Analysis of Diffusion Coefficients of Iron Monoboride and Diiron Boride Coating Formed on the Surface of AISI 420 Steel by Two Different Models: Experiments and Modelling

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.

Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel

Hard-coated surfacing of a few micrometers is widely applied to increase the efficiency of tools, e.g., for cutting, forming, and casting applications. Therefore, the base thermodiffusion surface treatment is a practical solution to these issues by hardening surface layers with interstitial elements such as carbon, nitrogen, and boron. In particular, within this study, the growth kinetics of an iron boride layer on ASTM 283 steel were investigated with two diffusion models of the powder-pack boriding technique in the temperature range of 1123-1273 K with different treatment periods. The first model, called the steady-state diffusion model, used the modified version of the mass balance equations at the Fe₂B/substrate growth interface, the parabolic growth law, and the solution of Fick's second law without time dependence. At the same time, the second diffusion model was based on Goodman's method, also called the integral heat balance method. Afterward, the diffusion coefficient of boron in the Fe₂B phase was calculated by fitting the experimental data to the models. Nevertheless, the estimated value for the activation energy of ASTM A238 steel in both diffusion models was coincident (168.2 kJ∙mol^-1). A mathematical analysis was implemented by means of a power series (Taylor series) to explain this similarity. The SEM examinations showed a solid tendency to saw-tooth morphology at the growth interface with the formation of the Fe₂B layer, whose presence was verified by XRD analysis. The tribological characterizations, including the tests of Rockwell-C indentation, pin-on-disc, and Vickers hardness test method, were used to analyze the antiwear features of the Fe₂B layers. Finally, this value of energy was compared to the literature for its experimental validation.