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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
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