Journal of the Japan Society of Powder and Powder Metallurgy

The Many-body problem is very important issue in physics. Usually perturbation calculations based on the Green's function have been used to analyze such a problem, however, infinite orders of perturbation calculations are required to obtain exact solutions, thus resulting in the analytical and numerical difficulties. To overhaul such difficulties, we propose the new calculation method based on the differential forms, which are able to evaluate exact solutions if Hamiltonian is composed of Fermi particles. Since our proposed method is based on time evolution equations, comparisons with the calculations derived from Feynman Kernel is possible, with showing complete agreement. Furthermore we applied this method to the simplest Anderson Hamiltonian to investigate the appearance of magnetic moment. The calculation results show that magnetic moment easily disappears with small Coulomb repulsive energy, possibly implying the spin fluctuations.

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Intermetallic compounds (IMCs), known for their hardness, play an important role in the precipitation strengthening of alloys. However, precipitation in excessive amounts or as large particles can result in embrittlement of the material. Thus, controlling the distribution of IMCs among the matrix is crucial for the design of strong and ductile alloys. In this research, a supersaturated Ti-Cu alloy formed by Laser Powder Bed Fusion (L-PBF) was heat-treated at different phase regions to produce lamellar, network, and dispersed distributions of Ti₂Cu IMC precipitates. To comprehensively understand the formation mechanisms of each IMC distribution structure, in-situ microstructure observation was performed during the heat-treatments. The lamellar IMC structure obtained from heat treatment above the beta-transus temperature, was found to derive from the rejection of Cu atoms towards the boundaries of lamellar alpha grains formed during cooling. The network IMC structure obtained from heat-treatment in the α+β phase region involved the formation of a Cu-rich β-Ti layer between α-Ti grains during heating, and subsequent precipitation of Ti₂Cu into an α-encapsulating network upon cooling. Finally, the dispersed structure of IMCs was observed to result from regular nucleation and growth of Ti₂Cu during heat treatment in the α+IMC region.

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