Abstract According to equilibrium state diagrams, compositions of liquid and solid phases are determined by corresponding diagram curves at the melt cooling to below the liquidus temperature. For equilibrium to occur, the following is necessary: the melt is kept indefinitely at each temperature; or the thermal conductivity of the liquid and solid phases, as well as the diffusion coefficients of their components, are infinitely large. This study attempts to find out how these processes occur in reality. An individual crystal growth during cooling of a two-component melt is considered. A mathematical model is designed based on the following standings: (i) a melt region with a volume per one grain, the periphery of which is cooled according to a certain law, is selected; (ii) at the initial time, the crystal nucleus with a certain minimal size is in the liquid; (iii) near the crystal surface, the compositions of the liquid and solid phases correspond to a state diagram for the considered temperature on its surface; and (iv) changes in temperature and composition in the liquid and solid phases occur according to the heat conduction and diffusion laws, respectively. As the melt cools and the crystal grows, the liquid phase is enriched in one component and depleted in another, while the solid phase occurs in reverse. The component’s diffusion coefficient in the solid phase is small. Therefore, its composition does not completely equalize over the cross section. The model proposed here makes it easier to study this phenomenon and to calculate the crystal composition for each cooling mode as it moves away from its center. The calculations showed that the temperature equalizes almost instantly while the composition equalization of the liquid phase occurs much slower. The solid phase’s composition during observation practically does not equalize. The obtained results will be useful for improving the production technology for alloys with an optimal structure.

中文翻译：

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平衡状态图在计算双组分熔体冷却过程中的偏析动力学中的应用

摘要 根据平衡态图，在熔体冷却至液相线温度以下时，液相和固相的组成由相应的图曲线确定。为了达到平衡，以下是必要的：熔体在每个温度下都保持无限期；或者液相和固相的热导率，以及它们的组分的扩散系数，是无限大的。本研究试图找出这些过程在现实中是如何发生的。考虑了双组分熔体冷却过程中的单个晶体生长。数学模型的设计基于以下观点： (i) 选择每粒体积的熔化区，其外围按一定规律冷却；(ii) 在最初的时候，具有一定最小尺寸的晶核在液体中；(iii) 在晶体表面附近，液相和固相的组成对应于其表面所考虑温度的状态图；(iv) 液相和固相的温度和组成分别根据热传导和扩散定律发生变化。随着熔体冷却和晶体生长，液相中一种成分富集而另一种成分耗尽，而固相则相反。该组分在固相中的扩散系数小。因此，它的组成在横截面上并不完全均衡。此处提出的模型可以更轻松地研究这种现象并计算每种冷却模式远离其中心时的晶体成分。计算表明，温度几乎立即平衡，而液相的成分平衡发生得慢得多。观察期间固相的组成实际上并不均衡。所得结果将有助于改进具有最佳结构的合金的生产工艺。