Phase formation of polycrystalline MgB2 at low temperature using nanometer Mg powder

The MgB2 superconductor synthesized in a flowing argon atmosphere using nanometer magnesium powder as the raw materials, denoted as Nano-MgB2, has been studied by the technique of in-situ high temperature resistance measurement (HT-RT measurement). The MgB2 phase is identified to form within the temperature range of 430 to 490 C, which is much lower than that with the MgB2 sample fabricated in the same gas environment using the micron-sized magnesium powder, denoted as Micro-MgB2, reported previously. The sample density of the Nano-MgB2 reaches 1.7 g/cm3 with a crystal porosity structure less than a micrometer, as determined by the scanning electron microscope (SEM) images, while the Micro-MgB2 has a much more porous structure with corresponding density of 1.0 g/cm3. This indicates that the Mg raw particle size, besides the sintering temperature, is a crucial factor for the formation of high density MgB2 sample, even at the temperature much lower than that of the Mg melting, 650 C. The X-ray diffraction (XRD) pattern shows a good MgB2 phase with small amount of MgO and Mg and the transition temperature, TC, of the Nano-MgB2 was determined as 39 K by the temperature dependent magnetization measurement (M-T), indicating the existence of a good superconducting property.Comment: 10 pages, 4 figure, Solid State Communicatio

Connection between closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation

It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation. Some discussion was made about the factorization of a 1D Schr\"{o}dinger equation.Comment: 14 pages, no figure