Vogel-Fulcher Law Research Articles

A study of relaxation effects in (1-x)BaZr0.2Ti0.8O3-xBa0.7Ca0.3TiO3 (x = 0.3, 0.35, 0.4) ferroelectric ceramics

Lead free (1-x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 (x = 0.3, 0.35, 0.4) ceramics were prepared via conventional two-step solid-state reaction technique. Temperature dependent dielectric measurements, conducted in the frequency range from 1 kHz to 1 MHz, indicate diffused phase transition for all the samples. The diffuseness of the transition has been studied by fitting the data with modified Curie-Weiss law. It is found that the composition with x = 0.3 behaves as a weak relaxor-ferroelectric, superposed by a non-relaxor behavior. Vogel-Fulcher law was used to characterize the relaxor-ferroelectric behavior while the analysis according to the Cole-Cole plots was used to characterize the non-relaxor features.

Enhanced temperature-stable dielectric properties in oxygen annealed 0.85(K0.5Na0.5)NbO3-0.15SrZrO3 ceramic

The structure, morphology and dielectric properties of the oxygen annealed (O2-annealed) and untreated (as-prepared) 0.85(K0.5Na0.5) NbO3-0·15SrZrO3 (KNN-15SZ) ceramics were investigated. The temperature dependence of dielectric permittivity shows two diffuse dielectric peaks associated with duplex core-shell structure, leading to relatively stable dielectric permittivity in a wide temperature range. Interestingly, the O2-annealed sample with the operating temperature range of −104 °C–157 °C could meet the EIA X8R specification, which is superior to the as-prepared one (−98 °C–130 °C) for the EIA X7R specification. Furthermore, the dielectric contribution from cores and shells of both samples was divided by the Lorentz fitting. The relation between relaxation frequency and temperature of both samples obeyed the Vogel-Fulcher law. This finding could pave a possible way to modify dielectric temperature stability for multilayer ceramic chip capacitors applications.

Effects of Cu doping on the electronic structure and magnetic properties of MnCo2O4 nanostructures

Reported here are the results and their analysis from our detailed investigations of the effects of Cu doping () on the electronic structure and magnetic properties of the spinel O4. A detailed comparison is given for the and cases for both the bulk-like samples and nanoparticles. The electronic structure determined from x-ray photoelectron spectroscopy and Rietveld analysis of x-ray diffraction patterns shows the structure to be: ()A]B i.e. substitutes for on the octahedral B-sites. For the bulk samples, the ferrimagnetic K for is lowered to K for the sample, this decrease being due to the effect of Cu doping. For the nanosize () sample, the lower K ( K) is observed using analysis, this lowering being due to finite size effects. For , fits of dc paramagnetic susceptibility data of versus T in nanosize samples to the Néel expression are used to determine the exchange interactions between the A and B sites with exchange constants: K (4.1 K), K (16.3 K) and K (13.8 K) for . The temperature dependence of ac susceptibilities and at different frequencies shows that in bulk samples of and , the transition at TC is the normal second order transition. But for the nanosize and 0.2 samples, analysis of the ac susceptibilities shows that the ferrimagnetic transition at TC is followed by a re-entrant spin-glass transition at lower temperatures K (138 K) for (). Analysis of the ac susceptibilities, and , versus T data is done in terms of two scaling laws: (i) Vogel–Fulcher law ; and (ii) power law of critical slowing-down . These fits confirm the existence of glassy behavior below TSG with the parameters (8.91), (9.6 × 10) and K (∼138 K) for the samples (0.2), with similar results obtained for other samples. The linear behavior of the peak maximum in versus (AT-line) further supports the existence of glassy states in nanosize samples. For , the temperature and composition dependence of the hysteresis loop parameters are investigated; all the samples with x ⩾ 0.1 have the coercivity HC and remanence . Since the results reported here in these nanostructures are significantly different from those in bulk , further investigations of their magnetic structures using neutron diffraction are warranted.

Statistics of twinning in strained ferroelastics

In this review, we show that the evolution of the microstructure and kinetics of ferroelastic crystals under external shear can be explored by computer simulations of 2D model materials. We find that the nucleation and propagation of twin boundaries in ferroelastics depend sensitively on temperature. In the plastic regime, the evolution of the ferroelastic microstructure under strain deformation maintains a stick-and-slip mechanism in all temperature regimes, whereas the dynamic behavior changes dramatically from power-law statistics at low temperature to a Kohlrausch law at intermediate temperature, and then to a Vogel–Fulcher law at high temperature. In the yield regime, the distribution of jerk energies follows power-law statistics in all temperature regimes for a large range of strain rates. The non-spanning avalanches in the yield regime follow a parabolic temporal profile. The changes of twin pattern and twin boundaries density represent an important step towards domain boundary engineering.

Relaxation behavior and electrical inhomogeneity in 0.9BaTiO3-0.1Bi(Mg1/2Ti1/2)O3 ceramic

Abstract In this paper, the relaxation behavior and electrical inhomogeneity of the 0.9BaTiO 3 - 0.1Bi(Mg 1/2 Ti 1/2 )O 3 ceramic which exhibits outstanding temperature stable dielectric and energy storage properties are investigated. The relaxation process is well described by the empirical Vogel-Fulcher law, also indicating a freezing process in the system simultaneously. Such a freezing process is also observed in the “Vogel-Fulcher” shaped temperature dependence of the universal relaxation exponent n. Furthermore, the electrical inhomogeneity, showing up as two dielectric anomalies in the temperature dependence of the dielectric constant, is ascribed to the compositional inhomogeneity between grains and grain boundaries. The grain and grain boundary contributions to the total polarization are separated by analyzing the complex impedance spectroscopy with equivalent circuit model. Finally, the compositional inhomogeneity is manifested by the confocal Raman microscopy, indicating that the grain is rich in BaTiO 3 , whereas the grain boundary has Bi(Mg 1/2 Ti 1/2 )O 3 concentrations.

Presence of glassy state and large exchange bias in nanocrystalline BiFeO3

We investigated the static and dynamic aspects of the magnetic properties for single phase nanocrystalline BiFeO3 with average crystallite size of 35nm. The frequency dependence of the peak is observed in the real part of ac susceptibility χ′ac vs T measurement and described well by the Vogel-Fulcher law as well as the power law. These analyses indicated the existence of cluster glass state with significant interaction among the spin clusters and results in cluster-glass like cooperative freezing at low temperature. The influence of temperature and magnetic field cooling on the exchange bias effect is investigated. A training effect is also observed. We have reported a significantly high ZFC & FC exchange bias of 200Oe & 450Oe at 300K and 900Oe & 2100Oe at 5K. The obtained results are interpreted in the framework of core-shell model, where the core of the BFO nanoparticles shows antiferromagnetic behavior and surrounded by CG-like ferromagnetic (FM) shell associated to uncompensated surface spins.

Evolution of structure and magnetic properties of stoichiometry and oxygen rich LaMnO3 nanoparticles

In this report, the evolution of structure and magnetic properties in stoichiometry and oxygen rich LaMnO3 samples synthesized by a simple, cost effective, conventional co-precipitation technique are systematically studied. While X-ray powder diffraction reveals a monoclinic, I2/a structure in both samples, Reitveld refinement demonstrates higher John-Teller (J-T) distortion in the former one. Higher J-T distortion is accompanied with a large deviation in MnO bond length. FESEM (Field Emission Scanning Electron Microscopy) analysis combined with crystallite size calculated from XRD peak profile suggest that the particles are of 50–60nm and are polycrystalline in nature. The antiferromagnetism observed in bulk LaMnO3 with TN=140K evolves towards a ferromagnetic order in both stoichiometry and oxygen rich samples. However, Curie temperature, TC, is found to be higher in oxygen rich sample due to higher MnOMn bond angle. The large effective magnetic moment calculated from Curie-Weiss plot is found to be higher in stoichiometry sample. Higher moment is ascribed to high oxygen vacancies evidenced from XPS analysis. Dispersion behavior observed in frequency dependent ac susceptibility (χ) indicates the spin-glass, cluster-glass and interacting superparamagnetic behavior. Fitting the susceptibility data with phenomenological models such as Neel-Arrhenius, Vogel-Fulcher and Power law, while canonical spin-glass, cluster-glass and interacting superparamagnetism is ruled out, the spin-glass behavior with a higher relaxation time in oxygen rich sample is confirmed.

Dielectric Properties of BaTiO3-KNbO3 Composites

ABSTRACTThis paper is focused on dielectric properties of potassium niobate (KN) –barium titanate (BT) composites with artificial morphotropic phase boundary (MPB). Ceramics with highest concentration of KN showed a glassy behaviour below 300 K temperature. Also two relaxation processes were observed, one in MHz and second at GHz range. The relaxation process in the MHz range follows Vogel-Fulcher law. The nature of the GHz dispersion is assumed to be electro-mechanical resonance.

Relaxations in Doped PZT and Epoxy-glue/Bi-Mn-O Composite

Effects of doping on ABO3 perovskite PZT compounds were studied. We determined effects of doping with Na ions (0.5–2.5 at.%) in A sublattice of Pb(Zr,Ti)O3 and (Pb,La)(Zr,Ti)O3 ceramics. The phase transition between ferro- and paraelectric phase was shifted, the dielectric losses decreased, and the piezoelectric coefficients, Kp and d33, were improved. The properties of bismuth manganite doped to PZT ceramics, (1-x)PZT-(x)BiMn2O5 (x = 0.055, 0.11), were studied. The effects of Bi doping in A sublattice and Mn doping in B sublattice were determined. The PZT-BiMn2O5 formed a composite of two solid solutions, one the ferroelectric rhombohedral R3m phase related to PZT, and the orthorhombic Pbam phase originated from bismuth manganite. Composition was estimated by using the scanning electron microscopy. Electrical impedance was measured in 100 Hz–1 MHz and 85–705 K ranges. Two types of the relaxations, manifested in the impedance spectra, were determined. One was attributed to charge transfer in B sublattice and/or polaronic mechanism. Second was fitted by using Vogel-Fulcher law that verified relaxor-like state for 0.89PZT-0.11BiMn2O5 compound. The epoxy-glue/bismuth-manganite composite was obtained. Vogel-Fulcher law confirmed glassy features for this material. Effective role of 0-3 connectivity in suppression of dielectric losses and transient currents was verified.

Substrate-induced dielectric polarization in thin films of lead-free (Sr0.5Bi0.5)2Mn2-xTixO6-δ perovskites grown by pulsed laser deposition

Thin films of SrBiMn2-xTixO6-δ have been fabricated by Pulsed Laser Deposition on SrTiO3 [100] and [111] substrates. Their texture, width, homogeneity and morphology are evaluated by means of XRD, SEM, XPS, whereas complex impedance spectroscopy is employed to analyze their electrical response. The thickness values range between 80 and 900nm depending on the experimental conditions. The epitaxial growing could be interpreted in terms of two contributions of microstructural origin: a matrix part and some polycrystalline surface formations (hemi-spheres). Texture studies suggest a fiber-type orientated morphology coherently with the Scanning Electron Microscopy images. XPS analyses indicate a segregation regarding A-sublattice cations, which features depend on the substrate orientation. This segregation could be connected to the development of nanopolar regions. Impedance data show the electrical polarization in the samples to be enhanced compared to bulk response of corresponding powdered samples. A relaxor behavior which fits a Vogel-Fulcher law is obtained for x=0.50 whereas an almost frequency-independent relaxor ferroelectric behavior is registered for the thinnest film of x=0.25 composition grown on SrTiO3 [111] substrate. The influence of compositional and structural aspects in the obtained dielectric response is analyzed.

Thermally induced magnetic relaxation in square artificial spin ice.

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice – we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.

Effects of Mn doping on dielectric properties of ferroelectric relaxor PLZT ceramics

A series of PLZT (8/65/35) ceramics with different Mn2O3 concentration (0.01, 0.1, 0.3, 1.0, and 3.0% by weight) have been synthesized to figure out its influence on their dielectric properties. The complex dielectric permittivity ε* = ε′−iε″ as function of frequency and temperature as well as polarisation loops P(E) have been studied as a function of Mn concentration.It was found that Mn doping is restrained the Vogel-Fulcher law held in the unmodified PLZT compound producing essential change of the dependence of ε* on temperature and frequency and of the shape of P(E). The observed effects are explained by gradual involvement of Debye and Maxwell-Wagner polarisation mechanisms in relaxation processes with the growth of the concentration of Mn concentration admixture. A decrease of the ε'(T) maximum value and shift of the maximum to higher temperatures is observed.The observed effects are attributed to impacts of Mn2+ and Mn3+ ions: formation of oxygen vacancies paired with Mn2+ as dipoles and Jahn-Teller distortion prompted by Mn3+ ions.

Modeling relaxor characteristics in systems of interacting dipoles

We present a model which derives typical relaxor characteristics from simple and plausible microscopic assumptions. The model is based on charges which fluctuate thermally activated in double well potentials. The double well potentials are asymmetric due to disorder in the system. The electrostatic interaction between the charges is considered via a mean field approach. This model yields the typical relaxor features: we find high susceptibilities in a broad temperature range with dynamics following the Vogel–Fulcher law. In the framework of the model no spontaneous polarization arises at cooling without strong external field in accordance to experimental findings for relaxors. Furthermore the model yields hysteresis loops which depend on the amplitude of the external field and which become more and more thin and deformed above the maximum temperature of the susceptibility.

Relaxor transition and properties of Mn-doped SrxBa1−xNb2O6 ferroelectric ceramics

Pure and Mn-doped SrxBa1−xNb2O6 (SBN) ceramics were prepared by the conventional solid state reaction method and their morphology, phase structure, relaxor behavior, ferroelectric and energy storage properties were investigated to reveal the effects of Mn doping on their properties. The results show that all the samples are single tetragonal tungsten bronze structure and the Mn element having few influences on their microstructures. The dielectric constant of pure SBN samples shows a classical relaxor behavior with obvious frequency dispersion and fits well with the Vogel–Fulcher law. However, the dielectric constant of Mn-doped samples does not show frequency dispersion. Then the relaxor behaviors of both pure and doped samples were further investigated by fitting the dielectric constant to the modified Curie-Weiss law. It was found that the diffusion parameters (γ) of Mn-doped samples are close to those pure samples, which indicates that the Mn-doped samples still have relaxor characteristics even without the classical dielectric frequency dispersion. Compared with the pure samples, the Mn-doped samples have a slimmer polarization-electric field (P-E) hysteresis loop, which can also prove their relaxor behaviors. The investigations of energy storage properties reveal that the Mn-doped samples have a higher energy storage density and efficiency.

Lead-free relaxor ferroelectric ceramics Sr4+x Ca1−x BiTi3Nb7O30 with tunable transition temperature

Based on nominal components, Sr4+xCa1−xBiTi3Nb7O30 (x = 0.25, 0.5, 0.75, 1) ceramics were prepared by means of solid-state reaction method. Their transition temperatures Tm can be experimentally tuned by controlling the atomic ratio of Sr2+/Ca2+. All the samples are demonstrated to exhibit relaxor ferroelectric property above room temperature, and Tm can be controlled effectively by changing the content of Sr2+ ion in A1 site. In addition, the linear relation between Tm and the x corresponding to Sr2+ ion of A1 site indicates that relaxor ferroelectric with wide-ranging transition temperatures can be obtained, catering for the potential applications. Meanwhile, the dielectric maximum temperature Tm of relaxation-I obeyed the Vogel–Fulcher law well, and Curie–Weiss fitting confirmed the displacive-type ferroelectric phase transition in these compounds.

Structure and dielectric dispersion in cubic-like 0.5K0.5Na0.5NbO3-0.5Na1/2Bi1/2TiO3 ceramic

The nature of the cubic-like state in the lead-free piezoelectric ceramics 0.5K0.5Na0.5NbO3-0.5Na1/2Bi1/2TiO3 (KNN-50BNT) has been examined in detail by synchrotron x-ray diffraction (SD), selected-area electron diffraction (SAED), neutron diffraction (ND), and temperature-dependent dielectric characterization. The SD pattern of KNN-50BNT presents a pure perovskite structure with pseudocubic symmetry. However, superlattice reflections were observed by SAED and completely indexed by tetragonal symmetry with P4bm space group in ND pattern. The relaxor behavior of KNN-50BNT is compared with Pb-based and Ba-based relaxors and discussed in the framework of the Vogel-Fulcher law and the new glass model. The KNN-50BNT ceramic exhibits the strongest dielectric dispersion among them.

Subterahertz dielectric relaxation in lead-free Ba(Zr,Ti)O3 relaxor ferroelectrics.

Relaxors are complex materials with unusual properties that have been puzzling the scientific community since their discovery. The main characteristic of relaxors, that is, their dielectric relaxation, remains unclear and is still under debate. The difficulty to conduct measurements at frequencies ranging from ≃1 GHz to ≃1 THz and the challenge of developing models to capture their complex dynamical responses are among the reasons for such a situation. Here, we report first-principles-based molecular dynamic simulations of lead-free Ba(Zr0.5Ti0.5)O3, which allows us to obtain its subterahertz dynamics. This approach reproduces the striking characteristics of relaxors including the dielectric relaxation, the constant-loss behaviour, the diffuse maximum in the temperature dependence of susceptibility, the substantial widening of dielectric spectrum on cooling and the resulting Vogel–Fulcher law. The simulations further relate such features to the decomposed dielectric responses, each associated with its own polarization mechanism, therefore, enhancing the current understanding of relaxor behaviour.

Spin-glass-like behaviour in Ni2InVO6

Magnetic measurements and specific heat under magnetic field showed the spin-glass-like behaviour below the freezing temperature Tf = 5 K in the phase Ni2InVO6. Positive value of the paramagnetic Curie–Weiss temperature θ = 5.3 K suggests ferromagnetic short–range interaction. On the other hand, the product of χ′⋅T versus T reaches almost zero, decreasing continuously upon cooling, which indicates fully compensated AFM interactions between the metal centres. These effects appear to be responsible for the spin frustration. The presence of an antiferromagnetic-like correlations in Ni2InVO6 is suggested by a shift of the maxima in the specific heat C(T) or C(T)/T data toward lower temperatures when the magnetic field is increasing. Also, the freezing temperature attributed to the temperature of maximum in the ac magnetic susceptibility obeys the Vogel-Fulcher law, which is characteristic of spin-glasses.

Reentrant spin-glass behavior and bipolar exchange-bias effect in “Sn” substituted cobalt-orthotitanate

We report the co-existence of longitudinal ferrimagnetic behavior with Néel temperature TN ∼ 46.1 K and reentrant transverse spin-glass state at 44.05 K in Tin (Sn) doped cobalt-orthotitanate (Co2TiO4). The ferrimagnetic ordering is resulting from different magnetic moments of Co2+ on the A-sites (3.87 μB) and B-sites (5.069 μB). The magnetic compensation temperature (TCOMP) shifts from 31.74 K to 27.1 K when 40 at. % of “Sn4+” substitutes “Ti4+” at B-sites where the bulk-magnetization of two-sublattices balance each other. For T > TN, the dc-magnetic susceptibility (χdc = M/Hdc) fits well with the Néel's expression for the two-sublattice model with antiferromagnetic molecular field constants NBB ∼ 15.44, NAB ∼ 32.01, and NAA ∼ 20.88. The frequency dependence of ac-magnetic susceptibility χac data follows the Vogel-Fulcher law, and the power-law of critical slowing-down with “zν” = 6.01 suggests the existence of spin-clusters (where “z” and “ν” being dynamic critical-exponent and correlation length of critical-exponent, respectively). This system exhibits unusual hysteresis loops with large bipolar exchange-bias effect (HEB ∼ 13.6 kOe at 7 K) after zero-field cooling process from an un-magnetized state, and a dramatic collapse of remanence (MR) and coercive field (HC) across TCOMP. The possible origins of such anomalous characteristics were discussed.

Relaxor Behaviors in xBaTiO3-(1-x)CoFe2O4Materials

Dielectric properties of xBaTiO₃–(1-x)CoFe₂O₄ composite materials have been investigated. Dielectric properties of BaTiO₃, CoFe₂O₄ and 0.5BaTiO₃–0.5CoFe₂O₄ samples show frequency dependence, which is classified as relaxor behavior with different relaxing degree. The relaxor behaviors were described using the modified Curier-Weiss and Vogel–Fulcher laws. Among three above samples, the BaTiO₃ sample has highest relaxing degree. Photoluminescence spectral indicated defects, which might in turn control relaxing degree.