含有化合物相的共晶转变理论模型

doi:10.11900/0412.1961.2020.00373

金属学报

2021, Vol. 57

Issue (10): 1320-1332 DOI: 10.11900/0412.1961.2020.00373

研究论文

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含有化合物相的共晶转变理论模型

许军锋¹^,²(

), 张宝东¹, Peter K Galenko²

^1.西安工业大学材料与化工学院西安 710021
^2.Otto Schott Institute of Materials Research, Friedrich-Schiller-Universit?t Jena, 07743, Germany

Model of Eutectic Transformation Involving Intermetallic Compound

XU Junfeng¹^,²(

), ZHANG Baodong¹, Peter K Galenko²

^1.School of Materials and Chemical Engineering, Xi'an Technological University, Xi'an 710021, China
^2.Otto Schott Institute of Materials Research, Friedrich-Schiller-Universität Jena, 07743, Germany

引用本文:

许军锋, 张宝东, Peter K Galenko. 含有化合物相的共晶转变理论模型[J]. 金属学报, 2021, 57(10): 1320-1332.
Junfeng XU, Baodong ZHANG, Galenko Peter K. Model of Eutectic Transformation Involving Intermetallic Compound[J]. Acta Metall Sin, 2021, 57(10): 1320-1332.

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摘要:

在经典理论Jackson-Hunt模型的基础上，导出有化合物相参与时的共晶生长模型表达式，补充了共晶生长扩散方程求解过程，以及溶质分配系数的确定和模型使用方法，进而类比给出其他共晶生长模型在有化合物相参与时的使用步骤。模型计算发现：同样过冷度下，共晶生长速率随着化合物相浓度(CB)减小而增大，这一参数变化弥补了化合物相因溶质分配系数小而生长阻力大的不足。由此可得：有化合物相参与的共晶转变，相图两端跨度一般会变窄；共晶两相溶质分配系数较小时，相图两端跨度一般比较窄。

关键词 ：凝固, 共晶生长, 过冷度, 生长速率

Abstract：

The classical eutectic growth theory, first developed by Jackson and Hunt in 1966, is simple and easy to use. However, the derivation of the classical model does not consider the model changes when one of the eutectic phases in transformation is an intermetallic compound. Moreover, the derivation of the model does not demonstrate the mathematical method to solve the diffusion equation and determine the Fourier coefficient, and without this, it is difficult to deeply understand and master the theoretical application. Based on the classical Jackson-Hunt theory, this study derives the eutectic growth model considering the compound phases and demonstrates the process involved in the solution of the diffusion equation to determine the solute distribution coefficient. The steps for using the model are supplemented and then the application methods of other similar models in eutectic transformations involving the compound phase are provided. The calculation of the model shows that under the same undercooling, the eutectic growth rate increases with the decrease of the compound phase concentration (CB). This parameter change compensates for the insufficient growth resistance of the compound phase owing to the small solute distribution coefficient. Therefore, the span of the eutectic phase diagram with the compound phase involved in the transition is narrowed; the smaller the solute partition coefficient of the eutectic phase, narrower is the phase diagram span.

Key words： solidification eutectic growth undercooling growth velocity

收稿日期: 2020-09-18

ZTFLH:

TG111.4

基金资助:国家自然科学基金项目(51971166);陕西省科技新星项目(2016KJXX-87);陕西省教育厅项目(18JS050)

作者简介: 许军锋，男，1981年生，副教授，博士

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https://www.ams.org.cn/CN/10.11900/0412.1961.2020.00373 或 https://www.ams.org.cn/CN/Y2021/V57/I10/1320

图1 含有化合物相的相图示意图(a) kα≠ 0, kβ≠ 0 (b) kα = 0, kβ≠ 0

图2 凝固界面的移动坐标系和静止坐标

图3 溶质分配系数的确定方法示意图

图4 Al-Al2Cu合金相图[30]和CuZr-CuZr2合金相图[31]

表1 Al-Al2Cu合金相关物理参数[30]

图5 实验与计算结果对比(a) ΔT-V curves of Al-Al2Cu alloy (ΔT—undercooling)(b) V-λ curves of Al-Al2Cu alloy and experimental data[30](c) interfacial concentration distribution C(x, z) of Al-Al2Cu alloy at two growth rates(d) calculation results and experiments[31] of CuZr-CuZr2 alloy

表2 CuZr-CuZr2合金相关物理参数[31]

图6 化合物相浓度CB对计算结果的影响(a) ΔT-V curve (b) ΔT-λ curve (c) λ-V curve (d) V-Csα(Csβ) curve

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