Random Distribution Of Defects Research Articles

Long Josephson Junctions Modulated by Defects and Superconducting Microdomains in YBCO Thin Films

The critical current Jc of superconducting films is about two order of magnitude larger than that of single crystals. The dependence of such Jc on field depends on the presence and distribution of defects. We speculate that High Temperature Superconducting (HTS) films can be modeled as an agglomeration of islands coupled via Josephson contacts and then considered as a network of Long Josephson Junctions (LJJ) between superconducting islands. In order to check this hypothesis we further developed a model firstly introduced by Fehrenbacher based on the modulation of critical current densities in LJJ by means of suitable distribution of defects. The defects act by modulating the coupling energy of the junction. Critical current densities are calculated in the case of periodic and random defect distributions.

Effect of laser-induced defects on luminescence in InP crystals

Experimental data on luminescence in laser-modified InP crystals are compared with the theory of radiative recombination of heavily doped, compensated semiconductors. It is established that the band with maximum at 1.35 eV observed at 77 K is due to radiative transitions through the tails of the density of states which are formed as a result of the random distribution of defects and impurities showing up after laser treatment. The effective depth of the tails of the density of states is estimated to be equal to 67 meV.

Nonstoichiometry of Ce 0.9Gd 0.1O 1.95− x

Oxygen nonstoichiometry of Ce 0.9Gd 0.1O 1.95− x , as a function of temperature and P O 2 , was gravimetrically measured at temperatures from 700 to 1100°C and oxygen partial pressures between 10 −24 and 1 atm. Based on the experimental data, a defect model was discussed and partial molar enthalpy, Δ H O , and entropy, Δ S O , of oxygen were calculated. At temperatures higher than 800°C, oxygen nonstoichiometry, x, is proportional to the −1/4 power of P O 2 , showing that oxygen vacancies are doubly charged. At 700°C, however, x is proportional to the −1/4.6 power of P O 2 . For small x, Δ H O is independent of x, and Δ S O is in agreement with a theoretical calculation based on random distribution of defects. When x becomes larger, Δ H O increases and Δ S O deviates from the theoretical calculation.

Relating the ac complex resistivity of the pinned vortex lattice to its shear modulus

We propose a way to determine the shear rigidity of the pinned vortex lattice in high-purity crystals from the dependence of its complex resistivity $\ensuremath{\rho}\^{}$ on frequency $(\ensuremath{\omega})$. The lattice is modeled as an elastic medium pinned by a sparse, random distribution of defects. We relate $\ensuremath{\rho}\^{}$ to the velocity of the small subset of pinned vortices via the lattice propagator $G(\mathbf{R},\ensuremath{\omega})$. Measuring $\ensuremath{\rho}\^{}$ versus $\ensuremath{\omega}$ is equivalent to determining $G(\mathbf{R},\ensuremath{\omega})$ versus $R$. The range of $G(\mathbf{R},\ensuremath{\omega})$ depends sensitively on the shear and tilt moduli. We describe the evaluation of $G(\mathbf{R},\ensuremath{\omega})$ in two-dimensional (2D) and 3D lattices. The 2D analysis provides a close fit to the frequency dependence of Re$\ensuremath{\rho}\^{}$ measured in an untwinned crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ at 89 K in a field of 0.5 and 1.0 T. We compare our results with earlier models.

The modelling of adhesion in multilayer films with layers of diamond-like and related materials

The mathematical model of adhesion in two-layer films, with one of the layers made by the PVD method, is considered. The model is built on the correlation of the linear mechanics of failure for the environment with the random distribution of defects on the border of the layers. Characteristics for determination of average critical stresses and specific adhesion work are proposed. The assessment of the model was carried out on the basis of experimental data, obtained by the scratch test. A method for the assessment of the coating durability is suggested.

The shift of surface phonon dispersion curves due to defects in alloy disordered surfaces

A formalism for calculating the shift of surface phonon dispersion curves due to the presence of defects in surface alloys is presented, using the matching technique and an effective field approach that goes beyond the virtual crystal approximation. Numerical results are examplified in the form of surface phonon dispersion curves for random distributions of defects, shifted as a function of defect concentrations, (0⩽ c ∗⩽1), defect mass (light and heavy), and realistic model values for defect-crystal and defect-defect interactions. Significant shifts ∽30% are found, that would be measurable within instrumental resolution of He atom scattering and EELS.

Theoretical Calculations of the Nonlinear Dielectric Function of Inhomogeneous Thin Films

ABSTRACTThe optical response of thin dielectric films can be influenced by grain morphology and the presence and distribution of defects. In the limit of random defects and small electric field amplitudes, approximate methods exist to model the real part of the dielectric constant in terms of volume fractions and bulk dielectric constants of the film components. Explicit inclusion of nonlinear polarizabilities and details of the microstructure, such as particle phase, shape, and orientation requires a more exact approach.We have developed a method to self-consistently determine the local internal electric field and polarization in the long wavelength limit for model films with a random distributions of defects of arbitrary phase and orientation. From this we have calculated the real part of the dielectric constant as a function of nonlinear polarizability of the components, and have shown the effect of defect phase and orientation on the dielectric constant of the film.

Scattering of thermal atoms by disordered surfaces: II. Adsorbed defects

We consider a periodic surface on which defects are absorbed. An incident particle is scattered by this surface and the solution of the scattering equation is given by an expansion where the term of order n gives the multiple scattering effects on n defects. The coherent peak intensities and the incoherent cross section are expressed as functions of matrix elements describing the scattering process and of the many body correlation functions of defect positions. The diffraction peak intensities of the perfect surface are modified by the presence of defects and on a flat surface they induce an increase of the small diffraction peak intensities. The incoherent cross section is periodic on the reciprocal lattice of defect sites and is reinforced around the most intense diffraction peaks. For small coverage, this cross section is equal to the product of a form factor and the Fourier transform of the two body correlation function. For a random distribution of defects, the correlation functions are constant and a measurement gives directly the form factor. For coverages near 0.5, the defects can gather in domains. In this case, one can show that an oscillation of diffraction peak heights or widths should be observed as the incident conditions vary.

Closed-time distribution of ionic channels. Analytical solution to a one-dimensional defect-diffusion model

A one-dimensional version of the model recently proposed by Läuger (1988) to explain the closed-time distribution of ionic channels in cell membranes is solved analytically. While the probability density f(t) for closed-time lengths may show a well-defined exponential behavior at short times, a power-law decay is predicted at long times. The influence of an additional random distribution of defects in the current-conducting protein is investigated and found to be dominating at long times. Explicit expressions that may be used for fitting experimental data are given for the closed-time distribution. Some of the available data are discussed and shown to be in good agreement with the predictions of the model.

Critical Currents in the YBaCuO Compound Superconducting Thin Films

This note contains information on the properties of epitaxial thin films of the high temperature YBaCuO compound superconductors. Some thoughts regarding critical current and mechanisms of vortex pinning are presented. It is suggested that one of the more effective mechanism of pinning is associated with a random distribution of defects which perturb the condensation energy. The defects are on the scale of the coherence length.

A neutron diffraction and 170Yb Mössbauer investigation of the perovskite ytterbium titanium oxide

A phase with the perovskite structure ( Pbnm) and a composition YbTiO 2.95 has been prepared by a high-temperature carbothermic method. Neutron diffraction shows a colinear ferrimagnetic structure at 7 K with Yb and Ti moments antiparallel along the c-axis of the orthorhombic cell and an Yb moment of 1.8(3)μ B. 170Yb Mössbauer measurements find a more precise and accurate value of 2.0(1)μ B from the maximum hyperfine field. From the temperature dependence of the hyperfine field a T c = 42(1) K is found. The Yb sublattice magnetization below T c follows a Brillouin function. At low temperature a distribution of hyperfine fields is observed which is attributed to a random distribution of defects surrounding the Yb sites. The magnetic structure is discussed in relation to possible values for the crystal field parameters, especially B 2 0.

Random strain broadening of hydrogenic donors in piezoelectric semiconductors and alloys

Static strains in piezoelectric semiconductors or alloys give rise to an electric field or potential which can have an effect on the electrical properties of the material. We calculate the effect of these fields due to a random distribution of defects or compositional disorder on the line shape of hydrogenic transitions of donor states. Our results may explain the very broad lines observed in III-V alloys.

Uncertainty on the mean strength and Weibull's modulus of an alumina batch as a function of the number of samples

Sintering of powders is the main process used to produce ceramic materials. It may induce various defects, such as pores, voids or inclusions. Moreover, other defects are induced when machining pieces (cutting, polishing, etc.) the most common of them being streaks and the pull-out of grains. The defects control the initiation of brittle fracture and their efficiency as crack initiators is dependent on their size and shape. Besides, this efficiency is greater when the critical defect lies in the vicinity of a high stress tensile zone. The random distribution of defects leads to a random distribution of the measured values of strength: so, these values can be understood only in the frame of a statistical analysis. Among the studies dealing with this question, Weibull's theory of the "weakest link" [1] is the most commonly used, but more refined analyses can be developed [2, 3]. From the experimental point of view, an important question concerns the number of samples which is required for an accurate determination of Weibull's parameters. The present note is devoted to this point. Weibull's analysis links the survival probability of a piece, Ps, to the applied stress, a, by means of the relation:

Defects in the Sine-Gordon model: Statics

The one-dimensional Sine-Gordon model where the field couples linearly to localized defects is studied. This model describes the phase fluctuations of one-dimensional charge density waves if amplitude fluctuations are neglected. For isolated defects the nonlinear stationarity conditions can be solved analytically. Given these stationary solutions the fluctuation spectrum consisting of a bound state and the scattering states and the relevant correlation functions can be computed exactly. The stationary states for a system of two defects are presented. The free energies as a function of the separation of the defects is computed for the absolutely stable states and for the local minima of the free energy function. This allows us to consider the interaction of the defects induced by the Sine-Gordon field. Finally we compute the order parameter correlation function for a random distribution of defects for small concentrationn. Devising a cumulant expansion the correlation function is found exactly in the first order inn. Our result contains the combined effect of the defects on the stationary states and on the phonon Green's function. It has applicability beyond the present context.

Dynamics of crystals with correlated defect positions

We present a treatment of crystals containing point defects in which deviations from random defect distributions are taken into account. Known averaging procedures which presuppose randomness of atomic disorder are generalized in order to deal with defect site correlations. The quasicrystalline-approximation-type theory obtained if the pure host crystal is taken as the reference system (which is applicable only to the case of low defect concentrations) is generalized by taking a (random) defect crystal as reference system. This allows a treatment of site-correlation effects also in materials with high defect concentrations. The method is applicable to solid solutions with an arbitrary number of components. For crystals with correlated defect sites, average Green's functions (no atom type specified at any lattice site), and conditionally averaged Green's functions (atom of a specific type---host or defect---at a certain site) are calculated. These two types of Green's functions are then used to determine scattering functions, dispersion curves, and fluctuations at host and defect sites. As a direct application to experiment the method is used to calculate explicitly the change of the polarization of a displacive ferroelectric due to defect site correlations. Realistic correlations are shown to lead to considerable ${T}_{c}$ shifts.

Analysis of solar cell array performance with open-circuit defects

The performance of solar cell arrays is greatly influenced if shading, open-circuit defects or short-circuit defects are present. The influence of these factors depends on the design configuration of the solar cell array, so it is important to search for solar cell arrays that are tolerant of such defects and give satisfactory performance with a wide range of defect structures. An analysis is presented here that concentrates on the effects of open-circuit defects in arrays with and without bypass diodes. Since an array of 10 4 cells or more has many series blocks and parallel branches, the algorithms for the analysis in the presence of a random distribution of defects become quite involved. Such algorithms are presented and a few examples are given of their application. This provides the basis for future comparative studies of desirable array configurations and the extension of the analysis to deal with short-circuit defects or lowered performance associated with shading or cell deterioration.

The core structure of shish-kebab crystals of polyethylene

Dark-field electron micrographs obtained from thin webs of ultra-high molecular weight polyethylene shish-kebab crystals grown at 106 and 112°C show a random distribution of crystal defects with a mean separation of about 30 nm. Thermal shrinkage of these crystals also indicates a random distribution of defects, but with a mean separation of ∼1 μm. However, shrinkage is only affected by defects equivalent to complete loss of crystalline order, whereas electron microscopy is affected by single dislocations. Thus the core consists of long, but finite, crystals containing many randomly distributed defects.

Modification of Poisson statistics: modeling defects induced by diffusion

This paper examines a model of LSI device failure and the departure from Poisson statistics that it necessitates. By visually mapping anodically decorated transistors, the authors found that in highly defective sites, emitter-collector shorts-pipes-tend to collect in clusters of totally defective areas. Less defective sites have a nearly random distribution of defects, though some limited clustering may still exist. In general, a slightly curved relationship is obtained when the logarithm of actual yield is plotted versus area. However, for a small enough area, such as a single chip, one can make a linear approximation and use it to estimate the fraction of the area that is totally defective, and the defect density. The paper describes an analytical method of modeling device failures, and of projecting yields for areas larger than the data base from which the parameters of the yield equation were estimated.

Defect characterization in CeO 2−x at elevated temperatures—II : Neutron diffraction

Polycrystalline CeO 2−x(0⩽ x⩽ 0.21) has been examined at 900°C by means of neutron diffraction to characterize the predominant atomic point defects responsible for nonstoichiometry. The stoichiometry was controlled by adjusting the oxygen partial pressure between 1 and 10 −21 atm. For x ⩽ 0.11, good agreement (residual ⩽ 1.0%) is obtained by assuming a random distribution of defects on the oxygen sublattice. Vacancy concentrations obtained from the neutron-data analysis are in agreement with thermogravimetric determinations. Over this region of x, the temperature factors of both the cation and anion increase with an increase in vacancy concentration, which implies greater root-mean-square (r.m.s.) displacement of the atoms. However, for x > 0.11, the analysis of the neutron data indicates a smaller anion vibrational amplitude than in the near-stoichiometric compositions and is accompanied by a shift in the equilibrium position of the oxygen atoms. The effect of anharmonic thermal motion has also been considered, but alone, cannot explain the neutron data. The results of the present study correlate well with the previous X-ray experiment.

On the scattering of X-rays by structures containing a random distribution of defects

A recent treatment of the diffuse scattering of X-rays by defect structures (Keating 1968) has been shown to contain an approximation which is incorrect in the first order of the concentration of the defects (Hall 1969). When correctly treated the diffuse scattering is referred to the mean (dilated) lattice and the diffuse scattering attenuated by the same factor as the Bragg reflections. This treatment avoids expanding any exponential in powers of its argument.