J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (4): 568-577.DOI: 10.1016/j.jmst.2018.09.037
• Orginal Article • Previous Articles Next Articles
Zhe Shen, Minghu Peng, Dongsheng Zhu, Tianxiang Zheng*(
), Yunbo Zhong*(), Weili Ren, Chuanjun Li, Weidong Xuan, Zhongming Ren
Received:2018-06-06
Revised:2018-07-17
Accepted:2018-09-03
Online:2019-04-05
Published:2019-01-28
Contact:
Zheng Tianxiang,Zhong Yunbo
Zhe Shen, Minghu Peng, Dongsheng Zhu, Tianxiang Zheng, Yunbo Zhong, Weili Ren, Chuanjun Li, Weidong Xuan, Zhongming Ren. Evolution of the microstructure and solute distribution of Sn-10wt% Bi alloys during electromagnetic field-assisted directional solidification[J]. J. Mater. Sci. Technol., 2019, 35(4): 568-577.
Fig. 1. Directional solidification of Sn-10 wt% Bi alloys with a simultaneous imposition of an external DC and a TSMF: (a) phase diagram of Sn-Bi alloy and (b) schematic diagram of the experimental apparatus.
Fig. 2. 3D numerical simulation model and simulation results: (a) computational domain and boundary conditions, (b) computed phase field after the solidification of 1600s under a 0.5 T TSMF, and (c) computed phase field result shown along the x-z plane.
Fig. 3. Longitudinal section microstructures of Sn-10 wt% Bi alloys directionally solidified under different intensities of the TSMF and current densities of the external DC: (a) 0 T; (b) 0.1 T; (c) 0.3 T; (d) 0.5 T; (e) 0.5 T, 1 × 104 A/m2; (f) 0.5 T, 4 × 104 A/m2; (g) 0.5 T, 8 × 104 A/m2; (h) 0.5 T, 1.6 × 105 A/m2.
| Properties | Magnitude |
|---|---|
| Density (ρ, kg/m3) | 7600 |
| Electric conductivity (σs, S/m) | 3.74 × 106 |
| Electric conductivity (σl, S/m) | 1.87 × 106 |
| Dynamic viscosity (μs, Pa s) | 2 × 106 |
| Dynamic viscosity (μl, Pa s) | 0.0014 |
| Thermal conductivity (λs, W/(m K)) | 60 |
| Thermal conductivity (λl, W/(m K)) | 30 |
| Heat capacity (cp, J/(kg K)) | 226 |
| Melting point of Sn-10 wt% Bi (TM, K) | 505 |
| Liquidus slope (ml, K/at.%) | 210 |
| Partition coefficient (kp) | 0.27 |
| Latent heat (L, J/kg) | 6 × 104 |
| Thermal expansion coefficient (βT, 1/K) | 9.5 × 10-5 |
| Solute expansion coefficient (βC, 1/wt%) | 3.8 × 10-3 |
| Solute diffusivity in liquid (DL, m2/s) | 3 × 10-9 |
| Reference temperature (Tref, K) | 489 |
| Reference solute concentration (Cref, wt%) | 10 |
| Internal thermoelectric current density (JTE, A/m2) | 1.1 × 104 |
Table 1 Thermophysical data of Sn-10 wt% Bi alloy and other parameters used in simulation [[19], [20], [21], [22], [23], [24]].
| Properties | Magnitude |
|---|---|
| Density (ρ, kg/m3) | 7600 |
| Electric conductivity (σs, S/m) | 3.74 × 106 |
| Electric conductivity (σl, S/m) | 1.87 × 106 |
| Dynamic viscosity (μs, Pa s) | 2 × 106 |
| Dynamic viscosity (μl, Pa s) | 0.0014 |
| Thermal conductivity (λs, W/(m K)) | 60 |
| Thermal conductivity (λl, W/(m K)) | 30 |
| Heat capacity (cp, J/(kg K)) | 226 |
| Melting point of Sn-10 wt% Bi (TM, K) | 505 |
| Liquidus slope (ml, K/at.%) | 210 |
| Partition coefficient (kp) | 0.27 |
| Latent heat (L, J/kg) | 6 × 104 |
| Thermal expansion coefficient (βT, 1/K) | 9.5 × 10-5 |
| Solute expansion coefficient (βC, 1/wt%) | 3.8 × 10-3 |
| Solute diffusivity in liquid (DL, m2/s) | 3 × 10-9 |
| Reference temperature (Tref, K) | 489 |
| Reference solute concentration (Cref, wt%) | 10 |
| Internal thermoelectric current density (JTE, A/m2) | 1.1 × 104 |
Fig. 4. Longitudinal and cross section microstructures of Sn-10 wt% Bi alloys directionally solidified under different intensities of the TSMF and current densities of the external DC: (a1, a2) 0 T; (b1, b2) 0.1 T; (c1, c2) 0.3 T; (d1, d2) 0.5 T; (e1, e2) 0.5 T, 4 × 104 A/m2; (f1, f2) 0.5 T, 8 × 104 A/m2.
Fig. 5. Primary dendrite spacing of directionally solidified Sn-Bi alloys under different intensities of the TSMF and current densities of the external DC.
Fig. 6. Schematic diagram of the electric field and flow field during the directional solidification of Sn-10 wt% Bi alloys under a TSMF with and without an external DC: (a) illustration of the TE current and the TEMC, (b) distribution of currents at the dendrite tip after the introduction of an external DC, and (c) illustration of the EMC.
Fig. 7. Computed phase field, flow field and solute field of directionally solidified Sn-10wt.% Bi alloys after the solidification of 1600s under different intensities of the TSMF and current densities of the external DC: (a) 0.5 T; (b) 0.5 T, 1 × 104 A/m2; (c) 0.5 T, 4 × 104 A/m2; (d) 0.5 T, 1.6 × 105 A/m2.
Fig. 8. Schematic diagram of the detection method of solute distribution along the longitudinal section of the sample.
Fig. 9. Distribution of Bi solute contents in two characteristic areas under different intensities of the TSMF and current densities of the external DC: (a1, b1) 0 T; (a2, b2) 0.5 T; (a3, b3) 0.5 T, 4 × 104 A/m2; (a4, b4) 0.5 T, 1.6 × 105 A/m2.
Fig. 10. Evolution of solute content in Bi poor/rich areas under different intensities of the TSMF and current densities of the external DC with assigned solid fraction by using the Ranksort method.
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