Three dimensional dendritic morphology and orientation transition induced by high static magnetic field in directionally solidified Al-10 wt.%Zn alloy

1. Introduction

Dendrite structure is widely existed in metallic materials during solidification and its branching arms tend to evolve along specific directions in related to the intrinsic of crystallography. In fcc aluminum, (111) is supposed to be the close-packed plane and [100] directions form the axes of the pyramid. As a consequence, [100] is usually expected to be the preferential growth direction in Al alloys or cubic metals in most cases [[1], [2], [3]]. However, dendrite structure formation during solidification would be tailed by many methods. A continuous dendrite orientation transition (DOT) from <100> to <110> was observed in Al-Zn alloys as the concentration of Zn(c_Zn) increases from 5 wt.% to 90 wt.% [[4], [5], [6], [7], [8]]. Further, a similar DOT and morphology transition phenomenon of α-Mg dendrite was found in Mg-Zn alloys with Zn additions increased from 10 wt.% to 50 wt.% [9,10]. Recently, as presented by Kurtuldu et al. [11], a trace addition of Cr in Al-20 wt.%Zn alloy was also demonstrated to alter growth direction of α-Al to <110> direction. These DOT phenomena were explained as either the influence of Zn on the solid/liquid interfacial free energy anisotropy which determines dendrite growth direction or the formation of twin grains or feathery grains [12]. Besides the alloying element, it has been proved that magnetic field can significantly affect the microstructure formation during solidification [[13], [14], [15], [16], [17], [18]]. Based on 2D microscopy, Li et al. [14] suggested that the applied magnetic field would modify the dendrite morphology and solid/liquid interfacial stability during directional solidification. Their experimental results confirmed that thermoelectric magnetic convection (TEMC) could play an important role in affecting dendrite formation when solidified under magnetic field. Moreover, magnetic field was also demonstrated to be able to control the growth direction of dendrite and align the columnar growth dendrites along the magnetic field [13]. However, these studies based on 2D metallographic or SEM are insufficient to completely elucidate the effect of magnetic field on the 3D dendritic morphology and the solid/liquid interface shape, especially the TEMC in front of the dendrite growth interface [[19], [20], [21], [22], [23]]. To the best of our knowledge, the transition of dendrite preferred growth orientation caused by magnetic field has not yet been reported.

Herein, a high static magnetic field (HSMF) was applied during directional solidification of Al-10 wt.%Zn alloy. The effects of HSMF on the 3D solid/liquid interface morphology and dendrite growth direction were studied by X-ray micro-computed tomography (CT) and EBSD/XRD respectively. Dendrite morphology and orientation transition were induced by HSMF and the results indicated the potential application of magnetic field in tuning dendrite morphology and preferred orientation during solidification.

2. Experimental methods

Al-10 wt.%Zn hypoeutectic alloy was prepared with commercial 99.99% pure Al and Zn in an induction furnace and suction casted with silicon tubes. Following this, cylindrical samples with diameter of $\widetilde{3}$mm and length of 150 mm were enveloped in high purity alumina tubes and directionally solidified under 5 T axial magnetic field with growth speed (R) of 10 μm/s and temperature gradient (G) of $\widetilde{6}$0 °C/cm. Samples solidified without magnetic field were also prepared as reference. The experimental setups are shown in Fig. 1 and more details were presented in Refs. [16,19]. The whole furnace (including sample) is located inside the magnet. During directional solidification, the relative position of solid/liquid interface (i.e the position where solidification happens) to the superconducting magnet was nearly fixed and close to the central plane, ensuring the sample solidified under a relatively uniform magnetic field.

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Fig. 1.   Schematic of directional solidification apparatus under high static magnetic field.

The X-ray micro-computed tomography (CT) experiments were carried out on a North Star Imaging (NSI) Micro-CT machine. The system is equipped with a 225 kV X-ray source with a minimum focal spot size of $\widetilde{2}$μm and a Perkin Elmer flat panel detector (2048 × 2048 pixels in 16 bit depth image). During CT scan the sample was illuminated by cone beam X-rays. X-ray was transmitted through the specimen rotated over 360° and detected by the flat panel detector. Then a series of two-dimension projections were collected to perform three-dimension reconstruction. During CT scan, the X-ray beam was filtered using a 0.25 mm Cu filter in order to reduce beam-hardening effect. A combination of acceleration voltage of 100 kV and target current of 40 μA was selected to optimize image quality. 1440 projections were captured over 360° with an exposure time of 1000 ms. Finally, a space resolution with voxel size of 2.2 μm was obtained after 3D reconstruction.

For the EBSD measurement, the samples were mechanically polished with increasing SiC paper (400-2000 grade), then the samples were further polished with 0.5 μm diamond particle spray followed by electropolishing in an A2 solution (72 mL ethanol, 20 mL 2buthoxyethanol and 8 mL perchloric acid at 71 pct concentration) for about 10 s with the voltage of 4 V, in order to remove the deformed surface layer so as to obtain a good index during EBSD measurement. The EBSD experiments were performed using a Zeiss Crossbeam 540 equipped with NordlysMax2 detector and HKL Channel 5 data analysis system. The XRD was conducted on a Bruker AXS-D8 Advance system from 20° to 90° with a speed of 6°/min.

3. Results and discussion

3.1. The effect of magnetic field on the solid/liquid interface morphology

Fig. 2(a-b) illustrates the longitudinal section showing the solid-liquid interfacial morphology of directionally solidified Al-10 wt%Zn alloy both with and without magnetic field. The regular columnar dendrites grow nearly parallel to the temperature gradient was revealed with the absence of magnetic field. In contrast, a completely irregular interface shape was observed for the alloy solidified under magnetic field and more dendritic structure with higher order of dendrite arms was also presented in comparison with sample free of magnetic field.

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Fig. 2.   Longitudinal sections showing the solidification microstructure at the quenched liquid/solid interface of Al-10 wt.%Zn alloy solidified with and without magnetic field. (a) 0 T; (b) 5 T. (c) Schematic of thermoelectric moment and magnetic force on the cell/dendrite under a magnetic field parallel to the solidified direction (modified based on Ref. [16,24]).

The 3D dendrite morphology and interface shape are depicted in Fig. 3, as can be seen from Fig. 3(a), in the case of no magnetic field, the solid/liquid interface is relatively flat with slight tilt and this is probably due to the unavoidable radial thermal gradient in practice. The longitudinal (Fig. 3b) and transverse sections (Fig. 3c) also indicate a regular columnar growth dendrite array. While for the sample solidified under axial magnetic field, the morphology of Solid/Liquid interface in the mushy zone is much more complicated and the growth direction of primary dendrite arms was found to deflect from the solidification direction with an angle of $\widetilde{4}$5° between temperature gradient (G) as shown in Fig. 3(d-f). The results suggest that the applied high static magnetic field breaks the stability of the solid/liquid interface and significantly influences the growth of dendrite array during direction solidification. The irregularity of growth interface under magnetic field might be attributed to the effect of magnetic field on the convection of the liquid in front of growth interface during directional solidification. It has been recognized that a new flow called thermoelectric magnetic convection (TEMC) would be induced by the interaction between the magnetic field and thermoelectric (TE) current [[15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25]]. Fig. 2(c) illustrates the influence of the TEMC in the case of an external magnetic field parallel to the growth direction, where TEMC induces a rotatory flow around dendrites.

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Fig. 3.   3D renderings of mushy zone areas or interface shapes of directionally solidified Al-10 wt.%Zn alloy (a, d) and longitudinal sections showing the morphologies of columnar growth dendritic structure (b, e) as well as the cross-sections (c, f). (a, b, c) 0 T; (d, e, f) 5 T.

Evident trajectories of the rotatory flow can be seen around the dendrite tips when solidified under high magnetic field, as indicated by yellow dashed arrows in Fig. 3(d). These trajectories can only be revealed from the 3D rendering of solid/liquid interface via X-ray tomography [26]. The result suggests that the application of an axis magnetic field during directional solidification indeed causes a circular convection in front of the solid/liquid interface as illustrated in Fig. 2c. It is worth to note that the thermoelectric magnetic force (TMF) induced by the interaction of magnetic field and thermoelectric effects was supposed to cause a new melt motion in the liquid side, namely TEMC [24]. The trajectories of the rotatory flow observed from the 3D microstructure further confirmed the existence of TEMC in front of dendrite growth interface under axis magnetic field. In the meaning time, the TMF will also work on the solid phase. In specific, a torque on the dendrite will be generated by the interaction between the TE current inside the dendrite and the applied magnetic field. As illustrated in Fig. 2(c), the moment at the dendrite tip is clockwise while at the bottom is anticlockwise, thus a twist force will be generated at the central region of the dendrite [24]. The torque might increase the instability of the growth interface and cause the cell or dendrite to break. Therefore, for the sample solidified under static magnetic field, the dendritic structures are more complicated and irregular than that without magnetic field.

3.2. Cellular to dendritic transition induced by magnetic field

Fig. 4a and b shows the orthogonal projections of Al-Zn alloys solidified without and with magnetic field, respectively. In the case of no magnetic field, a cellular like structure was observed from the cross-sections (the cross-section is located at 1.2 mm away from the solid/liquid interface), only a few secondary arms were found. In contrast, a dendritic structure with complex morphology was presented when solidified under 5 T magnetic field. The results suggested that a cellular to dendritic transition was caused by applying the strong magnetic field during directional solidification of Al-10 wt%Zn alloy. The cellular to dendritic transition has been investigated for many years and numerous mechanisms have been proposed. However, little research has been done on the cellular to dendritic transition induced by a high magnetic field during directional solidification. Basically, the transition from cellular crystal to dendritic structure is due to the instability of growth interface [27,28]. Based on the constitutional supercooling theory [29], the morphology selection of growth interface during directional solidification can be predicted by the following criterion:

$\frac{G_L}{R}=\frac{m_{l}C_{0}(1-k)}{kD_L}$ (1)

where G_L is the thermal gradient in the liquid phase, R is the growth rate of the grains, m_l is the slope of liquidus in phase diagram, C₀ is the nominal solute concentration of alloys, k is the equilibrium partition coefficient and D_L is the diffusion coefficient of solute in the liquid. The interface is tend to be unstable when

$\frac{G_L}{R}<\frac{m_{l}C_{0}(1-k)}{kD_L}$ (2)

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Fig. 4.   Orthogonal projections showing the morphologies of dendrite in Al-Zn alloys. (a) free of magnetic field; (b) with magnetic field (B = 5 T).

It was proved that the applied magnetic field was capable of affecting Gibbs free energy and chemical potential of the alloy system, as well as the phase equilibrium [17]. Therefore, the cellular to dendritic transition observed in this study might be attributed to the effect of magnetic field on the equilibrium of the alloy system. Specifically, the equilibrium partition coefficient k, the liquidus slope m_l of an alloy phase diagram and solute diffusion coefficient D_L might be changed by the magnetic field [15,24]. Under a certain solidification condition (where C0, G and R are fixed), the stability of solid/liquid interface is determined by equilibrium partition coefficient k, liquidus slope m_l and solute diffusion coefficient D_L. It is widely recognized that a strong magnetic field during solidification would cause a damping effect on the liquid phase on macro scale, slowing the diffusion of solute element [16]. In addition, the applied magnetic field was also found to decrease the equilibrium partition coefficient k or increase the liquidus slope ml [15]. Consequently, based on the criterion described in Eq. (2), the interface might be destabilized under magnetic field and thus a cellular to dendritic transition was observed in present study. Further, the TMF imposed on the dendrite might also play an important role in promoting the cellular to dendritic transition during directional solidification [21] as discussed in Section 3.1.

3.3. The effect of magnetic field on the dendrite orientation selection of primary α-Al

Fig. 5 illustrates the EBSD result and the corresponding inverse pole figure of longitudinal section of directionally solidified Al-10 wt.%Zn alloy. In the case where no magnetic field was applied, an expected <100> growth direction can be evidently recognized from the orientation map (Fig. 5a-d). The result agrees well with the previous studies where Zn concentration was lower than 20 wt.% of which α-Al dendrite preferred to grow along <100> direction [30]. However, it can be seen from Fig. 5e-h, dendrite arms were found to grow along <110> direction when a 5 T magnetic field was applied. The result indicates that the application of an axis magnetic field during directional solidification of Al-10 wt.%Zn alloy is able to cause a α-Al dendrite orientation transition (DOT) from <100> to <110>. Since Zn concentration is relatively low (less than 20 wt.%) in the present study, it is unlikely that the dendrite orientation transition was caused by the effect of Zn solute on the interfacial free energy anisotropy as suggested in ref. [30]. Thus the dendrite orientation transition should be ascribed to the influence of the static magnetic field during directional solidification.

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Fig. 5.   (a, e) SEM image of Al-10 wt.%Zn sample and (b, f) associated <001> or <101> pole figure measured in the whole scanned area showing the growth direction of the dendrite (indicated with dashed arrow in the figure) and (c, d and g, h) the corresponding EBSD orientation maps of longitudinal sections of observed in (a, e) showing the orientation selection of columnar dendrites. (a-d) without magnetic field; (e-h) with magnetic field.

When solidified under magnetic field, dendrite growth direction was affected by anisotropy due to the underlying crystallographic as well as the imposed magnetic field even for a non-magnetic substance [31,32]. It has been demonstrated that a high magnetic field is capable of aligning the dendrite array during directional solidification owing to the magnetic anisotropy of grains [14,33]. In general, a magnetic anisotropic grain will be rotated by the magnetic field to its lowest energy status when placed in a magnetic field [34]. The driving force is the anisotropic magnetic energy of the grains. Assuming that an anisotropic grain with volume V is placed in a magnetic field H, the magnetic energy of the grain as a function of the intensity of magnetic field can be written as

E_m(θ,H)=-(χ_ccos²θ+χ_absin²θ)VH²/2 (3)

where θ is the angle between magnetic field and the c-axis of the grain, χc is the paramagnetic susceptibility along the $\vec{c}$ direction and χ_ab is the paramagnetic susceptibility normal to the ab plane ($\vec{c}$ is the normal direction of ab plane). Substituting

sin²θ=1-cos²θ (4)

into Eq. (3), one obtain

E_m(θ,H)=-(χ_ab+Δχsin²θ)VH²/2 (5)

where Δχ is the difference in the volume susceptibility of the grain along different directions, i.e. $\vec{c}$ and ab plane. When assuming that θ=0

Em(0,H)=-Vχ_cH²/2 (6)

Similarly, when θ=π/2, we have

E_m($\frac{\pi}{2}$,H)=-Vχ_abH²/2 (7)

For the cases where χ_c>χ_ab, E_m(0,H)<E_m($\frac{\pi}{2}$,H) which means that the magnetic field tend to rotate the grains to θ=0 to reach a lower energy state. In contrast, when χ_c<χ_ab and E_m(0,H)>E_m($\frac{\pi}{2}$,H), the magnetic field tend to rotate the grain to θ=π/2. The above analysis indicates that the easy magnet axis of a paramagnetic grain tends to rotate along direction of applied magnetic field. Therefore, when directional solidification was carried out under magnetic field, the dendrite growth direction will be determined not only by the preferential orientation owing to the underlying crystalline anisotropy, but also the magnetic field which tends to rotate the easy magnetic axis to magnetic field direction. Thus, if the easy magnetic axis is not the same as the preferred orientation of the grain, the dendrite growth direction will deviate from the preferential orientation, as a consequence, for Al-10 wt.%Zn alloy directionally solidified under 5 T magnetic field, the dendrite growth direction under magnetic field was found to transform from <100> to <110>.

In order to further confirm the effect of applied magnetic field on the growth orientation selection of grains in Al-Zn alloys, X-ray diffraction measurements were also carried out for the samples solidified both with and without magnetic field. The X-ray diffraction patterns of Al-10 wt%Zn alloys are given in Fig. 6. As can be seen, highest peak of (200) (indicating the preferred growth direction of <100>) can be observed when no magnetic field was added, while in the case where 5 T magnetic field was imposed, the peaks of (220) and (311) were found to increase.

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Fig. 6.   X-ray diffraction pattern of cross section of directionally solidified Al-10 wt.%Zn with (up) and without (down) magnetic field.

As suggested by Sugiyama [32], a method to evaluate the degree of crystalline orientation from the intensity of X-ray diffraction lines obtained by X-ray diffraction analyzer (XRD) was proposed and given as Eq. (8).

where θ_T is defined as the facial angle measured from c-plane, θ_hkl is the facial angle between (hkl) and (00n) planes, I_hkl is the intensity of (hkl) plane obtained from the X-ray diffraction pattern. The facial angle θ_T is supposed to be 0° when all crystals are oriented to (00n) and 45° when oriented to (hk0) (h = k). The calculated facial angle (θ_T) of α-Al crystal with and without magnetic field are shown in Fig. 7. When without magnetic field, the α-Al crystal only tilted about 16.1° from the c-plane. While in the case of 5 T magnetic field, the crystal inclined to about 37.6°. This result agrees well with the EBSD measurement and further confirms the dendrite orientation transition from <100> to <110> in Al-10 wt.%Zn alloy induced by the application of strong static magnetic field.

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Fig. 7.   Deflection of facial angle from the magnetic field (a) 0 T, (b) 5 T.

4. Conclusion

In summary, Al-10 wt.%Zn alloy was directionally solidified with and without magnetic field, the three-dimensional dendritic morphology and solid/liquid interface shape were characterized by X-ray micro-computed tomography, indicating a cellular to dendritic transition of the columnar grains and the destabilization of solid/liquid interface caused by the applied static magnetic field. The thermoelectric magnetic convection resulting from magnetic field was found to destabilize the solid/liquid interface and tilt the columnar growth dendrite array. Further, the EBSD/XRD results demonstrated that dendrite orientation transition from <100> to <110> was induced by axial high static magnetic field. The DOT in directionally solidified Al-10 wt.%Zn alloy under magnetic field is probably due to interaction of crystallographic anisotropy and the magnetic energy anisotropy of grains when solidified under magnetic field.

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Grant Nos. 51690162, 51604171 and 51701112), China Postdoctoral Science Foundation (Grant Nos. 2017T100291 and 2017M611530), Shanghai Municipal Science and Technology Commission (No. 17JC1400602), and open funding of State Key Laboratory of Solidification Processing in NWPU (SKLSP201602 and SKLSP201706). The authors gratefully acknowledge the support from Shanghai Synchrotron X-ray Facility (SSRF) on experiment and data analysis.

The authors have declared that no competing interests exist.