Effect of a weak transverse magnetic field on solidification structure during directional solidification

Effect of a weak transverse magnetic field on solidification structure during directional solidification

Available online at www.sciencedirect.com ScienceDirect Acta Materialia 64 (2014) 367–381 www.elsevier.com/locate/actamat Effect of a weak transverse...

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Available online at www.sciencedirect.com

ScienceDirect Acta Materialia 64 (2014) 367–381 www.elsevier.com/locate/actamat

Effect of a weak transverse magnetic field on solidification structure during directional solidification X. Li a,b,⇑, Y. Fautrelle b, A. Gagnoud b, D. Du a, J. Wang a,b, Z. Ren a, H. Nguyen-Thi c,d, N. Mangelinck-Noel c,d a

Department of Material Science and Engineering, Shanghai University, Shanghai 200072, People’s Republic of China b SIMAP-EPM-Madylam/G-INP/CNRS, PHELMA, BP 75, 38402 St Martin d’Heres Ce´dex, France c Aix Marseille University, Campus Saint-Jerome, Case 142, 13397 Marseille Ce´dex 20, France d CNRS, IM2NP, Campus Saint-Jerome, Case 142, 13397 Marseille Ce´dex 20, France Received 9 October 2013; accepted 23 October 2013 Available online 5 December 2013

Abstract Six alloys were directionally solidified at low growth speeds (1–5 lm s1) under a weak transverse magnetic field (60.5 T). The results show that the application of a weak transverse magnetic field significantly modified the solidification structure. Indeed, it was found that, along with the refinement of cells/dendrites, the magnetic field caused the deformation of liquid–solid interfaces, extensive segregations (i.e., freckles and channels) in the mushy zone, and a change in the mushy zone length. Further, in situ monitoring of the initial transient of the directional solidification was carried out by means of synchrotron X-ray radiography. It was observed that dendrite fragments and equiaxed grains were moved approximately along the direction perpendicular to the magnetic field. This result shows that a thermoelectric magnetic force (TEMF) acted on the liquid or the solid during directional solidification under a weak magnetic field. The TEMF during directional solidification under a transverse magnetic field was investigated numerically. The results reveal that a unidirectional TEMF acted on the solid and induced thermoelectric magnetic convection (TEMC) in the liquid. Modification of the solidification structure under a weak magnetic field is attributed to TEMC-driven heat transfer and interdendritic solute transport and TEMF-driven motion of dendrite fragments. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Transverse magnetic field; Directional solidification; Solidification structure; Synchrotron radiation

1. Introduction Solidification in a magnetic field is an interesting topic and has attracted much attention from researchers. However, the effect of a static magnetic field on solidification has not been well understood, mainly because the experimental observations were made in different configurations, such as ingot solidification or directional solidification. In ingot solidification, the magnetic field brakes the convection in the liquid and reduces the heat-transfer rate [1,2]. In directional solidification, the magnetic field also brakes ⇑ Corresponding author at: SIMAP-EPM-Madylam/G-INP/CNRS, PHELMA, BP 75, 38402 St Martin d’Heres Ce´dex, France. E-mail address: [email protected] (X. Li).

the convection, but in directional solidification in the dendritic regime some unexpected behaviors are observed [3–7]. These behaviors depend on the composition of the alloy and the experimental conditions. Youdelis and Dorward [3,4] applied a 3.4 T transverse field on the directionally solidified Al–Cu alloy. The result showed that the value of the effective partition coefficient decreased with the presence of the field, as if the magnetic field enhanced mass transport in the liquid. Tewari et al. [5] found that the cellular array was severely distorted, and stripes of freckles on the plane perpendicular to the magnetic field formed when a Pb–Sn alloy was solidified vertically at very low growth speeds under a 0.45 T transverse magnetic field. The experiment were performed by Alboussie`re et al. [6] and Lakar [7] on Bi–60 wt.% Sn and Cu–45 wt.% Ag alloys, solidified

1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.10.050

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vertically under solutally and thermally stabilizing conditions with a 0.6 T transverse or 1.5 T axial magnetic field. Large freckles appear in this case, showing that a new movement has been created. Alboussie`re et al. [6] suggested that this new flow was induced by the interaction between the magnetic field and thermoelectric (TE) effects. Subse-

quently, Lehmann et al. [8] offered some experimental evidence for thermoelectromagnetic convection (TEMC). Regarding the forces induced by magnetic fields, three extra forces in the liquid as well as the solid may normally be introduced under the magnetic field. One is the magnetic force arising from the interaction of the magnetism of a

Fig. 1. Microstructures near the liquid–solid interface in six directionally solidified alloys both without and with a 0.5 T transverse magnetic field: (a) Al dendrite in Al–2.5 wt.% Cu alloy, 5 lm s1; (b) Sn dendrite in Sn–20 wt.% Bi alloy, 1 lm s1; (c) Al2Cu dendrite in Al–40 wt.% Cu alloy, 2 lm s1; (d) c dendrite in DZ417G Ni-based superalloy, 5 lm s1; (e) Al dendrite in Al–7 wt.% Si alloy, 2 lm s1; (f) Sn dendrite in Sn–20 wt.% Pb alloy, 1 lm s1.

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material and the magnetic field [9]. Moreover, when the liquid is moving, there is a second force, the Lorentz force, generated by the interaction between the induced electric current and the applied magnetic field [10]. The third force is the thermoelectric magnetic force (TEMF) induced by the interaction between the TE current and the magnetic field, which was first noticed by Shercliff [11]. The magnetic

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force and Lorentz force have been widely investigated [12–14], whereas little attention has hitherto been paid to the TEMF, and there is a lack of sufficient experimental evidence to prove the TEMF. Previous work [15] investigated the effect of the TEMF on solidification structure during directional solidification under an axial magnetic field. It was found that the TEMF

Fig. 2. Transverse structures in the directionally solidified Al–40 wt.% Cu, Al–7 wt.% Si and Ni-based alloys under various magnetic fields.

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significantly affects solidification structure during directional solidification. In this work, the effect of a transverse magnetic field on the solidification structure in six different alloys was been investigated experimentally. The results show that, along with refinement of the cell/dendrite, the magnetic field caused the deflection of the liquid–solid interfaces, extensive segregations (i.e., freckles and channels) in the mushy zone and a change in the mushy zone length. Furthermore, the processing of solidification experiment under the magnetic field was recorded by in situ synchrotron X-ray imaging. Dendrite fragments and equiaxed grains were observed to be moved approximately along the direction perpendicular to the magnetic field. Modification of the solidification structure under a weak magnetic field is attributed to the TEMC-driven heat transfer and interdendritic solute transport and the TEMF-driven motion of dendrite fragments. The aim of the present work is twofold: (1) to investigate the effect of a transverse magnetic field on the solidification structure during directional solidification; and (2) to study the effect of interdendritic TEMC on the solidification structure, thereby gaining a deeper under-

standing of the effect of interdendritic convection on the solidification structure. 2. Description of experiments Six alloys (i.e., Al–2.5 wt.% Cu, Sn–20 wt.% Pb, Ni-based DZ417G (C 0.18, Cr 8.96, Mo 3.08, Co 9.72, V 0.86, B 0.015, Al 5.41, Ti 4.50, Fe 0.23, P 0.002, S 0.002, Si 0.04, Mn 0.05, and Ni as balance, wt.%), Al–7 wt.% Si, Sn–20 wt.% Bi and Al–40 wt.% Cu alloys) were solidified directionally under a weak transverse magnetic field. Cast samples were enveloped in tubes of high-purity corundum with an inner diameter of 3 mm and a depth of 200 mm for directional solidification. The experimental device is composed of an electromagnet, a Bridgman– Stockbarge-type furnace, and a growth velocity and temperature controller. The electromagnet with a pole diameter of 20 cm and a pole separation of 18 cm can produce a transverse static magnetic field with adjustable intensity up to 1 T. The furnace, consisting of nonmagnetic material, has a negligible effect on the field

Fig. 3. Transverse microstructures below the eutectic isotherm in the directionally solidified Al–0.85 wt.% Cu alloy at a growth speed of 10 lm s1 under various magnetic fields: (a) 0 T; (b) 0.1 T; (c) 0.3 T; (d) 0.5 T.

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Fig. 4. Transverse microstructures below the eutectic isotherm in the directionally solidified Al–7 wt.% Si alloy at a growth speed of 50 lm s1 under various magnetic fields: (a) 0 T; (b) 0.01 T; (c) 0.1 T; (d) 0.5 T.

uniformity. The temperature in the furnace can reach 1600 °C, and was controlled with a precision of ±1 K. A water-cooled cylinder containing liquid Ga–In–Sn metal (LMC) was used to cool the sample. The temperature gradient in the sample was controlled by adjusting the temperature of the furnace hot zone, which was insulated from the LMC by a refractory disk. To perform directional solidification, the apparatus was designed so that the sample moves downwards, while the furnace remains fixed. During the experiment, the samples in the corundum crucibles were melted and directionally solidified in the Bridgman apparatus by pulling the crucible assembly into the LMC cylinder at various velocities. The etched samples obtained from these experiments were examined by optical microscope. Electron probe microanalysis (EPMA) was used to measure the distribution of the solute Cu. The numerical simulation was performed by using the finite element commercial code FLUX-EXPERTe,

available in the authors’ laboratory (SIMAP-EPM/GINP/CNRS). The study configuration is two-dimensional, and the two liquid and solid regions are considered. The liquid–solid interface is prescribed, and its shape is a simplified representation of a cell array. In this model, the electrical and hydrodynamic phenomena are modeled during the imposition of the temperature gradient and the magnetic field. Here, only the single component w of the velocity perpendicular to the plane is considered, and the unknowns of the problem are the electrical potential and the velocity perpendicular to the study plane. The basic equations of this problem are ! ! ! ! ! J ¼ ri r u  ri S i r T þ ri V  B ; i ¼ s in the solid or l in the liquid ! divð J Þ ¼ 0

ð1Þ ð2Þ

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(a) 150 130

Dnedritic spacing, λ (µm)

Cellular spacing, λ (µm)

(b) 500

5μm/s 10μm/s

140

120 110 100 90 80

20μm/s 50μm/s

450 400 350 300 250 200

70

150

60 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0

0.2

0.4

0.6

0.8

1.0

Magnetic field intensity, B (T)

Magnetic field intensity, B (T)

Fig. 5. Effect of the magnetic field on cellular/dendritic spacing: (a) cellular spacing as a function of the magnetic field intensity during directional solidification of Al–0.85 wt.% Cu alloy; (b) primary dendritic spacing as a function of the magnetic field intensity during directional solidification of Al– 7 wt.% Si alloy.

(a)

(b)

(c)

800µm

800µm

800µm

Mushy zone length, L (mm)

(d) 5

2μm/s 5μm/s

4

3

2

1 0.0

0.1

0.2

0.3

0.4

0.5

Magnetic field intensity, B (T)

Fig. 6. Microstructures near the liquid–solid interface in the directionally solidified Al–7 wt.% Si alloy at a growth speed of 2 lm s1 under various magnetic fields: (a) 0 T; (b) 0.05 T; (c) 0.5 T; (d) mushy zone length as a function of magnetic field intensity.

lDw þ

! ! J  B ¼0 z

ð3Þ

! where J is the electric current density, which consists of ! two components ðJ x ; J y Þ, V the fluid velocity, which has

a single component (0, 0, w), l is the dynamic viscosity, ! B is the applied magnetic field, which has a single component, u, T, Si respectively denote the electric potential, the temperature and the absolute TE power. The electrical

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Concentration (wt% Cu)

28 0T 0.1T 0.3T

24 20 16 12 8 4 0 0

500

1000

1500

2000

2500

3000

Distance (µm)

Concentration (wt% Cu)

1.0 0T 0.1T 0.3T

0.8 0.6 0.4 0.2 0.0

Distance (µm) Fig. 7. Radial distribution of the Cu content in the mushy zone at 0.1 mm below the liquid–solid interface of the samples in the directionally solidified Al–0.85 wt.% Cu alloy at a growth speed of 10 lm s1 under various magnetic fields.

conductivity ri as well as the absolute TE power Si takes different values in the liquid and solid phases. In order to take into account the thermoelectricity, an additional term proportional to the temperature gradient has to be added to classical forms of Ohm’s law. The magnetic field induced ! by the electric currents is neglected so that B stands for the applied magnetic field. Eq. (2) is solved both in the solid and liquid regions, while Eq. (3) holds only in the liquid region. As far as the temperature is concerned, the effect of the deviation of the temperature gradient with respect to the vertical applied one is neglected. More details for numerical simulation process can be found in Ref. [16]. 3. Results Six alloys (i.e., Al–2.5 wt.% Cu, Sn–20 wt.% Pb, Nibased DZ417G, Sn–20 wt.% Bi, Al–7 wt.% Si and Al– 40 wt.% Cu alloys) were solidified directionally with and without a 0.5 T transverse magnetic field. Fig. 1 shows the longitudinal structures near the quenched liquid–solid interface obtained in the directionally solidified abovementioned alloys at low growth speeds (1–5 lm s1). The growth length at quenching was 60 mm. The dendrite morphology without the magnetic field is typically columnar, and the liquid–solid interface is nearly protruding. However, when a transverse magnetic field is applied, the liquid–solid interface shape becomes sloping, and the

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mushy zone length decreases. Moreover, the cellular/dendritic spacing reduces, and segregation (i.e., freckles and channels) occurs under the magnetic field. The transverse microstructures below the eutectic isotherm in the above mentioned three alloys (i.e., Al–40 wt.% Cu, Al–7.0 wt.% Si and Ni-based DZ417G alloys) are shown in Fig. 2. As seen in the figures, freckles and channel segregation form on one side of the samples. The Al–0.85 wt.% Cu and Al–7 wt.% Si alloys were used to study the effect of the magnetic field on the cellular/dendritic spacing and the mushy zone length in detail. Figs. 3 and 4 indicate the transverse microstructures in the directionally solidified Al–0.85 wt.% Cu alloy at 10 lm s1 and the Al–7 wt.% Si alloy at 50 lm s1 under various magnetic fields, respectively. It can be observed that the cellular/dendritic spacing decreases as the magnetic field increases. The cellular and primary dendritic spacing as a function of the magnetic field intensity is shown in Fig. 5. Fig. 6 shows the longitudinal structures near the liquid–solid interface in the directionally solidified Al–7 wt.% Si alloy under various magnetic fields. Along with the refinement of the cell, the mushy zone length decreases as the magnetic field increases. The mushy zone length as a function of the magnetic field intensity under various growth speeds is shown in Fig. 6d. Here, it should be emphasized that the decrease in the mushy zone length and the refinement of the cell/ dendrite occur at the same time. This means that the same factor affects the mushy zone length and the cell/dendrite morphology. Moreover, the distributions of the solute Cu on the scales of the sample were measured by EPMA. Fig. 7 shows the radial distribution of the Cu content in the mushy zone at the position of 0.1 mm from the liquid–solid interface for the samples in the directionally solidified Al–0.85 wt.% Cu alloy at a growth speed of 10 lm s1 under 0 T, 0.1 T and 0.3 T magnetic fields. Comparison of the distribution of the Cu content without and with the magnetic field indicates that the concentration of the solute Cu in the solid increases from one side of the sample to the other side of the sample under the magnetic field. To visualize the evolution of solidification microstructure during directional solidification under the magnetic field, in situ synchrotron X-ray imaging of the directionally solidified Al–Cu alloy was performed. Fig. 8 shows the general assembly drawing of the experimental apparatus. In situ and real-time observation of the solidification process was realized using synchrotron X-ray radiography at the European Synchrotron Radiation Facility (ESRF). The main surface of a thin sheet-like sample (40  6  0.2 mm3) was set perpendicular to the incident monochromatic X-ray beam. Directional solidification was realized by the power-down method, with displacement of neither the sample nor the furnace. In this method, the temperatures of the hot and cold zones of the furnace were first adjusted to achieve the desired temperature gradient, in the range 20–40 K cm1. The energy of the monochromatic X-ray beam was adjusted to 14 keV, which is an

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(a)

(b)

(c)

Fig. 8. Sketch of the furnace with a transverse magnetic field for in situ observation: (a) general assembly drawing of the experiment apparatus; (b) ESRF, Grenoble, France; (c) Bridgman furnace.

appropriate value for hypoeutectic Al–Cu alloys. Real-time images were recorded by a fast readout–low noise CCD camera. Fig. 9 shows four typical X-ray images at successive times during the directional solidification of the Al– 4 wt.% Cu alloy at a temperature gradient of 20 K cm1 and a cooling rate of 120 K s1 under a 0.08 T transverse magnetic field. The X-ray images indicate that the sloping liquid–solid interface and channel segregation formed during directional solidification under a transverse magnetic field. This is good agreement with the results as shown in Figs. 1 and 2. Moreover, one can see that dendrite fragments were detached from dendrites and moved approximately along the direction perpendicular to the magnetic field. Although the movement of dendrite fragments under

the magnetic field was mentioned in Ref. [17], it is unclear which of the forces acting on the solid and the interdendritic convection in the liquid has induced the movement of dendrite fragments. Here, the Al–10 wt.% Cu alloy was directionally solidified at a temperature gradient of 20 K cm1 and a cooling rate of 120 K s1. Under this solidification condition, equiaxed grains form. Thus, the effect of interdendritic convection on the movement of grains is eliminated. Fig. 10 a1–a4 shows four typical X-ray images at successive times. The X-ray images indicate that equiaxed grains were moved approximately along the direction perpendicular to the magnetic field, as shown in Fig. 10b. This result suggests that some force has acted on the dendrite fragments and equiaxed grains during

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(a)

375

(b)

Recirculation loops

Cu 1mm

1mm (d)

(c)

Channel

1mm

1mm

Fig. 9. Successive in situ synchrotron X-ray images with a 0.08 T transverse magnetic field during directional solidification of Al–4 wt.% Cu alloy at a temperature gradient of 30 K cm1 and a cooling rate of 120 K s1: (a)–(d) show successive images.

directional solidification under a transverse magnetic field. Because grains are moved to one side of the sample under a transverse magnetic field, the number of grains across the sample is different. As a result, the size of grains across the sample is different. Indeed, EBSD analysis revealed that refined grains formed on one side of the sample under the magnetic field (see Fig. 10d). 4. Discussion 4.1. Effect of a transverse magnetic field on the liquid–solid interface shape and macrosegregation The above experimental results show that the application of a transverse magnetic field during directional solidification can modify the liquid–solid interface shape and cause the formation of segregations (i.e., freckles and channel) in the alloys examined. This result should be attributed to the effect of convection on the distribution of the solute in the bulk melt ahead of and in the mushy zone. When the

magnetic field is applied during directional solidification, a TEMF and TEMC will form. The TE magnetic effects during directional solidification can be characterized as fol! lows. In any material, a temperature gradient r T ! produces a Seebeck electromotive force S r T , where S is the TE power of the material [10]. If the media are submitted to a temperature gradient, a TE current may be generated in the system. Thus, the interaction between the TE current and the magnetic field will produce a TEMF, and TEMC will develop at the vicinity of the interface on the microscopic scale. It is easy to understand that the temperature at the tip of a cell/dendrite may be significantly higher than that at its base. Thus, a non-isothermal interface will form, and a TE current will be produced. In the case of the magnetic field parallel to the solidification direction, a rotary flow forms around the tip of a cell/dendrite. In the case of the magnetic field perpendicular to the solidification direction, a uniform TEMC forms within the mush just like “interdendritic forced convection”. Fig. 11a shows the TEMC during directional solidification

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Fig. 10. Effect of a transverse magnetic field on the movement of a-Al grains in directionally solidified Al–10 wt.% Cu alloy at a temperature gradient of 20 K cm1 and a cooling rate of 120 K s1: (a1–a4) successive in situ synchrotron X-ray images with a 0.08 T magnetic field; (b) schematic sketch of the movement of a-Al grains and the structure during directional solidification under a transverse magnetic field; (c) EBSD map of longitudinal structure without magnetic field; (d) EBSD map of longitudinal structure with a 0.08 T magnetic field.

under a transverse magnetic field in two cases, SS > SL and SS < SL. The TEMC will further induce recirculation loops in the bulk melt ahead of and in the mushy zone. The TEMC and the corresponding recirculation loops will cause heavier solute to move along the direction perpendicular to the magnetic field (i.e., the direction of the TEMF) as shown in Fig. 11b. As a consequence, the concentration of the solute increases from one side of the sample to the other side (see Fig. 7), and the sloping solid–liquid interface forms. Because the direction of the TEMC in the abovementioned two cases is different, the liquid–solid interface shape is different (see Fig. 1). To determine the amplitude and distribution of the TEMF and TEMC, numerical studies were conducted. Fig. 12a and b shows the distribution of a TE current and a TEMF around a modeled cell in an Al–Cu alloy under a 0.1 T transverse magnetic field. The physical properties used in the computations are presented in Table 1 of Annex 1. The electric current loops appear in the tip and

bottom of the cell, and a unidirectional TEMF will form in the liquid (see Fig. 12). The amplitude and distribution of the interdendritic TEMC under various magnetic fields are shown in Fig. 12c. The maximal value of the interdendritic TEMC increases as the magnetic field increases when a weak magnetic field (B 6 1 T) is applied. The numerical analysis shows that any anisotropy in the fluid flow will intensify some of these convection cells at the expense of others, ultimately leading to a localized accumulation of solute and inducing segregation [18]. Therefore, the TEMC in the bulk melt ahead of and in the mushy zone is most likely responsible for the formation of freckles and channel segregations (see Fig. 2). 4.2. Effect of a transverse magnetic field on the cellular/ dendritic spacing and the mushy zone length The above results also reveal that the application of a magnetic field caused the refinement of the cell/dendrite

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377

(a) G

JTE

JTE

Liquid

Liquid

F

F

Solid

Solid

SS> SL

SS< SL

(b)

Liquid

F

JTE

Channel

Solute concentration

Recirculation loops

Eutectic

Fig. 11. Schematic sketch of TEMF and interdendritic TEMC and their effects on solidification structure during directional solidification under a transverse magnetic field: (a) TEMF acting on the solid and liquid under a magnetic field perpendicular to the solidification direction in two cases; (b) TEMC near the sloping liquid–solid interface and TEMF acting on a grain in the liquid.

and the decrease in the mushy zone length. It is well known that the primary dendritic and cellular spacing derived for ellipsoidal morphology is [19] 1=2

k1 ¼ 4:3DT 0 ðDL C=DT 0 kÞ1=4 R1=4 GL

ð4Þ

where DT is the difference between the equilibrium liquidus and solidus temperature, DT0 is the temperature difference between the non-equilibrium solidus and the dendrite tip, DL is the solute liquid diffusion coefficient, k is the distribution coefficient, and C is the specific solid–liquid interface energy divided by melting entropy. The mushy zone length d is defined as the distance between the tip and the root of a dendrite trunk. Using the constitutional supercooling criterion for binary alloy systems in the absence of convection, d is given by d  mðC E  C 0 Þ=GT

ð5Þ

where CE is eutectic composition, and GT is the temperature gradient. The mushy zone length d is assumed to be equal to the distance between the liquidus temperature TL corresponding to Ct (Ct  C0) and the solidus temperature TS corresponding to CL, which is equal to CE when C0 > CSE. The refinement of the cell/dendrite and the decrease in the mushy zone length under the magnetic field may be attributed to the effect of the magnetic field on the constants in Eqs. (4) and (5). In previous studies [9], the present authors investigated the effect of magnetic field

on the thermodynamics constants, and the results showed that a magnetic field on the order of 10 T has negligible effects on thermodynamics constants. Moreover, the above results revealed that the refinement of the cell/dendrite and the decrease in the mushy zone length under the magnetic field occur at the same time (see Figs. 3–6). From Eqs. (4) and (5), it can be deduced that the application of the magnetic field during directional solidification may modify the temperature gradient (GT). To confirm that the temperature gradient indeed plays an important role in affecting the mushy zone length and cellular/dendritic spacing, the Al–7 wt.% Si alloy was directionally solidified under various temperature gradients. Fig. 13 shows the microstructures in the directionally solidified Al–7 wt.% Si alloy at a growth speed of 5 lm s1 with various temperature gradients. It can be observed that, with an increase in the temperature gradient, the mushy zone length and the cellular/dendritic spacing decrease. This result means that the application of the magnetic field during directional solidification enhances the temperature gradient. The increase in the temperature gradient during directional solidification under the magnetic field can be attributed to the enhancement of the heat-transfer rate caused by interdendritic TEMC. Moreover, the cellular/dendritic spacing is known to change in response to interdendritic constitutional supercooling (DT). Transparent metal model studies show that

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(a)

(c1)

(b)

B

0.01 T

(c2)

B

0.1 T

(c3)

B

(c4)

B

1T

0.5 T

Fig. 12. Computed TE current, TEMF and TEMC around a modeled cell in the directionally solidified Al–Cu alloy under a transverse magnetic field: (a) TE current; (b) TEMF in the liquid under a 0.1 T magnetic field; (c) TEMC in the liquid under various magnetic fields.

increased interdendritic constitutional supercooling drives cell branching and ternary growth, providing new primary arms and refining the spacing [20]. Buoyancy-driven flow has been shown to increase interdendritic constitutional supercooling by enhancing interdendritic solute transport [21]. Similarly, interdendritic TEMC will increase interdendritic constitutional supercooling and then drive the branching of the cells/dendrites. Because the value of interdendritic TEMC increases with the magnetic field (B 6 0.5 T), increases in the magnetic field in this range will enhance the decrease in the cellular/dendritic spacing and the mushy zone length (see Figs. 5 and 6).

Table 1 Physical properties of Al–Cu alloy and initial condition used during numerical simulation process. Properties

Magnitude 1

1

Electrical conductivity of solid (rs, X m ) Electrical conductivity of liquid (rL, X1 m1) Thermoelectric power of solid (SS, VK1) Thermoelectric power of liquid (SL, VK1) Temperature gradient (G, K/cm)

13.7  106 3.8  106 1.1  106 1.0  107 60

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(a)

(b)

300µm

(c)

300µm

300µm

300µm (f)

(e)

(d)

379

300µm

300µm

Fig. 13. Microstructures in the directionally solidified Al–7 wt.% Si alloy at a growth speed of 5 lm s1 under various temperature gradients (G). Longitudinal structures: (a) G = 90 K cm1, (b) G = 120 K cm1, (c) G = 150 K cm1; transverse structures: (d) G = 90 K cm1, (e) G = 120 K cm1, (f) G = 150 K cm1.

4.3. Movement behavior of dendrite fragments under a transverse magnetic field X-ray images revealed that dendrite fragments and equiaxed grains were moved along the direction perpendicular to the magnetic field. The movement behavior of dendrite fragments plays an important role in the solidification structure. Therefore, it is valuable to investigate the movement behavior of dendrite fragments under the magnetic field. As shown in Fig. 11 and Ref. [17], a unidirectional TEMF acts on dendrite fragments in the bulk melt ahead of the mushy zone, and the direction of the TEMF is the same as that acting on the dendrite trunk. Here, the TEMF acting on dendrite trunks and dendrite fragments in the mushy zone was investigated numerically. The results revealed that, under lower magnetic fields (B 6 1 T), although the amplitudes of the TEMF acting on dendrite trunks and dendrite fragments under various magnetic fields are different, the distribution of the TEMF under various magnetic fields is similar. Fig. 14 shows the computed TE current and TEMF

acting on dendrite trunks and dendrite fragments during the directional solidification of an Al–Cu alloy under a 0.1 T transverse magnetic field. It can be observed that the TEMF acting on a dendrite trunk is unidirectional. However, for dendrite fragments at different positions in the mushy zone, the distributions of the TEMF acting on grains are different. Indeed, for dendrites fragments near the tip of cells/dendrites in the mushy zone, the TEMF is multidirectional. However, for dendrite fragments near the bottom of cells/dendrites in the mushy zone, the TEMF is unidirectional, and the direction of the force is the same as that of the interdendritic TEMC. Fig. 15 shows the maximal values of the TEMF acting on the solid as a function of the magnetic field intensity. One can learn that the amplitude of the TEMF increases linearly with the magnetic field intensity. The above numerical results show that a TEMF may drive the movement of dendrite fragments during directional solidification under the magnetic field and that the movement behavior of dendrite fragments at various positions is different.

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(a)

(b)

F Fig. 14. Computed TE current and TEMF acting on modeled cells and equiaxed grains in the mushy zone in directionally solidified Al–Cu alloy under a 0.1 T transverse magnetic field: (a) TE current; (b) TEMF acting on modeled cells and equiaxed grains in the mushy zone.

25000

F (N/m3)

20000 15000 10000 5000 0 0.0

0.2

0.4

0.6

0.8

1.0

B (T) Fig. 15. Maximal values of the TEMF acting on a solid in the Al–Cu alloy as a function of the magnetic field intensity during directional solidification under a transverse magnetic field.

5. Conclusion The influence of a weak transverse magnetic field (60.5 T) on the morphology of the liquid–solid interface

and the microstructures of the solid was investigated during Bridgman growth of six alloys. The experimental results show that the application of a weak transverse magnetic field during directional solidification significantly modified the shape of the liquid–solid interface and the cellular/dendritic array in these alloys. Indeed, along with the refinement of the cell/dendrite, the magnetic field caused the deflection of liquid–solid interfaces, extensive segregations (i.e., freckles and channel) in the mushy zone and change in the mushy zone length in these alloys. Further, in situ monitoring of the initial transient of directional solidification was carried out by means of synchrotron X-ray radiography. It was observed that dendrite fragments and equiaxed grains were moved approximately along the direction perpendicular to the magnetic field. This result indicates that a TEMF has acted on the liquid or the solid during directional solidification under the magnetic field. The distribution and amplitude of the TEMF were numerically simulated. The results reveal that a unidirectional TEMF acts on the solid and induces interdendritic TEMC in the liquid and that the values of the TEMF and inderdendritic TEMC increase as the magnetic field increases.

X. Li et al. / Acta Materialia 64 (2014) 367–381

The modification of the solidification structure during directional solidification under the magnetic field can be attributed to the TEMC-driven heat transfer and interdendritic solute transport and the TEMF-driven motion of dendrite fragments. Acknowledgements This work is supported partly by the European Space Agency through the Bl-inter 09_473220, National Natural Science Foundation of China (Nos. 51271109, 51171106 and 2011CB610404) and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning. The authors are indebted to Prof. Thierry Duffar in EPM/CNRS, Grenoble, for helpful and fruitful discussions. References [1] Uhlmann DR, Seward TP, Chalmers B. Trans Metall Soc AIME 1966;236:527. [2] Kishida Y, Takeda K, Miyoshino I, Taleuchi E. ISIJ Int 1990;30:34. [3] Youdelis WV, Dorward RC. Can J Phys 1966;44:139. [4] Youdelis WV, Cahoon JR. Can J Phys 1970;48:805.

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