Modification of the Primary and Peritectic Phases in Directionally Solidified Cu-20 wt.% Sn Alloy by Magnetic Field

Abstract

Directional solidification experiments on Cu-20 wt.% Sn peritectic alloy were carried out in a direct current magnetic field device to investigate the modification of the primary and peritectic phases. A precipitation of the acicular martensitic structure of peritectic phase was observed below the solid-liquid interface. The magnetic field increased the length of precipitation zone and moved the solid-liquid interface to high temperature side. Solid-state transformation of the peritectic phase was observed below the eutectoid temperature. The magnetic field increased first and then decreased the transformation. A transition of the primary dendrites from arrayed to nonaligned growth under the magnetic field was characterized and analyzed. 3D numerical simulations of the thermoelectric magnetic flows and the thermoelectric magnetic forces were performed. The modification of the primary and peritectic phases under the magnetic field should be attributed to the fluid flows in the liquid and the forces on the solid.

1. Introduction

During the solidification process of liquid metal alloys, electromagnetic devices are widely used to control the solid structure.^1,2,3) Usually, direct current magnetic field device can damp the natural convection and promote the development of equiaxed structure by magnetohydrodynamics (MHD) damping effect. However, due to the thermoelectric effect, an inner thermoelectric current loop can form around the solid-liquid interface when there is a temperature difference between the joints. When the direction of thermoelectric current is not parallel with the magnetic field, the thermoelectric magnetic (TEM) forces can be produced on the solid and in the liquid by the combination of electric and magnetic. The TEM forces in the liquid will further induce the formation of TEM flows, which can drive interdendritic fluid flows. Shercliff⁴⁾ first predicted that thermoelectric current in the presence of magnetic field can induce pumping or stirring of fluid flows in 1979, but only recently has observed direct evidence of the TEM flows and the TEM forces by means of synchrotron X-ray radiography in situ.^5,6)

The effects of the TEM flows on the microstructures have been discussed for many years. Moreau et al.⁷⁾ suggested that the TEM flows are responsible for segregation. These authors estimated the velocity of interdendritic fluid flows in directionally solidified Cu–Ag alloys under a magnetic field. Lehmann et al.⁸⁾ developed the velocity model of the TEM flows, and found that the dendrite spacing decreases as the TEM flows increase. Kao et al.⁹⁾ modeled the mechanism of segregation and dendritic refinement under the magnetic field. Based on Wang’s¹⁰⁾ experimental dates, these authors suggested that the microstructure evolution is modified by the TEM flows driven solute transport. Shen et al.¹¹⁾ found that the magnetic field can modify the solidification morphology of Sn–Pn alloys. Li et al.^12,13,14,15) carried out extensive directional solidification experiments on single phase and eutectic alloys under the magnetic field. They found that the TEM flows could cause a series of phenomena, such as macro-segregation (freckles and channels), dendritic refinement, and solid-liquid interface deformation.

The study for the TEM forces on the solid has just started in the recently years. There are two main reasons for that. Firstly, the TEM flows will dominate the interaction on the solidification structures at low magnetic field. Secondly, the high magnetic field device, which can produce a large TEM forces, only began being commercial over the past decade. Wang et al.⁶⁾ directly observed the TEM forces driven fragment motion by means of synchrotron X-ray radiography in situ. Li et al.^16,17) reported that the TEM forces could cause the formation of twinned dendrites or array of dendrites in directionally solidified Al–Cu alloys. Wu et al.¹⁸⁾ found that the high magnetic field could cause the random distribution of the aggregated Al₃Fe phase in directionally solidified Al–Fe alloy. Li et al.¹⁹⁾ suggested that the high magnetic field could cause the crystallographic features of Al₆Mn phase tended to the magnetic field direction during solidification process of Al–Mn alloys. Therefore, it is important to study the effects of the magnetic field on the solidification structure during directional solidification.

Up to new, the effect of the magnetic field on the microstructures of single phase and eutectic alloys has been investigated extensively. However, very few studies have focused on the peritectic alloys. Although peritectic system is commonly observed in many engineering alloys, such as steels (Fe–C, Fe–Ni), copper alloys (Cu–Sn, Cu–Zn), and aluminium alloys (Al–Ti, Al–Ni).²⁰⁾ This could be due to the peritectic solidified systems exhibit a variety of solidification structures during directional solidification. In this work, Cu-20 wt.% Sn peritectic alloy is selected to study the effects of the magnetic field on the modification of primary and peritectic phases during directional solidification. Microstructures with and without the magnetic field are compared. The influences of the MHD damping effect, the TEM forces, and the TEM flows on the primary and peritectic phases are presented, respectively. Numerical simulations and simple analyses are carried out to characterize them.

2. Experimental Setup and Model Description

Directional solidification experiments on Cu-20 wt.% Sn alloy at different growth speeds without and with a static axial magnetic field are carried out. The initial alloys are suction cast from Cu and Sn of 99.99 wt.% purity in a vacuum induction suspension-melting furnace of water-cooled copper crucible. The suction cast rod has been re-melted and solidified in a Bridgman furnace equipped with a direct current magnetic field device. Detailed schematic diagram of the experimental apparatus can be found in Ref. 12. The direct current magnetic field device can produce a static axial magnetic field up to 5 T. The Bridgman furnace consists of a heater and a cooler. The heater is a graphite-heated tube placed in an argon protection environment, and the cooler is a water-cooled Ga-In-Sn liquid metal cooling stored in a cylindrical container. The suction cast rod is put into a high purity alumina tube with an inside diameter of 3 mm and length of 200 mm. The rod and tube are installed in the Bridgman furnace. One end of the tube is fixed inside the liquid metal cooling. After heating and temperature stabilization for 30 min, the tube is pulled into the liquid metal cooling at a predetermined velocity for a processing length of 60 mm without and with a magnetic field. Finally, the specimen is quenched in the liquid metal cooling at the end of the solidification. The temperature in the Bridgman furnace is controlled by a Pt/6Rh-Pt/30Rh thermocouple. The temperature gradient measured with an inside thermocouple is about 100 K/cm. The microstructure is examined in the etched condition by optical microscope. The distribution of solute content is measured by energy dispersive X-ray spectroscopy (EDS). The orientation characteristics are investigated by electronic backscatter diffraction (EBSD) in a high-resolution field emission gun scanning electron microscope (JEOL 6500F).

3D numerical simulations of the TEM flows and the TEM forces are performed by using the finite element commercial code COMSOL Multiphysics. In this numerical simulation section, electric, magnetic and hydrodynamic phenomena are modeled during the imposition of a temperature gradient under a static axial magnetic field. The morphology of the growth front of solid in the direction of temperature gradient is given. Here, only the force and convection are considered and the solute convection without the magnetic field is ignored.

These simulations are based on the principle of thermoelectric effect that a temperature gradient produces a thermoelectric current. The basic equation of the thermoelectric current under a magnetic field can be constructed according to the Ohm’s law:   

$$j=\sigma (u\times B)-\sigma SG$$(1)

where σ is the electrical conductivity, u is the velocity of fluid flows, B is the intensity of the magnetic field, S is the thermoelectric coefficient, and G is the temperature gradient.

The TEM flows are governed by the Navier-Stokes equation, which in the presence of the magnetic field can be written as:   

$$\rho \frac{\partial u}{\partial t}+\rho \left(u\cdot \nabla \right)u=-\nabla p+j\times B+\rho \mu {\nabla }^{2}u$$(2)

During the process of calculation, the boundary conditions are following:

(i) the electric current density must satisfy the continuity equation   

$$\nabla \cdot j=0$$(3)

(ii) the thermal field is oriented along the z-axis, i.e. the solidification direction   

$$\nabla T=G\cdot i_z$$(4)

where i_z is a unit vector along the z-axis.

(iii) the electric current and the temperature near the solid-liquid interface must be continuity   

$$-{\sigma }_l\frac{\partial V_l}{\partial n}-{\sigma }_l{S}_{l}G=-{\sigma }_s\frac{\partial V_s}{\partial n}-{\sigma }_s{S}_{s}G$$(5)

  

$$T_s=T_l$$(6)

where s and l are the solid and liquid phases, respectively, $\frac{\partial V_s}{\partial n}$ and $\frac{\partial V_l}{\partial n}$ are the units of the solid and liquid phases, respectively.

3. Experimental Results

According to the Cu–Sn phase diagram, the phase transformation of the Cu-20 wt.% Sn alloy starts with solidification of primary α phase. Then following peritectic reaction occurs at 1071 K, L+α→β. Then following eutectoid reaction occurs at 859 K, β→γ+α. At 793 K, following eutectoid reaction occurs, γ→δ+α. However, Liu et al.²¹⁾ reinvestigated this system and found that the β and γ domains are effectively a continuous two-stage transition. These authors suggested that the β→γ+α reaction is non-existent and the β and γ can be considered to be one and the same phase. Actually, two solid-state transformations within the peritectic phase can simplify the analysis of the resulting structure after quenched: one is the peritectic phase transformed into an (α+δ) structure via a eutectoid reaction at 793 K, and the other is the peritectic phase decomposed into an acicular martensitic structure for the composition from 22 to 24 wt.% Sn during quenching operation.^22,23)

Figure 1 shows the solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at various growth speeds without and with a 5 T magnetic field. The primary phase α appears in light brown, and the peritectic phase β corresponds to the gray regions. As can be seen in Fig. 1(a1), the top region of the micrograph below the solid-liquid interface corresponds to the α-islands. Moving toward the bottom, the fraction of α phase increases. Both the primary and peritectic phases present at the solid-liquid interface. However, the application of the magnetic field caused the planar front growth of the β phase at the time of quenching as shown in Fig. 1(a2). Unfortunately, it is not easy to determine clearly the growth front of the peritectic phase (morphology and position) behind the leading primary phase during quenching. Because of the quenching operation induced the decomposition of the peritectic phase into an acicular martensitic structure. For ease of description, we defined a precipitation zone of only peritectic phase that displays the region between the solid-liquid interface (position near the line a in Fig. 1(a2)) and the growth front of α phase (position near the line b in Fig. 1(a2)). The peritectic phase is decomposed into the acicular martensitic structure (β_P) in this domain. With the increase of growth speed, α phase changed into the dendritic morphology as shown in Figs. 1(b1) and 1(c1). The application of the magnetic field destroys and refines the primary dendrites as shown in Figs. 1(b2) and 1(c2). In addition, the precipitation zone of β_P decreased until it disappeared at high growth speed condition. Figure 2 shows the solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 1 μm/s under various magnetic fields. In the case of no magnetic field, during directional solidification for Cu-20 wt.% Sn peritectic alloy, the solidification of the solid will release the Sn solute into the liquid. As a result, the composition ahead of the solid-liquid interface increases. When the composition reaches a certain range (between 22 and 24 wt.% Sn), the acicular martensitic structure appears after the quenching operation. The application of the magnetic field enhanced the formation of the acicular martensitic structure and driven the solid-liquid interface into the high temperature side. This result indicates that the magnetic field caused the enrichment of solute and changed the degree of undercooling during solidification. Figure 3 shows the length of precipitation zone as a function of the growth speed and the magnetic field. It can be found that the length of precipitation zone increased by about 1 mm with the application of a 5 T magnetic field. According to Fig. 2, it indicates the increase of the position of solid-liquid interface. Since the constant temperature gradient in this experiment is about 100 K/cm, Fig. 3 indicates that the degree of constitutional undercooling decreases by amount 10 K under the magnetic field. This result implies that the application of the magnetic field increased the solute content at the growth front of the solid.

Fig. 1.

Solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at various growth speeds without and with a 5 T magnetic field: (a) 2 μm/s; (b) 5 μm/s; (c) 20 μm/s. (Online version in color.)

Fig. 2.

Solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 1 μm/s under various magnetic fields: (a) 0 T; (b) 1 T; (c) 3 T; (d) 5 T. (Online version in color.)

Fig. 3.

Effect of the magnetic field on the length of precipitation zone (L) during directional solidification: (a) the growth speed as a function of the L without and with a 5 T magnetic field; (b) the magnetic field as a function of the L at a growth speed of 1 μm/s. (Online version in color.)

Figure 4 shows a larger version of the microstructure of primary phase α within the (α+δ) eutectoid structure at the position of 0.5 mm below the eutectoid reaction interface in Fig. 2. In that case, the peritectic phase β has transformed into the (α+δ) eutectoid structure. Careful observation of the microstructure reveals that all the α grains are surrounded by a thick layer of eutectoid phase δ. When a 1 T magnetic field is applied, the fraction of δ phase increased. However, the fraction of δ phase decreased as the magnetic field continues to increase. Figure 5 shows the EBSD map and <001> pole figures corresponding to the α and δ phases in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 1 μm/s without and with a 1 T magnetic field. It can be found that the magnetic field increased the thickness of δ phase around the primary α grain. Although the δ phase grows around different α grain, only one orientation for the δ phase has been observed. This result implies that the eutectoid phase δ retains the orientation of β phase, and the β phase can be indexed by the δ phase.

Fig. 4.

A larger version of the microstructure of primary phase α within the (α+δ) eutectoid structure at the position of 0.5 mm below the eutectoid temperature in Fig. 2: (a) 0 T; (b) 1 T; (c) 3 T; (d) 5 T. (Online version in color.)

Fig. 5.

EBSD map and <001> pole figures corresponding to the α and δ phases in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 1 μm/s without and with a 1 T magnetic field: (a) 0 T; (b) 1 T. (Online version in color.)

Figure 6 shows the solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 10 μm/s under various magnetic fields. It can be found that the magnetic field caused a transition of the primary α dendrites from arrayed to nonaligned growth gradually. With the increase of the magnetic field, the number of nonaligned grain increases and the size decreases. Figure 7 shows the EBSD map and corresponding <001> pole figures for the solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at different growth speeds without and with a 5 T magnetic field. It can be found that the application of the magnetic field caused the formation of nonaligned grains with various random orientations during directional solidification.

Fig. 6.

Solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 10 μm/s under various magnetic fields: (a) 0 T; (b) 1 T; (c) 3 T; (d) 5 T. (Online version in color.)

Fig. 7.

EBSD map and corresponding <001> pole figures for the solidification structure near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at different growth speeds without and with a 5 T magnetic field: (a) 20 μm/s, 0 T; (b) 20 μm/s, 5 T; (c) 50 μm/s, 0 T; (d) 50 μm/s, 5 T. (Online version in color.)

In addition, the EDS technology was used to study the effect of the magnetic field on the solute content. Figure 8 shows the EDS analysis for the distribution of Sn content near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 1 μm/s under various magnetic fields. The black dotted line shows the position of the solid-liquid interface. It can be found that the application of the magnetic field caused the increase of Sn solute content ahead of the solid-liquid interface. With the increase of the magnetic field, the solute content enhances.

Fig. 8.

EDS analysis for the distribution of Sn content near the solid-liquid interface in directionally solidified Cu-20 wt.% Sn alloy at a growth speed of 1 μm/s under various magnetic fields: (a) 0 T; (b) 1 T; (c) 3 T; (d) 5 T. (Online version in color.)

4. Discussion

The application of a magnetic field can induce two competing effects on fluid flows during directional solidification. The MHD damping effect can damp the convection and the TEM forces in the liquid can drive the convection. The body forces in the liquid under a magnetic field can be expressed as follows:   

$$F=j\times B=\sigma (u\times B)\times B-\sigma SG\times B$$(7)

The first term on the right hand shows the damping forces by the MHD damping effect. The second term shows the driving forces by the TEM forces.

In this work, the planar interface growth of the β phase was obtained at the sample scale at low growth speeds during directional solidification. In case of flat interface and axial temperature gradient there would be no thermoelectric current at all. Therefore, the MHD damping effect will play a leading role in the fluid flows at the sample scale. The TEM flows, caused by the interaction between the MHD damping effect and the TEM forces in the liquid, will play a leading role in the fluid flows at the dendrite scale.

4.1. Precipitation of the Peritectic Phase under the Magnetic Field

The above results reveal that the application of the magnetic field caused the precipitation of the acicular martensitic structure of peritectic phase. Influence increased along with the magnetic field intensity. This result should be attributed to the effect of the MHD damping effect at the sample scale on the distribution of solute in the bulk melt. Generally, for vertical Bridgman crystal growth of Cu–Sn peritectic alloys with the melt above the crystal, the Sn solute is accumulating in the liquid ahead of the growth front of solid during directional solidification, as shown in Fig. 9(a). This is due to the solute flows balance and the lower content of the solute in solidifying phase. It is well known that radial temperature gradient can exist near the growth interface during directional solidification. Because the liquid density decreases as the temperature increases, the liquid density for the melt at the crucible wall is lower than the melt in the central region. A symmetric natural convection will be induced in the bulk melt due to the density gradient, as shown in Fig. 9(b). The natural convection can drive solute to move into the bulk melt along the directional of the convection, as shown in Fig. 9(c). Therefore, the natural convection increases the rate of solute transport and decreases the enrichment of solute ahead of the growth front of solid. When a static magnetic field is applied on the electrically conductive fluid, electric current is formed in the fluid. The interaction between the magnetic field and the electric current can produce a Lorentz force, i.e. MHD damping effect, which can damp the fluid flows. The produce of MHD damping effect can decrease the natural convection and increase the solute enrichment, as shown in Fig. 9(d). With the enrichment of solute, the composition at the growing interface is expected to increase. When the solute content ahead of the growth front of solid reached a certain level, the peritectic phase formed and further decomposed into an acicular martensitic structure by quenching operation. Therefore, the MHD damping effect damped solute convection at the sample scale should be responsible for the precipitation of the acicular martensitic structure of peritectic phase. Because the MHD damping effect enhances as the magnetic field, the length of precipitation zone increases.

Fig. 9.

Schematic illustration of the enrichment of Sn solute at the sample scale during directional solidification under a magnetic field: (a) solute diffusion; (b) natural convection (V_n); (c) the movement of Sn solute caused by the natural convection; (d) the enrichment of Sn solute under the magnetic field. (Online version in color.)

4.2. Eutectoid Transformation of the Peritectic Phase under the Magnetic Field

During solidification for Cu–Sn peritectic system, a solid-state transformation of the peritectic phase β have been confirmed that the β phase changed into an (α+δ) eutectoid structure at the temperature below the eutectoid temperature. The EBSD reconstructed microstructure of the eutectoid structure shown in Fig. 5 shows that various colors of the α grains present within a single grain of the eutectoid phase δ. This implies that the growth of the eutectoid phase in the β phase via a purely diffusive regime. When the eutectoid reaction is occurred, the δ phase nucleates and grows from the α/β interface into the β phase, which depleting the latter in solute. Therefore, the growth of the δ phase mainly depends on the diffusion coefficient in the β phase. Oikawa et al.²⁴⁾ reported that the diffusion coefficient D_S in the solid for Cu–Sn alloys can be expressed as follows:   

$$D_S\left(T\right)=2.0\times {10}^{13.3N_{Sn}}exp\left(-156\mathrm{\hspace{0.17em} }000/RT\right)$$(8)

where N_Sn is the atomic fraction of Sn solute in the solid. It can be found that, with the increase of N_Sn, the diffusion coefficient increases. This indicates that the modification of the δ phase under the magnetic field should be attributed to the effect of the TEM flows on the content of solute in the melt β phase between the dendrites.

In order to determine the velocity and distribution of the TEM flows between the primary dendrites, 3D numerical simulation is performed. Note that the velocity of the TEM flows is the result of the balance between the MHD damping effect and the TEM forces in the liquid. Table 1 shows the physical parameters used during the numerical simulation process. Figure 10(a) shows the 3D geometry model used for the simulation. Here, the cylinders are regarded as primary dendrites of α phase, and the spacing of these cylinders correspond to primary arm spacing. Figure 10(b) shows the computed thermoelectric current (j, in A/m²) at a temperature gradient of 100 K/cm. The arrows and colors respectively represented direction and density of the thermoelectric current. It can be found that the thermoelectric current forms loops around the dendrites. Figure 10(c) shows the computed TEM flows (in mm/s) under a 1 T magnetic field. Here, the arrows and colors respectively implied direction and velocity of the TEM flows. It can be found that the annular TEM flows form around each dendrite and the maximum value of its velocity exists near the dendrite tip. This is because the maximum angle between the thermoelectric current and the magnetic field appears at the tip of the dendrite.

Table 1. Physical parameters used during the numerical simulation process.

Symbol	Unit	Solid	Liquid
Thermoelectric coefficient, S	V/K	5.23×10−6	7.6×10−6
Electrical conductivity, σ	(Ω·m)−1	9×106	4×106
Dynamic viscosity, μ	Pa·s	–	1.25×10−3
Temperature gradient, G	[K/cm]	100

Fig. 10.

Numerical simulation of the TEM flows in the liquid between the dendrites in directionally solidified Cu–Sn peritectic alloys under a static axial magnetic field: (a) the geometry model; (b) the thermoelectric current (j, in 10⁶ A/m²) at a temperature gradient of 100 K/cm; (c) the TEM flows (in mm/s) under a 1 T magnetic field. (Online version in color.)

The eutectoid transformation of the peritectic phase without and with the magnetic field is compared through a schematic diagram as shown in Fig. 11. At the temperature lower than the eutectoid reaction temperature, the δ phase nucleates at the α/β interface and grows in the β phase. The formation of the δ phase depends on the content of solute in the β phase. In the case of no magnetic field, as shown in Fig. 11(a), the distribution of the δ phase appears mainly around the primary dendrites. This is because to the rejection of the solute Sn at the solidifying interface. With the application of the magnetic field, the annular TEM flows are produced as shown in Fig. 11(b). As we can see from the above results that the application of the magnetic field increased the solute concentration ahead of the growth front of the solid at the sample scale. Consequently, the TEM flows in the liquid promote the solute transport and yield uniform distribution of the solute in interdendritic melt, resulting in higher fraction of the δ phase between the dendrites as shown in Fig. 11(c). The maximum value of the velocity of the TEM flows as a function of the magnetic field is shown in Fig. 11(e). It can be found that the TEM flows increase first and then decrease, the maximal value is obtained at a 0.5 T magnetic field. The change trend of the TEM flows is a good agreement with the modification of the δ phase. Therefore, the effect of the magnetic field on the eutectoid transformation of the peritectic phase should be attributed to the TEM flows caused uniform distribution of the solute between the dendrites.

Fig. 11.

Schematic diagram for the distribution of eutectoid phase δ without and with the magnetic field: (a) the distribution of δ phase under the natural convection; (b) the TEM flows in the liquid; (c) the distribution of δ phase under the TEM flows; (d) the cross sectional view of the computed TEM flows; (e) the maximum value of the velocity of the TEM flows as a function of the magnetic field. (Online version in color.)

4.3. Transition of the Primary Dendrites from Arrayed to Nonaligned Growth under the Magnetic Field

The above results also indicate that the application of the magnetic field caused the destruction of primary dendrites, and induced a transition from arrayed to nonaligned growth. This phenomenon is very similar to the columnar-to-equiaxed transition during directional solidification. The transition occurs because the magnetic field can enhance the nucleation and growth of the equiaxed (or nonaligned) dendrites. According to Hunt’s²⁵⁾ model, equiaxed (or nonaligned) dendrites growth will occur when   

$$G<M{(N_0)}^{1/3}\mathrm{\Delta }{T}_C\left[1-\left(\frac{\mathrm{\Delta }{T}_N}{\mathrm{\Delta }{T}_C}\right)\right]$$(9)

where M is a constant, N₀ is the total number of heterogeneous particles available per unit volume, ΔT_N is the heterogeneous nucleation undercooling, ΔT_c is the local undercooling. It is not difficult to understand that the transition can be attributed to the effect of the magnetic field on the parameters in Eq. (9). Li et al.²⁶⁾ reported that, if the magnetic field is less than 10 T, the influence of the magnetic field on the thermodynamics parameters can be neglected. Moreover, the number of grains increases and the size decreases with the increase in the magnetic field (see Figs. 6 and 7). Therefore, the magnetic field increased the number of heterogeneous particles in the liquid should be responsible for the transition of the primary dendrites.

Due to the thermoelectric effect, the TEM forces can be produced on the solid during directional solidification under a magnetic field. The TEM forces break dendrites and increase the number of fractured grains. These fractured grains become new heterogeneous particles and induce the nonaligned growth of the primary dendrites. 3D numerical simulation of the TEM forces on the solid during directional solidification under a static axial magnetic field is performed as shown in Fig. 12. The arrows and colors respectively expressed direction and intensity of the TEM forces. According to the different directions of the thermoelectric current, the application of the magnetic field caused the formation of the TEM forces in the opposite direction at the top and bottom of the dendrites within the liquid. As a result, a torque is produced on the dendrite as shown in Fig. 12(a). When the TEM forces intensity reaches a certain value, the torque enhances and breaks dendrites. With the increase of the magnetic field, the maximum value of the intensity of the TEM forces increase as shown in Fig. 12(b). When a 6 T magnetic field is applied, the TEM forces about 10⁷ N/m³. These forces are high enough to break the dendrites. Consequently, the transition of the primary dendrites from arrayed to nonaligned growth under the magnetic field should be attributed to the TEM forces broken dendrites, which increased the number of heterogeneous substrate particles in the liquid.

Fig. 12.

Numerical simulation of the TEM forces on the solid in directionally solidified Cu–Sn peritectic alloys under a static axial magnetic field: (a) the TEM forces (in 10⁷ N/m³) under a 6 T magnetic field; (b) the maximum value of the intensity of the TEM forces as a function of the magnetic field. (Online version in color.)

5. Conclusions

Directional solidification of Cu-20 wt.% Sn peritectic alloy was performed under a static axial magnetic field up to 5 T. The experimental results show that the application of the magnetic field modified the morphology of primary and peritectic phases. The magnetic field caused the precipitation of the acicular martensitic structure of peritectic phase below the solid-liquid interface. Along with the increase of the magnetic field, the length of precipitation zone increased. This result should be attributed to the magnetic field damped the fluid flows and induced the solute enrichment ahead of the growth front of the solid by MHD damping effect at the sample scale. Eutectoid decomposition of the peritectic phase was observed at the magnetic fields from 0 to 5 T. The imposition of the magnetic field increased first and then decreased the formation of the eutectoid phase. The TEM flows driven solute transport and increased the content of solute in interdendritic melt should be responsible for the modification of the eutectoid transformation. The application of the magnetic field also caused the transition of primary dendrites from arrayed to nonaligned growth. This was thought to be due to the TEM forces broken dendrites, which increased the number of heterogeneous substrate particles in the liquid.

Acknowledgments

The authors would like to thank the financial supports from National foundation of Science (Nos. 51690164, 51571056), “Shuguang Program” from Shanghai Municipal Education Commission, the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, Science and Technology Commission of Shanghai Municipality (No. 11JC1413600), Shanghai Science and Technology Committee Grant (13DZ1108200, 13521101102) and United Innovation Program of Shanghai Commercial Aircraft Engine (AR910, AR911).

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