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Our research on applied mathematics is in line with the research scope of the journal. The phase-field model is applied to simulate the material and other areas. A phase-field model describing the non-isothermal solidification of an ideal multi-component alloy system is proposed in this paper. The time and space variation of a three-phase-field function and the governing equations of the temperature field are established. The global existence of weak solutions for three-dimensional parabolic differential equations is proved by the Faedo–Galerkin method. The existence of a maximum theorem is also extensively studied.

In this study, constitutional liquation in AZ91 cast alloy at 440°C and 465°C was experimentally simulated. Metallurgical examination was conducted to reveal the morphology of the constitutional liquid and dihedral angle was measured to evaluate the wettability of the liquid on grain boundary. Dihedral angle was found to be initially ~30 degree and thus grain boundaries were incomplete wet. During annealing, the metastable constitutional liquid resolidified, followed by grain growth. The extent of grain boundary wetting by the remaining liquid increased slightly with treating time. The rate of resolidification was also evaluated and the factors affecting this rate were discussed. [ABSTRACT FROM AUTHOR]

A novel method of producing nanocrystalline Fe–Al coatings on carbon steel has been proposed. A vibrating apparatus generated mechanical vibration to a retort, which was loaded with Al powder, alumina filler, ammonium chloride activator and alloy balls. The operation temperature was from 440 to 600°C. By combining the effects of ball impact, deposition of Al powders, nucleation of Al-rich phases, plastic deformation and fast inter-diffusions, a nanocrystalline Fe–Al intermetallic coating was produced. The grain size was less than 20 nm. Microstructural observation suggested that the coatings appeared to be homogeneous, with a high density, free of porosity and excellent adherence to the substrate. The coatings consisted mainly of η-Fe2Al5 with small amounts of θ-FeAl3 and β-FeAl. This method provided a new approach to produce nanostructured alloy or alloy–ceramic composite coatings with great energy and timesavings. [ABSTRACT FROM AUTHOR]