Abstract
In the present work, the AISI S1 steel was packborided in the temperature range 11231273 K for 2 8 h to form a compact layer of Fe_{2}B at the material surface. A recent kinetic approach, based on the integral method, was proposed to estimate the boron diffusion coefficients in the Fe_{2}B layers formed on AISI S1 steel in the temperature range 11231273 K. In this model, the boron profile concentration in the Fe_{2}B layer is described by a polynomial form based on the Goodman’s method. As a main result, the value of activation energy for boron diffusion in AISI S1 steel was estimated as 199.15 kJmol^{1} by the integral method and compared with the values available in the literature. Three extra boriding conditions were used to extend the validity of the kinetic model based on the integral method as well as other diffusion models. An experimental validation was made by comparing the values of Fe_{2}B layers’ thicknesses with those predicted by different diffusion models. Finally, an isothickness diagram was proposed for describing the evolution of Fe_{2}B layer thickness as a function of boriding parameters.
Keywords:
Incubation time; Diffusion models; Activation energy; Growth kinetics; Integral method
1. Introduction
The boriding process is a thermochemical treatment in which the boron atoms are diffused into the surface of a workpiece to form hard layers composed of iron borides and metallic boride in the case of high alloy steels^{1}1 Sinha AK. Boriding (Boronizing) of Steels. In: ASM Handbook. Volume 4. Heat Treating. Materials Park: ASM International; 1990. p. 437447.. For carbon steels, two kinds of iron borides can be formed by boriding in the temperature range 8001050°C.
The iron borides are interesting phases because of their high hardness. Nevertheless, the Fe_{2}B phase is preferred to FeB, when the resistance to wear under impact was required, since the doublé boride layer (FeB and Fe_{2}B) is prone to cracking during service. Among the boriding processes, the powderpack boriding is widely used in the industry because of its easy handling and low cost^{2}2 Keddam M, Chentouf SM. A diffusion model for describing the bilayer growth (FeB/Fe2B) during the iron powderpack boriding. Applied Surface Science. 2005;252(2):393399.. In this boriding method, a mixture of powders that consists of a boron yielding substance, an activator and a diluent is used. The samples to be borided are then packed in a stainless steel container and placed in the furnace.
In the literature, no kinetic study was reported on the boriding of AISI S1 steel. The modeling of boriding process can be used as a tool to optimize the boriding parameters to produce boride layers with sufficient thicknesses that meet the requirements during service life.
From a kinetic point of view, several approaches have beeen developed to study the kinetics of formation of Fe_{2}B layers on Armco iron and steels as substrates^{3}3 Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering.2017;11(6):563585.
4 Keddam M, OrtizDominguez M, EliasEspinosa M, ArenasFlores A, ZunoSilva J, ZamarripaZepeda D, et al. Kinetic Investigation and Wear Properties of Fe2B Layers on AISI 12L14 Steel. Metallurgical and Materials Transactions A.2018;49(5):18951907.
5 OrtizDomínguez M, FloresRentería MA, Keddam M, EliasEspinosa M, DamiánMejía O, AldanaGonzález JI, et al. Simulation of growth kinetics of Fe2B layers formed on gray cast iron during the powderpack boriding. Materials and Technology. 2014;48(6):905916.
6 EliasEspinosa M, OrtizDomínguez M, Keddam M, GómezVargas OA, ArenasFlores A, BarrientosHernández FR, et al. Boriding kinetics and mechanical behaviour of AISI O1 steel. Surface Engineering. 2015;31(8):588597.
7 Nait Abdellah Z, Keddam M, Chegroune R, Bouarour B, Haddour L, Elias A. Simulation of the boriding kinetics of Fe2B layers on iron substrate by two approaches. Matériaux et Techniques. 2012;100(67):581588.
8 FloresRentería MA, OrtizDomínguez M, Keddam M, DamiánMejía O, EliasEspinosa M, FloresGonzález MA, et al. A Simple Kinetic Model for the Growth of Fe2B Layers on AISI 1026 Steel During the Powderpack Boriding. High Temperature Materials and Processes. 2015;34(1):111.
9 Kouba R, Keddam M,Kulka M. Modelling of paste boriding process. Surface Engineering. 2015;31(8):563569.
10 Ramdan RD, Takaki T, Tomita Y. Free Energy Problem for the Simulations of the Growth of Fe2B Phase Using PhaseField Method. Materials Transactions.2008;49(11):26252631.
11 Campos I, Oseguera J,Figueroa U, Garcia JA, BautistaO, Kelemenis G. Kinetic study of boron diffusion in the pasteboriding process. Materials Science and Engineering: A. 2003;352(12):261265.^{}^{12}12 Mebarek B, Benguelloula A, Zanoun A. Effect of Boride Incubation Time During the Formation of Fe2B Phase. Materials Research. 2018;21(1):e20170647.DOI: http://dx.doi.org/10.1590/19805373mr20170647
https://doi.org/http://dx.doi.org/10.159...
.
All these diffusion models considered the principle of the mass balance equation at the (Fe_{2}B/substrate) interface under certain assumptions (with and without boride incubation times).For instance, OrtizDomínguez et al.^{5}5 OrtizDomínguez M, FloresRentería MA, Keddam M, EliasEspinosa M, DamiánMejía O, AldanaGonzález JI, et al. Simulation of growth kinetics of Fe2B layers formed on gray cast iron during the powderpack boriding. Materials and Technology. 2014;48(6):905916. have developed a kinetic model for studying the growth kinetics of Fe_{2}B layers on gray cast iron by introducing a kinetic parameter that depends on the values of upper and lower boron concentrations in Fe_{2}B and on the boride incubation time.EliasEspinosa et al.^{6}6 EliasEspinosa M, OrtizDomínguez M, Keddam M, GómezVargas OA, ArenasFlores A, BarrientosHernández FR, et al. Boriding kinetics and mechanical behaviour of AISI O1 steel. Surface Engineering. 2015;31(8):588597. have modeled the growth kinetics of Fe_{2}B layers on AISI O1 steel by using a diffusion model that assumes a nonlinear boron concentration profile with the presence of a constant boride incubation time. They have introduced a non dimensional kinetic parameter to evaluate the boron diffusion coefficients in the Fe_{2}B layers in the temperature range 11231273 K. Similarly, Nait Abdellah et al.^{7}7 Nait Abdellah Z, Keddam M, Chegroune R, Bouarour B, Haddour L, Elias A. Simulation of the boriding kinetics of Fe2B layers on iron substrate by two approaches. Matériaux et Techniques. 2012;100(67):581588. have also suggested a kinetic model based on the mass balance equation at the (Fe_{2}B/Fe) interface by assuming a nonlinear boron concentration profile through the Fe_{2}B layers on Armco substrate. They introduced the β(T) parameter that depends on the boriding temperature. FloresRentería et al.^{8}8 FloresRentería MA, OrtizDomínguez M, Keddam M, DamiánMejía O, EliasEspinosa M, FloresGonzález MA, et al. A Simple Kinetic Model for the Growth of Fe2B Layers on AISI 1026 Steel During the Powderpack Boriding. High Temperature Materials and Processes. 2015;34(1):111. have modelled the kinetics of formation of Fe_{2}B layers on AISI 1026 steel by using a kinetic model. In their model, they introduced a kinetic parameter called ε which is independent on the boriding temperature with a linear boron concentration profile in the Fe_{2}B layer.
In the present study, a recent kinetic approach based on the integral method ^{3}3 Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering.2017;11(6):563585.^{,}^{4}4 Keddam M, OrtizDominguez M, EliasEspinosa M, ArenasFlores A, ZunoSilva J, ZamarripaZepeda D, et al. Kinetic Investigation and Wear Properties of Fe2B Layers on AISI 12L14 Steel. Metallurgical and Materials Transactions A.2018;49(5):18951907. has been suggested to investigate the boriding kinetics of AISI S1 steel by taking into account the presence of boride incubation time.
The aim of the present work was to investigate the growth kinetics of Fe_{2}B layers on AISI S1 steel based on the integral method in the temperature range 11231273 K.
This diffusion problem can be solved either analytically or numerically.An analytic solution for the integral method has been obtained in order to estimate the boron diffusion coefficients in Fe_{2}B. An experimental validation of the integral method and other used diffusion models was also made for an upper boron concentration of 9 wt.% in Fe_{2}B.Furthermore, the value of activation energy for boron diffusion in AISI S1 steel was estimated on the basis of the integral method and compared with that obtained from another diffusion model ^{6}6 EliasEspinosa M, OrtizDomínguez M, Keddam M, GómezVargas OA, ArenasFlores A, BarrientosHernández FR, et al. Boriding kinetics and mechanical behaviour of AISI O1 steel. Surface Engineering. 2015;31(8):588597.. Finally, the estimated value of boron activation energy from the integral method was compared with the data available in the literature.
2. The Diffusion Model
The diffusion model deals with the growth kinetics of Fe_{2}B layer on a saturated matrix with boron atoms. The boron concentration profile along the Fe_{2}B layer is depicted in Figure 1.
The f(x,t) function shows the distribution of boron concentration within the substrate before the formation of Fe_{2}B phase
16 Krukovich MG, Prusakov BA, Sizov IG. The Components and Phases of Systems 'BoronIron' and 'BoronCarbonIron'.In: Krukovich MG, Prusakov BA, Sizov IG. Plasticity of Boronized Layers. Volume 237 of the Springer Series in Materials Science. Cham: Springer; 2016. P. 1321.^{}^{17}17 Goodman TR. Application of Integral Methods to Transient Nonlinear Heat Transfer. Advances in Heat Transfer.1964;1:51122..
The assumptions taken into account during the formulation of integral model are given in the reference works^{3}3 Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering.2017;11(6):563585.^{,}^{4}4 Keddam M, OrtizDominguez M, EliasEspinosa M, ArenasFlores A, ZunoSilva J, ZamarripaZepeda D, et al. Kinetic Investigation and Wear Properties of Fe2B Layers on AISI 12L14 Steel. Metallurgical and Materials Transactions A.2018;49(5):18951907.:
The initial and boundary conditions for the diffusion problem are given by:
t=0,x>0, with
wt..%Boundary conditions:
forThe Second Fick’s law describing the change in the boron concentration within the Fe_{2}B layer is given by Equation (4):
The three timedependent unknowns a(t), b(t) and u(t) have to meet the boundary conditions given by Equations (2) and (3). By applying the boundary condition on the surface, Equation (6) was obtained:
By integrating Equation (4) between 0 and u(t) and applying the Leibniz rule, the ordinary differential equation (ODE) given by Equation (7) was derived:
The mass balance equation at the (Fe_{2}B/substrate) interface can be formulated by Equation (8):
With
At the (Fe_{2}B/substrate) interface, the boron concentration remains constant and Equation (8) can be rewritten as follows:
Substituting Equation (4) into Equation (9) and after derivation with respect to the diffusion distance x(t), Equation (10) was deduced:
Equations (6), (7) and (10) constitute a set of differential algebraic equations (DAE) in a(t), b(t) and u(t) subjected to the initial conditions of this diffusion problem. To obtain the expression of boron diffusion coefficient in the Fe_{2}B layers, an analytic solution is possible by setting:
and
where u(t) is the Fe_{2}B layer thickness and k the corresponding parabolic growth constant at the (Fe_{2}B/substrate) interface. The two unknowns α and β which are positive have to be searched for solving this diffusion problem. After substitution of Equations (11), (12) and (13) into the DAE (differential algebraic equations) system and derivation, the expression of boron diffusion coefficient was obtained as follows:
where η is a dimensionless parameter.
with
along with the expressions of a(t) and b(t) given by Equations (15) and (16):
With
and
3. Experimental Details
3.1 The material and the boriding treatment
The AISI S1 steel was used as substrate for the powderpack boriding. The chemical composition of AISI S1 steel is listed (in weight percent) in Table 1.
The samples had a cubic shape with nominal dimensions of 10 mm×10 mm×10 mm. Before the boriding treatment, the samples were cut and the crosssections were polished metallographically and then etched by Nital solution to reveal the microstructure. The powderpack boriding was carried out by embedding the samples in a closedcontainer containing a mixture of powders as shown in Figure 2. The used boriding agent was composed of 20% B_{4}C, 10% KBF_{4} and 70% SiC. Figure 3 gives an SEM image of the mixture of powders having an average size of 30 µm.
Schematic view of the stainless steel AISI 304L container for the packpowder boriding treatment (1: lid; 2: powder boriding medium (B_{4}C + KBF_{4} + SiC); 3: sample; 4: container)
The container was placed in a conventional furnace under a pure argon atmosphere in the temperature range 11231223 K. Four treatment times (2, 4, 6 and 8 h) were selected for each temperature. Once the boriding treatment was finished the container was removed from the furnace and slowly cooled to room temperature.
3.2 Experimental techniques
The crosssections of formed boride layers were examined by SEM (JEOL JSM 6300 LV). The boride layer thickness was automatically measured by means of MSQ PLUS software. For the reproducibility of measurements, seventy tests were performed from a fixed reference on different sections of borided samples to estimate the Fe_{2}B layer thickness; defined as an average value of the long boride teeth. The presence of the iron boride formed at the surface of treated sample was verified by use of XRay Diffraction (XRD) equipment (Equinox 2000) with CoKα radiation of wavelength λ_{Co} = 0.179 nm.
4. Results and Discussions
4.1 SEM examinations of Fe _{2} B layers
Figure 4 shows the crosssections of borided samples at a temperature of 1173 K for different treatment times (2, 4, 6 and 8 h). It is seen the formation of a dense and compact Fe_{2}B layer with a peculiar morphology. The SEM pictures revealed the presence of a sawtooth morphology. Such morphology is typical for borided Armco iron and carbon steels where as for high alloy steels the obtained morphology is very different. In fact, when increasing the contents of alloying elements the (boride layer/substrate) interface tends to be flat as observed, for example, in the packborided AISI 316 L steel^{18}18 ReséndizCalderon CD, RodríguezCastro GA, MenesesAmador A, CamposSilva IE, AndracaAdame J, PalomarPardavé ME, et al. MicroAbrasion Wear Resistance of Borided 316L Stainless Steel and AISI 1018 Steel. Journal of Materials Engineering and Performance. 2017;26(11):55995609.. Carbucicchio et al.^{19}19 Carbucicchio M, Badani L,Sambogna G. On the early stages of high purity iron boriding with crystalline boron powder. Journal of Materials Science. 1980;15(6):14831490. explained the occurrence of a sawtooth morphology to the enhanced growth at the tips of boride needles. Consequently, the iron borides developed a textured growth along the preferred crystallographic direction [001] after Palombarini et al.^{20}20 Palombarini G, Carbucicchio M. Growth of boride coatings on iron.Journal of Materials Science Letters. 1987;6(4):415416..
SEM micrographs of the crosssections of borided AISI S1 steels at 1173 K during different exposure times: (a) 2 h, (b) 4 h, (c) 6 h, and (d) 8 h
The Fe_{2}B layer thickness increased with the treatment time at 1173 K. The value of Fe_{2}B layer thickness ranged from 41.93 ± 8.25 µm for 2 h to 95.48 ± 17.4 µm for 8 h at 1173 K.
Figure 5 gives the SEM micrographs of the boride layers formed on the AISI S1 steels at increasing temperatures and for an exposure time of 4 h. The (boride layer/substrate) interface exhibited a sawtooth morphology. The kinetics of formation of boride layers is a thermally activated phenomenon with a change in the layer thickness with increasing temperatures.
SEM micrographs of the crosssections of AISI S1 steels borided with exposure time of 4 h, during different boriding temperatures: (a) 1123 K, (b) 1173 K, (c) 1223 K and (d) 1273 K
4.2 XRD analysis
Figure 6 shows the XRD patterns obtained at the surface of borided AISI S1 steels at 1123, 1173 and 1223 K for 4 h of treatment. The XRD patterns revealed the presence of diffracting peaks belonging to the Fe_{2}B phase.The formation of Fe_{2}B layer is related to the quantity of active boron present in the boriding agent. The observed difference in the diffracted intensities can be explained by the textured growth along the easiest crystallographic direction 001 that minimizes the growth stress^{20}20 Palombarini G, Carbucicchio M. Growth of boride coatings on iron.Journal of Materials Science Letters. 1987;6(4):415416..
XRD patterns obtained at the surface of borided AISI S1 steels for three boriding conditions: (a) 1123 K for 4 h, (b) 1173 K for 4 h and (c) 1223 K for 4 h
4.3 Estimation of boron activation energy in AISI S1 steel
The experimental results are needed to evaluate the values of boron diffusion coefficients in Fe_{2}B in the temperature range 11231273 K by plotting the variation of the square of Fe_{2}B layer thickness as a function of treatment time. The intercept with the time axis yields the value of boride incubation time. Figure 7 gives the evolution of the square of Fe_{2}B layer thickness as a function of time for increasing values of boriding temperatures. The growth kinetics of Fe_{2}B layers is governed by the parabolic growth law. The slope of each straight line depicted in the Figure 7 represent the square of parabolic growth constant at each boriding temperature.
Square of boride layer thickness as a function of boriding time for increasing temperatures
The experimental values of parabolic growth constants at the (Fe_{2}B/substrate) interface along with the corresponding boride incubation times are shown in Table 2.
Experimental values of parabolic growth constants at the (Fe_{2}B/substrate) interface along with the corresponding boride incubation times.
It is seen that the values of boride incubation times are nearly constant. The following reason can be provided for this experimental observation. According to the design of the thermochemical treatment, the container is always placed at ambient temperature in a conventional furnace under a pure argon atmosphere until the boriding temperature (1123 K ≤ T ≤ 1273 K), the boride incubation time
The value of boron diffusion coefficient in Fe_{2}B at each temperature was estimated from Equation (14) based on the integral method. This value can be easily obtained from the slope of straight line shown in Figure 8. The value of 199.16 kJmol^{1} indicates the amount of energy for the boron mobility in the easiest path corresponding to the crystallographic direction [001] along the Fe_{2}B layer. Therefore, the expression describing the evolution of boron diffusion coefficients in Fe_{2}B versus temperature is given by Equation (17) in the temperature range 11231273 K:
where R = 8.314 J mol^{1} K^{1} and T the absolute temperature in Kelvin.
Table 3 shows a comparison between the values of activation energy for boron diffusion in Armco iron and some ferrous alloys (steels and gray cast iron) and the estimated value of activation energy for boron diffusion in AISI S1 steel^{3}3 Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering.2017;11(6):563585.^{,}^{12}12 Mebarek B, Benguelloula A, Zanoun A. Effect of Boride Incubation Time During the Formation of Fe2B Phase. Materials Research. 2018;21(1):e20170647.DOI: http://dx.doi.org/10.1590/19805373mr20170647
https://doi.org/http://dx.doi.org/10.159...
^{,}^{21}21 Sesen FE, ÖzgenÖS, Sesen MK. A Study on Boronizing Kinetics of an InterstitialFree Steel. Materials Performance and Characterization. 2017;6(4):492509.
22 Sen S, Sen U,Bindal C. An approach to kinetic study of borided steels. Surface and Coatings Technology. 2005;191(23):274285.
23 Jiang YF, BaoYF, Wang M.Kinetic Analysis of Additive on Plasma Electrolytic Boriding. Coatings. 2017;7(5):61.
24 Chegroune R, Keddam M, Nait Abdellah Z, Ulker S, Taktak S, Gunes I. Characterization and kineticsof plasmapasteborided AISI 316 steel. Materials and Technology. 2016;50(2):263268.
25 CamposSilva I, OrtizDominguez M. Modelling the growth of Fe2B layers obtained by the paste boriding process in AISI 1018 steel irons. International Journal of Microstructure and Materials Properties. 2010;5(1):2638.
26 EliasEspinosa M, OrtizDomínguez M, Keddam M, FloresRentería MA, DamiánMejía O, ZunoSilva J, et al. Growth Kinetics of the Fe2B Layers and Adhesion on Armco Iron Substrate. Journal of Materials Engineering and Performance. 2014;23(8):29432952.
27 OrtizDomínguez M, GómezVargas OA, Keddam M, ArenasFlores A, GarcíaSerrano J. Kinetics of boron diffusion and characterization of Fe2B layers on AISI 9840 Steel. Protection of Metals and Physical Chemistry of Surfaces. 2017;53(3):534547.^{}^{28}28 Azouani O, Keddam M, Allaoui O, Sehisseh A. Kinetics of the Formation of Boride Layers on ENGJL250 Gray Cast Iron. Materials Performance and Characterization. 2017;6(4):501522..
Comparison of activation energy for boron diffusion in AISI S1 steel with other borided materials.
It is observed that the obtained values of boron activation energy by different investigators are dependent on several factors such as: (the method of calculation, the boriding method, the nature of boriding agent, the chemical reactions involved and the chemical composition of the substrate.
For example, Şeşen et al.^{21}21 Sesen FE, ÖzgenÖS, Sesen MK. A Study on Boronizing Kinetics of an InterstitialFree Steel. Materials Performance and Characterization. 2017;6(4):492509. have borided an interstitial free (IF) steel by using the electrochemical boriding under different current densities. They produced a double boride layer (FeB and Fe_{2}B) where FeB was a dominant phase. A metastable iron boride was also identified by XRD analysis.
The calculated boron activation energies ranged between 80.70 and 100.16 kJ mol^{1}, depending on the value of current density in the range 0.1 0.4 A cm^{2}. It is noticed that these values are lower than those obtained from other reported works^{3}3 Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering.2017;11(6):563585.^{,}^{12}12 Mebarek B, Benguelloula A, Zanoun A. Effect of Boride Incubation Time During the Formation of Fe2B Phase. Materials Research. 2018;21(1):e20170647.DOI: http://dx.doi.org/10.1590/19805373mr20170647
https://doi.org/http://dx.doi.org/10.159...
^{,}^{21}21 Sesen FE, ÖzgenÖS, Sesen MK. A Study on Boronizing Kinetics of an InterstitialFree Steel. Materials Performance and Characterization. 2017;6(4):492509.
22 Sen S, Sen U,Bindal C. An approach to kinetic study of borided steels. Surface and Coatings Technology. 2005;191(23):274285.
23 Jiang YF, BaoYF, Wang M.Kinetic Analysis of Additive on Plasma Electrolytic Boriding. Coatings. 2017;7(5):61.
24 Chegroune R, Keddam M, Nait Abdellah Z, Ulker S, Taktak S, Gunes I. Characterization and kineticsof plasmapasteborided AISI 316 steel. Materials and Technology. 2016;50(2):263268.
25 CamposSilva I, OrtizDominguez M. Modelling the growth of Fe2B layers obtained by the paste boriding process in AISI 1018 steel irons. International Journal of Microstructure and Materials Properties. 2010;5(1):2638.
26 EliasEspinosa M, OrtizDomínguez M, Keddam M, FloresRentería MA, DamiánMejía O, ZunoSilva J, et al. Growth Kinetics of the Fe2B Layers and Adhesion on Armco Iron Substrate. Journal of Materials Engineering and Performance. 2014;23(8):29432952.
27 OrtizDomínguez M, GómezVargas OA, Keddam M, ArenasFlores A, GarcíaSerrano J. Kinetics of boron diffusion and characterization of Fe2B layers on AISI 9840 Steel. Protection of Metals and Physical Chemistry of Surfaces. 2017;53(3):534547.^{}^{28}28 Azouani O, Keddam M, Allaoui O, Sehisseh A. Kinetics of the Formation of Boride Layers on ENGJL250 Gray Cast Iron. Materials Performance and Characterization. 2017;6(4):501522.. It should be attributed to the absence of carbon and nitrogen as interstitial atoms leading to the increase in the boron mobility within the material substrate. In addition, the estimated value of activation energy for boron diffusion in AISI S1 steel is very comparable to the values estimated for AISI 9840 and AISI P20 steels by using the same chemical composition of boriding agent^{3}3 Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering.2017;11(6):563585.^{,}^{27}27 OrtizDomínguez M, GómezVargas OA, Keddam M, ArenasFlores A, GarcíaSerrano J. Kinetics of boron diffusion and characterization of Fe2B layers on AISI 9840 Steel. Protection of Metals and Physical Chemistry of Surfaces. 2017;53(3):534547..
4.4 Experimental validation of different diffusion models
To experimentally validate the diffusion model based on the integral method and four diffusion models, three extra boriding conditions were used for this purpose. Figure 9 gives the SEM images of the crosssections of Fe_{2}B layers formed at 1173 K for 3.5 h and 6.5 h and at 1223 K for 1.5 h, respectively.
SEM micrographs of the boride layers formed at the surfaces of AISI S1 steel for three extra boriding conditions: (a) 1173 K for 3.5 h, (b) 1173 K for 6.5 h and (c) 1223 K for 1.5 h
For such boriding conditions, a compact single phase layer of Fe_{2}B was produced with a sawtooth morphology.On the basis of integral method, the expression of Fe_{2}B layer thickness depending on the boriding parameters (time and temperature) is given by Equation (18):
with
where Q is the activation energy for boron diffusion (kJmol^{1}), D_{0} represents a preexponential constant (m^{2} s^{1}) and T is the absolute temperature in Kelvin.
Table 4 provides the expressions of Fe_{2}B layer thickness as a function of boriding parameters derived for four diffusion models with Equation (18) valid for the integral method. It is seen that the estimated value of boron activation energy for AISI S1 steel by using the diffusion model^{6}6 EliasEspinosa M, OrtizDomínguez M, Keddam M, GómezVargas OA, ArenasFlores A, BarrientosHernández FR, et al. Boriding kinetics and mechanical behaviour of AISI O1 steel. Surface Engineering. 2015;31(8):588597. is very close to that obtained from the integral method.
Values of boron activation energies estimated from all diffusion models with the expressions used to estimate the Fe_{2}B layer thickness.
Table 5 gives a comparison between the experimental values of Fe_{2}B layers’ thicknesses (obtained for three boriding conditions) and the predicted values using four different models and the integral method for an upper boron content in the Fe_{2}B phase equal to 9 wt.%.
Comparison between the experimental values of Fe_{2}B layers’ thicknesses (obtained for three boriding conditions ) and the predicted values using different models for an upper boron content in the Fe_{2}B phase equal to 9 wt.%.
It is seen that the experimental values in terms of Fe_{2}B layers’ thicknesses coincide in a satisfactory way with the predicted results.
Equation (18) can be employed as a simple tool to predict the optimum value of Fe_{2}B layer thickness as a function of boriding parameters (the treatment time and the process temperature) as shown in Figure 10 to match the case depth that meets requirements for a practical use of AISI S1 steel in the industry.
Isothickness diagram describing the evolution of Fe_{2}B layer thickness as a function of boriding parameters
5. Conclusions
In this current work, the AISI S1 steel was treated by the powderpack boriding in the temperature range 11231273 K with a variable treatment time (from 2 h to 8 h). The boriding agent was composed of 20% B_{4}C, 10% KBF_{4} and 70% SiC. The XRD analysis confirmed the presence of Fe_{2}B phase in the boride layer for all boriding conditions. For indication, the XRD patterns for the borided samples at 1123, 1173 and 1223 K for 4 h were only shown as experimental evidence. The SEM examinations revealed a saw tooth morphology for the Fe_{2}B layers formed on AISI S1 steel. The growth kinetics of Fe_{2}B layers on AISI S1 steel was described by the classical parabolic growth law with the occurrence of a constant boride incubation time. The value of activation energy for boron diffusion in AISI S1 steel was estimated as 199.16 kJmol^{1} on the basis of the integral method,and compared with that obtained from an alternative diffusion model. Furthermore, this value of boron activation energy was compared to the values found in the literature. The present kinetic approach based on the integral method and four diffusion models were experimentally validated by using three extra boriding conditions. As a consequence, a good agreement was noticed between the experimental values of Fe_{2}B layers’ thicknesses and the predicted thicknesses. Finally, an isothickness diagram was suggested to be used as a simple tool for selecting the optimized value of Fe_{2}B layer thickness for practical use of AISI S1 steel in the industry.
6. Acknowledgements
The work described in this paper was supported by a grant of PRDEP and CONACyT México (National Council of Science and Techonology). Likewise, FCS reconoce los fondos del Departamento de Física y Matemáticas y de la División de Investigación de la UIA.The authors wish to thank to the Laboratorio de Microscopía de la UIA.
7. References

^{1}Sinha AK. Boriding (Boronizing) of Steels. In: ASM Handbook. Volume 4. Heat Treating Materials Park: ASM International; 1990. p. 437447.

^{2}Keddam M, Chentouf SM. A diffusion model for describing the bilayer growth (FeB/Fe2B) during the iron powderpack boriding. Applied Surface Science 2005;252(2):393399.

^{3}Keddam M, EliasEspinosa M, OrtizDomínguez M, SimónMarmolejo I, ZunoSilva J. Packboriding of AISI P20 steel: Estimation of boron diffusion coefficients in the Fe2B layers and tribological behaviour. International Journal of Surface Science and Engineering2017;11(6):563585.

^{4}Keddam M, OrtizDominguez M, EliasEspinosa M, ArenasFlores A, ZunoSilva J, ZamarripaZepeda D, et al. Kinetic Investigation and Wear Properties of Fe_{2}B Layers on AISI 12L14 Steel. Metallurgical and Materials Transactions A.2018;49(5):18951907.

^{5}OrtizDomínguez M, FloresRentería MA, Keddam M, EliasEspinosa M, DamiánMejía O, AldanaGonzález JI, et al. Simulation of growth kinetics of Fe_{2}B layers formed on gray cast iron during the powderpack boriding. Materials and Technology 2014;48(6):905916.

^{6}EliasEspinosa M, OrtizDomínguez M, Keddam M, GómezVargas OA, ArenasFlores A, BarrientosHernández FR, et al. Boriding kinetics and mechanical behaviour of AISI O1 steel. Surface Engineering 2015;31(8):588597.

^{7}Nait Abdellah Z, Keddam M, Chegroune R, Bouarour B, Haddour L, Elias A. Simulation of the boriding kinetics of Fe_{2}B layers on iron substrate by two approaches. Matériaux et Techniques 2012;100(67):581588.

^{8}FloresRentería MA, OrtizDomínguez M, Keddam M, DamiánMejía O, EliasEspinosa M, FloresGonzález MA, et al. A Simple Kinetic Model for the Growth of Fe_{2}B Layers on AISI 1026 Steel During the Powderpack Boriding. High Temperature Materials and Processes 2015;34(1):111.

^{9}Kouba R, Keddam M,Kulka M. Modelling of paste boriding process. Surface Engineering 2015;31(8):563569.

^{10}Ramdan RD, Takaki T, Tomita Y. Free Energy Problem for the Simulations of the Growth of Fe_{2}B Phase Using PhaseField Method. Materials Transactions2008;49(11):26252631.

^{11}Campos I, Oseguera J,Figueroa U, Garcia JA, BautistaO, Kelemenis G. Kinetic study of boron diffusion in the pasteboriding process. Materials Science and Engineering: A 2003;352(12):261265.

^{12}Mebarek B, Benguelloula A, Zanoun A. Effect of Boride Incubation Time During the Formation of Fe_{2}B Phase. Materials Research 2018;21(1):e20170647.DOI: http://dx.doi.org/10.1590/19805373mr20170647
» https://doi.org/http://dx.doi.org/10.1590/19805373mr20170647 
^{13}Brakman CM, Gommers AWJ,Mittemeijer EJ. Boriding of Fe and FeC, FeCr, and FeNi alloys; Boridelayer growth kinetics. Journal of Materials Research 1989;4(6):13541370.

^{14}Yu LG, Chen XJ, Khor KA, Sundararajan G. FeB/Fe_{2}B phase transformation during SPS packboriding: boride layer growth kinetics. Acta Materialia2005;53(8):23612368.

^{15}Okamoto H. BFe (boronIron). Journal of Phase Equilibria and Diffusion 2004;25(3):297298.

^{16}Krukovich MG, Prusakov BA, Sizov IG. The Components and Phases of Systems 'BoronIron' and 'BoronCarbonIron'.In: Krukovich MG, Prusakov BA, Sizov IG. Plasticity of Boronized Layers. Volume 237 of the Springer Series in Materials Science Cham: Springer; 2016. P. 1321.

^{17}Goodman TR. Application of Integral Methods to Transient Nonlinear Heat Transfer. Advances in Heat Transfer1964;1:51122.

^{18}ReséndizCalderon CD, RodríguezCastro GA, MenesesAmador A, CamposSilva IE, AndracaAdame J, PalomarPardavé ME, et al. MicroAbrasion Wear Resistance of Borided 316L Stainless Steel and AISI 1018 Steel. Journal of Materials Engineering and Performance 2017;26(11):55995609.

^{19}Carbucicchio M, Badani L,Sambogna G. On the early stages of high purity iron boriding with crystalline boron powder. Journal of Materials Science 1980;15(6):14831490.

^{20}Palombarini G, Carbucicchio M. Growth of boride coatings on iron.Journal of Materials Science Letters 1987;6(4):415416.

^{21}Sesen FE, ÖzgenÖS, Sesen MK. A Study on Boronizing Kinetics of an InterstitialFree Steel. Materials Performance and Characterization 2017;6(4):492509.

^{22}Sen S, Sen U,Bindal C. An approach to kinetic study of borided steels. Surface and Coatings Technology 2005;191(23):274285.

^{23}Jiang YF, BaoYF, Wang M.Kinetic Analysis of Additive on Plasma Electrolytic Boriding. Coatings 2017;7(5):61.

^{24}Chegroune R, Keddam M, Nait Abdellah Z, Ulker S, Taktak S, Gunes I. Characterization and kineticsof plasmapasteborided AISI 316 steel. Materials and Technology 2016;50(2):263268.

^{25}CamposSilva I, OrtizDominguez M. Modelling the growth of Fe_{2}B layers obtained by the paste boriding process in AISI 1018 steel irons. International Journal of Microstructure and Materials Properties 2010;5(1):2638.

^{26}EliasEspinosa M, OrtizDomínguez M, Keddam M, FloresRentería MA, DamiánMejía O, ZunoSilva J, et al. Growth Kinetics of the Fe_{2}B Layers and Adhesion on Armco Iron Substrate. Journal of Materials Engineering and Performance 2014;23(8):29432952.

^{27}OrtizDomínguez M, GómezVargas OA, Keddam M, ArenasFlores A, GarcíaSerrano J. Kinetics of boron diffusion and characterization of Fe_{2}B layers on AISI 9840 Steel. Protection of Metals and Physical Chemistry of Surfaces 2017;53(3):534547.

^{28}Azouani O, Keddam M, Allaoui O, Sehisseh A. Kinetics of the Formation of Boride Layers on ENGJL250 Gray Cast Iron. Materials Performance and Characterization 2017;6(4):501522.
Publication Dates

Publication in this collection
16 July 2018 
Date of issue
2018
History

Received
07 Mar 2018 
Reviewed
25 Apr 2018 
Accepted
05 June 2018