The volume of a compact hyperbolic antiprism

We consider a compact hyperbolic antiprism. It is a convex polyhedron with $2n$ vertices in the hyperbolic space $\mathbb{H}^3$. This polyhedron has a symmetry group $S_{2n}$ generated by a mirror-rotational symmetry of order $2n$, i.e. rotation to the angle $\pi/n$ followed by a reflection. We establish necessary and sufficient conditions for the existence of such polyhedra in $\mathbb{H}^3$. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formulas expressing the volume of a hyperbolic antiprism in terms of the edge lengths

Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals

The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing

Contactless processing of SiGe-melts in EML under reduced gravity

The processing of semiconductors based on electromagnetic levitation is a challenge, because this kind of materials shows a poor electrical conductivity. Here, we report the results of measurements of the thermophysical properties obtained recently from highly doped semiconductors Si1-x Ge x under microgravity conditions in the framework of parabola flight campaigns. Due to the limited time of about 20 s of microgravity especially Ge-rich samples with low melting temperatures were investigated. The measurements were performed contactlessly by video techniques with subsequent digital image processing. Linear and volume thermal expansion coefficients were measured hereby from image data. An anomaly of volume changes near the solidus temperature is visible. Viscosity and surface tension were determined by the oscillating drop technique using optic and electronic data. It was observed that the alloying of Si into Ge increases the surface tension of the melts. The viscosity is following an Arrhenius equation and shows a crossover temperature which separates simple liquid at high temperatures from cooperative liquid at low temperatures

Further investigations of the deep double donor magnesium in silicon

The deep double donor levels of substitutional chalcogen impurities in silicon have unique optical properties which may enable a spin/photonic quantum technology. The interstitial magnesium impurity (Mg$_i$) in silicon is also a deep double donor but has not yet been studied in the same detail as have the chalcogens. In this study we look at the neutral and singly ionized Mg$_i$ absorption spectra in natural silicon and isotopically enriched 28-silicon in more detail. The 1s(A$_1$) to 1s(T$_2$) transitions, which are very strong for the chalcogens and are central to the proposed spin/photonic quantum technology, could not be detected. We observe the presence of another double donor (Mg$_{i*}$) that may result from Mg$_i$ in a reduced symmetry configuration, most likely due to complexing with another impurity. The neutral species of Mg$_{i*}$ reveal unusual low lying ground state levels detected through temperature dependence studies. We also observe a shallow donor which we identify as a magnesium-boron pair

A Mg-pair isoelectronic bound exciton identified by its isotopic fingerprint in 28^{28}Si

We use the greatly improved optical linewidths provided by highly enriched $^{28}$Si to study a photoluminescence line near 1017 meV previously observed in the luminescence spectrum of natural Si diffused with Mg, and suggested to result from the recombination of an isoelectronic bound exciton localized at a Mg-pair center. In $^{28}$Si this no-phonon line is found to be comprised of five components whose relative intensities closely match the relative abundances of Mg-pairs formed by random combinations of the three stable isotopes of Mg, thus confirming the Mg-pair hypothesis. We further present the results of temperature dependence studies of this center that reveal unusual and as yet unexplained behaviour.Comment: 5 pages, 4 figure

Thermal Behavior of Fluorinated Double-Walled Carbon Nanotubes

Double-walled carbon nanotubes (DWNTs), produced by a catalytic chemical vapor deposition method, have been fluorinated using a volatile mixture of BrF3 and Br2. Optical absorption spectroscopic study on the product detected nonfluorinated nanotubes, which could correspond to the inner walls of DWNTs. The fluorinated DWNTs have been annealed in vacuum at fixed temperatures, and X-ray photoelectron spectroscopy showed almost no fluorine in the sample heated to 300 °C. Comparison between X-ray fluorescent C KR spectra of the pristine DWNT sample and the annealed fluorinated sample revealed change of the atomic structure of graphitic shells in the process of thermal defluorination