Single-crystal growth under electron-beam rapid-directional-solidification: finite volume method and experimental studies

As an emerging strategy for the single-crystals growth, electron-beam rapid-directional-solidification (RDS) has emerged as a promising strategy, capable of growing single-crystal growth at a rapid growth rate, potentially enabling substantial enhancement in material properties by generating unprecedented microstructures. Heat transfer behavior of electron-beam rapid-directional-solidification strategy remains elusive for establishing the control method of multi-step processes, which is pivotal for the successful growth of single-crystals. Given the limitations of present techniques in directly monitoring temperature field, progress in understanding the heat transfer has been hindered. In this work, we developed an electron-beam heat source model and formulated a heat transfer model by the finite volume method. In simulations, we employed a stepwise approximation method to determine the processing window, based on predefined criteria related to the melting zone, solid-liquid interface, and temperature field. At each computational node, experimental observations of the solidification microstructures were carried out to validate the simulation outcomes. In this way, a novel paradigm for determining optimal processing procedures is proposed, with Tb-doped Fe-Ga magnetostrictive alloy as a demonstration. Guided by the simulations, we successfully grew a Tb-doped Fe-Ga single-crystal. The rapid cooling rate results in a non-equilibrium microstructure, leading to a ∼40% enhancement in magnetostriction from 282 ppm to 394 ppm. The paradigm is further extended to refractory metals including Nb, Mo and W, and its applicability is proven by the attainment of single crystals of these metals. This paradigm is expected to significantly accelerate the development process of various single-crystals, and pave the way for developing new single-crystals with unprecedented microstructures and properties.