Beyond the Parallel Tangent Method to Predict the Composition of the First Nucleating Phase from Oversaturated Solutions

IF 1.5 4区材料科学 Q4 CHEMISTRY, PHYSICAL

Journal of Phase Equilibria and Diffusion Pub Date : 2023-07-06 DOI:10.1007/s11669-023-01044-0

George Kaptay

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Abstract

The parallel tangent method widely applied to predict the composition and driving force to form a nucleus from an oversaturated solution is extended in this paper. The parallel tangent method is shown to (i) Over-estimates the composition difference between the first nucleus and the parent phase, (ii) Neglects the composition dependence of interfacial energies and (iii) Neglects the composition dependence of probability to form embryos prior to nucleation. New model equations are developed here for the composition dependence of the interfacial energies and probability to form the embryos as function of nucleus composition at given matrix composition. The most probable composition of the first nucleus is found at the maximum of the driving force of nucleation extended by the new model equations. The success of the extended method is demonstrated for an Al-Fe liquid alloy with 0.3 w% of Fe to predict the first nucleating intermetallic phases upon cooling after nucleation of the fcc phase. It is shown that although the prediction based on the parallel tangent method contradicts experimental observations, the prediction based on our extended method agrees with them.

Graphical Abstract

Abstract Image

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用平行切线法预测过饱和溶液中第一成核相的组成

本文推广了目前广泛应用于预测过饱和溶液组成和成核驱动力的平行切线法。平行正切法显示:(i)高估了第一个核和母相之间的组成差异，(ii)忽略了界面能的组成依赖性，(iii)忽略了在成核之前形成胚胎的概率的组成依赖性。本文建立了在给定基质组成下，界面能和胚胎形成概率随细胞核组成的变化关系的新模型方程。第一个核的最可能组成是在新模型方程所扩展的成核驱动力的最大值处。对于含铁量为0.3 w%的Al-Fe液态合金，该扩展方法成功地预测了fcc相成核后冷却后的第一个成核金属间相。结果表明，虽然基于平行切线方法的预测与实验观测结果相矛盾，但基于我们的扩展方法的预测与实验观测结果一致。图形抽象

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来源期刊

Journal of Phase Equilibria and Diffusion 工程技术-材料科学：综合

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

1 months

期刊介绍： The most trusted journal for phase equilibria and thermodynamic research, ASM International''s Journal of Phase Equilibria and Diffusion features critical phase diagram evaluations on scientifically and industrially important alloy systems, authored by international experts. The Journal of Phase Equilibria and Diffusion is critically reviewed and contains basic and applied research results, a survey of current literature and other pertinent articles. The journal covers the significance of diagrams as well as new research techniques, equipment, data evaluation, nomenclature, presentation and other aspects of phase diagram preparation and use. Content includes information on phenomena such as kinetic control of equilibrium, coherency effects, impurity effects, and thermodynamic and crystallographic characteristics. The journal updates systems previously published in the Bulletin of Alloy Phase Diagrams as new data are discovered.