mechanism involved in the material. Impedance analysis also indicates that below 300∘C, the electrical conduction in the material is due to grain interior only. At and above 325∘C, the contribution of grain boundary is clearly evident. The electrical processes in the material are found to be temperature-dependent and are due to the relaxation phenomena in it. A frequency-dependent maximum of the imaginary electrical impedance is found to obey the Vogel–Fulcher law.

Relaxor Behavior and Large Room‐Temperature Polarization of Ferroelectric Sr4CaBiTi3Nb7O30 Ceramics

A new relaxor ferroelectric ceramics, Sr4CaBiTi3Nb7O30, were prepared. The microstructure, morphology, dielectric, and ferroelectric properties were studied. The ceramics were found that growing in some directions preferentially. Two dielectric relaxations were observed below the Burns temperature TB = 460 K and relaxation‐I can be described by the Vogel–Fulcher law. The Curie–Weiss constant (C) of 1.33 × 105 K confirms the displacive‐type ferroelectric phase transition. The ceramics exhibit the first‐order diffuse ferroelectric phase transition feature. The diffusion exponent varies from 1.99 to 1.92 with different applied frequencies. Room‐temperature (RT) polarization was evaluated, and Pr = 2.6 μC/cm2, Ec = 15.2 kV/cm values were obtained. The high breakdown voltage (≥80 kV/cm) and low leakage current confirmed the high quality of Sr4CaBiTi3Nb7O30 ceramics. All of these features suggest that Sr4CaBiTi3Nb7O30 may be used to substitute lead‐based relaxor ferroelectric materials for environmental friendly. Raman spectra and polarization measured at different temperatures attribute the high‐ and low‐temperature dielectric relaxation to flipping and breathing of polar nanoregions, respectively.

Spin-glass behavior in a giant unit cell compound Tb117Fe52Ge113.8(1)

In this paper we demonstrate evidence of a cluster spin glass in Tb117Fe52Ge113.8(1) (a compound with a giant cubic unit cell) via ac and dc magnetic susceptibility, magnetization, magnetic relaxation and heat capacity measurements. The results clearly show that Tb117Fe52Ge113.8(1) undergoes a spin glass phase transition at the freezing temperature, ~38 K. The good fit of the frequency dependence of the freezing temperature to the critical slowing down model and Vogel-Fulcher law strongly suggest the formation of cluster glass in the Tb117Fe52Ge113.8(1) system. The heat capacity data exhibit no evidence for long-range magnetic order, and yield a large value of Sommerfeld coefficient. The spin glass behavior of Tb117Fe52Ge113.8(1) may be understood by assuming the presence of competing interactions among multiple non-equivalent Tb sites present in the highly complex unit cell.

Ac susceptibility of an assembly of nanomagnets: Combined effects of surface anisotropy and dipolar interactions

We compute the AC susceptibility of a weakly dipolar-interacting monodisperse assembly of magnetic nanoclusters with oriented anisotropy. For this purpose we first compute the relaxation rate in a longitudinal magnetic field of a single nanomagnet taking account of both dipolar interactions in the case of dilute assemblies and surface anisotropy. We then study the behavior of the real and imaginary components of the AC susceptibility as functions of temperature, frequency, surface anisotropy and inter-particle interactions. We find that the surface anisotropy induces an upward shift of the temperature at the maximum of the AC susceptibility components and that its effects may be tuned so as to screen out the effects of interactions. The phenomenological Vogel-Fulcher law for the effect of dipolar interaction on the relaxation rate is revisited within our formalism and a semi-analytical expression is given for the effective temperature is given in terms of inter alia the applied field, surface anisotropy and dipolar interaction.

Dielectric properties of PMT-PT crystals

Results of broadband dielectric investigations of 0.94PbMg1/3Ta2/3O3–0.06PbTiO3 (0.94PMT-0.06PT or PMT-PT) crystals in wide temperature range from 100 K to 950 K are presented. Below 300 K the dielectric properties of crystals are governed by polar nanoregions dynamics. However, at higher temperatures (above 600 K) the electrical conductivity effects also become important. The electrical conductivity occurs presumably due the hopping of oxygen vacancies and demonstrates change in the activation energy close to 750 K. The change in the activation energy can be explained by increase of concentration of single ionized vacancies. No anomaly in the temperature dependence of the static dielectric permittivity was observed in wide temperature range from 213 K to 950 K and the dependence was successfully described by spherical random bonds random fields theory. Moreover, two different contributions were successfully separated in the distributions of relaxation times in PMT-PT crystals. These contributions were attributed to different polar nanoregions dynamics. Moreover, the different freezing temperatures values were obtained for most probable and longest relaxation times, which was explained with an idea of continuous distribution of relaxation times broadening on cooling in relaxors. The critical remarks about the Vogel-Fulcher law application for relaxors are addressed in the paper.

Evidence for spin glass state of NdCo1−xNixO3 (x = 0.3−0.5)

Low-temperature magnetic properties of single phase NdCo1−xNixO3(x = 0.3−0.5) have been studied using ac and dc magnetic susceptibility measurements. Nickel substituted samples have been found to exhibit a different magnetic state at low temperature as compared to pristine NdCoO3. The temperature dependent dc magnetization M (T) revealed the presence of a sharp cusp occurring at characteristic temperatures TP, for x = 0.3, 0.4, 0.5. Below TP, clear effect of magnetic field can be seen in M (T) curves and TP decreases with increasing magnetic field as well as Ni substitution content. The isothermal magnetization measurements at low temperatures shows small unsaturated hysteresis loop at lowest temperature (10 K). The ac susceptibility results show a clear frequency dependent feature. These results are analyzed to distinguish superparamagnetic and spin glass behavior by using Néel-Arrhennius, Vogel-Fulcher law, and power law fitting. This analysis ruled out the superparamagnet like state and suggests the presence of significant inter-cluster interactions, giving rise to spin-glass like cooperative freezing.

Dielectric and AC-conductivity studies of Dy2O3 doped (K0.5Na0.5)NbO3 ceramics

(K0.5Na0.5)NbO3 + x wt.% Dy2O3 (x = 0–1.5) ferroelectric ceramics were prepared by conventional solid state reaction method. XRD patterns revealed that orthorhombic symmetry has transformed into psuedocubic symmetry with increasing the substitution of Dy3+ in the Na+ site. Temperature and frequency dependences of relative dielectric permittivity maximum conforms the transformation from normal ferroelectric to relaxor ferroelectric behaviour. Frequency dependence of the relative dielectric permittivity maximum temperature observed for the samples with x ≥ 1.0 and satisfied the Vogel–Fulcher law. The diffuseness exponent γ (1.27–1.95) estimated from the high temperature slopes of the diffused dielectric permittivity data reveals that the degree of relaxor behavior increases with increasing the amount of Dy2O3. The temperature dependence of AC-conductivity σAC (T) analysis in the range 310 K &amp;lt; T &amp;lt; 470 K reveals the existence of variable range hopping of charge carriers with average hopping length RH and hopping energy EH are in the range 8.5–27 Å and 48–153 meV, respectively. Voltage dependent dielectric constant measurements confirm the ferroelectric nature of KNN+ x wt% Dy2O3 ceramics.

Polar octahedral rotations, cation displacement and ferroelectricity in multiferroic SmCrO3

Our thorough synchrotron diffraction studies provide a clue on the origin of ferroelectricity in SmCrO3. Careful observation demonstrates that polar order develops in the paramagnetic state. Rietveld refinement of the diffraction data confirms that emergence of polar order is correlated with the structural transformation from centrosymmetric Pbnm to non-centrosymmetric Pna21 space group of the distorted orthorhombic structure. Rotations of polar CrO6 octahedra and Sm displacement are proposed to be correlated with the emergence of polar order, which is extended over a wide temperature range and increases gradually with decreasing temperature. This is consistent with the relaxor behavior as evident from the frequency-dependent dielectric response satisfying the Vogel-Fulcher law. A non-collinear to collinear spin transformation is suggested well below the spin reorientation transition. Appearance of ferroelectricity without any correlation to the antiferromagnetic order in SmCrO3 suggests a new class of ferroelectricity. All-electron full-potential first-principles calculation demonstrates significant Sm-Cr hybridization near the Fermi level, which substantiates the experimental findings.

Ferromagnetic Cluster-Glass State in Itinerant Electron System Sr1−xLaxRuO3

The magnetic and electronic properties of Sr1-xLaxRuO3 were studied by means of dc-magnetization, ac-susceptibility, specific heat, and electrical resistivity measurements. The dc-magnetization and ac-susceptibility measurements have revealed that the transition temperature and the ordered moment of the ferromagnetic order are strongly suppressed as La is substituted for Sr. The ac-susceptibility exhibits a peak at T* due to the occurrence of spontaneous spin polarization. Furthermore, we observed that T* shows clear frequency variations for x>= 0.3. The magnitude of the frequency shifts of T* is comparable to that of cluster-glass systems, and the frequency dependence is well described in terms of the Vogel-Fulcher law. On the other hand, it is found that the linear specific heat coefficient gamma enhances with the suppression of the ferromagnetic order. The relatively large gamma values reflect the presence of the Ru 4d state at Fermi level, and hence, the magnetism of this system is considered to be tightly coupled with the itinerant characteristics of the Ru 4d electrons. The present experimental results and analyses suggest that the intrinsic coexistence of the spatially inhomogeneous magnetic state and the itinerant nature of the Ru 4d electrons is realized in this system, and such a feature may be commonly involved in La- and Ca-doped SrRuO3.