[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657738-105":59,"doc-detail-657738-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","time-temperature-transformation-diagrams-for-the-growth-and-dissolution-of-inclusions-in-liquid-steels","TIME-TEMPERATURE-TRANSFORMATION DIAGRAMS FOR THE GROWTH AND DISSOLUTION OF INCLUSIONS IN LIQUID STEELS","","Time-temperature-transformation (TTT) diagrams are synthesized to describe how non-metallic inclusions form, grow, and dissolve in liquid steels. The paper presents a diffusion-controlled formalism that links time and temperature to inclusion growth and dissolution kinetics for steels with known compositions. Modeling assumptions fix local concentration fields and take activities of liquid iron and solid compounds as unity. Interface chemistry is defined by equilibrium constants derived from standard free energy changes, enabling calculation of interfacial concentrations and resulting TTT curves for growth and dissolution.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/time-temperature-transformation-diagrams-for-the-growth-and-dissolution-of-inclusions-in-liquid-steels/657738/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/time-temperature-transformation-diagrams-for-the-growth-and-dissolution-of-inclusions-in-liquid-steels/657738.png","ImageObject",300,407,{"name":92,"@type":93},"McGucket","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main objective of the paper?","Question",{"text":112,"@type":113},"To synthesize existing knowledge into a unified diffusion-controlled framework that explains inclusion growth and dissolution behavior in liquid steels and enables construction of TTT diagrams.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What assumptions are used to simplify the kinetics calculations?",{"text":117,"@type":113},"The model assumes constant concentration fields near each inclusion during growth/dissolution and sets activities of liquid iron and solid compounds to unity, while interface calculations focus only on the inclusion-forming elements.",{"name":119,"@type":110,"acceptedAnswer":120},"How are the TTT diagrams for growth and dissolution obtained?",{"text":121,"@type":113},"The approach computes interfacial concentrations from thermodynamic equilibrium relations, then uses diffusion-controlled rate equations to determine the time needed for inclusion radius changes at different temperatures, forming the TTT curves.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657738,1792987715,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},1236954412713,"https://us-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Scripta mater. 44 (2001) 847–852 ~~ ~~  \n[www.elsevier.com/locate/scriptamat](www.elsevier.com/locate/scriptamat)  \nTIME-TEMPERATURE-TRANSFORMATION DIAGRAMS FOR THE GROWTH AND DISSOLUTION OF INCLUSIONS IN  \nLIQUID STEELS  \nT. Hong and T. DebRoy  \nDepartment of Materials Science and Engineering, The Pennsylvania State University,  \nUniversity Park, PA 16802, USA  \n(Received September 15, 2000)  \n(Accepted October 9, 2000)  \nKeywords: Inclusion; Growth; Dissolution; TTT diagram  \nIntroduction  \nSeveral aspects of inclusion formation, growth and dissolution in liquid steels have been well studied. These include the thermodynamic stability and diffusion controlled growth and dissolution rates of inclusions [1,2] . By contrast, synthesis of the accumulated knowledge of these component processes has been largely overlooked. Examples in contemporary physical metallurgy indicate that such synthesis can be very useful. For example, the time-temperature-transformation (TTT) diagram has become an essential tool to understand phase transformation in alloys. Currently no such unified approach is available for understanding the growth and dissolution behavior of inclusions in liquid steels.  \nThe goal of this paper is to synthesize our current knowledge of stability and growth/dissolution kinetics of inclusions in liquid steels in a form that allows a clear understanding of their growth and dissolution behavior. In particular, a formalism is presented here that describes the effects of time and temperature on the diffusion controlled growth and dissolution kinetics of inclusions in steels of known compositions.  \nBackground  \nThe rates of growth and dissolution of inclusions in liquid steels are calculated based on the following assumptions in order to simplify calculations:  \n1. The concentration field near each inclusion was assumed to be constant during the growth or dissolution of inclusions.  \n2. The activities of liquid iron and all solid compounds were assumed to be unity.  \n3. At the interface between the inclusion and the liquid steel, only the concentrations of those elements that constitute the inclusion were calculated. The concentrations of all other elements were assumed to be the same as those in the bulk metal.  \n4. The growth and dissolution of inclusions were assumed to be controlled by the diffusion of non-metallic elements of inclusions in liquid steels.  \nThe following reaction is considered at the interface between an inclusion particle and liquid steel:  \n1359-6462/01/$–see front matter. © 2001 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00675-8  \n848 TTT DIAGRAMS FOR INCLUSIONS IN STEELS Vol. 44, No. 5  \nTABLE 1  \nStandard Free Energy Change for Various Reactions [7,8]  \nDG° 5 a 1 bT, kJ/mole  \n\n| Reaction | a | b |\n| --- | --- | --- |\n| 2Al 1 3O 5 Al2O3\u003Cbr>3Ti 1 5O 5 Ti3O5\u003Cbr>Ti 1 2O 5 TiO2\u003Cbr>Si 1 2O 5 SiO2\u003Cbr>Mn 1 O 5 MnO\u003Cbr>Ti 1 N 5 TiN\u003Cbr>Mn 1 2Al 1 4O 5 MnO.Al2O3 Si 1 2Al 1 5O 5 SiO2.Al2O3 Mn 1 Si 1 4O 5 MnO.SiO2 | 21209 | 0.391 |\n|  | 21756 | 0.571 |\n|  | 2675.6 | 0.234 |\n|  | 2589.7 | 0.229 |\n|  | 2287.9 | 0.125 |\n|  | 2338.2 | 0.104 |\n|  | 21545 | 0.524 |\n|  | 21338 | 0.407 |\n|  | 2838.8 | 0.314 |\n\nThe standard state for the solutes is hypothetical 1 wt% solution in iron.  \nxM 1 yQ º MxQy (1)  \nwhere M is a metallic element such as Al, Ni, Mn, Si or Ti, and Q stands for a nonmetallic element, such as O, N, or S. The equilibrium constant for the reaction is given by equation (2) .  \nkeq 5 aMxxQy 5  1  5 e 2DRGT0 (2)  \naMayQ @ fMciM\\#x @ fQc iQ\\#y  \nwhere aMxQy, aM, and aQ are the activities of MxQy, M and Q, ciM and ciQ are the interfacial concentrations of M and Q in weight percent, fM and fQ are the activity coefficients of M and Q, and DG0 is the standard free energy change for the reaction (1) . Considering the ratio of the fluxes of M and Q, the following equation can be derived [3]:  \nciM 5 cbM 2 xmymMQ ÎD~~ ~~QD~~ ~~M  ~cbQ 2 ciQ! (3)  \nwhere cbM an","cbCaichWcXMAsJp7","https://ap.wps.com/l/cbCaichWcXMAsJp7","pdf",222973,"English","# Introduction\n## Background\n## TTT Diagrams for Growth\n## TTT Diagrams for Dissolution","[{\"question\":\"What is the main objective of the paper?\",\"answer\":\"To synthesize existing knowledge into a unified diffusion-controlled framework that explains inclusion growth and dissolution behavior in liquid steels and enables construction of TTT diagrams.\"},{\"question\":\"What assumptions are used to simplify the kinetics calculations?\",\"answer\":\"The model assumes constant concentration fields near each inclusion during growth/dissolution and sets activities of liquid iron and solid compounds to unity, while interface calculations focus only on the inclusion-forming elements.\"},{\"question\":\"How are the TTT diagrams for growth and dissolution obtained?\",\"answer\":\"The approach computes interfacial concentrations from thermodynamic equilibrium relations, then uses diffusion-controlled rate equations to determine the time needed for inclusion radius changes at different temperatures, forming the TTT curves.\"}]","TIME-TEMPERATURE-TRANSFORMATION DIAGRAMS FOR THE GROWTH AND DISSOLUTION OF INCLUSIONS IN LIQUID STEELS | PDF",15]