Liquid-liquid phase separation of freely falling undercooled ternary Fe-Cu-Sn alloy

The active modulation and control of the liquid phase separation for high-temperature metallic systems are still challenging the development of advanced immiscible alloys. Here we present an attempt to manipulate the dynamic process of liquid-liquid phase separation for ternary Fe47.5Cu47.5Sn5 alloy. It was firstly dispersed into numerous droplets with 66 ~ 810 μm diameters and then highly undercooled and rapidly solidified under the containerless microgravity condition inside drop tube. 3-D phase field simulation was performed to explore the kinetic evolution of liquid phase separation. Through regulating the combined effects of undercooling level, phase separation time and Marangoni migration, three types of separation patterns were yielded: monotectic cell, core shell and dispersive structures. The two-layer core-shell morphology proved to be the most stable separation configuration owing to its lowest chemical potential. Whereas the monotectic cell and dispersive microstructures were both thermodynamically metastable transition states because of their highly active energy. The Sn solute partition profiles of Fe-rich core and Cu-rich shell in core-shell structures varied only slightly with cooling rate.


Structure patterns of phase separation
Both DSC thermal analysis and bulk undercooling experiments 33,34 indicate that liquid Fe 47.5 Cu 47.5 Sn 5 ternary alloy does not exhibit phase separation if its undercooling is smaller than 51 K. In such a situation, it solidifies in the normal way of stable peritectic alloy. However, liquid-liquid phase separation is initiated as soon as alloy undercooling exceeds the threshold value of 51 K. At the substantially undercooled state, this alloy displays the second critical undercooling of 196 K, below which liquid phase separation proceeds only to a microscopic extent so that it still behaves much like a normal peritectic alloy. Once undercooling increases beyond 196 K, macroscopic liquid phase separation takes place before the occurrence of solid phase nucleation. Afterwards the solidification process of highly undercooled alloy melts involves three stages: firstly γ Fe phase nucleates and grows, subsequently the peritectic reaction L+ γ Fe → (Cu) occurs at temperatures below 1068 K, and finally all the residual liquid phase is consumed up by another peritectic reaction L + (Cu) → β -Cu 5.6 Sn when its temperature becomes lower than 1013 K. Considering γ Fe phase is subject to a polymorphic transition in the due course, the phase constitution of rapidly solidified ternary Fe 47.5 Cu 47.5 Sn 5 alloy consists of α Fe and (Cu) solid solution phases together with some amount of β -Cu 5.6 Sn intermetallic compound. Figure 1 shows the structure patterns of ternary Fe 47.5 Cu 47.5 Sn 5 alloy droplets under free fall condition. For the largest droplet with a diameter of 810 μ m, the macrostructure displays that the nubbly Fe-rich phase forms a kind of monotectic cell microstructure which is surrounded by the Cu-rich phases, as seen in Fig. 1(a). With the decrease of droplet diameter, liquid phase separation takes place apparently and generates two-layer core-shell structure in the droplet range of 100 < D < 810 μ m, where the inner part is Fe-rich core, and the outer part is Cu-rich shell, as shown in Fig. 1(b). When the droplet diameter decreases to 66μ m, which is the smallest droplet during the experiments, the microstructure shows the dispersed pattern of α Fe phase particles distributed into the Cu-rich matrix. In Fig. 1(c), the black is α Fe phase, the grey is the (Cu) solid solution phase, and the white is Cu 5.6 Sn intermetallic compound. Therefore, the multiple solidification characteristics of liquid ternary Fe 47.5 Cu 47.5 Sn 5 alloy appear under free fall condition: monotectic cell, core shell and dispersed structure with the decrease of droplet diameter.
The microstructural morphologies of the different alloy droplets are illustrated in Fig. 1(d-f). At the largest droplet diameter of 810 μ m, primary α Fe phase grows into a monotectic cell of nubbly structure, which is surrounded by the grey (Cu) solid solution phase resulting from the first peritectic reaction, that is L + γ Fe → (Cu). β -Cu 5.6 Sn phase is produced through the second peritectic reaction and is distributed among interdendritic gaps. Once the droplet diameter decreases from 646 to 188 μ m, the Fe-rich and Cu-rich zones become clearly separated from each other and their boundary has evolved into a smooth interface, where α Fe and (Cu) solid solute phases distributed into the Cu-rich and Fe-rich zones, respectively, as seen in Fig. 1(e), whereas the peritectic β -Cu 5.6 Sn phase forms around the (Cu) phase in the due sequence. As the droplet diameter reduces to 66 μ m, the primary γ Fe phase grows in two morphologies: the equiaxed grains and the dendrite structures, which are dispersed randomly into the Cu-rich matrix, as shown in Fig. 1 Based on the experimental results, the dispersed and core-shell morphologies are the main structures of ternary Fe 47.5 Cu 47.5 Sn 5 alloy. Their forming probabilities at the different droplet diameters provide some important information to investigate the liquid phase separation characteristics of ternary Fe 47.5 Cu 47.5 Sn 5 alloy under the free fall condition. The statistical analysis displays that the core-shell structures are most frequently generated at the intermediate droplet diameters of 200 < D ≤ 800 m, and the forming probability attains 99.1% at D = 800 μ m. Whereas the dispersed structures form when the droplet diameters D < 200 μ m, and the forming probability is 100% at 66 μ m diameter, which is shown in Fig. 1(g). Clearly, the middle sized droplets are easy to experience macroscopic phase separation and form the core-shell structures.

Solute concentration field and Chemical potential evolutional characteristics
Phase separation plays an important role in the final structure morphology of monotectic or peritectic alloy. The phase field method is an effective way to simulate such a complicated process. The macrostructures demonstrated in Fig. 1 suggest that the Sn solute should have stronger affinity with the Cu solvent, rather than Fe solvent. EDS analysis also reveals that Fe-rich zone contains only 1.49 at.% Sn, and Cu-rich zone dissolves about 8.25 at.% Sn. Therefore, ternary Fe 47.5 Cu 47.5 Sn 5 alloy can be approximately regarded as the pseudo binary Fe 47.5 (Cu 0.905 Sn 0.095 ) 52.5 alloy during the phase field simulation 36,37 . The free energy expression is written as: where x is the Fe molar mass, (1− x) is the Cu 0.905 Sn 0.095 molar mass, g B and g A are molar free energy of Fe and Cu 0.905 Sn 0.095 respectively, T c is the critical temperature, Ω is the interaction parameter of alloy. The chemical potential of the alloy is expressed as: Based on the modified Model H, the phase field governing equation is expressed as: C f is the fluidity parameter of alloy melt. In small droplets, the Reynolds number is less than the magnitude of 10 −3 , thus the local velocity v can be taken as f = − ∇ F. ρ is the density of liquid alloy, R g the gas constant, ε the length scale, D L the diffusion coefficient, η the viscosity, and M the molar mass. The governing equations are dealt with a two-dimensional square grid by an explicit finite difference technique so as to simplify the numerical analysis process. This is justified by the normally spherical symmetry of the temperature and concentration fields within a freely falling alloy droplet. During the simulation, the initial velocity is zero. The liquidus temperature is 1722 K. The grid size is set as 200 × 200, the step of space is set as Δ x = Δ y = 1. The alloy droplet diameter is 200 μ m. The time step Δ τ is 0.001 which ensures the stability of numerical solution. The surface parameters are H = 0.38 and g = 0.4. The characteristic length of spatial heterogeneity ε = 1.0 μ m. Finally the calculations were performed in a Lenovo 1800 cluster system.
The Fe-rich and Cu-rich dispersed globules of ternary Fe 47.5 Cu 47.5 Sn 5 alloy move mainly by Marangoni migration and Stokes motion during liquid phase separation. The Marangoni migration of second phase globule is much more complicated in comparison with the Stokes motion, which involves both thermal Marangoni migration and solutal Marangoni migration. Therefore, it is necessary to compare the influences from two kinds of Marangoni migrations with that of the Stokes motion. The Stokes motion velocity V s of a single globule with radius r in the matrix phase is written by 35,36 : The thermal Marangoni migration velocity V mt of a single globule is expressed as 36,38 : where ρ 1 and ρ 2 are the densities of the matrix and dispersive phase, g is the residual gravitational acceleration, k 1 and k 2 are the thermal conductivities of the matrix and dispersive phases, while η 1 and η 2 are their viscosities respectively, g is estimated as 10 3 g 0 in the present experiment. Here g 0 = 9.8 m·s −2 is the normal gravitational acceleration.The interfacial tension gradient caused by temperature field is: The solutal Marangoni migration velocity V Mc of a single globule can be expressed by 36,39 : where D 1 and D 2 are the solute diffusion coefficients of the matrix and dispersive phases. ∇ σ c is the interfacial tension gradient resulting from concentration field, which is written as the following equation: The interfacial tension of Fe-rich and Cu-rich liquid phase is estimated on basis of Cahn-Hilliard model 36,40 : here N V is the atom number of unit volume, λ α the interface atom distance, k B the Boltzmann constant, and T c the critical temperature. The heat transfer equation is given in polar coordinates: The initial and boundary conditions during free fall are given as: where α is the thermal diffusivity of alloy melt, λ the heat conductivity, ε h the emissivity, σ SB the Stefan-Boltzmann constant, h the heat transfer coefficient, T 0 the initial temperature of alloy melt, T s the droplet surface temperature, and T e the ambient temperature. The 3D phase separation snapshots of phase field simulation for the pseudo binary Fe 47.5 (Cu 0.90 5 Sn 0.095 ) 52.5 alloy at different moments are presented in Fig. 2. Before the phase separation, the concentration of liquid phase remains homogeneous, which is seen in Fig. 2(a). Once the phase separation takes place, the morphology varies with the evolution time of phase separation, a large number of Fe-rich globules separate from the liquid phase and form the monotectic cell structure, which is shown in Fig. 2(b). Then the surface segregation layer forms owing to the effect of surface segregated potential. At τ = 0.2 ms, the surface segregation occurs prior to bulk decomposition, and forms the Cu-rich surface layer followed by the Fe-rich layer in the liquid phase due to the hydrodynamic and Marangoni migration. In the process of phase separation, the interfacial tension gradients drive the thermal Marangoni migration inwards and the concentration gradients tend to drive the solutal Marangoni migration outwards. With the extension of the evolution time, the Cu-rich surface segregated layer thickens gradually and the inner Cu-rich phase grows in the dispersive way. When the time extents to 0.6 ms, the second Cu-rich layer forms inside the liquid phase. The reason may be that the solutal Marangoni migration velocity is faster than the thermal Marangoni migration velocity, which leads to the Cu-rich globules collide randomly in the process of migration. When the evolution time exceeds 1 ms, the flow field quickly responses to the local force field, the inner Cu-rich phase aggregation becomes much faster through absorbing small globules around itself in the effect of the Ostwald ripening, and forms the triple-layer structure at τ = 400 ms. The surface segregated layer grows thicker and thicker by absorbing inner Cu-rich liquid phase in the following evolution, and displays the two-layer structure in the end. Obviously, the shorter evolution time results in the dispersed structure, as seen in Fig. 2(b). The longer evolution time, Marangoni migration and surface segregation can generate the core-shell structure. The monotectic cell structure is similar to the evolution profile at τ = 0.1 ms. The chemical potential reflects the system stability characteristics. Before the occurrence of phase separation, the Fe-rich and Cu-rich chemical potential distributes dispersively, which means that the alloy system is on the instable condition as the active energy is high, the maximum value is about 3.09 kJ/mol at τ = 0 ms, as shown in Fig. 3(a). With the extension of evolution time, the chemical potential plays the disorderly feature. Then the chemical potential near the droplet surface reduces quickly due to the effect of surface segregation potential, while the chemical potential at the center part shows the wave crest feature and also decreases gradually, which is illustrated in Fig. 3(b,c). Obviously, the chemical potential gradient occurs in the liquid phase. The chemical potential gradient always drives the solute to move toward the lower chemical potential on the influence of active energy, thus the surface segregation layer forms during liquid separation (τ = 400 ms). However, with the thickening of the surface segregation layer, the center chemical potential increases abruptly owing to the fact that the surface chemical potential absorbs solute from the center, which leads to the consequence that a large amount of Cu-rich solute gathers quickly, and forms the mountain-like profiles, as shown in Fig. 3(e). When the evolution time τ = 1000 ms, the hole-like feature occurs and the center chemical potential exhibits the minimum where the energy difference between the inner and outer layer is only about − 0.015 kJ/mol. It is certified that the evolution system achieves the stable state here. According to the above analysis, the two-layer core-shell structure is the most stable structure in the process of liquid phase separation.

Marangoni migration during liquid phase separation
The Marangoni migration has a significant influence on the movement of Cu-rich liquid phase during liquid phase separation, and its velocity decides the final macrostructure morphologies. Three types of motion characteristics at different droplet diameters are demonstrated in Fig. 4(a-c). Apparently, the larger globules have the larger Marangoni migration velocity for every droplet. The Stokes motion velocity of a 20 μ m radius globule is only about 10.7 nm/s, where the droplet diameters vary from 810 μ m to 66 μ m. This is because the gravitational acceleration has been reduced to 10 −3 g 0 in the drop tube experiment. Stokes motion velocity is far less than the thermal and solutal Marangoni migration velocity, therefore it can be neglected under free fall condition, as shown in Fig. 4(c).  The globule radius and droplet diameter have the significant fluences on the Marangoni migration velocity. From Fig. 4(a), the Cu-rich globule with a radius of 1 μ m shows a solutal Marangoni migration velocity of 26 nm/s within the largest alloy droplet of 810 μ m. This increases up to 528 nm/s at the globule radius 20 μ m. In contrast, it migrates at a velocity of 324 nm/s with 1 μ m globule radius inside the smallest alloy droplet of 66 μ m. The largest solutal Marangoni migration velocity appears at the globule radius 20 μ m in this droplet, which attains 6.48 mm/s. Clearly, the solutal Marangoni migration velocity of 20 μ m globule radius is almost 20 times larger than that of 1 μ m globule radius. Furthermore, such a velocity for a 20 μ m Cu-rich globule inside the smallest alloy droplet of 66 μ m diameter is enhanced by a factor of 12 times by comparison with the droplet diameter 810 μ m. Similarly, the thermal Marangoni migration velocity displays the same tendency as the solutal Marangoni migration velocity, as seen in Fig. 4(b). For example, the thermal Marangoni migration velocity of 1 μ m globule achieves 21 nm/s at the 810 μ m droplet diameter. It shows 421 nm/s migration velocity at the 20 μ m globule radius. In the case of the smallest alloy droplet with 66 μ m diameter, the thermal Marangoni migration velocity is 114 nm/s for 1 μ m globule radius, whereas it amounts up to 2.27 mm/s velocity for 20 μ m globule radius. The thermal Marangoni migration velocity of 66 μ m droplet is 5 times as large as that in the 810 μ m alloy droplet, where the globule radius is 20 μ m. It is apparent that the larger globule radius and smaller droplet diameter have the faster solutal and thermal Marangoni migration velocities for ternary Fe 47.5 Cu 47.5 Sn 5 alloy.
On the other hand, the solutal Marangoni migration is more rapid than the thermal Marangoni migration of Cu-rich globules inside Fe 47.5 Cu 47.5 Sn 5 alloy droplets. In the case of the largest alloy droplet with 810 μ m diameter, the solutal Marangoni migration velocity amounts to 528 nm/s at 20 μ m globule radius, which is 1.3 times as large as the thermal Marangoni migration velocity. Many Cu-rich globules are influenced by the solutal Marangoni migration and move outside alloy droplet, while a small number of Cu-rich globules are driven toward to the droplet center under effect of the thermal Marangoni migration. With the decrease of droplet diameter, the globule movement velocity accelerates inside alloy droplet. The solutal Marangoni migration velocity achieves 6.48 mm/s inside the smallest alloy droplet of 66 μ m diameter at 20 μ m globule radius, which is enhanced by a factor of about 2.85 times by comparison with the droplet diameter 810 μ m, as demonstrated in Fig. 4(a,b). It is apparent that the solutal Marangoni migration velocity increases farther than the thermal Marangoni migration velocity.
The solutal Marangoni migration velocity V Mc increases continuously with the decrease of temperature, whether the droplet diameter is large or small, as seen in Fig. 4(d). When the temperature decreases from 1727 K to 1427 K, the solutal Marangoni migration velocity V Mc increases from 3.8 nm/s to 369 nm/s for 5 μ m Cu-rich globules at the droplet diameter 810 μ m. In addition, it obtains the velocity from 4.6 mm/s to 4.53 mm/s when the droplet diameter is 66 μ m. Therefore, when the alloy the droplet is smaller and its temperature is lower, the solutal Marangoni migration velocity becomes higher in this alloy. However, the thermal Marangoni migration velocity shows different characteristics as compared with the solutal Marangoni migration velocity, which is illustrated in Fig. 4(e). With the decrease of temperature, the thermal Marangoni migration increases gradually. It achieves the maximum velocity of 106 nm/s at 1642 K in comparison with 74 nm/s velocity at 1727 K. Then it reduces with the further drop of temperature until 759 nm/s at 1427 K. The smaller droplet has the larger thermal Marangoni migration velocity, and has the shorter phase separation time and the higher temperature to drive the Cu-rich globule inwards alloy droplet during liquid phase separation.
Based on the above analysis, it seems probable that the smaller droplets are easier to experience phase separation and form the core-shell structure owing to the higher solutal Marangoni migration velocity. However, both the largest and smallest alloy droplets with diameter of 810 and 66 μ m do not form the core-shell structure. Therefore, the cooling rate may be another controlling factor during rapid solidification under free fall condition. Since the cooling rate is quite difficult to measure within the short falling time when a bulk alloy melt is dispersed into numerous small droplets to fall freely inside drop tube, the cooling rate is calculated by Equ.s 11-14. Figure 1(h) shows the variation of center cooling rate with droplet diameter. Apparently, those droplets with diameters smaller than 200 μ m possess very high initial cooling rates, but they also show much quicker decreasing tendency with the extension of falling time. For example, if the droplet diameter is the smallest, 66 μ m, the center cooling rate is 1.25 × 10 5 K/s. This droplet completely solidifies within only 0.13 s. Because of such a high cooling rate, the Fe-rich globules have no enough time to assemble together in the process of liquid phase separation, and finally form the dispersive structure. The decrease of cooling rate slows down as droplet diameter exceeds 335 μ m. The cooling rate reduces to about 1.6 × 10 −3 K/s when the droplet diameter is 810 μ m, and the corresponding phase separation time is less than 1 ms. The liquid phase is on the instable condition as the active energy is high (as seen in Figs 2 and 3), thus the macrostructure shows the nubbly Fe-rich monotectic cell morphology which are surrounded by the Cu-rich phases.
In terms of the above analyses, the final structures are determined by the effects of the evolution time, chemical potential stability, surface segregation, cooling rate and Marangoni migration together. On the one hand, the shorter evolution time and the larger cooling rate bring about the dispersed structure. On the other hand, the surface segregation, the longer evolution time and the larger solutal Marangoni migration produce the core-shell structure during liquid phase separation. The two-layer core-shell structure is the most stable morphology because it has the lowest chemical potential.

Actual solute distribution feature
To explore the solute redistribution characteristics during liquid phase separation, the average compositions of the Fe-rich and Cu-rich zones were measured by using EDS method, which are shown in Fig. 5. The EDS analysis results demonstrate that the solutes Cu and Sn are expelled from the Fe-rich core, whereas the Fe solute is rejected from the Cu-rich shell during liquid phase separation for alloy droplets with 188~646 μ m diameters. Furthermore, the macroscopic solute redistribution indicates the depletion of Sn concentration in the Fe-rich core and its enrichment in the Cu-rich shell. Figure 5(a) illustrates the average compositions of two different zones designated in the ternary Fe-Cu-Sn diagram, where the average composition of the Fe-rich core is marked as point C 1 and the average composition of the Cu-rich shell is marked as point C 2 . Obviously, the droplet solidification process of undercooled Fe 47.5 Cu 47.5 Sn 5 alloy involves two stages: the prior solidification of the Fe-rich core and the subsequent solidification of the Cu-rich shell. As seen in Fig. 5(b), the average Sn content of solidified Fe-rich core maintains a roughly constant value of about 1.4 at%Sn, while its average Cu content varies in the range of 13.2 ~ 17.0 at%Cu. With the decrease of droplet diameter, the average Fe content of solidified Cu-rich shell reduces from 43.7 to 28.7 at%Fe, but its average Sn content increases slightly from 4.8 to 8.3 at%Sn, which is shown in Fig. 5(c).
The actual solute distribution of primary α Fe phase in Fe-rich zone and that of (Cu) phase at Cu-rich zone were measured by EDS analysis, which are illustrated in Fig. 5(d,e). Figure 5(d) shows that the Cu solubility in primary α Fe phase is 14.8 at% Cu at droplet diameter D = 810 μ m. It slowly decreases at first with the decrease of droplet diameter and then increases until the largest value of 22 at% Cu at D = 66 μ m. A similar tendency from 6.9 to 5.9 at% Fe with decrease of droplet diameter is demonstrated in Fig. 5(e) for the Fe solubility in (Cu) phase. It is clear that the solute contents in the largest 810 μ m droplet and the smallest 66 μ m droplet are higher than those in other droplets displaying macrosegregation indicating that more solutes can be absorbed in the dispersed phases.
It should be noticed that the solute Sn content in the (Cu) phase is much larger than that in the primary α Fe phase, indicating that the (Cu) phase has a stronger affinity with the solute Sn, which is shown in Fig. 5(d,e). In the primary α Fe phase, the maximum content of Sn exhibits a sluggish increase from 1.3 to 1.4 at% Sn when the droplet diameters reduce from 810 to 188 μ m, then it rapidly increases to 2.4 at% Sn at D = 66 μ m, which is much smaller than the initial concentration of 5 at% Sn. In the (Cu) phase, the solubility of Sn is 6.9 at% at D = 810 μ m. Subsequently, it shows the rising tendency with the decrease of droplet diameters. When the droplet diameter decreases to 66 μ m, the solubility of Sn increases to 8.4 at% Sn.

Conclusion
In conclusion, the containerless rapid solidification inside drop tube provides an efficient access to modulate or control the liquid phase separation of high-temperature metallic alloys. As for ternary Fe 47.5 Cu 47.5 Sn 5 alloy, there appear three different kinds of phase separation patterns: monotectic cell, core shell and dispersed structures which are formed successively with the decrease of droplet diameter. The monotectic cell microstructure results from the combined effects of the moderate undercooling in the regime of 51 ~ 196 K, the short period of phase separation time less than 0.6 ms caused by the early nucleation of primary γ Fe phase, and the slow Marangoni migration velocity below 528 nm/s. The 3D phase field simulation discloses that the two-layer core shell structure is the most stable phase separation pattern, since it corresponds to the state with the lowest chemical potential. Such a macroscopically separated pattern requires a substantial undercooling over 196 K, a long period of phase separation time above 10 ms, and a rapid Marangoni migration velocity close to 1mm/s. Besides, the surface segregation effect is also a driving factor to yield core-shell structure. Although those smallest alloy droplets with less than 200 μ m diameters may achieve the largest undercoolings and the highest Marangoni migration velocities, their very rapid cooling rates of 10 4 ~ 10 5 K/s allows for too short a period of liquid phase separation time. Consequently the initial phase separation configuration is quenched and "frozen down" to form the dispersed microstructures. Owing to the reduced gravity of 10 −3 g 0 during free fall, the Stokes motion contributes very little to the evolution of liquid phase separation. As revealed by EDS analyses, the Sn solute partition profiles of Fe-rich core and Cu-rich shell vary only slightly with droplet diameter in core-shell structures. But the solute trapping effect becomes rather conspicuous for the dispersed microstructures.