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Morphological instability of cell and dendrite during directional solidification under a high magnetic field
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Acta Materialia 56 (2008) 3146–3161 www.elsevier.com/locate/actamat
Morphological instability of cell and dendrite during directional solidification under a high magnetic field Xi Li a,b,*, Yves Fautrelle b, Zhongming Ren a a
Department of Material Science and Engineering, Shanghai University, Shanghai 200072, China b EPM-Madylam/CNRS, ENSHMG, BP 95, 38402 St Martin d’Heres Cedex, France Received 3 November 2007; received in revised form 4 March 2008; accepted 5 March 2008 Available online 21 April 2008
Abstract The effects of a high magnetic field on the cellular and dendritic morphology in the Al–Cu alloy during directional solidification have been investigated, and results show that morphological instability of cell and dendrite has occurred. Indeed, at lower growth speeds, a high magnetic field of 10 T caused the cell and dendrite to twist and deflect from the solidification direction. Regular tilted structure forms at moderate growth speeds and the secondary dendritic arm in the upstream direction is more developed than the one in the downstream direction. In the case where the primary trunk has not deflected from the solidification direction, the field has caused the sidebranching and the tip-splitting of the cell. These experimental results may be attributed to the thermoelectric magnetic force in the solid cell and dendrite and the change of the surface chemical potential and surface tension of the cellular and dendritic tip. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: High magnetic field; Morphological stability; Cell and dendrite; Directional solidification
1. Introduction Morphological stability theory [1–3] describes in general the stability of the shape of a two-phase interface on the assumption of the isotropy interface properties. In a directional solidification experiment, as the interface velocity increases, a cellular pattern develops, which subsequently transforms into a dendrite structure. Moreover, the effect of slightly anisotropic surface tension and kinetics on the morphological stability has been investigated by Cahn [4] and Coriell and Hardy [5]. O’Hara et al. [6] have discussed the effects of the anisotropy on the interface stability of large facets. For nonfaceted crystals growing from the melt, a variety of morphologies can be assumed depending on the conditions of solidification and the physical properties of the material. Among the latter, the anisotropic properties of the solid–liquid interface capillary energy and/or *
Corresponding author. Address: Department of Material Science and Engineering, Shanghai University, Shanghai 200072, China. E-mail address: [email protected] (X. Li).
the kinetic attachment coefficient play a particular part. It is the anisotropy of these properties that ensures the stability of the dendrites and determines their selection rules. The effects of stress and the crystal orientation on surface tension and the morphological stability have been also investigated widely [7–10]. As a high magnetic field is capable of deflecting the primary dendrite and cell from the solidification direction and producing stress [11,12], the anisotropy on the interface may be changed. Thus, the morphological instability of cell and dendrite during the directional solidification under a high magnetic field will take place. However, hitherto little work has been reported on the effect of a high magnetic field on the morphological instability of cell and dendrite owing to the stress in solid and the change of anisotropic surface tension during the directional solidification. In our previous work [11], the effect of a high magnetic field on the columnar dendrite has been described. This paper extends our previous works and investigates the morphological instability of cell and dendrite under a high magnetic field and its influence factors. It is found that
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.03.018
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for the Al–4.5 wt.% Cu alloy, under a certain growth speed scope, the field is capable of deflecting the primary trunk from the solidification direction and with the increase of the magnetic field intensity, the deflection angle increases. Along with the deflection of the primary trunk, the secondary dendritic arm growth is changed greatly. Indeed, the secondary dendritic arm on upstream side is more developed than the one on downstream side. For the Al– 0.85 wt.% Cu alloy, a high magnetic field (610 T) is not capable of deflecting the dendrite and cell from the solidification direction; however, the field has caused the cell
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and dendrite to branch. The above experimental results are discussed from the thermoelectric magnetic force (TEMF) in solid cell and dendrite and the change of the surface chemical potential and surface tension caused by the TEMF and the deflection of the primary trunk from the solidification direction. 2. Experimental The Al–0.85 wt.% Cu and Al–4.5 wt.% Cu alloys used in this study were prepared with high-purity Al (99.99%)
Fig. 1. Microstructures near the solid–liquid interface directionally solidified the Al–4.5 wt.% Cu alloy at a temperature gradient in the liquid (G) of 38 K/ cm and various growth speeds with and without a 10 T magnetic field: (a) 2 lm/s; (b) 5 lm/s; (c) 50 lm/s; (d) 60 lm/s; (e) 100 lm/s; and (f) 200 lm/s.
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and Cu (99.99%) in an induction furnace. The alloy, being put in a high-purity graphite crucible of 10 cm diameter, was heated to 900 °C, magnetically stirred for half an hour and poured into a graphite mold to cast samples with a diameter of 3 mm and length of 200 mm. The cast sample was enveloped in a high-purity corundum tube with the inner diameter of 3 mm and length of 200 mm. The samples were directionally solidified in the Bridgman apparatus at various growth speeds. The experimental apparatus and many experimental details can be found in Ref. [12]. The temperature gradient and the growth speed were adjusted to form cellular and dendritic regions. Microstructural and crystallographic characteristics were investigated by means of the optical microscope, the X-ray diffraction (XRD) with Cu Ka and the electronbackscattered diffraction (EBSD) in a high-resolution scanning electron microscope equipped with a field emission gun (FE-SEM).
3. Results Fig. 1 shows the longitudinal microstructure near the solid–liquid interface in directionally solidified Al– 4.5 wt.% Cu alloy at various growth speeds without and with a high magnetic field of 10 T. It can be observed that at the lower growth speeds (i.e. 2 and 5 lm s1), the field has caused the cell or cellular-dendrite to become irregular and some dendrites to transform into the grains. When the growth speed increases to a moderate value of 50 or 60 lm s1, the primary trunk deflects from the solidification direction and forms the regular tilted structure under a high magnetic field. At a higher growth speeds (i.e. 100 and 200 lm s1), the deflecting effect of a high magnetic field on the primary truck becomes weak. The microstructure in directionally solidified the Al– 4.5 wt.% Cu alloy at 20 and 50 lm s1 under various magnetic field intensities has been investigated in detail. Fig. 2
Fig. 2. Microstructure in the mushy zone on sections parallel to the solidification direction solidified the Al–4.5 wt.% Cu alloy at a growth speed of 20 lm/ s and a temperature gradient of 62.8 K/cm under various magnetic field intensities: (a) 0 T; (b) 1 T; (c) 2 T; (d) 6 T; (e) 10 T; and (f) 12 T.
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shows the microstructure in the mushy zone of the samples solidified at 20 lm s1 under various magnetic field intensities. It can be observed that when a magnetic field of 1 T is applied, two regions appear: one is the columnar dendrite region; another is the seaweed-like dendrite one. The columnar dendrite begins to degenerate and to deflect from the solidification direction. With the increase of the magnetic field intensity, the columnar dendrite region decreases and the seaweed-like dendrite region increases; and at the same time, the deflection angle of the columnar dendrite increases. When the magnetic field increases to 10 T, the columnar dendrite region disappears totally and the sole seaweed-like structure has formed. Fig. 3 shows the microstructure in the mushy zone of the samples solidified at 50 lm s1 with various magnetic field intensities. It can be observed that at the lower magnetic fields (B < 3 T), the effect of a high magnetic field on the
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primary dendritic arm is not obvious. When the magnetic field exceeds 3 T, the primary dendritic arm begins to deflect from the solidification direction and with the increase of the magnetic field intensity, the deflection angle increases, then reaches a stable value of 45°. It should be emphasized that for the samples solidified at 50 lm s1 under a high magnetic field, the seaweed-like structure has not appeared. Moreover, compared with microstructure solidified at 20 lm s1, it can be learned that the effect of the magnetic field becomes weak during the directional solidification at 50 lm s1. Furthermore, the deflection angle of the primary dendrite arm has been measured and the result is shown in Fig. 4. It can be learned that for the microstructure solidified at 20 lm s1, with the increase of the magnetic field intensity, the columnar dendrite disappears when the deflection angle of the columnar dendrites exceeds 20°. However, for the microstructure
Fig. 3. Microstructure in the mushy zone on sections parallel to the solidification direction directionally solidified the Al–4.5 wt.% Cu alloy at a growth speed of 50 lm/s and a temperature gradient of 62.8 K/cm under various magnetic field intensities: (a) 0 T; (b) 1 T; (c) 2 T; (d) 3 T; (e) 8 T; and (f) 10 T. Arrows denote the direction of the primary dendrite arm.
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Angle between the primary trunk and solidification direction (deg.)
50
40
30
20
50um 20um
10
0 0
2
4
6
8
10
12
Magnetic field intensity B (T) Fig. 4. Relationship between the deflection angle of the primary dendrite arm and the magnetic field intensity for the sample directionally solidified at 50 and 20 lm/s, respectively (G = 62.8 K/cm).
solidified at 50 lm s1, with the increase of the magnetic field intensity, the deflection angle reaches a stable value of 45°. Further, the crystal orientation has also been investigated by the XRD analysis. Fig. 5 shows the XRD on the section perpendicular to the solidification direction. Compared with the XRD of cast, it can be learned that at a lower growth speed, the peaks of the (1 0 0) and (1 1 1) crystal planes have not obviously change. This means that there is not the occurrence of crystal orientation and the magnetic field has caused the [1 0 0] crystal direc-
Intensity, a.u
3500
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100μm/s
2500
80μm/s
2000
50μm/s 1500
20μm/s 1000
10μm/s 500
(111) cast
(100) 0 0
20
40
60
80
100
2θ, deg Fig. 5. XRD on the plane perpendicular to the solidification direction for the samples directionally solidified at various growth speeds under a 10 T magnetic field.
tion to deflect from the solidification direction. At a moderate growth speed, the peak of the (1 1 1) crystal planes increases. This means that the [1 1 1] crystal direction tends to orient along the solidification direction under a high magnetic field. With the increase of the growth speed, it can be observed that the peak on the (1 0 0) crystal plane increases. This means that the effect of the magnetic field on the orientation of the primary trunk becomes weak. The crystal orientation results agree well with the alignment of the primary dendrite arm in Fig. 1. In order to investigate the influence mechanism of a high magnetic field on the dendrite morphology in detail, the microstructure near the solid/liquid interface of the sample solidified at 20 and 50 lm s1 under a 10 T magnetic field has been observed from different planes and analyzed by the EBSD. Fig. 6 shows the microstructure on the different planes of the samples solidified at 20 lm s1 under a 10 T magnetic field and the EBSD result. Fig. 6b and c shows the microstructures on the two longitudinal planes as shown in Fig. 6a. It can be observed that the seaweed-like dendrites appear on the b-plane, and short and tilted dendrites appear on the c-plane. Further, the EBSD is applied to analyze the morphology and the crystal orientation of the dendrite. Fig. 6d and e shows the EBSD map and the pole figure for the microstructure near the solid/liquid interface, respectively. From the EBSD map and the pole figure, it can be learned that the dendrite has been twisted and the [1 1 1] crystal direction tends to orient along the solidification direction. This means the [1 0 0] crystal direction has deflected from the solidification direction. From the above results, the dendrite morphology can be deduced as shown in Fig. 6f. This means that the primary dendrite arm deflects from the solidification direction and becomes short; and with the deflection, the secondary dendritic arm becomes more developed. Fig. 7 shows the microstructures on the different planes of the sample solidified at 50 lm s1. It can be observed that on the b-plane, the dendrite is asymmetric and the secondary dendritic arm on the upstream direction is more developed than the one on the downstream direction. The dendrite morphology is asymmetrically ‘‘V” shaped on the c-plane and is symmetrically ‘‘V” shaped on the dplane. From the above microstructures on the different plane, the dendrite morphology can be deduced as shown in Fig. 7f. This means that an application of a 10 T magnetic field has affected the growth of the high-order dendritic arm along with the deflection of the primary dendritic arm from the solidification direction. Further, by means of the EBSD point analysis, the crystal orientation of the tilted dendrite has been measured. Fig. 8b shows the pole figure of twelve points on the tilted dendrite as shown in Fig. 8a. It can be learned that the [1 1 1] crystal direction tends to orient along the solidification direction (i.e. magnetic field direction). The above morphological change of the dendrite and cell during the directional solidification under a high magnetic field takes place in the case when the primary trunk
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Fig. 6. Microstructure and the pole figure of the Al–4.5 wt.% Cu alloy directionally solidified at a temperature gradient of 62.8 K/cm and a growth speed of 20 lm/s under a magnetic field of 10 T: (a) three-dimensional of the macrostructure close to the solid–liquid interface; (b) microstructure on the b-plane; (c) microstructure on the c-plane; (d) EBSD map close to the solid–liquid interface; (e) the pole figure; and (f) schematic diagram of seaweed-dendrite morphology.
has deflected from the solidification direction. To investigate the formation mechanism of the instability of the cellular and dendritic morphology, it is necessary to investigate the effect of a high magnetic field on dendritic and
cellular morphology in the case when the primary dendritic arm has not deflected from the solidification direction. In order to do this, the microstructure directionally solidified the Al–0.85 wt.% Cu alloy at 10 lm s1 with and without
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Fig. 7. Structure directionally solidified the Al–4.5 wt.% Cu alloy at a temperature gradient of 36 K/cm and a growth speed of 50 lm/s under a 10 T high magnetic field: (a) three-dimensional of the macrostructure close to the solid–liquid interface; (b) microstructure on b-plane; (c) microstructure on c-plane; (d) microstructure on b-plane; and (f) schematic diagram of the tilted dendrite morphology.
the magnetic field has been observed. Fig. 9b shows the microstructure when a 10 T magnetic field is applied during the entire solidification process. Compared with the microstructure in the case of no magnetic field (Fig. 9a), it can be seen that the cell transforms into the developed dendrites; however, the primary dendrite arm has not deflected from
the solidification direction. Further, the XRD analysis was applied to investigate the crystal orientation. Fig. 9f shows the XRD on the section perpendicular to the solidification direction (Fig. 9d) for the same sample as shown in Fig. 9b. It can be learned that the peak on the (1 0 0) plane is most strong and this means that the primary trunk (i.e. the [1 0 0]
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Fig. 8. EBSD point analysis for the tilted dendrite of the same sample as the one in Fig. 7: (a) SEM micrograph of the tilted dendrite and (b) the pole figure for 12 points as shown in (a).
crystal direction) has not deflected from the solidification direction. The above experimental results as to effect of a high magnetic field on the dendrite morphology took place under the condition that the crystals were grown after having nucleated in a high magnetic field. Perhaps the magnetic field has affected the nucleated process and resulted in the change of the dendritic morphology. In order to eliminate the effect of the high magnetic field on the nucleation, an experiment has been designed as follows: the sample was solidified directionally 40 mm (enough length to finish selecting the crystal) in the case of no magnetic field, and then a 10 T magnetic field was applied for 30 min and quenched. Fig. 9c shows the microstructure near the solid– liquid interface during the above experimental processing and it can be found that the cell still splits on the tip. This means that a high magnetic field is capable of branching cell and dendrite besides the deflection of the primary dendrite arm from the solidification direction.
Further, the effect of the high magnetic field intensity on the cellular morphology in the case where the primary dendrite has not deflected from the solidification direction has been studied. Fig. 10 shows the microstructure solidified directionally at 5 lm s1 under various magnetic field intensities. Comparison with the microstructure in the case of no magnetic field (Fig. 10a) shows that the application of a 4 T magnetic field has caused the side-branching of the cell (Fig. 10b and e), and the application of a 10 T magnetic field has caused the tip of cell to split (Fig. 10c and f). Moreover, the effects of a high magnetic field on cellular and dendritic microstructures in different composition alloy have been compared under the same condition (i.e. at the same growth speed and temperature gradient). Fig. 11 shows the microstructure solidified at 5 and 20 lm s1 without and with a magnetic field of 10 T. It can be observed that the effect of the magnetic field on the dendrite in the Al–4.5 wt.% Cu alloy is significant and the field has caused
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3000
Intensity, a.u
2500
(100)
2000 1500 1000 500 0 0
20
40
60
80
100
2θ, deg Fig. 9. Microstructure of the Al–0.85 wt.% Cu alloy directionally solidified at a growth speed of 10 lm/s and a temperature gradient of 62.8 K/cm: (a) without the magnetic field; (b) imposed of a 10 T magnetic field during the entire solidification process; (c) imposed of a 10 T magnetic field for 30 min after growing 40 cm in the case of no magnetic field; and (d) microstructure on the transverse section of the same sample as in (b); (f) the corresponding XRD on (d).
the disappearance of the columnar structure. However, for the Al–0.85 wt.% Cu alloy, although the field has changed the microstructure, the magnetic field of 10 T has not changed the direction of the primary trunk. This means that the effect of the magnetic field is different for different composition alloys and the effect of the magnetic field on the cell and dendrite in the Al–4.5 wt.% Cu alloy is larger than the one in the Al–0.85 wt.% Cu alloy. As a comparison with the directional solidification microstructure under a high magnetic field, the effect of a 10 T high magnetic field on the dendrite growth during the volume solidification process has been investigated. Fig. 12 shows the microstructure solidified the Al– 4.5 wt.% Cu alloy from 750 °C at a cooling rate of 18 K min1 without and with a high magnetic field of 12 T. Compared the microstructure with and without the magnetic field, it can be observed that an application of a high magnetic field has not aligned the dendrite or changed the dendrite growth significantly. This means that the magnetic anisotropy of the Al–dendrite is not strong enough to be aligned under a 12 T magnetic field. It can be deduced that the effect of a magnetic field on the cell and dendrite during the directional solidification should be attributed
to the complex effects between the magnetic field and the temperature gradient together. Further, the effect of the temperature gradient on the dendrite growth has been investigated under a 10 T magnetic field. Figs. 13 and 14 show the transverse microstructure directionally solidified at 30 lm s1 at various temperature gradients. It can be observed that in the case of no magnetic field, with the increase of the temperature gradient, the dendrites become more regular and the primary arm spacing becomes smaller. However, after the application of a 10 T magnetic field, it can be observed that with the increase of the temperature gradient, the columnar dendrites disappear gradually. This means that with the increase of the temperature gradient, the effect of the magnetic field on the dendrite array becomes more pronounced. This proves further that temperature gradient plays a great role in the influencing process of the magnetic field on the dendritic and cellular growth. 4. Discussion From the above experimental results and the ones in Ref. [11], it can be learned that the morphological instabil-
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Fig. 10. The branching of the cell in the case of no deflection of the primary trunk from the solidification direction: (a–c) showing the microstructure solidified the Al–0.85 wt.% Cu alloy at a growth speed of 5 lm/s under 0 T, 4 T and 10 T magnetic fields, respective; (d–f) showing the schematic diagram of the tip morphology in (a–c), respectively.
ity of cell and dendrite has occurred during the directional solidification under a high magnetic field and that the alloy composition, temperature gradient, growth speed and magnetic field intensity have played the important roles. For the cell and dendrite directionally solidified under a high magnetic field, two kinds of forces could be produced: one is the magnetic force which is caused by the magnetic anisotropy of the dendrite and cell; another is the thermoelectric magnetic force (TEMF) which is caused by the interaction between the thermoelectric current and the magnetic field. The above experimental results (Fig. 12) have proved that the magnetic anisotropy of the dendrite and cell is not strong enough to be aligned under a high magnetic field of 12 T. Moreover, the intensity of the thermoelectric current in the inter-dendrites has been predicted and the predicted intensity of the thermoelectric current is about 105 A m2 in aluminum with a 104 K m1 applied temperature gradient [13]. The TEMF under a 10 T magnetic field caused by the interaction between the magnetic field and the thermoelectric current is about 106 N m3 and this force is strong enough to change the dendritic and cellular morphology. Moreover, the above experimen-
tal results have shown that the temperature gradient which induces the thermoelectric current has played a crucial role. Therefore, it can be deduced that the TEMF should be responsible mainly for the morphological instability of cell and dendrite. 4.1. Effect of the TEMF in solid on the cellular and dendritic morphology It is well known that in any material a temperature gra~ produces a Seebeck electromotive force S rT ~ , dient rT where S is the thermoelectric power of the material [14]. If the gradients of S and T are not parallel, then a thermoelectric (TE) current is generated in the system. The TE current in the inter-dendrites has been investigated [13] and the following is an approximation for the electric current density jS in solid dendrites and jL in the neighboring liquid: rL rS fL ðS s S L ÞG rL fL þ rS fS rL rS fS jL ¼ ðS s S L ÞG rL fL þ rS fS
jS ¼
ð1Þ ð2Þ
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Fig. 11. Microstructure near the solid–liquid interface on sections parallel to the solidification direction without and with a 10 T magnetic field for different composition alloy: (a) 0.85 wt.% Cu, 5 lm/s; (b) 0.85 wt.% Cu, 20 lm/s; (c) 4.5 wt.% Cu, 5 lm/s; and (d) 4.5 wt.% Cu, 20 lm/s.
where rL, rS are the electrical conductivity of liquid and solid; fL, fS the liquid and solid fractions; SL, Ss the thermoelectric power of the liquid and solid; G the temperature gradient. When an external magnetic field B is applied, since the thermoelectric current JTE cannot be everywhere parallel to B, thus the Lorentz forces JTE B (i.e. TEMF) will produce in liquid and solid as shown in Fig. 15a. The TEMF in liquid will drive some motions (i.e. so-called thermoelectric magnetic convection (TEMC)). The velocity field is such that Lorentz forces are balanced by both viscous friction and electromagnetic braking arising from the electromotive term u B. The driving force varies as B, and the braking force varies as B2, therefore, as shown by Shercliff [14], there is an optimum strength of the magnetic field, such that the Hartmann number Ha ¼ 1=2 ðr=qmÞ BL is of order unity (where m and L represent the kinematic viscosity and a typical length scale). However, for the TEMF on solid, it will increase with the increase of the magnetic field intensity. In previous works [13,15], the TEMC in liquid on the crucible, the primary dendrite and high-order dendrite scales have been investigated. According to previous works, a 10 T magnetic field is strong enough to damp the TEMC in liquid at the macroscale (the scale of the crucible) and mecroscale (the scale of cell and primary dendrite). Therefore, the TEMC in liquid should not affect the cellular and dendritic growth. This means that the instability of cells and dendrites under a high magnetic field should be attributed to the TEMF in solid dendrite and cell. Inserting Eq. (1) into the Lorentz forces JTE B gives
FS ¼
rL rS fL ðS s S L ÞGB rL fL þ rS fS
ð3Þ
From Eq. (3), it can be learned that with the increase of the temperature gradient and the magnetic field intensity, the TEMF in the solid cell and dendrite increases. As a consequence, the effect of the magnetic field on the cellular and dendritic array increases. This is consistent with the above experimental results which show that with the increase of the magnetic field intensity and temperature gradient, the effect of the field on the cell and dendrite becomes stronger. Moreover, with the increase of the content of Cu, owing to the increase of the Ss SL value, the thermoelectric magnetic force will increase; as a consequence, the effect of the effect on the cell and dendrite array becomes strong. This agrees with the experimental results that the effect of a high magnetic field on the dendrite and cell in the Al– 4.5 wt.% Cu alloy is stronger than the one in the Al– 0.85 wt.% Cu alloy. The TEMF in the regular dendrite and cell will produce a torque on the tip of the cell and dendrite (Fig. 15a) and this torque will cause the regular dendrite and cell to break, twist and deform. As a consequence, dissociative grains and deformed and irregular cell and dendrite will form. For the dissociative grains, the TEMF will cause them to rotate round the solidification direction as shown in Fig. 15c. For the deformed and irregular cell and dendrite, owing to the morphological asymmetry, the TEMF on them will be asymmetrical as shown in Fig. 15b. As a consequence, a resultant force perpendicular to the solidification direction will impose on the
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primary arm, the secondary arm is subjected to TEMF and the TEMF on the secondary arm will balance the TEMF on the primary dendrite arm; as a consequence, when the deflection angle reaches 45°, a stable structure will form as shown in Figs. 16 and 18c. Thus, the [1 1 1] crystal direction will tend to orient along the solidification direction (i.e. the magnetic field direction). Moreover, for the columnar grains (i.e. cellular and cellular-to-dendritic structure at a lower growth speed) the crystal anisotropy is weak; the dendrite and cell are determined mainly by the TEMF. Thus, the irregular dendrite will appear. With the increase of the growth speed and the copper content, the growing crystal becomes more dendritic and the crystal anisotropy becomes strong. The primary dendrite direction is determined by two opposing factors: one is the nature of dendrites to grow in the [1 0 0] direction and the other is the TEMF effect, which tends to cause the primary arm to twist and deflect from the solidification direction. Therefore, the formation of the regular tilted dendrite appears only in moderate composition alloy and at moderate growth speed under the right magnetic field. It is easy to understand that the effect of the TEMF on the dendrite and cell occurs mainly in the mushy zone. Therefore, the mushy zone depth and the staying time of cell and dendrite in the mushy zone also play crucial roles. Since with the increase of the growth speed, the staying time in mushy zone decreases; therefore, the effects of a high magnetic field will become weak. Moreover, from the phase diagram of the Al–Cu alloy near Al as shown in Fig. 17, it can be leaned that the mushy zone of the Al–4.5 wt.% Cu alloy is larger than the one of the Al– 0.85 wt.% Cu alloy; therefore, the effect of a high magnetic field on the dendrite and cell in the Al–4.5 wt.% Cu alloy is stronger than the one in the Al–0.85 wt.% Cu alloy. 4.2. Effect of the change of the surface chemical potential and surface tension on the cellular and dendritic morphology under a high magnetic field
Fig. 12. Effect of a 12 T high magnetic field on the microstructure of the Al–4.5 wt.% Cu alloy during the volume solidification process: (a) microstructure without the field; (b) microstructure on the longitudinal section, 12 T; and (c) microstructure on the transverse section, 12 T.
tip of the cell and dendrite besides the torque. This resultant force on the tip of the cell and dendrite will result in the deflection of the cell and dendrite from the solidification direction. Thus, the asymmetry TEMF on the deformed and irregular cell and dendrite will tend to deflect the cell and dendrite from the solidification direction besides the rotation round the solidification direction. At the same time, with the increase of the deflection angle, the growth of the secondary arm on the upstream side will be enhanced and become developed. In the same way as the
The above experimental results have also shown that a high magnetic field has caused the cell to split and branch in the case that the primary trunk has not deflected from the solidification direction. This should be attributed to the change in the surface chemical potential and surface tension on the tip of cell and dendrite caused by the TEMF in solid cell and dendrite. It is well known that the development of stresses within solids can lead to morphological changes [16,17]. The evolution of the surface profiles is dictated by the chemical potential along the surface. The chemical potential along an interface, l, is typically written as [18] lðxÞ ¼ l0 þ cXjðxÞ rnn ðxÞX
ð4Þ
where l0 is the chemical potential of the equilibrium flat interface bounding an unstressed solid, c the interfacial tension, X an atomic volume, j the curvature of the interface
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Fig. 13. Macrostructure on the transverse section in directionally solidified the Al–4.5 wt.% Cu alloy at 30 lm/s and various temperature gradients without and with a high magnetic field of 10 T: (a, b) 48 K/cm; (c, d) 52 K/cm; (e, f) 58 K/cm; and (g, h) 66 K/cm.
Fig. 14. The corresponding microstructure on the transverse section of the same samples in Fig. 13 solidified at the following temperature gradient: (a, b) 48 K/cm and (c, d) 66 K/cm.
and rnn the stress on the solid. The second term on the right-hand side of Eq. (4) is the surface energy contribution to chemical potential. The third term accounts for the influence of the stress, normal to the interface, on the emission or absorption of an atom at that interface. During the directional solidification under a high magnetic field, there exists a thermoelectric magnetic stress rTE nn ; thus, the chemical potential will be modified as follows: ð5Þ lðxÞ ¼ l0 þ cXjðxÞ rnn þ rTE nn ðxÞX
Just as a temperature or concentration gradient can overcome the surface energy and destabilize a planar solidification front and branch the cell, a stress can destabilize a planar solidification front and branch the cell. Therefore, the side-branching and tip-splitting (Fig. 10b and c) should be attributed to the TEMF in the solid cell. For the dendrite that has deflected from the solidification direction under a high magnetic field, besides the change of the surface tension caused by the TEMF, the deflection of the dendrite also causes the surface tension
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Fig. 15. Schematic illustration of the TEMF in liquid and solid caused by the interaction between the thermoelectric current and the magnetic field and the effect of the TEMF on the cellular and dendritic array: (a) the TEMF imposed in liquid near the tip of the regular cell and the dendrite and on the tip of the cell and dendrite; (b) the TEMF imposed on the irregular and deformed cell and dendrite; and (c) three possible effects of the TEMF on the cellular and dendritic array.
Primary arm
G
Secondary arm
B
Fig. 16. Schematic illustration of the dendrite morphology: From (a) to (c) indicating the development of the dendritic morphology during the deflection of the cell and primary dendrite arm from the solidification direction.
Temperature (˚C)
700
ΔT01
675
d =
Liquidus
Δ T02
650
of the crystal. It is well known that surface tension anisotropy plays a crucial role in the formation of cells and dendrites’ microstructure [19]. Anisotropy in solidification originates from the capillary length, which is proportional to the surface stiffness as follows:
Δ T0 =TL-TS ΔT 0
625
G
Liquid Soliidus
β+L
S(α) TE 600 C01
575 0
Solid
CSE (5.7)10 0.85
4.5
20
30
CE (33.3)
Wt. %Cu
Fig. 17. Phase diagram of the Al–Cu alloy near Al.
to change and surface tension is related to the deflection angle. Therefore, the effective in-plane anisotropy depends on not only on the crystal itself, but also on the orientation
o2 cð^nÞ ð6Þ oa2 where c is surface tension and a angle between the normal to the interface ^n and the pulling direction [20]. Mathematically, the surface tension can be represented in three dimensions as
ec ð^nÞ ¼ cð^nÞ þ
cð^nÞ ¼ c0 ½1 þ e0 ðn41 þ n42 þ n43 Þ
ð7Þ
where c0 is the isotropic part of the surface tension and e0 is the degree of anisotropy. n1, n2 and n3 are the components of a unit vector ^n that parametrizes the function in three dimensions. cð^nÞ is the magnitude of the surface tension for a surface orientation so that its normal is along ^ n.
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Fig. 18 shows the crystal orientation of the cubic Al crystal in the case with and without an the magnetic field during the directional solidification, and corresponding surface stiffness (gray) and the anisotropic part of the surface tension (black). In the case of no magnetic field, the (1 0 0) plane faces the heat flow direction; the surface stiffness (gray) has the same symmetry as the surface tension (black). They are 90° out of phase and the fingers tend to grow towards maximum surface. Thus a stable dendrite will form with sidebranch at approximately right angles (Fig. 18b). As the magnetic field is capable of deflecting the primary dendrite arm from the solidification and resulting in orienting the [1 1 1] direction of Al crystal along the solidification direction during the directional solidification, the (1 1 1) plane will face the solidification direction. Thus, isotropic growth will take place as shown in Fig. 18d. This means that the growth of the dendrite along the [1 0 0], [0 1 0] and [1 0 0] directions is equal; as a consequence, the competitive growth of primary arms and secondary arms growing preferentially in the upstream direction will take place. Thus, a stable structure will form as shown in Figs. 16 and 18c. At the same time, the growth of the primary
dendrite arm becomes weak and the growth of secondary arms on the upstream side of a primary arm becomes faster. If the growth of a primary dendrite arm is stopped, the secondary arm growth from the primary arm adjacent on the downstream side of the stopped arm should laterally develop in the front of the stopped arm. From such a secondary arm a tertially arm will grow as if this arm were connected to the stopped primary arm. As a result, the seaweed-like dendrite will form. As the deflection angle is different at different growth speed and magnetic field intensity, the anisotropy is different; as a consequence, the dendrite morphology will appear varied. 5. Conclusion The cellular and dendritic morphology during the directional solidification under a high magnetic field has been investigated in detail experimentally. The results indicate that a high magnetic field has caused the occurrence of the cellular and dendritic morphological instability. Indeed, at lower growth speeds, a high magnetic field of 10 T has caused the cell and dendrite to twist and deflect from the
Fig. 18. Surface stiffness (gray) and the anisotropic part of the surface tension (black) for different Al crystal (cubic) orientation: (a) Al crystal orientation with a [1 0 0] crystal direction along the solidification direction; (b) the significant fourfold anisotropy in a (1 0 0) plane; (c) crystal orientation of Al with a [1 1 1] crystal direction along the solidification direction; and (d) isotropy in a (1 1 1) plane.
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solidification direction; and with the increase of the growth speed, the columnar cell and dendrite transform into seaweed-like dendrite and the tilted columnar dendrite gradually. For the tilted columnar dendrite, it is found that the secondary arm in the upstream side is more developed than the one in the downstream side. Furthermore, the effect of a high magnetic field on the cellular morphology in the case where the primary trunk has not deflected from the solidification direction (i.e. the [1 0 0] direction aligns along the growth direction) has been investigated, and the results show that the magnetic field has caused the side-branching and the tip-splitting of cell. Moreover, it has been found that the alloy composition, growth speed, temperature gradient and magnetic field intensity have played crucial roles in influencing the dendritic and cellular morphology. The above experimental results are discussed from the TEMF in solid and the change of the surface chemical potential and surface tension caused by the TEMF and the deflection of the primary trunk from the solidification direction. Acknowledgements This work is supported by the European Space Agency through the IMPRESS project and the Natural Science Foundation of China (Nos. 50234020, 50225416 and 59871026). The authors are indebted to Prof. R. Moreau
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and Prof. T. Duffar in CNRS, Grenoble, Prof. B. Billia in CNRS, Marseille; and Prof. C. Esling and Y.D. Zhang in Metz University for helpful and fruitful discussions. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
Mullins WW, Sekerka RF. J Appl Phys 1963;34:323. Mullins WW, Sekerka RF. J Appl Phys 1964;34:444. Sekerka RF. J Cryst Growth 1968;3/4:71. Cahn JW. In: Peiser HS, editor. Crystal growth. Oxford: Pergamon Press; 1967. p. 681. Coriell SR, Hardy SC. J Res Natl Bur Std 1969;73A:65. O’Hara S, Tarshis LA, Tiller WA, Hunt JP. J Cryst Growth 1968;3/ 4:555. Asaro RJ, Tiller WA. Metall Trans 1972;3:1789. Grinfeld MA. Dokl Akad Nauk SSSR 1986;290:1358. Yang WH, Srolovitz DJ. Phys Rev Lett 1993;71:1593. Akamatsu S, Faivre G, Ihle T. Phys Rev E 1995;51:4751. Li X, Fautrelle Y, Ren ZM. Acta Mater 2007;55:5347. Li X, Ren ZM, Fautrelle Y. Acta Mater 2006;54:5349. Lehmann P, Moreau R, Camel D, Bolcato R. Acta Mater 1998;46:4067. Shercliff JA. J Fluid Mech 1979;91:231. Li X, Fautrelle Y, Ren ZM. Acta Mater 2007;55:3803. Grinfeld MA. Sov Phys Dokl 1996;31:831. Asaro RJ, Tiller WA. Metall Trans A 1972;3:1789. Herring C. J Appl Phys 1950;21:437. Langer JS. Chance and matter. Amsterdam: North-Holland; 1987. p. 629. Utter B, Bodenschatz E. Phys Rev E 2002;66:051604.
Acta Materialia 56 (2008) 3146–3161 www.elsevier.com/locate/actamat
Morphological instability of cell and dendrite during directional solidification under a high magnetic field Xi Li a,b,*, Yves Fautrelle b, Zhongming Ren a a
Department of Material Science and Engineering, Shanghai University, Shanghai 200072, China b EPM-Madylam/CNRS, ENSHMG, BP 95, 38402 St Martin d’Heres Cedex, France Received 3 November 2007; received in revised form 4 March 2008; accepted 5 March 2008 Available online 21 April 2008
Abstract The effects of a high magnetic field on the cellular and dendritic morphology in the Al–Cu alloy during directional solidification have been investigated, and results show that morphological instability of cell and dendrite has occurred. Indeed, at lower growth speeds, a high magnetic field of 10 T caused the cell and dendrite to twist and deflect from the solidification direction. Regular tilted structure forms at moderate growth speeds and the secondary dendritic arm in the upstream direction is more developed than the one in the downstream direction. In the case where the primary trunk has not deflected from the solidification direction, the field has caused the sidebranching and the tip-splitting of the cell. These experimental results may be attributed to the thermoelectric magnetic force in the solid cell and dendrite and the change of the surface chemical potential and surface tension of the cellular and dendritic tip. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: High magnetic field; Morphological stability; Cell and dendrite; Directional solidification
1. Introduction Morphological stability theory [1–3] describes in general the stability of the shape of a two-phase interface on the assumption of the isotropy interface properties. In a directional solidification experiment, as the interface velocity increases, a cellular pattern develops, which subsequently transforms into a dendrite structure. Moreover, the effect of slightly anisotropic surface tension and kinetics on the morphological stability has been investigated by Cahn [4] and Coriell and Hardy [5]. O’Hara et al. [6] have discussed the effects of the anisotropy on the interface stability of large facets. For nonfaceted crystals growing from the melt, a variety of morphologies can be assumed depending on the conditions of solidification and the physical properties of the material. Among the latter, the anisotropic properties of the solid–liquid interface capillary energy and/or *
Corresponding author. Address: Department of Material Science and Engineering, Shanghai University, Shanghai 200072, China. E-mail address: [email protected] (X. Li).
the kinetic attachment coefficient play a particular part. It is the anisotropy of these properties that ensures the stability of the dendrites and determines their selection rules. The effects of stress and the crystal orientation on surface tension and the morphological stability have been also investigated widely [7–10]. As a high magnetic field is capable of deflecting the primary dendrite and cell from the solidification direction and producing stress [11,12], the anisotropy on the interface may be changed. Thus, the morphological instability of cell and dendrite during the directional solidification under a high magnetic field will take place. However, hitherto little work has been reported on the effect of a high magnetic field on the morphological instability of cell and dendrite owing to the stress in solid and the change of anisotropic surface tension during the directional solidification. In our previous work [11], the effect of a high magnetic field on the columnar dendrite has been described. This paper extends our previous works and investigates the morphological instability of cell and dendrite under a high magnetic field and its influence factors. It is found that
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.03.018
X. Li et al. / Acta Materialia 56 (2008) 3146–3161
for the Al–4.5 wt.% Cu alloy, under a certain growth speed scope, the field is capable of deflecting the primary trunk from the solidification direction and with the increase of the magnetic field intensity, the deflection angle increases. Along with the deflection of the primary trunk, the secondary dendritic arm growth is changed greatly. Indeed, the secondary dendritic arm on upstream side is more developed than the one on downstream side. For the Al– 0.85 wt.% Cu alloy, a high magnetic field (610 T) is not capable of deflecting the dendrite and cell from the solidification direction; however, the field has caused the cell
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and dendrite to branch. The above experimental results are discussed from the thermoelectric magnetic force (TEMF) in solid cell and dendrite and the change of the surface chemical potential and surface tension caused by the TEMF and the deflection of the primary trunk from the solidification direction. 2. Experimental The Al–0.85 wt.% Cu and Al–4.5 wt.% Cu alloys used in this study were prepared with high-purity Al (99.99%)
Fig. 1. Microstructures near the solid–liquid interface directionally solidified the Al–4.5 wt.% Cu alloy at a temperature gradient in the liquid (G) of 38 K/ cm and various growth speeds with and without a 10 T magnetic field: (a) 2 lm/s; (b) 5 lm/s; (c) 50 lm/s; (d) 60 lm/s; (e) 100 lm/s; and (f) 200 lm/s.
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and Cu (99.99%) in an induction furnace. The alloy, being put in a high-purity graphite crucible of 10 cm diameter, was heated to 900 °C, magnetically stirred for half an hour and poured into a graphite mold to cast samples with a diameter of 3 mm and length of 200 mm. The cast sample was enveloped in a high-purity corundum tube with the inner diameter of 3 mm and length of 200 mm. The samples were directionally solidified in the Bridgman apparatus at various growth speeds. The experimental apparatus and many experimental details can be found in Ref. [12]. The temperature gradient and the growth speed were adjusted to form cellular and dendritic regions. Microstructural and crystallographic characteristics were investigated by means of the optical microscope, the X-ray diffraction (XRD) with Cu Ka and the electronbackscattered diffraction (EBSD) in a high-resolution scanning electron microscope equipped with a field emission gun (FE-SEM).
3. Results Fig. 1 shows the longitudinal microstructure near the solid–liquid interface in directionally solidified Al– 4.5 wt.% Cu alloy at various growth speeds without and with a high magnetic field of 10 T. It can be observed that at the lower growth speeds (i.e. 2 and 5 lm s1), the field has caused the cell or cellular-dendrite to become irregular and some dendrites to transform into the grains. When the growth speed increases to a moderate value of 50 or 60 lm s1, the primary trunk deflects from the solidification direction and forms the regular tilted structure under a high magnetic field. At a higher growth speeds (i.e. 100 and 200 lm s1), the deflecting effect of a high magnetic field on the primary truck becomes weak. The microstructure in directionally solidified the Al– 4.5 wt.% Cu alloy at 20 and 50 lm s1 under various magnetic field intensities has been investigated in detail. Fig. 2
Fig. 2. Microstructure in the mushy zone on sections parallel to the solidification direction solidified the Al–4.5 wt.% Cu alloy at a growth speed of 20 lm/ s and a temperature gradient of 62.8 K/cm under various magnetic field intensities: (a) 0 T; (b) 1 T; (c) 2 T; (d) 6 T; (e) 10 T; and (f) 12 T.
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shows the microstructure in the mushy zone of the samples solidified at 20 lm s1 under various magnetic field intensities. It can be observed that when a magnetic field of 1 T is applied, two regions appear: one is the columnar dendrite region; another is the seaweed-like dendrite one. The columnar dendrite begins to degenerate and to deflect from the solidification direction. With the increase of the magnetic field intensity, the columnar dendrite region decreases and the seaweed-like dendrite region increases; and at the same time, the deflection angle of the columnar dendrite increases. When the magnetic field increases to 10 T, the columnar dendrite region disappears totally and the sole seaweed-like structure has formed. Fig. 3 shows the microstructure in the mushy zone of the samples solidified at 50 lm s1 with various magnetic field intensities. It can be observed that at the lower magnetic fields (B < 3 T), the effect of a high magnetic field on the
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primary dendritic arm is not obvious. When the magnetic field exceeds 3 T, the primary dendritic arm begins to deflect from the solidification direction and with the increase of the magnetic field intensity, the deflection angle increases, then reaches a stable value of 45°. It should be emphasized that for the samples solidified at 50 lm s1 under a high magnetic field, the seaweed-like structure has not appeared. Moreover, compared with microstructure solidified at 20 lm s1, it can be learned that the effect of the magnetic field becomes weak during the directional solidification at 50 lm s1. Furthermore, the deflection angle of the primary dendrite arm has been measured and the result is shown in Fig. 4. It can be learned that for the microstructure solidified at 20 lm s1, with the increase of the magnetic field intensity, the columnar dendrite disappears when the deflection angle of the columnar dendrites exceeds 20°. However, for the microstructure
Fig. 3. Microstructure in the mushy zone on sections parallel to the solidification direction directionally solidified the Al–4.5 wt.% Cu alloy at a growth speed of 50 lm/s and a temperature gradient of 62.8 K/cm under various magnetic field intensities: (a) 0 T; (b) 1 T; (c) 2 T; (d) 3 T; (e) 8 T; and (f) 10 T. Arrows denote the direction of the primary dendrite arm.
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Angle between the primary trunk and solidification direction (deg.)
50
40
30
20
50um 20um
10
0 0
2
4
6
8
10
12
Magnetic field intensity B (T) Fig. 4. Relationship between the deflection angle of the primary dendrite arm and the magnetic field intensity for the sample directionally solidified at 50 and 20 lm/s, respectively (G = 62.8 K/cm).
solidified at 50 lm s1, with the increase of the magnetic field intensity, the deflection angle reaches a stable value of 45°. Further, the crystal orientation has also been investigated by the XRD analysis. Fig. 5 shows the XRD on the section perpendicular to the solidification direction. Compared with the XRD of cast, it can be learned that at a lower growth speed, the peaks of the (1 0 0) and (1 1 1) crystal planes have not obviously change. This means that there is not the occurrence of crystal orientation and the magnetic field has caused the [1 0 0] crystal direc-
Intensity, a.u
3500
3000
100μm/s
2500
80μm/s
2000
50μm/s 1500
20μm/s 1000
10μm/s 500
(111) cast
(100) 0 0
20
40
60
80
100
2θ, deg Fig. 5. XRD on the plane perpendicular to the solidification direction for the samples directionally solidified at various growth speeds under a 10 T magnetic field.
tion to deflect from the solidification direction. At a moderate growth speed, the peak of the (1 1 1) crystal planes increases. This means that the [1 1 1] crystal direction tends to orient along the solidification direction under a high magnetic field. With the increase of the growth speed, it can be observed that the peak on the (1 0 0) crystal plane increases. This means that the effect of the magnetic field on the orientation of the primary trunk becomes weak. The crystal orientation results agree well with the alignment of the primary dendrite arm in Fig. 1. In order to investigate the influence mechanism of a high magnetic field on the dendrite morphology in detail, the microstructure near the solid/liquid interface of the sample solidified at 20 and 50 lm s1 under a 10 T magnetic field has been observed from different planes and analyzed by the EBSD. Fig. 6 shows the microstructure on the different planes of the samples solidified at 20 lm s1 under a 10 T magnetic field and the EBSD result. Fig. 6b and c shows the microstructures on the two longitudinal planes as shown in Fig. 6a. It can be observed that the seaweed-like dendrites appear on the b-plane, and short and tilted dendrites appear on the c-plane. Further, the EBSD is applied to analyze the morphology and the crystal orientation of the dendrite. Fig. 6d and e shows the EBSD map and the pole figure for the microstructure near the solid/liquid interface, respectively. From the EBSD map and the pole figure, it can be learned that the dendrite has been twisted and the [1 1 1] crystal direction tends to orient along the solidification direction. This means the [1 0 0] crystal direction has deflected from the solidification direction. From the above results, the dendrite morphology can be deduced as shown in Fig. 6f. This means that the primary dendrite arm deflects from the solidification direction and becomes short; and with the deflection, the secondary dendritic arm becomes more developed. Fig. 7 shows the microstructures on the different planes of the sample solidified at 50 lm s1. It can be observed that on the b-plane, the dendrite is asymmetric and the secondary dendritic arm on the upstream direction is more developed than the one on the downstream direction. The dendrite morphology is asymmetrically ‘‘V” shaped on the c-plane and is symmetrically ‘‘V” shaped on the dplane. From the above microstructures on the different plane, the dendrite morphology can be deduced as shown in Fig. 7f. This means that an application of a 10 T magnetic field has affected the growth of the high-order dendritic arm along with the deflection of the primary dendritic arm from the solidification direction. Further, by means of the EBSD point analysis, the crystal orientation of the tilted dendrite has been measured. Fig. 8b shows the pole figure of twelve points on the tilted dendrite as shown in Fig. 8a. It can be learned that the [1 1 1] crystal direction tends to orient along the solidification direction (i.e. magnetic field direction). The above morphological change of the dendrite and cell during the directional solidification under a high magnetic field takes place in the case when the primary trunk
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Fig. 6. Microstructure and the pole figure of the Al–4.5 wt.% Cu alloy directionally solidified at a temperature gradient of 62.8 K/cm and a growth speed of 20 lm/s under a magnetic field of 10 T: (a) three-dimensional of the macrostructure close to the solid–liquid interface; (b) microstructure on the b-plane; (c) microstructure on the c-plane; (d) EBSD map close to the solid–liquid interface; (e) the pole figure; and (f) schematic diagram of seaweed-dendrite morphology.
has deflected from the solidification direction. To investigate the formation mechanism of the instability of the cellular and dendritic morphology, it is necessary to investigate the effect of a high magnetic field on dendritic and
cellular morphology in the case when the primary dendritic arm has not deflected from the solidification direction. In order to do this, the microstructure directionally solidified the Al–0.85 wt.% Cu alloy at 10 lm s1 with and without
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Fig. 7. Structure directionally solidified the Al–4.5 wt.% Cu alloy at a temperature gradient of 36 K/cm and a growth speed of 50 lm/s under a 10 T high magnetic field: (a) three-dimensional of the macrostructure close to the solid–liquid interface; (b) microstructure on b-plane; (c) microstructure on c-plane; (d) microstructure on b-plane; and (f) schematic diagram of the tilted dendrite morphology.
the magnetic field has been observed. Fig. 9b shows the microstructure when a 10 T magnetic field is applied during the entire solidification process. Compared with the microstructure in the case of no magnetic field (Fig. 9a), it can be seen that the cell transforms into the developed dendrites; however, the primary dendrite arm has not deflected from
the solidification direction. Further, the XRD analysis was applied to investigate the crystal orientation. Fig. 9f shows the XRD on the section perpendicular to the solidification direction (Fig. 9d) for the same sample as shown in Fig. 9b. It can be learned that the peak on the (1 0 0) plane is most strong and this means that the primary trunk (i.e. the [1 0 0]
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Fig. 8. EBSD point analysis for the tilted dendrite of the same sample as the one in Fig. 7: (a) SEM micrograph of the tilted dendrite and (b) the pole figure for 12 points as shown in (a).
crystal direction) has not deflected from the solidification direction. The above experimental results as to effect of a high magnetic field on the dendrite morphology took place under the condition that the crystals were grown after having nucleated in a high magnetic field. Perhaps the magnetic field has affected the nucleated process and resulted in the change of the dendritic morphology. In order to eliminate the effect of the high magnetic field on the nucleation, an experiment has been designed as follows: the sample was solidified directionally 40 mm (enough length to finish selecting the crystal) in the case of no magnetic field, and then a 10 T magnetic field was applied for 30 min and quenched. Fig. 9c shows the microstructure near the solid– liquid interface during the above experimental processing and it can be found that the cell still splits on the tip. This means that a high magnetic field is capable of branching cell and dendrite besides the deflection of the primary dendrite arm from the solidification direction.
Further, the effect of the high magnetic field intensity on the cellular morphology in the case where the primary dendrite has not deflected from the solidification direction has been studied. Fig. 10 shows the microstructure solidified directionally at 5 lm s1 under various magnetic field intensities. Comparison with the microstructure in the case of no magnetic field (Fig. 10a) shows that the application of a 4 T magnetic field has caused the side-branching of the cell (Fig. 10b and e), and the application of a 10 T magnetic field has caused the tip of cell to split (Fig. 10c and f). Moreover, the effects of a high magnetic field on cellular and dendritic microstructures in different composition alloy have been compared under the same condition (i.e. at the same growth speed and temperature gradient). Fig. 11 shows the microstructure solidified at 5 and 20 lm s1 without and with a magnetic field of 10 T. It can be observed that the effect of the magnetic field on the dendrite in the Al–4.5 wt.% Cu alloy is significant and the field has caused
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3000
Intensity, a.u
2500
(100)
2000 1500 1000 500 0 0
20
40
60
80
100
2θ, deg Fig. 9. Microstructure of the Al–0.85 wt.% Cu alloy directionally solidified at a growth speed of 10 lm/s and a temperature gradient of 62.8 K/cm: (a) without the magnetic field; (b) imposed of a 10 T magnetic field during the entire solidification process; (c) imposed of a 10 T magnetic field for 30 min after growing 40 cm in the case of no magnetic field; and (d) microstructure on the transverse section of the same sample as in (b); (f) the corresponding XRD on (d).
the disappearance of the columnar structure. However, for the Al–0.85 wt.% Cu alloy, although the field has changed the microstructure, the magnetic field of 10 T has not changed the direction of the primary trunk. This means that the effect of the magnetic field is different for different composition alloys and the effect of the magnetic field on the cell and dendrite in the Al–4.5 wt.% Cu alloy is larger than the one in the Al–0.85 wt.% Cu alloy. As a comparison with the directional solidification microstructure under a high magnetic field, the effect of a 10 T high magnetic field on the dendrite growth during the volume solidification process has been investigated. Fig. 12 shows the microstructure solidified the Al– 4.5 wt.% Cu alloy from 750 °C at a cooling rate of 18 K min1 without and with a high magnetic field of 12 T. Compared the microstructure with and without the magnetic field, it can be observed that an application of a high magnetic field has not aligned the dendrite or changed the dendrite growth significantly. This means that the magnetic anisotropy of the Al–dendrite is not strong enough to be aligned under a 12 T magnetic field. It can be deduced that the effect of a magnetic field on the cell and dendrite during the directional solidification should be attributed
to the complex effects between the magnetic field and the temperature gradient together. Further, the effect of the temperature gradient on the dendrite growth has been investigated under a 10 T magnetic field. Figs. 13 and 14 show the transverse microstructure directionally solidified at 30 lm s1 at various temperature gradients. It can be observed that in the case of no magnetic field, with the increase of the temperature gradient, the dendrites become more regular and the primary arm spacing becomes smaller. However, after the application of a 10 T magnetic field, it can be observed that with the increase of the temperature gradient, the columnar dendrites disappear gradually. This means that with the increase of the temperature gradient, the effect of the magnetic field on the dendrite array becomes more pronounced. This proves further that temperature gradient plays a great role in the influencing process of the magnetic field on the dendritic and cellular growth. 4. Discussion From the above experimental results and the ones in Ref. [11], it can be learned that the morphological instabil-
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Fig. 10. The branching of the cell in the case of no deflection of the primary trunk from the solidification direction: (a–c) showing the microstructure solidified the Al–0.85 wt.% Cu alloy at a growth speed of 5 lm/s under 0 T, 4 T and 10 T magnetic fields, respective; (d–f) showing the schematic diagram of the tip morphology in (a–c), respectively.
ity of cell and dendrite has occurred during the directional solidification under a high magnetic field and that the alloy composition, temperature gradient, growth speed and magnetic field intensity have played the important roles. For the cell and dendrite directionally solidified under a high magnetic field, two kinds of forces could be produced: one is the magnetic force which is caused by the magnetic anisotropy of the dendrite and cell; another is the thermoelectric magnetic force (TEMF) which is caused by the interaction between the thermoelectric current and the magnetic field. The above experimental results (Fig. 12) have proved that the magnetic anisotropy of the dendrite and cell is not strong enough to be aligned under a high magnetic field of 12 T. Moreover, the intensity of the thermoelectric current in the inter-dendrites has been predicted and the predicted intensity of the thermoelectric current is about 105 A m2 in aluminum with a 104 K m1 applied temperature gradient [13]. The TEMF under a 10 T magnetic field caused by the interaction between the magnetic field and the thermoelectric current is about 106 N m3 and this force is strong enough to change the dendritic and cellular morphology. Moreover, the above experimen-
tal results have shown that the temperature gradient which induces the thermoelectric current has played a crucial role. Therefore, it can be deduced that the TEMF should be responsible mainly for the morphological instability of cell and dendrite. 4.1. Effect of the TEMF in solid on the cellular and dendritic morphology It is well known that in any material a temperature gra~ produces a Seebeck electromotive force S rT ~ , dient rT where S is the thermoelectric power of the material [14]. If the gradients of S and T are not parallel, then a thermoelectric (TE) current is generated in the system. The TE current in the inter-dendrites has been investigated [13] and the following is an approximation for the electric current density jS in solid dendrites and jL in the neighboring liquid: rL rS fL ðS s S L ÞG rL fL þ rS fS rL rS fS jL ¼ ðS s S L ÞG rL fL þ rS fS
jS ¼
ð1Þ ð2Þ
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Fig. 11. Microstructure near the solid–liquid interface on sections parallel to the solidification direction without and with a 10 T magnetic field for different composition alloy: (a) 0.85 wt.% Cu, 5 lm/s; (b) 0.85 wt.% Cu, 20 lm/s; (c) 4.5 wt.% Cu, 5 lm/s; and (d) 4.5 wt.% Cu, 20 lm/s.
where rL, rS are the electrical conductivity of liquid and solid; fL, fS the liquid and solid fractions; SL, Ss the thermoelectric power of the liquid and solid; G the temperature gradient. When an external magnetic field B is applied, since the thermoelectric current JTE cannot be everywhere parallel to B, thus the Lorentz forces JTE B (i.e. TEMF) will produce in liquid and solid as shown in Fig. 15a. The TEMF in liquid will drive some motions (i.e. so-called thermoelectric magnetic convection (TEMC)). The velocity field is such that Lorentz forces are balanced by both viscous friction and electromagnetic braking arising from the electromotive term u B. The driving force varies as B, and the braking force varies as B2, therefore, as shown by Shercliff [14], there is an optimum strength of the magnetic field, such that the Hartmann number Ha ¼ 1=2 ðr=qmÞ BL is of order unity (where m and L represent the kinematic viscosity and a typical length scale). However, for the TEMF on solid, it will increase with the increase of the magnetic field intensity. In previous works [13,15], the TEMC in liquid on the crucible, the primary dendrite and high-order dendrite scales have been investigated. According to previous works, a 10 T magnetic field is strong enough to damp the TEMC in liquid at the macroscale (the scale of the crucible) and mecroscale (the scale of cell and primary dendrite). Therefore, the TEMC in liquid should not affect the cellular and dendritic growth. This means that the instability of cells and dendrites under a high magnetic field should be attributed to the TEMF in solid dendrite and cell. Inserting Eq. (1) into the Lorentz forces JTE B gives
FS ¼
rL rS fL ðS s S L ÞGB rL fL þ rS fS
ð3Þ
From Eq. (3), it can be learned that with the increase of the temperature gradient and the magnetic field intensity, the TEMF in the solid cell and dendrite increases. As a consequence, the effect of the magnetic field on the cellular and dendritic array increases. This is consistent with the above experimental results which show that with the increase of the magnetic field intensity and temperature gradient, the effect of the field on the cell and dendrite becomes stronger. Moreover, with the increase of the content of Cu, owing to the increase of the Ss SL value, the thermoelectric magnetic force will increase; as a consequence, the effect of the effect on the cell and dendrite array becomes strong. This agrees with the experimental results that the effect of a high magnetic field on the dendrite and cell in the Al– 4.5 wt.% Cu alloy is stronger than the one in the Al– 0.85 wt.% Cu alloy. The TEMF in the regular dendrite and cell will produce a torque on the tip of the cell and dendrite (Fig. 15a) and this torque will cause the regular dendrite and cell to break, twist and deform. As a consequence, dissociative grains and deformed and irregular cell and dendrite will form. For the dissociative grains, the TEMF will cause them to rotate round the solidification direction as shown in Fig. 15c. For the deformed and irregular cell and dendrite, owing to the morphological asymmetry, the TEMF on them will be asymmetrical as shown in Fig. 15b. As a consequence, a resultant force perpendicular to the solidification direction will impose on the
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primary arm, the secondary arm is subjected to TEMF and the TEMF on the secondary arm will balance the TEMF on the primary dendrite arm; as a consequence, when the deflection angle reaches 45°, a stable structure will form as shown in Figs. 16 and 18c. Thus, the [1 1 1] crystal direction will tend to orient along the solidification direction (i.e. the magnetic field direction). Moreover, for the columnar grains (i.e. cellular and cellular-to-dendritic structure at a lower growth speed) the crystal anisotropy is weak; the dendrite and cell are determined mainly by the TEMF. Thus, the irregular dendrite will appear. With the increase of the growth speed and the copper content, the growing crystal becomes more dendritic and the crystal anisotropy becomes strong. The primary dendrite direction is determined by two opposing factors: one is the nature of dendrites to grow in the [1 0 0] direction and the other is the TEMF effect, which tends to cause the primary arm to twist and deflect from the solidification direction. Therefore, the formation of the regular tilted dendrite appears only in moderate composition alloy and at moderate growth speed under the right magnetic field. It is easy to understand that the effect of the TEMF on the dendrite and cell occurs mainly in the mushy zone. Therefore, the mushy zone depth and the staying time of cell and dendrite in the mushy zone also play crucial roles. Since with the increase of the growth speed, the staying time in mushy zone decreases; therefore, the effects of a high magnetic field will become weak. Moreover, from the phase diagram of the Al–Cu alloy near Al as shown in Fig. 17, it can be leaned that the mushy zone of the Al–4.5 wt.% Cu alloy is larger than the one of the Al– 0.85 wt.% Cu alloy; therefore, the effect of a high magnetic field on the dendrite and cell in the Al–4.5 wt.% Cu alloy is stronger than the one in the Al–0.85 wt.% Cu alloy. 4.2. Effect of the change of the surface chemical potential and surface tension on the cellular and dendritic morphology under a high magnetic field
Fig. 12. Effect of a 12 T high magnetic field on the microstructure of the Al–4.5 wt.% Cu alloy during the volume solidification process: (a) microstructure without the field; (b) microstructure on the longitudinal section, 12 T; and (c) microstructure on the transverse section, 12 T.
tip of the cell and dendrite besides the torque. This resultant force on the tip of the cell and dendrite will result in the deflection of the cell and dendrite from the solidification direction. Thus, the asymmetry TEMF on the deformed and irregular cell and dendrite will tend to deflect the cell and dendrite from the solidification direction besides the rotation round the solidification direction. At the same time, with the increase of the deflection angle, the growth of the secondary arm on the upstream side will be enhanced and become developed. In the same way as the
The above experimental results have also shown that a high magnetic field has caused the cell to split and branch in the case that the primary trunk has not deflected from the solidification direction. This should be attributed to the change in the surface chemical potential and surface tension on the tip of cell and dendrite caused by the TEMF in solid cell and dendrite. It is well known that the development of stresses within solids can lead to morphological changes [16,17]. The evolution of the surface profiles is dictated by the chemical potential along the surface. The chemical potential along an interface, l, is typically written as [18] lðxÞ ¼ l0 þ cXjðxÞ rnn ðxÞX
ð4Þ
where l0 is the chemical potential of the equilibrium flat interface bounding an unstressed solid, c the interfacial tension, X an atomic volume, j the curvature of the interface
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Fig. 13. Macrostructure on the transverse section in directionally solidified the Al–4.5 wt.% Cu alloy at 30 lm/s and various temperature gradients without and with a high magnetic field of 10 T: (a, b) 48 K/cm; (c, d) 52 K/cm; (e, f) 58 K/cm; and (g, h) 66 K/cm.
Fig. 14. The corresponding microstructure on the transverse section of the same samples in Fig. 13 solidified at the following temperature gradient: (a, b) 48 K/cm and (c, d) 66 K/cm.
and rnn the stress on the solid. The second term on the right-hand side of Eq. (4) is the surface energy contribution to chemical potential. The third term accounts for the influence of the stress, normal to the interface, on the emission or absorption of an atom at that interface. During the directional solidification under a high magnetic field, there exists a thermoelectric magnetic stress rTE nn ; thus, the chemical potential will be modified as follows: ð5Þ lðxÞ ¼ l0 þ cXjðxÞ rnn þ rTE nn ðxÞX
Just as a temperature or concentration gradient can overcome the surface energy and destabilize a planar solidification front and branch the cell, a stress can destabilize a planar solidification front and branch the cell. Therefore, the side-branching and tip-splitting (Fig. 10b and c) should be attributed to the TEMF in the solid cell. For the dendrite that has deflected from the solidification direction under a high magnetic field, besides the change of the surface tension caused by the TEMF, the deflection of the dendrite also causes the surface tension
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Fig. 15. Schematic illustration of the TEMF in liquid and solid caused by the interaction between the thermoelectric current and the magnetic field and the effect of the TEMF on the cellular and dendritic array: (a) the TEMF imposed in liquid near the tip of the regular cell and the dendrite and on the tip of the cell and dendrite; (b) the TEMF imposed on the irregular and deformed cell and dendrite; and (c) three possible effects of the TEMF on the cellular and dendritic array.
Primary arm
G
Secondary arm
B
Fig. 16. Schematic illustration of the dendrite morphology: From (a) to (c) indicating the development of the dendritic morphology during the deflection of the cell and primary dendrite arm from the solidification direction.
Temperature (˚C)
700
ΔT01
675
d =
Liquidus
Δ T02
650
of the crystal. It is well known that surface tension anisotropy plays a crucial role in the formation of cells and dendrites’ microstructure [19]. Anisotropy in solidification originates from the capillary length, which is proportional to the surface stiffness as follows:
Δ T0 =TL-TS ΔT 0
625
G
Liquid Soliidus
β+L
S(α) TE 600 C01
575 0
Solid
CSE (5.7)10 0.85
4.5
20
30
CE (33.3)
Wt. %Cu
Fig. 17. Phase diagram of the Al–Cu alloy near Al.
to change and surface tension is related to the deflection angle. Therefore, the effective in-plane anisotropy depends on not only on the crystal itself, but also on the orientation
o2 cð^nÞ ð6Þ oa2 where c is surface tension and a angle between the normal to the interface ^n and the pulling direction [20]. Mathematically, the surface tension can be represented in three dimensions as
ec ð^nÞ ¼ cð^nÞ þ
cð^nÞ ¼ c0 ½1 þ e0 ðn41 þ n42 þ n43 Þ
ð7Þ
where c0 is the isotropic part of the surface tension and e0 is the degree of anisotropy. n1, n2 and n3 are the components of a unit vector ^n that parametrizes the function in three dimensions. cð^nÞ is the magnitude of the surface tension for a surface orientation so that its normal is along ^ n.
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Fig. 18 shows the crystal orientation of the cubic Al crystal in the case with and without an the magnetic field during the directional solidification, and corresponding surface stiffness (gray) and the anisotropic part of the surface tension (black). In the case of no magnetic field, the (1 0 0) plane faces the heat flow direction; the surface stiffness (gray) has the same symmetry as the surface tension (black). They are 90° out of phase and the fingers tend to grow towards maximum surface. Thus a stable dendrite will form with sidebranch at approximately right angles (Fig. 18b). As the magnetic field is capable of deflecting the primary dendrite arm from the solidification and resulting in orienting the [1 1 1] direction of Al crystal along the solidification direction during the directional solidification, the (1 1 1) plane will face the solidification direction. Thus, isotropic growth will take place as shown in Fig. 18d. This means that the growth of the dendrite along the [1 0 0], [0 1 0] and [1 0 0] directions is equal; as a consequence, the competitive growth of primary arms and secondary arms growing preferentially in the upstream direction will take place. Thus, a stable structure will form as shown in Figs. 16 and 18c. At the same time, the growth of the primary
dendrite arm becomes weak and the growth of secondary arms on the upstream side of a primary arm becomes faster. If the growth of a primary dendrite arm is stopped, the secondary arm growth from the primary arm adjacent on the downstream side of the stopped arm should laterally develop in the front of the stopped arm. From such a secondary arm a tertially arm will grow as if this arm were connected to the stopped primary arm. As a result, the seaweed-like dendrite will form. As the deflection angle is different at different growth speed and magnetic field intensity, the anisotropy is different; as a consequence, the dendrite morphology will appear varied. 5. Conclusion The cellular and dendritic morphology during the directional solidification under a high magnetic field has been investigated in detail experimentally. The results indicate that a high magnetic field has caused the occurrence of the cellular and dendritic morphological instability. Indeed, at lower growth speeds, a high magnetic field of 10 T has caused the cell and dendrite to twist and deflect from the
Fig. 18. Surface stiffness (gray) and the anisotropic part of the surface tension (black) for different Al crystal (cubic) orientation: (a) Al crystal orientation with a [1 0 0] crystal direction along the solidification direction; (b) the significant fourfold anisotropy in a (1 0 0) plane; (c) crystal orientation of Al with a [1 1 1] crystal direction along the solidification direction; and (d) isotropy in a (1 1 1) plane.
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solidification direction; and with the increase of the growth speed, the columnar cell and dendrite transform into seaweed-like dendrite and the tilted columnar dendrite gradually. For the tilted columnar dendrite, it is found that the secondary arm in the upstream side is more developed than the one in the downstream side. Furthermore, the effect of a high magnetic field on the cellular morphology in the case where the primary trunk has not deflected from the solidification direction (i.e. the [1 0 0] direction aligns along the growth direction) has been investigated, and the results show that the magnetic field has caused the side-branching and the tip-splitting of cell. Moreover, it has been found that the alloy composition, growth speed, temperature gradient and magnetic field intensity have played crucial roles in influencing the dendritic and cellular morphology. The above experimental results are discussed from the TEMF in solid and the change of the surface chemical potential and surface tension caused by the TEMF and the deflection of the primary trunk from the solidification direction. Acknowledgements This work is supported by the European Space Agency through the IMPRESS project and the Natural Science Foundation of China (Nos. 50234020, 50225416 and 59871026). The authors are indebted to Prof. R. Moreau
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and Prof. T. Duffar in CNRS, Grenoble, Prof. B. Billia in CNRS, Marseille; and Prof. C. Esling and Y.D. Zhang in Metz University for helpful and fruitful discussions. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
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