The Al-Fe Intermetallic Compounds and the Atomic Diffusion Behavior at the Interface of Aluminum-Steel Welded Joint

Abstract

The formation of intermetallic compounds (IMC) at the Al/Fe interface determined the mechanical property of steel-aluminum welded joint. To understand the interfacial microstructure evolution and relate diffusion mechanism of atoms cross the Al/Fe interface, the effect of welding parameters on the interfacial IMC was studied, and the molecular dynamics method (MD) was used to simulate the diffusion process of Al and Fe atoms. Four temperatures (950 K, 1000 K, 1050 K, and 1100 K) were selected in the simulation model. The interfacial IMC are distributed in a laminar pattern, and their physical phases are mainly composed of Fe₂Al₅, controlling the Al/Fe atomic ratio of 5:2 in the IMC configuration, the Embedded Atom Method (EAM) potential is used to describe the interactions between Al and Fe atoms. In the Al-Fe system IMC conformation, the mean square displacement and diffusion (MSD) coefficient of Al atoms at different temperatures were small, and the main diffusion path is the Al atoms across the IMC conformation into the Fe crystal structure. The diffusion in the IMC conformation was mainly along the direction perpendicular to the interface. The diffusion mechanisms were mainly vacancy diffusion and interstitial diffusion mechanisms.

1. Introduction

In the automotive and aerospace fields, the joining of steel and aluminum is becoming increasingly important for the manufacture of lightweight and high performance. In recent years, the researchers used laser thermal conduction welding, double-beam laser welding, and arc-laser composite heat source welding to weld aluminum alloys and steel, and to study joint formation, weld microstructure, and interfacial intermetallic compound species and distribution [1]. The Fe-Al compounds, including Fe₃Al, FeAl, Fe₂Al₅, FeAl₂ and FeAl₃, have been the research focus in the fields of high-temperature structural materials, composite materials, material protective coatings and functional materials. The Fe-Al materials have been considered as very promising materials because they are considered as potential candidates to replace steel [2,3]. During the welding process, the high temperatures may enhance the diffusion between metal atoms and cause the formation of undesirable brittle Al-Fe-rich IMC layers. The mechanical properties of the composite material deteriorate due to reduced strength, ductility, and fracture toughness of the material.

Thick intermetallic compounds (usually brittle) will produce cracks at the interface, especially between steel connected by aluminum, titanium, and copper alloys. The formation of hazardous IMC at the Fe-Al interface is a major obstacle to the adoption of fused or solid-phase connection in Fe-Al bimetallic structures as load-bearing members in safety-critical structures [4,5]. According to Song et al. [6], the specific study of welding of 5A06 aluminum alloy and AISI 321 stainless steel using silicon-rich solder provides insight into the growth mechanism of IMC. Borrisutthekul et al. [7] suggested that higher heat input and welding speed, combined with lower current, would result in thinner IMC layers. It is worth noting that heat propagation through the steel can trigger the melting of aluminum without melting the entire thickness of the steel. Numerous studies have shown that the depth of melting penetration controlled by laser power and travel speed plays an important role in defect formation, IMC layer thickness and mechanical strength of the welded joint [8,9].

Many researchers have used different methods to understand the mechanisms of formation of equilibrium and nonequilibrium intermetallic compounds in heterogeneous materials. For example, some researchers have used atomic simulation to predict the mechanical strength of Fe-Al compounds [10,11]. Zhang et al. investigated the structural and mechanical properties of these compounds by EAM simulations [10]. There are researches show that the crystal structure of Fe₂Al₅ belongs to the orthorhombic space group [12], a prominent feature of the crystal structure is the presence of chains of six Al sites, and chains of partially occupied Al sites in aluminized steel are often thought to provide a fast atomic diffusion path to explain the columnar growth of Fe₂Al₅ along the c-axis [13,14,15].

The welding method also has an important role in the formation of IMC. Several hybrid welding methods have been reported including laser-TIG welding [16,17], Laser-MIG/MAG welding [18,19], Laser Stir Friction Welding [20], and TIG-stir friction welding [21]. Kobayashi et al. [22] immersed solid steel rods in molten aluminum for different times and temperatures and then analyzed the composition and thickness of the IMC formed. In the temperature range of 700 to 900 °C, Fe₂Al₅ is the main intermetallic compound formed on the surface of the steel. For the same temperature range, Bouche et al. [23] concluded that at temperatures between 700 and 900 °C, intermetallic com-pounds are mainly controlled by diffusion, before following parabolic growth, however, there is a linear growth phase with controlled chemical reaction properties.

The welding process of steel-aluminum and related simulation have been reported by above mentioned researches, the effect of temperature on diffusion process was studied in mesoscopic scale. However, few publications have reported the diffusion process of dissimilar Al and Fe in atomic level. The study of atomic diffusion will reveal the diffusion path, diffusion type and diffusion coefficient which can obtain a deep understanding of the atom diffusion across interface. Therefore, this work studied the effect of heat input on interfacial microstructure and simulated the atomic diffusion at different temperature by the MD method.

In this paper, the diffusion behavior of Al and Fe atoms at the interface of IMC was investigated by using the MD method. By comparing the interdiffusion of Al and Fe atoms at different temperatures and the concentration distribution, the MD method was used to describe the atomic motion trajectory. The MSD analyze of Al atoms at different temperatures and the diffusion coefficient was performed to study the interfacial microscopic diffusion mechanism.

2. Experiment Methods and Model of Atomic Diffusion

2.1. Material and Experiment

The galvanized steel with the size of 100 mm × 50 mm × 1 mm and 5A06 aluminum alloy with the size of 100 mm × 50 mm × 2 mm were joined by arc assisted laser welding method [24], as shown in the Figure 1, four linear heat input: 1 kJ/cm, 1.2 kJ/cm, 1.5 kJ/cm, and 1.7 kJ/cm were selected. All the specimens for microstructure analysis were cut from the beads along the direction perpendicular to the welding direction. The cross-section of the specimen was ground and polished to obtain a bright surface. Surface etching was performed with the Kellers etchant. The scanning electron microscope (SEM) was used to observe the microstructures. The energy dispersive spectrometry (EDS) was used to analyze the chemical composition of the IMC.

2.2. Establishment of the Molecular Dynamics Model

2.2.1. Initial Conditions

The MD method, as a method of numerically solving the equations of the atoms motion, which calculate the force equations, potential energy equations and atomic motion. It requires setting reasonable initial conditions to obtain a stable architecture for the computational cycle. The initial condition settings mainly include: initial position, initial velocity, boundary condition selection, integration step (time step), etc. The MD describes the motion of a particle by tracking its position and velocity in time. These factors must be specified as initial conditions. The system is in thermodynamic equilibrium at temperature T, then the initial velocity of the particle follows the Maxwell distribution [25]:

$$f\left(v_i\right)={\left(\frac{m}{2\pi kT}\right)}^{3/2}\exp \left\{-\frac{m}{2kT}\left(v_{ix}^2+v_{iy}^2+v_{iz}^2\right)\right\}$$

(1)

where, k is Boltzmann constant, m is the mass of particles, $v_i=\left(v_{ix},v_{iy},v_{iz}\right)$ is the velocity vector of particle i. Because Maxwell distribution is a probability density distribution function, therefore, the probability of finding particle i in the infinitesimal velocity range between v_i and $\left(v_i+d{v}_i\right)$ becomes $f\left(v_i\right)d{v}_i$. By treating the distribution function fx as the x velocity component, the characteristics of this function can be more directly understood. The probability density distribution function $\chi \left(v_i\right)$ of the velocity $v_i=\left(v_{{}_{ix}}^2+v_{{}_{iy}}^2+v_{{}_{iz}}^2\right)$ of particle i can be derived from the above formula.

$$\chi \left(v_i\right)=4\pi {\left(\frac{m}{2\pi kT}\right)}^{3/2}{v}_i^2\exp \left(-\frac{m}{2kT}{v}_i^2\right)$$

(2)

It is usually necessary to determine the time step of the system in conjunction with the specific system. A suitable integration step will not only save calculation time, but also improve the accuracy of the calculation. The integration steps for common atomic systems are shows in

Table 1. Integration step for atomic systems.

Atomic System	Atomic Motion Form	Integral Step (ps)
General atomic system	Moving	10−14
Rigid molecule	Moving, rotating	5 × 10−15
Soft molecule, limited bond length	Moving, rotating, twisting	2 × 10−15
Soft molecule, unlimited bond length	Moving, rotating, twisting, vibrating	10−15 or 5 × 10−16

[26].

2.2.2. Boundary Condition

The two commonly used boundary conditions in the MD method are: periodic boundary condition and Lees-Edwards boundary condition. In this paper, we choose periodic boundary conditions, which are characterized by the fact that when a particle in the cell moves outside the simulated system, at the same time there will be particles entering from the adjacent system from the relative direction, and its mathematical expression is:

$$A\left(x\right)=A\left(x+nL\right),n=\left(n_1,n_2,n_3\right)$$

(3)

where, L is the boundary length of the simulation system, n₁, n₂, n₃ any integer, A is physical quantity parameter.

For the overall treatment of the system, the MD approach uses a system synthesis theory based on the thermodynamic category. The atomic or molecular states that have the same structure and properties under certain constraints is described by means of temperature, volume, and pressure in the system. The common forms of synthesis are temperature (T), pressure (P), volume (V) and constant energy, which are mainly classified as micro-regular synthesis (NVE), regular synthesis (NVT), giant regular synthesis and isothermal and isobaric synthesis (NPT). Since this work focuses on the trans-interfacial behavior of Al and Fe atoms, whose motion is mainly affected by temperature, we mainly adopt an isovolumetric isobaric system synthesis to control the temperature of the simulated system, to describe the state of atomic at different temperatures. The Nose-Hoover heat bath method was used to control the system temperature [27].

After the initial conditions have been set, time integration calculations need to be performed for the atoms in the established system. The MD method is based on classical Newton’s laws of motion, where the trajectory of an atom is unique and deterministic. If the mass of i is expressed in terms of $m_i$ and the environmental molecule and the external field acting on the molecule i is denoted by $f_i$, the motion of the particle is described by Newton’s equation of motion [28].

$$m_i\frac{d^{2}ri}{d{t}^2}=f_i$$

(4)

If a system consists of N molecules, there are N sets of similar equations where the motion of N molecules interacts through intermolecular forces.

2.2.3. System Setup

Figure 2 shows the intermediate configuration model considering IMC in the Al-Fe system with dimensions of 84 × 71 × 182 (ų), and the configuration parameters in the calculated system are shown in

Table 2. Atomic configuration parameters.

Parameters	Fe	IMC	Al
Sizes	84 Å × 71 Å × 30 Å	84 Å × 71 Å × 25 Å	84 Å × 71 Å × 127 Å
Points Step	2 fs
Heating rate	1 K/fs

. The system uses a time step of 2 fs, and the same periodic boundary conditions are used in all three directions. A fixed boundary is used at the non-Al/Fe interface boundary to ensure that the atoms do not cross the set boundary and diffuse from the Al/Fe heterogeneous interface.

Since the interface is mainly composed of Fe₂Al₅ phase, the IMC conformation is set up by controlling the Al/Fe atomic ratio as 5:2 and setting the random vacancy distribution according to the literature [11], the IMC crystal structure is built using symmetric space group to define the lattice parameters as shown in

Table 3. IMC Lattice parameters [11].

Parameters	a (Å)	b (Å)	c (Å)	α	β	γ
Sizes	7.6559 ± 0.0008	6.4154 ± 0.0006	4.2184 ± 0.0004	90°	90°	90°

. The system temperature is increased to the desired temperature at a rate of 1 K/fs. The initial heating process and equilibrium are performed at constant atomic number, constant pressure, and constant temperature. The system is maintained for 8 ns at each specific temperature to facilitate the interdiffusion of atoms.

2.2.4. Atomic Potential Energy

The EAM potential is the most used typical many-body potential function, and the method is based on theories such as quasi-atomic theory, density functional and effective medium, the total energy in the setup system is divided into: the embedded potential energy part and the atomic pair potential part. The total energy form of the system can be expressed by the following equation [29]:

$$\left\{\begin{array}{l}{E}_{tot}={\displaystyle \sum _i^N{F}_i\left({\rho }_i\right)}+\frac{1}{2}{\displaystyle \sum _{i,j\left(i\ne j\right)}^N\varphi \left(r_{ij}\right)}\\ {\rho }_i={\displaystyle \sum _{j\left(\ne i\right)}^N{f}_{ij}\left(r_{ij}\right)}\end{array}\right.$$

(5)

where, $F_i$ is Embedded potential energy, which is the energy of an atom embedded at a collective electron density of A, ${\varphi }_{ij}$ Short-range two-body potential function, which is described the interactions between atomic, ${\rho }_i$ is the summation of the electron density of the nearest neighboring atoms, $r_{ij}$ is distance between atoms, $f_i$ is the $i$-atom density distribution, and where ${\rho }_i$ can be represented by the following Hartree-Fock equation, introducing a parameter N for the s electron.

$${\rho }_{ij}\left(r_{ij}\right)=N_s{\rho }_s\left(r\right)+\left(N-N_s\right){\rho }_d\left(r\right)$$

(6)

where, N is the total number of outer electrons, N_s is the s-layer electron, ${\rho }_s\left(r\right)$ and ${\rho }_d\left(r\right)$ are the densities of s-electrons and d electrons, respectively.

3. Results and Analysis

3.1. Evolution of Interfacial IMC Microstructure

As shown in the Figure 3, the interfacial microstructure of linear heat input for 1.2 kJ/cm, the layer IMC was observed at the interface of aluminum and steel. In order to determine the IMC type of the interface, EDS line scanning and point analysis were performed on the interface. From the element distribution of EDS line scan, the mutual diffusion of Al and Fe atoms mainly occurs on both sides of the interface. Only a small number of IMC are randomly distributed in the aluminum weld side. According to EDS line scan, IMC layer can be divided into two layers: layer I and layer II. In layer I, the fraction of Al and Fe elements remains relatively constant with the change of distance. In layer II, the closer to the aluminum weld side, the lower the iron content and the higher the aluminum content. This element concentration change shows that IMC in layer I have different structures from those in layer II. It is worth noting that there are few other elements in the IMC layer. The EDS point analysis is carried out at points A and B marked in Figure 3. The atomic ratio of elements at each point is listed in

Table 4. Results of EDS point analysis (at. %).

Location	Al	Fe	Mg	Mn
A	71.95	28.05	-	-
B	75.45	24.26	0.29	-

. The atomic ratio of aluminum to iron at points A near the steel is close to 5:2, and the ratio of point B near the aluminum weld is about 3:1. According to the Al-Fe binary phase diagram, the two kinds generate double-layer Al-Fe intermetallic compound at the interface, in which the “sawtooth” interface layer I near the steel side is Fe₂Al₅ and the “point block” interface layer II near the aluminum weld side is Fe₄Al₁₃.

In the welding process, the heat input of the weld mainly comes from the laser, and the laser heat input will have a great impact on the interface IMC. The thickness and microstructure of IMC layer are two important factors affecting the tensile strength of welded joint. Figure 4 shows the microscopic morphology evolution of interface IMC under different liner heat input. Figure 4 shows the change of IMC layer morphology of interface when the laser line energy range is 1.0~1.7 kJ/cm. It can be seen from figure that the IMC layer is formed at the interface of aluminum alloy and steel. The thickness of intermetallic compound increases with the increase of laser heat input, and the morphology of Fe₄Al₁₃ phase near the aluminum side changes from point-like to needle-like, and grows towards the aluminum weld. When the laser linear energy is less than 1.2 kJ/cm, the Fe₂Al₅/steel interface near the steel side is mainly serrated, and the interface becomes flat with the increase of laser heat input. When the laser heat input is greater than 1.5 kJ/cm, cracks along the interface are formed at the interface. The thermal expansion coefficient of different phases varies greatly (23.6 × 10⁻⁶ K⁻¹ for aluminum, 1.2 × 10⁻⁶ K⁻¹ for steel), which causes cracks to form during cooling. The thicker intermetallic compound layer will produce larger residual stress, which will also lead to cracks in the brittle intermetallic compound layer. In addition, as reported by Costanza et al., the thermal gradients arising during the cooling stage might cause the formation of crack [30]. Some feather-like microstructure was observed in Figure 4c, as reported by Deng et al. [31], it was the free IMC phase which immigrated from interface since the violent flow of molten. On the other hand, the thickness of IMC layer increases with the increase of laser line energy, as shown in Figure 4. This is because with the increase of laser power, more aluminum and iron atoms are activated, and the interface reaction becomes stronger.

3.2. Effect of Temperature on Atomic Interdiffusion

According to the experiment observations, the temperature was the main factor to affect the IMC layer. To understand the diffusion of Al and Fe atoms at the interface, a molecular dynamics model was established as described in Section 2. Figure 5 shows the trajectory and diffusion depth of the system atomic diffusion within 8 ns at temperature 950~1100 K. In the IMC configuration, thermal activation of Fe atoms at the interface front position deviates from the equilibrium position at all simulated temperatures and no significant diffusion occurs. Under this condition, the Al-Fe system is dominated by the diffusion of Al atoms into the IMC box. When the temperature is 1100 K, the diffusion depth is maximum, and the higher the temperature, the deeper the diffusion depth. It shows that the number of diffusing atoms is highly dependent on temperature. Since the radius of Fe atoms is larger than that of Al atoms, it is difficult for Fe atoms to diffuse across IMC. Al atoms occupy the vacancies formed in IMC and diffuse into IMC, and this diffusion behavior indicates that when IMC are formed, their diffusion layer growth is mainly determined by the diffusion of Al atoms.

The concentration of atoms in the z-axis in the interfacial system can be quantified by analyzing the atomic distribution, as shown in Figure 6. The plateau of Al and Fe atomic concentrations at the IMC configuration can be obtained from the figure, and the Al atoms are close to 5:2 with Fe atoms at this atomic plateau. The concentration of Al atoms at IMC can be seen at different temperatures, with increasing diffusion duration and temperature, this indicates a gradual increase in the diffusion depth of Al atoms, implying a gradual increase in the thickness of the interfacial diffusion layer. Al atoms will diffusely migrate across the IMC layer to the IMC/Fe interface front at high enough temperature and time, and react with Fe atoms to increase the thickness of IMC layer. Compared to Al atoms Fe atoms almost no diffusion occurs, and increasing Al diffusion layer thickness with time is more obvious than Al atoms. So, the main contribution to the growth of the diffusion layer is provided by the diffusion of liquid Al to the interfacial IMC.

3.3. Diffusion Coefficient

The interfacial mixing of Fe and Al atoms at different temperatures was investigated with MSD. Statistical analysis of MSD for Al atoms only, since little diffusion of Fe atoms occurs. As shown in Figure 7a, the MSD of Al atoms at different temperatures in 8 ns time is linear with respect to time. The MD simulations can estimate their transport properties, such as diffusion coefficients. The diffusion coefficient is a quantity measured in units of (area/time) and describes the mass of material flowing through an area per unit time. One way to calculate the diffusion coefficient in molecular dynamics is to calculate the mean square displacement (MSD) of the atom, as in Equation (7):

$$MSD=〈r^2\left(t\right)〉=\frac{1}{N}{\displaystyle \sum _{i=1}^{Na}\left({\left|r\left(t\right)-r\left(0\right)\right|}^2\right)}$$

(7)

Equation (7) defines the MSD as the variation of the particle (r) position with time (t), relative to its initial reference position, summed over N_a atoms in N dimensions (taken as 3).

The fitted line in the linear region of the MSD-time curve for Al atoms can be used to derive the diffusion coefficient using the following relationship:

$$D=\underset{t\to \infty }{\lim }\frac{MSD}{2Nt}$$

(8)

where, t is the time, System dimension N = 3.

By calculating the MSD of Al atoms at the interface, the diffusion coefficient of Al atoms at the interface was further estimated as shown in Figure 7b. The diffusion coefficient increases with increasing temperature; however, it can be found that the diffusion coefficient is significantly smaller at different temperatures. Probably due to the high vacancy formation energy of the crystal structure of IMC, there are not enough vacancies to provide diffusion in the simulated temperature interval. The MSD increases with increasing simulation time, indicating that the atoms in both metals move a greater distance with increasing simulation time. The increase in MSD is due to the increase in atomic kinetic energy due to the increase in temperature.

By analyzing the MSD curves versus time and the difference of diffusion coefficients at different temperatures, it was found that the MSD size did not change significantly with increasing time at the simulated temperature of 950 K, and the diffusion coefficient of Al atoms at this time was small, the possible reason is that the energy provided at this temperature is less than the energy required for the immigration of Al atoms. As shown in Figure 7a, at the beginning of the period, the MSD is not significantly linear with respect to time, mainly because at this time it needs to cross the equilibrium lattice and no diffusive motion occurs.

4. Discussion

The diffusion mechanism of Al atoms was analyzed by following the path trajectories of Al atoms. In the Al-Fe system IMC conformation is mainly the diffusion of Al across IMC into Fe. The concentration of IMC vacancies increases under holding conditions, and Al atoms can occupy the vacancies for diffusion, while Fe is difficult to diffuse into the IMC layer due to the large atomic radius. In some cases, the diffusion path is altered by nearby layer or dislocation lines. The diffusion path of Al affected only by vacancy formation is shown in Figure 8, the atomic diffusion is mainly along the vertical interface direction, and this simulation result better verifies the growth orientation of intermetallic compounds, at the same time, Al atoms undergo irregular jumps when occupying a certain position, and this irregular jump also indicates that the diffusion coefficient in Al atoms into IMCs will be smaller.

As shown in Figure 9, the Al atoms immigrate might in three paths: nearest neighbor jumping, second nearest neighbor jumping, and gap jumping. The first two belong to the vacancy diffusion mechanism. The Al atoms diffuse to the Fe side, occupying the lattice of Al atoms, and then the Fe atoms leap to the adjacent vacancies. The third mechanism is the diffusion of Al atoms to the Fe side, where they become octahedral gap atoms and then jump to another position in the octahedral gap.

According to the above calculation and discussion, the formation and growth of the IMC phase at different stages were discussed in this part. As shown in Figure 10a, some Fe₂Al₅ nuclei appeared at the Al/steel interface, which are randomly distributed on the steel side. In the second stage, new nucleation and growth of IMC occur simultaneously, culminating in the formation of a layer of IMC (Fe₂Al₅) phase on the steel side, as shown in Figure 10b. As can be seen in Figure 10c, some new phases appear at the Fe₂Al₅/Al interface. The Fe₄Al₁₃ phase is formed in the lower temperature range and that the formation of Fe₄Al₁₃ may be caused by the Fe₂Al₅ + Al (l) → Fe₄Al₁₃. Figure 10d shows the solidification morphology of Al-Fe phase at the interface. The final IMC layer consists of two sublayers, namely Fe₂Al₅ phase layer and Fe₄Al₁₃ phase layer, which are consistent with the results reported in [32,33,34]. On the other hand, the interface morphology of Fe₂Al₅/steel is serrated, the interface morphology of Fe₄Al₁₃/Al is needle like, and Fe₂Al₅ phase grows in columnar structure and faces the steel matrix, the model can accurately reflect the element distribution trend and growth orientation of IMC layer.

As the rapid growth of the Fe₂Al₅ phase IMC layer is mainly due to the rapid diffusion of Al atoms along the C-axis direction of the IMC (perpendicular to the interface direction). The rapid growth phase is followed by a third stage, which has a slower growth rate than the second stage. The lower growth rate in this stage may be due to the formation of the Fe₂Al₅ phase in the second stage, which leads to a longer diffusion distance of Al atoms and a longer time to reach the interface front thus causing a lower growth rate. In the final stage, the growth rate is lowest due to the decrease in local temperature, which reduces the migration rate of the Al atoms.

5. Conclusions

In this paper, the Al-Fe IMC layer was formed at the interface of steel-aluminum welded joint. The effect of heat input on the interfacial microstructure was studied. The Al-Fe IMC system modeled was based on MD, the MSD and diffusion coefficient of Al original at different temperatures were calculated and the following conclusions were obtained:

• The Al-Fe IMC layer which includes Fe₂Al₅ and Fe₄Al₁₃ phases was formed at the welded interface. The thickness of IMC layer increases with the increase of linear heat input, and some cracks were formed at high heat input.
• The diffusion MSD of Al and Fe atoms increases with the increase of simulation temperature and time, and the vacancy diffusion mechanism is the main mechanism for the diffusion of Al and Fe atoms.
• In the IMC configuration of Al-Fe system, Fe atoms hardly diffuse across the interface, and the atomic diffusion is mainly from Al crystal structure into the IMC configuration, and the Al diffusion coefficient is much higher than that of Fe.
• After tracing the Al atom path trajectory, it was found that Al atoms diffuse mainly along the vertical interface direction.