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An electron microscopic study of gas condensates in the system Mg-Si-O-H

Condensates of MgSiO_3 and SiO_2 from a gas formed by evaporation of enstatite at an H_2 pressure of 4.4×10^ bar and a temperature of 1525℃ by B. O. MYSEN and I. KUSHIRO (Am. Mineral. (in press), 1988) and I. KUSHIRO and B. O. MYSEN (Advances in Physical Geochemistry, New York, Springer (in press), 1988) were investigated with an analytical transmission electron microscope (ATEM), a scanning electron microscope (SEM) and an electron probe microanalyzer (EPMA). With decreasing temperature at an approximately constant total pressure the Mg/(Mg+Si) atomic ratio of the condensate (mixture of MgSiO_3 and SiO_2 polymorphs) decreases first, then increases, and finally reaches a constant value. This compositional change of the condensate is inconsistent with the equilibrium condensation model. The TEM studies suggest that metastable condensation of coesite and probably of protoenstatite and cristobalite took place. Coesite probably condensed by heterogeneous nucleation on protoenstatite. Fibrous quartz was also formed by heterogeneous nucleation on molybdenum fibers which condensed from a molybdenum vapor by a partial evaporation of a Knudsen cell used in the experiment. Heterogeneous nucleation might have played an important role in condensation process in the solar nebula. The texture of the experimental clinopyroxene condensate is different from that in interplanetary dust particles (J. P. BRADLEY et al., Nature, 301,473,1983)

Unusual Low-Temperature Phase in VO2_2 Nanoparticles

We present a systematic investigation of the crystal and electronic structure and the magnetic properties above and below the metal-insulator transition of ball-milled VO$_2$ nanoparticles and VO$_2$ microparticles. For this research, we performed a Rietveld analysis of synchrotron radiation x-ray diffraction data, O $K$ x-ray absorption spectroscopy, V $L_3$ resonant inelastic x-ray scattering, and magnetic susceptibility measurements. This study reveals an unusual low-temperature phase that involves the formation of an elongated and less-tilted V-V pair, a narrowed energy gap, and an induced paramagnetic contribution from the nanoparticles. We show that the change in the crystal structure is consistent with the change in the electronic states around the Fermi level, which leads us to suggest that the Peierls mechanism contributes to the energy splitting of the $a_{1g}$ state. Furthermore, we find that the high-temperature rutile structure of the nanoparticles is almost identical to that of the microparticles.Comment: 7 pages, 8 figures, 2 table

Prolongation on regular infinitesimal flag manifolds

Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact structures, certain types of generic distributions and partially integrable almost CR-structures of hypersurface type. The aim of this article is to develop for a large class of (semi-)linear overdetermined systems of partial differential equations on regular infinitesimal flag manifolds $M$ a conceptual method to rewrite these systems as systems of the form $\tilde\nabla(\Sigma)+C(\Sigma)=0$, where $\tilde\nabla$ is a linear connection on some vector bundle $V$ over $M$ and $C: V\rightarrow T^*M\otimes V$ is a (vector) bundle map. In particular, if the overdetermined system is linear, $\tilde\nabla+C$ will be a linear connection on $V$ and hence the dimension of its solution space is bounded by the rank of $V$. We will see that the rank of $V$ can be easily computed using representation theory.Comment: 35 pages; typos corrected and minor changes, final version to appear in International Journal of Mathematic