Coupled diffusional/displacive transformations: Part II. Solute trapping
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I.
INTRODUCTION
M A R T E N S I T I C transformation of austenite in steels has long been recognized to involve the diffusionless nucleation and growth of supersaturated plates. There is a large difference in the diffusivities of interstitial carbon and iron (or substitutional solutes). The possibility then arises that the substitutional lattice can be transformed by a displacive mechanism, while the carbon atoms redistribute between the parent and product phases, t~] Circumstances could arise whereby the transformation interface then advances sufficiently slowly to enable the equilibrium or paraequilibrium partitioning of carbon. Alternatively, only some of the carbon may redistribute during transformation, the rest being trapped by the advancing interface. Since any diffusion field is, by its very nature, subject to random perturbations, opportunities must arise for the field to adjust toward lower free energy states. It follows that there will be a tendency for the growth process to collapse toward equilibrium. Hence, growth involving partial supersaturation has to be stabilized by some process which occurs in series with the diffusion of solute. t2,31 One such stabilizing process is that of structural change across the interfaceJ 31 The rate at which the interface moves depends both on its intrinsic mobility (related to the process of structural change across the interface) and on the ease with which the partitioned solute can diffuse ahead of the moving interface. Since the two processes are in series, the interfacial velocity as G.B. OLSON, Professor, is with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208. H.K.D.H. BHADESHIA, Lecturer, is with the Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 3QZ, United Kingdom. M. COHEN, Institute Professor Emeritus, is with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. This paper is based on a presentation made in the symposium "International Conference on Bainite" presented at the 1988 World Materials Congress in Chicago, IL, on September 26 and 27, 1988, under the auspices of the ASM INTERNATIONAL Phase Transformations Committee and the TMS Ferrous Metallurgy Committee. METALLURGICAL TRANSACTIONS A
calculated from the interface mobility must always equal that computed from the diffusion of solute ahead of the interface. By considering the simultaneous solution of the interface mobility and diffusion field velocity functions, we modeled the displacive transformation of Fe-C austenite to plates of ferrite which were partially supersaturated with carbon, t31 The interface mobility law characteristic of martensitic transformations t3,*-61 was utilized as one of the velocity solutions (or "interface response functions"), the other being the Ivantsov solution t3,7j for the diffusion field velocity. Since the number of unknowns to solve for is three (the supersaturation, the composition in the austenite at the interface
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