Simulation of the incubation time for the formation of (FeB/Fe₂B) bilayer on pure iron

In this work, a mathematical model was used in order to study the growth kinetics of (Fe₂B/FeB) bilayer during bori-ding process basing on the second Fick’s law and mass balance equation. The run of the numerical simulation allowed calculating the incubation time (τ) of each boronized layer (Fe₂B or FeB), and estimating the effect of this parameter on the growth of the boronized layer. The boride incubation time for forming the FeB or Fe₂B layer on the pure iron substrate was incorporated into the present mathematical model. To simulate the value of the growth rate constant and the incubation time for the bilayer configuration, the experimental data available in the literature concerning the boronizing of pure iron were considered. Based on the experimental and simulation results, it was shown that the incubation time decreases with increasing temperature in the FeB and Fe₂B phases.

It was concluded from this study that the thickness of each boride layer depended on its growth rate constant and on another parameter k_τ which was the rate constant of incubation time.The obtained results confirmed the validity of the present mathematical model and gave a good estimate of the incubation time during the formation of each boride layer as well as formulated the variation of this parameter with a mathematical equation. Furthermore, the comparison of experimental data with the simulated results of boronized layer thickness allowed to validate the present model.