合金溶液中溶质间活度相互作用系数预测模型

doi:10.11900/0412.1961.2022.00202

金属学报

2023, Vol. 59

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

本期目录 | 过刊浏览

合金溶液中溶质间活度相互作用系数预测模型

居天华¹, 舒念¹, 何维¹, 丁学勇²(

)

^1.广西大学资源环境与材料学院南宁 530004
^2.东北大学冶金学院沈阳 110819

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

引用本文:

居天华, 舒念, 何维, 丁学勇. 合金溶液中溶质间活度相互作用系数预测模型[J]. 金属学报, 2023, 59(11): 1533-1540.
Tianhua JU, Nian SHU, Wei HE, Xueyong DING. A Predicted Model for Activity Interaction Coefficient Between Solutes in Alloy Solutions[J]. Acta Metall Sin, 2023, 59(11): 1533-1540.

全文: PDF(816 KB) HTML

摘要:

利用基于组分间性质差建立的统一外推模型(UEM)，结合Miedema模型、Tanaka过剩熵关系式，给出了计算任意基体中溶质间活度相互作用系数的模型。该模型不仅在数学上可以覆盖由传统外推模型耦合Miedema模型导出的活度相互作用系数模型，还可以利用组分间的性质差大小定性解释由传统外推模型给出的活度相互作用系数模型的预测特点及其适用体系，且与实验结果吻合良好。

关键词 ：活度相互作用系数, 合金溶液, Miedema模型, 外推模型

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

收稿日期: 2022-04-29

ZTFLH:

TF01

通讯作者: 丁学勇，dingxy@smm.neu.edu.cn，主要从事合金熔体热力学模型的开发及计算的研究

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

作者简介: 居天华，男，1989年生，博士

	服务

	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	居天华
	舒念
	何维
	丁学勇
44.8K

链接本文:

https://www.ams.org.cn/CN/10.11900/0412.1961.2022.00202 或 https://www.ams.org.cn/CN/Y2023/V59/I11/1533

表1 本模型中贡献系数值与常见外推模型导出的活度相互作用系数模型之间的对应关系

表2 1873 K铁液中活度相互作用系数εCPb、εCMn、εMnCr和εAlSi在贡献系数取不同值条件下的计算值εi(Calc.)j与实验值εi(Exp.)j[6]比较

图1 εCj和εSij模型计算值与实验值[6]的对比

1	Wagner C. Thermodynamics of Alloys [M]. Cambridge, MA: Addison-Wesley Press, 1952: 1
2	Sigworth G K, Elliott J F. The thermodynamics of dilute liquid copper alloys [J]. Can. Metall. Q., 1974, 13: 455 doi: 10.1179/cmq.1974.13.3.455
3	Sigworth G K, Elliott J F. The thermodynamics of liquid dilute iron alloys [J]. Met. Sci., 1974, 8: 298 doi: 10.1179/msc.1974.8.1.298
4	Sigworth G K, Elliott J F. The thermodynamics of dilute liquid cobalt alloys [J]. Can. Metall. Q., 1976, 15: 123 doi: 10.1179/cmq.1976.15.2.123
5	Sigworth G K, Elliott J F, Vaughn G, et al. The thermodynamics of dilute liquid nickel alloys [J]. Can. Metall. Q., 1977, 16: 104 doi: 10.1179/cmq.1977.16.1.104
6	Hino M, Ito K. Thermodynamic Data for Steelmaking [M]. Sendai: Tohoku University Press, 2010: 1
7	Mikhailov G G, Zherebtsov D A. On the interaction of calcium and oxygen in liquid iron [J]. Mater. Sci. Forum, 2016, 843: 52 doi: 10.4028/www.scientific.net/MSF.843
8	Sugiyama K, Ueda S, Gao X, et al. Measurement of interaction parameter between Cu and Al in molten high Al steel [J]. ISIJ Int., 2017, 57: 625 doi: 10.2355/isijinternational.ISIJINT-2016-676
9	Niu J P, Shan Z Q, Geng S Q, et al. Calculation of interaction coefficient e N T i and activity coefficient f_N of titanium to nitrogen in nickel-based superalloy [J]. Vacuum, 2018, 55(3): 45 doi: 10.1016/S0042-207X(99)00122-0
9	牛建平, 单志强, 耿双奇等. 镍基高温合金中钛对氮相互作用系数 e N T i 和活度系数f_N的计算 [J]. 真空, 2018, 55(3): 45
10	Do K H, Jang J M, Son H S, et al. Effect of silicon on tin formation in liquid iron [J]. ISIJ Int., 2018, 58: 1437 doi: 10.2355/isijinternational.ISIJINT-2018-087
11	Ono H, Miki T, Nakamoto M. Determination of interaction parameters between elements in molten iron by evaporation and chemical equilibration techniques [J]. Tetsu Hagané, 2019, 105: 344
11	小野英樹, 三木貴博, 中本将嗣. 蒸気圧法ならびに化学平衡法による溶鉄中元素間の相互作用パラメータの測定 [J]. 鉄と鋼, 2019, 105: 344
12	Zajączkowski A, Suruło A. Thermodynamics of copper-rich liquid Cu-Fe-Bi alloys determined by vapour pressure measurements [J]. Calphad, 2019, 64: 272 doi: 10.1016/j.calphad.2018.12.012
13	Alcock C B, Richardson F D. Dilute solutions in molten metals and alloys [J]. Acta Metall., 1958, 6: 385 doi: 10.1016/0001-6160(58)90017-8
14	Alcock C B, Richardson F D. Dilute solutions in alloys [J]. Acta Metall., 1960, 8: 882 doi: 10.1016/0001-6160(60)90157-7
15	Guggenheim E A. Mixtures: The Theory of the Equlibrium Properties of Some Simple Classes of Mixtures Solutions and Alloys [M]. Oxford: Clarendon Press, 1952: 1
16	Lupis C H P, Elliott J F. Generalized interaction coefficients [J]. Acta Metall., 1966, 14: 1019 doi: 10.1016/0001-6160(66)90190-8
17	Tanaka T, Gokcen N A, Iida T, et al. Thermodynamic relationship between the enthalpy interaction parameter and entropy interaction parameter in liquid iron-nitrogen based ternary alloys [J]. Z. Metallkd., 1994, 85: 696
18	Tao D P. Prediction expressions of component activity coefficients in Si-based melts [J]. Metall. Mater. Trans., 2014, 45B: 142
19	Iwata K, Matsumiya T, Sawada H, et al. Prediction of thermodynamic properties of solute elements in Si solutions using first-principles calculations [J]. Acta Mater., 2003, 51: 551 doi: 10.1016/S1359-6454(02)00437-8
20	Matsumiya T. Estimation of activity coefficients and interaction parameters of solutes in silicon melts [J]. Metall. Mater. Trans., 2012, 43B: 726
21	Ueno S, Waseda Y, Jacob K T, et al. Theoretical treatment of interaction parameters in multicomponent metallic solutions [J]. Steel Res., 1988, 59: 474 doi: 10.1002/srin.1988.59.issue-11
22	Waseda Y. Interaction parameters in metallic solutions estimated from liquid structure and the heat of solution at infinite dilution [J]. High Temp. Mater. Proc., 2012, 31: 203
23	Ding X Y, Wang W Z, Han Q Y. Thermodynamic calculation of Fe-P-j system melt [J]. Acta Metall. Sin., 1993, 29(12): 21
23	丁学勇, 王文忠, 韩其勇. Fe-P-j三元系熔体的热力学计算 [J]. 金属学报, 1993, 29(12): 21
24	Ding X Y, Fan P, Han Q Y. Models of activity and activity interaction parameter in ternary metallic melt [J]. Acta Metall. Sin., 1994, 30(14): 49
24	丁学勇, 范鹏, 韩其勇. 三元系金属熔体中的活度和活度相互作用系数模型 [J]. 金属学报, 1994, 30(14): 49
25	Ding X Y, Wang W Z, Guo D, et al. Thermodynamic model calculation in copper liquid [J]. Chin. J. Nonferrous Met., 1994, 4(2): 34
25	丁学勇, 王文忠, 郭丹等. 铜液中的热力学模型计算 [J]. 中国有色金属学报, 1994, 4(2): 34
26	Ding X Y, Wang W Z, Fan P. Thermodynamic calculation for alloy systems [J]. Metall. Mater. Trans., 1999, 30B: 271
27	Miedema A R, de Châtel P F, de Boer F R. Cohesion in alloys—Fundamentals of a semi-empirical model [J]. Physica B + C, 1980, 100: 1 doi: 10.1016/0378-4363(80)90054-6
28	de Boer F R, Boom R, Mattens W C M, et al. Cohesion in Metals: Transition Metal Alloys [M]. Amsterdam: North-Holland, 1988: 1
29	Miedema A R. On the heat of formation of solid alloys. II [J]. J. Less-Common Met., 1976, 46: 67 doi: 10.1016/0022-5088(76)90180-6
30	Chou K C, Austin Chang Y. A study of ternary geometrical models [J]. Ber. Bunsenges. Phys. Chem., 1989, 93: 735 doi: 10.1002/bbpc.v93:6
31	Lupis C H P, Elliott J F. Generalized interaction coefficients: Part I: Definitions [J]. Acta Metall., 1966, 14: 529 doi: 10.1016/0001-6160(66)90320-8
32	Toop G W. Predicting ternary activities using binary data [J]. Trans. Metall. Soc. AIME, 1965, 223: 850
33	Ding X Y, Fan P, Luo L H. Thermodynamic Model, Prediction Value and Software Development of Alloy Melt [M]. Shenyang: Northeastern University Press, 1998: 1
33	丁学勇, 范鹏, 罗利华. 合金熔体的热力学模型、预测值及其软件开发 [M]. 沈阳: 东北大学出版社, 1998: 1
34	Hillert M. Empirical methods of predicting and representing thermodynamic properties of ternary solution phases [J]. Calphad, 1980, 4: 1 doi: 10.1016/0364-5916(80)90016-4
35	Chartrand P, Pelton A D. On the choice of “geometric” thermodynamic models [J]. J. Phase Equilib., 2000, 21: 141 doi: 10.1361/105497100770340192
36	Dogan A, Arslan H. Comparative thermodynamic prediction of integral properties of six component, quaternary, and ternary systems [J]. Metall. Mater. Trans., 2015, 46A: 3753
37	Chou K C. A new solution model for predicting ternary thermodynamic properties [J]. Calphad, 1987, 11: 293 doi: 10.1016/0364-5916(87)90048-4
38	Malakhov D V, Tokuda M. “Equidistant method” to estimate thermodynamic properties of multicomponent solutions by using data on binary boundary systems [J]. Mater. Trans. JIM, 1995, 36: 757 doi: 10.1016/j.matdes.2011.12.004
39	Chou K C, Wei S K. A new generation solution model for predicting thermodynamic properties of a multicomponent system from binaries [J]. Metall. Mater. Trans., 1997, 28B: 439
40	Pelton A D. A general “geometric” thermodynamic model for multicomponent solutions [J]. Calphad, 2001, 25: 319 doi: 10.1016/S0364-5916(01)00052-9
41	Jacob K T, Fitzner K. The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path [J]. Thermochim. Acta, 1977, 18: 197 doi: 10.1016/0040-6031(77)80019-1
42	Kohler F. Estimation of the thermodynamic data for a ternary system from the corresponding binary systems [J]. Monatsh. Chem., 1960, 91: 738 doi: 10.1007/BF00899814
43	Muggianu Y M, Gambino M, Bros J P. Enthalpies de formation des alliages liquides bismuth-étain-gallium à 723 k. Choix d'une représentation analytique des grandeurs d'excès intégrales et partielles de mélange [J]. J. Chim. Phys., 1975, 72: 83 doi: 10.1051/jcp/1975720083
44	Fan P, Chou K C. A model for predicting thermodynamic properties of metallic solutions from fundmental physical quantities of constituent elements [J]. Acta Metall. Sin., 1999, 35: 421
44	范鹏, 周国治. 由组元的物性参数预测金属熔体的热力学性质 [J]. 金属学报, 1999, 35: 421
45	Fan P, Chou K C. A self-consistent model for predicting interaction parameters in multicomponent alloys [J]. Metall. Mater. Trans., 1999, 30A: 3099
46	Zhang N, Chen W L, Chen X Q, et al. Modeling activity and interaction coefficients of components of multicomponent alloy melts: An example of iron melt [J]. High Temp. Mater. Proc., 2013, 32:215 doi: 10.1515/htmp-2012-0123
47	Ju T H, Ding X Y, Chen W L, et al. A new perspective on geometric thermodynamic models [J]. J. Phase Equilib. Diff., 2019, 40: 715 doi: 10.1007/s11669-019-00757-5
48	Ju T H, Ding X Y, Zhang L, et al. A general model for solutes activity interaction parameters in dilute metallic solutions [J]. ISIJ Int., 2020, 60: 2416 doi: 10.2355/isijinternational.ISIJINT-2019-564
49	Tanaka T, Gokcen N A, Morita Z I. Relationship between enthalpy of mixing and excess entropy in liquid binary alloys [J]. Z. Metallkd., 1990, 81: 49
50	Tanaka T, Gokcen N A, Morita Z I, et al. Thermodynamic relationship between enthalpy of mixing and excess entropy in liquid binary alloys [J]. Z. Metallkd., 1993, 84: 192
51	Tanaka T, Gokcen N A, Kumar K C H, et al. Thermodynamic relationship between enthalpy of mixing and excess entropy in solid solutions of binary alloys [J]. Z. Metallkd., 1996, 87: 779
52	Boom R, de Boer F R. Enthalpy of formation of binary solid and liquid Mg alloys—Comparison of Miedema-model calculations with data reported in literature [J]. Calphad, 2020, 68: 101647 doi: 10.1016/j.calphad.2019.101647
53	Neuhausen J, Eichler B. CH0300080 [R]. Villigen: Paul Scherrer Institut, 2003
54	Ju T H, Ding X Y, Zhang L, et al. On the definition of the components' difference in properties in the unified extrapolation model [J]. Fluid Phase Equilib., 2020, 515: 112588 doi: 10.1016/j.fluid.2020.112588
55	Ju T H, Ding X Y, Yan X L, et al. New expression for property difference in components for the unified extrapolation model [J]. J. Mol. Liq., 2020, 320: 114469 doi: 10.1016/j.molliq.2020.114469

[1]	刘力恒,车淳山,孔纲,卢锦堂,张双红. 热镀Zn-0.2%Al镀层中Fe-Al抑制层失稳机理及其热力学评估^*[J]. 金属学报, 2016, 52(5): 614-624.
[2]	蒋光锐; 刘源; 李言祥; 苏彦庆; 郭景杰 . 多元合金熔体组元活度系数计算方法的改进[J]. 金属学报, 2007, 43(5): 503-508 .
[3]	乐启炽; 张新建; 崔建忠; 路贵民 . 金属合金溶液热力学模型研究进展[J]. 金属学报, 2003, 39(1): 35-42 .
[4]	侯怀宇; 谢刚 . 用NRTL方程预测三元,四元液态合金体系的热力学数据[J]. 金属学报, 1999, 35(3): 292-295 .
[5]	罗利华;丁学勇;郭丹;曹文斌;邹宗树;王文忠. 活度、活度相互作用系数数据库软件开发[J]. 金属学报, 1998, 34(4): 388-392.
[6]	郭上型;董元篪. Fe-Mn-C-P系高锰熔体的热力学研究[J]. 金属学报, 1995, 31(18): 241-246.
[7]	丁学勇;范鹏;韩其勇. 三元系金属熔体中的活度和活度相互作用系数模型[J]. 金属学报, 1994, 30(14): 49-60.
[8]	丁学勇;王文忠;韩其勇. Fe-P-j三元系熔体的热力学计算[J]. 金属学报, 1993, 29(12): 21-26.
[9]	倪瑞明;马中庭;魏寿昆. Mn-C-j熔体热力学性质的研究[J]. 金属学报, 1990, 26(2): 93-97.
[10]	王丛桦;韩其勇. Ni液中Mg-S反应平衡的研究[J]. 金属学报, 1988, 24(6): 524-526.

Viewed

Full text

Abstract

Cited

Shared

Discussed