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Influence of a static magnetic field on the distribution of solute Cu and interdendritic constitutional undercooling in directionally solidified Al-4.5wt.%Cu alloy
Materials Letters 248 (2019) 73–77
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Influence of a static magnetic field on the distribution of solute Cu and interdendritic constitutional undercooling in directionally solidified Al-4.5wt.%Cu alloy Li Zhu a, Cui Han a, Long Hou a, Annie Gagnoud b, Yves Fautrelle b, Zhongming Ren a, Xi Li a,b,⇑ a b
State Key Laboratory of Advanced Special Steels, Shanghai University, Shanghai 200072, PR China SIMAP-EPM-Madylam/G-INP/CNRS, PHELMA, BP 75, 38402 St. Martin d’Heres Cedex, France
a r t i c l e
i n f o
Article history: Received 24 October 2018 Received in revised form 18 March 2019 Accepted 30 March 2019 Available online 1 April 2019 Keywords: Magnetic field Solute distribution Rank Sort method 3D-CT technology
a b s t r a c t The 3D-CT technology and Rank Sort method are applied to investigate the influence of a static magnetic field on the morphology of the liquid/solid interface and the distribution of the solute Cu in directionally solidified Al-4.5wt.%Cu alloy. The results reveal that cells/dendrites refine, and the results of numerical simulation confirm that the magnetic field forms thermoelectric (TE) magnetic convection, resulting in the enrichment of the solute Cu in the liquid ahead of the liquid/solid interface. The cells/dendrites refinement under the magnetic field should be attributed to the increase of the interdendritic constitutional undercooling caused by the enhancement of the solute Cu. Ó 2019 Published by Elsevier B.V.
1. Introduction The properties of castings and engineering materials are determined by their microstructures. The distribution of the solute in front of the liquid/solid interface significantly affects the final solidification structure. It is well known that the convection at the liquid/solid interface affects the transportation of the solute, and then impacts the microstructure during solidification process [1]. Lots of works have revealed that the change of the dendrite morphology is due to the change of the solute distribution in the diffusion boundary layer [2]. The effect of the magnetic field on the convection, segregation and cell/dendrite spacing has been investigated extensively [3]. However, so far little attention has been given to the effect of the static magnetic field on the distribution of the solute Cu and the interdendritic constitutional undercooling during directional solidification.
magnetically stirred for half an hour and form an ingot with 3 mm in diameter and 180 mm in length. The as-cast ingot was then encased in a high-purity corundum tube with 3 mm inner diameter for the directional solidification. The schematic diagram of Bridgman solidification equipment can be found in Ref. [4]. The 3D-CT technology experiments were carried out on NSIX5000-255 with a voxel size of 1.86032 1.86008 1.86011 lm3. The X-ray energy of 28 keV was used to penetrate the specimens. The volume data visualization and quantification were processed with ImageJ (NIH, US) and Avizo (FEI, France). Finally, a 3D region growth algorithm was employed for segmentation different phases. Moreover, the energy dispersive spectrometer (EDS) was used to study the solute distribution, covering several dendrites in an area of about 400 400 lm2 at the center near the liquid/solid interface.
3. Result and discussions 2. Experimental device The Al-4.5wt.%Cu alloys used in the present work were prepared with high-purity Al (99.99 wt%) and Cu (99.99 wt%) in a graphite crucible induction furnace. The alloy was heated to 950 °C, ⇑ Corresponding author at: State Key Laboratory of Advanced Special Steels, Shanghai University, Shanghai 200072, PR China. E-mail address: [email protected] (X. Li). https://doi.org/10.1016/j.matlet.2019.03.142 0167-577X/Ó 2019 Published by Elsevier B.V.
Fig. 1 shows the longitudinal microstructures near the liquid/solid interfaces in the directionally solidified Al-4.5wt.%Cu alloys without and with a static magnetic field. It can be noticed that, the shape of the liquid/solid interface becomes slope when the magnetic field is applied (Fig. 1(a)). Along with the slope of the interface, the cell/dendrite spacing gradually decreases with the increase of the magnetic field at the same growth speed. Fig. 2 shows the 3D morphology of the liquid/solid interface at
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L. Zhu et al. / Materials Letters 248 (2019) 73–77
Fig. 1. Longitudinal structures near the quenched liquid/solid interfaces directionally solidified at various growth speeds with and without the magnetic field.
the growth speed of 1 lm/s with and without a 0.1 T magnetic field. It can be observed that the interface becomes slope over to left side in the 3D morphology of isolated a-Al phase under a 0.1 T magnetic field (Fig. 2(a)) and the Al2Cu/eutectic phases distribute uniformly around corundum tube (Fig. 2(b1)-(d1)). The Al2Cu/eutectic phases occupy the interspace between a-Al phases (Fig. 2(b2)-(d2)) and enrich at the left side of the sample. Fig. 3(a)-(c) show that the distribution maps of the solute Cu measured by the EDS. Fig. 3(d)-(f) show the compositional profiles of the solute Cu in the liquid without and with the magnetic field by the Rank Sort method [5]. In the absence of magnetic field, the content of the solute Cu decreases with the increase of the solid fraction (Fig. 3(d)) and the distributing curves of the solute Cu are impacted to growth speed. When a 0.3 T magnetic field is applied, the curves at different growth speeds are almost same (Fig. 3(e)). Obviously, the magnetic field has greater influence on the enrichment of solute Cu at a higher growth speed. One can notice that with the increase of the magnetic field, the curve moves upward at the growth speed of 5 lm/s (Fig. 3(f)). This implies that the application of the magnetic field induces the enrichment of the solute Cu in the liquid ahead of the liquid/solid interface. Here, Fig. 4(a) and (b) show the distribution of the TE magnetic convection at the sample and dendrite scales under the 0.1 T magnetic field by numerical simulation. It can be found that the TE magnetic convection flows from one side to the other side of the
sample or dendrite and returns to the liquid on the top in the mushy zone. Furthermore, the effect of the TE magnetic convection on the transport of the solute Cu is simulated by the model of particle tracing (Fig. 4(c) and (d)), and the magnetic field causes the enrichment of the solute Cu between the cells/dendrites. Thus, for vertical Bridgman crystal growth of Al-Cu alloys, the heavier species Cu migrates down to the protruding liquid/solid interface due to the gravity force (Fig. 4(e)). When the magnetic field is applied, the TE magnetic convection will further induce recirculation loops in the mushy zone, and those will cause heavier solute to move on one side. Consequently, the concentration of the solute increases on the left and the sloping solid/liquid interface forms as shown in Fig. 4(f). It is well known that the distribution of the solute Cu in the liquid ahead of the liquid/solid interface will affect the interdendritic undercooling (DT) in Fig. 4(g). Now, let us recall the DT during the growth of the cells/dendrites. The DT can be defined as [6]:
DT ¼ T L T T ¼ DT K þ DT r þ DT D
ð1Þ
where TL, TT, DTK, DTr, and DTD are liquidus temperature, each volume element finds itself at a temperature, the kinetic undercooling, the curvature undercooling and the interdendritic constitutional undercooling, respectively. Normally, DTK is assumed to be negligibly small compared with DTD and DTr for metals. Thus, Eq. (1) becomes
L. Zhu et al. / Materials Letters 248 (2019) 73–77
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Fig. 2. 3D reconducted structures at a growth speed of 1 lm/s with and without a 0.1 T magnetic field: (a) a-Al phases at the liquid/solid interface; (b), (c) and (d) Al2Cu/ eutectic phases near the liquid/solid interface and at 2 mm below the liquid/solid interface.
DT ¼ DT r þ DT D
ð2Þ
DT D ¼ mðC 0 C t Þ ¼ mDC
ð3Þ
1 DT r ¼ h R1 1 þ R2
ð4Þ
where C0 is the composition of the starting alloy, Ct is the composition of the liquid at a growing interface and m is the liquidus slope, R1 and R2 are the principal radii of curvature of the solid, h is the curvature undercooling constant. In the present work, as the magnetic field is weaker, the effect of the magnetic field on the DTr is negligible. From Eq. (3), it can be deduced that the DTD which
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L. Zhu et al. / Materials Letters 248 (2019) 73–77
Fig. 3. The mapping distributions and compositional profiles of the solute Cu in the liquid near the liquid/solid interface: (a)-(c) the mapping distributions of the solute Cu; (d)-(f) the compositional profiles of the solute Cu.
increases with the enrichment of the solute Cu is foremost. Fig. 4(g) shows the schematic illustration for the distribution of the solute Cu and the DT during the growth of the cell without and with the magnetic field. As we know, the primary spacing and tip radius of the cells/ dendrites adjust in response to the value of the DT. Transparent metal-model studies have allowed the observation of the dendrite spacing adjustment mechanisms. Increased DTD drives ternary growth to provide new primary arms-refining spacing. Moreover, the tip radius (R) can be written as [7]:
R2 ¼
CD
C0 1
r kDTV C r nc
ð5Þ
where U, D, k and V are Gibbs-Thomson coefficient, diffusion coefficient in the liquid, equilibrium distribution coefficient, and growth speed, respectively. From Eq. (4), it can be concluded that the R will decrease since the magnetic field increases the DTD. Therefore, it is reasonable to attribute the refinement of the cells /dendrites under
the magnetic field to the increase in the DT caused by the enrichment of the solute.
4. Conclusions The effect of the magnetic field (0.3 T) on the distribution of the solute Cu and the interdendritic undercooling in the directionally solidified Al-4.5wt.%Cu alloys have been studied. Experimental results reveal that the magnetic field caused the enrichment of the solute Cu in the liquid near the liquid/solid interface and the refinement of the cells/dendrites. The interface becomes slope over to left side with magnetic field in the 3D morphology. Numerical results show that the TE magnetic convection can cause the enrichment of the solute Cu in the mushy zone. The modification of the microstructures and solute distribution under the magnetic field should be attributed to the effect of the TE magnetic convection on the solute distribution and the interdendritic constitutional undercooling.
L. Zhu et al. / Materials Letters 248 (2019) 73–77
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Fig. 4. TE magnetic convection during directional solidification and its effect on the distribution of the solute Cu in the liquid near the liquid/solid interface: (a) and (b) numerical simulation for the TE magnetic convection at the sample and dendrite scales in the Al-Cu alloy under a 0.1 T magnetic field; (c) and (d) numerical simulation for the distribution of the solute Cu between dendrites without and with a 0.1 T magnetic field; (e) and (f) schematic illustration for the distribution of the solute Cu without and with the magnetic field; (g) schematic illustration for the various components and the dendrite tip undercooling superimposed on a phase diagram without and with the magnetic field.
Conflict of interest
Appendix A. Supplementary data
The authors declared that they have no conflicts of interest to this work.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.matlet.2019.03.142. References
Acknowledgment This work is supported partly by the European Space Agency through the Bl-inter 09_473220, National Natural Science Foundation of China (Nos. 51571056 and 51690164), ‘‘Shuguang Program” from Shanghai Municipal Education Commission, Shanghai Science and Technology Committee Grant (15520710900).
[1] [2] [3] [4] [5] [6] [7]
H. Conrad, Mater. Sci. Eng. A 287 (2000) 209. M.G. Worster, J. Fluid Mech. 167 (1986) 498. R.P. Liu, T. Volkmann, D.M. Herlach, Acta Mater. 19 (2001) 441. X. Li, Y. Fautrelle, Z.M. Ren, J. Cryst. Growth 306 (2007) 188. M. Ganesan, D. Dye, P.D. Lee, Metall. Mater. Trans. A 36 (2005) 2194. M.H. Burden, J.D. Hunt, J. Cryst. Growth 22 (1974) 109. J.D. Hunt, Solidification and Casting of Metals, The Metal Society, London, 1979, p. 3.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Influence of a static magnetic field on the distribution of solute Cu and interdendritic constitutional undercooling in directionally solidified Al-4.5wt.%Cu alloy Li Zhu a, Cui Han a, Long Hou a, Annie Gagnoud b, Yves Fautrelle b, Zhongming Ren a, Xi Li a,b,⇑ a b
State Key Laboratory of Advanced Special Steels, Shanghai University, Shanghai 200072, PR China SIMAP-EPM-Madylam/G-INP/CNRS, PHELMA, BP 75, 38402 St. Martin d’Heres Cedex, France
a r t i c l e
i n f o
Article history: Received 24 October 2018 Received in revised form 18 March 2019 Accepted 30 March 2019 Available online 1 April 2019 Keywords: Magnetic field Solute distribution Rank Sort method 3D-CT technology
a b s t r a c t The 3D-CT technology and Rank Sort method are applied to investigate the influence of a static magnetic field on the morphology of the liquid/solid interface and the distribution of the solute Cu in directionally solidified Al-4.5wt.%Cu alloy. The results reveal that cells/dendrites refine, and the results of numerical simulation confirm that the magnetic field forms thermoelectric (TE) magnetic convection, resulting in the enrichment of the solute Cu in the liquid ahead of the liquid/solid interface. The cells/dendrites refinement under the magnetic field should be attributed to the increase of the interdendritic constitutional undercooling caused by the enhancement of the solute Cu. Ó 2019 Published by Elsevier B.V.
1. Introduction The properties of castings and engineering materials are determined by their microstructures. The distribution of the solute in front of the liquid/solid interface significantly affects the final solidification structure. It is well known that the convection at the liquid/solid interface affects the transportation of the solute, and then impacts the microstructure during solidification process [1]. Lots of works have revealed that the change of the dendrite morphology is due to the change of the solute distribution in the diffusion boundary layer [2]. The effect of the magnetic field on the convection, segregation and cell/dendrite spacing has been investigated extensively [3]. However, so far little attention has been given to the effect of the static magnetic field on the distribution of the solute Cu and the interdendritic constitutional undercooling during directional solidification.
magnetically stirred for half an hour and form an ingot with 3 mm in diameter and 180 mm in length. The as-cast ingot was then encased in a high-purity corundum tube with 3 mm inner diameter for the directional solidification. The schematic diagram of Bridgman solidification equipment can be found in Ref. [4]. The 3D-CT technology experiments were carried out on NSIX5000-255 with a voxel size of 1.86032 1.86008 1.86011 lm3. The X-ray energy of 28 keV was used to penetrate the specimens. The volume data visualization and quantification were processed with ImageJ (NIH, US) and Avizo (FEI, France). Finally, a 3D region growth algorithm was employed for segmentation different phases. Moreover, the energy dispersive spectrometer (EDS) was used to study the solute distribution, covering several dendrites in an area of about 400 400 lm2 at the center near the liquid/solid interface.
3. Result and discussions 2. Experimental device The Al-4.5wt.%Cu alloys used in the present work were prepared with high-purity Al (99.99 wt%) and Cu (99.99 wt%) in a graphite crucible induction furnace. The alloy was heated to 950 °C, ⇑ Corresponding author at: State Key Laboratory of Advanced Special Steels, Shanghai University, Shanghai 200072, PR China. E-mail address: [email protected] (X. Li). https://doi.org/10.1016/j.matlet.2019.03.142 0167-577X/Ó 2019 Published by Elsevier B.V.
Fig. 1 shows the longitudinal microstructures near the liquid/solid interfaces in the directionally solidified Al-4.5wt.%Cu alloys without and with a static magnetic field. It can be noticed that, the shape of the liquid/solid interface becomes slope when the magnetic field is applied (Fig. 1(a)). Along with the slope of the interface, the cell/dendrite spacing gradually decreases with the increase of the magnetic field at the same growth speed. Fig. 2 shows the 3D morphology of the liquid/solid interface at
74
L. Zhu et al. / Materials Letters 248 (2019) 73–77
Fig. 1. Longitudinal structures near the quenched liquid/solid interfaces directionally solidified at various growth speeds with and without the magnetic field.
the growth speed of 1 lm/s with and without a 0.1 T magnetic field. It can be observed that the interface becomes slope over to left side in the 3D morphology of isolated a-Al phase under a 0.1 T magnetic field (Fig. 2(a)) and the Al2Cu/eutectic phases distribute uniformly around corundum tube (Fig. 2(b1)-(d1)). The Al2Cu/eutectic phases occupy the interspace between a-Al phases (Fig. 2(b2)-(d2)) and enrich at the left side of the sample. Fig. 3(a)-(c) show that the distribution maps of the solute Cu measured by the EDS. Fig. 3(d)-(f) show the compositional profiles of the solute Cu in the liquid without and with the magnetic field by the Rank Sort method [5]. In the absence of magnetic field, the content of the solute Cu decreases with the increase of the solid fraction (Fig. 3(d)) and the distributing curves of the solute Cu are impacted to growth speed. When a 0.3 T magnetic field is applied, the curves at different growth speeds are almost same (Fig. 3(e)). Obviously, the magnetic field has greater influence on the enrichment of solute Cu at a higher growth speed. One can notice that with the increase of the magnetic field, the curve moves upward at the growth speed of 5 lm/s (Fig. 3(f)). This implies that the application of the magnetic field induces the enrichment of the solute Cu in the liquid ahead of the liquid/solid interface. Here, Fig. 4(a) and (b) show the distribution of the TE magnetic convection at the sample and dendrite scales under the 0.1 T magnetic field by numerical simulation. It can be found that the TE magnetic convection flows from one side to the other side of the
sample or dendrite and returns to the liquid on the top in the mushy zone. Furthermore, the effect of the TE magnetic convection on the transport of the solute Cu is simulated by the model of particle tracing (Fig. 4(c) and (d)), and the magnetic field causes the enrichment of the solute Cu between the cells/dendrites. Thus, for vertical Bridgman crystal growth of Al-Cu alloys, the heavier species Cu migrates down to the protruding liquid/solid interface due to the gravity force (Fig. 4(e)). When the magnetic field is applied, the TE magnetic convection will further induce recirculation loops in the mushy zone, and those will cause heavier solute to move on one side. Consequently, the concentration of the solute increases on the left and the sloping solid/liquid interface forms as shown in Fig. 4(f). It is well known that the distribution of the solute Cu in the liquid ahead of the liquid/solid interface will affect the interdendritic undercooling (DT) in Fig. 4(g). Now, let us recall the DT during the growth of the cells/dendrites. The DT can be defined as [6]:
DT ¼ T L T T ¼ DT K þ DT r þ DT D
ð1Þ
where TL, TT, DTK, DTr, and DTD are liquidus temperature, each volume element finds itself at a temperature, the kinetic undercooling, the curvature undercooling and the interdendritic constitutional undercooling, respectively. Normally, DTK is assumed to be negligibly small compared with DTD and DTr for metals. Thus, Eq. (1) becomes
L. Zhu et al. / Materials Letters 248 (2019) 73–77
75
Fig. 2. 3D reconducted structures at a growth speed of 1 lm/s with and without a 0.1 T magnetic field: (a) a-Al phases at the liquid/solid interface; (b), (c) and (d) Al2Cu/ eutectic phases near the liquid/solid interface and at 2 mm below the liquid/solid interface.
DT ¼ DT r þ DT D
ð2Þ
DT D ¼ mðC 0 C t Þ ¼ mDC
ð3Þ
1 DT r ¼ h R1 1 þ R2
ð4Þ
where C0 is the composition of the starting alloy, Ct is the composition of the liquid at a growing interface and m is the liquidus slope, R1 and R2 are the principal radii of curvature of the solid, h is the curvature undercooling constant. In the present work, as the magnetic field is weaker, the effect of the magnetic field on the DTr is negligible. From Eq. (3), it can be deduced that the DTD which
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L. Zhu et al. / Materials Letters 248 (2019) 73–77
Fig. 3. The mapping distributions and compositional profiles of the solute Cu in the liquid near the liquid/solid interface: (a)-(c) the mapping distributions of the solute Cu; (d)-(f) the compositional profiles of the solute Cu.
increases with the enrichment of the solute Cu is foremost. Fig. 4(g) shows the schematic illustration for the distribution of the solute Cu and the DT during the growth of the cell without and with the magnetic field. As we know, the primary spacing and tip radius of the cells/ dendrites adjust in response to the value of the DT. Transparent metal-model studies have allowed the observation of the dendrite spacing adjustment mechanisms. Increased DTD drives ternary growth to provide new primary arms-refining spacing. Moreover, the tip radius (R) can be written as [7]:
R2 ¼
CD
C0 1
r kDTV C r nc
ð5Þ
where U, D, k and V are Gibbs-Thomson coefficient, diffusion coefficient in the liquid, equilibrium distribution coefficient, and growth speed, respectively. From Eq. (4), it can be concluded that the R will decrease since the magnetic field increases the DTD. Therefore, it is reasonable to attribute the refinement of the cells /dendrites under
the magnetic field to the increase in the DT caused by the enrichment of the solute.
4. Conclusions The effect of the magnetic field (0.3 T) on the distribution of the solute Cu and the interdendritic undercooling in the directionally solidified Al-4.5wt.%Cu alloys have been studied. Experimental results reveal that the magnetic field caused the enrichment of the solute Cu in the liquid near the liquid/solid interface and the refinement of the cells/dendrites. The interface becomes slope over to left side with magnetic field in the 3D morphology. Numerical results show that the TE magnetic convection can cause the enrichment of the solute Cu in the mushy zone. The modification of the microstructures and solute distribution under the magnetic field should be attributed to the effect of the TE magnetic convection on the solute distribution and the interdendritic constitutional undercooling.
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77
Fig. 4. TE magnetic convection during directional solidification and its effect on the distribution of the solute Cu in the liquid near the liquid/solid interface: (a) and (b) numerical simulation for the TE magnetic convection at the sample and dendrite scales in the Al-Cu alloy under a 0.1 T magnetic field; (c) and (d) numerical simulation for the distribution of the solute Cu between dendrites without and with a 0.1 T magnetic field; (e) and (f) schematic illustration for the distribution of the solute Cu without and with the magnetic field; (g) schematic illustration for the various components and the dendrite tip undercooling superimposed on a phase diagram without and with the magnetic field.
Conflict of interest
Appendix A. Supplementary data
The authors declared that they have no conflicts of interest to this work.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.matlet.2019.03.142. References
Acknowledgment This work is supported partly by the European Space Agency through the Bl-inter 09_473220, National Natural Science Foundation of China (Nos. 51571056 and 51690164), ‘‘Shuguang Program” from Shanghai Municipal Education Commission, Shanghai Science and Technology Committee Grant (15520710900).
[1] [2] [3] [4] [5] [6] [7]
H. Conrad, Mater. Sci. Eng. A 287 (2000) 209. M.G. Worster, J. Fluid Mech. 167 (1986) 498. R.P. Liu, T. Volkmann, D.M. Herlach, Acta Mater. 19 (2001) 441. X. Li, Y. Fautrelle, Z.M. Ren, J. Cryst. Growth 306 (2007) 188. M. Ganesan, D. Dye, P.D. Lee, Metall. Mater. Trans. A 36 (2005) 2194. M.H. Burden, J.D. Hunt, J. Cryst. Growth 22 (1974) 109. J.D. Hunt, Solidification and Casting of Metals, The Metal Society, London, 1979, p. 3.