The Influences of Micro-Alloying Element Sn and Magnetic Field on the Microstructure Evolution of Al–Bi Immiscible Alloys

Abstract

An investigation was conducted through directional solidification experiments to explore the impact of micro-alloying element Sn and a magnetic field on the solidification behavior of immiscible Al–Bi alloys, as well as the combined effect of Sn and the magnetic field. Experimental results show that the size distribution of the dispersed particles in the low-speed solidified Al–3.4 wt.%Bi alloy presents two peaks, while it only shows one peak when solidified at a relatively high speed. The addition of Sn not only can enhance the nucleation rate and the number density of the Bi-rich droplets in the sample, but also decrease the Marangoni migration velocity and the axial resultant velocity of minority phase droplets in front of the solidification interface. Thereby it promotes the formation of Al–Bi alloys with a well-dispersed microstructure. A static magnetic field with the strength of 0.2 T increases the number density of the dispersed particles and decreases the average size and the size distribution width of the dispersed particles. Under the effect of Sn addition and static magnetic field, the average radius of the dispersed particles $⟨R⟩$ and the solidification velocity $V_0$ satisfy $⟨R⟩\propto V_0{}^{-1/3}$ when the alloy was solidified at a relatively low velocity, $⟨R⟩$ and $V_0$ satisfy $⟨R⟩\propto V_0{}^{-1/2}$ when the alloy is solidified at a high velocity.

1. Introduction

Immiscible alloys exhibit a specific type of phase diagram characterized by a miscibility gap in the liquid state [1,2,3,4]. When cooling into the miscible gap, decomposition will happen, a homogeneous single-phase liquid separates into two liquids that are immiscible with each other and will form distinct phases [5,6,7,8,9]. Immiscible alloys are of particular interest because they can exhibit unique properties that are not found in their individual component metals. Many of them have a variety of industrial application potential in the chemical, automotive, machinery, electronic, and other fields. For instance, immiscible alloys based on Al–Bi and Al–Pb are potential materials for sliding bearings due to their self-lubricating properties [10,11,12], Cu–Fe alloys are materials with high strength and high conductivity [13,14,15,16,17,18]. However, the liquid–liquid decomposition can lead to the formation of phase-segregated microstructure and circumvent their applications. In recent years, extensive research has been dedicated to the investigation of immiscible alloys, driven by their distinctive properties and promising applications. Numerous experimental investigations have explored the solidification behavior of these alloys, encompassing diverse conditions such as microgravity, rapid solidification, and the application of external fields like electric current. Previous studies have focused on establishing models to describe the solidification process of immiscible alloys and calculating the resulting microstructure under various conditions. However, there is a research gap regarding the investigation of the impact of micro-alloying elements and magnetic fields on the solidification process and microstructure evolution of these alloys. Limited attention has been given to exploring these specific effects, highlighting the need for further research in this area.

In this study, directional solidification experiments were carried out by a vertical Bridgman-type furnace (Figure 1) with a static magnetic field device, and the effects of micro-alloying elements Sn and static magnetic field on the solidification of Al–Bi alloys are studied. The solidification behavior of Al–Bi immiscible alloys and the influence mechanism of micro-alloying element Sn and static magnetic field on the microstructure evolution of immiscible alloys are discussed in detail.

2. Experimental Procedure

Directional solidification experiments were carried out by a Bridgman-type solidification apparatus. The Al–3.4 wt.%Bi (monotectic composition) and Al–3.4 wt.%Bi−0.05 wt.%Sn alloys are prepared by pure aluminum (99.99 wt.%), Bi (99.99 wt.%), and Sn (99.99 wt.%). The alloys were then heated in a cylindrical crucible placed in a resistance furnace to a high temperature above their immiscible gap to 973 K, stirred, and kept at this temperature for 40 min to ensure the formation of a single-phase liquid. Then, the melt was solidified by withdrawing the crucible into a bath of Ga–In–Sn liquid alloy under the effect of a static magnetic field (0.2 T), with the withdrawal velocity ranging from 5 µm/s to 5 mm/s (5 µm/s, 10 µm/s, 20 µm/s, 28 µm/s, 2 mm/s, 3 mm/s, 4 mm/s, and 5 mm/s), and the magnetic field was transverse to the alloy growth direction. The cylindrical samples were obtained with a diameter and length of 6 and 120 mm, respectively. The samples were then cut longitudinally along the center plane and polished. The microstructure was examined by scanning electron microscopy (Hitachi S-3400 N) in the backscatter mode, and quantitative metallographic analysis was performed using SISC IAS V8.0 software to determine the size distribution and average diameter of the minority phase particles.

3. Results

3.1. The Effect of Micro-Alloying Element Sn on the Microstructure of Al–Bi Samples

Figure 2 shows the microstructures of Al–3.4 wt.%Bi alloys (monotectic composition) solidified at different rates under the effect of micro-alloying element Sn. Energy dispersive X-ray spectroscopy (EDS) analysis shows that the dark and white phases are Bi-rich particles and Al-rich matrix phases, respectively. Figure 2 and Figure 3 show the size distributions and the average size of the dispersed particles in the samples. It demonstrates that the Al–3.4 wt.%Bi alloy exhibits two peaks at a low solidification rate (28 μm/s), but only one peak at a relatively high solidification rate (5 mm/s). Moreover, the size distribution of the dispersed phase particles in all Al–3.4 wt.%Bi−0.05 wt.%Sn samples always has only one peak. Quantitative metallographic analysis indicates that the addition of micro-alloying element Sn can increase the number density of dispersed particles, and reduce the average particle size and the width of the size distribution. That is, the addition of micro-alloying element Sn promotes the formation of Al–Bi alloy samples with a well-dispersed microstructure.

3.2. Microstructure Evolution of Al–Bi–(Sn) Samples Solidified under the Effect of Magnetic

Figure 4 shows the relationship between the average diameter of the dispersed particles in the samples and the solidification velocity. Figure 5 and Figure 6 show the microstructures of Al–3.4%Bi and Al–3.4%Bi−0.05%Sn samples solidified under the effect of 0.2 T static magnetic field. It can be demonstrated that the application of a magnetic field can increase the number density of the dispersed particles. As expected, the size of Bi-rich particles decreases with the solidification rate, and the 0.2 T static magnetic field does not change this general trend, but the static magnetic field can increase the number density of dispersed particles and reduce the average size and size distribution width of dispersed particles. In other words, for Al–3.4%Bi and Al–3.4%Bi−0.05%Sn alloys, the static magnetic field results in the formation of samples with finely dispersed microstructures.

4. Discussions

4.1. Microstructure Evolution of Al–Bi Samples

During the solidification of Al–Bi alloy, solute Bi will accumulate in front of the liquid-solid interface and form a Bi-rich boundary layer due to the low solubility in α-Al, as shown in Figure 7. When the concentration of the solute element Bi in the diffusion boundary layer reaches a critical value, the minority phase droplets will precipitate and the nucleation position depends on the interfacial energy between the two liquid phases (${\sigma }_{L_1{L}_2}$), the interfacial energy between the matrix liquid phase and α-Al (${\sigma }_{\alpha L_1}$), and the interfacial energy between the minority phase droplet and α-Al (${\sigma }_{\alpha L_2}$). The minority phase droplets nucleate heterogeneously on α-Al surface during the liquid-liquid phase transformation when ${\sigma }_{\alpha L_2}<{\sigma }_{\alpha L_1}+{\sigma }_{L_1{L}_2}$ (see Figure 8a), and the minority phase droplets nucleate in the enriched boundary layer during the liquid-liquid phase transformation when ${\sigma }_{\alpha L_2}>{\sigma }_{\alpha L_1}+{\sigma }_{L_1{L}_2}$ (see Figure 8b). According to references [19], for Al–Bi alloys, ${\sigma }_{L_1{L}_2}=0.0578 \mathrm{J}\cdot {\mathrm{m}}^{-2}$, ${\sigma }_{\alpha L_1}=0.16 \mathrm{J}\cdot {\mathrm{m}}^{-2}$, ${\sigma }_{\alpha L_2}=0.23 \mathrm{J}\cdot {\mathrm{m}}^{-2}$, they satisfy ${\sigma }_{\alpha L_2}>{\sigma }_{\alpha L_1}+{\sigma }_{L_1{L}_2}$, so the minority phase droplets in the Al–Bi alloys nucleate in the enriched boundary layer and the heterogeneous nucleation of minor phase cannot take place on α-Al. The variation in the solute concentration in front of the solid/liquid (S/L) interface is determined by two opposing aspects: the nucleation and growth of minority phase droplets decrease the solute concentration while the solute redistribution increases the solute concentration. In the early stage of nucleation, the nucleation rate and the number density of minority phase droplets are very low, and the solute concentration is controlled by the solute redistribution, which leads to an increase in the solute concentration, and causes a rapid increase in the nucleation rate and the number density of the minority phase droplets. As a result, due to the nucleation and growth of the bismuth-rich droplets, the consumption of Bi solute increases, and the composition of the matrix liquid begins to approach a stable composition, as shown in Figure 7.

After nucleation, the minority phase droplets in the melt exhibit distinct movements caused by the specific gravity disparities between phases and the presence of temperature gradients. These movements are commonly known as Stokes motion, which is driven by the differences in specific gravity, and Marangoni migration, which arises from temperature variations. Stokes motion refers to the movement of droplets due to buoyancy forces, while Marangoni migration involves the migration of droplets driven by surface tension gradients resulting from temperature differences. [20,21,22]:

$${\mathit{u}}_s=-\frac{2g\left({\rho }_{\beta }-{\rho }_m\right)}{3}\frac{\left({\eta }_m+{\eta }_{\beta }\right)}{{\eta }_m\left(2{\eta }_m+3{\eta }_{\beta }\right)}{R}^2{\mathit{e}}_{\mathit{z}}$$

(1)

$${\mathit{u}}_M=-\frac{2{\lambda }_{m}R}{\left(2{\lambda }_m+{\lambda }_{\beta }\right)\left(2{\eta }_m+3{\eta }_{\beta }\right)}\frac{\partial {\sigma }_{L_1{L}_2}}{\partial r}\nabla T$$

(2)

where ${\mathit{u}}_s$ and ${\mathit{u}}_M$ are respectively the Stokes motion velocity and Marangoni migration velocity. ${\rho }_m$ and ${\rho }_{\beta }$ are the densities of the matrix and the droplets. ${\lambda }_m$ and ${\lambda }_{\beta }$ are the thermal conductivities of the matrix and the droplets, ${\eta }_m$ and ${\eta }_{\beta }$ the dynamic viscosities of the liquid matrix and the droplets. ${\mathit{e}}_{\mathit{z}}$ is the unit vector in the axial direction and $\nabla T$ is the temperature gradient.

The approximate estimation of the axial resultant velocity of minority phase droplets in the vicinity of the solidification interface can be expressed as follows:

$$V=\left|u_{Mz}\right|-\left|u_S\right|-V_0$$

(3)

where $V_0$ is the solidification rate, $u_{Mz}$ is the axial component of the Marangoni migration velocity of the droplets. When the axial resultant velocity is negative, the minority phase droplets will migrate toward the S/L interface. When the axial resultant velocity is positive, the minority phase droplets will migrate far away from the S/L interface.

In Figure 9, the relationship between the resultant velocity of minority phase droplets in front of the solidification interface and their droplet diameter is presented. The findings indicate that at high solidification velocities, minority phase droplets of all sizes, located at any position in front of the solidification interface, migrate towards the interface. Consequently, the size distribution of minority phase particles exhibits a single peak.

In contrast, when the alloy is solidified at a relatively lower velocity, the migration of minority phase droplets is influenced by their size. Under the combined effects of Marangoni migration, Stokes motion, and sample movement, minority phase droplets with diameters smaller than d_min or larger than d_max migrate toward the solidification interface. On the other hand, minority phase droplets within a specific size range (between d_min and d_max) may exhibit backward movement toward the solidification interface. As a result, a size distribution of minority phase particles with two peaks is observed.

These observations highlight the influence of solidification velocity and droplet size on the migration behavior of minority phase droplets in relation to the solidification interface. After the nucleation, the minority phase droplets will grow and coarse, and all of them migrate towards the solidification interface before the size reaches d_min. Some of them near the solidification interface can be engulfed, and they correspond to the first peak of the size distribution, while the droplets far away from the solidification interface have more time to grow, and their size will exceed d_min before reaching the solidification interface and being engulfed. Then they will move far away from the solidification interface until their size reaches d_max, these droplets correspond to the second peak of the size distribution. The analytical results are in favorable agreement with the experimental ones, as shown in Figure 3.

4.2. Effect of Sn on the Microstructure Evolution of Al–Bi Samples

The estimation of tensioactivity for component C at the interface of a three-component system A-B-C involves calculating the separate adsorption energies from A-rich ($L_1$) and B-rich ($L_2$) liquids [23]. The tensioactivity of component C can be mathematically expressed as:

$${\tau }_{L_1{L}_2}=\frac{K_{L_1{L}_2}{\tau }_{L_1}+{\tau }_{L_2}}{1+K_{L_1{L}_2}}$$

(4)

In Equation (4), ${\tau }_{L_1}$ and ${\tau }_{L_2}$ represent the changes in energy during the adsorption of component C from the volume of liquid $L_1$ and liquid $L_2$ to the interface, respectively. The partitioning coefficient, $K_{L_1{L}_2}$, characterizes the distribution of component C (with concentration X_C) between liquid $L_1$ and liquid $L_2$ in an infinite solution. A negative value of ${\tau }_{L_1{L}_2}$ indicates the segregation of component C at the interface between the $L_1$ and $L_2$ liquid phases. The magnitude of ${\tau }_{L_1{L}_2}$ determines the extent of adsorption, with a more negative value indicating more significant adsorption and a greater reduction in interfacial tension ${\sigma }_{L_1{L}_2}$. Conversely, for positive values of ${\tau }_{L_1{L}_2}$, solute C will desorb from the interface.

The tensioactivity parameter ${\tau }_{L_1{L}_2}$ for Al–Bi–Sn ternary system was calculated with Equation (4) based on the thermodynamical data provided by Kaban et al. [24]. It is found that ${\tau }_{L_1{L}_2}/RT\approx -2$ for Sn in the Al–Bi–Sn system at 933 K. Thus, the addition of Sn can reduce the interfacial tension between the two liquid phases by the adsorption of Sn at the (L₁–L₂) interface.

Perepezko [25] and Uebber [26] used the classical nucleation theory to predict the onset of the nucleation in monotectic alloys, and the nucleation rate of the minority phase droplets can be given by [27]:

$$I=N_{0}O\Gamma Z\mathit{exp}(-\frac{16\pi {\sigma }_{L_1{L}_2}^3}{3k_{B}T\Delta G_V^2})$$

(5)

where I is the nucleation rate, N₀ is the number density of atoms, $O=4n_c^{2/3}$ with n_c the number of atoms in a sphere of critical radius $R^{\ast }=2{\sigma }_{L_1{L}_2}/\Delta G_v$, and $\Delta G_v$ is the gain of volume free energy on nucleation. Γ = 6D/λ is the attachment rate, λ is the average jump distance of a solute atom due to diffusion. Z is the Zeldovich factor, k_B and T are the Boltzmann’s constant and the absolute temperature, respectively.

Adding a small amount of Sn (0.01–0.1 wt.%) to the Al–Bi alloy has negligible influence on the phase diagram and the morphology of the S/L interface. Sn mainly affects the microstructure formation through decreasing the interfacial energy between the matrix and the minority phase liquids, which can increase the nucleation rate and number density of the Bi-rich droplets in the sample. This promotes the decrease in the average size of the Bi-rich phase and the formation of Al–Bi alloys with a well-dispersed microstructure. On the other hand, the Marangoni migration velocity and the axial resultant velocity of minority phase droplets in front of the solidification interface will decrease with the decrease of interfacial energy, as shown in Figure 10. When the axial resultant velocity is less than zero, the minority phase droplets of all sizes located at any position in front of the solidification interface will migrate towards the solidification interface, leading to a size distribution of the minority phase particles with only one peak, as shown in Figure 3.

4.3. Effect of Static Magnetic Field on the Microstructure Evolution

When a substance is subjected to a magnetic field, the presence of magnetization leads to a modification in the Gibbs free energy. In the context of magnetic free energy, the gain of volume free energy is expressed as: [28]:

$$\Delta G_v^{\prime }=\Delta G_v-\frac{1}{2}{\mu }_0\left({\chi }_{L_2}-{\chi }_{L_1}\right)·H_m^2$$

(6)

where $\Delta G_v$ is the gain of volume free energy without the magnetic field, ${\mu }_0$ is the permeability of free space, ${\chi }_{L_1}$ and ${\chi }_{L_2}$ are the magnetic susceptibilities of the matrix liquid and the spheres, respectively. When nucleated homogeneously, the ratio of the nucleation rate with and without magnetic field can be given by [28]:

$$\frac{I^{\prime }}{I}=\mathit{exp}\left(\frac{16\pi {\sigma }_{L_1{L}_2}^3}{3k_{B}T}\frac{\left(\Delta {G^{\prime }}_v^2-\Delta G_v^2\right)}{\Delta G_v^2\Delta {G^{\prime }}_v^2}\right)$$

(7)

In this study, ${\chi }_{L_1}$ is positive while ${\chi }_{L_2}$ is negative [28]. From Equation (6), it can be concluded that $\Delta {G^{\prime }}_v^2>\Delta G_v^2$, which means that the ratio of the nucleation rate in Equation (7) is significantly larger than one. As a result, the static magnetic field enhances the nucleation of Bi-rich spheres and promotes their refinement, as observed in Figure 1, Figure 3, Figure 4 and Figure 5.

Since both the Bi-rich sphere and Al-rich liquid matrix are conductive, applying a magnetic field results in inductive drag or magnetic viscosity on the flow motion [29]. The effectiveness of the magnetic field in damping convective flows depends on the value of the Hartman number ($Ha=Bd{\left(\frac{\sigma }{{\eta }_m}\right)}^{\frac{1}{2}}$). When this number exceeds unity, inductive drag or magnetic viscosity becomes dominant [29]. Here, B is the magnetic field strength, d is the characteristic length, $\sigma$ is the electrical conductivity, and ${\eta }_m$ is the magnetic viscosity. Since the magnetic field is transverse to the alloy growth direction, the diameter of the sample can be taken as the characteristic length. In this experiment, the magnetic field strength is 0.2 T, and the Hartmann number is approximately 70. The magnetic field increases the effective viscosity in front of the solid/liquid interface, leading to suppression of movement of minority phase droplets. Consequently, the magnetic field promotes formation of a well-dispersed microstructure.

4.4. Effect of Sn and Static Magnetic Field on the Growth of the Droplets

The nucleated droplets in a supersaturated matrix grow through the diffusional transport of solute. The rate of growth for a droplet can be expressed as [20]:

$$v=\frac{dR}{dt}=D\frac{C^m-C_I}{C^{\beta }-C_I}·\frac{1}{R}[1+R\left(4\pi N〈R〉{)}^{1/2}\right]{(1+\frac{2}{3\pi }\frac{{\eta }_m}{{\eta }_m+{\eta }_{\beta }}Pe)}^{1/2}$$

(8)

where D is the diffusion coefficient of Bi element, R is the droplet radius, <R> is the average radius of the droplet radius, N is the number density of the droplet, ${\eta }_m$ and ${\eta }_{\beta }$ are the effective viscosities of the matrix melt and the droplets, respectively. Pe is the Peclet number, $C^m$ is the mean field concentration in the matrix liquid, $C^{\beta }$ is the concentration of the liquid within the droplet, and $C_I$ is the concentration in the matrix at the interphase boundary. $C_I$ depends on R according to the Gibbs–Thomson relation, and it can be written as [19]:

$$C_I=C_{\infty }·\mathit{exp}\left(\frac{{\alpha }_S}{R}\right)\simeq C_{\infty }·\left(1+\frac{{\alpha }_S}{R}\right)$$

(9)

where $C_{\infty }$ is the equilibrium concentration at a flat interface boundary. ${\alpha }_S=\frac{2{\Omega }_d{\sigma }_{L_1{L}_2}}{k_{\beta }T}$ is the capillary length, ${\Omega }_d$ is the atomic volume of the minority phase droplets.

When solidifying the alloy under the effect of Sn addition and static magnetic field, since the average diameter and the volume fraction of the minority phase droplets are both small, and the melt flow is restrained, the effects of the melt flow and the diffusional interactions between droplets can be neglected. Equation (8) can be written as:

$$v=\frac{dR}{dt}=D\frac{C^m-C_I}{C^{\beta }-C_I}·\frac{1}{R}$$

(10)

Substituting Equation (9) into Equation (10):

$$v=D\frac{C^m-C_{\infty }-C_{\infty }\cdot \left(\frac{{\alpha }_S}{R}\right)}{C^{\beta }-C_{\infty }-C_{\infty }\cdot \left(\frac{{\alpha }_S}{R}\right)}·\frac{1}{R}$$

(11)

For the Al–Bi system, $C^{\beta }\gg C^m$, so $\left(C^{\beta }-C_{\infty }\right)\gg C_{\infty }\cdot \left(\frac{{\alpha }_S}{R}\right)$, if the solidification rate is enough quick, the supersaturation of the melt will be high, it is namely that $(C^m-C_{\infty })\gg C_{\infty }\cdot \left(\frac{{\alpha }_S}{R}\right)$, then Equation (11) can be written as:

$$v\cong \alpha \cdot \frac{1}{R}$$

(12)

where $\alpha =D\frac{C^m-C_{\infty }}{C^{\beta }-C_{\infty }}$.

By integrating Equation (12), the following equation can be obtained:

$$\frac{1}{2}{R}^2=\alpha \cdot t+\beta$$

(13)

where $\beta$ is constant, t is the growth/coarsening time. During cooling the melt, the growth/coarsening time (t) is inversely proportional to the solidification rate ($V_0$), so the average radius of the droplets can be given by:

$$〈R〉\propto V_0{}^{-1/2}$$

(14)

If the solidification rate is very slow, the supersaturation of the melt will be small, Ostwald ripening occurs and the average radius of the droplets can be written by [19]:

$$<R{>}^3=K_{LSW}\cdot t$$

(15)

Or:

$$〈R〉\propto V_0{}^{-1/3}$$

(16)

where $K_{LSW}$ is the Ostwald ripening constant.

The actual solidification rate is usually between the above two conditions, and the dependence of the average radius of the minority phase particles varies from <R>∝V₀^−1/3 to <R>∝V₀^−1/2 with the increase of the solidification rate, as shown in Figure 11. It also demonstrates that when the alloy was solidified at a relatively low velocity, the average radius of the dispersed particles $〈R〉$ has a power function relationship with the solidification velocity $V_0$, which satisfies to $〈R〉\propto V_0{}^{-1/3}$, and when the alloy is solidified at a high velocity, $〈R〉$ and $V_0$ satisfy $〈R〉\propto V_0{}^{-1/2}$.

5. Conclusions

In summary, directional solidification experiments have been carried out to investigate the effect of micro-alloying element Sn and magnetic field on the solidification process of Al–Bi immiscible alloys. The conclusions are as follows:

(1)

The size distribution of the dispersed particles in the low-speed solidified Al–3.4 wt.%Bi alloy shows two peaks, while it only shows one peak when solidified at a relatively high velocity;

(2)

The introduction of Sn into the system leads to a reduction in the interfacial tension between the two liquid phases. This reduction has multiple effects: It enhances the nucleation rate and increases the number density of Bi-rich droplets within the sample. Additionally, it decreases the velocity of Marangoni migration and the resultant axial velocity of minority phase droplets near the solidification interface. These changes are beneficial for achieving a smaller average size of the Bi-rich phase and promoting the formation of well-dispersed microstructures in Al–Bi alloys;

(3)

By applying a static magnetic field of 0.2 T, it is observed that the number density of dispersed particles increases while the average size and size distribution width of these particles decrease;

(4)

In the presence of Sn addition and a static magnetic field, the average radius of the dispersed particles $〈R〉$ exhibits a strong dependence on the solidification velocity $V_0$. Specifically, when the alloy is solidified at a relatively low velocity, $〈R〉$ follows a power function relationship with $V_0$, given by $〈R〉\propto V_0{}^{-1/3}$. On the other hand, when the alloy is solidified at a high velocity, $〈R〉$ also exhibits a power dependence on $V_0$, but with a different exponent: $〈R〉\propto V_0{}^{-1/2}$.