Quantifying the Solute Drag Effect on Ferrite Growth in Fe-C-X Alloys Using Controlled Decarburization Experiments
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TRODUCTION
IT is well known that segregated impurity atoms can drastically reduce the mobility of grain boundaries in pure metals. Lucke and Detert[1] developed the first quantitative treatment of this effect to explain their observations that the recrystallization rate of high purity Al could be reduced by many orders of magnitude by the addition of 0.01 pct Mn or Fe. They attributed the effect to an interaction between the solute atoms in solution and the moving grain boundaries. The phenomenon is now considered to be a general effect and is usually referred to as the ‘solute-drag effect’. The solute-drag effect has received considerable attention both because of its scientific interest and because of the central role of interface motion during the thermomechanical processing of many industrially important alloys. Soon after the initial treatment of Lucke and Detert, Cahn[2] presented his theoretical treatment, which was later followed by similar approaches by Lucke and Stuwe[3,4] and this ‘force’ approach has become one of two solute drag theories that have come to dominate the physical metallurgy literature. The force approach invokes an interaction energy profile, E(x), between a solute atom and a grain boundary and by solving the diffusion CONG QIU, Ph.D. Student and CHRISTOPHER HUTCHINSON, Associate Professor and ARC Future Fellow, are with the Department of Materials Engineering, Monash University, Clayton, VIC 3800, Australia. Contact e-mail: [email protected] HATEM ZUROB, Associate Professor, GARY PURDY, Professor, and DAMON PANAHI, Ph.D. Student, are with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON, Canada, YVES BRECHET, Professor, is with the SIMAP, Institut National Polytechnique de Grenoble, 38402 St Martin D’He`res, France. Manuscript submitted June 30, 2012. Article published online December 11, 2012 3472—VOLUME 44A, AUGUST 2013
equation for the solute across the migrating boundary the solute concentration profile across the boundary as a function of boundary velocity can be found. The behavior of the solute under the extremes of grain boundary motion is self-evident. When the grain boundary moves with a velocity that is very slow compared to the diffusion of the solute in the vicinity of the grain boundary, the concenh i profile for a tration profile will be close to the equilibrium stationary boundary, CðxÞ ¼ Co exp EðxÞ kT , where Co is the bulk solute content. If the grain boundary velocity is fast compared to the diffusion of the solute, then the concentration profile approaches the uniform bulk alloy composition Co, through the boundary. However, at intermediate velocities, more interesting, asymmetric concentration profiles are possible. It should be emphasised that to calculate such profiles it is necessary to quantitatively describe the solute interaction profile with the boundary, E(x), and the solute diffusivity across the boundary, D(x), neither of which is known with much certainty. Cahn argued that an impurity atom will be attracted to the cent
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