Pergamon ,4eta metall, mater. Vol. 43, No. 10, pp. 3763-3774, 1995 ElsevierScience Ltd Copyright© 1995Acta Metallurgica Inc. 0956-7151(95)00071-2 Printed in Great Britain.All rights reserved 0956-7151/95$9.50+ 0.00 A SOLUTE DRAG TREATMENT OF THE EFFECTS OF ALLOYING ELEMENTS ON THE RATE OF THE PROEUTECTOID FERRITE TRANSFORMATION IN STEELS G. R. PURDY I and Y. J. M. BRECHET 2 ~Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario, Canada and 2LTPCM, ENSEEG, Institut National Polytechnique de Grenoble, St Martin d'Heres, France (Received 14 April 1994; in revised form 10 January 1995) A~traet--The problem of diffusional growth of a proeutectoid constituent in a ternary steel is considered, taking into account the interfacial diffusion of a slow-diffusingsubstitutional solute, under conditions which do not permit its long-range redistribution between parent and daughter phases. It is assumed that the faster diffusing interstitial solute (carbon) controls the rate of the transformation. The substitutional solute profile within (across) the interface is estimated as a function of interface velocity; the interstitial chemical potential differenceis allowed to vary with, and balance, the solute drag due to the substitutional component. A transition to paraequilibrium is found at high interface velocities,and a variety of behaviour is predicted for intermediate states, depending on the relative rates of diffusion of the two solutes and their energetic interactions with each other and with the interphase boundary. INTRODUCTION We are interested in the diffusional growth of a proeutectoid constituent (ferrite) in a ternary steel. The analysis will hold in principle for the initial growth of a grain-boundary precipitate from a super- saturated austenite containing two solutes whose diffusivities are very different; this is often the case for interstitial solutes (e.g. carbon or nitrogen) which coexist with substitutional solutes (e.g. manganese or molybdenum). The present work owes much to previous analyses; its genealogy can be traced to independent origins in the work of Kirkaldy and coworkers at McMaster University [1-3], and of Hultgren and Hillert and their coworkers at the Royal Institute of Technology, Stockholm [4-7]. In these treatments, structural inhi- bitions to growth are not considered, planar or steady interface migration into a semi-infinite parent phase is assumed, and the local equilibrium interfacial condition is taken as a starting point; indeed the three-component local equilibrium growth problem is surprisingly complicated [2], because, in contrast to the binary case, the tie-line on the Gibbs triangle which determines the equilibrium interfacial concen- trations is a priori unknown, and must be determined as part of the solution of sets of coupled ternary diffusion equations and mass balances. A simplification arises due to the great difference between the diffusivities of the interstitial (component 1) and subtitutional (component 2) solutes; when DII>>D22, the mass balances (which must be simul- taneously satisfied), require that the ternary isotherm be divided into two regions: one, of low supersatura- tion, where the slow diffusing solute must partition and thereby control the rate of the transformation; and a second, at higher supersaturation, where the slow-diffusing solute can only redistribute locally (resulting in a solute "spike" in front of the interface), and not partition. In the latter case, the rate of interface migration is controlled by the diffusion of component 1, whose interfacial concentration in the parent austenite, C*, is determined in part by the presence of component 2. The two regions are shown schematically in Fig. 1, where the "envelope of zero partition", as defined by Purdy et al. [2], marks the kinetic boundary between fast (carbon controlled) and slow (alloying element controlled) transform- ation kinetics. In the foregoing review, diffusional processes within the transformation interface have been im- plicitly neglected, and simplifications which derive from the fact that the two solutes diffuse at very different rates emphasized. However, the same prop- erty that allows these limiting approximations raises another well-recognized problem: Because D22 is small, the estimated diffusional penetration in the parent austenite (for typical rates of interface motion) is often very small, of the order of the interatomic spacing, and the neglect of dissipative processes within and immediately adjacent to the interface can no longer be justified. In recognition of this problem, a further limiting case has been defined, and called "paraequilibrium" by Hultgren [4] and Hillert [5], "no-partition equi- librium" by Aaronson et al. [9]. This hypothetical 3763