The effective diffusion coefficient of boron in the Fe₂B layers formed on the iron substrate

Abstract

Abstract. In this current work, the boron diffusion coefficient in Fe 2 B was firstly evaluated using a diffusion model. It considers the effect of the incubation times required to form the Fe 2 B layers by the paste-boriding process on the iron substrate. This model solves the mass balance equation at the (Fe 2 B/substrate) interface under certain assumptions. Afterwards, the effective boron diffusion coefficient in Fe 2 B was evaluated through an application of a simple equation. As a result, the estimated value of boron activation energy in the presence of chemical stresses was found to be equal to 146.5 kJ mol -1 on the basis of experimental data taken from the literature.

Effect of Boride Incubation Time During the Formation of Fe2B Phase

“…After a certain time of incubation τ ≠ 0 as shown in 23,24 , the crystals of the Fe 2 B phase form as needles, growing in the crystallographic direction [0 0 2], parallel to the boron diffusion flow.…”

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

“…The kinetic data and the boron activation energy in the pure iron were found in the reference , the diffusion coefficients of boron in the α-Fe and γ-Fe phases are taken from the reference [14][15][16][17][18][19][20][21][22][23][24]27].…”

“…The first Fe 2 B needles appear on the most reactive points of the substrate surface (scratches, grain boundaries, dislocations). So the incubation time corresponds to the appearance of the first crystals of Fe 2 B at the substrate surface of steel or pure iron [24]. However, some publications indicated that the first phase, formed on the steel surface, was FeB boride [25,26] because of the lower values of the Gibbs free energy of the reaction during the FeB formation.…”

Dybkov model for the estimation of boron diffusion in the FeB/Fe2B bilayer on AISI 316 steel

“…To estimate the boron activation energy, we must have a minimum of three processing temperatures with three durations for each temperature to obtain the corresponding layers' thicknesses. Based on the experimental data, we can estimate the activation energy of boron diffusion in the treatedsteel using the following Equation (30): exp ( 29) exp (30) The variable u represents the thickness of FeBlayer and v that of (FeB+ Fe 2 B) layer given in (µm), is the boron diffusion coefficient (µm 2 /s), t is the boriding time, Q i is the value of the activation energy measured in Joule/mol, R is the gas constant and T is the temperature in Kelvin.It is easy to estimate the value of the activation energy Q i using Arrhenius's Law in a linear form given by equation (29), where Q i can be easily deduced from the slope of the straight line expressed in (kJ/mol).…”

“…To determine the effect of different parameters (temperature, boriding time, boron concentration) on this process, an LS-SVM method was employed [27], in another study, Dybkov et al [28] have proposed and developed a kinetic approach. Theirmathematical model consisting in studying the growth of the bilayer (FeB/Fe 2 B) on binary alloys.Through this approach, the parabolic growth law for boride layers was assumed and the kinetics can alternatively be described by a system of two nonlinear differential equations.For the calculation of the diffusion coefficient, many modelsexist and being used to estimate the value of this parameter [29,30]. In another work,ElGuerri et al [31] studied the impact of the diffusion coefficient calculation on predicting the boride layer thickness.…”