合金溶液中溶质间活度相互作用系数预测模型
收稿日期: 2022-04-29
修回日期: 2022-06-24
网络出版日期: 2022-11-16
A Predicted Model for Activity Interaction Coefficient Between Solutes in Alloy Solutions
Received date: 2022-04-29
Revised date: 2022-06-24
Online published: 2022-11-16
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 . DOI: 10.11900/0412.1961.2022.00202
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.
| 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 |
| 3 | Sigworth G K, Elliott J F. The thermodynamics of liquid dilute iron alloys [J]. Met. Sci., 1974, 8: 298 |
| 4 | Sigworth G K, Elliott J F. The thermodynamics of dilute liquid cobalt alloys [J]. Can. Metall. Q., 1976, 15: 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 |
| 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 |
| 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 |
| 9 | Niu J P, Shan Z Q, Geng S Q, et al. Calculation of interaction coefficient e N T i and activity coefficient fN of titanium to nitrogen in nickel-based superalloy [J]. Vacuum, 2018, 55(3): 45 |
| 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fN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 |
| 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 |
| 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 | Zaj?czkowski A, Suru?o A. Thermodynamics of copper-rich liquid Cu-Fe-Bi alloys determined by vapour pressure measurements [J]. Calphad, 2019, 64: 272 |
| 13 | Alcock C B, Richardson F D. Dilute solutions in molten metals and alloys [J]. Acta Metall., 1958, 6: 385 |
| 14 | Alcock C B, Richardson F D. Dilute solutions in alloys [J]. Acta Metall., 1960, 8: 882 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 Chatel P F, de Boer F R. Cohesion in alloys—Fundamentals of a semi-empirical model [J]. Physica B + C, 1980, 100: 1 |
| 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 |
| 30 | Chou K C, Austin Chang Y. A study of ternary geometrical models [J]. Ber. Bunsenges. Phys. Chem., 1989, 93: 735 |
| 31 | Lupis C H P, Elliott J F. Generalized interaction coefficients: Part I: Definitions [J]. Acta Metall., 1966, 14: 529 |
| 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 |
| 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 |
| 35 | Chartrand P, Pelton A D. On the choice of “geometric” thermodynamic models [J]. J. Phase Equilib., 2000, 21: 141 |
| 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 |
| 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 |
| 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 |
| 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 |
| 42 | Kohler F. Estimation of the thermodynamic data for a ternary system from the corresponding binary systems [J]. Monatsh. Chem., 1960, 91: 738 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
/
| 〈 |
|
〉 |
