Impact of the DC intensity and electrode distance on pulsed-DC powder-pack boride layer growth kinetics

Boriding is the process of growing boride layer on the material’s surface at high temperatures through the diffusion of B atoms. The driving force for the diffusion of B involves temperature, time, and B concentration gradient along the boride layer-substrate system. Historically, boriding has been used for improving the surface properties of ferrous materials; however, it is applied to various nonferrous materials, cemented carbides and cermets, refractory metals, and some superalloys.^1–5 Additionally, boriding has been applied to parts produced using additive manufacturing and in recent years, researchers have been studying simultaneous homogenization and boriding to enhance the mechanical properties of parts intended for repair purposes.^6,7

Although boriding is relatively slow compared to other surface hardening processes, a judicious choice of the boriding temperature/time and the boriding medium can significantly increase the process rate. Notably, the powder-pack boriding is widely used due to its easy handling, low-cost requirements, and the possibility of changing the composition of the powder mixture;⁸ the common powder mixture consists of B₄C (B source), SiC (diluent), and KBF₄ (activator). The powder-pack boriding usually is carried out at 850–1100 °C for exposure times of 2–24 h with high consumption of energy and time.

During the last years, “hybrid” boriding (related to a combination of chemical-physical techniques) such as ultra-fast boriding,⁹ fluidized bed boriding,¹⁰ plasma-paste boriding,¹¹ and the powder-pack boriding assisted by DC¹² or AC have received attention to reduce the boriding temperature and increasing the growth kinetics of boride layers on the material’s surface. The “hybrid” boriding techniques offer a relatively low energy consumption and they are friendly to the environment.

Based on the enhancement effect of the direct current field on powder-pack boriding,^13–15 a novel technique called pulsed-DC powder-pack boriding (PDCPB) was developed.¹⁶ This technique involves applying a direct current field between two electrodes in the powder mixture, with the material to be borided positioned between the electrodes. The PDCPB employs a DC power supply coupled with a programmable electronic control device to generate cyclic polarity changes in the flux of B⁺ ions. The pulsed-DC field provides the same amount of B⁺ ions on both surfaces exposed to the current field, causing the formation of similar boride layer thicknesses.

The study of the growth kinetics of boride layers on different materials is essential for aligning the boride layer thickness with the intended industrial application and the base material. Various deterministic approaches have been employed to model B diffusion and the growth rate of the boride layers, including the mass balance model,¹⁷ the chemical reaction model,¹⁸ the heat balance integral method,¹⁹ and the mean diffusion coefficient model,²⁰ among others. However, there have been relatively few studies that propose a statistical approach, using ANOVA analysis, which allows for the evaluation of boride layer growth in relation to other independent variables, beyond boriding temperature and exposure time.²¹ 

In this study, novel results about the contribution of the current intensity and the electrode distance on the FeB-Fe₂B layer growth on AISI 1018 and AISI 4140 steels during the PDCPB are obtained. An analysis of variance (ANOVA) was performed to determine the influence of current intensity and the electrode distance, while a regression analysis was performed to estimate an empirical equation that describes the boride layer thickness on both steels as a function of the independent variables. Finally, the electrical behavior of the powder mixture and the effect of Joule heating were estimated for the different current intensities and electrode distances.

Cylindrical specimens of AISI 1018 and AISI 4140 steels with 20 mm of diameter and 5 mm of thickness were used in this study. The PDCPB (Fig. 1) consists of a regulated DC source (1) connected to a programmable electronic control device (2); the specimen (9) is placed into an AISI 304 steel container (6) and between two rectangular electrodes (8) (made from an AISI 304 steel) positioned at a constant distance. The specimen (9) and the electrodes (8) [that are coupled to the programmable electronic control device (2)] are embedded in a 70% B₄C, 20% SiC, and 10% KBF₄ powder mixture (7). The temperature of the powder mixture (7) was monitored by a type-B thermocouple (3) connected to a data acquisition system (4) and a computer (5).

The container (6) is hermetically sealed and introduced in a conventional electric muffle (10); when the boriding temperature is reached, a constant current flux is supplied by the regulated DC source (1) to the electrodes (8). During the PDCPB, the electrodes (8) change their polarity symmetrically with the aid of the programmable electronic control device (2).

In this work, the electrode distance was modified in 10, 15, and 20 mm with current intensities of 2.5, 5, and 7.5 A for each electrode distance, applying cyclic polarity changes of 10 s. The PDCPB was performed at 900 °C for 2700 s according to the experimental procedure proposed by Castillo-Vela et al.²² in AISI 1018 and AISI 4140 steels. On the other hand, the powder mixture resistance was measured for each 50 °C starting from room temperature to 900 °C, using an ohmmeter connected in parallel to the electrodes. When the temperature of 900 °C was reached, the electric field was induced, and the resistance of the powder mixture was estimated considering Ohm’s law; the voltage and current measurements were obtained each 60 s from the regulated DC source until complete the exposure time. At the end of the PDCPB, the container was removed from the electric muffle and cooled to room temperature.

The borided steel specimens were prepared metallographically for the observation of the boride layers on the steels’ surface. From a fixed reference of the borided surface, 50 boride layer thickness measurements were estimated on both surfaces exposed to the DC field, using an optical microscope coupled to a computer that contains the image pro-plus v.10.0 software. The XRD patterns on the borided surfaces were obtained with the aid of Rigaku Lab equipment using a CuK_α radiation (0.154 nm), step size of 0.01° s⁻¹, and 2θ range of 20°–90°.

The variance method (ANOVA) was used to quantify the effect of the current intensity and the electrode distance (independent variables) on the total boride layer thickness (dependent variable) with three levels for each variable. Statistical analysis was performed by using statgraphics centurion xvi.i software, in which the level of statistical significance was tested using the p-value. A confidence interval of 95% was established for the statistical significance test; a p-value less than 0.05 demonstrates a significant effect between the independent and dependent variables. The percentage of influence of each independent variable and their interaction on the dependent variable was estimated using the F-test. Finally, a multiple linear regression model was applied to the experimental data to estimate the boride layer thickness at the different values of the factors employed. The ordinary least squares regression was used for estimating the coefficients, which describe the relationship among the independent variables and the dependent variable.

A schematic representation of the growth of boride layer during the PDCPB^16,22 is depicted in Figs. 2(a)–2(d).

The flux of electrons produced by the current field collides with the particles of the powder mixture. A part of the kinetic energy is dissipated into heat (Joule effect), which increases the temperature inside the container. This thermal effect enhances the decomposition and the chemical reactions of the powder mixture. The DC current field hastens the delivery of active B atoms from the powder mixture, being positively charged (B⁺) [Fig. 2(a)]. The B⁺ ions follow the direction of the DC field to the steel surface due to an electron flux momentum transfer in the direction of the electric field lines [from anode (S₁) to cathode (S₂)]. The symmetrical inversion of the electric field [from anode (S₂) to cathode (S₁)] is promoted by the programmable electronic control device, causing an equally amount of B⁺ on both steel surfaces [Fig. 2(b)]. Furthermore, the electron flux in the steel’s substrate causes an “attraction-repulsion” phenomenon, which increases the defect mobility and the concentration of the point defects in the substrate. The B⁺ ions are directly diffused into the negatively charged vacancy [Fig. 2(c)] and by an interstitial mechanism; the formation of boride nuclei begins when the B concentration on the steel surface reaches the required level of boride phases. Finally, the boride crystals grow and joint together to form a compact boride layer [Fig. 2(d)].

The PDCPB results on the surfaces of AISI 1018 steel [Figs. 3(a)–3(c)] and AISI 4140 steel [Figs. 3(e)–3(g)] revealed a jagged layer microstructure, which consisted of FeB (outer layer) and Fe₂B (inner layer). According to the XRD patterns of Fig. 4, FeB and Fe₂B have a pronounced {002} texture and consist of columnar crystals oriented in the diffusion direction [001] because of the enhanced diffusion paths in the crystal lattices of both phases.^23,24 From the XRD pattern of borided AISI 4140 steel [Fig. 4(b)], alloying elements of the substrate (i.e., Cr and Mo) dissolve on the Fe sublattice of the borides,²⁵ forming interstitial compounds such as CrB, Cr₂B, and Mo₂B.

Table I illustrates the influence of current intensity and electrode distance on the thickness of the FeB-Fe₂B layer in AISI 1018 and AISI 4140 steels. The corresponding results are depicted in Fig. 5, while the “threshold” boride layer thickness values were obtained through conventional powder-pack boriding of AISI 1018 and AISI 4140 steels at 900 °C for 2700 s as shown in Figs. 3(d) and 3(h), respectively. The slight differences of boride layer thickness between the borided steels were influenced by the Cr content on AISI 4140 steel, which hindered the boron diffusion in the FeB-Fe₂B layer.

The effect of the current intensity on the FeB-Fe₂B layer thickness is related to the electromigration, the electrical resistivity of the powder mixture, and the Joule heating. First, when the current intensity became greater, the chemical reactions in the powder mixture were enhanced, thereby increasing the activity and productivity of active B. Particularly, the current flux interacted with active B, resulting in the ionization of B. Consequently, the movement of B⁺ in the powder mixture was directed by the current field, thus, led to a faster boride layer growth.

Before the induction of the electric field [Fig. 6(a)], the powder mixture resistivity varied from 0.4 Ω m (with a 10 mm electrode distance) to 0.2 Ω m (with a 20 mm electrode distance). However, since the melting point of KBF₄ is approximately 500 °C, the resistivity of the powder mixture decreased to values ∼15 × 10⁻³ Ω m for the different electrode distance, promoting a liquid KBF₄ flux through the powder mixture porosities.²² This process creates “small bypasses” that fill up the pores, allowing the free flow of the electric field. After the induction of the electric field at 900 °C, the increase in current intensity, from 2.5 to 7.5 A, resulted in a reduction of the resistivity of the powder mixture, which behaves as a semiconductor²² [Figs. 6(b)–6(d)]. As shown in Fig. 6(d), this effect was more pronounced when the electrode distance was greater, leading to an increased flux of B⁺ ions to the steel surface. Following that, the behavior of powder mixture resistivity remained constant during the 2700 s of exposure for the different experimental conditions.

Otherwise, the thermal effect arising due to Joule heating on the growth of the FeB-Fe₂B layer at the surface of AISI 1018 steel and AISI 4140 steel can be linked to the current intensity flowing through the powder mixture. For example, the amount of heat generated during PDCPB is directly proportional to the increase in current intensity. This results in a rise in temperature within the powder mixture, an increase in the diffusivity of B⁺ ions, thereby hastening the growth of the FeB-Fe₂B layer.

From the results of Figs. 6(e)–6(g), the highest temperature of the powder mixture (approximately of 1070 °C) was obtained at 7.5 A/20 mm (current intensity/electrode distance) compared to the lowest value (around of 910 °C) estimated for 2.5 A/10 mm.

The results of Table II demonstrate that W(B) increases with respect to the electrode distance; $W ( B ) FeB$⁠, and $W ( B ) F e 2 B$ depend only on FeB and Fe₂B layer thicknesses. It is important to note that the results are completely ideal and does not consider the depletion of KBF₄ and the performance of the chemical reactions in the powder mixture.

On the other hand, Figs. 7(a) and 7(b) depict the relationship between the required amount of B in the FeB-Fe₂B layer thickness with the electrode distance for the different current intensities. These findings present an opportunity to optimize the quantity of powder mixture used in the PDCPB.

The experimental data were analyzed using ANOVA to examine the impact of current intensity (X) and electrode distance (Y) on the total FeB-Fe₂B layer thickness (d) for borided AISI 1018 steel and borided AISI 4140 steel (see Table III). The analyses were conducted with a 95% confidence interval and a significance level of 0.05. Furthermore, the F-test was employed to determine which experimental variable had a significant effect on the boride layer thickness.^21,28 For both borided steels, the p-values of current intensity and electrode distance were less than 0.05, indicating that both factors had significant impact on the boride layer thickness. The difference in F-test values indicated that current intensity had a greater influence on layer thickness compared to electrode distance. The weight coefficients for current intensity were approximately 51% for borided AISI 1018 steel (compared to 43% for electrode distance) and approximately 56% for borided AISI 4140 (with electrode distance contributing around 38%). The interaction between the factors (current intensity and electrode distance) accounted for approximately 3.5% for both borided steels.

Multiple linear regression was used for estimating the coefficients which describe the relationship among the independent variables (X,Y) and the dependent variable (d). ANOVA analyses for the two linear regression models, as presented in Table IV, yielded p-values less than 0.05 for all terms, indicating their statistical significance.

The confidence levels for the regression models of borided AISI 1018 steel and borided AISI 4140 steel were 95.55% and 96.45%, respectively. The FeB-Fe₂B layer thickness results were plotted at different current intensities and electrode distances as shown in Fig. 8.

The statistical analyses were validated by carrying out the PDCPB considering 7 A/12 mm and 3.5 A/17 mm for both steels; the experimental FeB-Fe₂B layer thicknesses are depicted in Fig. 9.

At 7 A/12 mm, the experimental FeB-Fe₂B layer thickness on AISI 1018 was measured to be 95 ± 6 μm, while on AISI 4140 steel was 84 ± 4 μm. When using 3.5 A/17 mm, the experimental FeB-Fe₂B layer thicknesses were 73 ± 4 μm for borided AISI 1018 steel and 62 ± 3 μm for borided AISI 4140 steel. These values differed by approximately 5% when compared to the estimated from the regression models.

The effect of current intensity and electrode distance during the PDCPB on the growth kinetics of FeB-Fe₂B layers at 900 °C for 2700 s was studied. The FeB-Fe₂B layer thickness on AISI 1018 and AISI 4140 steels increased with higher current intensity and electrode distance. This increase was attributed, principally, to electromigration, the Joule heating, and the B availability of powder mixture between electrodes. At the extreme experimental condition of 7.5 A/20 mm, the heat generated in the powder mixture elevated the temperature to approximately 1070 °C. This led to an increase of the chemical reactions within the powder mixture and a reduction in its resistivity due to the electrode distance. Moreover, the enhanced mobility of point defects due to the electrical field on the steel facilitated the reaction of B⁺ ions on the surface to generate the boride nuclei, and consequently, the diffusion of B⁺ in the FeB-Fe₂B. Additionally, the required amount of B for the formation of the boride layer was estimated. As expected, a thicker boride layer corresponded to an increase in the required B amount, regardless of the electrode distance.

On the other hand, the ANOVA analyses for both borided steels indicated that current intensity was ∼10% more significant on the FeB-Fe₂B layer thickness than the electrode distance. Finally, the regression models used to determine the boride layer thickness as a function of current intensity and electrode distance exhibited an error of approximately 5% when compared to the experimental FeB-Fe₂B layer thickness.

Based on the results obtained in this work, potential future findings in PDCPB could include: (1) investigating the influence of symmetrical inversion periods of the electric field on the growth kinetics of the boride layer, and (2) exploring the effects of low boriding temperatures, exposure times and powder mixture compositions on boride layer thickness.

This study was supported by research Grant Nos. 20230167 and 20227018 from the Secretaria de Investigacion y Posgrado of the Instituto Politecnico Nacional.

The authors have no conflicts to disclose.

I. Campos-Silva: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Supervision (equal); Writing – original draft (equal). L. E. Castillo-Vela: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). I. Mejía-Caballero:Conceptualization (equal); Formal analysis (equal); Investigation (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). J. L. Rosales-Lopez: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). M. Olivares-Luna: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). K. D. Chaparro-Pérez: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). F. P. Espino-Cortes: Formal analysis (equal); Investigation (equal); Methodology (equal). J. M. González-Carmona: Methodology (equal); Validation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.