Microstructure formation in centrifugally cast Al–Bi alloys

Computational Materials Science 49 (2010) 121–125

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Microstructure formation in centrifugally cast Al–Bi alloys J.Z. Zhao *, H.L. Li, H.Q. Li, C.Y. Xing, X.F. Zhang, Q.L. Wang, J. He Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

a r t i c l e

i n f o

Article history: Received 25 March 2010 Accepted 24 April 2010 Available online 26 May 2010 Keywords: Immiscible alloy Centrifugal casting Solidification Microstructure evolution Modeling

a b s t r a c t A numerical model describing the microstructure evolution in a centrifugally cast alloy with a miscibility gap in the liquid state is developed. Centrifugal casting experiments were carried out with Al–Bi alloy. The microstructure formation in the centrifugally cast Al–Bi tube was calculated. The calculations demonstrate that generally the moving velocity of the minority phase droplets due to the centrifugal force is much larger compared to the Marangoni migration velocity of the droplets during the liquid–liquid phase transformation. Thus, a layer rich in Bi particles forms on the outside surface and a region poor in Bi particles forms on the inner surface of the centrifugally cast Al–Bi tube. The numerical results show a good agreement with the experimental ones. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Many alloys show a miscibility gap in the liquid state. Some of them are excellent candidates to be used in industry if they form alloys with finely dispersed microstructure. These alloys, however, have an essential drawback that just the miscibility gap, as depicted in Fig. 1, poses problems during solidifications. When an alloy is cooled into the miscibility gap, it develops into two liquids. Generally, the liquid–liquid phase transformation leads to a quick spatial phase separation during the solidification processing on earth. Many efforts have been made to use the demixing phenomenon for the production of the finely dispersed metal–metal composite materials [1–10]. It is demonstrated that the centrifugal casting technique is promising in the manufacturing of immiscible alloys such as Cu–Pb [11]. But up to date, little was done on the theoretical aspect of the microstructure formation in a centrifugal cast immiscible alloy. Thus, we perform centrifugal casting experiments with Al–Bi alloy. A model is presented to describe the microstructure formation. The model is verified by comparing with the experimental results and then used to investigate the kinetic details of the microstructure evolution in the centrifugally cast Al–Bi alloy. 2. Formulations controlling the microstructure evolution Solidification of immiscible alloys is preceded by a large compositional segregation into two liquid phases. The liquid–liquid decomposition begins with the nucleation of the minority phase * Corresponding author. Tel.: +86 024 23971918. E-mail address: [email protected] (J.Z. Zhao). 0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2010.04.034

droplets. These droplets grow then by diffusion of solute in the matrix. They can also move due to the temperature gradient (Marangoni migration) and external force field. Under the concurrent actions of all these factors, the microstructure evolution in a centrifugal cast immiscible alloy is controlled by:

   @f ðR; r; tÞ @ dR 1 @ðudr rf ðR; r; tÞÞ @I  þ f ðR; r; tÞ þ ¼  @t @R dt r @r @R R¼R udr ¼ uM þ uE þ v r @ rL1=L2 @T 2km uM ¼ R ð2gm þ 3gd Þð2km þ kd Þ @T @r uE ¼

2v 2h ðqd  qm Þ gm þ gd R2 3r gm ð2gm þ 3gd Þ

ð1aÞ ð1bÞ ð1cÞ ð1dÞ

where f(R,r,t) is the size distribution function. It is so defined that f(R,r,t)dR gives the number of droplets per unit volume at position r and time t in a size class from droplet radius R to R + dR. I is the is the diffusional growth rate [9]. R* is the critnucleation rate and dR dt ical nucleation radius. udr is the radial vector of the droplet moving velocity. uM is the Marangoni migration velocity of droplets. uE is the droplet moving velocity due to the centrifugal force. vr is the radial vector of the convective flow velocity. gm and gd are the viscosities, qm and qd are the densities, km and kd are the thermal conductivities of the matrix liquid and the droplet, respectively. rL1/L2 is the interfacial tension between the two liquids. T is temperature. vh is the tangential velocity of the melt. In Eq. (1a) the first term describes the time dependence of the distribution function. The second term describes the contribution of the diffusional growth of droplets to the change of the size distribution function. The third term describes the effect of the spatial motions of droplets on the distribution function. The term on the right hand side is the

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Fig. 1. Schematic of phase diagram of the immiscible alloys and microstructure evolution in a centrifugal cast tube.

source term due to nucleation. Generally the process of the liquid– liquid decomposition would also be accompanied by collisions and coagulations of droplets. We did not take these into consideration because the calculation of the collisions and coagulations between droplets is very time consuming. In the case of Al–5 wt%Bi alloy, the volume fraction of minority phase droplets during cooling in the miscibility gap is smaller than 1%. The low volume fraction leads to a wide separation between droplets and thus a low collision probability. The neglect of the effect of collision events may, to our knowledge, causes an error about 10% in the numerical result for the Al–5 wt%Bi alloys cooled at the rate of a few decades K per second.

Considering that the volume fraction of the minority phase droplets is very low for Al–5 wt%Bi alloy, we treated the melt as a single phase liquid in the calculation of the flow field. The flow field of the melt is determined by:

@ q 1 @ðqr v r Þ 1 @ðqv h Þ þ ¼0 þ @r r @h @t r

ð2Þ

@ðqv r Þ 1 @ðqr v r v r Þ 1 @ðqv h v r Þ qv 2h þ þ  @t r @r r  @h  r   1 @ @v r 1 @ @v r 2 @v h @p ¼ g rg þ qg r þ F þ 2  2 g  r @r r @h r @r @r @r @h ð3aÞ

(a) @ðqv h Þ 1 @ðr qv r v h Þ 1 @ðqv h v h Þ qv r v h þ þ þ @t r @r r @h r !     @ @v h 2 @v r 1 @2v h 1 @p rg þ qg h þ 2 g þ 2 g 2  ¼ r@r r r r @h @r @h @h

ð3bÞ

where q and g are the density and viscosity of the alloy, respectively. gr and gh are the radial and tangential vector of the gravitational acceleration, respectively. p is pressure. F is the centrifugal force. Fig. 2 shows the calculated flow field. It indicates that the alloy melt flow mainly in the tangential direction. The radial vector of the flow velocity is negligible small. The temperature and concentration fields are determined by:

(b)

R1   d m 3 @ðqC p TÞ 1 @ @T 4p @½r 0 udr f ðqd C p  qm C p ÞT  R dR ¼ rk  r@r @t r @r @r 3 ð4Þ R1   d m 3 @C 1 @ @S 4p @½r 0 udr f ðC  C Þ  R dR ¼ rD  @t r @r @r 3 r@r

νθ , m/s

3

2

1 36

39

42

45

r, mm Fig. 2. Flow field (a) and tangential velocity (b) of the melt when the mold rotates at the speed of 1000 rpm.

ð5Þ

where Cp and k are the specific heat and thermal conductivity of the d alloy, respectively. C m p and C p are the specific heat of the matrix liquid and the droplets, respectively. C is the concentration of the alloy. Cm and Cd are the concentration of the matrix liquid and the m droplets. S ¼ C m  C m 1 is the supersaturation. C 1 is the equilibrium concentration. The microstructure evolution in a centrifugally cast tube of immiscible alloys can be investigated by solving numerically the above equations together. For the details of the numerical method please refer to reference [12].

J.Z. Zhao et al. / Computational Materials Science 49 (2010) 121–125

3. Microstructure evolution in a centrifugally cast Al–Bi alloy 3.1. Experiments and results Centrifugal casting experiments were carried out with Al– 5 wt%Bi alloy. The alloy was first melted at 830 °C for 30 min to form a homogeneous single phase liquid, and then degassed using C2Cl6 and poured into a steel mold inserted into a horizontal centrifugal machine. The mold was preheated at 770 °C. The alloy melt solidified when the mold rotated at a speed of 1000 rpm. The measured temperature curve is shown in Fig. 3. A tube with the inner diameter of 36 mm and wall thickness of 9 mm was obtained. The tube shows a dispersed microstructure, as shown in Fig. 4. Generally the sample consists of three regions: the surface region which is rich in the Bi particles, the central region where the Bi particles show an even distribution along the radial direction of the tube and the inner surface region which is poor in the Bi particles. The sizes and areas of the Bi particles were measured on the section plane of the tubes. A typical size distribution of the particles is shown in Fig. 5. Figs. 4 and 5 demonstrate that the Bi-rich particles

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can be divided into two classes: the bigger particles produced by the liquid–liquid decomposition (the primary particles) and the smaller particles produced by the monotectic reaction. We care here mainly the sizes and the spatial distribution of the ‘‘primary particles”. The average apparent (2d) diameter and area fraction (which gives the local volume fraction of particles) of the Bi particles are shown in Figs. 6 and 7 as a function of radial position. 3.2. Numerical results and discussions The microstructure evolution in the centrifugally cast tube was calculated. The phase diagram used was constructed directly from the excess Gibbs energy of Al–Bi alloy [13]. The temperature dependence of the mole fraction of Bi in the matrix liquid and droplets are respectively given by:

C m ðTÞ ¼ 2:88  105  2:35  106 expð0:008:19  103 TÞ

ð6aÞ

C d ðTÞ ¼ 0:1737 þ ð2:71  103  1:74  106 TÞT

ð6bÞ

The interface tension between the droplet and the matrix is given by [14]:



rL1=L2 ¼ 0:289 1  700

1:3 T 1310

ð7Þ

o

T, C

The viscosities of the two liquids are approximated by the viscosities of the pure Al [15] and Bi [16] as:

650 45

55

65

75

85

time, s Fig. 3. Measured (squares) and calculated (solid line) cooling curve for a given position in the centrifugally cast tube.

gm ¼ 104:3 e3:34T=½T0:25T m 

ð8aÞ

gd ¼ 0:419e774:61=T

ð8bÞ

The diffusion coefficient is calculated from the viscosity of pure Al by using the Stokes–Einstein relation [17]:

D¼

kB T 6pgm r a

where ra = 0.51 Å is the ionic radius of Al.

Fig. 4. Microstructure of the Al–5 wt%Bi alloy tube solidified at a rotating rate of 1000 rpm. (a) Surface region; (b) central region; (c) inner surface region.

ð9Þ

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Fig. 8 shows the supersaturation of the matrix and the nucleation rate of the minority phase droplets as a function of the radial position for the centrifugally cast Al–Bi alloy. The number density is shown in Fig. 9. The numerical results indicate that for a given position, the alloy becomes supersaturated when the local temperature is lower than the binodal line. The supersaturation increases until it reaches a critical value so that the nucleation of the minor-

20

10 13

36

39

42

45

130

5

10

15

Particle diameter, μm Fig. 5. Size distributions of Bi-rich particles in the center region of the tube solidified at a rotating speed of 1000 rpm. The first peak and second peak present the particles produced by the monotectic reaction and the liquid–liquid decomposition, respectively.

Group 3

Group 1: t=47.7s Group 2: t=48.1s Group 3: t=48.5s

13

2.0x10

Group 2

13

1.5x10

5

0

Nucleation rate, m s

0

-3 -1

2.5x10

120 13

1.0x10

12

5.0x10

Average diameter, μm

Group 1 0.0

9

36

39

110 45

42

r, mm 6

Fig. 8. Supersaturation of the matrix liquid (dashed lines) and nucleation rate of the minority phase droplets (solid lines) along the radial direction of the centrifugally cast tube at different cooling times. The nucleation of the minority phase droplets occurred on the surface of the tube when t = 47.7 s. But it is very low.

3

0 42

45

10

12

10

11

10

10

-3

39

r, mm Fig. 6. Measured (squares) and calculated (solid line) average 2d-diameter of the primary Bi-rich particles as a function of radial position of the tube.

Number density, m

36

2.0

10

9

10

8

10

7

10

6

t=48.5s 36

t=48.1s 39

t=47.7s

42

1.5

fBi,%

Supersaturation, 10 Mole fraction

Probability,%

30

45

r, mm Fig. 9. Number density of the minority phase droplets along the radial direction of the centrifugally cast tube at different cooling times.

1.0

0.0 36

39

42

45

r, mm Fig. 7. Measured (squares) and calculated (solid line) volume fraction of the Bi-rich particles as a function of radial position of the tube.

The mold temperature TW and the convective heat transfer coefficient h are so chosen that the calculated temperature profile has a good agreement with the measured one, as shown in Fig. 3. The calculated average apparent diameter and volume fraction of Bi-rich particles are shown in Figs. 6 and 7, respectively. It can be seen that the agreement between the numerical results and the experimental ones are acceptable, indicating that the model presented describes the microstructure formation process well.

Moving velocity, mm/s

0.5 1 0.1

t=48.5s 0.01

t=59.3s 1E-3 1E-4 1E-5 36

38

40

42

44

46

r, mm Fig. 10. Moving velocities of the Bi-rich droplets of average size due to the centrifugal force (solid lines) and temperature gradient (dashed lines) at different cooling times.

J.Z. Zhao et al. / Computational Materials Science 49 (2010) 121–125

ity phase droplets begins. Since then the change of the local supersaturation is mainly the result of the action of two opposing effects: the nucleation and diffusional growth of the minority phase droplets decrease the supersaturation and the continuous decrease of the local temperature increases it in as much as the binodal line varies with temperature. The local supersaturation does not decrease immediately after the beginning of the nucleation but increases for a while because both the local nucleation rate and the number density of droplets are very small, and the change of the supersaturation is dominated by the decrease of the temperature. The enhancement of the supersaturation leads to a rapid increase in the local nucleation rate and the number density of droplets. Thus, soon the nucleation and diffusional growth of the droplets becomes the dominating factor. The local supersaturation begins to decrease, and the nucleation rate decreases rapidly and ceases shortly. The local nucleation of the droplets last only a very short period of time. During the nucleation period the number density of droplets increases rapidly, as can be seen in Fig. 9. With the increase of the droplet size the droplet motion becomes obvious as shown in Fig. 10. Since then the microstructure evolution is the results of the concurrent actions of the nucleation, growth and motions of the minority phase droplets. Under the centrifugal casting conditions, the Marangoni migration velocity of droplets due to the temperature gradient in the melt is negligible small and the motions of droplets are dominated by the centrifugal force. The resultant droplet velocity points to the outside surface of the tube. The motions of the droplets cause the formation of a layer rich in Bi particles on the outside surface of the tube and a region poor in Bi particles on the inner surface of the tube. 4. Conclusions Centrifugal casting experiments were carried out with Al–Bi alloy. The tubes with dispersed microstructure were obtained. A

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numerical model is developed describing the microstructure evolution in the centrifugally cast alloy with a miscibility gap in the liquid state. The microstructure formation in the tube was calculated. The numerical results show a good agreement with the experimental ones. They demonstrate that the moving velocity of the minority phase droplets due to the centrifugal force is much larger compared to the Marangoni migration velocity of the droplets during the liquid–liquid phase transformation. Thus, generally the centrifugally cast Al–Bi tube consists of three regions: the surface region rich in the Bi particles, the central region where the Bi particles distribute along the radial direction of the tube evenly and the inner surface region poor in the Bi particles. Acknowledgement The authors are grateful for financial support from the National Natural Science Foundation of China (Nos. 50771097, 5u0837601). References [1] T. Carlberg, H. Fredriksson, Metall. Trans. A 11A (1980) 1665. [2] K. Lohberg, V. Dietl. NASA TM78125, 1978, p. VI-1. [3] G.B. Rudrakshi, V.C. Srivastava, J.P. Pathak, S.N. Ojha, Mater. Sci. Eng. A 383 (2004) 30–38. [4] T. Berrenberg, P.R. Sahm, Z. Metallkd. 87 (1996) 187–194. [5] B. Prinz, A. Romero, L. Ratke, J. Mater. Sci. 30 (1995) 4715–4719. [6] G.B. Gouthama, S.N. Rudrakshi, J. Mater. Technol. 189 (2007) 224–230. [7] J.J. Guo, Y. Liu, J. Jia, Y.Q. Su, H.S. Ding, Acta Metall. Sin. 37 (2001) 363. [8] C.D. Cao, B.B. Wei, J. Mater. Sci. Technol. 18 (2002) 73. [9] J.Z. Zhao, L. Ratke, Scripta Mater. 50 (2004) 543–546. [10] H. Ahlborn, H. Neumann, H.J. Schott, Z. Metallkd. 84 (1993) 748–754. [11] D. Li, PhD Thesis, Harbin Institute of Technology, 1986. [12] H.L. Li, J.Z. Zhao, Comput. Mater. Sci. 46 (2009) 1069–1075. [13] R.N. Singh, F. Sommer, Report Progress Phys. 60 (1997) 57–150. [14] I. Kaban, W. Hoyer, M. Merkwitz, Z. Metallkd. 94 (2003) 831–834. [15] S.Z. Beer, Liquid Metal, Marcel Dekker Inc., New York, 1972. p. 415. [16] M.G. Frohber, K. Özbagi, Z. Metallkd. 72 (1981) 630. [17] A.I. Pommrich, A. Meyer, D. Holland-Moritz, T. Unruh, Appl. Phys. Lett. 9 (2008) 241922.