Backbone of conductivity in two-dimensional metal-insulator composites

In percolation theory, the backbone is defined by chopping off dangling ends from the percolating cluster. For structures with high degree of spatial correlation, as they are typical for porous thin films, trimming of the full structure to reveal the part determining the electrical conductivity is more subtle than the classic definition of the backbone. To expand the applicability of the concept, we present a purely geometric definition for the backbone of a two-dimensional percolating cluster. It is based on a sequence of image analysis operations defining the backbone in terms of an image filter. The change of both area fraction and effective conductivity induced by applying the backbone filter to various binary images and a two-parameter family of sets is assessed by numerical means. It is found that the backbone filter simplifies the geometry of complex microstructures significantly and at the same time preserves their electrical DC behavior. We conclude that the backbone will be useful as a first ingredient for a geometric estimator of the effective conductivity of metal-insulator composites

Microstructure of melt-processed Bi2Sr2CaCu2Oy and reaction mechanisms during post heat treatment

Phase compositions and microstructures of melt processed 2212 were studied. 2212 starting powder was cooled from temperatures between 910 °C and 1100 °C in air at rates ranging from 350 K/min to 0.083 K/min. The solidification sequence was established for all cooling rates. Under all conditions the Bi-free (Sr, Ca)CuO2 (01x1) is the primary phase. The one-layer solid solution 11905 nucleates on this phase. The residual liquid solidifies to a glassy state, decomposes into the eutectic of Cu2O and Bi2Sr2.1Ca0.9Ox, or reacts with the primary phase and the 11905 forming 2212 at high, intermediate, or low cooling rates, respectively. Post solidification heat treatment at 850 °C in air leads to partial remelting. The Cu-rich liquid reacts with 11905 and 01x1 forming 2212. Subsequent solid/solid reactions lead to a high volume fraction of 2212 with almost ideal 2 : 2 : 1 : 2 stoichiometr

From imperfect to perfect Bi2Sr2CaCu2Ox (Bi-2212) grains

The 2212 phase formation during annealing of melt textured Bi-2212 (Bi2Sr2CaCu2Ox) was investigated using differential thermal analysis, thermal gravimetric analysis, x-ray diffraction, scanning electron microscopy, energy dispersive x-ray analysis, and high resolution transmission electron microscopy. After zone melting, the material is multiphase consisting of 2212, 2201, Sr1−xCaxCuO2, and the eutectic. The 2212 phase formed is highly perfect with less than 5% intergrowths of 2201 layers; the 2201 phase shows no intergrowth of 2212 at all. In the first period of the annealing, remelting of the eutectic leads to fast oxygen diffusion and a high 2212 formation rate. The 2201 → 2212 transformation proceeds via intermediate states of high defect density. The 2212 grains contain up to 30-70% 2201 intergrowths. Further heat treatments lead to an annihilation of the great majority of intergrown 2201 layers. We propose a model for the formation of 2212 grains with a low planar defect density, based on frequent stacking faults, that allows diffusion of Ca- and Cu-atoms over a short distance. The model provides a schematic description of this solid-state process and correlates it to the characteristic microstructural features of melt-processed Bi-221

Thermodynamic modeling of La2O3-SrO-Mn2O3-Cr2O3 for solid oxide fuel cell applications

The thermodynamic La-Sr-Mn-Cr-O oxide database is obtained as an extension of thermodynamic descriptions of oxide subsystems using the calculation of phase diagrams approach. Concepts of the thermodynamic modeling of solid oxide phases are discussed. Gibbs energy functions of SrCrO4, Sr2.67Cr2O8, Sr2CrO4, and SrCr2O4 are presented, and thermodynamic model parameters of La-Sr-Mn-Chromite perovskite are given. Experimental solid solubilities and nonstoichiometries in La1−x Sr x CrO3−δ and LaMn1−x Cr x O3−δ are reproduced by the model. The presented oxide database can be used for applied computational thermodynamics of traditional lanthanum manganite cathode with Cr-impurities. It represents the fundament for extensions to higher orders, aiming on thermodynamic calculations in noble symmetric solid oxide fuel cell

Generation of Porous Particle Structures using the Void Expansion Method

The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller "void-particles". Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles' mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure

Thermodynamic modeling of La₂O₃-SrO-Mn₂O₃-Cr₂O₃ for solid oxide fuel cell applications

ISSN:0884-2914ISSN:2044-532

The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February 2012

From imperfect to perfect Bi2Sr2CaCu2Ox (Bi–2212) grains

ISSN:0884-2914ISSN:2044-532