On the formation of Widmanst€ atten ferrite in binary Fe–C – phase-field approach Irina Loginova a, * , John  Agren b , Gustav Amberg a a Department of Mechanics, KTH, S-100 44 Stockholm, Sweden b Department of Materials Science and Engineering, KTH, S-100 44 Stockholm, Sweden Received 10 November 2003; received in revised form 10 May 2004; accepted 11 May 2004 Available online 19 June 2004 Abstract A phase-field method, based on a Gibbs energy functional, is formulated for c ! a transformation in Fe–C. The derived phase- field model reproduces the following important types of phase transitions: from C diffusion controlled growth through Wid- manst€ atten microstructures to massive growth without partitioning of C. Applying thermodynamic functions assessed by the Calphad technique and diffusional mobilities available in the literature, we study two-dimensional growth of ferrite side plates emanating from an austenite grain boundary. The morphology of the ferrite precipitates is defined by a highly anisotropic interfacial energy. As large values of anisotropy lead to an ill-posed phase-field equation we present a regularization method capable of cir- cumvent non-differentiable domains of interfacial energy. Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Phase-field method; Widmanst€ atten plates; Diffusion; Morphological instability 1. Introduction The transformation of austenite to ferrite upon cooling is one of the most studied and well documented subjects in physical metallurgy. Nevertheless, some as- pects, which are technologically important as well as of fundamental interest, still remain less well understood and they often lead to controversies. It is generally ac- cepted that at low undercooling more or less equiaxed and rather coarse ferrite particles form along austenite grain boundaries, so-called allotriomorphic ferrite. They grow with a rate controlled by carbon diffusion in aus- tenite. Calculations based on carbon diffusion and local equilibrium at the austenite/ferrite phase interface yield growth rates that essentially agree with the experimen- tally observed ones. At higher undercoolings ferrite ra- ther grows with a plate-like so-called acicular or Widmanst€ atten morphology [1]. On the broad sides the austenite/ferrite phase interface is partly coherent and already a long time ago the K–S orientation relationship between austenite and ferrite was reported by Mehl et al. [2]. Analytical solutions based on carbon diffusion control and the Ivantsov solution seem capable of rep- resenting the experimentally observed growth rates if local equilibrium is assumed and proper account is ta- ken for the effect of interfacial energy at the curved tip. At even higher undercooling the ferrite growth turns partitionless, i.e. there is no redistribution of carbon, and results in a characteristic blocky microstructure, so- called massive transformation. The transition to parti- tionless transformation was recently analyzed by the present authors by means of the phase-field method and solute drag modeling [3]. For the transition from allotriomorphic to plate-like growth at least two different opinions have been ex- pressed. Townsend and Kirkaldy [4] suggested that plates would develop from grain-boundary allot- riomorphs by a morphological instability of a similar type as discussed by Mullins and Sekerka [5] during solidification. On the other hand, Aaronson et al. [6] suggest that a plate on a grain boundary allotriomorph * Corresponding author. Tel.: +46-879-068-71; fax: +46-879-698-50. E-mail address: irina@mech.kth.se (I. Loginova). 1359-6454/$30.00 Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.05.033 Acta Materialia 52 (2004) 4055–4063 www.actamat-journals.com