Engineering methods for surface hardening of steels.

## Abstract

Boriding is a thermochemical surface treatment, a diffusion process similar to carburizing and nitriding in that boron is diffused into a metal base. An indispensable tool to choose the suitable process parameters for obtaining boride layer of an adequate thickness is the modeling of the boriding kinetics. Moreover, the simulation of the growth kinetics of boride layers has gained great interest in the recent years. In this chapter, the AISI 12L14 steel was pack-borided in the temperature range of 1123–1273 K for treatment times between 2 and 8 h. A parabolic law for the kinetics of growth of Fe2B layers formed on the surface of AISI 12L14 steel was deducted. Two diffusion models were proposed for estimating the boron diffusion coefficients through the Fe2B layers. The measurements of the thickness (Fe2B), for different temperature of boriding, were used for calculations. As a result, the boron activation energy for the AISI 12L14 steel was estimated as 165.0 kJ/mol. In addition, to extend the validity of the present models, two additional boriding conditions were done. The Fe2B layers grown on AISI 12L14 steel were characterized by use of the following experimental techniques: X-ray diffraction, scanning electron microscopy and energy dispersive X-ray spectroscopy.

### Keywords

- diffusion model
- activation energy
- parabolic growth law
- diffusion coefficient
- growth kinetics

## 1. Introduction

Surface hardening of steel can be achieved, mainly through two procedures: modifying the chemical composition of the surface by diffusion of some chemical element (carbon, nitrogen, boron, sulfur, etc.) in which case it is known as thermochemical treatment (Table 1) or modifying only the microstructure of the surface by thermal treatment, then known as surface treatment. The current technological demands highlight the need to have metallic materials with high performance under critical service conditions, consequently, the increase in the wear resistance, preserving its ductility and the toughness of the core.

According to Table 1, there are three methods of surface hardening:

Diffusion process that modifies the chemical composition where a component in a solid mixture can diffuse through another at a speed is measurable, if there is a suitable concentration gradient and the temperature is high enough. The effects of diffusion in solids are very important in metallurgy (increase surface hardness) as well: The continuous flux of carbon, nitrogen, boron, and so on, can form a hard coating, where the mass transfer is described by Fick’s laws.

Applied energy process, the interesting about these processes is that it is not necessary to incorporate any element to the substrate. For example, tempering is a heat treatment in which steel is heated up to austenization temperatures and subsequently it is cooled rapidly, with in order to obtain a transformation that provides a structure martensitic hard and resistant. Surface tempering is generally used to components that need a hard surface and a substrate with a high value of fracture toughness.

Coating and surface hardness, the coating covers the surface of the substrate, obtained after the deposition process, substrates considerably increase the physical characteristics of hardness and corrosion resistance, maintaining the original morphological characteristics (roughness and brilliance) unchanged, making the functional and decorative coating at the same time.

The current technological requirements highlight the need to have metallic materials with specific characteristics, for increasingly critical service conditions. For example, the metal dies used in the metallurgical processes of cold working and hot metals need a high toughness and surface hardness, especially at high temperature. Surface hardening of steel can be achieved, basically, by two processes: modifying the chemical composition of the surface by diffusion of some chemical elements (carbon, nitrogen, sulfur, boron, aluminum, zinc, chromium, and so on). Only boriding process for surface hardening is briefly reviewed in this chapter, boriding is a thermochemical treatment in which boron atoms are diffused into the surface of a workpiece and form borides with the base metal. Apart from constructional materials, which meet these high demands, processes have been developed which have a positive effect on the tribological applications including abrasive, adhesive, fatigue and corrosion wear of the component surface [1, 2, 3]. Boride layers are of particular benefit when the components have to withstand abrasive wear. The fundamental advantage of the borided layers (FeB and Fe_{2}B) is that they can reach high hardness near the surface (1800 HV_{0.1} and 2000 HV_{0.1}), maintained at high temperatures [4, 5, 6, 7, 8]. In this chapter, the growth kinetics of single phase layer (Fe_{2}B) on the ferrous substrate was studied during the iron powder-pack boriding (steady state and non-steady state). The parabolic growth law for the borided layers was mathematically estimated. Likewise, a mass balance equation was proposed at the Fe_{2}B/substrate (AISI 12L14) interface. Moreover, the boron diffusion coefficients (_{2}B layers were determined considering two mathematical models for mass transfer. The Fe_{2}B layers formed on the alloy surface is controlled by the diffusion of boron atoms, and the presence of the Fe_{2}B layers was checked by the XRD technique. Finally, the distribution of the alloy elements in AISI 12L14 borided steel was verified by chemical microanalysis technique (EDS) used in conjunction with SEM.

### 1.1 The diffusion models

One of the most important parameters that characterizes the Fe_{2}B layers is the thickness, since the properties of the coating depend on it, such as: resistance to wear, fatigue, hardness, and dynamic loads, as well as to a large extent determining the grip with the substrate. Having an expression that allow estimating the layer thickness during the boriding process, facilitates the appropriate selection of the technological parameters, in order to guarantee the desired properties. The layer thickness exhibits a time dependence such that:

#### 1.1.1 Derivation of the parabolic growth law

In diffusion processes, parabolic kinetics occurs when the mass gain on a sample is proportional to the square root of time. In general, parabolic kinetics indicates that diffusion of reactants (such as boron) through a growing layer is rate-determining. If the diffusion of B atoms is rate-determining, the layer rate is proportional to the flux through the substrate:

El flux,

where ^{3} and is the velocity _{2}B layer in m/s, ^{2} s. The velocity of a particle is proportional to the force, *F*, on the particle:

where

for a Fe_{2}B layer with thickness *x*. Combining Eq. (4) and (5) yields

from the relationship

where

In an ideal system, the concentration,

As shown in Eq. (2),

so that a combination of Eqs. (2) and (9) gives

If we assume that the potential is fixed at each boundary of the Fe_{2}B layer, we can replace

Combining Eqs. (11) and (12) then gives

Eq. (13) can be rewritten as

Upon integration of Eq. (14),

We arrive at the parabolic growth law:

#### 1.1.2 Steady state diffusion model

Steady state means that there will not be any change in the composition profile with time. A linear boron concentration profile is considered along the depth of the Fe_{2}B layer as depicted in Figure 1. The *f*(*x*) represents to the boron distribution in the substrate before the nucleation of iron boride layers on AISI 12L14 steel. _{2}B phase. Moreover, _{2}B layer (_{2}B/substrate interface (

The term _{2}B layer, *C*_{0} is the boron concentration in the substrate (AISI 12L14) assumed as null [10, 12, 13]. During the establishment of the steady-state diffusion model, a linear concentration-profile of boron along the Fe_{2}B layer is considered. Likewise, the assumptions proposed by Campos-Silva et al. [8], are taken account.

v_{0} is the first boride layer formed on the surface of the substrate (ASI 12 L14) during the boride incubation time [14], its thickness is very small in magnitude compared to the thickness of the boride layer (v). Moreover, regarded the mass balance equation at the growth interface (Fe_{2}B/substrate), which is described as follows [15, 16, 17, 18]:

When the concentration field is independent of time and

By solving Eq. (18), and applying the boundary conditions proposed in Figure 1, the distribution of boron concentration in Fe_{2}B is expressed as:

By substituting the derivative of Eq. (19) with respect of the distance *x*(*t*) into Eq. (17), we have

for

By substituting Eq. (16) into Eq. (20)

#### 1.1.3 Non-steady state diffusion model in one dimension

The general diffusion equation for one-dimensional analysis under non-steady state condition is defined by Fick’s second law. The growth of single phase layer (Fe_{2}B) with one diffusing element (boron) is observed as illustrated in Figure 2.

The _{2}B phase as a function of time. Likewise, for analysis, the kinetic model is imposing the same restrictions as in the previous model, except the last one, it is replaced by:

The concentration-profile of boron is the solution of the Fick’s second law and depends on initial and boundary conditions through the Fe

_{2}B zone.

The mass balance equation at the (Fe_{2}B/substrate) interface can be formulated by Eq. (22) as follows:

Fick’s second law, isotropic one-dimensional diffusion,

By solving Eq. (23), and applying the boundary conditions proposed in Figure 2, the boron concentration profile in Fe_{2}B is expressed by Eq. (24), if the boron diffusion coefficient (_{2}B is constant for a particular temperature:

By substituting Eq. (24) into Eq. (22), Eq. (25) is obtained:

for

Substituting the expression of the parabolic growth law obtained from Eq. (16) (

The diffusion coefficient (*C*_{0}, do not depend significantly on temperature (in the considered temperature range) [10].

### 1.2 Materials and methods

#### 1.2.1 Powder pack boriding process

AISI 12L14 steel was used for investigation. It had a nominal chemical composition of 0.10–0.15% C, 0.040–0.090% P, 0.15–0.35% Pb, 0.80–1.20% Mn, 0.25–0.35% S, 0.10% Si. The typical applications are: brake hose ends, pulleys, disc brake pistons, wheel nuts and inserts, control linkages, gear box components (case hardened), domestic garbage bin axles, concrete anchors, padlock shackles, hydraulic fittings, vice jaws (case hardened). The samples were sectioned into cubes with dimensions of 10 mm × 10 mm × 10 mm. Prior to the boriding process, the samples were polished with SiC sandpaper up 2500 grade, ultrasonically cleaned in an alcohol solution and deionized water for 15 min at room temperature, and dried and stored under clean-room conditions. The mean hardness was 237 HV. The samples were embedded in a closed cylindrical case (AISI 316L) as shown in Figure 3, using Ekabor 2 as a boron-rich agent.

The powder-pack boriding process was performed in a conventional furnace under a pure argon atmosphere. It is important to note that oxygen-bearing compounds adversely affect the boriding process [1]. The thermochemical treatment was performed at temperatures of 1123, 1173, 1223, and 1273 K with 2, 4, 6 and 8 h of exposure time. When the boriding process was concluded, the steel container was removed from the heating furnace and placed in a room temperature.

#### 1.2.2 Characterization of boride layers

The borided samples were prepared metallographically for their characterization using GX51 Olympus equipment. As a result of preliminary experiments it was estimated that boriding started at approximately

The resultant microstructure of Fe_{2}B layers appears to be very dense and homogenous, exhibiting a sawtooth morphology where the boride needles with different lengths penetrate into the substrate [19, 20]. These elements tend to concentrate in the tips of boride layers, reducing the boron flux in this zone. The Fe_{2}B crystals preferably grow along the crystallographic direction [0 0 1], because it is the easiest path for the diffusion of boron in the body-centered tetragonal lattice of the Fe_{2}B phase [19].

It is seen that the thickness of Fe_{2}B layer increased with an increase of the boriding temperature (Figure 4) since the boriding kinetics is influenced by the treatment time. To estimate the boride layer thickness, 50 measurements were made from the surface to the long boride teeth in different sections, as shown in Figure 5; the boride layer thickness was measured using specialized *software* [20, 21, 22].

The identification of phases was carried out on the top surface of borided sample by an X-ray diffraction (XRD) equipment (Equinox 2000) using

### 1.3 Results and discussions

#### 1.3.1 SEM observations and EDS analysis

The metallography of coating/substrate formed in AISI 12L14 borided steel at different exposure times (2, 4, 6 and 8 h) and for 1173 K of boriding temperature are shown in Figure 4. The EDS analysis obtained by SEM is shown in Figure 6(a) and (b).

The results show in Figure 6(a) that the sulfur can be dissolve in the Fe_{2}B phase, in fact, the atomic radiuses of S (= 0.088 nm) is smaller than that of Fe (= 0.156 nm), and it can then be expected that S dissolved on the Fe sublattice of the borides. In Figure 6(b), the resulting EDS analyses spectrums revealed that the manganese, carbon and silicon do not dissolve significantly over the Fe_{2}B phase and they do not diffuse through the boride layer, being displaced to the diffusion zone, and forms together with boron, solid solutions [10, 23, 24]. On boriding carbon is driven ahead of the boride layer and, together with boron, it forms borocementite, Fe_{3}(B, C) as a separate layer between Fe_{2}B and the matrix with about 4 mass% B corresponding to Fe_{3}(B_{0.67}C_{0.33}) [10]. Thus, part of the boron supplied is used for the formation of borocementite. Likewise, silicon forming together with boron, solid solutions like silicoborides (FeSi_{0.4}B_{0.6} and Fe_{5}SiB_{2}) [24].

#### 1.3.2 X-ray diffraction analysis

Figure 7 shows the XRD pattern recorded on the surface of borided AISI 12L14 steel at a temperatures of: 1123 K for a treatment time of 2 h, and 1273 K for a treatment time of 8 h. The patterns of X-ray diffraction (see Figure 7) show the presence of Fe_{2}B phase which is well compacted. Likewise, the patters show that there is a preferential orientation in the crystallographic plane (0 0 2) whose strength increases as the depth of the analysis increases. In a study by Martini et al. [18], the growth of the iron borides (Fe_{2}B) near at the Fe_{2}B/substrate interface only shows the diffraction peak of Fe_{2}B in the crystallographic plane (002).

#### 1.3.3 Estimation of boron activation energy with steady state model

The growth kinetics of Fe_{2}B layers formed on the AISI 12L14 steel was used to estimate the boron diffusion coefficient through the Fe_{2}B layers by applying the suggested steady state diffusion model. In Figure 8 is plotted the time dependence of the squared value of Fe_{2}B layer thickness for different temperatures.

In Figure 8, the square of boride layer thicknesses were plotted vs. the treatment time, the slopes of each of the straight lines provide the values of the parabolic growth constants _{2}B at each temperature. The results, which are summarized in Table 2, reflect a diffusion-controlled growth of the boride layers.

Diffusion methods | Applied energy methods | Coating and surface modification |
---|---|---|

Carburizing Nitriding Carbonitriding Boriding Thermal diffusion process | Flame hardening Induction hardening Laser beam hardening Electron beam hardening | Hard chromium planting Electroless nickel plating Thermal spraying Weld hardfacing Chemical vapor deposition Physical vapor deposition Ion implantation Laser surface processing |

Temperature (K) | Type of layer | Growth constants ^{2} s^{−1}) | ^{2} s^{−1}) |
---|---|---|---|

1123 | Fe_{2}B | 2.91 × 10^{−13} | 5.13 × 10^{−11} |

1173 | 6.12 × 10^{−13} | 1.08 × 10^{−10} | |

1223 | 1.291 × 10^{−12} | 2.27 × 10^{−10} | |

1273 | 2.29 × 10^{−12} | 4.04 × 10^{−10} |

In Table 2, the boron diffusion coefficient in the Fe_{2}B layers (

As a consequence, the boron activation energy (*D*_{0}) can be calculated from the slopes and intercepts of the straight line shown in coordinate system: _{2}B layers was deducted by steady state diffusion model as:

where: *T* absolute temperature [K]. From the Eq. (27), the pre-exponential factor

#### 1.3.4 Estimation of boron activation energy with non-steady state diffusion model

In Table 2 provides the growth constants (

Temperature (K) | Type of layer | ^{2} s^{−1}) |
---|---|---|

1123 | Fe_{2}B | 4.362 × 10^{−11} |

1173 | 9.174 × 10^{−11} | |

1223 | 1.933 × 10^{−10} | |

1273 | 3.433 × 10^{−10} |

The boron activation energy

The boron diffusion coefficient through Fe_{2}B layers was deducted by non-steady state diffusion model as:

#### 1.3.5 The two diffusion models

In this section we want to illustrate the differences between the two diffusion models have been used to describe the growth kinetics of boride layers. It is noticed that the estimated values of boron activation energy

According to the numerical value of the

Similarly for the real exponential function

Thus, Eq. (31) can be written as:

By substituting the Eqs. (30) and (32) into Eq. (26), we have

The result obtained by Eq. (34) is the same as that obtained in Eq. (21) estimated by steady state diffusion model. The result from the Eq. (21) would appear to imply that the non-steady state diffusion model is superior to the steady state diffusion model and so should always be used. However, in many interesting cases the models are equivalent.

### 1.4 Fe_{2}B layer’s thicknesses

The estimation of the Fe_{2}B layers’ thicknesses can be determined through the Eqs. (35) and (36).

Steady state diffusion model

Non-steady state diffusion model

Hence, Eqs. (35) and (36) can be used to estimate the optimum boride layer thicknesses for different borided ferrous materials.

## 2. Conclusions

The following conclusions can be drawn from the present study:

Two simple kinetic models were proposed for estimating the boron diffusion coefficient in Fe

_{2}B (steady state and non-steady state).A value of activation energy for AISI 12L14 steel was estimated as 165.0 kJ mol

^{−1}.Two useful equations were derived for predicting the Fe

_{2}B layer thickness as a function of boriding parameters (time and temperature).

Finally, these diffusion models are in general not identical, but are equivalent models, and this fact 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.

## Acknowledgments

The work described in this paper was supported by a grant of National Council of Science and Technology (CONACyT) and PRODEP México.

## Conflict of interest

The author declares that there is no conflict of interests regarding the publication of this paper.

## Nomenclature

boride layer thickness (m).

_{0}

is a thin layer with a thickness of ≈ 5 nm that formed during the nucleation stage.

rate constant in the Fe_{2}B phase (m^{2}/s).

effective growth time of the Fe_{2}B layer (s).

*t*

treatment time (s).

boride incubation time (s).

upper limit of boron content in Fe_{2}B (= 60 × 10^{3} mol/m^{3}).

lower limit of boron content in Fe_{2}B (= 59.8 × 10^{3} mol/m^{3}).

*C*

_{0}

terminal solubility of the interstitial solute (≈ 0 mol/m^{3}).

boron concentration profile (≈0 mol/m^{3}).

boron diffusion coefficient (m^{2}/s).