Applied Physics A

, Volume 113, Issue 3, pp 763–770

Correlated process of phase separation and microstructure evolution of ternary Co-Cu-Pb alloy


  • N. Yan
    • Department of Applied PhysicsNorthwestern Polytechnical University
  • W. L. Wang
    • Department of Applied PhysicsNorthwestern Polytechnical University
  • S. B. Luo
    • Department of Applied PhysicsNorthwestern Polytechnical University
  • L. Hu
    • Department of Applied PhysicsNorthwestern Polytechnical University
    • Department of Applied PhysicsNorthwestern Polytechnical University

DOI: 10.1007/s00339-013-7586-6

Cite this article as:
Yan, N., Wang, W.L., Luo, S.B. et al. Appl. Phys. A (2013) 113: 763. doi:10.1007/s00339-013-7586-6


The phase separation and rapid solidification of liquid ternary Co45Cu42Pb13 immiscible alloy have been investigated under both bulk undercooling and containerless processing conditions. The undercooled bulk alloy is solidified as a vertical two-layer structure, whereas the containerlessly solidified alloy droplet is characterized by core-shell structures. The dendritic growth velocity of primary α(Co) phase shows a power-law relation to undercooling and achieves a maximum of 1.52 m/s at the undercooling of 112 K. The Pb content is always enriched in Cu-rich zone and depleted in Co-rich zone. Numerical analyses indicate that the Stokes motion, solutal Marangoni convection, thermal Marangoni convection, and interfacial energy play the main roles in the correlated process of macrosegregation evolution and microstructure formation.

1 Introduction

As one of the most important phase transformation phenomena, phase separation is commonly observed in various condensed matter systems such as polymers, oxides, and metallic alloys [13]. Especially for metallic alloys, the phase separation process of immiscible alloy melts has attracted extensive research both theoretically and experimentally in relevant fields for several decades [4, 5]. Such alloys provide an effective approach to the development of novel advanced composite materials applied to self-lubricating bearings and high electrical conductivity devices [6]. The properties of these alloys are determined, to a great extent, by their solidification mechanism and final microstructure. A uniformly dispersive structure is expected to form under microgravity condition or during rapid solidification due to the suppression of gravity-dependent phenomena such as buoyancy-driven convection. However, the removal of the effect of gravity alone cannot insure a dispersive structure for immiscible alloys, but induce the formation of various morphologies [7]. Many gravity independent factors, such as thermocapillary convection, the minimization of interfacial energy between immiscible liquids [7] and the preferential wetting of container wall by one of the liquid phases [8] may also cause migration, coalescence, and massive segregation of immiscible liquids.

The dendritic growth within undercooled immiscible alloy melts has also drawn more and more attention due to its potential technological applications [9, 10]. When bulk undercooling becomes large, the dendrite growth velocity is usually enhanced and the solidification kinetics is far from equilibrium condition. The related nonequilibrium effects have been studied by many researchers for simple alloys [11]. Similarly, the phase separation of binary immiscible alloys has been extensively investigated [8]. In contrast, the research on ternary immiscible alloys has been mainly focused on some simple systems [12]. Further investigations remain to be done on the phase separation and dendrite growth mechanisms of more complicated ternary immiscible alloys. The Co-Cu based alloy, which is characteristic of metastable phase separation has been widely investigated owing to their excellent giant magnetoresistance (GMR) properties [13]. In order to control the phase separation and solidification microstructure of the alloy, different third elements have been introduced to binary Co-Cu alloy systems [14]. The objective of this work is to investigate the macrosegregation formation and microstructure evolution mechanisms of ternary Co-Cu-Pb immiscible alloy under both bulk undercooling and containerless processing conditions. Special attention is also paid to the dendritic growth of primary α(Co) phase within undercooled ternary Co45Cu42Pb13 immiscible alloy.

2 Experimental methods

The bulk samples were prepared from the high purity elements Co (99.95 %), Cu (99.999 %), and Pb (99.999 %). Co and Cu were primarily melted in an arc-melting furnace and then melted together with Pb by induction heating under the protection of B2O3 fluxing agent in argon atmosphere. Each sample had the mass of 1 g and was contained in an 8 mm internal diameter × 10 mm outer diameter × 12 mm length alumina crucible together with a suitable amount of 70 % B2O3 + 20 % Na2B4O7 + 10 % CaF2 fluxing agent. The vacuum chamber was evacuated to 2×10−4 Pa and then backfilled with argon gas until 105 Pa. The sample was melted and superheated to 200∼300 K above its liquidus temperature. After being maintained at the overheating state for 3∼5 min, the sample was cooled naturally by switching off the induction heating power. Its heating and cooling curves were recorded by an infrared pyrometer, while the dendrite growth velocity during rapid solidification was measured with an infrared photodiode device.

As an alternative approach to achieve rapid solidification, the bulk alloy melt was atomized into a series of tiny droplets with diameters from 100 to 800 μm. These alloy droplets fell freely inside a 3 m drop tube [7] and were solidified in a containerless state. After the experiments, the solidified samples were sectioned, polished, and then etched with a solution of 5 g FeCl3 + 10 ml HCl + 50 ml H2O for about 8 s. The phase constitution and solute distribution of the solidified alloy were examined with Rigaku D/max 2500 X-ray diffractometer and Oxford INCA Energy 300 energy dispersive spectrometer, respectively. Their microstructural morphologies were analyzed with a Zeiss Axiovert 200MAT optical microscope and FEI Sirion 200 scanning electron microscope.

3 Results and discussion

3.1 Macrosegregation formation and dendritic growth under bulk undercooled condition

The chemical composition of Co45Cu42Pb13 alloy locates near the middle line between Co and Cu vertexes in the composition triangle of ternary Co-Cu-Pb alloy system, as illustrated in Fig. 1(a). X-ray diffraction (XRD) analyses are performed to determine the phase constitution of Co45Cu42Pb13 alloy, since the Co-Cu-Pb ternary phase diagram has not been available. It is revealed that the solidification microstructure of this alloy is evidently composed of α(Co), (Cu), and (Pb) solid solution phases with fcc crystal structures under both free fall and bulk undercooled conditions. There are no new phases formed in ternary Co45Cu42Pb13 alloy as compared with the three related binary phase diagrams.
Fig. 1

Schematic of alloy composition selection and phase separation process of ternary Co45Cu42Pb13 alloy: (a) alloy location in Co-Cu-Pb composition triangle, (b) solute contents of Cu-rich zone versus droplet diameter, and (c) solute contents of Co-rich zone versus droplet diameter

The bulk undercooling of liquid immiscible alloy is usually defined as the temperature difference ΔT between its liquidus temperature TL and the nucleation temperature TN of primary solid phase, that is ΔT=TLTN. The liquidus temperature of Co45Cu42Pb13 alloy is determined to be 1628 K according to the heating curves. Figure 2(a) shows the typical cooling curves of undercooled bulk alloy. It is found that this immiscible alloy is quite difficult to undercool. A maximum undercooling of ΔT=112 K (0.07TL) has been achieved by ternary Co45Cu42Pb13 immiscible alloy in the present work. Since alloy samples were naturally cooled without quenching, their cooling rates Rc were only 11∼18 K/s. The cooling rates corresponding to the three curves (I, II, III) are 13, 15, 11 K/s, respectively. In such a case, the liquid immiscible alloy was kept in the undercooled state for a time period of 2.7∼6.4 s.
Fig. 2

Typical cooling curves of bulk Co45Cu42Pb13 alloy and dendritic growth velocity of primary α(Co) phase: (a) cooling curves corresponding to different undercoolings, and (b) dendritic growth velocity versus undercooling

Figure 3 presents the typical macrosegregation pattern and microstructure morphology of bulk undercooled ternary Co45Cu42Pb13 immiscible alloy with an undercooling of 112 K. Apparently, liquid phase separation has taken place and leads to the formation of two segregated zones. As seen in Fig. 3(b), the boundary between Co-rich zone which floats up to sample top and Cu-rich zone, which settles down to sample bottom becomes more smooth and round if compared with that undercooled by 30 K. This is mainly caused by the longer phase separation time between the initiation of phase separation and the nucleation of primary α(Co) phase during solidification. After the completion of macroscopic phase separation in liquid ternary Co45Cu42Pb13 immiscible alloy, the Co-rich and Cu-rich zones solidify according to different routes when the temperature decreases. Firstly, the Co-rich zone solidifies and its microstructure is shown in Fig. 3(c). It is characterized by the dendritic growth of primary α(Co) phase, which has a grain size of about 5∼10 μm. Then the (Cu) phase nucleats and distributes among the interdendritic spacings of α(Co) dendrites, leaving some small particles of (Pb) phase formed at the grain boundaries of α(Co) and (Cu) phases. Subsequently, the α(Co) phase nucleates and grows in the Cu-rich liquid phase. Later on, the majority of remnant alloy melt in the Cu-rich zone solidifies in the way just like peritectic reaction, that is α(Co)+L→(Cu), forming large amounts of (Cu) phase surrounding the primary α(Co) phase. Finally, the (Pb) phase solidifies around the existing (Cu) phases, as presented in Fig. 3(d). The primary α(Co) phase is always separated by the (Cu) phase from the (Pb) phase. Besides, EDS analysis shows that the alloy melt separates into a Co-rich zone with the composition Co85.9Cu13.9Pb0.2 (designated as point B1) and a Cu-rich zone with the composition Co3.7Cu71.9Pb24.4 (marked as point B2), as shown in Fig. 1(a).
Fig. 3

Macrosegregation and microstructure of bulk Co45Cu42Pb13 alloy undercooled by 112 K undercooling: (a) macrosegregation pattern; (b) microstructure near segregation boundary; (c) microstructure of Co-rich zone, and (d) microstructure of Cu-rich zone

It is shown that the solidification process of Co-rich zone is characterized by the dendritic growth of primary α(Co) phase. In order to explore the kinetic mechanism of rapid dendritic growth, the growth velocity of primary α(Co) phase is measured as a function of undercooling, and the result is presented in Fig. 2(b). With the increase of undercooling, the dendrite growth velocity increases. At the small undercooling of 30 K, the dendritic growth velocity is merely 0.86 m/s. As bulk undercooling increases to 112 K, the primary α(Co) phase grows at a velocity of 1.52 m/s. A power relation is derived from fitting the dendrite growth velocity V with respect to bulk undercooling ΔT:
$$ V = 0.82 + 5.1 \times 10^{ - 4}\Delta T^{1.7} $$
As a comparison, the growth velocity of α(Co) phase dendrite in binary Co81.2Cu18.8 alloy [13] was also plotted in Fig. 2(b). Obviously, the dendritic growth velocity of the primary α(Co) phase in undercooled Co45Cu42Pb13 ternary alloy is much slower than that in binary Co81.2Cu18.8 alloy at the same undercooling level. The above results indicate that the introduction of Pb element has reduced the growth velocity of α(Co) phase. Similarly, the addition of Ni element can also reduce the growth velocity of α(Co) phase [14]. However, the undercooling range obtained in the experiment of bulk Co-Cu-Pb alloy is much smaller. This indicates that the undercoolability of Co-Cu-Ni alloy is much larger than that of Co-Cu-Pb alloy. Within the undercooling range achieved in Co-Cu-Pb alloy, the growth velocity of α(Co) phase increases monotonously with the enhancement of undercooling. In Co-Cu-Ni alloy, the growth velocity of (Co) phase firstly increases and then decreases with the increase of melt undercooling within the large undercooling range.

3.2 Phase separation and microstructure evolution during free fall

Typical solidification microstructures of Co45Cu42Pb13 alloy droplets solidified under the free fall condition inside drop tube are shown in Fig. 4. It shows two typical morphologies observed in the solidified droplets: one is the core-shell structure, and the other is the dispersed structure. Figures 4(a) and (b) presents two different macroscopic core-shell morphologies obtained in the droplets with diameters of 800 μm and 250 μm, respectively. In the case of Fig. 4(a), it appears that a large Co-rich sphere, which contains many small Cu-rich spheres is located in the central part of the droplet, and a Cu-rich layer surrounds the Co-rich sphere. The other one is the triple-layer core-shell structure in Fig. 4(b), consisting of a large Co-rich core, a thin (Cu) phase layer formed at the Co-rich core surface, and a Cu-rich shell layer. With the further decrease of droplet diameter, the microstructure of droplets transforms into a pattern of Co-rich particles distributed in the Cu-rich zone, as demonstrated in Fig. 4(c).
Fig. 4

Microstructure evolution of Co45Cu42Pb13 alloy droplets solidified during free fall: (a) two-layer core/shell structure; (b) three-layer core/shell structure, and (c) dispersed microstructure

To have a clear understanding of the solute redistribution characteristics in rapidly solidified Co45Cu42Pb13 alloy droplets, EDS analysis was used. The average compositions of Co-rich and Cu-rich zones are demonstrated in Figs. 1(b) and (c). It is shown that the content of solute elements in liquid phases decreases with the reduction of droplet diameter. When the droplet diameter is 800 μm, the Co and Pb solute contents in Cu-rich zones are 9.2 and 14.9 at%, respectively. With the decrease of droplet diameter, the solubilities of Co and Pb in Cu-rich zones reduce to 5.8 and 14.1 at% in the droplet with a diameter of 200 μm. Also, in the Co-rich zone, the Cu and Pb solute contents display a declining variation of 36.2–27.2 at% Cu and 2.5–1.5 at% Pb when the droplet diameter changes from 800 to 200 μm. The Pb element content is always rich in the Cu-rich zone and poor in Co-rich zone. As is clearly seen in Fig. 1(a), in the droplet with diameter of 800 μm, the alloy melt separates into a Co-rich zone with the composition Co61.3Cu36.2Pb2.5 (designated as point C1) and a Cu-rich zone with the composition Co9.2Cu75.9Pb14.9 (marked as point C2). Similarly, in an alloy droplet of 200 μm diameter, the alloy melt is separated into a Co-rich zone with the composition Co71.3Cu27.2Pb1.5 (designated as point D1) and a Cu-rich zone with the composition Co5.8Cu80.1Pb14.1 (marked as point D2). It should also be noticed that the solubility of Pb in Cu-rich zone is almost five times larger than that in Co-rich zone, indicating that Pb element has a stronger affinity with the Cu liquid and a repulsive behavior with the Co liquid.

As it is very difficult to measure the actual temperature and undercooling of tiny droplets during free fall inside a drop tube, theoretical estimations are performed by the Newtonian heat transfer model [7]. Evidently, the cooling rate of alloy droplets increases when droplet size reduces. The range of cooling rate Rc in the solidified droplets varies from 1.5×103 to 4.3×104 K/s in the droplets with diameter of 120∼800 μm, as shown in Fig. 5(a). In fact, the estimated calculation results of cooling rate demonstrate that the structure transition from core-shell to dispersive structure in the alloy droplets is essentially caused by rapid solidification during free fall.
Fig. 5

Calculated cooling rate and liquid-liquid interfacial energy: (a) cooling rate versus time and (b) interfacial energy versus temperature

3.3 Dynamic characteristics of phase separation process

In order to explain the distribution of the above three elements in different zones, the interfacial energies among the Co-, Cu-, and Pb-rich liquids are roughly evaluated, where the three phases are assumed to coexist in the liquid state. Cahn and Hilliad [15] developed a model for calculating the interfacial energy of nonuniform systems that display solid or liquid immiscibility. The expression for the interfacial energy σLL between two immiscible liquids takes the following form:
$$ \sigma_{\mathrm{LL}} = 1.2N_{\mathrm{v}}\lambda k_{\mathrm{B}}T_{\mathrm{c}}\biggl(1 - \frac{T}{T_{\mathrm{c}}}\biggr)^{1.22} $$
where Nv is the number of atoms per unit volume, Nv=ρ0NA/M,NA the Avogadro constant, M the atomic mass, ρ0 the liquid phase density, λ the atomic interaction distance, and was taken to be \(a_{0}/\sqrt{3}\) for nearest-neighbor interactions, a0 the interatomic distance, kB the Boltzmann constant, Tc the critical temperature of the liquid-miscibility gap. The physical parameters used for calculations are listed in Table 1, which have been derived from [16].
Table 1

Physical parameters for evaluating the interfacial energies of immiscible liquids








ρ0/103 kg m−3




Critical temperature





Interatomic distances

a0/10−10 m




Interaction distance

λ/10−10 m




aThe value for each X–Y system is linearly fitted according to Neumann–Kopp’s rule for liquid alloy composition of X50Y50 at melting point

In calculation, the (Co), (Cu), and (Pb) phases are taken as f.c.c. crystal structures. Figures 5(b) shows the calculated results of interfacial energies between pseudobinary liquid phases of Co-Cu, Cu-Pb, and Co-Pb systems in respective miscibility gaps [17, 18]. The interfacial energy is zero at each critical temperatures and increases with the decrease of temperature. The interfacial energy between the Co-Pb system is much larger than that of Cu-Pb and Co-Cu systems. This means that the Pb-rich liquid has a weak wettability with the Co-rich liquid if the Co-, Cu-, and Pb-rich liquids can coexist in the ternary system at a certain temperature. Thus, Pb element tends to exist in the Cu-rich liquid and is always isolated from (Co) phase by a thin layer of (Cu) phase.

During the phase separation process under glass fluxing and free fall conditions, the movement of dispersed globules of ternary Co45Cu42Pb13 alloy is mainly governed by Stokes motion and Marangoni migration. Within the field of gravitational force, Stokes motion induced by the buoyancy-driven convection is a dominating effect during the solidification of immiscible alloys. The one with higher density tends to descend inside alloy droplet under the influence of gravity. Stokes motion velocity Vs is expressed as [7, 19]
$$ V_{\mathrm{s}} = \frac{2( \rho_{2} - \rho {}_{1} )}{3\eta_{1}}\frac{( \eta_{1} + \eta_{2} )}{( 2\eta_{1} + 3\eta_{2} )}gr^{2} $$
where ρ1 and ρ2 are the density of the matrix and dispersive phase, η1 and η2 the viscosity of the matrix and dispersive phases, respectively, r is the radius of a single globule, g the residual gravitational acceleration, while g0=9.8 m s−2 is the gravitational acceleration under normal condition.
The Stokes motion velocity of Cu-rich liquid globules in alloy samples under different gravity levels is shown in Fig. 6(a). In the undercooled bulk alloy under normal gravity condition, the Cu-rich liquid globule with a radius of 20 μm will settle down at a velocity of 158 μm s−1. However, in the alloy droplet solidifying under reduced gravity condition, the Vs value of Cu-rich globule with the radius of 20 μm is 0.21 μm s−1. This is about three orders of magnitude smaller than that of bulk alloy solidified under normal condition. Therefore, Cu-rich globules rapidly descend to the bottom and Co-rich globules remain in the top area under normal gravity condition. It is also demonstrated that Stokes migration is significantly suppressed in the phase separation process during free fall under reduced gravity condition. Stokes motion is the major dynamic mechanism during the formation of vertical macrosegregation patterns under normal gravity condition in the undercooled bulk alloy.
Fig. 6

Stokes motion velocity and Marangoni migration velocity versus Cu-rich globule radius: (a) Stokes motion velocity under different gravity conditions, and (b) Marangoni migration velocity in different alloy droplets

In comparison with Stokes motion, Marangoni migration is classified into two types. One type is thermal Marangoni migration, which is caused by the temperature gradient in the droplets. Such migration will cause minor liquid phases to move towards the droplet center. The thermal Marangoni migration velocity VMt of a single globule in such a state is given by [7, 19]
$$ V_{\mathrm{Mt}} = - \frac{2k_{1}\nabla \sigma_{t}}{(2k_{1} + k_{2})(2\eta_{1} + 3\eta_{3})}r $$
$$ \nabla\sigma_{t} = \frac{\partial \sigma_{\mathrm{LL}}}{\partial T} \cdot\frac{\partial T}{\partial R} $$
here, k1 and k2 are the thermal conductivities of the matrix and dispersive phases, ∇σt is the interfacial energy gradient caused by temperature field, ∂σLL/∂T is the temperature-dependent coefficients of interfacial energy, whereas ∂T/∂R refers to the temperature gradient within alloy droplet in radial direction.
The other type is the solutal Marangoni migration, which is induced by the concentration gradient inside alloy droplet. The solutal Marangoni migration velocity VMc of a single globule can be expressed by [20]:
$$ V_{\mathrm{Mc}} = - \frac{2D_{1}\nabla \sigma_{\mathrm{c}}}{(2D_{1} + D_{2})(2\eta_{1} + 3\eta_{2})}r $$
where D1 and D2 are the solute diffusion coefficients of the matrix and dispersive phases. ∇σc is the interfacial energy gradient resulting from concentration distribution. Since ternary Co45Cu42Pb13 alloy contains two solutes of Cu and Pb, the ∇σc term consists of the following two terms:
$$ \nabla\sigma_{\mathrm{c}} = \frac{\partial \sigma_{\mathrm{LL}}}{\partial C_{\mathrm{Cu}}} \cdot\frac{\partial C_{\mathrm{Cu}}}{\partial R} + \frac{\partial \sigma_{\mathrm{LL}}}{\partial C_{\mathrm{Pb}}} \cdot\frac{\partial C_{\mathrm{Pb}}}{\partial R} $$
CCu and CPb represent the concentrations of the solute elements in alloy droplet. Clearly, ∂σ/∂CCu and ∂σ/∂CPb are the concentration-dependent coefficients of interfacial energy, and ∂CCu/∂R and ∂CPb/∂R are the corresponding concentration gradients of alloy droplet in radial direction. The physical parameters used in calculations are listed in Table 2 [16].
Table 2

Physical parameters of two different alloy droplets

Physical parameter


D=200 μm

D=800 μm

Thermal conductivity of Co-rich liquid phase, k1 (W m−1 K−1)



Thermal conductivity of Cu-rich liquid phase, k2 (W m−1 K−1)



Viscosity of Co-rich liquid phase, η1 (Pa s−1)



Viscosity of Cu-rich liquid phase, η2 (Pa s−1)



Density of Co-rich liquid phase, ρ1 (kg m−3)



Density of Cu-rich liquid phase, ρ2 (kg m−3)



The calculated results for the above two types of Marangoni migrations of Cu-rich globules are demonstrated in Fig. 6(b). The Cu-rich globule with a radius of 20 μm displays a thermal Marangoni migration velocity of 0.52 mm s−1 within the alloy droplet of 800 μm diameter. In contrast, it migrates at a solutal Marangoni migration velocity of 16.8 mm s−1, which is about thirty times as large as the thermal Marangoni migration velocity. Since a smaller alloy droplet with 200 μm diameter maintains a larger temperature and concentration gradients [7], the corresponding thermal and solutal Marangoni convections propel a Cu-rich globule of 20 μm radius to migrate at velocities as high as 0.86 and 40.3 mm s−1, respectively. It is noteworthy that the solutal Marangoni migration velocity is much larger than thermal Marangoni migration velocity within the alloy droplet during phase separation. And the above two Marangoni migration velocities of Cu-rich globules are about three to five orders of magnitude larger than the Stokes motion velocities. Solutal Marangoni migration can completely dominate the phase separation process inside freely falling alloy droplets. Under such conditions, the Cu-rich liquid globules mostly accumulate at the droplet surface, forming a Cu-rich shell layer surrounding the Co-rich core. Therefore, Marangoni convection contributes significantly to the phase separation and structure evolution of ternary Co45Cu42Pb13 immiscible alloy under free fall condition.

4 Conclusions

The rapid solidification and macrosegregation pattern of ternary Co45Cu42Pb13 immiscible alloy were investigated experimentally under both bulk undercooling and containerless processing conditions. The main points are summarized as follows:
  1. (1)

    The solidification microstructure is always composed of α(Co), (Cu) and (Pb) solid solution phases. The undercooling of bulk alloy varies from 30 to 112 K at the cooling rate of 11∼18 K/s. In contrast, the cooling rate of alloy droplets attains 1.5×103 to 4.3×104 K/s in drop tube.

  2. (2)

    The macrosegregation pattern of the undercooled bulk alloy solidified under glass fluxing condition shows a vertical two-layer structure, which is composed of a top Co-rich zone and a bottom Cu-rich zone. As a comparison, the containerlessly solidified alloy droplets in drop tube are mainly characterized by two- or three-layer core-shell structures, where the Co-rich zone is located at droplet center and the Cu-rich shell surrounds the Co-rich core.

  3. (3)

    The measured dendritic growth velocity of primary α(Co) phase increases with the enhancement of undercooling by a power relation, which achieves a maximum value of 1.52 m/s at the undercooling of 112 K.

  4. (4)

    The Pb solute has a stronger affinity with Cu-rich liquid and a repulsive behavior with Co-rich liquid, which is mainly caused by the high interfacial energy within Co-Pb system.

  5. (5)

    Stokes motion is the major dynamic mechanism of Cu-rich globules during the phase separation of undercooled bulk alloy. However, it is significantly suppressed and the solutal Marangoni convection becomes the dominant role in the macrosegregation formation process during the containerless rapid solidification inside drop tube.



The authors are grateful to Dr. W.J. Xie, Dr. H.P. Wang, Mr. J. Chang, and Mr. S.S. Xu for their help with the experiments and helpful discussion. This work was financially supported by National Natural Science Foundation of China under Grant Nos. 50971105 and 51101123, and the Fundamental Research Fund of Northwestern Polytechnical University under Grant No. JC20110278.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013