Journal of Materials Science & Technology, 2020, 50(0): 86-91 DOI: 10.1016/j.jmst.2020.03.002

Research Article

Controlling and adjusting the concentration distribution during solidification process using static magnetic fields

Pinfang Jianga, Jiantao Wanga, Long Houa, Yves Fautrelleb, Xi Li,a,b,*

aState Key Laboratory of Advanced Special Seels, Shanghai University, Shanghai, 200072. PR China

bSIMAP-EPM-Madylam/G-INP/CNRS, PHELMA, BP 75, 38402 St Martin d'Heres Cedex, France

Corresponding authors: * State Key Laboratory of Advanced Special Steels,Shanghai University, Shanghai, 200072, PR China.E-mail address:Ixnet@sina.com(X. Li).

Received: 2020-12-4   Accepted: 2020-01-27   Online: 2020-08-1

Abstract

As concentration distribution changes have important effects on material structures and properties, controlling the concentration distribution is essential to alloy performance. The aim of the present work is to control and adjust the concentration distribution by the static magnetic field. It is found that the magnetic field disperses grain boundary segregation and causes the uniform distribution of concentration. Further, by the three-dimensional computed tomography (3D-CT) reconstruction, the flow distribution is seen and the effect mechanism of the magnetic field is revealed. The present work may clarify the ambiguous understanding on the effect of the static magnetic field on solidification process.

Keywords: Static magnetic field ; Concentration distribution ; Structures

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Cite this article

Pinfang Jiang, Jiantao Wang, Long Hou, Yves Fautrelle, Xi Li. Controlling and adjusting the concentration distribution during solidification process using static magnetic fields. Journal of Materials Science & Technology[J], 2020, 50(0): 86-91 DOI:10.1016/j.jmst.2020.03.002

1. Introduction

Controlling the solidification of metallic alloy is of significant importance, which mainly decides the final properties of most alloys by modulating their structures and compositions during solidification. One of the most intensively studied issues is the distribution of solute concentration which is inherent to solidification. These concentration variations, also known as segregations, will appear in a solidified sample at various scales: microscopic, mesoscopic and/or macroscopic (crucible) scale [[1], [2], [3], [4], [5]]. As these concentration changes have important effects on material properties, minimizing segregation and controlling the distribution of solute concentration are essential to alloy performance. As an effective method of mass transfer, the diffusion always plays an important role in modulating the composition of alloy in solidification process.

The effect of the static magnetic field on the concentration distribution and diffusion has been frequently investigated [[6], [7], [8], [9], [10], [11], [12]]. For instance, it was reported that with the increase of the magnetic field intensity the partition coefficient increased at low growth rates and decreased at higher growth rates in solidified Al-Cu alloys. These results were attributed to the variation of the solute diffusion coefficient with the applied magnetic field. However, they found that this interpretation was not consistent with the expected orders of magnitude [6]. Some experimental results revealed that the static magnetic field inhibited the diffusion [7,8], whereas others demonstrated that static magnetic field accelerated the diffusion [[9], [10], [11]]. There were also some reports claiming that the magnetic field had no influence on the diffusion rate [12]. Therefore, so far, the influence of the static magnetic field on the distribution of solute concentration and the diffusion during directional solidification is ambiguous.

The aim of the present work is to investigate the influence of the magnetic field on the concentration distribution and control the concentration distribution using the magnetic field. It is found that the application of the magnetic field enhances the concentration uniformities and increases the solid solution during directional solidification. Further, by the 3D-CT reconstruction, the flow distribution is seen and the magnetic field enhances the solidification progress. The TE magnetic effects should be mainly responsible for the change in the concentration distribution and structures under the magnetic field. The above results may clarify some ambiguous understanding on the effect of the static magnetic field on the diffusion and segregation. Moreover, a new method is proposed to enhance the concentration uniformities by the static magnetic field.

2. Experimental procedure

Al-Cu alloys used in this study were prepared by melting high-purity raw elements (5 N). The alloys were melted under argon atmosphere in high purity alumina crucibles. The rod-like specimens with a diameter of 3 mm and a length of 120 mm were put into a corundum tube. The schematic view of the directional solidification apparatus under an axial magnetic field can be found in Ref. [13]. The prepared specimens were processed metallographically parallel and perpendicular to the solidification direction. Scanning electron images were made for microstructure observation. The compositional variation of the alloy was measured by energy dispersive spectroscopy (EDS). To enhance the accuracy, element distribution maps were collected from 400 selected points in a 20 × 20 matrix using EDS point analysis. In order to obtain a series of more effective and reliable data, the living collecting time for every point was set as 20 s. Thus, a statistically significant number of individual measurement points were used to capture the micro-segregation. The weighted interval rank sort (WIRS) method was utilized to exploit all the EDS data [14]. An electron probe micro analyzer (EPMA) was also used to measure the distribution of the solute Cu. As a direct visualization tool, the 3D-CT technology provides great convenience for the characterization of microstructure and the quantification of microstructural evolution during the solidification of metallic alloy and has become a commonly available tool in the material science community [[15], [16], [17], [18], [19], [20]]. Using the 3D-CT technology, the three-dimensional (3D) morphologies of structures during directional solidification were reconstructed and the quantification of the phase volume fraction were performed. In the 3D-CT measurement, the diamond light source in our Lab-State Key Laboratory of Advanced Special Steels was equipped with a monochromatic beam of 53 KeV. A PCO edge high-resolution camera was used as a detector with a pixel size of 1.3 × 1.3 μm2, and an exposure time of 5 ms was chosen to guarantee sufficient transmission and good contrast. The field of view was 3.3 × 2.8 mm2, and 1800 frames were collected for a complete 3D tomography. The detailed description of 3D tomography apparatus and reconstruction methods are available in Ref. [15]. The volume data visualization and quantification were carried out using Aviso 7 and MATLAB. The detailed procedures were described in Ref. [21].

3. Experimental results and discussions

Fig. 1 shows the contour maps of the Cu concentration in selected areas of the Al-4.5 wt.%Cu alloy and corresponding concentration versus solid fraction profiles. It can be found that the microsegregation between the dendrite core and inter-dendrite decreases due to the application of magnetic field (see Fig. 1(a) and (b)). Fig. 1(c) shows the Cu concentration versus the solid fraction profiles under various magnetic fields. One can notice that in a given solidification condition the Cu concentration gradually increases and then a sharp increase in concentration occurs at the end of the solidification, i.e. the formation of the non-equilibrium eutectics. At the initial solidification stage, the Cu concentration under the magnetic field is higher than that without magnetic field. Moreover, the higher the magnetic field intensity is, the higher the concentration is. At a high solid fraction, the Cu concentration decreases with the increase of the magnetic field intensity. This result is well agreed with the mass conservation. It can be proposed that the application of the magnetic field will reduce the microsegregation. Fig. 2(a) and (b) show the SEM-BSE images on the transverse section in the directionally solidified Al-4.5 wt.%Cu alloy at the growth rates of 10 μm/s and 20 μm/s without and with a 12 T magnetic field. The microstructures consist of the primary α-Al phase (black) and eutectic Al-Al2Cu phase (white). It can be found that the volume fraction of the eutectic phase decreases as the magnetic field increases. With the increase of the growth rate, the effect of the magnetic field on the volume fraction of the eutectic phase becomes less. Fig. 2(c) and (d) show the volume fraction of the eutectic phase as a function of the magnetic field and growth rate, respectively.

Fig. 1.

Fig. 1.   Experimentally determined Cu concentration contour plot in the directionally solidified Al-4.5 wt.%Cu alloy under various magnetic fields (GT = 60 K/cm and R = 10 μm/s): (a) and (b) Transverse microstructures and experimentally determined Cu concentration contour plot without and with a 12 T magnetic field; (c) Cu concentration versus solid fraction profiles in the transverse sections of directionally solidified Al-4.5 wt%Cu alloys under various magnetic field intensities. The inset at the top right shows relative solute concentration at a solid fraction of 0.85. The below inset is a magnified solute concentration profiles at initial solidification stage.


Fig. 2.

Fig. 2.   SEM-BSE images on the transverse section in the directionally solidified Al-4.5 wt.%Cu alloy under various magnetic fields: (a) 10 μm/s; (b) 20 μm/s; (a1) and (b1) 0 T; (a2) and (b2) 6 T; (a3) and (b3) 12 T; (c) the volume fraction of the eutectic phase as a function of the growth speed without and with a 12 T magnetic field; (d) volume fraction of the eutectic phase as a function of the magnetic field intensity at a growth rate of 10 μm/s.


Subsequently, the 3D-CT reconstruction technology is applied to investigate the structure during directional solidification. Fig. 3 shows the 3D-CT reconstruction structures in the directionally solidified Al-4.5 wt.% Cu alloy at the growth rate of 10 μm/s under various magnetic fields. In this 3D reconstruction structure, the eutectic and liquid phases, which occupy the interspaces between columns, have been eliminated from the 3D view to expose the α-Al phase. Compared with the shape of the liquid-solid interface without the magnetic field, the interface becomes more protruding under the magnetic field. This is supposed to be the consequence of the flow tracks (marked by the blue dotted line) which appear under the magnetic field (see Fig. 3(a)). The flow tracks appear at the boundary of the sample (see Fig. 3(a2)) under a lower magnetic field (B = 0.1 T). When the magnetic field increases to 0.5 T, the scale of the flow tracks decreases (see Fig. 3(a3)). Under the magnetic field of 10 T, the flow tracks appear at the dendrite scale (see Fig. 3(a4)). Fig. 3(b1)-(b4) show respectively the transverse microstructures at the position of 3 mm far from the liquid-solid interface under various magnetic fields. One can see that with the increase of the magnetic field, the fraction of the solid phase increases. Further, the microstructures at various positions in the mushy zone were observed using the 3D-CT technology and the result is shown in Fig. 3(c) and (d). A comparison of the microstructures with and without the magnetic field reveals that the magnetic field enhances the solidification progress. In order to quantify the fraction of the solid phase, the 3D-CT tomography data are plotted as a function of the distance from the liquid-solid interface as shown in Fig. 3(e). This clearly demonstrates that the application of the magnetic field increases the fraction of the solid phase and decreases the local solidification time during directional solidification.

Fig. 3.

Fig. 3.   Effect of the magnetic field on the liquid-solid interface and the fraction of the solid phase in the mushy zone in the directionally solidified Al-4.5 wt.%Cu alloy at the growth rate of 10 μm/s: (a) 3D-CT reconstruction structures and (b) the corresponding transverse microstructures under various magnetic fields (i.e., 0 T, 0.1 T, 0.5 T and 10 T); (c) and (d) transverse microstructures at various positions in the mushy zone for the samples solidified without and with a 10 T magnetic field; (e) the volume fraction (f) of the α-Al primary phase in the mushy zone as a function of the distance from the liquid-solid interface (L) measured without and with the magnetic field.


Fig. 3 clearly show that there exists a global flow rotation in the liquid. Therefore, some of the results can be explained by analyzing the local fluid flow. Normally, the static magnetic field has two main effects with respect to the liquid motions: one is the magneto-hydrodynamic damping (MHD), in which the flow is damped when the Hartmann value is sufficiently large [22], and the other is thermoelectric (TE) magnetic convection, which induces a particular flow in the melt [23]. With an increase in the magnetic field amplitude, the natural convection vanishes whereas the TE magnetic convection first increases and then decreases due to the damping effect for a very large magnetic field strength. Consequently, the TE magnetic convection reaches a maximum for a large Hartmann number equal to approximately 10 [24]. The Hartmann number Ha is defined as follows: $Ha=BL(\sigma /\rho \nu )$, where L, B, $\sigma $, $\rho $ and $\nu$ denote a typical length scale of the problem, the magnetic field intensity, the electrical conductivity, the density and the kinematic viscosity, respectively. Here, the Hartmann numbers at the scales of the sample and dendrite are evaluated. In the Al-Cu alloy, $\sigma$ = 4 × 106 S/m, $\nu$ = 0.0013 Pa·s. At the sample scale (D = 3 mm), the value of HaD is about 1664 under a magnetic field of 10 T. This means that the Hartmann number corresponding to the global rotation is very large, and the flow can be rapidly suppressed by the magnetic field of 10 T. As far as the flow at the scale of the dendrites (D = 100 $\mu m$), damping will take place when $H{{a}_{\lambda }}$ is greater than 10-100. Thus, the magnetic field amplitude must be at least of the order of 10-20 T to have a significant damping effect. Therefore, under a large magnetic field, the interdendritic TE magnetic convection mainly works and affects the concentration distribution. It is evident that the interdendritic TE magnetic convection in the mushy zone promotes stirring of the liquid at the boundary of the dendrite and accelerates the solidification progress (i.e., decreases the local solidification time). Consequently, the grain boundary segregation is dispersed and the solid solubility increases under the higher magnetic field. Fig. 4(a) and (b) show the schematic diagram of one volume element in the mushy zone and the solute distribution near the liquid-solid interface on this volume element without and with the magnetic field. To prove the above proposal, the following measurement has been done. The distribution of the solute Cu in the solidified directionally Al-0.85 wt.%Cu alloy is measured, and the results are shown in Fig. 4(c). Notably, the content of solute Cu in the solid at the liquid-solid interface under the 10 T magnetic field is approximately the same as the case with no magnetic field. With the solidification progressing, the content of the solute Cu increases gradually under the magnetic field. This indicates that the application of the magnetic field does not change the partition coefficient (${{k}_{0}}$), but modifies the apparent diffusion behavior of the liquid or/and solid diffusion in the mushy zone. Here, the effect of the magnetic field on the diffusion coefficient in the liquid phase is evaluated. Garandet et al. supposed that the additional convective contribution to mass transportation could be simply added to the liquid diffusion term, which can be written as [25]:

${{D}_{\text{eff}}}=\text{D}(1+\frac{1}{4}{{H}^{2}}\frac{{{u}^{2}}}{{{D}^{2}}})$

Fig. 4.

Fig. 4.   Effect of the magnetic field on the solute diffusion at the liquid-solid and the dendrite core-segregation zone interfaces during directional solidification: (a) One volume element in the mushy zone; (b) schematic diagram of the solute distribution near the liquid-solid interface without and with the magnetic field; black and yellow lines showing the solute distribution in the solid phase without and with the magnetic field; (c) the distribution of the solute Cu in the Al-0.85 wt.%Cu alloy along the axial direction; (d) schematic illustration of the influence of the TE magnetic effects on the solid diffusion; (e) schematic diagram of the experimental setup for the eliminating grain boundary segregation during the heat treatment process under the temperature gradient and the magnetic field; (f) the distribution of the solute Cu and the corresponding structure in the Al-4.5 wt.%Cu alloy during the heat treatment under the temperature gradient and the magnetic field (GT = 60 K/cm).


where Deff is the apparent liquid diffusion coefficient, $\text{D}$ the actual liquid diffusion coefficient, H characterizing length, u is flow velocity. Taking D = 5.59 × 10-9 m2 s-1 [26], H = 10-4 m, u = 2 × 10-5 m s-1 [27] yields an apparent diffusion coefficient of 8.45 × 10-9 m2 s-1. The diffusion coefficient in the liquid phase increases by 12% under the action of the TE magnetic convection. As the interdendritic TE magnetic convection increases with the magnetic field intensity (up to the order of 10 T), the modifications of the dendrite boundary segregation and the solid solubility are enhanced as the magnetic field increases in the range of 10 T (see Fig. 1).

Moreover, owing to the difference between the TE powers of the dendrite core and the segregation zone (${{S}_{\text{D}}}-{{S}_{\text{S}}}$) in the solid phase, the TE current is also produced in the segregation zone during directional solidification as shown in Fig. 4(d). Lehmann et al. studied the interdendritic TE current and provided the equation of the interdendritic TE current [28]. Similarly, the TE current in the segregation zone can be written as:

$J_{\text{TE}}^{\text{S}}=\frac{{{\sigma }_{\text{D}}}\sigma _{\text{S}}^{2}}{{{\left( {{\sigma }_{\text{D}}}-{{\sigma }_{\text{S}}} \right)}^{2}}}{{f}_{\text{D}}}\left( {{S}_{\text{D}}}-{{S}_{\text{S}}} \right)G$

where $J_{\text{TE}}^{\text{S}}$ is the TE current of the segregation zone, SD and SS the TE powers of the dendrite core and the segregation zone, respectively, ${{S}_{\text{D}}}$ and ${{\sigma }_{\text{D}}}$ the electrical conductivity of the dendrite core and the segregation zone, respectively, and ${{f}_{\text{D}}}$ the volume fraction of the dendrite trunk. Thus, a TE magnetic force forms at the interface between the dendrite core and segregation zone during directional solidification under the magnetic field as follows:

$F_{\text{TEM}}^{\text{S}}=B\frac{{{\sigma }_{\text{D}}}\sigma _{\text{S}}^{2}}{{{\left( {{\sigma }_{\text{D}}}-{{\sigma }_{\text{S}}} \right)}^{2}}}{{f}_{\text{D}}}\left( {{S}_{\text{D}}}-{{S}_{\text{S}}} \right)G$

From Eq. (3), it is evident that the TE magnetic force increases with the increase in the magnetic field. Here, it is assumed that the interface potential at the interface between the dendrite core and the segregation region satisfies the multi-atom layer model with a double electron-layer [29]. Thus, solute atoms carry electric charges at the interface [30], and the TE magnetic force is emerged to solute atoms in the segregation zone. The TE magnetic force may change the migration trajectories of solute atoms and enhance the diffusion in the solid phase. Consequently, the application of the magnetic field will disperse dendrite boundary segregation and increase the solid solution. Here, a special experiment was designed to study the influence of the TE magnetic effects in the solid phase on the dendrite boundary segregation during heat treatment. Fig. 4(e) shows the schematic of the experimental setup of the heat treatment during imposing both the temperature gradient and the static magnetic field. Firstly, the sample was prepared by the directional solidification at a certain growth rate. Subsequently, the obtained sample was heat-treated under a certain temperature gradient. Fig. 4(f) shows the transverse structure and the corresponding distribution of solute Cu for the directionally solidified Al-4.5 wt.%Cu treated for two hours at a temperature gradient of 60 K/cm without and with a 10 T magnetic field. A comparison between the structures with and without the magnetic field shows that the dendrite boundary segregation is eliminated significantly under the magnetic field. As the TE magnetic force acting on the segregation increases with the increase in the magnetic field, the reduction of the dendrite boundary segregation is enhanced with the increase in the magnetic field. The above experimental results may result in a new method to eliminate the dendrite boundary segregation and enhance solute concentration uniformity in alloy via the TE magnetic effects during the heat treatment.

4. Conclusions

In the present work, the influence of the static magnetic field on the solute distribution and structure in the Al-4.5 wt.%Cu alloy is investigated during directional solidification. The main conclusions are drawn as follows:

(1) The magnetic field disperses the grain boundary segregation and causes the uniform distribution of concentration.

(2) The 3D-CT reconstruction technology is used to observe the microstructures in the mushy zone. The flow tracks are seen under the magnetic field and the scale of the flow track decreases with the increase in the magnetic field.

(3) The application of the magnetic field increases the fraction of the solid phase and decreases the local solidification time.

(4) The magnetic field-enhanced concentration uniformities should mainly be attributed to the interdendritic TE magnetic convection promoting the solidification process. Moreover, the influence of the TE magnetic effects on the solid diffusion is also responsible for the magnetic field-enhanced concentration uniformities.

Acknowledgments

This work is financially supported partly by National Natural Science Foundation of China (Nos. 51571056 and 51690164), “Shuguang Program” from Shanghai Municipal Education Commission, Shanghai Science and Technology Committee Grant (19XD1401600, 19010500300).

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