Relaxation structure analysis of Li inserted γ-Fe2O3

γ-Fe₂O₃ has a spinel structure with cation vacancy and is expected to perform as a favorable electrode material for secondary lithium-ion battery. When lithium is inserted electrochemically into γ-Fe₂O₃, prolonged potential change is observed after the insertion. In this study, we inserted various amount of Li into γ-Fe₂O₃ (x = 0.66, 1.1, 1.5 in terms of Li_XFe₂O₃), then made the circuit open, measured X-ray diffraction (XRD) patterns at various elapsed time, and analyzed the crystal structure change of γ-Fe₂O₃ with time by the Rietveld method. The X-ray Rietveld analysis revealed that the iron occupancy of 8a site decreased and that of 16c site increased with lithium insertion process and after lithium insertion, the iron occupancy of 8a site increased and that of 16c site decreased gradually with relaxation time. It is indicated that lithium prefer 8a site to occupy kinetically, on the other hand, prefer 16c site thermodynamically.     

Semiumbilic points for minimal surfaces in Euclidean 4-space

We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete gradient shrinking and steady Ricci solitons with vanishing Weyl tensor are rotationally symmetric, from which their classification follows.     

Highly planar amphiphilic porphyrins

A first synthesis of an asymmetric and amphiphilic β-substituted porphyrin is reported. The porphyrin can be integrated into various types of nanostructures with the amphiphilic characters in hydrophilic solvents. The one-dimensional integration may induce a magnetic interaction between the central metals.     

Beam profile measurement with CR-39 track detector for low-energy ions

A CR-39 track detector was successfully used to measure the outline of thin low-energy ion beams. After the etching, the surface of the detector was examined with an observation system composed of a Normarski microscope, a CCD camera and a digital image processing computer. Beam images obtained with the system were in good agreement on the outline of the beam formed with a beam aperture. Also, the resolving power in the beam outline measurement was roughly explained from the consideration of the ion range and the etch-pit growth in the chemical etching for the CR-39 detector.     

Bonding properties and structures of titanium clusters on (10, 0) single wall carbon nano capsule

We optimize whole structures of Ti clusters, Ti_n (n=1, 3 and 7), on a zigzag-type (10, 0) single wall carbon nano capsule, C₁₆₀, by using the first principles molecular dynamics within the spin density functional approximation, and discuss the bonding properties of Ti clusters on the C₁₆₀. For all the clusters, the most stable configuration includes a site above a center of C-hexagonal or pentagonal ring. The shape of Ti₇ cluster is very different by the located site. The cluster in which Ti atoms are located around centers of hexagon has a flat bottom and flatten the curvature of C wall below it.     

A vanishing theorem for modular symbols on locally symmetric spaces

A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally Hermitian symmetric spaces of type IV. Received: December 8, 1996