统一外推模型与传统外推模型在Ag-Bi-Cu、In-Li-Sn和Al-Sn-Zn三元合金系混合焓计算中的性能对比

doi:10.19976/j.cnki.43-1448/TF.2024120

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摘要合金溶液的热力学性质是评估合金相稳定性及计算相图的重要数据,准确预测这些数据对开发新合金材料、优化冶金过程、提高产品质量和降低生产成本具有重要意义。本文利用统一外推模型(unified extrapolation model, UEM)计算了Ag-Bi-Cu、In-Li-Sn和Al-Sn-Zn三元合金系在不同组成下的混合焓,并与多种常用的外推模型(Kohler、Muggianu、Toop和通用溶液模型)的计算结果以及文献中的实验数据进行对比。结果表明,UEM的预测结果整体上优于其他模型,在热力学性质预测方面表现出较高的准确性和适用性。

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	吕洋
	吕启文
	廖玲慧
	刘东云
	居天华

关键词 ：多元合金溶液, 热力学模型, 外推模型, 热力学性质, 混合焓

Abstract：The thermodynamic properties of alloy solutions are crucial for evaluating phase stability and calculating phase diagrams. Accurate prediction of these data is of great significance for the development of new alloy materials, optimization of metallurgical processes, improvement of product quality, and reduction of production costs. In this study, the unified extrapolation model (UEM) was employed to calculate the enthalpy of mixing of the Ag-Bi-Cu, In-Li-Sn, and Al-Sn-Zn ternary alloy systems at various compositions. The results were compared with those obtained from several commonly used extrapolation models, including the Kohler, Muggianu, Toop, and general solution models, as well as experimental data reported in the literatures. The findings indicate that UEM provides overall superior predictions compared to other models, demonstrating higher accuracy and applicability in the prediction of thermodynamic properties.

Key words： multicomponent alloy solution thermodynamic model extrapolation model thermodynamic property enthalpy of mixing

收稿日期: 2024-12-31 出版日期: 2025-07-28

ZTFLH:

TF01

基金资助:广西科技基地和人才专项资助项目(AD23026259)

通讯作者: 居天华,助理教授,博士。电话：18642084587;E-mail: jutianhua@gxu.edu.cn

引用本文:

吕洋, 吕启文, 廖玲慧, 刘东云, 居天华. 统一外推模型与传统外推模型在Ag-Bi-Cu、In-Li-Sn和Al-Sn-Zn三元合金系混合焓计算中的性能对比[J]. 粉末冶金材料科学与工程, 2025, 30(3): 193-203.
LÜ Yang, LÜ Qiwen, LIAO Linghui, LIU Dongyun, JU Tianhua. Performance comparison of unified and traditional extrapolation models in calculating enthalpy of mixing of Ag-Bi-Cu, In-Li-Sn, and Al-Sn-Zn ternary alloy systems. Materials Science and Engineering of Powder Metallurgy, 2025, 30(3): 193-203.

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http://pmbjb.csu.edu.cn/CN/10.19976/j.cnki.43-1448/TF.2024120 或 http://pmbjb.csu.edu.cn/CN/Y2025/V30/I3/193

[1] 乔慧, 胡标, 曾港, 等. Zr-Cr-Y体系相平衡的实验测定和热力学计算[J]. 粉末冶金材料科学与工程, 2022, 27(4): 351-359.
QIAO Hui, HU Biao, ZENG Gang, et al.Experimental determination and thermodynamic assessment of the Zr-Cr-Y ternary system[J]. Materials Science and Engineering of Powder Metallurgy, 2022, 27(4): 351-359.
[2] 毛学良, 李晓静, 刘树红, 等. Ag-Cu-Co体系的相图热力学研究[J]. 粉末冶金材料科学与工程, 2022, 27(5): 460-470.
MAO Xueliang, LI Xiaojing, LIU Shuhong, et al.Thermodynamic investigation of the Ag-Cu-Co system[J]. Materials Science and Engineering of Powder Metallurgy, 2022, 27(5): 460-470.
[3] 周国治. 新一代的溶液几何模型及其今后的展望[J]. 金属学报, 1997, 33(2):126-132.
ZHOU Guozhi.New generation solution geometrical model and its further development[J]. Acta Metallrugica Sinica, 1997, 33(2): 126-132.
[4] CHOU K C.General solution model and its new progress[J]. International Journal of Minerals, Metallurgy and Materials, 2022, 29(4): 577-585.
[5] CHOU K C.Application of phenomenological theory to chemical metallurgy[J]. ISIJ International, 2018, 58(5): 785-791.
[6] ZHANG J, DONG H F, DONG X, et al.First-principles investigation of the structure and thermodynamic properties of titanium hydrides[J]. Computational Materials Science, 2024, 238: 112851.
[7] SAENGDEEJING A, SAHARA R, TODA Y.Al-Ni-Ti thermodynamic database from first-principles calculations[J]. Calphad, 2024, 84: 102658.
[8] YANG F, ZHANG L, TANG X H, et al.First-principles study of structural and optical properties contrast for liquid (GeTe)x (x=1, 2, 3)-Sb₂Te₃ compounds[J]. Journal of Non-Crystalline Solids, 2020, 539: 120051.
[9] WAN J F, CHEN S P, HSU T Y.The stability of transition phases in Fe-Mn-Si based alloys[J]. Calphad, 2001, 25(3): 355-362.
[10] ALJARRAH M, ALNAHAS J, ALHARTOMI M.Liquidus projections and isothermal sections of Mg-Al-Ca system using different geometrical models[C]// CHING Y C, HUI L. AIP Conference Proceedings: Volume 2743. New York, USA: AIP Publishing, 2023: 020011.
[11] LI Y D, LIU C J, ZHANG T S, et al.Phase diagram assessment of CaO-Al₂O₃-La₂O₃ system[J]. Canadian Metallurgical Quarterly, 2017, 56(3): 245-251.
[12] TRUMIC B, ZIVKOVIC D, ZIVKOVIC Z, et al.Comparative thermodynamic analysis of the Pb-Au_0.7Sn_0.3 section in the Pb-Au-Sn ternary system[J]. Thermochimica Acta, 2005, 435(1): 113-117.
[13] LIU Y, LIANG D.A contribution to the Al-Pb-Zn ternary system[J]. Journal of Alloys and Compounds, 2005, 403(1/2): 110-117.
[14] SINGH V, PATHOTE D, JAISWAL D, et al.Measurements of enthalpies of mixing of Sn-Ga-In ternary alloy system by calorimetric technique[J]. Metals and Materials International, 2025, 31(1): 182-192.
[15] DHUNGANA A, YADAV S K, MEHTA U, et al.Thermodynamic and surface properties of liquid Al-Cu-Ni alloys[J]. Journal of Materials Engineering and Performance, 2025, 34(1): 368-378.
[16] SHI L, HU W X, LI C, et al.Application of an optimized geometrical model in predicting the physicochemical properties of Sn-based alloys[J]. Calphad, 2022, 76: 102385.
[17] YADAV S K, MEHTA U, ADHIKARI D.Optimization of thermodynamic and surface properties of ternary Ti-Al-Si alloy and its sub-binary alloys in molten state[J]. Heliyon, 2021, 7(3): e06511.
[18] SHROTRI V, MUHMOOD L.Application of geometric models for calculation of viscosity and density of LiNO₃ and CsNO₃ based ternary nitrate salt systems[J]. Calphad, 2020, 68: 101749.
[19] MEHTA U, YADAV S K, KOIRALA I, et al.Thermo-physical properties of ternary Al-Cu-Fe alloy in liquid state[J]. Philosophical Magazine, 2020, 100(19): 2417-2435.
[20] DHUNGANA A, YADAV S K, ADHIKARI D.Thermodynamic and surface properties of Al-Li-Mg liquid alloy[J]. Physica B: Condensed Matter, 2020, 598: 412461.
[21] CHOU K C, YU Z G.Calculation of the physicochemical properties for ternary solution with limited solubility[J]. Ceramics International, 2018, 44(17): 20955-20960.
[22] MANASIJEVIĆ D, ŽIVKOVIĆ D, ŽIVKOVIĆ Ž.Prediction of the thermodynamic properties for the Ga-Sb-Pb ternary system[J]. Calphad, 2003, 27(4): 361-366.
[23] HILLERT M.Empirical methods of predicting and representing thermodynamic properties of ternary solution phases[J]. Calphad, 1980, 4(1): 1-12.
[24] 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]. Journal de Chimie Physique et de Physico-Chimie Biologique, 1975, 72: 83-88.
MUGGIANU Y M, GAMBINO M, BROS J P.Formation enthalpies of liquid bismuth-tin-gallium alloys at 723 K. Choice of an analytical representation for integral and partial excess mixing properties[J]. Journal of Physical Chemistry and Biological Physical-Chemistry, 1975, 72: 83-88.
[25] TOOP G W.Predicting ternary activities using binary data[J]. Trans. TMS-AIME, 1965, 223: 850-855.
[26] KOHLER F.Zur berechnung der thermodynamischen daten eines ternären systems aus den zugehörigen binären systemen[J]. Monatshefte Für Chemie und Verwandte Teile Anderer Wissenschaften, 1960, 91(4): 738-740.
KOHLER F.On the calculation of thermodynamic data of a ternary system from the corresponding binary systems[J]. Monthly Journal for Chemistry and Related Fields of Other Sciences, 1960, 91(4): 738-740.
[27] JU T H, HUANG Z L, DING X Y, et al.A unified extrapolation thermodynamic model for multicomponent solutions based on binary data[J]. Thermochimica Acta, 2024, 740: 179824.
[28] JU T H, DING X Y, CHEN W L, et al.A new perspective on geometric thermodynamic models[J]. Journal of Phase Equilibria and Diffusion, 2019, 40(5): 715-724.
[29] 居天华, 舒念, 何维, 等. 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.
JU Tianhua, SHU Nian, HE Wei, et al.A predicted model for activity interaction coefficient between solutes in alloy solutions[J]. Acta Metallurgica Sinica, 2023, 59(11): 1533-1540.
[30] JU T H, DING X Y, ZHANG L, et al.A general model for solutes activity interaction parameters in dilute metallic solutions[J]. ISIJ International, 2020, 60(11): 2416-2424.
[31] WU Y, LV Y, LV Q W, et al.Effect of the excess entropy on the calculated activity interaction coefficient under the Miedema model and extrapolation method[J]. Calphad, 2025, 88: 102792.
[32] JU T H, DING X Y, YAN X L, et al.New expression for property difference in components for the unified extrapolation model[J]. Journal of Molecular Liquids, 2020, 320: 114469.
[33] 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 Equilibria, 2020, 515: 112588.
[34] CHOU K C, WEI S K.A new generation solution model for predicting thermodynamic properties of a multicomponent system from binaries[J]. Metallurgical and Materials Transactions B, 1997, 28(3): 439-445.
[35] CHOU K C.A general solution model for predicting ternary thermodynamic properties[J]. Calphad, 1995, 19(3): 315-325.
[36] REDLICH O, KISTER A T.Thermodynamics of nonelectrolyte solutions: x-y-t relations in a binary system[J]. Industrial & Engineering Chemistry, 1948, 40(2): 341-345.
[37] REDLICH O, KISTER A T.Algebraic representation of thermodynamic properties and the classification of solutions[J]. Industrial & Engineering Chemistry, 1948, 40(2): 345-348.
[38] PELTON A D.A general “geometric” thermodynamic model for multicomponent solutions[J]. Calphad, 2001, 25(2): 319-328.
[39] YU Z G, LENG H Y, LUO Q, et al.New insights into ternary geometrical models for material design[J]. Materials & Design, 2020, 192: 108778.
[40] CHOU K C, AUSTIN CHANG Y.A study of ternary geometrical models[J]. Berichte der Bunsengesellschaft Für Physikalische Chemie, 1989, 93(6): 735-741.
CHOU K C, AUSTIN CHANG Y.A study of ternary geometrical models[J]. Reports of the German Bunsen Society for Physical Chemistry, 1989, 93(6): 735-741.
[41] CHOU K C, LI W C, LI F S, et al.Formalism of new ternary model expressed in terms of binary regular-solution type parameters[J]. Calphad, 1996, 20(4): 395-406.
[42] ZHANG G H, CHOU K C.General formalism for new generation geometrical model: application to the thermodynamics of liquid mixtures[J]. Journal of Solution Chemistry, 2010, 39(8): 1200-1212.
[43] FISCHER L, FLANDORFER H.Calorimetric study of the enthalpy of mixing in the liquid systems In-Li and In-Li-Sn[J]. Journal of Molecular Liquids, 2025, 417: 126527.
[44] FIMA P, FLANDORFER H.Enthalpy of mixing of liquid Ag-Bi-Cu alloys at 1 073 K[J]. Thermochimica Acta, 2014, 575: 336-342.
[45] KNOTT S, FLANDORFER H, MIKULA A.Calorimetric investigations of the two ternary systems Al-Sn-Zn and Ag-Sn-Zn[J]. International Journal of Materials Research, 2005, 96(1): 38-44.
[46] HASSAM S, GAMBINO M, PIERRE BROS J.Enthalpy of formation of liquid Ag-Bi and Ag-Bi-Sn alloys[J]. International Journal of Materials Research, 1994, 85(7): 460-471.
[47] FITZNER K, GUO Q T, WANG J W, et al.Enthalpies of liquid-liquid mixing in the systems Cu-Ag, Cu-Au and Ag-Au by using an in-situ mixing device in a high temperature single-unit differential calorimeter[J]. Journal of Alloys and Compounds, 1999, 291(1/2): 190-200.
[48] KLEPPA O, WATANABE S.Thermochemistry of alloys of transition metals: part Ⅲ. copper-silver, -titanium, zirconium, and -hafnium at 1 373 K[J]. Metallurgical Transactions B, 1982, 13: 391-401.
[49] GĄSIOR W, MOSER Z. Thermodynamic properties of Li-Sn (lithium-tin) liquid solutions[J]. Archives of Metallurgy, 1999, 44(1): 83-92.
[50] DAVID N, EL AISSAOUI K, FIORANI J M, et al.Thermodynamic optimization of the In-Pb-Sn system based on new evaluations of the binary borders In-Pb and In-Sn[J]. Thermochimica Acta, 2004, 413(1/2): 127-137.
[51] QIAO Z Y, XING X, PENG M, et al.Thermodynamic criterion for judging the symmetry of ternary systems and criterion applications[J]. Journal of Phase Equilibria, 1996, 17(6): 502-507.