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

Non-equilibrium effects of core-cooling and time-dependent internal heating on mantle flush events

International audienceWe have examined the non-equilibrium effects of core-cooling and time-dependent internal-heating on the thermal evolution of the Earth's mantle and on mantle flush events caused by the two major phase transitions. Both two- and three-dimensional models have been employed. The mantle viscosity responds to the secular cooling through changes in the averaged temperature field. A viscosity which decreases algebraically with the average temperature has been considered. The time-dependent internal-heating is prescribed to decrease exponentially with a single decay time. We have studied the thermal histories with initial Rayleigh numbers between 2 x 107 and 108 . Flush events, driven by the non-equilibrium forcings, are much more dramatic than those produced by the equilibrium boundary conditions and constant internal heating. Multiple flush events are found under non-equilibrium conditions in which there is very little internal heating or very fast decay rates of internal-heating. Otherwise, the flush events take place in a relatively continuous fashion. Prior to massive flush events small-scale percolative structures appear in the 3D temperature fields. Time-dependent signatures, such as the surface heat flux, also exhibits high frequency oscillatory patterns prior to massive flush events. These two observations suggest that the flush event may be a self-organized critical phenomenon. The Nusselt number as a function of the time-varying Ra does not follow the Nusselt vs. Rayleigh number power-law relationship based on equilibrium (constant temperature) boundary conditions. Instead Nu(t) may vary non-monotonically with time because of the mantle flush events. Convective processes in the mantle operate quite differently under non-equilibrium conditions from its behaviour under the usual equilibrium situations

Xenon Plasma Focused Ion Beam Milling for Obtaining Soft X ray Transparent Samples

We employ xenon (Xe) plasma focused ion beam (PFIB) milling to obtain soft X-ray transparent windows out of bulk samples. The use of a Xe PFIB allows for the milling of thin windows (several 100 nm thick) with areas of the order of 100 µm × 100 µm into bulk substrates. In addition, we present an approach to empirically determine the transmission level of such windows during fabrication by correlating their electron and soft X-ray transparencies. We perform scanning transmission X-ray microscopy (STXM) imaging on a sample obtained by Xe PFIB milling to demonstrate the conceptual feasibility of the technique. Our thinning approach provides a fast and simplified method for facilitating soft X-ray transmission measurements of epitaxial samples and it can be applied to a variety of different sample systems and substrates that are otherwise not accessibleISSN:2073-435

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