In the present work, two mathematical diffusion models have been used to estimate the growth of the iron monoboride and diiron boride coating formed on AISI 420 steel. The boronizing of the steel was carried out with the solid diffusion packing method at a boronizing temperature of 1123 K-1273 K. Experimental results show the two-coating system consists of an outer monoboride and an inner diiron boride coating with a predominantly planar structure at the propagation front. The depth of the boride coating increases according to temperature and treatment time. A parabolic curve characterizes the propagation of the boride coatings. The two proposed mathematical models of mass transfer diffusion are founded on the solution corresponding to Fick's second fundamental law. The first is based on a linear boron concentration-penetration profile without time dependence, and the second model with time dependence (exact solution). For both models, the theoretical law of parabolic propagation and the average flux of boron atoms (Fick's first fundamental law) at the growth interfaces (monoboride/diiron boride and diiron boride/substrate) are considered to estimate the propagation of the boride coatings (monoboride and diiron boride). To validate the mathematical models, a programming code is written in the MATLAB program (adaptation 7.5) designed to simulate the growth of the boride coatings (monoboride and diiron boride). The following parameters are used as input data for this computer code: (the layer thicknesses of the FeB and Fe2B phases, the operating temperature, the boronizing time, initial formation time of the boride coating, the surface boron concentration limits, FeB/Fe2B and Fe2B/Fe growth interfaces, and the mass transfer diffusion coefficient of boron in the iron monoboride and diiron boride phases). The outputs of the computer code are the constants εFeB and εFe2B. The assessment of activation energies of AISI 420 steel for the two mathematical models of mass transfer is coincident (QFeB=221.9 kJ∙mol-1 and QFe2B=209.1 kJ∙mol-1). A numerical analysis was performed using a standard Taylor series for clarification of the proximity between the two models. SEM micrographs exhibited a strong propensity toward a flat-fronted composition at expansion interfaces of the iron monoboride and diiron boride coating, confirmed by XRD analysis. Tribological characterizations included the Vickers hardness test method, pin-on-disc, and Daimler-Benz Rockwell-C indentation adhesion tests. After thorough analysis, the energies were compared to the existing literature to validate our experiment. We found that our models and experimental results agreed. The diffusion models we utilized were crucial in gaining a deeper understanding of the boronizing behavior of AISI 420 steel, and they also allowed us to predict the thicknesses of the iron monoboride and diiron boride coating. These models provide helpful approaches for predicting the behavior of these steels.
Keywords: activation energy of FeB and Fe2B; diffusion models; hardness; powder-pack boronizing; propagation of the boride coatings; wear resistance.