Joaquin Oseguera 1 and Francisco Castillo 2 Layer Growth Kinetics during Post-Discharge Nitriding ABSTRACT: A mathematical simulation of the evolution of nitrogen concentration profiles in iron samples is presented. The nitrogen concentration profiles are produced by a nitrogen microwave post-discharge. This mathematical model takes into account the nitrogen concentration evolution from the very beginning of the process and describes the formation and growth of compact nitride layers. This model also proposes a description of how the solubility limits in each growing phase are attained during the layer formation. An approximate analytical solution of Goodman’s type for the model is sought. This leads to a system of differ- ential algebraic equations (DAE). Then, the DAE is finally numerically solved. The steady state of the process is also studied within the model. In this case, analytical representations of the nitrogen concentra- tion profiles and the diffusion coefficients are found KEYWORDS: mathematical simulation, nitriding, diffusion Introduction Thermo-chemical nitriding treatments allow important enhancements of different attributes of iron and steel alloys: an improvement of fatigue and wear resistance, a decrease of friction coefficients in different tribological systems, and a significant improvement in corrosion resistance. These features provide techno- logical relevance to the nitriding process of iron and steels. Different reports of mathematical simulations of the concomitant growth of nitride compact layers point out that the mass balance at growing interfaces between layers plays an important role in describing the layer growth kinetics [1–10]. There are several processes that enable the transportation of nitrogen into iron and steel specimens. The salt bath nitriding process, also known as the Tenefer process, allows the generation of a nitrogen flux when the specimen is immersed in a medium containing cyanides and cyanites. Also, the thermo-chemical equilibria with surrounding atmospheres involving hydrogen and ammonia mixtures produce an adequate atomic nitrogen concentration on the surface during ammonia dissociation, which in turn supplies the nitrogen transport into the specimen [11]. Plasma assisted processes allow the transportation of nitrogen in an environment generated by a weakly ionized plasma containing nitrogen and hydrogen mixtures. Post- discharges with mixtures of nitrogen and hydrogen [12], which are produced by microwave post-discharge in plasma, enable the existence of an environment with a high atomic nitrogen concentration. During post- discharge, the transportation of nitrogen into the solid strongly depends on its concentration [13]. Structural defects such as grain boundaries, dislocations, and grain orientation significantly affect the diffusion of nitrogen into the solid. These defects can be observed, for instance, in Ref [14], in which images of the nitride layers in the initial stages appear. The formation of nitride compact layers strongly depends on structural defects. The growth of compact layers has been studied generally by many authors [15–20] in cases when the layers are already formed. Furthermore, these authors usually assume that the layer growth follows a parabolic regime from the initial stages. Nevertheless, other references have pointed out that this is not necessarily the case [21,22]. In this work, a model that describes the concomitant evolution of nitride compact layers is presented. This evolution is modeled from the very beginning of nitrogen diffusion into the solid, and no assumptions regarding their growth regime are posed. Manuscript received November 11, 2010; accepted for publication September 20, 2011; published online October 2011. 1 Instituto Tecnolo ´gico y de Estudios Superiores de Monterrey, Campus Estado de Me ´xico, Carretera al Lago de Guadalupe km. 3.5, Atizapa ´n, 52926 Estado de Me ´xico, Mexico, e-mail: joseguera@itesm.mx 2 Instituto Tecnolo ´gico y de Estudios Superiores de Monterrey, Campus Estado de Me ´xico, Carretera al Lago de Guadalupe km. 3.5, Atizapa ´n, 52926 Estado de Me ´xico, Mexico e-mail: francast@itesm.mx Copyright V C 2012 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. Journal of ASTM International, Vol. 9, No. 2 Paper ID JAI103568 Available online at www.astm.org