Diffusion model for growth of Fe₂B layer in pure iron

Abstract

A simple diffusion model is proposed to estimate the growth kinetics of Fe 2 B layers created at the surface of pure iron. This model employs the mass balance equation at the Fe 2 B/substrate interface to evaluate the boron diffusion coefficient (D Fe 2 B ) in the boride layer. The Fe 2 B layers were formed using the paste boriding process, at four temperatures with different exposure times. Analysing the results, the evolution of the parabolic growth constant (k) of the Fe 2 B layer is presented as a function of boron concentration and boride incubation time [t 0 (T)]. Furthermore, the instantaneous velocity of the Fe 2 B/substrate interface and the weight gain of borided pure iron were estimated for different boriding temperatures. Finally, to validate the diffusion model, the boride layer thicknesses were predicted and experimentally verified for two boriding temperatures and for different treatment times.

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

“…The experimental results available in reference [7] were firstly used to evaluate the diffusion coefficient of boron in Fe 2 B using Equation (6), and secondly to determine the effective diffusion coefficient of boron in Fe 2 B based on Equation (9). The past-boriding process was carried out on the iron substrate under an argon atmosphere in a conventional furnace at 4 temperatures (1223, 1253, 1273 and 1323 K) and for variable times (2, 4, 6 and 8 h).…”

“…Due to the saw-tooth morphology of the (boride layer/substrate) interface, twenty five measurements were done on different cross-sections of the borided samples to estimate the Fe 2 B layer thickness. In Figure 2 is plotted the variation of the squared value of experimental boride layer thickness [7] as a function of the treatment time. Variation of the squared value of the experimental boride layer thickness [7] versus the boriding time at increasing temperatures.…”

“…In Figure 2 is plotted the variation of the squared value of experimental boride layer thickness [7] as a function of the treatment time. Variation of the squared value of the experimental boride layer thickness [7] versus the boriding time at increasing temperatures.…”

Kinetic study and characterization of borided AISI 4140 steel

“…The e parameter is then determined by solving the mass-balance equation for the Fe 2 B/substrate interface (Equation (11)) using the Newton-Raphson method. Table 1 lists the estimated value of boron diffusion coefficient in Fe 2 B at each temperature along with the squared value of normalized growth parameter e determined from Equation (11). e D Fe B 2 ) for each boriding temperature.…”

“…In particular, many models reported in the literature were used for analyzing the kinetics of the Fe 2 B layers grown on different substrates [6][7][8][9][10][11][12][13][14][15][16] , with and without the boride incubation times.…”