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    Overheating threshold and its effect on time–temperature-transformation diagrams of zirconium based bulk metallic glasses

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    A pronounced effect of overheating is observed on the crystallization behavior for the three zirconium-based bulk metallic glasses: Zr41.2Ti13.8Cu12.5Ni10Be22.5, Zr57Cu15.4Ni12.6Al10Nb5, and Zr52.5Cu17.9Ni14.6Al10Ti5. A threshold overheating temperature is found for each of the three alloys, above which there is a drastic increase in the undercooling level and the crystallization times. Time–temperature-transformation (TTT) diagrams were measured for the three alloys by overheating above their respective threshold temperatures. The TTT curves for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and Zr57Cu15.4Ni12.6Al10Nb5 are very similar in shape and scale with their respective glass transition temperatures, suggesting that system-specific properties do not play a crucial role in defining crystallization kinetics in these alloys. The critical cooling rates to vitrify the alloys as determined from the TTT curves are about 2 K/s for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and 10 K/s for Zr57Cu15.4Ni12.6Al10Nb5. The measurements were conducted in a high-vacuum electrostatic levitator

    General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

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    For a particle that is constrained on an (N−1N-1)-dimensional (N≥2N\geq2) curved surface, the Cartesian components of its momentum in NN-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the su(2)su(2) algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion.Comment: 8 pages, no figure. Presentation improve
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