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Unidirectional solidification of Al–Cu eutectic with the accelerated crucible rotation technique
Journal of Crystal Growth 194 (1998) 398—405
Unidirectional solidification of Al—Cu eutectic with the accelerated crucible rotation technique D. Ma *, W.Q. Jie, W. Xu , Y. Li, S. Liu Department of Materials Science, National University of Singapore, Singapore 119260, Singapore The State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi+an 710072, People+s Republic of China Received 9 January 1998; accepted 7 August 1998
Abstract The accelerated crucible rotation technique (ACRT) has been applied to the unidirectional solidification of Al—Cu eutectic to reveal the effect of forced convection on the solidification microstructures by a systematic experimental investigation combining different rotation methods (the maximum rotation rate X "100—400 rpm) with various
growth velocities (» "5—60 lm/s). The results can be concluded as follows: (1) Forced convection introduced by ACRT dramatically changes the eutectic microstructures. When the fluid flow is weaker (Re(270), a great number of lamellar faults occur in the eutectic; on the other hand, when the flow is stronger (Re'500), fluctuation structure forms in the eutectic; (2) the lamellar spacing is not uniformly distributed in the radial direction of the solidified sample with ACRT, and the maximum spacing occurs near the crucible wall while the minimum one at the center of the crucible. The average lamellar spacing obtained by ACRT is smaller than that without ACRT and decreases upon increasing the convection intensity (i.e. increasing X ); (3) whether or not a normal Bridgman process is performed before ACRT shows little
influence on the growth of the nonfacet—nonfacet eutectic. 1998 Elsevier Science B.V. All rights reserved. Keywords: ACRT; Unidirectional solidification; Eutectic growth
1. Introduction The accelerated crucible rotation technique (ACRT), first proposed in the 1970s [1], has been a novel method to produce large and high-quality single crystals of functional materials [2—4]. During the ACRT crystal growth process, the crucible rotates with varying speed in a given
* Corresponding author. Fax: #65 776 3604; e-mail: [email protected].
method and forced convection is produced in the front of solid—liquid interface. The fluid flow suppresses the adverse effects of constitutional supercooling [1], permits the realization of stable planar interface crystal growth at higher critical velocity than that in normal Bridgman process [5] and improves the crystallinity [6]. Therefore, ACRT has been widely applied to Czochralski (CACRT) and Bridgman (ACRT-B) crystal growth processes. In order to search for a new technique of in situ preparation of composites and improve the
0022-0248/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 7 3 5 - 0
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
understanding upon the effect of forced convection on solidification microstructures, several works [7—9] on the application of ACRT to the eutectic alloys have been done during the last two decades. The experimental studies of Popov and Wilcox [7] on Pb—Sn eutectic showed that the stirring by ACRT increased the spiral rate of the microstructure and reduced the length of eutectic zone cooperatively, but had no influence on the lamellar spacing. In the unidirectional solidification of Bi—MnBi with ACRT, Eisa and Wilcox [8] found that the coarseness of MnBi quasiregular fibers was caused by the accelerated crucible rotation at a growth velocity of 9 mm/h. Jie [9] applied ACRT to Al—Si eutectic growth and found that the initial condition before ACRT influenced the growth morphology of Si phase. To this typical nonfacet—facet eutectic, if the crucible rotated at the beginning of the unidirectional solidification, irregular eutectic with short bars and chunks of silicon would form; but if a normal Bridgman process was performed before the crucible rotation, a more satisfactory directional needle-like silicon structure would grow up. On the other hand, the studies on the application of ACRT to eutectic growth process mostly concentrated on the conditions of low growth velocities and low convection intensities (i.e. smaller X ).
There is also no reported evidence upon the influence of the initial conditions on nonfacet—nonfacet eutectic growth process. With the interest concentrated on the effect of the forced convection on the eutectic structures and lamellar spacing, the application of ACRT to Al—Cu eutectic, a widely studied nonfacet—nonfacet eutectic, has been investigated in which different initial conditions, growth velocities and crucible rotation methods have been systematically carried out.
399
The Al—Cu eutectic alloy was melted in the vacuum furnace with 99.99% Al and 99.99% Cu, and cast into bars (ID 8 mm;120 mm long) for further experiments. The graphite crucible with the inner diameter of 8 mm was used for unidirectional solidification. The coolant of liquid Ga—In eutectic was used to strengthen the temperature gradient. The temperature gradient of 200 K/cm was measured in the normal Bridgman process by inserting a thermocouple into the alloy when the hot side of sample was heated over 900°C. During ACRT process, the dynamic temperature gradient was determined to increase with the increase of maximum crucible rotation rate. During the experimental process, the crucible mounted on the rotator was positioned in the hightemperature region of furnace to melt the alloy and then the tip of the crucible was dipped into the coolant about 10 mm to establish a stable temperature gradient. After this, unidirectional solidification with or without ACRT was carried out. For the ACRT process, two groups of experiments were conducted to examine the effect of the initial condition on the eutectic growth. In first group of experiments, a normal Bridgman process was performed before the crucible rotation was applied. In the second group, the crucible rotated at the beginning of the unidirectional solidification. For each group, five growth velocities (» "5, 10, 20, 30, 60 lm/s) in combination with four rotation methods (shown in Fig. 1a—Fig. 1d) were used. The solidified samples were cut along different sections and polished and etched for metallographic analysis. Measurement of lamellar spacing was conducted with an image analyzer (Quantimet 500) where at least six readings were taken to obtain a mean value.
3. Experimental results 2. Experimental methods
3.1. Microstructures by the normal Bridgman method
The experiments were carried out with the ACRT Crystal Growth Equipment described in details elsewhere [9]. The equipment consists of a crucible rotation system, a furnace drawing system, and a thermal field controlling system which can work independently.
During the normal Bridgman process (without crucible rotation), the morphology of the eutectic consists of regular lamellae as shown in Fig. 2 and the interface is nearly planar. The lamellar spacing decreases as the growth velocity increases. Regression analysis shows that the relation between
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Fig. 1. (a)—(d) Crucible rotation methods.
growth velocity and lamellar spacing satisfies » j"88.4 lm/s, which is in good agreement with the theoretical prediction given by Jackson and Hunt [10]. 3.2. Microstructures by the accelerated crucible rotation technique 3.2.1. Eutectic microstructures The fluid flow exerted by the crucible rotation influenced the eutectic structures depending on the applied ACRT methods. At lower X ,
the eutectic microstructures were nearly the same as that by normal Bridgman methods, but there occurred a great number of lamellar faults, as shown in Fig. 3a. At higher X as shown in
Fig. 1b—Fig. 1d, fluctuation structure (Fig. 3b) formed in the eutectic, whose periodic length were approximately equated to » ¹, where ¹ was the period of rotation rate change (here ¹"10 s for all the applied ACRT methods). From Fig. 3c, it can be seen clearly in larger magnification that there
Fig. 2. SEM micrograph of longitudinal section of Al—Cu eutectic grown at 10 lm/s by normal Bridgman method. Growth direction from left to right.
were two stages in each fluctuation period and the lengths of these two stages were approximately equal. Furthermore, it should be noted in Fig. 3c that the lamellar spacing also varied periodically
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
401
Fig. 3. SEM micrographs of longitudinal sections of Al—Cu eutectic showing the effect of ACRT method on solidification structures. (a) » "10.0 lm/s, X "100 rpm, ACRT method shown in Fig. 1a; (b) » "10.0 lm/s, X "200 rpm, ACRT method shown in
Fig. 1b, magnification 200;; (c) » "10.0 lm/s, X "200 rpm, ACRT method shown in Fig. 1b, magnification 400;. Growth
direction from left to right.
with the same periodic length, though the stage with larger spacing was shorter by a factor of 3 than that with smaller spacing. 3.2.2. Lamellar spacing The convection during ACRT-B process induced a decrease in the lamellar spacing. As shown in Fig. 4, lamellar spacing did not remain the same value along the radial direction as that in the nor-
mal Bridgman process. The spacing was smaller at the center of the sample, but became larger at the edge. Fig. 5 indicated that the difference of lamellar spacing between the center and edge of the sample decreased upon increasing the growth velocity and the rotation rate. Although lamellar spacing was not uniform along the radial direction, they distributed symmetrically about the center of the sample. Therefore, one can determine the average lamellar
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Fig. 4. SEM micrographs of a transverse section of Al—Cu eutectic showing the microstructure difference at different radial positions where » "10.0 lm/s, X "300 rpm, and the
ACRT method shown in Fig. 1c. (a) Center of the sample; (b) edge of the sample.
Fig. 5. The variation of lamellar spacing at the edge and center of the sample with the growth velocity in the studied ACRT methods. (a) X "200 rpm, rotation method shown in
Fig. 1b. (b) X "400 rpm, rotation method shown in Fig. 1d.
spacing by statistical measurement of many points on the transverse section of the solidified sample. Fig. 6 was obtained by this method, which showed that the average lamellar spacing solidified with ACRT was smaller than that without ACRT, and the larger X becomes, the smaller the spacing
will be. Regression equations of the three curves in Fig. 6 are as follows: Curve 1: j"9.3776»\ , Curve 2: j"6.2916»\ , Curve 3: j"3.9464»\ ,
Fig. 6. The variation of average lamellar spacing of Al—Cu eutectic with the growth velocity using different Bridgman and ACRT methods.
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
403
Fig. 8. Schematic representation of Ekman flow: (a) spin-up; (b) spin-down (after Schulz-Dubois [2]). Fig. 7. Effect of ACRT methods on average lamellar spacing of Al—Cu eutectic under given growth velocities.
which indicated that the well-known relation for eutectic growth, i.e. » j"constant [10], was not applicable to the case where forced convection existed during solidification process. The variation of average lamellar spacing with the maximum rotation rate was plotted in Fig. 7, which showed that for a given growth velocity the lamellar spacing decreased with the increase of maximum rotation rate and when the growth velocity exceeded 30 lm/s, the forced convection had little effect on the average lamellar spacing. 3.3. The effect of initial conditions The above results corresponded to the first group of experiments, in which a normal Bridgman process was performed before the crucible rotation. In order to show the effect of initial condition on nonfacet—nonfacet eutectic growth, another group of experiments were carried out in which the crucible was rotated at the beginning of the unidirectional solidification. In this group, similar phenomena as discussed above occurred which indicated that the initial condition before crucible rotation had little influence on the nonfacet—nonfacet eutectic growth. The reason seemed to be that nonfacet—nonfacet eutectic growth was slightly dependent on crystallographic anisotropy rather than that of facet—nonfacet eutectic such as Al—Si eutectic [9].
4. Discussion 4.1. Transportation condition and formation of fluctuation structure There are three types of forced convection exerted by the crucible rotation, namely, spiralshear flow, Couette flow and Ekman flow [11]. Spiral-shear flow can improve the uniformity of solute and temperature distribution cooperatively. Couette flow can produce more complete mixing in liquid during spin-down process. As for crystal growth process, Ekman flow is of much importance than the former two because it directly acts on S/L interface so as to influence the solidification microstructure. During ACRT-B process, Ekman flow adjusts its flow direction periodically as shown in Fig. 8, which results in the periodical variation of the temperature of S/L interface [12,13] and the fluctuation of the real growth velocity of interface [14]. In the spin-up process, the fluid pumped out is being forced up the side walls and returns more slowly through the bulk of the fluid; and in the spin-down process, the reverse situation occurs. Therefore, Ekman flow induces two transitions in one growth period: spin-up/spin-down transition and spin-down/spin-up transition. In spin-down/ spin-up transition, the hotter fluid from high-temperature liquid zone comes down to the interface so that the interface is warmed up and the thickness of heat boundary layer is decreased. During this process, the real growth velocity of interface is reduced so that some lamellae overgrow locally [10] and as a result the spacing is increased. On the other hand,
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D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
in spin-up/spin-down transition, the cooler fluid near the crucible wall comes down and increases the thickness of heat boundary layer. At this transition, the real growth velocity of the interface is increased so that the lamellae adjust to grow through the movement of lamellar faults and the spacing is decreased [10]. Consequently, the eutectic lamellar spacing changes periodically according to the periodic change of Ekman flow. The transition time can be evaluated by the decay (or setup) time for Ekman flow, i.e. q"a(lu)\ where a is the inner radius of the crucible, l is the viscosity coefficient and u"2pX . In the present case,
assuming a"0.4 cm, l"0.005 cm/s, X "
200 rpm, the transition time is about 1.5 s. Therefore, the time for stable Ekman flow can be estimated as 3.5 s which corresponds to the periods where rotation rate is constant (0 or X ) and the
stable growth length is approximately 35 lm during this period. This evaluation is consistent with the observation shown in Fig. 3c. 4.2. Effect of crucible rotation methods During ACRT process, the intensity of forced convection can be described by Reynolds number which indicates the ratio of the inertia force to the viscous force [11], i.e. Re"a*X/l, where *X is the step change of rotation rate. In our experiments there exists *X"X !X "X since the
minimum rotation rate X "0 rpm. Therefore,
the Reynolds number can be rewritten as Re"aX /l. When the crucible rotation is
placed at a lower rate (X (100 rpm), Ekman
flow is weaker (Re(270). In this case, Ekman flow cannot bring about a large fluctuation in the growth velocity but can lead to the inclination of solute field downward to the flow [16]. Therefore, a great number of lamellar faults are formed corresponding to this flow. On the other hand, larger crucible rotation rate (X '200 rpm)
can lead to stronger Ekman flow (Re'500) which results in the formation of fluctuation eutectic structures. Actually, the two-phase coupled eutectic growth is controlled by the solute interdiffusion which is confined in the boundary layer in front of the S/L interface. The thickness of boundary layer is in the
order of lamellar spacing, i.e. a few microns. If ACRT process provides well-mixing in the liquid ahead of the interface, this will reduce the thickness of boundary layer and therefore decrease the lamellar spacing. But if the growth velocity is large enough (i.e. »'30 lm/s), the original unperturbed boundary layer will be so thin that the effect of convection during ACRT process cannot reach it. This may be attributed to the fact that the application of ACRT at high growth velocity has no significant effect on the eutectic spacing.
4.3. Effect of forced convection on the lamellar spacing Although it has been found in some forced convection solidification experiments that the eutectic spacing increased with increasing the stirring intensity, for Fe—Fe B and Ti—Ti Si [15], Pb—Sn and Cd—Zn [16], our results showed that the lamellar spacing of Al—Cu eutectic decreased upon increasing the rotation rate during ACRT process. In addition, our results do agree with the experimental observation on the unidirectional solidification of Al—4.5% Cu alloy with ACRT [17], which indicated that the primary arm spacing of dendrite also decreased upon increasing the convection intensity, i.e. maximum rotation rate X .
On the other hand, it was found that the lamellar spacing of Al—Cu eutectic did not uniformly distribute along the radial direction during ACRT process. The lamellar spacing increased along the radial direction which was consistent qualitatively with the theoretical prediction given by Baskaran and Wilcox [16]. The reason was that the velocity of local Ekman flow and its gradient in front of the solidification front changes dramatically along the radial direction when the rotation rate of the crucible was large. For example, the estimated difference in flow velocity between center and edge was about 4 cm/s and the difference in the gradient of flow velocity ahead of S/L interface can be up to 10 cm/s for X "200 rpm. Such a great differ ence could be attributed to the difference in spacing between the center and edge which can be up to 1.5 lm in the sample grown at low growth velocity with larger rotation rate.
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
5. Conclusions 1. In the normal Bridgman process, the lamellar spacing and growth velocity of Al—Cu eutectic satisfies » j"88.4 lm/s, which is in good agreement with that predicted by Jackson and Hunt’s model. 2. When the crucible rotates at a lower rate, a great number of lamellar faults are formed in the eutectic structure; when the rotation rate is larger, fluctuation eutectic structure occurs. 3. The lamellar spacing is no longer uniformly distributed in the radial direction of the solidified sample with ACRT. The maximum spacing occurs near the crucible wall while the minimum at the center of the sample. The average lamellar spacing decreases with the increase in the crucible rotation rate. 4. Whether or not a normal Bridgman process is performed before ACRT shows little effect on the nonfacet—nonfacet eutectic growth. References [1] H.J. Scheel, J. Crystal Growth 13/14 (1972) 560.
405
[2] H.J. Scheel, E.O. Schulz-Dubois, J. Crystal Growth 8 (1972) 304. [3] P. Capper, I.G. Gale, F. Grainger, J.A. Rokerts, J. Crystal Growth 92 (1988) 1. [4] Ph. Buffat, J.D. Ganiere, M. Rappaz, D.F. Rytz, J. Crystal Growth 749 (1986) 353. [5] A. Horowitz, D. Gazit, J. Makovsky, J. Crystal Growth 61 (1983) 323. [6] P. Capper, J.J. Gosney, C.L. Jones, J. Crystal Growth 70 (1984) 356. [7] P. Popov, W.R. Wilcox, J. Crystal Growth 78 (1986) 175. [8] G. Eisa, W.R. Wilcox, J. Crystal Growth 78 (1986) 159. [9] J.I.E. Wanqi, Metall. Trans. 23A (1992) 1363. [10] K.A. Jackson, J.D. Hunt, Trans. Metall. Soc. AIME 236 (1966) 1129. [11] J.C. Brice, P. Capper, C.L. Jones, J.J.G. Gosney, Prog. Crystal Growth and Charact. 13 (1986) 197. [12] V.M. Masalov, G.A. Emel’chenko, J. Crystal Growth 119 (1992) 297. [13] A.G. Kirdyashkin, V.E. Distanov, Int. J. Heat Mass Transfer 33 (1990) 1397. [14] J. Zhou, M. Larrousse, W.R. Wilcox, L.L. Regel, J. Crystal Growth 71 (1985) 579. [15] J.M. Quenisset, R. Naslain, J. Crystal Growth 54 (1981) 465. [16] V. Baskaran, W.R. Wilcox, J. Crystal Growth 67 (1984) 343. [17] X.P. Guo, W. Xu, R.Z. Hong, F. Nie, W.Q. Jie, Acta Aeronaut. Astronaut. Sinica 18 (1997) 310.
Unidirectional solidification of Al—Cu eutectic with the accelerated crucible rotation technique D. Ma *, W.Q. Jie, W. Xu , Y. Li, S. Liu Department of Materials Science, National University of Singapore, Singapore 119260, Singapore The State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi+an 710072, People+s Republic of China Received 9 January 1998; accepted 7 August 1998
Abstract The accelerated crucible rotation technique (ACRT) has been applied to the unidirectional solidification of Al—Cu eutectic to reveal the effect of forced convection on the solidification microstructures by a systematic experimental investigation combining different rotation methods (the maximum rotation rate X "100—400 rpm) with various
growth velocities (» "5—60 lm/s). The results can be concluded as follows: (1) Forced convection introduced by ACRT dramatically changes the eutectic microstructures. When the fluid flow is weaker (Re(270), a great number of lamellar faults occur in the eutectic; on the other hand, when the flow is stronger (Re'500), fluctuation structure forms in the eutectic; (2) the lamellar spacing is not uniformly distributed in the radial direction of the solidified sample with ACRT, and the maximum spacing occurs near the crucible wall while the minimum one at the center of the crucible. The average lamellar spacing obtained by ACRT is smaller than that without ACRT and decreases upon increasing the convection intensity (i.e. increasing X ); (3) whether or not a normal Bridgman process is performed before ACRT shows little
influence on the growth of the nonfacet—nonfacet eutectic. 1998 Elsevier Science B.V. All rights reserved. Keywords: ACRT; Unidirectional solidification; Eutectic growth
1. Introduction The accelerated crucible rotation technique (ACRT), first proposed in the 1970s [1], has been a novel method to produce large and high-quality single crystals of functional materials [2—4]. During the ACRT crystal growth process, the crucible rotates with varying speed in a given
* Corresponding author. Fax: #65 776 3604; e-mail: [email protected].
method and forced convection is produced in the front of solid—liquid interface. The fluid flow suppresses the adverse effects of constitutional supercooling [1], permits the realization of stable planar interface crystal growth at higher critical velocity than that in normal Bridgman process [5] and improves the crystallinity [6]. Therefore, ACRT has been widely applied to Czochralski (CACRT) and Bridgman (ACRT-B) crystal growth processes. In order to search for a new technique of in situ preparation of composites and improve the
0022-0248/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 7 3 5 - 0
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
understanding upon the effect of forced convection on solidification microstructures, several works [7—9] on the application of ACRT to the eutectic alloys have been done during the last two decades. The experimental studies of Popov and Wilcox [7] on Pb—Sn eutectic showed that the stirring by ACRT increased the spiral rate of the microstructure and reduced the length of eutectic zone cooperatively, but had no influence on the lamellar spacing. In the unidirectional solidification of Bi—MnBi with ACRT, Eisa and Wilcox [8] found that the coarseness of MnBi quasiregular fibers was caused by the accelerated crucible rotation at a growth velocity of 9 mm/h. Jie [9] applied ACRT to Al—Si eutectic growth and found that the initial condition before ACRT influenced the growth morphology of Si phase. To this typical nonfacet—facet eutectic, if the crucible rotated at the beginning of the unidirectional solidification, irregular eutectic with short bars and chunks of silicon would form; but if a normal Bridgman process was performed before the crucible rotation, a more satisfactory directional needle-like silicon structure would grow up. On the other hand, the studies on the application of ACRT to eutectic growth process mostly concentrated on the conditions of low growth velocities and low convection intensities (i.e. smaller X ).
There is also no reported evidence upon the influence of the initial conditions on nonfacet—nonfacet eutectic growth process. With the interest concentrated on the effect of the forced convection on the eutectic structures and lamellar spacing, the application of ACRT to Al—Cu eutectic, a widely studied nonfacet—nonfacet eutectic, has been investigated in which different initial conditions, growth velocities and crucible rotation methods have been systematically carried out.
399
The Al—Cu eutectic alloy was melted in the vacuum furnace with 99.99% Al and 99.99% Cu, and cast into bars (ID 8 mm;120 mm long) for further experiments. The graphite crucible with the inner diameter of 8 mm was used for unidirectional solidification. The coolant of liquid Ga—In eutectic was used to strengthen the temperature gradient. The temperature gradient of 200 K/cm was measured in the normal Bridgman process by inserting a thermocouple into the alloy when the hot side of sample was heated over 900°C. During ACRT process, the dynamic temperature gradient was determined to increase with the increase of maximum crucible rotation rate. During the experimental process, the crucible mounted on the rotator was positioned in the hightemperature region of furnace to melt the alloy and then the tip of the crucible was dipped into the coolant about 10 mm to establish a stable temperature gradient. After this, unidirectional solidification with or without ACRT was carried out. For the ACRT process, two groups of experiments were conducted to examine the effect of the initial condition on the eutectic growth. In first group of experiments, a normal Bridgman process was performed before the crucible rotation was applied. In the second group, the crucible rotated at the beginning of the unidirectional solidification. For each group, five growth velocities (» "5, 10, 20, 30, 60 lm/s) in combination with four rotation methods (shown in Fig. 1a—Fig. 1d) were used. The solidified samples were cut along different sections and polished and etched for metallographic analysis. Measurement of lamellar spacing was conducted with an image analyzer (Quantimet 500) where at least six readings were taken to obtain a mean value.
3. Experimental results 2. Experimental methods
3.1. Microstructures by the normal Bridgman method
The experiments were carried out with the ACRT Crystal Growth Equipment described in details elsewhere [9]. The equipment consists of a crucible rotation system, a furnace drawing system, and a thermal field controlling system which can work independently.
During the normal Bridgman process (without crucible rotation), the morphology of the eutectic consists of regular lamellae as shown in Fig. 2 and the interface is nearly planar. The lamellar spacing decreases as the growth velocity increases. Regression analysis shows that the relation between
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Fig. 1. (a)—(d) Crucible rotation methods.
growth velocity and lamellar spacing satisfies » j"88.4 lm/s, which is in good agreement with the theoretical prediction given by Jackson and Hunt [10]. 3.2. Microstructures by the accelerated crucible rotation technique 3.2.1. Eutectic microstructures The fluid flow exerted by the crucible rotation influenced the eutectic structures depending on the applied ACRT methods. At lower X ,
the eutectic microstructures were nearly the same as that by normal Bridgman methods, but there occurred a great number of lamellar faults, as shown in Fig. 3a. At higher X as shown in
Fig. 1b—Fig. 1d, fluctuation structure (Fig. 3b) formed in the eutectic, whose periodic length were approximately equated to » ¹, where ¹ was the period of rotation rate change (here ¹"10 s for all the applied ACRT methods). From Fig. 3c, it can be seen clearly in larger magnification that there
Fig. 2. SEM micrograph of longitudinal section of Al—Cu eutectic grown at 10 lm/s by normal Bridgman method. Growth direction from left to right.
were two stages in each fluctuation period and the lengths of these two stages were approximately equal. Furthermore, it should be noted in Fig. 3c that the lamellar spacing also varied periodically
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
401
Fig. 3. SEM micrographs of longitudinal sections of Al—Cu eutectic showing the effect of ACRT method on solidification structures. (a) » "10.0 lm/s, X "100 rpm, ACRT method shown in Fig. 1a; (b) » "10.0 lm/s, X "200 rpm, ACRT method shown in
Fig. 1b, magnification 200;; (c) » "10.0 lm/s, X "200 rpm, ACRT method shown in Fig. 1b, magnification 400;. Growth
direction from left to right.
with the same periodic length, though the stage with larger spacing was shorter by a factor of 3 than that with smaller spacing. 3.2.2. Lamellar spacing The convection during ACRT-B process induced a decrease in the lamellar spacing. As shown in Fig. 4, lamellar spacing did not remain the same value along the radial direction as that in the nor-
mal Bridgman process. The spacing was smaller at the center of the sample, but became larger at the edge. Fig. 5 indicated that the difference of lamellar spacing between the center and edge of the sample decreased upon increasing the growth velocity and the rotation rate. Although lamellar spacing was not uniform along the radial direction, they distributed symmetrically about the center of the sample. Therefore, one can determine the average lamellar
402
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Fig. 4. SEM micrographs of a transverse section of Al—Cu eutectic showing the microstructure difference at different radial positions where » "10.0 lm/s, X "300 rpm, and the
ACRT method shown in Fig. 1c. (a) Center of the sample; (b) edge of the sample.
Fig. 5. The variation of lamellar spacing at the edge and center of the sample with the growth velocity in the studied ACRT methods. (a) X "200 rpm, rotation method shown in
Fig. 1b. (b) X "400 rpm, rotation method shown in Fig. 1d.
spacing by statistical measurement of many points on the transverse section of the solidified sample. Fig. 6 was obtained by this method, which showed that the average lamellar spacing solidified with ACRT was smaller than that without ACRT, and the larger X becomes, the smaller the spacing
will be. Regression equations of the three curves in Fig. 6 are as follows: Curve 1: j"9.3776»\ , Curve 2: j"6.2916»\ , Curve 3: j"3.9464»\ ,
Fig. 6. The variation of average lamellar spacing of Al—Cu eutectic with the growth velocity using different Bridgman and ACRT methods.
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
403
Fig. 8. Schematic representation of Ekman flow: (a) spin-up; (b) spin-down (after Schulz-Dubois [2]). Fig. 7. Effect of ACRT methods on average lamellar spacing of Al—Cu eutectic under given growth velocities.
which indicated that the well-known relation for eutectic growth, i.e. » j"constant [10], was not applicable to the case where forced convection existed during solidification process. The variation of average lamellar spacing with the maximum rotation rate was plotted in Fig. 7, which showed that for a given growth velocity the lamellar spacing decreased with the increase of maximum rotation rate and when the growth velocity exceeded 30 lm/s, the forced convection had little effect on the average lamellar spacing. 3.3. The effect of initial conditions The above results corresponded to the first group of experiments, in which a normal Bridgman process was performed before the crucible rotation. In order to show the effect of initial condition on nonfacet—nonfacet eutectic growth, another group of experiments were carried out in which the crucible was rotated at the beginning of the unidirectional solidification. In this group, similar phenomena as discussed above occurred which indicated that the initial condition before crucible rotation had little influence on the nonfacet—nonfacet eutectic growth. The reason seemed to be that nonfacet—nonfacet eutectic growth was slightly dependent on crystallographic anisotropy rather than that of facet—nonfacet eutectic such as Al—Si eutectic [9].
4. Discussion 4.1. Transportation condition and formation of fluctuation structure There are three types of forced convection exerted by the crucible rotation, namely, spiralshear flow, Couette flow and Ekman flow [11]. Spiral-shear flow can improve the uniformity of solute and temperature distribution cooperatively. Couette flow can produce more complete mixing in liquid during spin-down process. As for crystal growth process, Ekman flow is of much importance than the former two because it directly acts on S/L interface so as to influence the solidification microstructure. During ACRT-B process, Ekman flow adjusts its flow direction periodically as shown in Fig. 8, which results in the periodical variation of the temperature of S/L interface [12,13] and the fluctuation of the real growth velocity of interface [14]. In the spin-up process, the fluid pumped out is being forced up the side walls and returns more slowly through the bulk of the fluid; and in the spin-down process, the reverse situation occurs. Therefore, Ekman flow induces two transitions in one growth period: spin-up/spin-down transition and spin-down/spin-up transition. In spin-down/ spin-up transition, the hotter fluid from high-temperature liquid zone comes down to the interface so that the interface is warmed up and the thickness of heat boundary layer is decreased. During this process, the real growth velocity of interface is reduced so that some lamellae overgrow locally [10] and as a result the spacing is increased. On the other hand,
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D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
in spin-up/spin-down transition, the cooler fluid near the crucible wall comes down and increases the thickness of heat boundary layer. At this transition, the real growth velocity of the interface is increased so that the lamellae adjust to grow through the movement of lamellar faults and the spacing is decreased [10]. Consequently, the eutectic lamellar spacing changes periodically according to the periodic change of Ekman flow. The transition time can be evaluated by the decay (or setup) time for Ekman flow, i.e. q"a(lu)\ where a is the inner radius of the crucible, l is the viscosity coefficient and u"2pX . In the present case,
assuming a"0.4 cm, l"0.005 cm/s, X "
200 rpm, the transition time is about 1.5 s. Therefore, the time for stable Ekman flow can be estimated as 3.5 s which corresponds to the periods where rotation rate is constant (0 or X ) and the
stable growth length is approximately 35 lm during this period. This evaluation is consistent with the observation shown in Fig. 3c. 4.2. Effect of crucible rotation methods During ACRT process, the intensity of forced convection can be described by Reynolds number which indicates the ratio of the inertia force to the viscous force [11], i.e. Re"a*X/l, where *X is the step change of rotation rate. In our experiments there exists *X"X !X "X since the
minimum rotation rate X "0 rpm. Therefore,
the Reynolds number can be rewritten as Re"aX /l. When the crucible rotation is
placed at a lower rate (X (100 rpm), Ekman
flow is weaker (Re(270). In this case, Ekman flow cannot bring about a large fluctuation in the growth velocity but can lead to the inclination of solute field downward to the flow [16]. Therefore, a great number of lamellar faults are formed corresponding to this flow. On the other hand, larger crucible rotation rate (X '200 rpm)
can lead to stronger Ekman flow (Re'500) which results in the formation of fluctuation eutectic structures. Actually, the two-phase coupled eutectic growth is controlled by the solute interdiffusion which is confined in the boundary layer in front of the S/L interface. The thickness of boundary layer is in the
order of lamellar spacing, i.e. a few microns. If ACRT process provides well-mixing in the liquid ahead of the interface, this will reduce the thickness of boundary layer and therefore decrease the lamellar spacing. But if the growth velocity is large enough (i.e. »'30 lm/s), the original unperturbed boundary layer will be so thin that the effect of convection during ACRT process cannot reach it. This may be attributed to the fact that the application of ACRT at high growth velocity has no significant effect on the eutectic spacing.
4.3. Effect of forced convection on the lamellar spacing Although it has been found in some forced convection solidification experiments that the eutectic spacing increased with increasing the stirring intensity, for Fe—Fe B and Ti—Ti Si [15], Pb—Sn and Cd—Zn [16], our results showed that the lamellar spacing of Al—Cu eutectic decreased upon increasing the rotation rate during ACRT process. In addition, our results do agree with the experimental observation on the unidirectional solidification of Al—4.5% Cu alloy with ACRT [17], which indicated that the primary arm spacing of dendrite also decreased upon increasing the convection intensity, i.e. maximum rotation rate X .
On the other hand, it was found that the lamellar spacing of Al—Cu eutectic did not uniformly distribute along the radial direction during ACRT process. The lamellar spacing increased along the radial direction which was consistent qualitatively with the theoretical prediction given by Baskaran and Wilcox [16]. The reason was that the velocity of local Ekman flow and its gradient in front of the solidification front changes dramatically along the radial direction when the rotation rate of the crucible was large. For example, the estimated difference in flow velocity between center and edge was about 4 cm/s and the difference in the gradient of flow velocity ahead of S/L interface can be up to 10 cm/s for X "200 rpm. Such a great differ ence could be attributed to the difference in spacing between the center and edge which can be up to 1.5 lm in the sample grown at low growth velocity with larger rotation rate.
D. Ma et al. / Journal of Crystal Growth 194 (1998) 398–405
5. Conclusions 1. In the normal Bridgman process, the lamellar spacing and growth velocity of Al—Cu eutectic satisfies » j"88.4 lm/s, which is in good agreement with that predicted by Jackson and Hunt’s model. 2. When the crucible rotates at a lower rate, a great number of lamellar faults are formed in the eutectic structure; when the rotation rate is larger, fluctuation eutectic structure occurs. 3. The lamellar spacing is no longer uniformly distributed in the radial direction of the solidified sample with ACRT. The maximum spacing occurs near the crucible wall while the minimum at the center of the sample. The average lamellar spacing decreases with the increase in the crucible rotation rate. 4. Whether or not a normal Bridgman process is performed before ACRT shows little effect on the nonfacet—nonfacet eutectic growth. References [1] H.J. Scheel, J. Crystal Growth 13/14 (1972) 560.
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[2] H.J. Scheel, E.O. Schulz-Dubois, J. Crystal Growth 8 (1972) 304. [3] P. Capper, I.G. Gale, F. Grainger, J.A. Rokerts, J. Crystal Growth 92 (1988) 1. [4] Ph. Buffat, J.D. Ganiere, M. Rappaz, D.F. Rytz, J. Crystal Growth 749 (1986) 353. [5] A. Horowitz, D. Gazit, J. Makovsky, J. Crystal Growth 61 (1983) 323. [6] P. Capper, J.J. Gosney, C.L. Jones, J. Crystal Growth 70 (1984) 356. [7] P. Popov, W.R. Wilcox, J. Crystal Growth 78 (1986) 175. [8] G. Eisa, W.R. Wilcox, J. Crystal Growth 78 (1986) 159. [9] J.I.E. Wanqi, Metall. Trans. 23A (1992) 1363. [10] K.A. Jackson, J.D. Hunt, Trans. Metall. Soc. AIME 236 (1966) 1129. [11] J.C. Brice, P. Capper, C.L. Jones, J.J.G. Gosney, Prog. Crystal Growth and Charact. 13 (1986) 197. [12] V.M. Masalov, G.A. Emel’chenko, J. Crystal Growth 119 (1992) 297. [13] A.G. Kirdyashkin, V.E. Distanov, Int. J. Heat Mass Transfer 33 (1990) 1397. [14] J. Zhou, M. Larrousse, W.R. Wilcox, L.L. Regel, J. Crystal Growth 71 (1985) 579. [15] J.M. Quenisset, R. Naslain, J. Crystal Growth 54 (1981) 465. [16] V. Baskaran, W.R. Wilcox, J. Crystal Growth 67 (1984) 343. [17] X.P. Guo, W. Xu, R.Z. Hong, F. Nie, W.Q. Jie, Acta Aeronaut. Astronaut. Sinica 18 (1997) 310.