Vogel-Fulcher Law Research Articles

Growth and Characterization of Relaxor Ferroelectric Pb(Fe2/3W1/3)O3—PbTiO3 Single Crystals

Single crystals of the complex perovskite solid solution (1-x)Pb(Fe2/3W1/3)O 3 —xPbTiO3 [(1−x)PFW—xPT], with x = 0, 0.07, 0.13, 0.27 and 0.75, have been synthesized by the high temperature solution growth using PbO as flux, and characterized by X-ray diffraction and dielectric measurements. With the increasing amount of PT, the crystal structure at room temperature changes from a pseudo-cubic (x = 0, 0.07 and 0.13) to a tetragonal phase (x ≥ 0.27). The dielectric properties of the crystals exhibit a typical relaxor behaviour for x = 0 to 0.27 with frequency-dependent peak temperature (T m ) satisfying the Vogel-Fulcher law, while the crystals with higher PT-content undergo a first-order transition at the ferroelectric Curie temperature T C .

Investigation of frequency dependent and independent dielectric maxima in relaxor ferroelectric thin films

Highly oriented Pb(Sc0.5Nb0.25Ta0.25)O3 (PSNT) thin films were prepared by pulsed laser deposition. The transmission electron microscopy studies showed an epitaxial strain between the layers due to the in-plane oriented heterostructure. PSNT showed a decrease in the frequency dependent dielectric maximum temperature (Tm) compared to the bulk and a frequency independent dielectric maximum at 520K around the Burns temperature (Td). The linear fit of the modified Curie-Wiess law at Tm provides γ∼2 and Δ=90K, indicating diffuse phase transition and strong relaxor behavior, further supported by nonlinear fitting of Vogel-Fulcher law. Well-behaved hysteresis loops indicated ferroelectric relaxor nature of the PSNT thin films.

Theory of Structural Glasses and Supercooled Liquids

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature T(g). These include the following: the viscosity catastrophe and heat-capacity jump at T(g), and their connection; the nonexponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractal cooperative rearrangements; deviations from the Stokes-Einstein relation close to T(g); aging and its correlation with fragility; and the excess density of states at cryogenic temperatures owing to two-level tunneling systems and the Boson peak.

Anisotropic Static and Dynamic Nonlinear Response of Relaxor Ferroelectrics

It has recently been shown in the framework of the static random bond–random field model of relaxor ferroelectrics that the deformation of polar nanoregions by homogeneous lattice strains gives rise to anisotropy of the static nonlinear response. Here we investigate a similar mechanism for the dynamic nonlinear response using a phenomenological approach proposed by Glazounov and Tagantsev. Assuming that the characteristic relaxation time of each polarization decay mode obeys the Vogel-Fulcher (VF) law, the time dependent dielectric polarization is averaged over an ensemble with a suitable statistical distribution of VF temperatures T 0.

Ferroelectric to relaxor crossover and dielectric phase diagram in the BaTiO3–BaSnO3 system

The (1−x)BaTiO3–xBaSnO3 (0⩽x⩽0.30) perovskite solid solution ceramics were prepared by solid state reaction and studied by dielectric spectroscopy. The complex dielectric permittivity was measured as a function of frequency (0.1Hz–100kHz) in the temperature (T) range of 123–573K. The transition from the high-temperature paraelectric state where the dielectric constant obeys the Curie-Weiss law to the ergodic cluster state is found to occur at the same temperature of 485K in all the compositions of x⩾0.04 and at lower temperatures in those with a smaller x. For 0⩽x⩽xc=0.19, the temperature of the dielectric peak Tm, corresponding to the diffuse transition from the ergodic polar cluster state to the ferroelectric state, decreases with increasing x and does not depend on frequency. The diffuseness of the peak gradually increases. For x>xc, the permittivity exhibits relaxor behavior with the frequency-dependent Tm satisfying the Vogel-Fulcher law. The temperature variation of the permittivity on the high-temperature slope of the peak (T>Tm) is characterized by the characteristic Lorenz-type quadratic law for relaxors, with the diffuseness increasing with the increase of x. The mechanisms of the dielectric response in different parts of the phase diagram are discussed. In particular, the crossover from diffuse ferroelectric phase transition to relaxor ferroelectric behavior is attributed to the appearance at x>xc of the additional dielectric contribution arising from the flipping of the local polarization of the polar clusters. The temperature-composition phase diagram of the Ba(Ti1−xSnx)O3 system has been established, which delimits the paraelectric, ergodic polar cluster, nonergodic ferroelectric, and relaxor phases (states) and indicates the crossover from ferroelectric to relaxor behavior at x=xc.

Unfolding of Proteins and Long Transient Conformations Detected by Single Nanopore Recording

We study the electrophoretic blockades due to entries of partially unfolded proteins into a nanopore as a function of the concentration of the denaturing agent. Short and long pore blockades are observed by electrical detection. Short blockades are due to the passage of completely unfolded proteins, their frequency increases as the concentration of the denaturing agent increases, following a sigmoidal denaturation curve. Long blockades reveal partially folded conformations. Their duration increases as the proteins are more folded. The observation of a Vogel-Fulcher law suggests a glassy behavior.

Crossover Between Ferroelectric Order and Dipolar Glass Disorder in CuInP2(S0.25Se0.75)6 Crystals

Dielectric properties of CuInP 2 (S 0.25 Se 0.75 ) 6 crystals were investigated in the temperature range 80 < T < 300 K and frequency range 20 Hz < ν < 1.25 GHz. Very broad dielectric relaxation was analyzed in terms of distribution of relaxation times, using Tichonov regularization method. It revealed slowing down of the longest and most probable relaxation times obeying Vogel-Fulcher and Arrhenius laws respectively. The distribution of relaxation times splits into two components near T m at 1 kHz, and origin of both components are discussed.

Glass phenomenology from the connection to spin glasses

Typical features of glass phenomenology such as the Vogel-Fulcher law, the Kauzmann paradox, and the Adam-Gibbs relationship are shown to follow from the recently discovered mapping of glasses to Ising spin glasses in a magnetic field. There seems to be sufficient universality near the glass transition temperature T{g} such that study of the spin-glass system can provide semiquantitative results for supercooled liquids.

Anomalous Broad Distribution of Relaxation Times in Mixed PMN-PSN Ceramics

Dielectric permittivity of 0.8PMN-0.2PSN ceramic was measured in the frequency range from 20 Hz to 3 GHz. The typical ferroelectrics relaxor dielectric dispersion was observed. From the frequency dependence of complex dielectric permittivity, the distribution of relaxation times was calculated. The low frequency limit of the distribution of relaxation times diverges according to the Vogel–Fulcher law with the freezing temperature T f = 226 K which is lower than in PMN ceramics, obtained previously. The comparison of distributions of relaxation times between 0.8PMN-0.2PSN and pure PMN tends to the conclusion about smaller polar nano regions in 0.8PMN-0.2PSN ceramic.

Broadband dielectric spectroscopy of PSN ceramics

The complex dielectric permittivity of ordered and disordered PSN ceramics was measured in the frequency range from 20 Hz to 3 GHz. The anomaly of dielectric permittivity is clearly seen in the region of 115 °C for ordered PSN at all measured frequencies. Disordered PSN exhibits typical relaxor behaviour with a huge frequency dispersion below 125 °C. Calculated distribution of relaxation times shows noticeable influence of polar clusters to the total dielectric spectrum of disordered PSN below 80 °C with the longest relaxation times edge diverging according to the Vogel–Fulcher law. In the case of ordered PSN, two almost not overlapping peaks in the distribution of relaxation times represent displacive lead motions at high frequencies and possible conductivity phenomena at low frequencies and high temperatures.

Frequency dependence of the transition temperature of the high-pressure magnetic phases in Fe 68.1Ni 31.9 and Co 52.5Fe 38Cr 9.5

We have performed AC susceptibility measurements at various frequencies for high-pressure magnetic phases in Fe 68.1Ni 31.9 and Co 52.5Fe 38Cr 9.5 Invar alloys. In the high-pressure magnetic phases of both alloys, χ′– T curve shows a cusp, and the peak temperature of the cusp ( T P) shifts to lower temperature side with decreasing frequency. The orders of the magnitude of the frequency shift of T P are similar to those of the spin glass phases and smaller than that of the super parramagnetism. In addition, the frequency dependences of T P almost follow with Vogel-Fulcher law. These results are corresponding to the previous report for the spin glass phases.

Magnetic study of Mg 0.95Mn 0.05Fe 2O 4 ferrite nanoparticles

The magnetic properties of Mg 0.95Mn 0.05Fe 2O 4 ferrite samples with an average particle size of ∼6.0±0.6 nm have been studied using X-ray diffraction, Mössbauer spectroscopy, dc magnetization and frequency dependent real χ ′ ( T ) and imaginary χ ″ ( T ) parts of ac susceptibility measurements. A magnetic transition to an ordered state is observed at about 195 K from Mössbauer measurements. The zero-field-cooled (ZFC) and field-cooled (FC) magnetization have been recorded at low field and show the typical behavior of a small particle system. The ZFC curve displays a broad maximum at T mean = 195 ± 5 K , a temperature which depends upon the distribution of particle volumes in the sample. The FC curve was nearly flat below T mean , as compared with monotonically increasing characteristics of non-interacting superparamagnetic systems indicating the existence of strong interactions among the nanoparticles. A frequency-dependent peak observed in χ ′ ( T ) is well described by Vogel–Fulcher law, yielding a relaxation time τ 0 = 5.8 × 1 0 − 12 s and an interaction parameter T 0 = 195 ± 3 K . Such values show the strong interactions and rule out the possibility of spin-glass (SG) features among the nanoparticle system. On the other hand fitting with the Néel–Brown model and the power law yields an unphysical large value of τ 0 (∼6×10 −69 and 1.2×10 −22 s respectively).

Infrared and broadband dielectric spectroscopy of PZN-PMN-PSN relaxor ferroelectrics: Origin of two-component relaxation

Dielectric spectra of several solid solutions of $\mathrm{Pb}{\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{Sc}}_{1∕2}{\mathrm{Nb}}_{1∕2}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3}$ (PMN-PSN-PZN) relaxor ferroelectrics were investigated in a broad frequency range from $20\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ up to $100\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$ by a combination of dielectric spectroscopy $(20\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}\char21{}53\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$, time-domain terahertz spectroscopy $(0.1\char21{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{THz})$, and infrared reflectivity ($20\char21{}3000\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, $0.6\char21{}90\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$). The very strong and broad dielectric relaxation observed below phonon frequencies was analyzed in terms of the distribution of relaxation times, using the Tichonov regularization method. This revealed slowing down of the longest and mean relaxation times obeying the Vogel-Fulcher law. The relaxation splits into two components near ${T}_{m}$ and the origin of both components is discussed. The formation of polar clusters below the Burns temperature $(700\char21{}800\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ is manifested by the appearance of dielectric relaxation in the terahertz range and by splitting of the polar modes in the infrared spectra. On heating from low temperatures, the ${A}_{1}$ component of the strongly split ${\mathrm{TO}}_{1}$ mode softens toward the Burns temperature, but the softening ceases near $400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which could be a signature of a polar cluster percolation temperature.

Jamming Percolation and Glassy Dynamics

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S. Fisher (Toninelli et al., Phys. Rev. Lett. 96, 035702, 2006). Furthermore, we review some of our previous works on Kinetically Constrained Models.The Knight models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when ρ ↗ ρ c . These properties give rise for Knight models to an ergodicity breaking transition at ρ c : at and above ρ c a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.

Dielectric Dispersion in Pure PMN and PMN with 10% PT Single Crystals

Dielectric permittivity of PMN and PMN with 10% PT single crystals was measured in the frequency range from 20 Hz to 3 GHz. Dielectric dispersion was observed in all investigated frequency range. From the frequency dependence of the real and imaginary parts of dielectric permittvity, the distribution of relaxation times was calculated. The low frequency limit of the distribution of the relaxation times diverges according to the Vogel–Fulcher law with the freezing temperature T f = 228 K for PMN, which is in good agreement with the mean relaxation time temperature dependence obtained from Cole–Cole, equation and T f = 282 K for 0.9 PMN–0.1 PT, which is higher than obtained from Cole–Cole equation. Broadening of the relaxation time distribution function at low temperatures clearly indicates the existence of at least two different components making contribution to the total dielectric spectrum of PMN. One of the components can be attributed to polar nano regions, whose dynamics slows down and freezes at T f , and the another component is the paraelectric matrix, which stays stable even at low temperatures.

Relaxor Behavior in Ba(Ti0.72Sn0.28)O3 Solid Solution

Dielectric properties of the Ba(Ti0.72Sn0.28)O3 solid solution ceramics are studied as a function of frequency (0.01 Hz–100 kHz) in the temperature range of 300°C to −150°C. A broad dielectric peak with strong frequency dispersion is observed. The temperatures T m of real and imaginary dielectric peaks fit well to the Vogel-Fulcher law. Both the high-temperature and low-temperature slopes of the real permittivity peak can be described by a Lorenz-type formula. The dielectric hysteresis loops are displayed at low temperatures as well as at temperatures significantly higher than T m . The Curie-Weiss law is observed at temperatures much higher than T m .

Dynamic crossovers and activated regimes in a narrow distribution poly(n-butyl acrylate):an ESR study

The rotational dynamics of the spin probe cholestane dissolved in a narrow distributionpoly(n-butyl acrylate) sample has been investigated via electron spin resonance (ESR)spectroscopy. The measurements were carried out in a wide temperature range: differentdynamic regions have been recognized, and the coupling of the probe dynamics to theα and secondary relaxations has been revealed. In particular, the coupling withthe structural relaxation is ruled by two fractionary Vogel–Fulcher laws (VF).The crossover from one VF region to the other occurs at the temperatureTC = 1.17Tg, signalling the onset of the cooperativity in the dynamics and confirming a behaviourpreviously observed in ESR studies carried out on polymeric glass-formers. Furthermore, inthis work we discuss the activated regime at the highest temperatures and show thatthe activation energy does not depend on the length of the polymer main- andside-chains, while its onset temperature linearly depends on the chain length.

A mixture of ferritin and magnetite nanoparticles mimics the magnetic properties of human brain tissue

Magnetic properties of a two-component system, consisting of horse spleen ferritin (HoSF) which contains a $5--8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ sized antiferromagnetic ferrihydrite $(5{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}∙9{\mathrm{H}}_{2}\mathrm{O})$ core and ferrimagnetic magnetite $({\mathrm{Fe}}_{3}{\mathrm{O}}_{4})$ nanoparticles (MNP) with an average size of $10--20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, have been investigated by using four different methods: induced magnetization versus (1) temperature and (2) field; (3) AC susceptibility; and (4) first-order reversal curves (FORC). All measurements were done on a mixed system of HoSF and MNP, as well as separately on the individual components. The average blocking temperature $({T}_{\mathrm{B}})$ of the mixed system at $50\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ is $15.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is a shift towards higher temperatures compared to pure HoSF $({T}_{\mathrm{B}}=12\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. The contribution of the MNP component to magnetic ordering is evident only as a separation of the zero-field-cooled and field-cooled measurement curves. ac susceptibility is dominated by the ferrimagnetic MNP and shows strong frequency dependence. The peak ac susceptibilities can be described by the Vogel-Fulcher law, indicating the influence of interactions within the system. Hysteresis measurements at $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ show a wasp-waisted shape due to the mixture of a high coercivity phase (HoSF) with a low coercivity phase (MNP). Initial magnetization curves above ${T}_{\mathrm{B}}$ can be fitted by a sum of Langevin functions, showing superparamagnetic behavior of both components. FORC diagrams are effective in illustrating the change from that of blocked MNP particles together with the superparamagnetic HoSF at $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ to purely superparamagnetic behavior in both components above $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We conclude that the mixed nanoparticle system is a good model for complex natural samples, such as human brain tissue.

Description of the paramagnet-spin glass transition in the Edwards-Anderson model using critical-dynamics methods

Possibility of description of the glass transition in terms of critical dynamics considering a hierarchy of the intermodal relaxation time is shown. The generalized Vogel-Fulcher law for the system relaxation time is derived in terms of this approach. It is shown that the system satisfies the fluctuating--dissipative theorem in case of the absence of the intermodal relaxation time hierarchy.

Effect of interparticle interaction on the magnetic relaxation in NiO nanorods

Temperature variation (5 K–300 K) of the AC magnetic susceptibilities (χ′ and χ″) at frequency f=0.1, 1, 50, 100, 500, 1000, 2000, 5000, and 10, 000 Hz are reported in 5 nm diameter nanorods of NiO, with and without oleic acid (OA) coating. Using the peak in χ′ as the blocking temperature TB, it is observed that TB increases with increasing f. The data for the two samples fit the Vogel-Fulcher law: f=f0exp[−Ea∕k(TB−T0)], with f0=9.2×1011Hz, Ea∕k=1085 K, and T0=165 K (0 K) for the uncoated (coated) particles. This shows that T0 provides a good measure of the effects of interparticle interactions on magnetic relaxation and that these interactions are essentially eliminated with the OA coating.