Author's personal copy Linear stability analysis of a c 0 -Fe 4 N nitride layer growing in pure iron Benoı ˆt Appolaire a, * , Mohamed Goune ´ b a LSG2M, Ecole des Mines, Parc de Saurupt, 54042 Nancy Cedex, France b LSGS, Ecole des Mines, Parc de Saurupt, 54042 Nancy Cedex, France Received 4 October 2005; received in revised form 26 January 2006; accepted 27 January 2006 Abstract In nitriding processes of steels, corrugations are commonly observed at the interface between nitride layers and the ferritic matrix. These corrugations have been explained as the consequence of the destabilization of the interface. We have performed a linear stability analysis in the flavour of the Mullins–Sekerka analysis on the interface separating a growing nitride layer in pure iron. This analysis shows that the corrugations cannot be due to a Mullins–Sekerka type instability, because the interface is absolutely stable, the compo- sition field and the interfacial energy being both stabilizing. We conclude by a discussion on the role of the stress fields in the appearance of the corrugations. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Morphological stability; Nitriding 1. Introduction Nitriding is a thermochemical surface treatment of great importance in practice because it improves the surface quality, especially the mechanical and the anticorrosion properties [1]. Generally, in the case of gaseous nitriding, the reactive nitrogen atoms at the solid surface results from the decomposition of the gas phase NH 3 in the presence of aH 2 –N 2 gas mixture [2]. Then, the diffusion of nitrogen atoms through the surface and into the solid can occur. In the case of nitriding of pure iron at 570 °C, the diffusing nitrogen interacts with the iron matrix to form: (i) A compound layer at the surface that is mainly composed of the iron nitrides e-Fe 2 N 1x and c 0 -Fe 4 N 1x . The presence of these iron nitrides depends mainly on the nitrogen composition imposed at the surface. (ii) A diffu- sion zone underneath the compound layer that consists of nitrogen atoms interstitially dissolved in the a ferrite lattice. The trend for process automation, particularly in gaseous treatments, requires developing some physical based models describing the growth kinetics of the com- pound layer (e + c 0 ) and of the diffusion zone. Their main goal is to determine the influence of process parameters such as gas composition and temperature, on the formation of compound layer. These last years, several attempts [3–6] have been made to describe nitrogen diffusion in pure iron, relying on the Fick’s laws solved in one-dimensional geom- etry, and on the nitrogen mass balance equations at the e/c 0 and c 0 /a interfaces. Recently, some improvements have been proposed by using thermodynamic and diffusion approaches and by taken into account the concentration dependence of the nitrogen diffusivity in e and c 0 [7]. This infatuation for modelling allowed disposing some detailed information on (i) the composition ranges of iron nitrides (e and c 0 ) that led to the thermodynamic assessments of the binary Fe–N diagram [8,9], and on (ii) the diffusion coefficients in the various phases, mainly e and c 0 [5–7]. The published data concerns the self-diffusion coefficients as well as the intrinsic diffusion coefficients as required in models treating the growth of compound layer. However, these works as a whole are based on the main assumption that the layer/substrate interfaces are planar although the 0927-0256/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2006.01.016 * Corresponding author. Tel.: +33 (0)3 83 58 42 20; fax: +33 (0)3 83 58 40 56. E-mail address: benoit.appolaire@mines.inpl-nancy.fr (B. Appolaire). www.elsevier.com/locate/commatsci Computational Materials Science 38 (2006) 126–135