Three different kinds of morphology are found in undercooled Pd80Si20, and they dominate at different undercooling regimens ΔT, defined as ΔT = T1 – Tk, where T1 is the liquidus of Pd80Si20 and Tk is the kinetic crystallization temperature. In the small undercooling regimen, i.e., for ΔT ≤ 190 K, the microstructures are typically dendritic precipitation with a eutecticlike background. In the intermediate undercooling regimen, i.e., for 190 ≤ ΔT ≤ 220 K, spherical morphologies, which arise from nucleation and growth, are identified. In addition, Pd particles are found throughout an entire undercooled specimen. In the large undercooling regimen, i.e., for ΔT ≥ 220 K, a connected structure composed of two subnetworks is found. A sharp decrease in the dimension of the microstructures occurs from the intermediate to the large undercooling regimen. Although the crystalline phases in the intermediate and the large undercooling regimens are the same, the crystal growth rate is too slow to bring about the occurrence of grain refinement. Combining the morphologies observed in the three undercooling regimens and their crystallization behaviors, we conclude that phase separation takes place in undercooled molten Pd80Si20.
Investigation of solvability condition for sixth-order boundary value problem
