Formation of Kirkendall Pores in Aluminized Steel Sheets and Effect of Si in Aluminizing Bath

Abstract

Aluminized steel sheets are highly resistant to elevated temperature. When they are heated for several hours above 800°C, part of the coating layer may delaminate owing to the presence of continuous Kirkendall pores, which are formed between the bcc_A2 and bcc_B2 phases because of the differences in the diffusion coefficients of Al and Fe in each phase. In this study, a numerical simulation was performed to predict the occurrence of Kirkendall pores, and the simulation results were compared with experimental results. The Si in the aluminizing bath significantly increased the number of Kirkendall pores owing to its effect on the ratio of the intrinsic diffusion coefficients (D_Fe/D_Al) in the bcc_B2 phase.

1. Introduction

Hot-dip aluminized steel sheets have been used in various types of heating appliances because of their excellent heat resistance and corrosion resistance.^1,2) There are two types of aluminized steel sheets: Si-containing type 1, which is designed for heat resistance, and Si-free type 2, which is designed for corrosion resistance. Since the 2000s, they have also been widely used in the manufacture of high-strength parts by using hot stamping (also called hot pressing, die quenching, and press hardening).^3,4,5)

Aluminized steel sheets, which afford excellent heat resistance, are often used on parts to which heat is applied. In high-temperature environments, an alloying reaction proceeds between the aluminized layer and the steel base, and the aluminized layer is transformed to an Al–Fe-based or Al–Fe–Si-based intermetallic compounds. According to the Al–Fe binary phase diagram⁶⁾ shown in Fig. 1, at 800°C, for example, there are five types of intermetallic compounds depending on the composition. Al diffuses into the steel base to form a bcc (bcc_A2) phase, in which Al is dissolved as a solid solution, and the compound FeAl, which has an ordered bcc phase structure (bcc_B2), is formed adjacent to this phase in the region closest to the steel sheet. These two phases have a continuous composition, with Al atomic fractions ranging from 0 to approximately 0.5. A void band is reportedly formed at a certain distance from the surface of the aluminized layer when an aluminized steel sheet is heated for several hours at a high temperature, e.g. 800°C.⁷⁾ It has also been reported that the band is formed near the interface between the bcc_A2 and bcc_B2 phases.^8,9) The pores formed here are considered to be Kirkendall pores, and they are formed by vacancy accumulation due to the difference in the diffusion rates of Al and Fe in the bcc_A2 and bcc_B2 phases.

Fig. 1.

Al–Fe phase diagram.⁶⁾ (Online version in color.)

To date, the number of pores that form has been estimated by the numerical calculation of diffusion in, for example, the Fe–Pd system,¹⁰⁾ because Kirkendall pores are described purely by diffusion. In this study, pore formation is estimated by performing the same calculation for the Al–Fe system. Further, there are very few reports on the effects of steel composition and aluminizing bath composition on pore formation in aluminized steel sheets.^7,8) As mentioned previously, there are two types of aluminized steel sheets, and both have been found to contain pores.¹¹⁾ However, it is not clear whether pores are more likely to be formed in one type or the other. Therefore, the effect of Si in the aluminizing bath on pore formation is investigated in this study, and the number of observed pores is compared with the number obtained using the diffusion calculation.

2. Numerical Calculation of Kirkendall Pores

Kirkendall pores are caused by the accumulation of vacancies resulting from a difference in the diffusion coefficients of the elements in binary, ternary, or higher-order alloy systems. Several attempts have been made to calculate the formation distribution of Kirkendall pores by solving the diffusion equation.^10,12,13,14) Results for the Fe–Pd and Ni–Pd systems,¹⁰⁾ Fe–Ni system,¹³⁾ Sn–Cu system,¹⁴⁾ and others have been reported. There are no reported studies of the Al–Fe and Al–Fe–Si systems, which we attempted to calculate in this study considering only target phases of bcc_A2 and bcc_B2. The reason is that pores are actually formed in these phases. The calculation procedure is shown below. The calculation was performed for the Al–Fe binary system for simplicity, although the aluminizing bath typically used to aluminize steel sheets often contains 8–10 mass% Si.

According to Höglund et al.,¹⁰⁾ the vacancy flow velocity ${J^{‘}}_{Va}$ in the lattice is expressed as Eq. (1). They also established the following relationship between the spatial derivative of the vacancy flow velocity and the time derivative of the vacancy fraction y_Va.   

$$J_{Va}=-(J_A+J_B)=(D_B-D_A)\frac{1}{V_m}\frac{\partial x_B}{\partial z}$$(1)

  

$$\frac{1}{V_m}\frac{\partial y_{Va}}{\partial t}=-\frac{\partial J_{Va}}{\partial z}=-\frac{\partial }{\partial z}\left[\left(D_B-D_A\right)\frac{1}{V_m}\frac{\partial x_B}{\partial z}\right]$$(2)

Here, J_A and J_B represent the flow velocities of components A and B, respectively; D_A and D_B represent the intrinsic diffusion coefficients of components A and B, respectively; V_m represents the molar volume; x_B represents the atomic fraction of component B; z represents the position; and t represents time. The vacancy flow velocity results from the difference in the flow velocities of components A and B, which indicates that it is described by their diffusion coefficients.

The time derivative of the vacancy fraction can be obtained by experimentally measuring the concentration distributions of Al, Fe, and Si and using them to calculate the right side of Eq. (2). By integrating this derivative with time, y_Va can be calculated. The final pore fraction f_p is obtained as follows.   

$$f_p=\frac{y_{Va}}{1+y_{Va}}$$(3)

The ratios of the intrinsic diffusion coefficients of Fe and Al in the bcc_B2 and bcc_A2 phases, α and β, respectively, are introduced in this study, because the interdiffusion coefficient can be calculated from the concentration distribution. The Sauer–Freise method¹⁵⁾ was used to calculate the interdiffusion coefficient from the concentration distribution; specifically, pydiffusuion,¹⁶⁾ a diffusion library in Python, was used.

3. Review of Al–Fe–Si Diffusion Studies

In this study, calculations of the Al–Fe binary system were performed for simplicity. The effect of Si was taken into account by considering its effect on the diffusion coefficient of Al or Fe. Specifically, the ratios of the diffusion coefficients of Fe and Al in the bcc_B2 and bcc_A2 phases, α and β, were introduced to indicate these effects. Previous diffusion studies of the Fe corner of the Al–Fe binary system or the Fe corner of the Al–Fe–Si ternary system are reviewed below in order to estimate these values appropriately.

Helender and Ågren¹⁷⁾ performed a diffusion study of the bcc_A2 and bcc_B2 regions of the Al–Fe system. They extracted the reasonable Al–Fe diffusion coefficient data before their study and compared with their model. It was shown that the interdiffusion coefficient in the Al–Fe system is maximum near the composition at the boundary between bcc_A2 and bcc_B2. In addition, Sohn et al. reported that the ratio of the intrinsic diffusion coefficients of Al and Fe (D_Al/D_Fe) at 1000°C is approximately 1.5 at Al atomic fractions of 0.17 and 0.29.¹⁸⁾ Salamon and Mehrer calculated the tracer diffusion coefficients of Al and Fe in the bcc_A2 and bcc_B2 phases and showed that the diffusion rate of Al is equal to or slightly higher than that of Fe.¹⁹⁾ Furthermore, Cui et al. investigated the temperature and composition dependence of D_Al/D_Fe in this system and reported that the diffusion coefficient of Al is higher under almost all conditions and that this is more notable at high temperature and high Al concentration.²⁰⁾ In summary, the diffusion coefficient of Al was reported to be higher than the diffusion coefficient of Fe in most studies to date.

By contrast, there are very few studies on the diffusion coefficients of the Al–Fe–Si ternary system, although one study was recently reported.²¹⁾ Here, various diffusion parameters of the Al–Fe–Si ternary system in the bcc_A2 phase [${\mathrm{\Phi }}_B^i$, ${}^r\mathrm{\Phi }{}_B^{i,j}$, etc. in Eq. (4)] were obtained using the method of Andersson and Ågren.²²⁾   

$$\begin{array}{l}{\mathrm{\Phi }}_B=\sum _i{x}_i{\mathrm{\Phi }}_B^i+\sum _i\sum _{j>i}{x}_i{x}_j\left[\sum _{r=1}^m{}^r\mathrm{\Phi }{}_B^{i,j}{\left(x_i-x_j\right)}^r\right]\\ \hspace{1em}\hspace{0.5em}+{\sum }_i\sum _{j>i}\sum _{k>j}{x}_i{x}_j{x}_k\left[\sum _s{v}_{ijk}^s{}^s\mathrm{\Phi }{}_B^{i,j,k}\right];\left(s=i,j,k\right)\end{array}$$(4)

  

$$v_{ijk}^s=x_s+(1-x_i-x_j-x_k)/3$$(5)

  

$$M_B=\frac{M_B^0}{RT}exp\left(\frac{-Q_B}{RT}\right)$$(6)

  

$$M_B^0=exp\left({\mathrm{\Phi }}_B\right)$$(7)

In Eq. (4), x_i,j,k indicates the molar concentration of each component, and $v_{ijk}^s$ is expressed by Eq. (5). By using these parameters and Eqs. (6) and (7), the mobility M_B of each element at the experimental temperature (1088 K) can be calculated in the current study, and the tracer diffusion coefficient of each element can also be calculated using $D_B^{*}$ = RTM_B, where $D_B^{*}$ indicates the tracer diffusion coefficient of component B, R indicates the gas constant, and T indicates the absolute temperature. In Eq. (6), Q_B indicates the activation enthalpy. Although not all the parameters in the second and third terms of Eq. (4) are complete, the second and third terms on the right side of Eq. (4) make relatively small contributions; thus, the general tendency can be calculated.

When these parameters are calculated, the diffusion rates of Al and Fe are found to be almost equal in the Al–Fe system, which does not contain Si. However, at Si atomic fractions of 0.02 and 0.03, the diffusion rate of Fe is approximately 5 and 10 times that of Al, respectively, suggesting that Si significantly affects the diffusion rate of Fe in the bcc_A2 phase. Although the behavior in the bcc_B2 phase is unknown, it seems reasonable to assume that Si also increases the diffusion rate of Fe in this phase. Thus, subsequent calculations were performed assuming that D_Fe/D_Al exceeds 1 in the bcc_A2 and bcc_B2 phases, and the difference becomes larger as the Si atomic fraction increases in the Al–Fe–Si system.

In the calculation, bcc_B2 with an Fe atomic fraction of 0.5 was placed on the left side, and bcc_A2 with an Fe fraction of 1 was placed on the right side; the thickness of each side was set to 15 μm, and the pore incidence after diffusion for a predetermined time was plotted against the distance.

4. Experimental Method

4.1. Test Material

In the experiment, interstitial-free(IF) steel with few additive elements was used as the aluminizing base sheet, considering that the steel composition might affect the diffusion in the Al–Fe system. Table 1 shows the composition of the steel sheet, which had a thickness of 0.8 mm.

Table 1. Steel composition of specimens (mass%).

C	Si	Mn	P	S	Al	N	Ti	Nb
0.002	0.008	0.13	0.01	0.007	0.044	0.0023	0.017	0.012

4.2. Aluminizing and Annealing Conditions

The test material described above was sheared to dimensions of 100 mm × 200 mm and was aluminized. Aluminizing without Si addition and aluminizing in a 6 mass% Si bath were performed using a hot-dip simulator (Rhesca). The annealing conditions were 100 s at 800°C under an atomic fraction N₂-0.03 H₂ atmosphere. The bath composition was Al-2.8 mass% Fe or Al-6.2 mass%Si-2.6 mass% Fe. The bath temperature was 700°C for pure aluminizing and 660°C for aluminizing with Si, and the immersion time was 3 s in both cases. The thickness of the aluminized layer was adjusted by gas wiping, with a target of 30 μm for pure aluminizing and 20 μm for aluminizing with Si.

Then, the aluminized steel sheet was sheared to dimensions of 20 mm × 20 mm, followed by annealing in ambient atmosphere. Temperatures of 815°C and 900°C were selected for the experiment because the ratio of the α and γ phases of the steel base depends on the annealing temperature. However, although the diffusion rates were different, the results in terms of pore formation were almost the same at both temperatures. Therefore, only the results at 815°C are described in the following sections. The retention time after the sample reached 815°C was varied from 10 to 100 min.

4.3. Analytical Method

After a sample was annealed at 815°C for a predetermined time, it was embedded in a resin, and cross-sectional polishing was performed. Backscattered electron images of the cross section were obtained by scanning electron microscopy (SEM, Hitachi S-3400) without etching. In addition, the elemental distribution on the cross-sectional surface was measured using the attached energy-dispersive spectrometer (EDS). The analysis was performed in a region without pores, because diffusion is prevented in regions where pores are formed.

5. Experimental Results, Calculation Results, and Discussion

5.1. Pore Formation after Annealing

Figure 2 shows the cross-sectional backscattered electron images before and after heating of the aluminized steel sheets with and without Si in the aluminizing bath. For the sample as aluminized, an alloy layer of approximately 20 μm or more grew in the pure aluminized material, and the coating thickness reached around 40 μm. The roughness at the interface between the alloy layer and the steel base became marked and exhibited a tongue-like morphology.¹¹⁾ In the sample to which 6 mass% Si was added, this rough alloy layer was absent, and the thickness was 3 to 4 μm. The reduction in alloy layer thickness caused by the addition of Si to the aluminizing bath was similar to that reported in the literature.¹¹⁾ When the pure aluminized steel was annealed at 815°C, the roughness between the steel sheet and the alloy layer remained for 10 min, and the interface was almost completely smooth after 30 min.

Fig. 2.

Cross section of aluminized steel sheets before and after heating at 815°C. (Online version in color.)

The formation of Kirkendall pores is described below. In the bath with 6 mass% Si, continuous pores were formed near the interface between the steel sheet and the aluminized layer which was alloyed to the surface. They were not formed so much after 10 min, but the pores became almost continuous after 30 min. By contrast, although pores were formed near the interface between the steel sheet and the alloyed layer in the aluminizing bath without Si, the formation frequency was significantly lower than that in the bath containing Si. That is, Si in the aluminizing bath was found to promote pore formation. Note that pore formation was also observed near the surface of the alloyed layer in the 6 mass% Si bath, but the pores in this region were not examined in this study.

5.2. Elemental Distribution and Interdiffusion Coefficient

Next, the concentration distribution was measured from the cross section by SEM with energy-dispersive spectroscopy using these heated samples. As mentioned above, it is necessary to analyze the concentration distribution in this region in detail because pores are formed near the bcc_A2/bcc_B2 interface. In the aluminized steel sheet heated in the 6 mass% Si bath for 10 min, this region was thin (5 μm or less); therefore, the samples heated for 30 min were used.

The results are shown in Fig. 3. The elemental concentrations are expressed as atomic ratios. The scale on the horizontal axis is different in each panel because the thickness of the aluminized layer is different. In the pure aluminized material, the Al atomic fraction is approximately 0.7 at approximately 8 to 22 μm from the surface, and the Al atomic fraction is approximately 0.65 from approximately 22 to 40 μm. A comparison with the phase diagram in Fig. 1 reveals that Fe₂Al₅ and FeAl₂ were formed respectively. By contrast, in the aluminized material to which 6 mass% Si was added, the Al atomic fraction is approximately 0.7 at approximately 5 to 24 μm from the surface, excluding the region from approximately 10 to 13 μm, and Fe₂Al₅ is formed in this region. The Al concentration decreases and the Si concentration increases between approximately 10 and 13 μm. Maki et al.²³⁾ reported the formation of such an intermediate region with a composition similar to that of the bcc_B2 phase, and TEM-EDS analysis of this intermediate region showed that it was composed of fine grains of Al–Fe and Al–Fe–Si compounds.

Fig. 3.

Elemental profiles of specimens after heating for 30 min. (Online version in color.)

The elemental composition of bcc_A2 and bcc_B2 regions where pores formed is enlarged in Fig. 4. The size of the horizontal axis is adjusted for each samples, and the composition at the bcc_A2/bcc_B2 interface in the Al–Fe binary system is shown versus Fe atomic fraction. In the pure aluminized material, the Al and Fe distributions became somewhat flat near this interface. The interdiffusion coefficient may have become high in this region. In the aluminized material to which 6 mass% Si was added, Si tended to be concentrated on the side closer to the surface (24 to 28 μm), and the Si-rich region almost completely overlapped the bcc_B2 region.

Fig. 4.

Elemental profiles of bcc_A2 and bcc_B2 phases. (Online version in color.)

The interdiffusion coefficient was calculated using the concentration distribution curve in Fig. 4. The Si atomic fraction was approximately 0.1. In the Al–Fe–Si ternary system, the atomic radius of Si is closer to that of Al than to that of Fe, and both Al and Si have bcc_A2 and bcc_B2 structures in the phase diagram with Fe. Therefore, Si is thought to replace Al in the bcc_A2 and bcc_B2 regions. Thus, the Fe concentration distribution was used to calculate the interdiffusion coefficient in this study to eliminate the effect of Si. The calculated results are shown in Fig. 5. In the pure aluminized material, the interdiffusion coefficient took a maximum value at an Fe atomic fraction of approximately 0.75; it decreased slowly as the Fe atomic fraction decreased from 0.75 to 0.6 and increased again slightly as the Fe atomic fraction approached 0.5. This tendency is consistent with the reported values of the Al–Fe interdiffusion coefficients.^17,19,20) The maximum value in bcc_A2 and bcc_B2 phases was about 5 × 10⁻¹⁴, which was slightly higher than previously reported values. By contrast, in the material prepared in the bath with 6 mass% Si, the maximum value of the interdiffusion coefficient appeared at an Fe atomic fraction of 0.73 to 0.83, and the interdiffusion coefficient was a fraction of that of pure Al.

Fig. 5.

Interdiffusion coefficient of specimens after heating for 30 min. (Online version in color.)

5.3. Numerical Calculation Results

The number of pores formed at the bcc_A2/bcc_B2 interface was calculated using the method described in Section 2 using the interdiffusion coefficient distribution calculated in the previous subsection. The ratios α and β of the intrinsic diffusion coefficients of Fe and Al in bcc_B2 and bcc_A2, respectively, were determined as follows.

First, the pure aluminized steel sheet can be considered as resembling an Al–Fe binary system. According to the results of Cui et al. at a temperature of 1100 K,²⁰⁾ the ratio of the diffusion coefficients of Al and Fe, D_Fe/D_Al, tends to become approximately 1 in bcc_B2 and less than 1 in bcc_A2, so α (D_Fe/D_Al in bcc_B2) was set to 1, and β (D_Fe/D_Al in bcc_A2) was set to 0.9 in this study. Next, in the aluminized steel sheet prepared using the 6 mass% Si bath, Si was shown to increase the diffusion coefficient of Fe in bcc_A2, as described in Section 2. From the results of Fig. 4, the Si atomic fraction in bcc_A2 is 0.01 to 0.04, and the diffusion coefficient of Fe is assumed to be several times that of Al. Furthermore, although the detailed diffusion behavior in bcc_B2 is unclear, the value of α was assumed to be twice that of β because bcc_B2 has a Si atomic fraction of 0.1 or more. Therefore, this calculation was performed using α = 4 and β = 2.

The calculation results are shown in Fig. 6. The pore formation behavior near the bcc_A2/bcc_B2 interface was reproduced in both the pure aluminized material and the aluminized material using 6 mass% Si bath. Furthermore, greater probability of pore formation in the presence of 6 mass% Si was also reproduced. As shown in Fig. 5, the absolute value of the maximum interdiffusion coefficient is approximately 4 to 5 times higher in the pure aluminized material than in the 6 mass% Si material. Nevertheless, the number of pores formed is several times larger in the material containing Si; this result is attributed to the difference in α and β. The diffusion behavior of Fe and Al in bcc_A2 and bcc_B2 is discussed below.

Fig. 6.

Kirkendall pore distribution calculated using interdiffusion coefficient. (Online version in color.)

5.4. Diffusion Behavior of Al and Fe in bcc_A2 and bcc_B2

Pore formation in aluminized steel sheets after long-duration heating at high temperature has rarely been investigated in detail. However, pores are reportedly formed near the bcc_A2/bcc_B2 interface.^8,24) When Kirkendall pores are formed near this interface, one of the following is thought to occur. Either the number of Fe atoms becomes insufficient at the interface as Fe that diffused from the steel diffuses rapidly to bcc_B2, or, by contrast, the number of Al atoms becomes insufficient as Al that diffused from bcc_B2 diffuses rapidly to bcc_A2. Because the diffusion of Fe in bcc_A2 is promoted by the effect of Si in the Al–Fe–Si system, and it is probably also promoted in bcc_B2, it can be estimated that the former probability is high in the Al–Fe(–Si) system. The fact that the diffusion rate of Fe in bcc_B2 is higher than that in bcc_A2 becomes the condition for pore formation.

When different numerical values of α and β are used in the numerical calculation of pores, the number of pores formed changes significantly. Figure 7 shows the pore formation rate calculated using various values of α and β and the interdiffusion coefficient of the 6 mass% Si material. When both α and β are 1, the diffusion rates of Al and Fe in bcc_A2 and bcc_B2 are the same, and no pores are formed. When α is set to 2 without changing β, that is, when the diffusion rate of Fe in bcc_B2 is increased, some pores are formed on the bcc_B2 side of the bcc_A2/bcc_B2 interface. Even when α is increased to 4 and β is increased to 2, the total number of pores does not increase significantly. That is, when the ratio of the diffusion coefficients of Fe and Al in the bcc_B2 phase exceeds 1, pore formation is strongly affected.

Fig. 7.

Effect of intrinsic diffusion coefficient ratio (D_Fe/D_Al) in bcc_A2 and bcc_B2 phases. (Online version in color.)

The Si in the aluminizing bath greatly affected the Kirkendall pores, which were formed when the aluminized steel sheet was heated for a long time. The increase in the diffusion rate of Fe in bcc_B2 resulting from the presence of Si promotes pore formation. This study makes it possible to predict, to some extent, the formation of Kirkendall pores when aluminized steel is heated and also to quantitatively predict the effect of the third component.

As mentioned in Section 1, the addition of Si to the aluminizing bath is considered to promote heat resistance. It was reported in the 1960s that coating layer delaminates when an aluminized steel sheet is heated at 500°C to 700°C and that this delamination is suppressed by adding Si to the aluminizing bath.^25,26) The temperature range at which coating delaminated in previous studies and the delamination of coating layer due to Kirkendall pores investigated in this study are different and are assumed to have completely different mechanisms.

6. Conclusion

The formation of Kirkendall pores near the bcc_A2/bcc_B2 interface when hot-dip aluminized steel sheets were heated and the effect of Si in the aluminizing bath on pore formation were investigated. The following results were obtained.

(1) When aluminized steel sheets were heated at 815°C for 30 min, more pores were formed in the material prepared in a bath containing 6 mass% Si than in pure Al plating.

(2) This finding cannot be explained by the difference in the interdiffusion coefficient between the two phases, but it can be explained by the hypothesis that Si promotes Fe diffusion in bcc_A2 and bcc_B2.

(3) The numerical calculation of Kirkendall pores in the Al–Fe–Si system was consistent with the experimental results, and it was possible to predict pore formation quantitatively.

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