Characterization of Boride Layers on S235 Steel and Calculation of Activation Energy Using Taylor Expansion Model

Abstract

S235 low-carbon steel was boronized between 1123 K and 1273 K using a commercial powder mixture (Durborid) to study the formation and growth behavior of boride layers. The type of interface and thickness of the resulting layers were determined with scanning electron microscopy (SEM). The technique of X-ray diffraction (XRD) confirmed the formation of a predominantly single-phase Fe₂B layer under most processing conditions. To assess the diffusion behavior, the kinetic model with a Taylor series expansion was implemented to calculate the B diffusion coefficients in the Fe₂B layer under a transient diffusion regime. The B activation energy in Fe₂B was determined to be 157 kJ/mol, which aligns well with values derived from the literature.

1. Introduction

A highly effective surface treatment for enhancing the properties of mechanical components is the boriding process. This technique promotes the appearance of boride layers on steel surfaces [1]. During the process, B atoms from the boronizing agent diffuse through the steel surface, leading to the formation of either an Fe₂B layer or a bilayer (FeB/Fe₂B).

The application of boriding significantly improves the tribological characteristics and resistance to corrosion of the treated steels. Boriding of iron alloys is typically carried out at temperatures ranging from 800 °C to 1050 °C, resulting in the formation of iron borides on steel surfaces.

Numerous boronizing methods [2,3,4,5,6,7] have been explored in laboratory settings, and some have been successfully scaled up for industrial applications due to their effectiveness and advantages. Among these, powder-pack boriding is the most widely adopted industrial method thanks to its low cost, ease of implementation, and flexibility in powder composition.

The proportion of each component in the powder mixture has a great effect in determining the types of iron borides formed through the thermodiffusion process. To exemplify this, in the reference work [8], the authors employed a boriding agent with the proportions 33.5% B₄C, 5.4% KBF₄, and 61.1% SiC in weight percent to produce an Fe₂B layer on ASTM A283 steel. In another study, Sari et al. [9] investigated how varying the proportions of six different powder components affected the boronizing kinetics and resistance to wear of AISI 304 steel. Notably, a mixture containing 20% B₄C, 50% KBF₄, 10% SiC, and 20% graphite yielded the thickest boride layers with the highest surface hardness.

This same composition also resulted in the lowest wear rate observed during their experiments. For potential industrial applications of borided steel components, optimizing the boride coating thickness is a critical factor in meeting operational requirements. The selection of this thickness for the boride coating is a decisive factor in resisting surface wear in industrial sectors such as the automotive, equipment for agriculture, textiles, extrusion, and injection molding. For instance, thin boronized layers not exceeding 20 µm are typically employed to combat the wear of the adhesive type. In contrast, the thicker layers are more effective in resisting the severe wear conditions of abrasion. For low-alloy steels, the optimal boride layer thickness can reach up to 250 µm. In contrast, high-alloy steels require a thinner optimal layer, typically between 25 µm and 76 µm [1].

Therefore, modeling the kinetics of the boriding process is crucial for optimizing the boride coating thickness and ensuring the practical application of treated steel in industry. Various mathematical models [2,8,9,10,11,12,13,14,15,16,17,18] have been implemented to analyze the formation kinetics of boride layers on ferrous alloys, particularly in the case of Fe-based alloys. To exemplify this, Ortiz-Dominguez et al. [8] applied two different models to study the boriding kinetics of ASTM 283 steel. The first model assumed a steady-state diffusion regime, where the boron concentration varied linearly with diffusion distance. The second model employed the integral method, which involved solving a system of differential-algebraic equations under specific initial conditions while accounting for a transient diffusion regime. The model proposed by Morales-Robles et al. [10] was used in the present work to calculate the B diffusion coefficients in Fe₂B for S235 steel, due to its simple mathematical formulation. Yu et al. [12] investigated the effect of boron depletion on the kinetics of the spark plasma sintering (SPS) pack-boriding of mild steel. They proposed a model for a bilayer system (FeB/Fe₂B) by considering boron diffusion in the Fe phase. Over a prolonged treatment time, the bilayer system underwent a phase transformation in which the FeB layer was eliminated due to boron depletion. The vast majority of these models are based on solving Fick’s law in combination with mass conservation equations. Some models have used alternative methods, such as the Adomian decomposition method (ADM) [13], the least squares method [15] and the stochastic model [18], while others have employed neural network techniques [15].

The objective of this study was to surface-harden the S235 steel by employing solid boriding within the range of 1173–1273 K. The crystalline structure of the resulting iron borides was identified using X-ray diffraction (XRD), while the morphology of the boride layers was microscopically examined with SEM. Additionally, the model described in the reference [10] was employed to evaluate the B diffusion coefficients and to determine the B activation energy of the system. The obtained activation energy value was then analyzed and contrasted with the data reported in the literature.

2. The Taylor Expansion Model

The model given in [10] was applied to assess the boron diffusion coefficients across the boronized layer on S235 steel by expanding the boron distribution along the distance diffusion as a second-order Taylor series within saturated matrix with boron atoms. In this context, Morales-Robles et al. [10] investigated the growth of Fe₂B layers on low-alloy 35NiCrMo4 steel. A powder mixture containing 33.5 wt.% B₄C, 61.1 wt.% SiC, and 5.4 wt.% KBF₄ was used, resulting in the formation of a single-phase Fe₂B layer under all boronizing conditions. To evaluate the B activation energy of the system, the Taylor expansion model was used, assuming negligible boron solubility in the substrate and expressing the distribution of B content within the Fe₂B layer as a Taylor series under a transient diffusion regime. The validity of this model was further assessed under two extra processing conditions. Figure 1 gives a schematic illustration of boron concentration profiles developed along the boronized layer on S235 steel.

$C_{up}^{F{e}_{2}B}$ (=9.00 wt.%) refers to the upper B content in the Fe₂B phase, while $C_{low}^{F{e}_{2}B}$ (=8.83 wt.%) denotes the lower B content in the Fe₂B phase. $u$ is the boronized layer thickness. $C_{ads}$ designates the adsorbed quantity of boron at the steel surface [12]. $C_0$ is the soluble B content in the substrate, which is very low ($\approx$0 wt.%) [17].

Initial condition:

$$t=0, for x\succ 0, with C(x,t=0)=C_0\approx 0 wt.\%$$

(1)

$$C(x=0,t=0)=C_{up}^{F{e}_{2}B} for C_{ads}\succ 8.83 wt.\%$$

(2)

$$C(x=u,t=0)=C_{low}^{F{e}_{2}B} for C_{ads}\prec 8.83 wt.\%$$

(3)

The time change in the boronized layer thickness is provided by Equation (4):

$$u=k\sqrt{t}$$

(4)

The parameter $k$ is a kinetic constant depending upon the temperature. This diffusion problem is governed by the following differential equation of the first order:

$${\displaystyle \frac{(C_{up}^{F{e}_{2}B}+C_{low}^{F{e}_{2}B})}{2D}}(u{\displaystyle \frac{du}{dt}})[1+{\displaystyle \frac{1}{2D}}(u{\displaystyle \frac{du}{dt}})]=(C_{up}^{F{e}_{2}B}-C_{low}^{F{e}_{2}B})$$

(5)

Equation (5) has an exact solution by considering the dimensional parameter $g$ given by Equation (6):

$$g={\displaystyle \frac{1}{D}}(u{\displaystyle \frac{du}{dt}})$$

(6)

After some mathematical manipulations, Equation (7) is derived:

$$g^2+2g-4{\displaystyle \frac{(C_{up}^{F{e}_{2}B}-C_{low}^{F{e}_{2}B})}{(C_{up}^{F{e}_{2}B}+C_{low}^{F{e}_{2}B})}}=0$$

(7)

The positive solution to Equation (7) can be easily determined as follows:

$$g=-1+\sqrt{1+4{\displaystyle \frac{(C_{up}^{F{e}_{2}B}-C_{low}^{F{e}_{2}B})}{(C_{up}^{F{e}_{2}B}+C_{low}^{F{e}_{2}B})}}}$$

(8)

From Equation (6), the solution to the problem in terms of thickness can be derived as follows:

$$u=\sqrt{2gDt}$$

(9)

Finally, the relation allowing the calculation of B diffusion coefficients in Fe₂B can be determined from Equation (10):

$$D={\displaystyle \frac{k^2}{2g}}$$

(10)

3. Material and Experimental Techniques

The material to be boronized was S235 steel, whose nominal chemical composition is given in

Table 1. Chemical composition of 235 steel.

Element (wt.%)	C	Si	Mn	S
S 235 steel	0.22	0.05	1.60	0.05

.

Samples were cut from a cylindrical rod and underwent metallographic preparation using standard procedures. The cross-sections of the borided samples were ground with sandpapers of progressively finer grit sizes. Polishing followed, using diamond pastes with decreasing particle sizes ranging from 6 µm to 1 µm, to achieve a mirror-like finish suitable for microscopic examination. Subsequently, the samples were cleaned, and contaminants were eliminated by immersion into acetone for 10 min. Prior to the boronizing treatment, they were placed in a crucible made from stainless steel filled with a commercial Durborid powder mixture. The samples were then heat-treated in an electric resistance furnace at a temperature of 1173, 1223, 1248, or 1273 K for durations of 3, 5, and 7 h at each temperature. Following this process, the crucible was taken out the furnace, and the samples were allowed to cool naturally to ambient temperature. For microscopic analysis, the samples were chemically etched using a 3% Nital solution (a mixture of nitric acid and ethyl alcohol) for 60 s. The morphology of the boride layers was examined using a JEOL JSM-7600F scanning electron microscope (SEM) (Tokyo, Japan). The thicknesses of the boride layers were measured by employing the procedure given by Kunst and Schaaber [19], based on over twenty measurements taken at different locations on the cross-sections. The technique of X-ray diffraction (XRD) was employed to characterize the iron boride phases with Panalytical Empyrean diffractometer (Malvern Panalytical Ltd., Malvern, UK). Measurements were conducted over a 2 theta range of 10° to 120°, with a step size of 0.05°. The resulting diffraction peaks were analyzed using HighScore Plus software, version 3.0.5 with the ICSD FIZ Karlsruhe database.

4. Results and Discussions

4.1. SEM Observations of Boronized Layers

Figure 2 presents SEM images showing the boronized layers formed on S235 steel after 3 h of treatment at increasing boriding temperatures. At first glance, the images reveal the characteristic columnar morphology of the boronized layer, a typical feature observed in borided Armco iron and borided carbon steels [2,8,10,20]. Regardless of the boriding temperature, an apparent single boride layer is observed in all cases; however, confirmation of the phase composition requires further analysis using X-ray diffraction (XRD). The formation of boride needles begins after a certain incubation period, during which nucleation occurs. These needles eventually cover the entire surface as they grow and merge, forming a distinctive growth texture. The thickness of the boride coating thickness is increased as the temperature goes up, ranging from approximately 45 ± 7 µm for 1173 K treatment to 88.9 ± 8 µm for 1273 K treatment. This trend is consistent with the thermally activated nature of boron diffusion, which typically follows a parabolic growth law, as reported in various studies [2,3,6,7,8,9,10,20,21]. Some pores are visible after treatment at either 1248 or 1273 K, likely due to the high chemical reactivity of the boriding medium and the release of reactive gases at the solid–gas interface during the process. Malakhov and DeBoer [22] performed a thermodynamic analysis of various powder mixtures used in the pack boronizing process. Using Thermo-Calc software (Version Q), they calculated and interpreted the results related to boron activity while considering the chemical composition of the powder mixtures. Particularly, when analyzing the commercial boriding agent known as Ekabor, their calculations indicated that the boron activity in this agent is influenced solely by the processing temperature, and not by the proportion of the boron source within the mixture.

4.2. XRD Results

Figure 3 and Figure 4 present XRD diffractograms, revealing the appearance of diffraction peaks corresponding to the Fe₂B iron boride across all processing conditions. Additionally, minor peaks associated with the FeB phase are observed only in samples borided at 1173 K for 5 h and 1273 K for 7 h. These XRD results support the SEM observations, confirming the generally monophasic nature of the boronized layers.

When using the Durborid boriding agent, the formation of an FeB phase may occur at extended treatment times due to the phase transformation reaction, B + Fe₂B = 2FeB, which is driven by excess B atoms diffusing from the boronizing agent. However, the formation of this boron-rich phase (FeB) can be prevented by carefully optimizing the proportion of each component in the powder mixture, as demonstrated in several studies [8,10,20]. For instance, Vidal-Torres et al. [20] successfully produced single-phase Fe₂B layers on Armco iron using the solid boriding method at 850 °C for 1, 2, or 3 h. This was achieved with a powder mixture consisting of 70 wt.% SiC, 20 wt.% B₄C, and 10 wt.% KBF₄.

4.3. Calculation Results from the Taylor Expansion Model

To assess the B activation energy of the system, an analysis of the boriding kinetics is essential. By assuming that the incubation period is negligible compared to the total holding or exposure time, the time change in the layer thickness was plotted. Figure 5 illustrates the time variation in the layer thickness at different processing temperatures.

The numerical values of the kinetics constants, summarized in

Table 2. Experimental parabolic growth constant values in the range of 1173 to 1273 K.

T (K)	$\mathit{k}$ (µm s −0.5)
1173	0.4661
1223	0.6522
1248	0.7571
1273	0.8804

, were calculated by taking the slopes of the resulting linear plots.

Table 3. B diffusion coefficients in Fe₂B calculated with Equation (10).

T (K)	$\mathit{D}(\times {10}^{-12}{\mathrm{m}}^2{\mathrm{s}}^{-1})$
1173	5.75
1223	11.26
1248	15.17
1273	20.52

lists the B diffusion coefficients in Fe₂B calculated using Equation (10) with $g=0.01889$.

By plotting the temperature change in the diffusion coefficient according to the Arrhenius relationship, Equation (11) was derived as follows:

$$D=6.07\times {10}^{-5}\exp (-{\displaystyle \frac{157.70 \mathrm{k}\mathrm{J} \mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}}{RT}})$$

(11)

with R = 8.314 J mol⁻¹ K⁻¹ and T the treatment temperature in Kelvin.

Table 4. Comparing the calculated B activation energy with the values of the literature data.

Material	Boriding Method	Temperature Interval (K)	Activation Energy (kJmol−1)	Computation Method	Ref.
Armco Fe	Gas	1073–1273	78.03 (FeB) 120.65 (Fe2B)	Kinetic model	[23]
Armco Fe	Paste	1123–1323	157 (Fe2B)	Diffusion model	[24]
Armco Fe	Powder	1123–1323	157.6 (Fe2B)	Diffusion model	[25]
AISI 1018	PDCPB	973–1123	133.8–152.3 (FeB) 129.5–145.9 (Fe2B)	Dybkov model	[2]
AISI 1018	Powder	1173–1273	91.20–155.22 (FeB + Fe2B)	Empirical parabolic law	[26]
SLM AISI 316 L	Powder	1123–1223	256.61 (FeB) 161.61 (Fe2B)	Diffusion model	[21]
AISI 1018	Electrochemical	1123–1223	172.75 ± 8.6 (FeB + Fe2B)	Empirical parabolic law	[27]
S235	Powder	1173–1273	157.70 (Fe2B)	Taylor expansion model	This work

compares the calculated value of activation energy in S235 steel with other values available in the literature [2,21,23,24,25,26,27]. One striking fact is that the activation energy value is tightly related to key factors such as the nominal chemical composition of the steel, the physical state of the boron source, the boron activity of the boron source, the type of boriding method, the chemistry and electrochemistry of the medium, and the approach to calculating the activation energy. When examining different formulations of kinetic models used for boronizing kinetics, both differences and similarities should be discussed. For example, Campos et al. [24] employed a kinetic model that considered the difference in specific volumes between Fe₂B and the austenite phase under a steady-state diffusion regime. Additionally, the expression for the boron mobility in Fe₂B was found to depend on the square of the parabolic growth constant and to be proportional to a dimensional parameter defined as the natural logarithm of the ratio of the treatment time to the boride incubation time. In another study, M. Elias-Espinosa et al. [25] applied the error function diffusion model to describe the boronizing kinetics of Armco iron in the presence of an Fe₂B layer. By formulating the mass conservation equation at the growing interface, they were able to determine the B activation energy in Fe₂B. In this case, the B distribution in the Fe₂B phase can be considered a function that can be expanded as a Taylor series of the n-th order. Chaparro-Pérez et al. [2] adopted the Dybkov model [28] to examine the growth of a bilayer (FeB/Fe₂B) on AISI 1018 steel. In fact, the Dybkov model [28] is based on solving two differential equations derived from the two partial chemical reactions occurring at the growing interfaces, namely, B + Fe₂B = 2FeB and Fe + FeB = Fe₂B. Recently, Chaparro-Pérez et al. [2] applied the PDCPB (Pulsed Direct-Current Pack Boriding) treatment to AISI 1018 steel to produce a bilayer microstructure (FeB + Fe₂B) between 700 °C and 850 °C over a short duration of 3 h. The occurrence of an induced electric field during the process led to lower activation energy values for the system, as determined using the Dybkov kinetic model [28], and compared to those obtained from the conventional pack boriding method. As an outcome, the activation energy for FeB ranged from 133.8 to 152.3 kJ·mol⁻¹, while for Fe₂B, it varied between 129.5 and 145.9 kJ·mol⁻¹ depending upon the current intensity value. In another study, Keddam et al. [23] performed gas boronizing of Armco iron at temperatures ranging from 1073 to 1273 K in a H₂–BCl₃ atmosphere. Unlike the conventional solid boronizing process (paste [24] or powder [25]), the B activation energy in FeB is lower compared to that in Fe₂B. This is attributed to the higher thermodynamic stability of FeB compared to Fe₂B. In the reference [26], the authors examined the effect of varying the diameter of cylindrical AISI 1018 steel samples, all with a fixed length of 7 mm, on the boriding kinetics. The B activation energy was determined to be in the range of 91.20 to 155.22 kJ·mol⁻¹ depending upon the amount of matter participating in the mass transport of boron atoms. Demerci and Tuncay [21] utilized Selective Laser Melting (SLM) to manufacture AISI 316L steel and subsequently surface-harden it by boronizing it. In their work, a diffusion model using the error function was applied to estimate the B mobilities in FeB and Fe₂B. The B activation energy was then determined to be 256.56 kJ mol⁻¹ in FeB and 161.61 kJ mol⁻¹ in Fe₂B from this kinetic model. Kartal et al. [27] boronized AISI 1018 steel using an electrochemical method at a current density of 200 mA cm^{- 2}, resulting in the generation of iron borides (FeB and Fe₂B). The evaluated B activation energy in this process was 172.75 ± 8.6 kJ mol⁻¹. Due to the nature of the electrochemical reactions, B atoms rapidly saturated the steel surface, making this method significantly faster than the conventional pack boriding technique. As a result, relatively thick boronized layers were achieved in a very reduced treatment time of up to 2 h. In summary, the determined B activation energy in Fe₂B for S235 steel is consistent with values reported in the literature [24,25], which can be attributed to its low carbon content. Furthermore, the calculation of boron activation energy depends on the approach used, whether empirical or theoretical. It is observed that steels with high alloying element content [21] exhibit higher activation energy for solid boriding with powders, as the B diffusion is hindered by the presence of precipitates such as metallic borides and carbides. In contrast, low-carbon steels tend to have lower activation energy values [26], which can be similar to that of Armco iron, as observed in the current study.

5. Conclusions

The S235 low-carbon steel was boronized between 1123 K and 1273 K using a commercial powder mixture known as Durborid, and the boron activation energy was also evaluated.

This study led to the following concluding points:

(1)

The boride layers exhibited a jagged morphology, characterized by varying lengths of boride needles, resulting in compact and dense coatings.

(2)

XRD analysis confirmed the occurrence of an Fe₂B layer under most boriding conditions. However, very low diffraction peaks corresponding to the FeB phase were observed in two specific cases.

(3)

The time change in the layer thickness revealed a parabolic growth law with a thickness ranging from 45 ± 7 to 141.40 ± 14 µm.

(4)

The B activation energy in Fe₂B was estimated to be 157.70 kJ mol⁻¹ using the Taylor expansion model, which is consistent with values reported in the literature.

(5)

For future studies, the Taylor expansion model may be adopted with other alloys involving the diffusion of elements such as boron, carbon, and nitrogen to simulate their diffusion kinetics.