{"title":"On the transition from local equilibrium to paraequilibrium during the growth of ferrite in Fe-Mn-C austenite","authors":"Zi-Kui Liu, J. Ågren","doi":"10.1016/0001-6160(89)90187-9","DOIUrl":null,"url":null,"abstract":"<div><p>The concept of paraequilibrium, introduced a long time ago by Hultgren and analyzed thermodynamically by Hillert, has been analyzed in detail by means of a kinetic model. The concept applies to alloy systems where there is a large difference in mobility of the different components, e.g. in steels where substitutional elements diffuse many orders of magnitude slower than interstitial solutes like <em>H</em>, <em>C</em> and <em>N</em>. By definition paraequilibrium means that only the mobile elements are equilibrated while the sluggish ones behave as a single element. In the present work we have applied a phenomenological model that takes into account the diffusion in the matrix in front of a moving phase interface, a finite interface mobility, the effect of surface tension and the sluggishness of diffusion across the phase interface, i.e. the solute drag. We have studied theoretically the edgewise growth of a ferrite platelet in Fe-Mn-C alloys. In particular we have studied how the growth process depends on the Mn content. We have investigated under what conditions paraequilibrium or full thermodynamic equilibrium is established locally at a moving phase interface.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 12","pages":"Pages 3157-3163"},"PeriodicalIF":0.0000,"publicationDate":"1989-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90187-9","citationCount":"58","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Metallurgica","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0001616089901879","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 58
Abstract
The concept of paraequilibrium, introduced a long time ago by Hultgren and analyzed thermodynamically by Hillert, has been analyzed in detail by means of a kinetic model. The concept applies to alloy systems where there is a large difference in mobility of the different components, e.g. in steels where substitutional elements diffuse many orders of magnitude slower than interstitial solutes like H, C and N. By definition paraequilibrium means that only the mobile elements are equilibrated while the sluggish ones behave as a single element. In the present work we have applied a phenomenological model that takes into account the diffusion in the matrix in front of a moving phase interface, a finite interface mobility, the effect of surface tension and the sluggishness of diffusion across the phase interface, i.e. the solute drag. We have studied theoretically the edgewise growth of a ferrite platelet in Fe-Mn-C alloys. In particular we have studied how the growth process depends on the Mn content. We have investigated under what conditions paraequilibrium or full thermodynamic equilibrium is established locally at a moving phase interface.