Thermal–solutal flows and segregation and their control by angular vibration in vertical Bridgman crystal growth

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Thermal–solutal ﬂows and segregation and their control by angular vibration

in vertical Bridgman crystal growth

Y.C. Liu

a

, W.C. Yu

b

, B. Roux

c

, T.P. Lyubimova

d

, C.W. Lan

a,∗

a_{Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC} b_{Department of Molecular Science and Engineering, National Taipei University of Technology, Taiwan, ROC} c_{Laboratoire Modélisation et simulation numérique en mécanique, L3M: CNRS-Universités d’Aix-Marseille, France}

d_{Institute of Continuous Media Mechanics UB RAS, Perm, Russia}

Received 18 July 2006; received in revised form 1 September 2006; accepted 1 September 2006 Available online 8 September 2006

Abstract

Thermal–solutal flows and their induced segregation and supercooling are important in the growth of an alloy crystal. For the vertical Bridgman crystal growth having a stabilized thermal profile, in addition to the thermal convection induced by radial thermal gradients, solute gradients can either induce or suppress the flow depending on the solute density. Such thermal–solutal flows significantly affect the segregation behavior, constitutional supercooling, and thus the morphological instability of the solidification front. A transparent Bridgman growth of succinonitrile containing a lighter (acetone) or heavier (salol) solute was investigated. The evolution of the interface shape as well as morphological instability was visualized and was interpreted through computer simulation. To further control the flow and segregation, angular vibration was applied and its effects on the thermal–solutal flows and morphological instability were investigated.

PACS: 44.25.+f; 47.27.Te; 81.10.Fq; 02.60.c6; 02.70.Fj

Keywords: Thermal–solutal ﬂows; Angular vibration; Convection; Morphology; Segregation; Bridgman crystal growth

1. Introduction

The vertical Bridgman or gradient freeze technique is a popular method for crystal growth, refining, and purification. Particularly, its simplicity in operation and the low thermal gradients are very suitable to the growth of compound semicon-ductor crystals (Brice, 1986; Monberg, 1994). The stabilized thermal configuration is also a great advantage offering weak convection and less growth striations due to the stable flow. Nevertheless, for the growth of an alloy crystal, the solutal gradients could induce solutal convection or suppress thermal convection depending on the density of the solute (Adornato and Brown, 1987; Lan and Chen, 1996). In some cases, the in-teraction of the thermal–solutal flows could lead to flow insta-bility (Ghorayeb et al., 1999; Zhou and Zebib, 1994; Nishimura

∗_{Corresponding author. Tel./fax: +886 2 2363 3917.} E-mail address:[email protected](C.W. Lan).

et al., 1998; Shi and Lu, 2006). Because of the lack of active melt stirring, the thermal–solutal flows sometimes cause large radial and axial uniformities due to the poor mixing and solute segregation. More importantly, the morphological instability could be easily induced by constitutional supercooling (Tiller et al., 1953; Mullins and Sekerka, 1964) as a result of local solute accumulation (Singh et al., 1996; Lan and Tu, 2001). Therefore, a better understanding of the flow behavior and find-ing an active control mean over the melt convection are use-ful for this process (Lan, 2004). For example, the accelerated crucible rotation technique (ACRT) (Scheel, 1971) and angular vibration method (Yu et al., 2004) are particularly effective. In a recent study (Lan, 2005), the angular vibration seems to be more effective in radial segregation control, as compared with ACRT, while no significant flow oscillations are induced.

In this paper, we present the visualized morphological evo-lution during a transparent Bridgman growth of succinonitrile (SCN) containing acetone (a lighter solute) or salol (a heavier

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Fig. 1. Sketch of the experimental setup for vertical Bridgman crystal growth with angular vibration; the furnace proﬁle Tf(z) was used for simulation.

solute) to illustrate the effects of the thermal–solutal ﬂow on the interface shape and morphological instability. The angu-lar vibration technique was also adopted to control the ﬂows, and thus the segregation and the interface morphology. To ex-plain the observed morphological transition, computer simula-tion was further conducted.

In the next section, the experimental setup and solidiﬁcation experiments are described. Section 3 is devoted to the numerical model. The results and discussion are arranged in Section 4 before a short conclusion is given.

2. Experimental

SCN containing about 0.064 wt% acetone or 0.15 wt% salol was directionally solidified in a transparent vertical Bridgman system, as sketched inFig. 1. The use of the higher salol con-centration was due to its higher segregation coefficient K (0.16 for salol and 0.1 for acetone). Before experiments, SCN (Acros, Inc., about 99% purity) was purified first by vacuum distilla-tion at 50 m torr for five times. The distilled sample, collected in a 17-mm diameter Pyrex ampoule (2.5 mm in thickness), was further purified by three-zone refining for more than 60 passes. The purified sample was then examined by directional solidification. No morphological breakdown was observed up to 7m/s of the solidification speed for a thermal gradient of

8–10 K/cm. To perform crystal growth experiments, acetone or salol was injected into the sample through a 5l micro-syringe inserted into the bottom of the sample. The total sample length was about 20 cm.

The furnace for directional solidification consisted of two heating zones made of copper blocks each with a Nichrome wire inside as a heating element. In between, a transparent in-sulation zone made of Plexiglas was used. The hot- and cold-zone temperatures were controlled independently by two PID controllers and the temperatures were set to 80◦C (top) and 40◦C (bottom), respectively. The thermal gradient at the in-terface was measured by an immersed thermocouple traveling with the sample. By taking an average of the gradients at the interface from solidification and melting curves, the thermal gradient was measured being about 8–10 K/cm. To translate the ampoule accurately, a microstepping motor was used to drive a screw slide; the translation rate was controlled at 1.6m/s in this study. During solidification, a digital video camera was used to record the evolution of the interface morphology with a back lighting to enhance the contrast of the image. Also, to al-low a smooth rotational motion, the ampoule was tightly fitted into a pair of bearings (top and bottom) that were both mounted on the translating system. Furthermore, to generate angular vi-bration, as shown inFig. 1, a stepping motor was used to rotate a disk having a shaft connected to the other disk that mounted the sample. The vibration amplitude was controlled by the posi-tion of the shaft in the disk, while the frequency was controlled by the rotation speed of the stepping motor. In the experiments, the dimensionless amplitude was about 0.045, i.e., a fraction of 2.

3. Governing equations and numerical solution

The vertical Bridgman crystal growth depicted in Fig. 1is simulated, where the furnace environment is described by an effective heating profile Tf(z, t). To start crystal growth from a stationary state (without ampoule movement) in simulation, this profile is moved upward at speed Uh. In the experiments, the furnace was kept stationary, while the ampoule was mov-ing downward at a given speed after the growth started. The angular vibration is applied in the azimuthal angle direction with an amplitude bv(a fraction of 2) and angular frequency (or frequency f in Hertz); = 2f . Because the heating was rather uniform and the observed interface shape was nearly symmetric, the system for simulation is assumed axisymmet-ric. Accordingly, the flow and temperature fields, as well as the growth front (the melt/crystal interface, hc(r, t)). The melt is further assumed incompressible and Newtonian, while the flow is laminar. The Boussinesq approximation is also adopted. Di-mensionless variables are defined by scaling length with the crystal diameter Rc, time t with Rc2/m, velocity withm/Rc, temperature with the melting point Tm, and solute concentra-tion by the initial concentraconcentra-tion C0, wherem is the thermal

diffusivity of the melt. For the convenience of representation, all the variables defined afterwards with a superscript * are di-mensionless unless otherwise stated. The governing equations for the time-dependent fluid flow and heat and mass transfer in

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terms of dimensionless stream function∗, vorticity ∗, az-imuthal velocity v∗, temperature T∗ and solute concentration C∗_{can be written as the following:}

Equation of motion: j∗ jt∗ + j jr∗ _∗ r∗ j∗ jz∗ −_jzj_∗ _∗ r∗ j∗ jr∗ + Pr j jr∗ 1 r∗ j jr∗(r∗∗) + j jz∗ 1 r∗ j jz∗(r∗∗) + j jz v2 r − Pr RaTjT ∗ jr∗ + Pr RaS jC∗ jr∗ = 0. (1) Stream equation: j jz∗ 1 r∗ j∗ jz∗ + j jr∗ 1 r∗ j∗ jr∗ + ∗= 0. (2) Circulation equation: −jv_jt_∗∗ +_r1_∗2 _j jr∗ r∗v∗j∗ jz∗ −_jzj_∗ r∗v∗j∗ jr∗ + Pr j jr∗ 1 r∗ j(r∗_v∗ ) jr∗ + j jz∗ 1 r∗ j(r∗_v∗ ) jz∗ = 0. (3) Energy equation: −jT_jt_∗∗ −_jrj_∗(r∗u∗T∗) −_jzj_∗(r∗v∗T∗) + j jz∗ r∗_i_(T∗_{) j}T∗ jz∗ +_jrj_∗ r∗i(T∗) jT ∗ jr∗ = 0, i = (m, c). (4) Solute equation: −jC_jt_∗∗−_jrj_∗(r∗u∗C∗) −_jzj_∗(r∗v∗C∗) +Pr Sc j jz∗ r∗jC∗ jz∗ + j jr∗ r∗jC∗ jr∗ = 0. (5)

The solute diffusion in the solid phase is neglected. In the above equations, Pr is the Prandtl number (Pr≡ m/m), where m

is the kinematic melt viscosity, Sc the Schmidt number (Sc≡ m/D), and D the solute diffusivity in the melt. Also, i is the thermal diffusivity of phase i; i= c for the crystal and m for the melt. Two important dimensionless variables, RaT and RaS, in the source term of the equation of motion are deﬁned as follows: RaT ≡ g0 TTmR 3 C mm , RaS ≡ g₀ SC0R3_C mm ,

where g is the gravitational acceleration and T and S are the

thermal and solutal expansion coefﬁcients, respectively. The stream function∗and vorticity∗in the above equations are deﬁned in terms of the radial (u∗) and axial (v∗) velocities as u∗= −_r1_∗j∗ jz∗, v∗= 1 r∗ j∗ jr∗, (6) ∗=ju_jz_∗∗−jv_jr∗_∗. (7)

To solve the above governing equations, boundary condi-tions are also required. Most of the boundary condicondi-tions for melt flow and heat and mass transfer can be found elsewhere (Lan and Liang, 1998). In short, the energy and solute conservation are applied to the growth interface. At the ampoule/material interfaces, heat flux continuity is forced, while the solute flux is set to zero. The melt surface is set to be stress free. The no-slip boundary condition is used for the solid boundaries of the interface. Therefore, the angular vibration of the crucible can be described by the sinusoidal azimuthal velocity as the following:

v∗= 2bvf∗r∗sin(2f∗t∗), (8)

where 2bv is the angular vibration amplitude and f∗ the dimensionless vibration frequency scaled by m/Rc2. Because

the solidiﬁcation time in experiments last for hours, it is too time consuming to perform direct numerical simulation (DNS) using Eq. (8) as the boundary condition for high-frequency vibrations. Instead, if the frequency is high such that the thick-ness of viscous boundary layer is small in comparison with all characteristics, an averaged ﬂow approach using the Schlicht-ing boundary layer approximation (SBLA) is possible. In other words, if the Schlichting boundary layer is very thin, we can take this slip tangential velocity (u∗_t) for the growth front as the following (Yu et al., 2006):

u∗ t =

b2 v(f∗)r∗

2 sin(), (9)

where is the angle between the tangent to the growth front and the axis of vibration axis. With this boundary condition, the simulation cost for angular vibration is greatly reduced be-cause the time step for the simulation could be much larger than the period of the vibration. We refer this approach the SBLA. However, there are some limitations of using this approxima-tion. When the frequency is not very high, the boundary layer thickness, i.e., =√m/f , is not small enough. The use of

this boundary condition could be erroneous (Yu et al., 2006). In this report, DNS was used for low-frequency vibrations (3 and 5 Hz), while SBLA was used for the higher frequencies (10 and 20 Hz).

The above governing equations and boundary conditions are discretized by a ﬁnite volume method, and the resultant dif-ferential/algebraic equations are solved by DASPK solver with adaptive step size control (Lan and Liang, 1998). The total number of unknowns after the ﬁnite volume approximation is 34 052, and all the calculations are performed in a personal computer (P4-3 GHz CPU).

4. Results and discussion

4.1. Interface morphology

Figs. 2a and b show the interface shape evolution during Bridgman growth of SCN containing 0.064 wt% acetone and

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0.15 wt% salol, respectively, at the pulling speed of 1.6m/s. For acetone, at stationary, the interface was ﬂat due to the nearly equal thermal conductivities of the melt and the crystal. As the solidiﬁcation started, the interface moved downward and slightly deformed. At around 40 min, a depression occurred at the center due to the local accumulation of acetone. Such a depression having a cusp tip broke down, due to constitutional supercooling, at about the same time. Further breakdown and enlargement of the pattern can be seen from the photographs at 60 and 80 min, respectively.

The evolution of interface morphology for SCN/salol showed a similar behavior. However, as shown inFig. 2b, the depres-sion shape was wider. The morphological breakdown occurred at about the same time being about 40 min. The bottom of the breakdown area was much ﬂatter than that of SCN/acetone. We have enlarged the interface shapes at 60 min of both cases for comparison inFig. 3. As shown, the shapes of the breakdown area were quite different. As will be explained later by numer-ical simulation, this was cased by the different solutal distribu-tions at the interface.

Computer simulations were further carried as shown in

Figs. 4a and b for SCN/acetone and SCN/salol, respectively. In each plot, the left-hand side is the streamlines, and the right-hand side the solutal ﬁelds (iso-concentrations). As shown in

Fig. 4a, at stationary, the interface was flat and the convection near the interface was extremely weak. The upper cell was caused by the radial heating. As the solidification started, the interface became concave and the flow cell near the interface

Fig. 2. Interface evolution of vertical Bridgman growth of SCN containing: (a) 0.064 wt% of acetone; (b) 0.15 wt% of salol. The ampoule pulling speed is 1.6m/s.

Fig. 3. Enlarged photograph and the sketch of the interface and the lower boundary of the breakdown morphology: (a) SCN/acetone; (b) SCN/salol. Fig. 4. Calculated ﬂow and solute ﬁelds: (a) SCN/acetone; (b) SCN/salol; the ampoule pulling speed is 1.6m/s. In (a) at t= 0,min= −1.8 × 10−4g/s, max=3.037×10−5_{g/s, and C/C}_{0=1 and at t=1 h,}_{min=−1.8×10}−4_g/s, max=3.037×10−5_{g/s, maximum C/C}_{0=16.2693, and minimum C/C0=1.} In (b) t= 0, min= −1.798 × 10−4g/s, max= 3.110 × 10−5g/s, and C/C0=1; at t =2400 s,min=−1.489×10−4_g/s,_max_=2.500×10−4_g/s, maximum C/C0 = 6.0851, and minimum C/C0 = 1; at t = 4800 s, min = −1.486 × 10−4g/s, max = 2.534 × 10−4g/s, maximum C/C0= 16.145, and minimum C/C0= 1.

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Fig. 5. Comparison of calculated radial solute segregations of different solutes at the growth interface; t=60 min. The wiggle of the radial salol concentration near r=0 was due to numerical breakdown caused by the large supercooling.

was enhanced. As a result, the acetone rejected during solidifi-cation was redistributed by the flow having an increasing ace-tone concentration toward the center of the interface. Because acetone is lighter than SCN, the radial acetone gradients also enhance the flow leading to a highly localized solute distribu-tion at the center of the interface. The local acetone accumula-tion further caused a suppression of the interface there, which became obvious at about 40 min. As will be discussed shortly through calculations, constitutional supercooling also occurred at about 35 min. As the supercooling was established, morpho-logical breakdown could occur when the supercooling over-came the interfacial energy. The simulated results at 60 and 80 min show a deep depression at the interface center, where high constitutional supercooling exists. However, in reality, the microscopic planar interface could no longer exist, as those shown inFig. 2a. The supercooled interface has a cellular or dendritic structure. Because of the morphological breakdown, the accumulated acetone in front of the interface was trapped and the supercooling was reduced. However, the present sim-ulation is not able to take this into account. Therefore, the simulation results after the morphological breakdown are only qualitative.

For SCN/salol, the convection near the interface was much weaker, as shown inFig. 4b. Such a weaker flow was due the heavier solute, which suppressed the flow. In other words, the radial density due to thermal gradients was counter balanced by the solutal gradients; one could observe this contribution from the source term of Eq. (1). In addition, the flow cell near the interface was closer to the ampoule wall as compared with that inFig. 4a. More importantly, the concentration profile was quite uniform near the interface, i.e., the much flatter iso-concentration lines. This also indicated the convective effect on the solute transport was much weaker.

The radial solute concentrations at 60 min fromFig. 4were plotted inFig. 5for further comparison. As shown, the distri-bution near the interface center for SCN/salol was much wider than that for SCN/acetone. The solute distributions happened to

Fig. 6. Calculated constitutional superheating at the center of the interface for SCN/acetone and SCN/salol; constitutional supercooling occurs whenG <0.

be consistent with the shapes of the morphological breakdown shown in Fig. 3. Moreover, because the convection near the solidiﬁcation interface in SCN/salol was weaker, this caused the poorer global salol mixing there. As a result, the accumu-lation of salol was more than that of acetone.

To illustrate the onset of the constitutional supercooling, we extracted the superheating gradient from the previous simu-lated results as shown inFig. 6. In the ﬁgure, the superheating gradientG is deﬁned as follows:

G = dT /dn − m dC/dn, (10)

where m is the slope of the liquidus line obtained from the phase diagram and n the normal distance from the interface; the superheatings inFig. 6were at the center of the interface. At stationary, the solute is uniform, so thatG = dT /dz is the thermal gradient at the interface (in the melt side). As shown inFig. 6, the superheating gradients for both cases decreased monotonically with time. However, constitutional supercooling occurred slightly earlier for SCN/acetone. The earlier onset of the supercooling for SCN/acetone was attributed to the local acetone accumulation at the depression area as a result of the convection. The simulated results having a large supercooling were often accompanied by numerical breakdown at the in-terface. Therefore, the simulated results after 60 min were not reliable.

4.2. Effect of angular vibration

To further control the solute ﬁeld and interface morphol-ogy, angular vibration was applied. The effect of vibration fre-quency on the interface morphology at 60 min after the am-poule translation is shown in Figs. 7a and b, for SCN/acetone and SCN/salol, respectively. For SCN/acetone inFig. 7a, there was no morphological breakdown in 60 min for the frequency greater than 3 Hz; at 3 Hz, the interface was not quite smooth. Also, from 0 to 5 Hz, the interface concavity decreased with

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Fig. 7. Effects of angular vibration frequency on the interface shape and morphological instability at 60 min: (a) SCN/acetone; (b) SCN/salol.

Fig. 8. Simulated ﬂow and solute ﬁelds and the comparison with the observed interface at different vibration frequency at 60 min: (a) SCN/acetone; (b) SCN/salol.

the vibration frequency. However, the interface concavity in-creased again from 5 to 20 Hz. Interestingly, a wavy interface was found at 20 Hz, and the variation was along the angular direction. The effect of vibration for SCN/salol had a similar trend as shown inFig. 7b. However, at 3 Hz, the area of the morphological breakdown was signiﬁcantly larger as compared with that of no vibration. The interface concavity also decreased from 3 to 5 Hz, and then increased again from 5 to 20 Hz. At 20 Hz, a wavy interface was observed as well.

Computer simulation was further carried out, and the com-parison with the interface was shown in Figs. 8a and b for SCN/acetone and SCN/salol, respectively. As shown, the simu-lated interface concavity for both cases agreed quite well with the experiments. It should be noticed that the interface was at the upper boundary of the breakdown area. More importantly, from 0 to 5 Hz, the interface concavity decreased with the fre-quency, while from 5 to 20 Hz, the concavity increased with the frequency. The reason is quite clear from the simulation. From 0 to 5 Hz, the flow above the interface was weakened by vibration because of the radial outward streaming flow induced by the angular vibration. As a result, the solute distribution be-came more uniform and this reduced the interface concavity cased by the local solute accumulation. On the other hand, from 5 to 20 Hz, the Schlichting flow became dominant. Since the flow was in clockwise direction and the isotherms were dis-torted with the flow, the interface concavity increased with the vibration intensity (frequency).

Fig. 9. Effect of angular vibration on the radial solute segregation: (a) SCN/acetone; (b) SCN/salol.

The radial solute concentrations extracted from the simulated results inFig. 8were plotted inFigs. 9a and b for SCN/acetone and SCN/salol, respectively. As shown, for both cases, the ra-dial segregation reversed from 0 to 5 Hz. This indicated that the Schlichting streaming flow was strong enough to overcome the buoyancy force and was able to push the solute from the in-terface center to the rim. From bothFigs. 8and9, it was clear that when the frequency was greater than 10 Hz, the Schlicht-ing flow dominated and the solutal effect became insignificant, which could be seen from the solutal fields as well as the radial solute segregation profiles.

Fig. 10 shows the effect of the vibration frequency on the superheating gradient. As shown, in 1 h, it appeared a large su-percooling for 0 Hz and a small susu-percooling for 3 Hz at the interface center. Both were consistent with the observed result; the interface for 3 Hz had a little breakdown area in 1 h, as shown inFig. 7a. For SCN/salol, the supercooling occurred for the frequency being less than 10 Hz. However, in the experi-ment, as shown inFig. 7b, we did not observed a clear interface breakdown at the interface center for 5 Hz. Instead, the mor-phological breakdown for 5 Hz occurred near the rim of the interface. As shown inFig. 11, there was no supercooling for the frequency greater than 10 Hz.

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Fig. 10. Effect of angular vibration on the calculated constitutional superheat-ing at the center of the interface for SCN/acetone; constitutional supercoolsuperheat-ing occurs whenG <0.

Fig. 11. Effect of angular vibration on the calculated constitutional superheat-ing at the center of the interface for SCN/salol; constitutional supercoolsuperheat-ing occurs whenG < 0.

We also monitored the onset of supercooling at different places of the interface for 3 Hz.Fig. 12 shows the evolution of the superheating gradients at three places of the interface for SCN/acetone. An observed interface at 80 min is shown as well. Interestingly, the area of the breakdown (from a to b) was consistent with the simulation (having a negativeG at about 80 min). Similarly, the evolution of the superheating at three different places of the interface for SCN/salol is shown inFig. 13. Again, the simulation also predicted the supercooled area (from a to b) correctly.

Fig. 12. Evolution of the superheating gradients at three different places of the interface for SCN/acetone at 3 Hz.

Fig. 13. Evolution of the superheating gradients at three different places of the interface for SCN/salol at 3 Hz.

5. Conclusion

The effect of thermal–solutal flows on the interface shape and morphology in a vertical Bridgman crystal growth was in-vestigated using succinonitrile alloys. Both lighter (acetone) and heavier (salol) solutes were considered. Based on the in-terface shape and its breakdown pattern, it was clear that the heavier solute (salol) significantly suppressed the flow near the growth interface. Computer simulation was further carried out and the simulated results were in good agreement with experi-mental observations. To further control the solute segregation, angular vibration was applied and the effect of frequency was investigated. Clearly, the induced Schlichting flow significantly modified the flow near the interface. As a result, the constitu-tional supercooling was effectively removed by vibration. At low frequencies, the interface concavity was reduced with the increasing frequency due to the solute redistribution. However,

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at high frequency, the interface concavity increased with the frequency due to the enhanced convective heat transfer by the Schlichting ﬂow. The simulation also predicted reasonably well the area of the morphological breakdown based on the consti-tutional supercooling.

Notation

bv vibration amplitude

C solute concentration

Cp speciﬁc heat

D solute diffusivity in the melt ez unit vector in z-direction

f vibration frequency

g₀ gravitational acceleration hc height of growth front

H heat of fusion

k thermal conductivity

L length of ampoule

m slope of the liquidus line in the phase diagram n normal distance from the interface

Pr Prandtl number, vm/m

r cylindrical coordinate

Rc radius of crystal

RaS solutal Rayleigh number, sR3cg0C0/mm RaT thermal Rayleigh number, TR3cg0Tm/mm

Sc Schmidt number,m/D

t time

T temperature

Teff effective heater temperature

Tm melting point

u r-component of velocity

ut tangential velocity at the Schlichting boundary layer v z-component of velocity v azimuthal velocity z cylindrical coordinate Greek letters thermal diffusivity

S solutal expansion coefﬁcient T thermal expansion coefﬁcient Schlichting boundary layer thickness

m viscosity

m kinematic viscosity,m/ m

density

the angle between the tangent to the growth front and the axis of rotation

stream function

vorticity

angular vibration frequency Superscript * dimensionless variables Subscripts 0 initial value amp ampoule c crystal m melt max maximum min minimum Acknowledgment

This work was supported by the National Science Council (NSC) of the Republic of China, the Russian Foundation for Basic Research, and the Orchid Program between NSC and the PIA of France.

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