A Predicted Model for Activity Interaction Coefficient Between Solutes in Alloy Solutions

doi:10.11900/0412.1961.2022.00202

Acta Metall Sin

2023, Vol. 59

Issue (11): 1533-1540 DOI: 10.11900/0412.1961.2022.00202

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A Predicted Model for Activity Interaction Coefficient Between Solutes in Alloy Solutions

JU Tianhua¹, SHU Nian¹, HE Wei¹, DING Xueyong²(

)

^1.School of Resources, Environment and Materials, Guangxi University, Nanning 530004, China
^2.School of Metallurgy, Northeastern University, Shenyang 110819, China

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JU Tianhua, SHU Nian, HE Wei, DING Xueyong. A Predicted Model for Activity Interaction Coefficient Between Solutes in Alloy Solutions. Acta Metall Sin, 2023, 59(11): 1533-1540.

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Abstract

Activity interaction coefficients for solutes in alloy melts can be predicted by combining Miedema model with extrapolation models. However, the treatment of the binary interaction terms in traditional extrapolation models lacks a clear physical mechanism, which reduces the prediction reliability of models based on traditional extrapolation. The unified extrapolation model (UEM) can mathematically cover all traditional extrapolation models by introducing the contribution coefficient determined by property difference between two elements. In this study, a new model for activity interaction coefficients was built by using UEM to couple with the Miedema model and Tanaka excess entropy relation. The new model can explain the prediction characteristics and application scope of models based on traditional extrapolation in terms of the relation between the contribution coefficient and the property difference. The obtained results favorably agree with the experimental results.

Key words: activity interaction coefficient alloy solution Miedema model extrapolation model

Received: 29 April 2022

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Corresponding Authors: DING Xueyong, professor, Tel: 13840290680, E-mail: dingxy@smm.neu.edu.cn

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https://www.ams.org.cn/EN/10.11900/0412.1961.2022.00202 OR https://www.ams.org.cn/EN/Y2023/V59/I11/1533

$α i (i j) k$	$α j (i j) k$	$α i (i k) j$	$α j (j k) i$	Extrapolation model + Miedema model	Asymmetric component
1/2	1/2	1/2	1/2	Muggianu model^[43] + Miedema model^[27-29]	-
0	1	0	0	Toop-Kohler model^[32] + Miedema model^[27-29]	i
1	0	0	0	Toop-Kohler model^[32] + Miedema model^[27-29]	j
1/2	1/2	1	1	Toop-Muggianu model^[34] + Miedema model^[27-29]	k
0	1	0	1/2	Toop-Muggianu model^[34] + Miedema model^[27-29]	i
1	0	1/2	0	Toop-Muggianu model^[34] + Miedema model^[27-29]	j
Similarity coefficient of Chou's model方正汇总行^[39]				Chou's model^[39] + Miedema model^[27-29]

Table 1 Correspondences between the values of the contribution coefficients in the present model and the activity interaction parameters models built based on the traditional extrapolation models

k-i-j	$α i (i j) k$	$α j (i j) k$	$α i (i k) j$	$α j (j k) i$	$ε i (C a l c .) j$	$ε i (E x p .) j$
Fe-C-Pb	1	0	0	0	4.15	5.73
	0	1	0	0	1.32
	0	1	1	1	-7.56
	1	0	1	1	-4.73
	1	0	0	1	-1.34
	1	0	1	0	0.76
	0	1	0	1	-4.17
	0	1	1	0	-2.07
Fe-C-Mn	1	0	0	0	-8.96	-1.88
	0	1	0	0	-1.62
	0	1	1	1	-5.01
	1	0	1	1	-12.35
	1	0	0	1	-8.96
	1	0	1	0	-12.35
	0	1	0	1	-1.62
	0	1	1	0	-5.01
Fe-Mn-Cr	1	0	0	0	0.74	0.90
	0	1	0	0	0.74
	0	1	1	1	0.73
	1	0	1	1	0.74
	1	0	0	1	0.74
	1	0	1	0	0.74
	0	1	0	1	0.73
	0	1	1	0	0.74
Fe-Al-Si	1	0	0	0	6.03	6.97
	0	1	0	0	6.01
	0	1	1	1	6.80
	1	0	1	1	6.82
	1	0	0	1	6.51
	1	0	1	0	6.34
	0	1	0	1	6.49
	0	1	1	0	6.32

Table 2 Calculated values

ε i (C a l c .) j

of activity interaction coefficients

ε C P b

ε C M n

ε M n C r

, and

ε A l S i

in liquid iron alloy at 1873 K under specified contribution coefficient values, together with the corresponding experimental data

ε i (E x p .) j

from Ref.[6]

Fig.1 Comparisons of calculated value and experiment's value from Ref.[6] for $ε C j$ and $ε S i j$
(a) Fe-C-j (b) Fe-Si-j

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