Estimation variances for estimators of product densities and pair correlation functions of planar point processes

Approximation, estimation variance, pair correlation function, Poisson process, product density, simulation,

Stereological analysis and modeling of gradient structures

Gradient structures are inhomogeneous along a particular gradient direction but homogeneous perpendicular to that direction. Consequently, structural parameters such as volume fraction or surface area density are local characteristics which depend on the \u2018vertical\u2019 coordinate with respect to the \u2018vertical\u2019 gradient axis. Analogously, models for gradient structures have model parameters depending on the vertical coordinate z. For example, a Voronoi tessellation with a gradient is generated by a gradient point process with a local intensity which is a function of z. Similarly, a gradient germ grain model is obtained from a gradient point process where the grain size distribution may also depend on z. For a gradient Boolean model, local volume fraction VV(z) and local surface area density SV(z) can be calculated from the model parameters. Stereological methods for gradient structures are based on vertical sections parallel to the gradient direction. Estimation of VV(z), SV(z) and local length density LV(z) is done by lineal analysis using horizontal test lines with vertical coordinate z. Similarly, lineal analysis is used to estimate local mean cell volume of gradient tessellations. For the estimation of local particle number density and size in the spirit of the Wicksell problem the use of kernel methods and distributional assumptions is required

Diffusion processes in hot-deformed Nd-Fe-B magnets with DyF3 additions

Nd-Fe-B melt spun ribbons have been hot-compacted and subsequently die-upset together with DyF3 in order to increase coercivity in nanocrystalline hot-deformed magnets. Magnetic measurements reveal enhanced coercivities for low and reduced coercivities for high Dy-fractions. This behaviour is due to a superposition of the formation of (Dy,Nd)(2)Fe14B and non-magnetic Dy and Nd fluoride and oxide phases. Energy dispersive and wavelength dispersive X-ray elemental maps verified this feature. Heat treatments at 600 degrees C induce a strong F diffusion along the flake boundaries without inducing grain growth. This diffusion is correlated with the changes in magnetic properties

Effect of melt convection on the secondary dendritic arm spacing in peritectic Nd-Fe-B alloy

Dendrites are one of the major microstructural constituents of peritectic alloys. In the present work, the effect of melt convection on the secondary dendritic arm spacing (SDAS) and volume fraction of properitectic alpha-Fe was investigated during solidification of stoichiometric Nd-Fe-B alloys using the forced crucible rotation technique. The resulting microstructure of the alloy in consideration of melt convection has been investigated using scanning electron microscopy and optical microscopy. The average SDAS was determined for each sample from the whole cross-section of the cylindrical test samples using image analyzing software LEICA QWIN. A detailed statistical analysis of the spacing distribution was performed on the basis of the variation of SDAS values, averaged from about 80 to 120 dendrites in different zones. The alpha-Fe volume fraction, measured by vibrating sample magnetometer (VSM), reduces with increasing crucible rotation frequency. Similarly, the SDAS values decrease with increasing rotation frequency. These results are explained from the viewpoint of a reduced melt convection state under steady forced crucible rotation leading to a reduced effective mass transfer coefficient. (C) 2009 Published by Elsevier B.V

Operation of spatial light modulators in DUV light

The Fraunhofer Institute for Microelectronic Circuits and Systems (FhG-IMS) has developed spatial light modulators (SLM), which are used in a pattern generator for DUV laser mask writing developed by Micronic Laser Systems. They consist of micromirror arrays and allow massive parallel writing in UV mask writers. The chip discussed here consists of 2048 × 512 individually addressable mirrors and can be run at a frame rate of 1 to 2 kHz. For this application it is necessary that the SLMs can be operated under DUV light without changing their performance. This paper discusses a failure mechanism of the SLMs when operated in DUV light and countermeasures to eliminate this effect