Macroscopic Inhomogeneities Research Articles

Features of the temperature dependence and magnetic-field dependence of the critical current density close to the critical temperature in YBa2Cu3O7−δ thin films

The temperature dependence of the critical density of superconducting current jc(τ) [τ=(1−T∕Tc), and Tc is the critical temperature] of two epitaxial c-oriented YBa2Cu3O7−δ thin films grown on LaAlO3 and SrTiO3 substrates has been investigated by the method of dynamic magnetic susceptibility. In both samples, the jc(τ) dependence has two sections with power dependences jc∼τ3∕2 and jc∼τ2 in the temperature region from 77K to Tc, with crossover between them. Measurements were made of the temperature dependences of the dynamic relaxation rate Q(τ) (magnetic flux creep), which turned out to be unconnected with the observed crossovers. It is shown that the observed features of jc(τ) are not caused, as was assumed earlier, by the limitation of the critical depairing current density in the interdislocation gaps of the interblock boundaries of YBa2Cu3O7−δ epitaxial thin films. Based on numerical calculations, it is shown that the existence of crossovers and the breakdown of H∕τ scaling detected in one of the samples (H is the dc magnetic field) in the jc(τ,H) magnetic-field dependences close to Tc can be explained by the manifestation of macroscopic inhomogeneity of the samples in the local values of the critical temperature Tc (Tc inhomogeneity). The absence of observable breakdown of the H∕τ scaling in the second sample is explained by the smaller width of the distribution over Tc in it by comparison with the first sample.

SUPERFLUID VORTEX UNPINNING AS A COHERENT NOISE PROCESS, AND THE SCALE INVARIANCE OF PULSAR GLITCHES

The scale-invariant glitch statistics observed in individual pulsars (exponential waiting-time and power-law size distributions) are consistent with a critical self-organization process, wherein superfluid vortices pin metastably in macroscopic domains and unpin collectively via nearest-neighbor avalanches. Macroscopic inhomogeneity emerges naturally if pinning occurs at crustal faults. If, instead, pinning occurs at lattice sites and defects, which are macroscopically homogeneous, we show that an alternative, noncritical self-organization process operates, termed coherent noise, wherein the global Magnus force acts uniformly on vortices trapped in a range of pinning potentials and undergoing thermal creep. It is found that vortices again unpin collectively, but not via nearest-neighbor avalanches, and that, counterintuitively, the resulting glitch sizes are scale invariant, in accord with observational data. A mean-field analytic theory of the coherent noise process, supported by Monte Carlo simulations, yields a power-law size distribution, between the smallest and largest glitch, with exponent a in the range −2 ⩽ a ⩽ 0. When the theory is fitted to data from the nine most active pulsars, including the two quasi-periodic glitchers PSR J0537−6910 and PSR J0835−4510, it directly constrains the distribution of pinning potentials in the star, leading to two conclusions: (1) the potentials are broadly distributed, with the mean comparable to the standard deviation; and (2) the mean potential decreases with characteristic age. Fitting the theory to the data also constrains the pinned vortex fraction and the rate of thermal creep. An observational test is proposed to discriminate between nearest-neighbor avalanches and coherent noise: the latter process predicts a statistical excess of large glitches ("aftershocks") following a large glitch, whereas the former process does not. Its discriminatory power is discussed under various microphysical scenarios.

Inhomogeneity of deformation of solids at the nanometer level

A new method for processing interferometrically recorded deformation data has been implemented for studying an inhomogeneity in the rate and parameters of deformation jumps at the nanostructure level, which provides detection of deformation jumps of less than 300 nm. It is shown that the lower limit for deformation jumps lies in the range 10–30 nm for aluminum and is 130 nm for amorphous polymer (poly(methyl methacrylate)). It is assumed that the sizes of jumps correspond to scales of ordered structures, as was previously established for higher level structures. The results obtained make it possible to investigate more thoroughly the multilevel character of deformation and to evaluate the sizes of the nanostructural units, their evolution during deformation and under the effect of external fields, as well as their relation to the microscopic and macroscopic inhomogeneities of deformation.

Effect of nature and type of flaw on the properties of a natural rubber compound

Fracture in rubber, like in all other materials, is initiated at imperfections inadvertently present or introduced in the body of the material or on the surface during processing. The point of initiation of fracture in the rubber is usually at flaws which are macroscopic or microscopic imperfections or inhomogeneities in the rubber. In order to investigate the effect of these flaws on the properties of a natural rubber compound, cuts to mimic weld lines were introduced before and near scorch at various cure temperatures, and the time for a complete healing of these cuts determined. The tensile properties were not significantly affected by the introduction of weld lines before scorch provided sufficient time was allowed for healing. Healing time reduced with increase in cure temperature. The intrinsic flaw sizes in a material inherently affect the material tensile properties and depend significantly on the size of the flaw. Pinhole flaws of varying sizes introduced after cure had a significant effect on both tensile strength and fatigue life with the pinhole equivalent intrinsic flaw size estimated to be about 200 μm.

Sensitivity of feedback‐enhanced MRI contrast to macroscopic and microscopic field variations

Nonlinear feedback interactions have been shown to amplify contrast due to small differences in resonance frequency arising from microscopic susceptibility variations. Determining whether the selectivity of feedback-based contrast enhancement for small resonance frequency variations remains valid even in the presence of macroscopic field inhomogeneity is important for transitioning this new methodology into in vivo applications in imaging systems with lower field strengths and poorer homogeneity. This work shows that contrast enhancement under the radiation damping (RD) feedback field is sensitive to microscopic intravoxel frequency variations. Feedback-enhanced contrast provides superior signal differentiation from voxels with distinct microscopic frequency distributions compared with T(2)*-weighted imaging, while remaining robust to macroscopic field gradients, which frequently give rise to artifacts by other frequency-sensitive methods. Applying multiple RF pulses during evolution under RD and actively adjusting the phase and amplitude of the feedback field are shown to further improve signal differentiation. Experimental results reveal that feedback-enhanced contrast can generate positive contrast, reflecting microscopic field variations induced by strong local dipole fields, such as those created by blood vessels and superparamagnetic iron oxide nanoparticles. Extensions to in vivo imaging at lower field strengths are discussed in the context of amplifying the RD field via active electronic feedback.

Reduction of susceptibility-induced signal losses in multi-gradient-echo images: Application to improved visualization of the subthalamic nucleus

T2⁎-weighted gradient echo (GE) images yield good contrast of iron-rich structures like the subthalamic nuclei due to microscopic susceptibility induced field gradients, providing landmarks for the exact placement of deep brain stimulation electrodes in Parkinson's disease treatment. An additional advantage is the low radio frequency (RF) exposure of GE sequences. However, T2⁎-weighted images are also sensitive to macroscopic field inhomogeneities, resulting in signal losses, in particular in orbitofrontal and temporal brain areas, limiting anatomical information from these areas. In this work, an image correction method for multi-echo GE data based on evaluation of phase information for field gradient mapping is presented and tested in vivo on a 3 Tesla whole body MR scanner. In a first step, theoretical signal losses are calculated from the gradient maps and a pixelwise image intensity correction is performed. In a second step, intensity corrected images acquired at different echo times TE are combined using optimized weighting factors: in areas not affected by macroscopic field inhomogeneities, data acquired at long TE are weighted more strongly to achieve the contrast required. For large field gradients, data acquired at short TE are favored to avoid signal losses. When compared to the original data sets acquired at different TE and the respective intensity corrected data sets, the resulting combined data sets feature reduced signal losses in areas with major field gradients, while intensity profiles and a contrast-to-noise (CNR) analysis between subthalamic nucleus, red nucleus and the surrounding white matter demonstrate good contrast in deep brain areas.

Causes of incorrect carrier-type identification in van der Pauw–Hall measurements

The impact of macroscopic sample inhomogeneity and contact placement on the measured carrier type and concentration in the widely used van der Pauw–Hall method is investigated using finite-element analysis of the electrostatics. A variety of likely macroscopic inhomogeneities in mobility or carrier concentration across a square-shaped sample are considered. Inhomogeneities in mobilities do not affect the measured carrier type and concentration, as long as the carrier concentration remains homogeneous. Inhomogeneities in carrier concentrations can result in an incorrect assignment of the carrier type. However, when contacts are placed at the sample corners and not inside the sample area, the correct carrier type is recovered. Our calculations provide an explanation for recent measurements on ZnO [Ohgaki et al., J. Mater. Res. 23, 2293 (2008)]. Guidelines for avoiding incorrect interpretation of van der Pauw–Hall measurements are provided.

A single‐scan T mapping method based on two gradient‐echo images with compensation for macroscopic field inhomogeneity

T2*-weighted imaging (T2*WI) and quantitative T2* mapping with conventional gradient-echo acquisition are often hindered by severe signal loss induced by macroscopic field inhomogeneity. Various z-shimming approaches have been developed for T2*WI/T2* mapping in which the effects of macroscopic field inhomogeneity are suppressed while the sensitivity of T2*-related signal intensity to alterations in the microscopic susceptibility is maintained. However, this is often done at the cost of significantly increased imaging time. In this work, a fast T2* mapping method with compensation for macroscopic field inhomogeneity was developed. A proton density-weighted image and a composite T2*-weighted image, both of which were essentially free from macroscopic field inhomogeneity-induced signal loss, were used for the T2* calculation. The composite T2*-weighted image was reconstructed from a number of gradient-echo images acquired with successively incremented z-shimming compensation. Because acquisition of the two images and z-shimming compensation were realized in a single scan, the total acquisition time for obtaining a T2* map with the proposed method is the same as the time taken for a conventional multiecho gradient-echo imaging sequence without compensation. The performance and efficiency of the proposed method were demonstrated and evaluated at 4.7 T.

How acoustic waves are guided in buried subsurface channels in unconsolidated granular media

We show the existence of natural subsurface channels that guide acoustic waves for periodic arrays of spherical grains under the influence of gravity. Downward propagation of acoustic rays can be stopped altogether as a result of a caustic whose origin lies in the continuous bending of rays as a result of a gravitationally induced increase of rigidity with depth. Upward propagation of acoustic rays, on the other hand, is attenuated by Bragg reflection arising from the continuous diminishing of rigidity in the direction of the surface, resulting in a vertical propagation constant that approaches a limited allowed value. Waves with different frequencies are shown to travel at different depths below the surface. The key conditions for the manifestation of the predicted wave modes are microscopic periodicity and macroscopic inhomogeneity of the medium.

Control of susceptibility-related image contrast by spin-lock techniques

Macroscopic magnetic field inhomogeneities might lead to image distortions, while microscopic field inhomogeneities, due to susceptibility changes in tissues, cause spin dephasing and decreasing T(2)() relaxation time. The latter effects are especially observed in the trabecular bone and in regions adjacent to air-containing cavities when gradient-echo sequences are applied. In conventional MRI, these susceptibility-related signal voids can be avoided by applying spin-echo (SE) techniques. In this study, an alternative method for the examination and control of susceptibility-related effects by spin-lock (SL) radiofrequency pulses is presented: SL pulses were applied in two different susceptibility-sensitive sequence types: (a) between the jump and return 90 degrees pulses in a 90 degrees (x)-tau-90 degrees (-x) magnetization-prepared Fast Low Angle Shot (FLASH) sequence and (b) between the 90 degrees pulse and the 180 degrees pulse in an asymmetric SE sequence. The range of Larmor frequencies used for spin locking can be determined for different B(1) amplitudes of the SL pulses, allowing control of image contrast by the amplitude of the SL pulses.

Last Passage Percolation in Macroscopically Inhomogeneous Media

In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the deterministic limiting shape of the maximal path. We obtain a sufficient analytical condition for uniquenes of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.

Cathodoluminescence Study of InGaN/GaN Quantum-Well LED Structures Grown on a Si Substrate

Crack-free InGaN/GaN quantum-well (QW) light-emitting diode (LED) structures were grown on a patterned Si substrate. Spatially resolved cathodoluminescence was studied on these LED wafers. Cathodoluminescence (CL) emission spectra at room temperature and low temperature (82 K) were measured. A main LED peak (∼2.7 eV) and an additional peak (∼3.1 eV) in the emission spectra at 82 K were observed. Using CL spectra mapping measurements on a cross section of the sample, it can be clearly seen that the ∼3.1 eV emission comes from the interfacial layer between the p-AlGaN and the QWs. This observation was further verified by comparing spectra of specific points on the cross section by line scanning. The origin of such emission is discussed. Cathodoluminescence images, emission spectra, and x-ray energy dispersion spectra (EDS) showed that the In composition at a specific corner of the mesa was higher than that in the rest of the mesa. Such macroscopic inhomogeneity might be caused by gas dynamics on the patterned substrate.

Nonsaturating magnetoresistance of inhomogeneous conductors: Comparison of experiment and simulation

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and nonsaturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as 10μm. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random-resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag_(2±δ)Se and Ag_(2±δ)Te, in magnetic fields up to 55T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments.

Strain localization in compressed ZrO2(Y2O3) ceramics

Spatiotemporal distributions of local components of the distortion tensor of a nonplastic material—yttria partially stabilized tetragonal zirconia (YTZ) ceramics—have been studied under active compressive straining conditions using double-exposure speckle photography techniques. The strain localization patterns are presented and the features of macroscopic strain inhomogeneity in the elastic state of YTZ ceramics are considered.

T2* measurements in human brain at 1.5, 3 and 7 T

Measurements have been carried out in six subjects at magnetic fields of 1.5, 3 and 7 T, with the aim of characterizing the variation of T2* with field strength in human brain. Accurate measurement of T2* in the presence of macroscopic magnetic field inhomogeneity is problematic due to signal decay resulting from through-slice dephasing. The approach employed here allowed the signal decay due to through-slice dephasing to be characterized and removed from data, thus facilitating an accurate measurement of T2* even at ultrahigh field. Using double inversion recovery turbo spin-echo images for tissue classification, an analysis of T2* relaxation times in cortical grey matter and white matter was carried out, along with an evaluation of the variation of T2* with field strength in the caudate nucleus and putamen. The results show an approximately linear increase in relaxation rate R2* with field strength for all tissues, leading to a greater range of relaxation times across tissue types at 7 T that can be exploited in high-resolution T2*-weighted imaging.

Interfacial morphology and correlations in adsorption at a chemically structured substrate—exact results ind = 2

Adsorption at a one-dimensional planar substrate equipped with a localized chemical inhomogeneity is studied within the framework of a continuum interfacial model from the point of view of interfacial morphology and correlation function properties. Exact expressions for the one-point and two-point probability distribution functions PΓ(lΓ) and being the interface position above a fixed point Γ of the substrate, are derived for temperature corresponding to the inhomogeneity's wetting transition. It is demonstrated that in the limit of macroscopic inhomogeneity's size the net effect of the remaining homogeneous parts of the substrate on the interfacial morphology above the inhomogeneity is exactly equivalent to appropriate pinning of the interface at its boundaries. The structure of the average interfacial morphology and correlation function in this limit are discussed and compared to earlier results obtained for systems with homogeneous substrate.

Reaction–diffusion fronts with inhomogeneous initial conditions

Properties of reaction zones resulting from type reaction–diffusion processes are investigated by analytical and numerical methods. The reagentsA andB areseparated initially and, in addition, there is an initial macroscopic inhomogeneity in the distributionof the B species. For simple two-dimensional geometries, exact analytical results are presented forthe time evolution of the geometric shape of the front. We also show using cellularautomata simulations that the fluctuations can be neglected both in the shape and in thewidth of the front.

XRD evidence of macroscopic composition inhomogeneities in the graphite–lithium electrode

In situ and ex situ X-ray diffraction (XRD) measurements were carried out on lithiated graphite electrodes at different states of charge. Data were collected from both sides of electrode. We found macroscopic inhomogeneities in the lithium concentration along the electrode thickness even when the electrode was allowed to rest for 24 h. The electrode side facing the lithium counter electrode in the coin type half-cell displays higher lithium concentration as compared to the side opposed to the XRD window. Residual stage 2 compound is found in the supposedly fully lithiated and fully delithiated electrode. It seems that the differences in the chemical potential between stage 2 and stage 1 is too small to average the lithium composition through chemical diffusion at ambient temperature in reasonable times.

Nonlinearity of resistive impurity effects on van der Pauw measurements

The dependence of van der Pauw resistivity measurements on local macroscopic inhomogeneities is shown to be nonlinear. A resistor grid network models a square laminar specimen, enabling the investigation of both positive and negative local perturbations in resistivity. The effect of inhomogeneity is measured both experimentally, for an 11×11 grid, and computationally, for both 11×11 and 101×101 grids. The maximum “shortlike” perturbation produces 3.1±0.2 times the effect predicted by the linear approximation, regardless of its position within the specimen, while all “openlike” perturbations produce a smaller effect than predicted. An empirical nonlinear correction for f(x,y) is presented which provides excellent fit over the entire range of both positive and negative perturbations for the entire specimen.

Microstructural limits of TSMG REBCO bulk superconductors

The diameter of TSMG (top-seeded melt-growth) REBCO bulks is directly proportional to the trapped magnetic field. Unfortunately, the microstructural changes, which negatively influence superconducting and mechanical properties of the bulk, are associated with increasing sample diameter. Subgrains increase their misalignment with the growth length. The other microstructural phenomena limiting properties is a macroscopic inhomogeneity in 211 particle concentration. The refinement of 211 particles to increase critical current density (Jc) leads to their pushing mainly by the c-growth front. High 211 particle concentration inhomogeneity induces high thermal dilatation stresses into the bulk. Therefore, looking for new particles by additional alloying is fully approved. The shortening of lattice parameters with the oxygen concentration in the REBa2Cu3Ox phase is responsible for formation of cracks in the a/b- and a/c-planes during oxygenation. The role of these cracks is controversial. They significantly enhance oxygen penetration into the sample and shorten oxygenation time. High density of the a/c-cracks can allow for relaxation of macroscopic stresses and prevent fatal cracking of the sample. On the other hand they reduce the overall Jc of the sample.