{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T14:15:24Z","timestamp":1770905724281,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,22]],"date-time":"2018-10-22T00:00:00Z","timestamp":1540166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2017YFB0603800, 2017YFB0603801 and 2017YFB0603802"],"award-info":[{"award-number":["2017YFB0603800, 2017YFB0603801 and 2017YFB0603802"]}]},{"name":"National Natural Science Foundation","award":["51604049"],"award-info":[{"award-number":["51604049"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It is important to know the activity interaction parameters between components in melts in the process of metallurgy. However, it\u2019s considerably difficult to measure them experimentally, relying still to a large extent on theoretical calculations. In this paper, the first-order activity interaction parameter (     e s j     ) of j on sulphur in Fe-based melts at 1873 K is investigated by a calculation model established by combining the Miedema model and Toop-Hillert geometric model as well as considering excess entropy and mixing enthalpy. We consider two strategies, with or without using excess entropy in the calculations. Our results show that: (1) the predicted values are in good agreement with those recommended by Japan Society for Promotion of Science (JSPS); and (2) the agreement is even better when excess entropy is considered in the calculations. In addition, the deviations of our theoretical results from experimental values      |   e  S  (  exp  )   j  \u2212  e  S  (  cal  )   j   |      depend on the element j\u2019s locations in the periodic table.<\/jats:p>","DOI":"10.3390\/e20100808","type":"journal-article","created":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T08:43:36Z","timestamp":1540284216000},"page":"808","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Estimation of Activity Interaction Parameters in Fe-S-j Systems"],"prefix":"10.3390","volume":"20","author":[{"given":"Tianhua","family":"Ju","sequence":"first","affiliation":[{"name":"School of Metallurgy, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueyong","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Metallurgy, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingyi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Metallurgical Engineering, Anhui University of Technology, Maanshan 243002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiliang","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Metallurgy, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangkui","family":"Cheng","sequence":"additional","affiliation":[{"name":"Institute of International Vanadium Titanium, Panzhihua University, Panzhihua 617000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Metallurgy, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingxin","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Metallurgy, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinlin","family":"Yan","sequence":"additional","affiliation":[{"name":"Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"833","DOI":"10.2355\/isijinternational.39.833","article-title":"The influence of composition on the hot ductility of steels and to the problem of transverse cracking","volume":"39","author":"Mintz","year":"1999","journal-title":"ISIJ Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1038\/415770a","article-title":"Why stainless steel corrodes","volume":"415","author":"Ryan","year":"2002","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/S1001-0521(06)60077-6","article-title":"Thermodynamic aspects of inclusion engineering in steels","volume":"25","year":"2006","journal-title":"Rare Met."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gollapalli, V., Rao, M.B.V., Karamched, P.S., Borra, C.R., Roy, G.G., and Srirangam, P. (2018). Modification of oxide inclusions in calcium-treated Al-killed high sulphur steels. Ironmak. Steelmak., 1\u20138.","DOI":"10.1080\/03019233.2018.1443382"},{"key":"ref_5","unstructured":"Wagner, C. (1952). Thermodynamics of Alloys, Addison-Wesley Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/0001-6160(66)90320-8","article-title":"Generalized interaction coefficients","volume":"14","author":"Lupis","year":"1966","journal-title":"Acta Metall."},{"key":"ref_7","first-page":"80","article-title":"Thermodynamics of binary metallic solutions","volume":"239","author":"Darken","year":"1967","journal-title":"Trans. Met. Soc. AIME"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1007\/BF02665320","article-title":"A modified interaction parameter formalism for non-dilute solutions","volume":"17","author":"Pelton","year":"1986","journal-title":"Metall. Trans. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1007\/BF02647247","article-title":"The unified interaction parameter formalism: Thermodynamic consistency and applications","volume":"21","author":"Bale","year":"1990","journal-title":"Metall. Trans. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.2298\/JMMB150901001C","article-title":"Interaction parameters of oxygen and deoxidants in liquid iron","volume":"52","year":"2016","journal-title":"J. Min. Metall. Sect. B Metall."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1515\/htmp-2012-0023","article-title":"Interaction parameters in metallic solutions estimated from liquid structure and the heat of solution at infinite dilution","volume":"31","author":"Waseda","year":"2012","journal-title":"High Temp. Mater. Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s11663-999-0056-z","article-title":"Thermodynamic calculation for alloy systems","volume":"30","author":"Ding","year":"1999","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_13","first-page":"49","article-title":"Models of activity and activity interaction parameter in ternary metallic melt","volume":"30","author":"Ding","year":"1994","journal-title":"Acta Metall. Sin."},{"key":"ref_14","first-page":"474","article-title":"Theoretical treatment of interaction parameters in multicomponent metallic solutions","volume":"59","author":"Ueno","year":"1988","journal-title":"Process Metall."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3099","DOI":"10.1007\/s11661-999-0220-8","article-title":"A self-consistent model for predicting interaction parameters in multicomponent alloys","volume":"30","author":"Fan","year":"1999","journal-title":"Metall. Mater. Trans. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s11663-997-0133-0","article-title":"A model for calculating interaction coefficients between elements in liquid and iron-base alloy","volume":"28","author":"Wang","year":"1997","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1515\/htmp-2012-0123","article-title":"Modeling Activity and Interaction Coefficients of Components of Multicomponent Alloy Melts: An Example of Iron Melt","volume":"32","author":"Zhang","year":"2013","journal-title":"High Temp. Mater. Process."},{"key":"ref_18","unstructured":"Ding, X., Fan, P., and Luo, L. (1998). Alloy Melts Thermodynamic Model: Prediction and Software Development, Northeastern University Press. (In Chinese)."},{"key":"ref_19","unstructured":"Neuhausen, J., and Eichler, B. (2003). Extension of Mediema\u2019s Macroscopic Atom Model to the Elements of Group 16 (O, S, Se, Te, Po), Paul Scherrer Inst."},{"key":"ref_20","unstructured":"Hino, M., and Ito, K. (2010). Thermodynamic Data for Steelmaking, Tohoku University Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/srin.199401184","article-title":"Calcium desulfurization equilibrium in liquid iron","volume":"65","author":"Inoue","year":"1994","journal-title":"Steel Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0364-5916(80)90016-4","article-title":"Empirical methods of predicting and representing thermodynamic properties of ternary solution phases","volume":"4","author":"Hillert","year":"1980","journal-title":"Calphad"},{"key":"ref_23","first-page":"192","article-title":"Thermodynamic relationship between enthalpy of mixing and excess entropy in liquid binary alloys","volume":"84","author":"Tanaka","year":"1993","journal-title":"Zeitschrift f\u00fcr Metallkunde"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0378-4363(80)90054-6","article-title":"Cohesion in alloys\u2014Fundamentals of a semi-empirical model","volume":"100","author":"Miedema","year":"1980","journal-title":"Physica B+C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/0378-4363(88)90296-3","article-title":"Enthalpies of formation of liquid and solid binary alloys based on 3d metals: IV. Alloys of cobalt","volume":"151","author":"Niessen","year":"1988","journal-title":"Physica B+C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0364-5916(83)90030-5","article-title":"Model predictions for the enthalpy of formation of transition metal alloys II","volume":"7","author":"Niessen","year":"1983","journal-title":"Calphad"},{"key":"ref_27","first-page":"62","article-title":"Calculation of the Heat of Formation of Ternary Compounds\u2014P-Ga-as, N-Ga-as, N-Ga-P","volume":"4","author":"Wu","year":"1995","journal-title":"Acta Phys. Sin."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.2355\/isijinternational.43.1705","article-title":"Deoxidation and desulfurization equilibria of liquid iron by calcium","volume":"43","author":"Taguchi","year":"2003","journal-title":"ISIJ Int."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0022-5088(85)90321-2","article-title":"Thermodynamics of rare earth elements in liquid iron","volume":"110","author":"Wu","year":"1985","journal-title":"J. Less-Common Met."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1063\/1.1499510","article-title":"Proposed model for calculating the standard formation enthalpy of binary transition-metal systems","volume":"81","author":"Zhang","year":"2002","journal-title":"Appl. Phys. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.cplett.2011.07.076","article-title":"An improved atomic size factor used in Miedema\u2019s model for binary transition metal systems","volume":"513","author":"Sun","year":"2011","journal-title":"Chem. Phys. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.calphad.2006.04.004","article-title":"Miedema\u2019s model revisited: The parameter for Ti, Zr, and Hf","volume":"30","author":"Chen","year":"2006","journal-title":"Calphad"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1361\/105497100770340192","article-title":"On the choice of \u201cGeometric\u201d thermodynamic models","volume":"21","author":"Chartrand","year":"2000","journal-title":"J. Phase Equilib."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/10\/808\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:25:31Z","timestamp":1760196331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/10\/808"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,22]]},"references-count":33,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["e20100808"],"URL":"https:\/\/doi.org\/10.3390\/e20100808","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,22]]}}}