Mean Field Region Research Articles

Influence of sintering temperature on excess conductivity in Bi-2223 superconductors

Structural examinations and resistivity measurements were made onBi1.75Pb0.35Sr2Ca2Cu3O10 samples sintered at different temperatures. The excess conductivity region was analysed usingthe Aslamazov–Larkin (AL) expression. In agreement with the theoretical predictions, theln(Δσ/σ300)–ln(ε) plots exhibited three different regions, namely, critical, mean field and short wavefluctuation regions. In the mean field region, the interlayer coupling strengthν, the effectivelayer thickness d, and the zero-temperature coherence lengthζ(0) were estimated using the Lawrence–Doniach (LD) expression.

Fluctuation-Induced Excess Conductivity in R1−x Ca x : 123 Superconductors

Fluctuation induced conductivity of Ca substitution at R sites of R1−xCax: 123 superconductors with various x and R is investigated. This work is done by using the reported data of Sedky et al. (Phys. Rev. B 58(18):12495, 1998). The logarithmic plots of Δσ and reduced temperature € reveal three different exponents corresponding to two different crossover temperatures. The first exponent at ln € (−1≥ln €≥−2) and its values are close to 1, for which order parameter dimensionalities (OPD) are two dimensional (2D). The second exponent at ln € (−2≥ln €≥−3.5) and its values are close to 2, for which OPD are neither two dimensional (2D) nor three dimensional (3D). The third exponent at ln € (−3.5≥ln €≥−8) and its values are close to 0.5, for which OPD are three dimensional (3D). The different values of the interlayer coupling are also calculated in the normal and mean field regions, respectively. Our results are discussed in terms of oxygen disorder and system anisotropy produced by Ca substitution in R1−xCax: 123 systems.

Comment on “Critical behavior of ferroelectricSrTiO318”

Recently reported [C. Filipi\ifmmode \check{c}\else \v{c}\fi{} and A. Levstik, Phys. Rev. B 73, 092104 (2006)] and reinforced [J. F. Scott et al., J. Phys.: Condens. Matter 18, L205 (2006)] critical exponents $\ensuremath{\gamma}=1.0$ and $\ensuremath{\beta}=0.5$ of the isotope-substituted ferroelectric $\mathrm{Sr}\mathrm{Ti}^{18}\mathrm{O}_{3}$ are revisited and found to merely describe the mean-field region of this system. Careful evaluation of dielectric susceptibility and second harmonic generation data within the near-critical regime near to ${T}_{c}\ensuremath{\approx}24\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ yields nonclassic effective exponents, $\ensuremath{\gamma}=1.65\ifmmode\pm\else\textpm\fi{}0.03$ and $\ensuremath{\beta}=0.21\ifmmode\pm\else\textpm\fi{}0.02$. Quantum corrections are relevant, albeit not crucial. Scaling relations and asymptotic criticality are discussed.

Fluctuation conductivity analysis on the Bi‐based superconductors processed under same conditions

AbstractWe report electrical conductivity fluctuation measurements on different Bismuth‐based granular samples synthesized under same processing conditions.Using the fluctuation conductivity Δσ as a function of the reduced temperature ϵ in the range –7 < ln ϵ < 1, we identified Gaussian and critical fluctuation conductivity in (Bi,Pb)‐2223 and Bi‐2212 samples. Within the mean field region, samples show predominately two dimensional (2D) behaviour with exponent λ = –1. Closer to critical temperature T C, we have observed a crossover of λ from –2/3 to –1/3 in the critical region. The obtained exponents are consistent with 3D‐XY model predictions. The regime with the critical exponent –2/3 is dominate in the case of (Bi,Pb)‐2223 sample. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of Al2O3 nanometer particles addition on the fluctuation conductivity in (Bi,Pb)‐2223 superconductors

AbstractNanometer Al2O3 particles were added to (Bi,Pb)2Sr2Ca2Cu3Ox (Bi,Pb)‐2223 precursor powders during the final sintering cycle of a multi‐step preparation process. The temperature dependence of the resistance in 0 and 0.2% Al2O3‐added (Bi,Pb)2Sr2Ca2Cu3Ox samples was measured. Data about the dimensionality of the fluctuation is obtained by analyzing the fluctuation conductivity Δσ as a function of ε = ln (T/TC) on the basis of the Aslamazov–Larkin theory. Within the mean field region, we first observe a regime dominated by 2D Gaussian fluctuation. With decreasing temperature a crossover occurs at a temperature TG and the obtained regime was described by critical fluctuations. The Ginzburg number and fluctuation amplitude, increase with addition of nanometer Al2O3 particles. Correlation between fluctuation amplitude and JC has been discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fluctuation conductivity and inhomogeneity in granularYBa2Cu3O7−y/Ag composite thick films

We analyse the effect of interplay of the different types of inhomogeneities and the thermalfluctuation of the superconducting order parameter on the excess conductivity in a set ofYBa2Cu3O7−y/Ag composite thick films. We show that the mesoscopic inhomogeneities arising due tomost of the Ag residing at the grain boundaries strongly influence the tailingand the critical regions below and above the mean field transition temperature,Tc, respectively. A small fraction of Ag diffusing into the grains also produces microscopicinhomogeneities. Though these inhomogeneities are not expected to influence the SCOPF, we foundthat TLD, corresponding to the transition from the two to three dimensional fluctuation of the orderparameter in the mean field region, as well as the inter-planar coupling strength, stronglydepend on the Ag content in the composites. The effect of Ag induced inhomogeneities onthe temperature window corresponding to different phases in the mean field and thecritical regions are depicted in the form of a phase diagram. The large variation ofTLD, and nearinvariance of Tc with Ag content in the films as seen in the phase diagram, are explained by invoking therole of Ag in modifying the overall electronic structure of the grains.

EXCESS CONDUCTIVITY IN THE MEAN FIELD AND PARACOHERENCE REGIMES OF (La1.6Y0.4)Ba2Ca0.8Cu4.8Oz SUPERCONDUCTORS

The temperature variations of electrical resistivity have been measured on pure and 5 wt% Ag doped ( La 1.6 Y 0.4) Ba 2 Ca 0.8 Cu 4.8 O z superconductors. These data were analyzed in terms of fluctuation-induced excess conductivity in the mean field regime by using the Aslamazov–Larkin (AL), Lawrence–Doniach (LD) and Maki–Thompson (MT) models. The fluctuations in the amplitude of order parameter are found to be two dimensional in nature in the mean field region. The estimated values of the average phase breaking time τϕ (100 K) are found to be 3.9×10-16 s and 4.6×10-16 s for pure and Ag doped samples respectively. The resistivity data were also analyzed in terms of excess conductivity due to phase fluctuations of the order parameter in the paracoherence region. The critical exponent is found to be mostly comparable to that of the 3D XY ferromagnet in the vicinity of zero resistivity temperature and the diluted Heisenberg model at a higher temperature.

Probing the Almeida-Thouless line away from the mean-field model

Results of Monte Carlo simulations of the one-dimensional long-range Ising spin glass with power-law interactions in the presence of a (random) field are presented. By tuning the exponent of the power-law interactions, we are able to scan the full range of possible behaviors from the infinite-range (Sherrington-Kirkpatrick) model to the short-range model. A finite-size scaling analysis of the correlation length indicates that the Almeida-Thouless line does not occur in the region with non-mean-field critical behavior in zero field. However, there is evidence that an Almeida-Thouless line does occur in the mean-field region.

Effects of rescattering in(e,e′p)reactions within a semiclassical model

The contribution of rescattering to final state interactions in (e,e'p) cross sections is studied for medium and high missing energies using a semiclassical model. This approach considers two-step processes that lead to the emission of both nucleons. The effects of nuclear transparency are accounted for in a Glauber inspired approach and the dispersion effects of the medium at low energies are included. It is found that rescattering is strongly reduced in parallel kinematics. At high missing energy and momenta, the distortion of the short-range correlated tail of the spectral function is dominated by a rearrangement of that strength itself. In perpendicular kinematics, a further enhancement of the experimental yield is due to strength that is originally in the mean field region. This contribution becomes negligible at large missing momenta.

Stability and structure of two coupled boson systems in an external field

The lowest adiabatic potential expressed in hyperspherical coordinates is estimated for two boson systems in an external harmonic trap. Corresponding conditions for stability are investigated and the related structures are extracted for zero-range interactions. Strong repulsion between non-identical particles leads to two new features, respectively when identical particles attract or repel each other. For repulsion new stable structures arise with displaced center of masses. For attraction the mean-field stability region is restricted due to motion of the center of masses.

Q-state Potts model with power-law decaying interactions: Along the tricritical line

By relying on a recently proposed multicanonical algorithm adapted to long-ranged models, we shed new light on the critical behavior of the long-ranged q-state Potts model. We refine the controversial phase diagram by an order of magnitude, over a large range of q values, by applying finite-size scaling arguments to spinodal curves. We further offer convincing evidence that the phase transition on the line of inverse-square interactions is not of the first order, by virtue of a very unusual, previously unnoticed, finite-size effect. Finally, we obtain estimates of critical couplings near the mean-field region, which clearly reinforce Tsallis conjecture.

Mean-field and anomalous behavior on a small-world network.

We consider various equilibrium statistical mechanics models with combined short- and long-range interactions and identify the crossover to mean-field behavior, finding anomalous scaling in the width of the mean-field region, as well as in the mean-field amplitudes. We then show that this model enables us, in many cases, to determine the universal critical properties of systems on a small-world network. Finally, we consider nonequilibrium processes.

Fluctuation conductivity of polycrystalline Hg, Tl-1223

Detailed resistivity measurements were made for polycrystalline Hg1−xTlxBa2Ca2Cu3O8+δ (x=0 and 0.2) in zero field and above the superconducting Tc. The fluctuation conductivity Δσ is analyzed. With decreasing temperature two crossover temperatures could be identified for each sample; i.e. T∗ from two to three dimensional fluctuations in the mean field region (MFR), and TG from the MFR to the critical region. All results are in agreement with the Lawrence–Doniach model. The c-axis coherence length and the interlayer coupling factor were obtained.

Quantum spin glass with long-range random interactions

A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance ${r}_{\mathrm{ij}}$ apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.

Analysis of fluctuation conductivity in melt-textured YBa 2Cu 3O 7− y superconductors with Ag-doping

The difference in the properties between Ag-doped and undoped YBa 2Cu 3O 7− y (YBCO) melt-textured samples was investigated by fluctuation-conductivity analysis. The temperature dependence of the resistance in those samples was measured. Data about the dimensionality and amplitude of the fluctuation were obtained by analyzing the fluctuation conductivity on the basis of the Aslamazov–Larkin theory. The fluctuation conductivity of the undoped sample shows three-dimensional behavior in the mean-field region (MFR) with a one-dimensional (1D) character at further higher temperature. The effect of a small amount of Ag addition is manifested on a fractal conduction behavior in the 1D region of the undoped sample. Upon further Ag-doping, the conduction behavior is two-dimensional in the MFR with evidence for a rapid suppression of the short-wavelength fluctuation. The conduction behavior is discussed on the relevance to structural features of melt-textured YBCO samples with and without Ag-doping.

Effect of grain boundaries on paraconductivity of YBa2Cu3Ox

To investigate the effect of grain boundaries on paraconductivity of YBa2Cu3Ox, melt-textured and c-axis oriented thin films with controlled grain boundaries (superconducting transition width, ΔT, varying between 0.54 and 2.85K) were prepared, and dc-conductivity has been measured as a function of temperature. In the logarithmic plots of excess-conductivity (Δσ) and reduced temperature (ϵ), starting from low values of ϵ, we have observed three different regions namely critical region, mean field region and short wave fluctuation region. A correlation is observed between the range of critical region and ΔT, which is found to increase with ΔT. While for ΔT values smaller than 2.5K only static critical region is observed, for higher ΔTs both static and dynamic critical regions are observed. In the mean field region a crossover from 3D to 2D was observed for all the samples. At ϵ values larger than 0.24, the excess-conductivity decreased sharply as ϵ−3, which suggested the existence of the short wave fluctuations.

Effect of cooling rate and strontium doping on the formation of(Hg, Tl)-1234 phase

Superconductor samples of nominal compositionHg1-xTlxBa2Ca3Cu4O10+δ (0.3⩽x⩽1.0) areprepared at ambient pressure using a closed quartz tube at 850 °C.X-ray powder diffraction for the prepared samples is carried out and theresults show that the structure of this system is a tetragonal. The latticeparameters a and c are calculated, and the data indicate that a is notaffected by the substitution of Tl3+ into Hg2+, whereas cdecreases as the Tl content increases. The superconductivity is investigatedusing the electrical resistance and ac magnetic susceptibility measurements.All the samples have a superconducting behaviour except when x = 0.3. Toimprove the superconducting properties of this system, the cooling rate forthe sample with x = 0.7 is studied; also the replacement of Ca by Sr for bothx = 0.3 and x = 0.5 have been investigated. The excess conductivity forx = 0.3 shows that the dimensionality is changed from two-dimensional in thehigh-temperature region to three-dimensional in the mean field region.

Flow dichroism in critical colloidal fluids.

Due to long-range correlations and slow dynamics of concentration fluctuations in the vicinity of the gas-liquid critical point, shear flow is very effective in distorting the microstructure of near-critical fluids. The anisotropic nature of the shear-field renders the microstructure highly anisotropic, leading to dichroism. Experiments on the dichroic behavior can thus be used to test theoretical predictions on microstructural order under shear flow conditions. We performed both static and dynamic dichroism and turbidity measurements on a colloid-polymer mixture, existing of silica spheres (radius 51 nm) and polydimethylsiloxane polymer (molar weight 204 kg/mol). Sufficiently far away from the critical point, in the mean-field region, the experimental data are in good agreement with theory. Very close to the critical point, beyond mean field, for which no theory exists yet, an unexpected decrease of dichroism on approach of the critical point is observed. Moreover, we do not observe critical slowing down of shear-induced dichroism, right up to the critical point, in contrast to the turbidity.

Phase structures and morphologies determined by self-organization, vitrification, and crystallization: confined crystallization in an ordered lamellar phase of PEO-b-PS diblock copolymer

Phase morphology, crystal orientation, and overall crystallization kinetics as determined by self-organization of the diblock copolymer, vitrification of the amorphous block, and crystallization of the crystallizable blocks have been investigated for a lamellar-forming poly(ethylene oxide)-b-polystyrene (PEO-b-PS) diblock copolymer. The diblock copolymer has number-average molecular weights of 8700g/mol for the PEO blocks and 9200g/mol for the PS blocks. Based on wide angle X-ray diffraction (WAXD) observations, the PEO crystals possess the same crystal structure as pure PEO. When the crystallization temperature (Tc) is below 40°C, the PEO crystals melt below 55°C, which is much lower than the melting point of their homopolymer analogs. The glass transition temperature of the PS blocks is 62°C, determined by the 50% heat capacity change during vitrification observed in differential scanning calorimetry (DSC). The order–disorder transition temperature is determined to be 160°C using a one-dimensional (1D) small angle X-ray scattering (SAXS) experiment. The mean-field segmental interaction parameter is determined to be χEO/St=−7.05×10−3+21.3/T, based on the SAXS scattering intensity analysis for T>TMF (crossover temperature from the concentration-fluctuation region to the mean-field region). Using real-time resolved simultaneous SAXS and WAXD techniques, the PEO block is observed to crystallize within the confined lamellae provided by the glassy PS layers. The crystal (the ĉ−axis) orientation within the confined lamellae is determined by combined two-dimensional (2D) SAXS and WAXD experiments. The PEO crystals are observed to tilt away from the lamellar surface normal (n̂) at Tc<35°C, while they are oriented parallel to n̂ when crystallized above 35°C. The thickness changes in the lamellar phase morphology after isothermal crystallization can also be observed when compared with that in the molten state using 1D SAXS. After the crystallization of PEO blocks, the phase lamellar thickness slightly decreases with decreasing Tc when Tc<35°C. When Tc>35°C, the lamellar thickness slightly increases with increasing Tc. At Tc=35°C, the thickness remains identical to that in the molten state. The increase of phase lamellar thickness may be a result of both dimensional change of the crystal growth via thickening of PEO lamellar crystals, and weakening of the confinement of the PS glass layers. The isothermal crystallization kinetics and melting results observed in DSC also support these conclusions.

Influence of thermodynamic fluctuations on the thermoelectric coefficient in Ag-doped Bi-samples

We present a study of the thermoelectric coefficient L(T) of polycrystalline Ag-doped BSCCO superconducting samples. Polycrystalline samples of nominal composition (Bi 1.6Pb 0.4)Sr 2Ca 2(Cu 1−xAg x) 3O 10+δ and (Bi 1.6Pb 0.4)Sr 2Ca 3(Cu (1−x)Ag x) 4O 12+δ with 0⩽x⩽0.1 were analyzed. For low level doping (0⩽x⩽0.005) the experimental results suggest that in the mean field region, L(T) be not affected by thermodynamic fluctuations of the superconducting order parameter (OPF).