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Evolution kinetics of microgravity facilitated spherical macrosegregation within immiscible alloys
Journal of Alloys and Compounds 763 (2018) 808e814
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Evolution kinetics of microgravity facilitated spherical macrosegregation within immiscible alloys Y.H. Wu, W.L. Wang, J. Chang, B. Wei* Department of Applied Physics, Northwestern Polytechnical University, Xi'an 710072, PR China
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Article history: Received 18 December 2017 Received in revised form 22 April 2018 Accepted 2 June 2018 Available online 4 June 2018
The evolution kinetics of microgravity facilitated spherical macrosegregation within model Fe-Cu immiscible alloys has been systematically investigated by drop tube experiments and 3D phase-field simulations. In microgravity environment, liquid phase separation of Fe-Cu alloys induced the appearance of spherical macrosegregation patterns with various core-shell structures. The formation probability and evolution characteristics of these phase-separated core-shell morphologies depended on the volume fraction of surface active Cu-rich liquid together with the cooling rate. As the cooling rate decreased, the duration time of phase separation extended and the formed dispersed structures showed a tendency to form as core-shell structures influenced by the effects of Marangoni convection and surface segregation. Meanwhile, core grew larger while the shell became thinner. The occurrence probability of spherical macrosegregation firstly increased and then decreased with the rise in the copper concentration, and core-shell morphologies changed from three-layer to two-layer which was accompanied by core shrinkage and shell thickening. © 2018 Elsevier B.V. All rights reserved.
Keywords: Phase separation Microstructure Metals and alloys Rapid solidification Simulation and modeling
1. Introduction The properties of immiscible alloys are strongly dependent on their macrosegregation characteristics [1e6]. By modulating the liquid phase separation processes in these immiscible alloys, various macrosegregation patterns have been obtained [7e14]. During conventional solidification, Stokes sedimentation dominates the liquid phase separation process and facilitates the formation of a layered macrosegregation structure [10e14]. As the solidification process of immiscible alloys is performed in microgravity, the gravity effects on the phase separation are considerably weakened [3,5,7], and the Marangoni convection [10,15,16] becomes the key factor to control the movement of the two coexisting liquids. This induces the appearance of two typical macrosegregation patterns, namely a core-shell structure and a dispersed structure [3,17e23]. To date, the formation mechanisms of these macrosegregation patterns have been sufficiently discussed based on both experiments and simulations [3,5,7,10e14,17e19,23]. During the phase separation, the liquid phase with a larger density sinks while the
* Corresponding author. E-mail address: [email protected] (B. Wei). https://doi.org/10.1016/j.jallcom.2018.06.022 0925-8388/© 2018 Elsevier B.V. All rights reserved.
other liquid phase floats upward under the effect of Stokes motion [3,5,7,10,23]. Owing to the surface segregation, the liquid phase with a lower surface energy tends to move toward the sample surface and forms a surface segregation layer [5]. In contrast, Marangoni convection contributes to the migration of minor phase globules from the low-temperature regions to the relatively highertemperature regions [3]. We believe that the cooling rate, the volume fraction variation and the surface free energy with respect to the two-coexisting immiscible liquids greatly influence the liquid phase separation process and even alter the final macrosegregation configuration, especially within the microgravity environment. The attention to this research is not very significant due to the limited opportunity for, and high cost of, a space experiment. Because of that, at present the evolution kinetics of microgravity facilitated spherical macrosegregation for immiscible alloys is not completely understood within the broad ranges of both alloy compositions and cooling rates. After selecting three model alloys with compositions Fe65Cu35, Fe50Cu50 and Fe35Cu65 as shown in Fig. 1(a) [24], we set the purpose of this work as to study in a threedimensional regime the phase separation kinetics and
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Fig. 1. Solidification mechanisms of Fe-Cu alloy droplets inside a drop tube: (a) two zones of solidification mechanism selection, (b) typical solidification microstructures, (c) calculated cooling rate Rc versus droplet diameter D.
microstructure evolution mechanisms in the reduced-gravity experiments inside a drop tube [25] and through the phase-field simulations [3]. 2. Methodology 2.1. Drop tube experiment Drop tube experiments of liquid Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloys were conducted to clarify the effects of alloy compositions and cooling rates on the liquid phase separation kinetics under microgravity conditions. These master alloys were prepared from high purity elements of iron (99.999%) and copper (99.99%) in a high vacuum arc-melting furnace. Each sample with a mass of approximately 3 g was placed inside a quartz tube with a 16 mm diameter, a 150 mm length and a small orifice at the bottom. After loading, the quartz tube was installed on the top of a high vacuum chamber in the drop tube facility. Before the experiments, the vacuum chamber was evacuated to 3.0 105 Pa and backfilled with He cooling gas. Subsequently, induction heating was used to melt the alloy sample, and the molten alloy was dispersed into many alloy droplets from the orifice of the quartz tube by the jetting gas. As a consequence, these alloy droplets fell and rapidly solidified in the containerless and reduced-gravity environment. The solidified alloy droplets were mounted, polished and etched by a solution composed of 5 g FeCl3 þ 5 mL HCl þ 20 mL H2O. The microstructures were analysed with a Zeiss Axiovert 200 MAT optical microscope and a FEI Sirion electron microscope. The phase
constitution was investigated by an Oxford INCA Energy 300 energy-dispersive spectrometer.
2.2. Phase-field simulation The metastable phase separation and microstructure evolution for liquid Fe-Cu immiscible alloys were explored theoretically using a three-dimensional phase-field model. This model considers the phase separation influenced by the effects of surface segregation and Marangoni convection [3,16]. In this model, the free energy function of the Fe-Cu alloy droplet was simulated by
F ¼ Fb þ Fg þ Fs
(1)
where F is the total Gibbs free energy, and Fb, Fg and Fs represent the bulk free energy, the free energy of the concentration gradient and the surface free energy [3], respectively. Furthermore, the value of this free energy function varies with the spatial coordinates r, the evolutionary time t, and the mole concentration C. The dimensionless concentration-field governing equation can be expressed as
vC dF V$ðnCÞ þ V$x ¼ V$ Cð1 CÞV vt dC
(2)
where C is the mole concentration of Cu, t is the evolution time, v is the local velocity and x is the random Gaussian white noise. The definitions of physical symbols can be found elsewhere [3]. The
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concentration-field governing equation was supplemented with the following boundary conditions:
n$VCjr¼R ¼ 0
(3)
n$V
dF ¼0 dC r¼R
(4)
where n denotes the normal direction at the droplet surface. In a microgravity environment, surface segregation and Marangoni convection mainly dominate the phase separation. The surface segregation term is taken into account in the free energy function F. To introduce the effects of Marangoni convection into this 3D model, the temperature-field information of Fe-Cu alloy droplets should be clarified, especially the radial temperature gradient. The temperature-field characteristics can be understood by solving the following heat transfer equation.
vT v2 T 2 vT ¼ aT þ vt vr 2 r vr
!
Tðr; 0Þ ¼ T0 k
vT jr¼R ¼ εh sSB Ts4 Te4 þ hðTs Te Þ vr
(5)
Based on the heat transfer model in Section 2.2, the cooling rate Rc of Fe-Cu alloy droplets in the drop tube experiments can be calculated accordingly. The physical parameters used in the calculations were taken from Ref. [27]. In contrast with the droplet-size effects, the effect of the copper concentration on the cooling rate was so small that it was ignored. Taking the Fe65Cu35 alloy as an example, the droplet cooling rate Rc was estimated as a function of droplet diameter D, and the obtained results are plotted in Fig. 1(c). It can be seen that the cooling rate increases rapidly with a reduction in droplet size. Furthermore, the cooling rate of the smallest alloy droplet is almost two orders of magnitude higher than that of the largest alloy droplet. As mentioned above, metastable phase separation will occur if the droplet diameter decreases below a threshold value. Since the duration of the metastable phase separation is closely related to the droplet cooling rate, the dynamic characteristics of the phase separation are strongly dependent on the droplet cooling rate. The evolution of various phase-separated morphologies with increasing cooling rate will be sufficiently clarified in the following sections. 3.2. Formation ability of spherical macrosegregation
(6) (7)
where T is the temperature, aT is the thermal diffusivity, k is the heat conductivity, εh is the emissivity, sSB is the Stefan-Boltzmann constant, h is the heat transfer coefficient, and T0, Te and Ts are the initial temperature, the environment temperature and the droplet surface temperature, respectively. Equations (5)e(7) roughly describe the droplet heat dissipation prior to the phase separation. Although the possible effects from the phase separation and fluid flow inside the small droplets were ignored, they were still helpful for exploring the evolution kinetics of spherical macrosegregation in microgravity [5]. 3. Results and discussion 3.1. Two solidifying zones in the Fe-Cu phase diagram During free fall, liquid Fe-Cu alloys rapidly solidified in the form of numerous droplets with various sizes. Previous investigations demonstrated that the undercooling of tiny alloy droplets is closely related to the droplet diameter, and a smaller alloy droplet generally undergoes a larger undercooling [7]. As the alloy droplet diameter decreases below a critical value, liquid Fe-Cu alloys can be undercooled into the metastable miscibility gap and a conspicuous phase separation occurs. To experimentally determine the critical diameter Dc for the occurrence of metastable phase separation (MPS), the evolution of the solidification microstructure with droplet size was analysed based on metallographic observations. It can be seen that peritectic solidification microstructures tend to form for large alloy droplets, whereas the phase-separated morphologies tend to be preserved for small alloy droplets. The critical diameters for the MPS occurrence were 245, 1175 and 597 mm for Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloy droplets, respectively, as shown in Fig. 1(a). Considering the Fe65Cu35 alloy as an example in Fig. 1(b), it can be observed that near-equilibrium peritectic solidification proceeds in the large diameter regime above Dc, whereas metastable phase separation occurs if the droplet diameter is smaller than Dc. In addition, non-equilibrium peritectic solidification may be favoured when Fe-Cu alloy droplets are sufficiently small [26].
During drop tube experiments, the metastable liquid phase separation of Fe-Cu alloy droplets resulted in the appearance of two typical phase-separated morphologies. One is a core-shell structure (i.e, spherical macrosegregation) and the other is a dispersed structure. In microgravity, the appearance probability of spherical macrosegregation can be used to represent its formation ability to some extent. The formation probabilities of typical phase-separated morphologies for Fe-Cu alloy droplets were statistically measured as a function of the cooling rate Rc, as shown in Fig. 2. Here, the formation probabilities of core-shell and dispersed phaseseparated morphologies were defined as
PðCSÞ ¼ NðCSÞ=ðNðCSÞ þ NðDSÞÞ
(8)
PðDSÞ ¼ NðDSÞ=ðNðCSÞ þ NðDSÞÞ
(9)
where N(CS) and N(DS) denote the numbers of alloy droplets with the core-shell and dispersed phase-separated morphologies, respectively, and P(CS) and P(DS) are the corresponding formation probabilities. For every alloy composition, the formation probability P for the core-shell structure monotonously increases as the droplet cooling rate Rc is lowered, as shown in Fig. 2(a). In contrast, the P variation of the dispersed structure with Rc shows the opposite phenomenon, as shown in Fig. 2(b). This result implies that the small cooling rate contributes significantly to the formation of the core-shell microstructure. In addition, the formation probability P of the core-shell structure for the Fe50Cu50 alloy is always largest compared with the Fe65Cu35 and Fe35Cu65 alloys in the studied cooling rate range. This result demonstrates that it is much easier for the Fe50Cu50 alloy to develop core-shell structures than the Fe65Cu35 and Fe35Cu65 alloys. 3.3. Characteristic variation of spherical macrosegregation The spherical core-shell microstructures could be classified into three types according to their layer numbers: two-layer core-shell (CS-2), three-layer core-shell (CS-3) and multilayer core-shell (CSM, M 4), as shown in Fig. 3(a). Interestingly, multilayer core-shell (CS-M, M 4) structures were only observed for the Fe50Cu50 alloy, and their formation probability was 5.8%. The phase-separated core-shell morphologies mainly appeared as two-layer and threelayer structures. Subsequently, special attention was paid to
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Fig. 2. Formation probabilities P of typical phase-separated morphologies for undercooled Fe-Cu alloy droplets versus droplet cooling rate Rc: (a) core-shell structure, (b) dispersed structure.
Fig. 3. Evolution characteristics of phase-separated core-shell morphologies for Fe-Cu alloy droplets versus cooling rate Rc: (a) characteristic parameter definition, (b) core radius, (c) surface shell thickness, (d) middle shell thickness.
exploring the evolution characteristics of phase-separated coreshell morphologies versus the cooling rate for Fe-Cu alloy droplets, as shown in Fig. 3(b)-3(d). In the present work, the reduced radius (rc ¼ r/R) of the core, the reduced thickness (dsc ¼ ds/R) of the surface shell and the reduced thickness (dmc ¼ dm/R) of the middle shell were adopted to understand the evolution characteristics of core-shell morphologies with the variation of the cooling rate Rc. Here, ds is the surface shell thickness, dm is the middle shell thickness, r is the core radius and R is the alloy droplet radius. It can be clearly seen that the core radius and the shell thickness are closely related to the cooling rate Rc. With the enhancement of the cooling rate Rc, the core radius becomes smaller, and the shell thickness trends upward. In such a case, the migration of minor phase globules to the droplet centre to form a core is more difficult due to the limited migration time, and the core size gradually decreases, irrespective of alloy compositions. Meanwhile, the shell becomes more conspicuous, which suggests that the high cooling rate
accelerates the growth of the surface segregation during the phase separation [5,28]. In addition, the core-shell morphology characteristics are greatly influenced by the alloy composition. As the copper content for Fe-Cu alloys is enhanced, the reduced thickness of the surface shell increases, while the reduced radius of the core displays the opposite trend. 3.4. Evolution kinetics of spherical macrosegregation To reveal the phase separation kinetics of these Fe-Cu alloy droplets, typical phase separation processes were reproduced by the 3D phase-field model, and the numerical results are shown in Fig. 4(a)e(c). For the Fe65Cu35 and Fe35Cu65 alloy droplets, the minority liquid phase is always separated from the parent liquid phase in the form of tiny globules. These globules collide and coalesce to form larger ones, as shown in Fig. 4(a1)-(a2) and Fig. 4(c1)-(c2). On the other hand, a bicontinuous (BC) liquid phase develops within
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Fig. 4. Phase-field simulation and microgravity experimental confirmation of liquid phase separation for undercooled Fe-Cu alloy droplets inside a drop tube: (aec) liquid phase separation of Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloys, (d) layer number and critical time for core-shell formation. Here, the symbols of NPS, CS-2 and CS-3 denote no phase separation, two-layer and three-layer core-shell (CS) structures, respectively.
the Fe50Cu50 alloy droplet, in which each phase forms a continuous interconnected structure, as illustrated in Fig. 4(b2). Owing to the Marangoni convection induced by the temperature gradient between the droplet centre and surface, second-phase globules in Fig. 4(a) and (c) migrate to the higher-temperature region at the droplet centre and form a core, while the bicontinuous phase aggregates along the radial direction and then forms a series of ringlike morphologies. Because of the surface energy difference between the Fe-rich and Cu-rich liquids, the Cu solute continuously migrates towards the droplet surface and subsequently forms a surface segregation layer for every composition of the Fe-Cu alloy. With the continuation of phase separation, the microstructure morphologies of Fe65Cu35 alloy droplets experience an evolution from a homogeneous dispersed structure to a multicore-shell (MCS) structure and then to a three-layer core-shell (CS-3) structure. The phase-separated morphologies of Fe35Cu65 alloy droplets transform from a dispersed (DS) structure into a multicore (MC) structure and a two-layer core-shell (CS-2) structure. In contrast, the binary Fe50Cu50 alloy droplet undergoes a series of metastable and intermediate morphologies, including a homogeneous dispersed (DS) structure, a bicontinuous (BC) structure, a core-shell structure with more than three layers (CS-M, M 4) and a threelayer core-shell (CS-3) structure. In fact, these three-layer core-
shell (CS-3) structures require a very long time to evolve into stable two-layer core-shell (CS-2) structures. With the aid of computer simulations, the corresponding experimental evidence for the phase-separated morphology evolution can be found and is provided in Fig. 4(a)-4(c). EDS analyses show that the light colour represents the Cu-rich zone and the dark colour denotes the Fe-rich zone. When the droplet size increases, the droplet cooling rate rapidly decreases, and the phase separation time remarkably extends [3]. As a result, the phase-separated morphology usually experiences an evolution from a dispersed (DS) structure to an intermediate (IS) structure and then to a coreshell (CS) structure. For the Fe65Cu35 alloy, DS is characterized by many Cu-rich globules randomly dispersed within the Fe-rich matrix, as shown in Fig. 4(a1). The IS and CS display multicoreshell (MCS) and three-layer core-shell (CS-3) morphologies, as shown in Fig. 4(a2) and 4(a3), respectively. With the rise in the copper content, the DS of Fe50Cu50 appears as numerous Fe-rich globules dispersed inside the Cu-rich matrix, as presented in Fig. 4(b1), and the IS and CS show a bicontinuous (BC) morphology and a CS-3 morphology, respectively, as shown in Fig. 4(b2) and 4(b3). If the copper content is far greater than the iron content, the DS of Fe35Cu65 is very similar to that of Fe50Cu50. The only difference between them is that the volume fraction of Fe-rich globules is
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remarkably reduced. With the enhancement of the droplet size, these globules begin to aggregate and finally form a multicore (MC) structure composed of three Fe-rich cores and a Cu-rich matrix, as shown in Fig. 4(c2). Once these Fe-rich cores further aggregate, a two-layer core-shell (CS-2) structure forms in the end, as demonstrated in Fig. 4(c3). Since CS-3 structures require a long period of time to evolve into most stable CS-2 structures, those CS-2 structures are sometimes preserved within the Fe65Cu35 and Fe50Cu50 alloy droplets, but their formation probabilities are very low in contrast with CS-3 structures. Thus, the 3D numerical simulations are in good agreement with the experimental observations. According to the Fe-Cu phase diagram, phase separation occurs for an alloy composition range of approximately 10 at.% ~90 at.% Cu. To clarify the composition effects on the phase separation kinetics, the phase separation kinetics of Fe-C0 at.% Cu (10 C0 90) alloy droplets were studied using 3D phase-field simulations. Fig. 4(d1) shows the calculated layer number of core-shell phase-separated morphologies as a function of the alloy composition C0. As the FeCu alloy droplets possess 10e60 at.% Cu, they usually form threelayer core-shell (CS-3) structures. Assuming that the copper content varies from 60 to 90 at.%, a two-layer core-shell (CS-2) structure tends to form in the end. Compared with experimental results, the numerical calculations are basically consistent with the experimental results in both this work and Refs. [19,26], which verifies the validity of this 3D phase-field model in predicting the phase separation kinetics within a microgravity environment. Fig. 4(d2) shows the critical time for core-shell formation as a function of alloy composition C0. In the small C0 regime below 50 at.% Cu, the critical time for core-shell formation during the phase separation shortens with the rise in C0, which implies that the core-shell formation ability is gradually enhanced. When C0 increases to 50 at.% Cu, the critical time for core-shell formation attains the smallest value of approximately 60 ms, and the coreshell formation ability becomes the strongest. Once C0 rises above the threshold value, the critical time of core-shell formation starts to display an upward trend. This result suggests that the core-shell formation ability gradually weakens. These calculated results are in accord with the experimental results in Fig. 2(a). In view of the phase-field simulations, the effects of the cooling rate and alloy composition on the phase-separated morphology evolution can be further understood. When the cooling rate Rc decreases, the phase separation proceeds for a longer period of time, and the dynamic condition for core-shell formation is easier to achieve. In such a case, the dispersed structure at the beginning of liquid phase separation first transforms into an intermediate structure and finally evolves into a core-shell structure. When the initial copper content C0 of Fe-Cu alloys is enhanced in the small C0 regime below 50 at.% Cu, the volume fractions of separated Cu-rich and Fe-rich liquids are more suitable for the development of coreshell structures. The thermodynamic condition for core-shell formation becomes easier to meet in this case, and the formation probability of the CS structure increases greatly. If C0 increases beyond this value, then satisfying the thermodynamic condition of core-shell formation becomes more difficult, and the dispersed structure is more easily formed. Thus, the thermodynamic and dynamic conditions for core-shell formation (CSF) are the dominant factors that drive the phase-separated morphology evolution in microgravity. Because both Fe-Cu and Co-Cu alloys belong to peritectic systems with a large positive mixing enthalpy [26,29,30], they usually undergo metastable phase separation when the alloy melts are undercooled into their miscibility gaps. Under normal gravity conditions (such as DSC experiments [29,30]), metastable liquid phase separation sometimes occurs and then facilitates the formation of steamed-bun-like macrosegregation with a core-type
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structure under the effects of Stokes motion and surface segregation. Furthermore, the core seriously deviates away from the sample centre. Within the microgravity environment, liquid phase separation is mainly dominated by the surface segregation and Marangoni convection. This contributes to the development of spherical core-shell phase-separated morphologies with good symmetry. Compared with those observed during DSC [29] or glass fluxing [30] experiments of Fe-Cu and Co-Cu alloys, both the phase separation kinetics and the phase-separated morphologies in microgravity show significant differences, such as the dynamic mechanisms responsible for liquid phase separation, sample shape, and core-shell macrosegregation characteristics. Thus, the present work can shed light on the use of the liquid phase separation processes in microgravity to design and prepare more complicated core-shell structures for potential applications. 4. Conclusions In summary, the phase separation and microstructure evolution for liquid Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloy droplets were investigated via drop tube experiments and phase field simulations. The phase-separated morphologies of Fe65Cu35 alloy droplets were mainly characterized by a dispersed structure and a multicore-shell structure at small droplet diameters and by a three-layer core-shell structure at large droplet diameters. With the rise in droplet size, the phase-separated morphologies of Fe50Cu50 alloy droplets transitioned from a dispersed structure to a bicontinuous structure and finally to a three-layer core-shell structure. In contrast, large droplets of Fe35Cu65 alloy tended to form a multicore or a two-layer core-shell structure, while the small alloy droplets preferentially displayed a dispersed structure. With a reduction in the droplet size, the droplet cooling rate rapidly rose, and the core and shell became smaller and thicker, respectively. Numerical calculations showed that both the alloy composition and the phase separation time greatly influence the phase separation kinetics and microstructure evolution mechanisms. With the continuation of liquid phase separation, the phase-separated morphology experienced a transition of dispersed structures / intermediate structures / core-shell structures. Meanwhile, the dynamic condition for coreshell formation was easier to achieve in this case, and core-shell structures occurred more frequently. In the small C0 regime below 50 at.% Cu, the thermodynamic condition for core-shell formation became easier to meet if the initial content C0 of component Cu increased. Once C0 exceeded 50 at.% Cu, satisfying the thermodynamic condition of core-shell formation became more difficult and preserving the dispersed structure became much easier. Acknowledgements The authors are very grateful to Mr. X.P. Qin and Ms. S. Sha for their help with the experiments. This work is financially supported by the National Natural Science Foundation of China (51327901, 5177154 and 51571163, 51401167). References [1] F. Abdeljawad, P. Lu, N. Argibay, B.G. Clark, B.L. Boyce, S.M. Foiles, Grain boundary segregation in immiscible nanocrystalline alloys, Acta Mater. 126 (2017) 528e539. [2] A. Bachmaier, J. Schmauch, H. Aboulfadl, A. Verch, C. Motz, On the process of co-deformation and phase dissolution in a hard-soft immiscible Cu-Co alloy system during high-pressure torsion deformation, Acta Mater. 115 (2016) 333e346. [3] Y.H. Wu, W.L. Wang, Z.C. Xia, B. Wei, Phase separation and microstructure evolution of ternary Fe-Sn-Ge immiscible alloy under microgravity condition, Comput. Mater. Sci. 103 (2015) 179e188. [4] F.T.N. Vüllers, R. Spolenak, From solid solutions to fully phase separated
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Evolution kinetics of microgravity facilitated spherical macrosegregation within immiscible alloys Y.H. Wu, W.L. Wang, J. Chang, B. Wei* Department of Applied Physics, Northwestern Polytechnical University, Xi'an 710072, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2017 Received in revised form 22 April 2018 Accepted 2 June 2018 Available online 4 June 2018
The evolution kinetics of microgravity facilitated spherical macrosegregation within model Fe-Cu immiscible alloys has been systematically investigated by drop tube experiments and 3D phase-field simulations. In microgravity environment, liquid phase separation of Fe-Cu alloys induced the appearance of spherical macrosegregation patterns with various core-shell structures. The formation probability and evolution characteristics of these phase-separated core-shell morphologies depended on the volume fraction of surface active Cu-rich liquid together with the cooling rate. As the cooling rate decreased, the duration time of phase separation extended and the formed dispersed structures showed a tendency to form as core-shell structures influenced by the effects of Marangoni convection and surface segregation. Meanwhile, core grew larger while the shell became thinner. The occurrence probability of spherical macrosegregation firstly increased and then decreased with the rise in the copper concentration, and core-shell morphologies changed from three-layer to two-layer which was accompanied by core shrinkage and shell thickening. © 2018 Elsevier B.V. All rights reserved.
Keywords: Phase separation Microstructure Metals and alloys Rapid solidification Simulation and modeling
1. Introduction The properties of immiscible alloys are strongly dependent on their macrosegregation characteristics [1e6]. By modulating the liquid phase separation processes in these immiscible alloys, various macrosegregation patterns have been obtained [7e14]. During conventional solidification, Stokes sedimentation dominates the liquid phase separation process and facilitates the formation of a layered macrosegregation structure [10e14]. As the solidification process of immiscible alloys is performed in microgravity, the gravity effects on the phase separation are considerably weakened [3,5,7], and the Marangoni convection [10,15,16] becomes the key factor to control the movement of the two coexisting liquids. This induces the appearance of two typical macrosegregation patterns, namely a core-shell structure and a dispersed structure [3,17e23]. To date, the formation mechanisms of these macrosegregation patterns have been sufficiently discussed based on both experiments and simulations [3,5,7,10e14,17e19,23]. During the phase separation, the liquid phase with a larger density sinks while the
* Corresponding author. E-mail address: [email protected] (B. Wei). https://doi.org/10.1016/j.jallcom.2018.06.022 0925-8388/© 2018 Elsevier B.V. All rights reserved.
other liquid phase floats upward under the effect of Stokes motion [3,5,7,10,23]. Owing to the surface segregation, the liquid phase with a lower surface energy tends to move toward the sample surface and forms a surface segregation layer [5]. In contrast, Marangoni convection contributes to the migration of minor phase globules from the low-temperature regions to the relatively highertemperature regions [3]. We believe that the cooling rate, the volume fraction variation and the surface free energy with respect to the two-coexisting immiscible liquids greatly influence the liquid phase separation process and even alter the final macrosegregation configuration, especially within the microgravity environment. The attention to this research is not very significant due to the limited opportunity for, and high cost of, a space experiment. Because of that, at present the evolution kinetics of microgravity facilitated spherical macrosegregation for immiscible alloys is not completely understood within the broad ranges of both alloy compositions and cooling rates. After selecting three model alloys with compositions Fe65Cu35, Fe50Cu50 and Fe35Cu65 as shown in Fig. 1(a) [24], we set the purpose of this work as to study in a threedimensional regime the phase separation kinetics and
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Fig. 1. Solidification mechanisms of Fe-Cu alloy droplets inside a drop tube: (a) two zones of solidification mechanism selection, (b) typical solidification microstructures, (c) calculated cooling rate Rc versus droplet diameter D.
microstructure evolution mechanisms in the reduced-gravity experiments inside a drop tube [25] and through the phase-field simulations [3]. 2. Methodology 2.1. Drop tube experiment Drop tube experiments of liquid Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloys were conducted to clarify the effects of alloy compositions and cooling rates on the liquid phase separation kinetics under microgravity conditions. These master alloys were prepared from high purity elements of iron (99.999%) and copper (99.99%) in a high vacuum arc-melting furnace. Each sample with a mass of approximately 3 g was placed inside a quartz tube with a 16 mm diameter, a 150 mm length and a small orifice at the bottom. After loading, the quartz tube was installed on the top of a high vacuum chamber in the drop tube facility. Before the experiments, the vacuum chamber was evacuated to 3.0 105 Pa and backfilled with He cooling gas. Subsequently, induction heating was used to melt the alloy sample, and the molten alloy was dispersed into many alloy droplets from the orifice of the quartz tube by the jetting gas. As a consequence, these alloy droplets fell and rapidly solidified in the containerless and reduced-gravity environment. The solidified alloy droplets were mounted, polished and etched by a solution composed of 5 g FeCl3 þ 5 mL HCl þ 20 mL H2O. The microstructures were analysed with a Zeiss Axiovert 200 MAT optical microscope and a FEI Sirion electron microscope. The phase
constitution was investigated by an Oxford INCA Energy 300 energy-dispersive spectrometer.
2.2. Phase-field simulation The metastable phase separation and microstructure evolution for liquid Fe-Cu immiscible alloys were explored theoretically using a three-dimensional phase-field model. This model considers the phase separation influenced by the effects of surface segregation and Marangoni convection [3,16]. In this model, the free energy function of the Fe-Cu alloy droplet was simulated by
F ¼ Fb þ Fg þ Fs
(1)
where F is the total Gibbs free energy, and Fb, Fg and Fs represent the bulk free energy, the free energy of the concentration gradient and the surface free energy [3], respectively. Furthermore, the value of this free energy function varies with the spatial coordinates r, the evolutionary time t, and the mole concentration C. The dimensionless concentration-field governing equation can be expressed as
vC dF V$ðnCÞ þ V$x ¼ V$ Cð1 CÞV vt dC
(2)
where C is the mole concentration of Cu, t is the evolution time, v is the local velocity and x is the random Gaussian white noise. The definitions of physical symbols can be found elsewhere [3]. The
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concentration-field governing equation was supplemented with the following boundary conditions:
n$VCjr¼R ¼ 0
(3)
n$V
dF ¼0 dC r¼R
(4)
where n denotes the normal direction at the droplet surface. In a microgravity environment, surface segregation and Marangoni convection mainly dominate the phase separation. The surface segregation term is taken into account in the free energy function F. To introduce the effects of Marangoni convection into this 3D model, the temperature-field information of Fe-Cu alloy droplets should be clarified, especially the radial temperature gradient. The temperature-field characteristics can be understood by solving the following heat transfer equation.
vT v2 T 2 vT ¼ aT þ vt vr 2 r vr
!
Tðr; 0Þ ¼ T0 k
vT jr¼R ¼ εh sSB Ts4 Te4 þ hðTs Te Þ vr
(5)
Based on the heat transfer model in Section 2.2, the cooling rate Rc of Fe-Cu alloy droplets in the drop tube experiments can be calculated accordingly. The physical parameters used in the calculations were taken from Ref. [27]. In contrast with the droplet-size effects, the effect of the copper concentration on the cooling rate was so small that it was ignored. Taking the Fe65Cu35 alloy as an example, the droplet cooling rate Rc was estimated as a function of droplet diameter D, and the obtained results are plotted in Fig. 1(c). It can be seen that the cooling rate increases rapidly with a reduction in droplet size. Furthermore, the cooling rate of the smallest alloy droplet is almost two orders of magnitude higher than that of the largest alloy droplet. As mentioned above, metastable phase separation will occur if the droplet diameter decreases below a threshold value. Since the duration of the metastable phase separation is closely related to the droplet cooling rate, the dynamic characteristics of the phase separation are strongly dependent on the droplet cooling rate. The evolution of various phase-separated morphologies with increasing cooling rate will be sufficiently clarified in the following sections. 3.2. Formation ability of spherical macrosegregation
(6) (7)
where T is the temperature, aT is the thermal diffusivity, k is the heat conductivity, εh is the emissivity, sSB is the Stefan-Boltzmann constant, h is the heat transfer coefficient, and T0, Te and Ts are the initial temperature, the environment temperature and the droplet surface temperature, respectively. Equations (5)e(7) roughly describe the droplet heat dissipation prior to the phase separation. Although the possible effects from the phase separation and fluid flow inside the small droplets were ignored, they were still helpful for exploring the evolution kinetics of spherical macrosegregation in microgravity [5]. 3. Results and discussion 3.1. Two solidifying zones in the Fe-Cu phase diagram During free fall, liquid Fe-Cu alloys rapidly solidified in the form of numerous droplets with various sizes. Previous investigations demonstrated that the undercooling of tiny alloy droplets is closely related to the droplet diameter, and a smaller alloy droplet generally undergoes a larger undercooling [7]. As the alloy droplet diameter decreases below a critical value, liquid Fe-Cu alloys can be undercooled into the metastable miscibility gap and a conspicuous phase separation occurs. To experimentally determine the critical diameter Dc for the occurrence of metastable phase separation (MPS), the evolution of the solidification microstructure with droplet size was analysed based on metallographic observations. It can be seen that peritectic solidification microstructures tend to form for large alloy droplets, whereas the phase-separated morphologies tend to be preserved for small alloy droplets. The critical diameters for the MPS occurrence were 245, 1175 and 597 mm for Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloy droplets, respectively, as shown in Fig. 1(a). Considering the Fe65Cu35 alloy as an example in Fig. 1(b), it can be observed that near-equilibrium peritectic solidification proceeds in the large diameter regime above Dc, whereas metastable phase separation occurs if the droplet diameter is smaller than Dc. In addition, non-equilibrium peritectic solidification may be favoured when Fe-Cu alloy droplets are sufficiently small [26].
During drop tube experiments, the metastable liquid phase separation of Fe-Cu alloy droplets resulted in the appearance of two typical phase-separated morphologies. One is a core-shell structure (i.e, spherical macrosegregation) and the other is a dispersed structure. In microgravity, the appearance probability of spherical macrosegregation can be used to represent its formation ability to some extent. The formation probabilities of typical phase-separated morphologies for Fe-Cu alloy droplets were statistically measured as a function of the cooling rate Rc, as shown in Fig. 2. Here, the formation probabilities of core-shell and dispersed phaseseparated morphologies were defined as
PðCSÞ ¼ NðCSÞ=ðNðCSÞ þ NðDSÞÞ
(8)
PðDSÞ ¼ NðDSÞ=ðNðCSÞ þ NðDSÞÞ
(9)
where N(CS) and N(DS) denote the numbers of alloy droplets with the core-shell and dispersed phase-separated morphologies, respectively, and P(CS) and P(DS) are the corresponding formation probabilities. For every alloy composition, the formation probability P for the core-shell structure monotonously increases as the droplet cooling rate Rc is lowered, as shown in Fig. 2(a). In contrast, the P variation of the dispersed structure with Rc shows the opposite phenomenon, as shown in Fig. 2(b). This result implies that the small cooling rate contributes significantly to the formation of the core-shell microstructure. In addition, the formation probability P of the core-shell structure for the Fe50Cu50 alloy is always largest compared with the Fe65Cu35 and Fe35Cu65 alloys in the studied cooling rate range. This result demonstrates that it is much easier for the Fe50Cu50 alloy to develop core-shell structures than the Fe65Cu35 and Fe35Cu65 alloys. 3.3. Characteristic variation of spherical macrosegregation The spherical core-shell microstructures could be classified into three types according to their layer numbers: two-layer core-shell (CS-2), three-layer core-shell (CS-3) and multilayer core-shell (CSM, M 4), as shown in Fig. 3(a). Interestingly, multilayer core-shell (CS-M, M 4) structures were only observed for the Fe50Cu50 alloy, and their formation probability was 5.8%. The phase-separated core-shell morphologies mainly appeared as two-layer and threelayer structures. Subsequently, special attention was paid to
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Fig. 2. Formation probabilities P of typical phase-separated morphologies for undercooled Fe-Cu alloy droplets versus droplet cooling rate Rc: (a) core-shell structure, (b) dispersed structure.
Fig. 3. Evolution characteristics of phase-separated core-shell morphologies for Fe-Cu alloy droplets versus cooling rate Rc: (a) characteristic parameter definition, (b) core radius, (c) surface shell thickness, (d) middle shell thickness.
exploring the evolution characteristics of phase-separated coreshell morphologies versus the cooling rate for Fe-Cu alloy droplets, as shown in Fig. 3(b)-3(d). In the present work, the reduced radius (rc ¼ r/R) of the core, the reduced thickness (dsc ¼ ds/R) of the surface shell and the reduced thickness (dmc ¼ dm/R) of the middle shell were adopted to understand the evolution characteristics of core-shell morphologies with the variation of the cooling rate Rc. Here, ds is the surface shell thickness, dm is the middle shell thickness, r is the core radius and R is the alloy droplet radius. It can be clearly seen that the core radius and the shell thickness are closely related to the cooling rate Rc. With the enhancement of the cooling rate Rc, the core radius becomes smaller, and the shell thickness trends upward. In such a case, the migration of minor phase globules to the droplet centre to form a core is more difficult due to the limited migration time, and the core size gradually decreases, irrespective of alloy compositions. Meanwhile, the shell becomes more conspicuous, which suggests that the high cooling rate
accelerates the growth of the surface segregation during the phase separation [5,28]. In addition, the core-shell morphology characteristics are greatly influenced by the alloy composition. As the copper content for Fe-Cu alloys is enhanced, the reduced thickness of the surface shell increases, while the reduced radius of the core displays the opposite trend. 3.4. Evolution kinetics of spherical macrosegregation To reveal the phase separation kinetics of these Fe-Cu alloy droplets, typical phase separation processes were reproduced by the 3D phase-field model, and the numerical results are shown in Fig. 4(a)e(c). For the Fe65Cu35 and Fe35Cu65 alloy droplets, the minority liquid phase is always separated from the parent liquid phase in the form of tiny globules. These globules collide and coalesce to form larger ones, as shown in Fig. 4(a1)-(a2) and Fig. 4(c1)-(c2). On the other hand, a bicontinuous (BC) liquid phase develops within
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Fig. 4. Phase-field simulation and microgravity experimental confirmation of liquid phase separation for undercooled Fe-Cu alloy droplets inside a drop tube: (aec) liquid phase separation of Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloys, (d) layer number and critical time for core-shell formation. Here, the symbols of NPS, CS-2 and CS-3 denote no phase separation, two-layer and three-layer core-shell (CS) structures, respectively.
the Fe50Cu50 alloy droplet, in which each phase forms a continuous interconnected structure, as illustrated in Fig. 4(b2). Owing to the Marangoni convection induced by the temperature gradient between the droplet centre and surface, second-phase globules in Fig. 4(a) and (c) migrate to the higher-temperature region at the droplet centre and form a core, while the bicontinuous phase aggregates along the radial direction and then forms a series of ringlike morphologies. Because of the surface energy difference between the Fe-rich and Cu-rich liquids, the Cu solute continuously migrates towards the droplet surface and subsequently forms a surface segregation layer for every composition of the Fe-Cu alloy. With the continuation of phase separation, the microstructure morphologies of Fe65Cu35 alloy droplets experience an evolution from a homogeneous dispersed structure to a multicore-shell (MCS) structure and then to a three-layer core-shell (CS-3) structure. The phase-separated morphologies of Fe35Cu65 alloy droplets transform from a dispersed (DS) structure into a multicore (MC) structure and a two-layer core-shell (CS-2) structure. In contrast, the binary Fe50Cu50 alloy droplet undergoes a series of metastable and intermediate morphologies, including a homogeneous dispersed (DS) structure, a bicontinuous (BC) structure, a core-shell structure with more than three layers (CS-M, M 4) and a threelayer core-shell (CS-3) structure. In fact, these three-layer core-
shell (CS-3) structures require a very long time to evolve into stable two-layer core-shell (CS-2) structures. With the aid of computer simulations, the corresponding experimental evidence for the phase-separated morphology evolution can be found and is provided in Fig. 4(a)-4(c). EDS analyses show that the light colour represents the Cu-rich zone and the dark colour denotes the Fe-rich zone. When the droplet size increases, the droplet cooling rate rapidly decreases, and the phase separation time remarkably extends [3]. As a result, the phase-separated morphology usually experiences an evolution from a dispersed (DS) structure to an intermediate (IS) structure and then to a coreshell (CS) structure. For the Fe65Cu35 alloy, DS is characterized by many Cu-rich globules randomly dispersed within the Fe-rich matrix, as shown in Fig. 4(a1). The IS and CS display multicoreshell (MCS) and three-layer core-shell (CS-3) morphologies, as shown in Fig. 4(a2) and 4(a3), respectively. With the rise in the copper content, the DS of Fe50Cu50 appears as numerous Fe-rich globules dispersed inside the Cu-rich matrix, as presented in Fig. 4(b1), and the IS and CS show a bicontinuous (BC) morphology and a CS-3 morphology, respectively, as shown in Fig. 4(b2) and 4(b3). If the copper content is far greater than the iron content, the DS of Fe35Cu65 is very similar to that of Fe50Cu50. The only difference between them is that the volume fraction of Fe-rich globules is
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remarkably reduced. With the enhancement of the droplet size, these globules begin to aggregate and finally form a multicore (MC) structure composed of three Fe-rich cores and a Cu-rich matrix, as shown in Fig. 4(c2). Once these Fe-rich cores further aggregate, a two-layer core-shell (CS-2) structure forms in the end, as demonstrated in Fig. 4(c3). Since CS-3 structures require a long period of time to evolve into most stable CS-2 structures, those CS-2 structures are sometimes preserved within the Fe65Cu35 and Fe50Cu50 alloy droplets, but their formation probabilities are very low in contrast with CS-3 structures. Thus, the 3D numerical simulations are in good agreement with the experimental observations. According to the Fe-Cu phase diagram, phase separation occurs for an alloy composition range of approximately 10 at.% ~90 at.% Cu. To clarify the composition effects on the phase separation kinetics, the phase separation kinetics of Fe-C0 at.% Cu (10 C0 90) alloy droplets were studied using 3D phase-field simulations. Fig. 4(d1) shows the calculated layer number of core-shell phase-separated morphologies as a function of the alloy composition C0. As the FeCu alloy droplets possess 10e60 at.% Cu, they usually form threelayer core-shell (CS-3) structures. Assuming that the copper content varies from 60 to 90 at.%, a two-layer core-shell (CS-2) structure tends to form in the end. Compared with experimental results, the numerical calculations are basically consistent with the experimental results in both this work and Refs. [19,26], which verifies the validity of this 3D phase-field model in predicting the phase separation kinetics within a microgravity environment. Fig. 4(d2) shows the critical time for core-shell formation as a function of alloy composition C0. In the small C0 regime below 50 at.% Cu, the critical time for core-shell formation during the phase separation shortens with the rise in C0, which implies that the core-shell formation ability is gradually enhanced. When C0 increases to 50 at.% Cu, the critical time for core-shell formation attains the smallest value of approximately 60 ms, and the coreshell formation ability becomes the strongest. Once C0 rises above the threshold value, the critical time of core-shell formation starts to display an upward trend. This result suggests that the core-shell formation ability gradually weakens. These calculated results are in accord with the experimental results in Fig. 2(a). In view of the phase-field simulations, the effects of the cooling rate and alloy composition on the phase-separated morphology evolution can be further understood. When the cooling rate Rc decreases, the phase separation proceeds for a longer period of time, and the dynamic condition for core-shell formation is easier to achieve. In such a case, the dispersed structure at the beginning of liquid phase separation first transforms into an intermediate structure and finally evolves into a core-shell structure. When the initial copper content C0 of Fe-Cu alloys is enhanced in the small C0 regime below 50 at.% Cu, the volume fractions of separated Cu-rich and Fe-rich liquids are more suitable for the development of coreshell structures. The thermodynamic condition for core-shell formation becomes easier to meet in this case, and the formation probability of the CS structure increases greatly. If C0 increases beyond this value, then satisfying the thermodynamic condition of core-shell formation becomes more difficult, and the dispersed structure is more easily formed. Thus, the thermodynamic and dynamic conditions for core-shell formation (CSF) are the dominant factors that drive the phase-separated morphology evolution in microgravity. Because both Fe-Cu and Co-Cu alloys belong to peritectic systems with a large positive mixing enthalpy [26,29,30], they usually undergo metastable phase separation when the alloy melts are undercooled into their miscibility gaps. Under normal gravity conditions (such as DSC experiments [29,30]), metastable liquid phase separation sometimes occurs and then facilitates the formation of steamed-bun-like macrosegregation with a core-type
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structure under the effects of Stokes motion and surface segregation. Furthermore, the core seriously deviates away from the sample centre. Within the microgravity environment, liquid phase separation is mainly dominated by the surface segregation and Marangoni convection. This contributes to the development of spherical core-shell phase-separated morphologies with good symmetry. Compared with those observed during DSC [29] or glass fluxing [30] experiments of Fe-Cu and Co-Cu alloys, both the phase separation kinetics and the phase-separated morphologies in microgravity show significant differences, such as the dynamic mechanisms responsible for liquid phase separation, sample shape, and core-shell macrosegregation characteristics. Thus, the present work can shed light on the use of the liquid phase separation processes in microgravity to design and prepare more complicated core-shell structures for potential applications. 4. Conclusions In summary, the phase separation and microstructure evolution for liquid Fe65Cu35, Fe50Cu50 and Fe35Cu65 alloy droplets were investigated via drop tube experiments and phase field simulations. The phase-separated morphologies of Fe65Cu35 alloy droplets were mainly characterized by a dispersed structure and a multicore-shell structure at small droplet diameters and by a three-layer core-shell structure at large droplet diameters. With the rise in droplet size, the phase-separated morphologies of Fe50Cu50 alloy droplets transitioned from a dispersed structure to a bicontinuous structure and finally to a three-layer core-shell structure. In contrast, large droplets of Fe35Cu65 alloy tended to form a multicore or a two-layer core-shell structure, while the small alloy droplets preferentially displayed a dispersed structure. With a reduction in the droplet size, the droplet cooling rate rapidly rose, and the core and shell became smaller and thicker, respectively. Numerical calculations showed that both the alloy composition and the phase separation time greatly influence the phase separation kinetics and microstructure evolution mechanisms. With the continuation of liquid phase separation, the phase-separated morphology experienced a transition of dispersed structures / intermediate structures / core-shell structures. Meanwhile, the dynamic condition for coreshell formation was easier to achieve in this case, and core-shell structures occurred more frequently. In the small C0 regime below 50 at.% Cu, the thermodynamic condition for core-shell formation became easier to meet if the initial content C0 of component Cu increased. Once C0 exceeded 50 at.% Cu, satisfying the thermodynamic condition of core-shell formation became more difficult and preserving the dispersed structure became much easier. Acknowledgements The authors are very grateful to Mr. X.P. Qin and Ms. S. Sha for their help with the experiments. This work is financially supported by the National Natural Science Foundation of China (51327901, 5177154 and 51571163, 51401167). References [1] F. Abdeljawad, P. Lu, N. Argibay, B.G. Clark, B.L. Boyce, S.M. Foiles, Grain boundary segregation in immiscible nanocrystalline alloys, Acta Mater. 126 (2017) 528e539. [2] A. Bachmaier, J. Schmauch, H. Aboulfadl, A. Verch, C. Motz, On the process of co-deformation and phase dissolution in a hard-soft immiscible Cu-Co alloy system during high-pressure torsion deformation, Acta Mater. 115 (2016) 333e346. [3] Y.H. Wu, W.L. Wang, Z.C. Xia, B. Wei, Phase separation and microstructure evolution of ternary Fe-Sn-Ge immiscible alloy under microgravity condition, Comput. Mater. Sci. 103 (2015) 179e188. [4] F.T.N. Vüllers, R. Spolenak, From solid solutions to fully phase separated
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