Droplet Evolution and Refinement During Liquid–Liquid Decomposition of Zn-6 Wt Pct Bi Immiscible Alloy Under High Static Magnetic Fields

Our previous study[18] revealed that a very small amount of the solid Bi-rich phase (S₂) aggregated at the bottom of the samples. Therefore, the region located approximately 2 to 3 mm from the bottom edge of the sample along the central axis, which was photographed in this study, was considered representative to estimate the segregation in each ingot. Figure 2 shows the BSE images of the longitudinal microstructures at the bottom of the Zn-6 wt pct Bi samples solidified at R = 1600 °C/min with and without an HSMF. The solid Zn-rich phase (S₁) appears gray, whereas the S₂ phase is white. A layered microstructure is visible in the sample solidified without an HSMF (Figure 2(a)). As the magnetic flux density (B) was increased from 14 to 29 T, the degree of segregation decreased dramatically (from Figures 2(b) through (e)). However, when the temperature difference (ΔT) caused by the radial temperature gradient was large, slight segregation occurred at the edge of the sample solidified under a 29-T HSMF (Figure 2(f)). The average diameter (d_a) of the S₂ particles decreased to less than 10 μm when B was greater than 18 T. However, the maximum diameter (d_m) of the particles remained greater than 10 μm until B exceeded 24 T. The d_m values were 7.79 and 3.8 μm at B of 24 and 29 T, respectively (Figure 2(g)). The number of S₂ particles increased from 0.45 × 10⁻³ to 7.4 × 10⁻³ μm⁻² as B rose from 14 to 29 T, as shown in Figure 2(h). Previous studies[19,20] indicated that droplets with a diameter of 1 μm are large enough to produce a substantial surface tension difference between the hot and cool parts, thus facilitating Marangoni migration. Stokes sedimentation occurs when the droplet diameter is greater than 10 μm. Thus, segregation occurred when B was lower than 14 T because the average size of particles was larger than 10 μm in this case. Marangoni migration was the predominant factor leading to the segregation of the microstructure when B exceeded 18 T.

Comparing the BSE images showing the macrostructure of the Zn-6 wt pct Bi sample solidified by natural cooling under 0 T with that solidified under 18 T (Figure 3) revealed an interesting phenomenon that has only been observed previously under microgravity conditions.[3,4] That is, for the sample solidified under an 18-T HSMF, S₁ was surrounded by S₂ to form a shell-type macrostructure. The thickness of the S₂ shell was uniform around S₁ on the left side of the sample, but it was discontinuous on the right side, as shown in Figure 3(b). In this experiment, an 18-T HSMF was applied during the solidification process, whereas low-gravity conditions were used in the reported studies.[3,4] This indicates that the application of HSMFs produced an experimental environment that was similar to that obtained under microgravity conditions.

To carry out an exhaustive investigation on the evolution process during solidification, the microstructure of the alloy samples near the quartz crucible was carefully studied. Figure 4 compares the samples solidified without an HSMF at different R. Some Rayleigh-type regular arrays of S₂ particles, which have only previously been observed in directional solidification experiments,[21‐23] appeared in the region close to the crucible wall. The particle arrays extended along the radial direction to the central axis of the sample. The average spacing (λ) of the arrays was approximately 1.5 μm.

Figure 5(a) reveals that the sample solidified under an 18-T HSMF at 1600 °C/min has the same Rayleigh-type arrays of S₂ particles in the left middle margin. λ of the particle arrays was 1.3 μm, which is smaller than that without an HSMF (1.5 μm). Comparing Figures 4(c) with 5(c) showed that the average length of the particle arrays in Figure 4(c) (13 μm) was longer than that of the particle arrays in Figure 5(c) (8 μm). Meanwhile, Figure 5(b) shows that a uniform S₂ shell with a thickness of 48.9 μm formed under an external HSMF. In addition, the S₁ phase near the S₂ shell was different from the inner S₁ phase. Many defects and an interface between S₂ and S₁ were found in this limited region. The reason for the formation of defects will be discussed below.

Figure 6 shows that some parallel reaction bands with a chain-like pattern existed near the crucible wall for the sample solidified under an 18-T HSMF with R = 60 °C/min. The thickness of each band decreased as the distance from the wall to the center increased (Figure 6(a)). Figure 6(b) illustrates the transient microstructure between the parallel reaction bands (Figure 6(a)) and Rayleigh-type microstructure (Figure 6(c)). The reaction bands turned into a Rayleigh-type microstructure similar to the microstructures shown in Figures 4(a) and 5(a).

Figure 7 shows the Rayleigh-type microstructure observed at the bottom regions of samples solidified at 1600 °C/min under HSMFs of 0 and 18 T. Based on the measured data, λ of the particle arrays in the sample solidified under 0 T was 2.0 μm, which is larger than that of the sample solidified under 18 T (1.1 μm). The average length of the particle arrays shown in Figure 7(a) (15 μm) was longer than that in Figure 7(b) (5 μm). Thus, Rayleigh-type particle arrays appeared not only at the outer edge but also at the bottom region of the samples.

Based on the results in Figures 2(g) and (h), it was hypothesized that the nucleation process was affected by the HSMF. It is known that during the solidification process, Zn-6 wt pct Bi enters both the metastable and unstable regions of the Zn-Bi phase diagram.[10] The mixed liquid phase or mother liquid melt (L) then decomposes into a liquid Zn-rich matrix (L₁) and liquid Bi-rich phase (L₂) below the binodal line, not only through nucleation and growth in the metastable region but also by spinodal decomposition in the unstable region. The size of the metastable region is larger than that of the unstable region for the Zn-6 wt pct Bi alloy. Thus, the liquid–liquid decomposition occurs mainly through nucleation and growth in the metastable region. Naturally, there is an energy barrier to overcome during the nucleation stage of the L₂ droplets. Under an HSMF, a magnetic Gibbs free energy (ΔG_M = ΔG_m·V, where ΔG_m is the magnetic Gibbs free energy per unit volume and V is the volume of the droplet) is produced with the appearance of the L₂ droplets, and it acts as a driving force for phase transformation. ΔG_m equals −ΔχB²/2μ₀,[24‐26] where Δχ is the difference of magnetic susceptibility per volume between L and an L₂ droplet and μ₀ is the permeability of vacuum and equals 4π × 10⁻⁷ H/m. We assumed that L can be represented by the Zn melt and the L₂ droplet can be represented by Bi melt. Both liquid Zn and liquid Bi are known as abnormal diamagnetic phases with magnetic susceptibilities of about − 6.58×10⁻⁷ (measured at 419 °C) and − 0.38×10⁻⁷ (measured at 450 °C), respectively.[27‐29] Then, Δχ was calculated to be 6.2×10⁻⁷. ΔG_m decreases with increasing B, as shown in Figure 8. When B is 29 T, ΔG_m is calculated to be about – 250 J/mol. However, this is much smaller than the thermal energy of 2.5 kJ/mol at room temperature. Therefore, the HSMF has little effect on the nucleation of L₂ droplets in the liquid matrix. That is, it can be deduced that the magnetohydrodynamic effect is the main reason for the refinement of S₂ particles in Figure 2(c) and magnetothermodynamic effect can be neglected under HSMFs of less than 29 T.

After the nucleation process, the L₂ droplets grow gradually. They are driven by the Marangoni motion when the droplet diameter (d) is less than 10 μm and by additional Stokes motion when d exceeds 10 μm. In addition, the L₂ droplets tend to collide with each other to form larger droplets. If we assume that a single L₂ droplet (d > 10 μm) settled with a certain velocity at the bottom of the sample, the HSMF decreases the velocity to a constant value (V₁) through the induced Lorentz forces inside the L₁ melt, both at the front and back of the L₂ droplet (Figure 9(a)). The melt flow has horizontal components at the front and back of the L₂ droplet. The horizontal component of the melt flow and HSMF efficiently induce an eddy current; that is, clockwise and counterclockwise currents are induced at the front and back sides, respectively. Then, the electromotive forces (F₁ and F₂) induced by electromagnetic induction decrease the deformation of the melt and simultaneously slow the motion of the L₂ droplets. F₁ and F₂ are viscous resistances that can be analyzed in terms of the Hartmann number (Ha),[9,30] which can be written aswhere r is the radius of the L₂ droplet, and σ and η₁ are the electrical conductivity and viscosity of L₁, respectively. If we assume that L₁ and L₂ are pure Zn and pure Bi, respectively, then the relationship between Ha and B at the melting point of Zn (419.6 °C) can be calculated (Figure 10(a)). In the melt, the additional viscous resistance (F_η) without an HSMF can be defined bywhere V_s is the moving velocity of the L₂ droplet in the melt without an HSMF and η₂ is the viscosity of the L₂ droplet. The viscous resistance under the effect of an HSMF (F_η′) can be expressed as[9,30,31]

We can use Eqs. [2] and [3] to determine the terminal velocity of a droplet falling vertically in the melt. In this case, forces F_η and F_η′ compensate for the gravity-induced buoyancy force P, which can be expressed aswhere ρ₁ and ρ₂ are the densities of L₁ and L₂, respectively; and g is the acceleration caused by gravity. The movement of an L₂ droplet becomes stable after balancing these forces. This state is described as below:

Then, we can obtain the ratio V_S′/V_S, which is used to quantify the effect of the HSMF and has been described in our previous work.[18]

The physical parameters used in the equations can also be found in Reference 18. Then, we can obtain the relationship between V_S′/V_S and B, as seen in Figure 10(b). The suppression of the Stokes sedimentation can be expressed by δ_S = (V_S – V_S′)/V_S × 100 pct. For an L₂ droplet with a radius of 10 μm, δ_S values are approximately 50, 70, and 80 pct when B values are 10, 20, and 30 T, respectively. The L₂ droplet in the L₁ melt also displays another type of motion, as shown in Figure 9(b). In this case, the direction of motion of the L₂ droplet is perpendicular to the HSMF; therefore, no eddy currents are induced on either the front or back side of the L₂ droplet along its moving direction. The movement of the L₂ droplet is free in the HSMF. The Marangoni migration of the L₂ droplets occurred when there was a large temperature gradient along the radial direction of the sample (perpendicular to the direction of the HSMF). This led to slight segregation at the edge of the sample (Figure 2(f)).

The coalescence of droplets under an HSMF can also be explained by considering the melt flow around the immiscible droplets. Figures 11(a) and (b) show the coalescence of two L₂ droplets in the vertical and horizontal directions, respectively. In the case of coalescence of two droplets moving parallel to the HSMF, the L₁ melt is ejected from the gap between the two L₂ droplets. The melt flow of L₁ to the top part of the upper droplet and bottom part of the lower droplet is also induced. The electromagnetic induction caused by the flow pattern around the droplets is equal to that shown in Figure 9(a). The eddy currents (J₁ and J₂) induced by the melt flow around the droplets are represented by solid black lines. Lorentz forces induced by the eddy current and HSMF, which are shown in Figure 11(a), act as a braking force to prevent the collision between the two L₂ droplets. Thus, the HSMF lowers the coalescence rate in the direction parallel to the HSMF. The situation shown in Figure 11(b) is the same as that observed in Figure 11(a). In this case, the horizontal component of the L₁ melt flow at the top part of the two droplets induces a clockwise current (J₁). The L₁ melt flow at the bottom part of the two droplets also induces a clockwise current (J₂). The HSMF and clockwise currents induce Lorentz forces that resist the L₁ melt flow from the gap to the back of the droplets. The coalescence of the L₂ droplets in the horizontal direction is also suppressed by the HSMF. Thus, coalescence in both the vertical and horizontal directions is hindered by applying an HSMF. This means that the Marangoni motion at the edge of the sample can also be decreased, as we described in our previous work.[18]

The measured data showed that the radius of the L₂ droplet was smaller than 10 μm when B ≥ 18 T, which resulted in no Stokes sedimentation, and thus the growth process was no longer controlled by the Stokes sedimentation. In this situation, the movement of the L₂ droplets should be considered as a creep flow. Diffusion interfaces around L2 embryos are produced simultaneously with droplet appearance. The velocity of a growing sphere by pure diffusion can be described by Zener’s solution[32] aswhere t is the growth time; D is the diffusion coefficient; c_m is the concentration of the matrix melt, which is a constant far from the diffusion interface; c₁ is the concentration of the liquid matrix at the diffusion interface; and c₂ is the concentration of the liquid droplets far from the diffusion interface. In general, the growth of the liquid droplets is controlled by diffusive or convective effects that mainly depend on the Peclet number (Pe = Vr/D) and Reynolds number (Re = Vr/μ), where μ is the kinematic viscosity of the matrix. Substituting V_S′ (i.e., Eq. [5]) and D (which is estimated to be of the order of 10⁻⁸ to 10⁻⁹ m²/s in an immiscible liquid system)[33] into Pe and Re showed that Pe ≪ 1 and Re ≪ 1; they both have a magnitude of 10⁻³. Based on the above description and analyses, it can be understood that pure diffusion growth can be used to describe the growth of L₂ droplets when B ≥ 18 T under our experimental conditions.

The surface of an ingot rapidly cooled to ambient temperature normally consists of equiaxed grains. Thus, it exhibits directional solidification in the radial direction. In our samples, droplet arrays formed because Rayleigh instability emerged in the surface equiaxed grains. For the samples quenched at either 0 or 18 T, the Marangoni migration should be ascribed to the large temperature gradient. To decrease the interfacial tension, large numbers of L₂ droplets migrated to the higher-temperature region along the radial direction.

The temperature gradient along the radial direction decreases as the distance from the outer surface to the central axis (s) increases. Thus, the dispersion of the L₂ droplets in a grain can be divided into a planar growth stage and cellular growth stage. Figure 12 illustrates that during the planar growth stage, the real temperature distribution (T_r) in front of the solid–liquid interface was much larger than the local isothermal solidification temperature distribution (T_i) when the solidification distance was smaller than s₁. In this stage, the S₁ phase grew without constitutional supercooling. The solid–liquid interface was planar, and the droplets were dispersed in the S₁ phase (planar growth in Figure 12). Conversely, during the cellular stage (s > s₁), T_r was lower than T_i, which resulted in constitutional supercooling. Considering the interfacial tension, the constitutional supercooling acts as a driving force. At the same time, the solid–liquid interface oscillates at a certain wavelength (λ_i), which can be written aswhere \( \varGamma = \sigma_{{{\text{S}}_{1} {\text{L}}_{2} }} /\Delta S \) is the Gibbs–Thomson coefficient, in which \( \sigma_{{{\text{S}}_{1} {\text{L}}_{2} }} \) is the solid–liquid interface energy between the solid S₁ phase and liquid L₂ phase, and ΔS is the volume solidification entropy; V is the growth velocity of the grain; and ΔT₀ is the temperature difference between the critical temperature for the original concentration (T_c) and the monotectic reaction temperature also for the original concentration (T_m). Thus, a groove forms in the gap between the two dendrites. Then, because of the decreasing temperature gradient in front of the solid–liquid interface, Rayleigh instability occurred easily in the grooves when the system was perturbed. λ_i of the solid–liquid interface equals λ of the Rayleigh-type droplet arrays shown in Figures 4(a), 5(a), and 7.

For monotectic alloys, the eutectic reaction is another important feature in the phase diagram (Supplementary Figure 1). The residual L₂ after the monotectic reaction undergoes desolventizing decomposition and a eutectic reaction. During the desolventizing decomposition stage, Zn separates out from L₂. Then, the eutectic reaction occurs in the residual L₂. At this stage, nanoscale zinc particles separate out from L₂ and move along the direction of the temperature gradient. The morphology depicted in Figure 6 formed for two reasons. First, the cooling rate in the region adjacent to the wall of the quartz crucible was faster than that in the region close to the interface between the L₂ shell and L₁, which led to an increase in the diffusion distance of zinc particles along the growth direction (shown in Figure 6(d)). Second, the HSMF slows the migration of these nanoscale zinc particles. Thus, a eutectic microstructure with many dispersed nanoscale zinc particles at the initial stage and regular zinc droplet arrays at the final stage of the eutectic reaction forms along the growth direction (Figure 6(d)). This morphology and growth process are similar to those of the lamellar microstructure of a classical eutectic microstructure.

Studies[10‐12] have shown that TEMC induced by TEMF is generated during the solidification process of alloys under magnetic fields. In our experiments, during the bulk solidification process of the Zn-6 wt pct Bi immiscible alloy, the melt was segregated at the immiscible interval (T_c − T_m). The L₂ phase gradually sunk to the bottom of the ingot because of its greater density than that of L₁, whereas the upper part was mainly L₁. Based on the phase diagram, it can be understood that the upper Zn-rich phase is a liquid in the gap of the immiscible temperature and a solid between the monotectic temperature (T_m) and eutectic temperature (T_e, see Supplementary Figure 1) with L₂ under L₁ or S₁ when the melt was cooled at a slow rate. After the eutectic reaction, the L₂ phase solidifies into S₂. Therefore, there are three kinds of interfaces in the sample: the liquid–liquid (L₁–L₂) interface, the liquid–solid (S₁–L₂) interface, and the solid–solid (S₁–S₂) interface. In addition, a radial thermoelectric current (J_TE) is produced at all three interfaces because of the temperature gradient in the radial direction of the ingot (Figure 13(a)). J_TE plays an important role in affecting the interfaces during the bulk solidification under an HSMF, and it mainly forms the L₁–L₂ and S₁–L₂ interfaces because of the Seebeck effect along the radial direction. Thus, a TEMF is generated by the interaction of J_TE and the perpendicular HSMF at the L₁–L₂ and S₁–L₂ interfaces (Figures 13(a) and (b)). On the one hand, the flat interface of L₁–L₂ becomes concave under the action of the TEMF as a stirring force (Figure 13(a)). Because of the fluidity of the liquid phase, TEMC induced by the TEMF can only exist in the liquid phase (L₁ or L₂); it is not present in the solid phase (S₁ or S₂). If L₁ solidified as S₁ or L₂ solidified as S₂, the interface would not be changed by the TEMF. This is because the solid phase is not fluid. For this reason, the TEMF only caused the L₁–L₂ interface to form a concave shape (Figure 13(a)) and as a result, the S₁–L₂ interface also has a concave shape (Figure 13(b)). On the other hand, based on the contact angle between S₁, S₂, and the internal surface of the quartz crucible, it is concluded that the L₂ phase can wet the quartz crucible wall more easily than the L₁ phase (Figure 3(a)). The L₁ phase rotates in a clockwise direction (ω₁) under the effect of a TEMF in L₁ or S₁ and the L₂ phase rotates in a counterclockwise direction (ω₂) under the effect of a TEMF in L₂ (Figure 13(c)). Finally, the combined effect of TEMC and wettability leads to the formation of a shell-like structure under an 18-T HSMF (Figure 3(b)). After this relative rotation, the thickness of the shell becomes more uniform. In addition, the interface between S₂ and S₁ becomes weak and contains many defects (Figures 5(b) and (d)).

The L₂ droplets separated out from the L₁ phase and a radial temperature gradient existed around the droplets in the immiscible gap. Consequently, the TEMF effect should be investigated because of the markedly different Seebeck coefficients between L₁ and L₂. To simplify the analysis, we considered that the radial temperature gradient was constant. TEMF was produced at the interface between the L₂ droplet and L₁ melt (Figure 14(a)). The TEMF in the L₂ droplet acted as a circumferential force, dragging the L₂ droplet in the circumferential direction inside the cylindrical melt. This constant force made the L₂ droplet move with an accelerating motion. The circumferential velocity transformed to a centrifugal force, pushing the L₂ droplet nearer to the L₂ shell, as shown in Figure 14(b). The centrifugal force can be written aswhere m is the mass of the L₂ droplet, v is the circumferential velocity, R is the distance between the L₂ droplet and central axis, F_M represents the TEMF, and t is the motion time of the droplet. Equation [9] indicates that F_c increases with F_M and t and decreases with the radius of the L₂ droplet. Therefore, with the increasing cooling time and B, the L₂ droplet is pushed toward the L₂ shell, which increases the shell thickness. Thus, the L₂ droplet moves freely toward the outer surface. That is, the HSMF did not affect the droplet’s centrifugal migration. Therefore, the regular centrifugal migration of Bi-rich droplets caused by the TEMF resulted in the final shell-like structure of the Zn-6 wt pct Bi immiscible alloy (Figure 5(b)).