Model of Eutectic Transformation Involving Intermetallic Compound

doi:10.11900/0412.1961.2020.00373

Acta Metall Sin

2021, Vol. 57

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

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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

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XU Junfeng, ZHANG Baodong, Peter K Galenko. Model of Eutectic Transformation Involving Intermetallic Compound. Acta Metall Sin, 2021, 57(10): 1320-1332.

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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

Received: 18 September 2020

ZTFLH:

TG111.4

Fund: National Natural Science Foundation of China(51971166);Science and Technology Program of Shaanxi Province(2016KJXX-87);Foundation of Shaanxi Provincial Department of Education(18JS050)

About author: XU Junfeng, associate professor, Tel: 13572495176, E-mail: xujunfeng@mail.nwpu.edu.cn

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https://www.ams.org.cn/EN/10.11900/0412.1961.2020.00373 OR https://www.ams.org.cn/EN/Y2021/V57/I10/1320

Fig.1 Phase diagrams containing compound phases(T_E is the eutectic equilibrium temperature; C_E is the eutectic concentration; m_α and m_β are the_{liquidus line slopes on α-phase and β-phase, respectively; C_s_α and ΔC_s_β are the concentrations in the solid of α-phase and β-phase, respectively;_{ΔC_α, ΔC_β are the concentration differences between phases α, β and eutectic point (T_E_{, C}_E) respectively; ΔC₀ is concentration differences between α phase and β phase; CB is right-hand-side concentration of phase diagrams; k_α, k_βare solute distribution coefficients of α phase and β phase, respectively)}}

Fig.2 The moving and the stationary coordinate systems of the solidified interface (S_α and S_β represent the half of interlamellar spacing for each phase such that λ = 2(S_α + S_β) is the lamellar spacing; V is the growth velocity; θ_α and θ_β are the contact angles at the triple point junction)

Fig.3 Schematic diagram for determining solute distribution coefficient (α_α and α_β are the points where the liquid phase and the solid phase intersect)

Fig.4 Phase diagrams of Al-Al₂Cu alloy^[30] (a) and CuZr-CuZr₂ alloy^[31] (b) (T—temperature)

Table 1 The parameters for the model calculation of Al-Al₂Cu eutectic growth^[30]

Fig.5 Results of the experiments and calculation of alloys

Table 2 The parameters for the model calculation of CuZr-CuZr₂ eutectic growth^[31]

Fig.6 Influence of composition CB on the calculation results at the two-phase interfaces

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