ON THE KINETICS OF INTERFACE-DIFFUSION- CONTROLLED PERITECTOID REACTIONS L. KLINGER 1 , Y. BRE Â CHET 2 and G. PURDY 3 1 Department of Materials Engineering, Technion, HaõÈfa, 32000, Israel, 2 L.T.P.C.M., Groupe ``physique du meÂtal'', Domaine Universitaire de Grenoble, BP75, 38402 Saint Martin d'Heres Cedex, France and 3 Department of Materials Science and Engineering, McMaster University, 1280 Main Street West, Hamilton, Ont., Canada L8S 4L7 (Received 19 November 1997; accepted 23 November 1997) AbstractÐWe consider the peritectoid reaction a + b 4 o as it occurs at previously existing planar a/b interfaces, and at suciently low temperatures that volume diusion is negligible and interphase boundary diusion is rate-controlling. With the further assumption that the participating phases have ®xed compo- sitions and that the interfacial diusion process is driven by gradients in interfacial curvature, we obtain a unique solution for the growth of the product o layer along the a/b interface. Both the layer thickness and the steady lengthening velocity are predicted. The layer thickness is of the same order as the capillary length; it would be dicult to detect by conventional means, but could be revealed for example by T.E.M. The layer growth is determined entirely by the undercooling, the interfacial energies and the relevant kin- etic quantities. The presence of such thin layers at parent phase interfaces is expected to exert a profound in¯uence on microstructurally determined properties. # 1998 Acta Metallurgica Inc. 1. INTRODUCTION When alloys are driven far from equilibrium at rela- tively low temperatures, bulk diusion cannot always provide the mass transport required to respond to the driving force, and in many cases interfacial diusion becomes the key kinetic process. In a previous contribution [1] we have considered the kinetics and mechanisms of homogenization of a multilayer by surface diusion along the moving interface, a phenomenon which is reminiscent of DIGM. In that case the parent phases were pure metals, the daughter phase a solid solution (contain- ing concentration gradients) and the transport at the interface was mainly driven by concentration gradi- ents. The other extreme case in this class of pro- blems concerns the situation where both the parent phases and the daughter phase have de®nite compo- sitions. In this situation, the driving force for surface diusion will be the gradient in interface curvature. In the present paper, which can be seen as a compa- nion to [1], we investigate this problem from various viewpoints: what are the kinetic laws and what is the morphology of a new phase growing by inter- facial diusion between two parent phases? Throughout this paper we will consider a situation where the ao and the bo interfaces may have dier- ent thermodynamics and transport properties, and we will also investigate the eect of this dierence on the anisotropy of the growth morphologies. The general problem considered here is the peri- tectoid reaction: a + b 4 o specialized to the case of o growth along a planar a/b interface by inter- facial diusion. This situation will arise, for example when a lamellar eutectic product, formed at high temperature, is cooled below a peritectoid temperature, as suggested by schematic phase dia- gram of Fig. 1. Of course, any high-temperature precipitation reaction that produces planar a/b interfaces (e.g. WidmanstaÈtten precipitation, discontinuous precipi- tation, eutectoid decomposition) would serve equally well as a precursor for peritectoid trans- formation considered here. For the sake of simplicity we will deal with ideal binary stoichiometric compounds for which the free energy diagram G(c) is very sharp so that the com- position of the various phases a, b and o are pre- scribed to c a , c b and c o (c denotes the mole fraction of element B and 1  c the mole fraction of A). In particular the equilibrium composition of these phases is essentially independent of the local curva- ture. We will also assume that the atomic volumes O in the various phases are identical. The main con- sequence of this assumption is the absence of trans- formation stresses due to mis®t between participating phases. Concerning notation, infor- mation pertaining to phases will be shown as sub- scripts and that concerning elements will be given in superscript. For instance m ao A will denote the chemical potential of element A at the interface between the a and the o phases, g ao and K ao the surface energy and the curvature of the interface between a and o, G a (c) will represent the free energy function of the a phase and P a the capillary pressure acting on this phase, and so on. The refer- ence free energy (i.e. in the absence of any capillary Acta mater. Vol. 46, No. 8, pp. 2617±2621, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 PII: S1359-6454(97)00471-0 2617