Effect of a transverse magnetic field on structure in directional solidified Sn–Pb alloys

Effect of a transverse magnetic?eld on solidi?cation structure in

directionally solidi?ed Sn–Pb hypoeutectic alloys

Dafan Du a,Zhenyuan Lu a,Annie Gagnoud b,Yves Fautrelle b,Zhongming Ren a,

Xionggang Lu a,Rene Moreau b,Xi Li a,b,n

a Department of Material Science and Engineering,Shanghai University,Shanghai200072,PR China

b SIMAP-EPM-Madylam/G-INP/CNRS,PHELMA,BP75,38402St Martin d’Heres Cedex,France

a r t i c l e i n f o

Article history:

Received19April2014

Accepted11June2014

Communicated by M.Rettenmayr

Available online26June2014

Keywords:

A1.Directional solidi?cation

A1.Transverse magnetic?eld

A2.Dendrite spacing

B1.Segregation

B1.Sn–Pb alloys

a b s t r a c t

Effect of a transverse magnetic?eld on the macrosegregation and the growth of the Sn dendrite in the

directionally solidi?ed Sn–Pb alloys was investigated experimentally.The results indicated that the

magnetic?eld modi?ed the shape of the liquid/solid interface and the dendrite morphology signi?-

cantly.Indeed,the application of the magnetic?eld caused the formation of the sloping interface and the

re?nement of the dendrite.It is also found that the magnetic?eld decreased the mushy zone length.

These effects were enhanced with the increase of the magnetic?eld intensity and the decrease of the

growth speed.Further,the Seebeck thermoelectric force(E S)at the liquid/solid interface in the Sn-20wt

%Pb alloy was measured in-situ and the results indicated that the value of the Seebeck thermoelectric

force was about1m V.The modi?cation of the solidi?cation structure during directional solidi?cation

under the magnetic?eld may be attributed to the interdendritic thermoelectric magnetic convection

(TEMC).

&2014Published by Elsevier B.V.

1.Introduction

Solidi?cation processing is one of the important routes to

produce materials as it is not only widely used for shaping materials

to desired products but also for controlling the macro-and micro-

structures,which are intimately related to the?nal properties of

alloys.Convection effects often play a crucial role in most crystal

growth studies at low velocities[1–3].As the magnetic?eld is

capable of damping the melt convection,the effect of the magnetic

?eld on solidi?cation structure has been investigated for several

decades[4–6].However,Boettinger et al.[5]found that no in?uence

on the microstructure was detected during the directional solidi?-

cation of the Pb-57wt%Sn alloy under a transverse or an axial

magnetic?eld of0.1T.Tewari et al.[3]studied the effect of a

stronger transverse magnetic?eld of0.45T on cellular array in the

directionally solidi?ed hypoeutectic Pb-17.7wt%Sn alloy and the

results showed that the cellular array was severely distorted at a

lower growth speed(R r1μm/s).Alboussiere[7]and Laskar[8]

systematically studied the effect of the magnetic?eld on solidifying

Bi-60wt%Sn and Cu-45wt%Ag alloys,and suggested that convec-

tion could arise during directional solidi?cation in the presence

of the magnetic?eld.They proposed that the convection was

produced by the interaction between the magnetic?eld and

thermoelectric(TE)effects.Subsequently,Lehmann et al.[6]gave

quantitative experiments of the so-called thermoelectric magnetic

convection(TEMC)effect.In our previous works,the in?uence of a

static axial magnetic?eld on liquid/solid interface shape and

cellular morphology has been investigated[9],and the experimen-

tal results showed that a weak magnetic?eld(B r0.5T)caused the

formation of the ring-like structure.Present work aims to investi-

gate the in?uence of a transverse magnetic?eld on the macro-

segregation and the Sn-dendrite growth in the directionally solidi?ed

Sn-20wt%Pb alloy.It is found that the sloping interface is formed

during directional solidi?cation under a transverse magnetic?eld.

Moreover,the application of the magnetic?eld caused the

decrease of the dendrite spacing and the mushy zone length at

the same time.This effect was enhanced with the increase of the

magnetic?eld intensity.We attributed the above results to the

thermoelectric magnetic convection(TEMC)in the mushy zone

during directional solidi?cation under the magnetic?eld.Present

work may deepen the understanding of the effect of the magnetic

?eld and the convection on the solidi?cation structures during

directional solidi?cation.

2.Experiment

The samples of the Sn-20wt%Pb and Sn-5wt%Pb alloys used

in this study were prepared with high-purity Sn(99.99%)and

Contents lists available at ScienceDirect

journal homepage:https://www.360docs.net/doc/634086438.html,/locate/jcrysgro

Journal of Crystal Growth

https://www.360docs.net/doc/634086438.html,/10.1016/j.jcrysgro.2014.06.031

0022-0248/&2014Published by Elsevier

B.V.

n Corresponding author.Tel.:+86330476825242;fax:+86330476825211.

E-mail address:lx_net@https://www.360docs.net/doc/634086438.html,(X.Li).

Journal of Crystal Growth402(2014)319–324

500μm 500μm 500μm

B

B

500μm

500μm

500μm

B B

Fig.1.Microstructures near the liquid/solid interface in the directionally solidi ?ed Sn-20wt%Pb alloys at a growth speed of 1μm/s under transverse magnetic ?elds with various intensities:(a,d)0T,(b,e)0.1T,and (c,f)0.6T.

500μm

500μm

500μm

500μm

500μm 500μm

B

B B Fig.2.Microstructures near the liquid/solid interface in the directionally solidi ?ed Sn-5wt%Pb alloys at various growth speeds with and without a 0.3T transverse magnetic ?eld:(a)and (d)2μm/s;(b)and (e)10μm/s;(c)and (f)20μm/s.

D.Du et al./Journal of Crystal Growth 402(2014)319–324

320

Pb (99.99%)in an induction furnace.The alloys were placed in a high-purity graphite crucible and heated to 6001C,magnetically stirred for half an hour and poured into a graphite mold to cast samples with 3mm in diameter and 200mm in length.The cast sample was enveloped in a high-purity corundum tube with an inner diameter of 3mm and a length of 200mm for the directional

solidi ?cation experiment.The samples were directionally solidi-?ed in a Bridgman apparatus at a speci ?ed growth speed.The experimental apparatus consists of a static electromagnet,a Bridgman –Stockbarge-type furnace and a growth velocity and temperature controller.The electromagnet can produce a trans-verse static magnetic ?eld with an adjustable intensity up to 1T.A water-cooled cylinder containing liquid Ga –In –Sn metal (LMC)was used to cool the specimen.The furnace chamber is controlled by NiSi –NiCr thermocouples with the precision of 71K.The apparatus is designed such that the specimen moves downward while the furnace remains stationary.In order to observe the morphology of the solid/liquid interface during solidi ?cation process,quenching experiments are carried out by quickly with-drawing the specimen into the LMC cylinder to cool the specimen immediately to room temperature.The samples obtained from the experiments were examined in etched condition by the optical microscope.The distribution of the Sn contents in the mushy zone was measured by using a ?eld-emission scanning electron micro-scope (SEM;SU-70,HITACHI)equipped with an energy dispersive X-ray spectrometer (EDS;Genesis APEX2,AMETEK).

3.Results

Fig.1shows the structures near the liquid/solid interface in the directionally solidi ?ed Sn-20wt%Pb hypoeutectic alloy at a growth speed of 1μm/s under various transverse magnetic ?elds.It can be observed that in the case of no magnetic ?eld,the dendrite morphology is typically a columnar dendrite with a signi ?cant macroscopic curvature due to the radial concentration variation caused by thermosolutal convection.However,when the magnetic ?eld was applied,the dendrite morphology and the interface shape were modi ?ed dramatically.Indeed,one can notice that the Sn-dendrite is re ?ned and the interface becomes sloping.It is also found that the mushy zone length decreases under the magnetic ?eld.Fig.2shows the structures near the liquid/solid interface in the directionally solidi ?ed Sn-5wt%Pb hypoeutectic alloy at various growth speeds with and without a 0.3T transverse magnetic ?eld.An application of the magnetic ?eld caused the formation of the sloping liquid/solid interface and the decrease of the dendrite spacing.Fig.3shows the mushy zone length and the primary dendrite spacing as a function of the magnetic ?eld.It can be learned that the length of the mushy zone (L )and the primary dendrite spacing (λ)decrease as the magnetic ?eld increases.At a

40

6080100

120140

1400

1600180020002200

24002600B

(T)

L (μm )

B (T)

λ (μm )

Fig.3.Effect of the magnetic ?eld on the mushy zone length (L )and the primary dendrite spacing (λ)in the Sn-20wt%Pb alloys.(a)The mushy zone length (L)vs the magnetic ?eld intensity (B )and (b)the dendrite spacing (λ)vs the magnetic ?eld intensity (B ).

2000400060008000

1000012000

14000

Distance (μm)

C o n t

Fig.4.(a)EDS analysis for the distributions of the Sn contents at 300μm above the eutectic isothermal of the samples directionally solidi ?ed at a growth speed of 1μm/s under various magnetic ?elds and (b)schematic sketch for the measurement position.

D.Du et al./Journal of Crystal Growth 402(2014)319–324321

lower growth speed of 1μm/s,the dendrite spacing decreases by 46%with an increase in the ?eld from 0to 0.6T,and the value is 42%at a higher growth speed of 10μm/s.

Furthermore,the effect of the magnetic ?eld on the distribution of the Sn contents in the mushy zone was investigated.Fig.4(a)shows the distribution of the Sn contents in the mushy zone at the position of 300μm above the eutectic isothermal and the measurement position is shown in Fig.4(b).The comparison of the distribution of the Sn contents under various magnetic ?elds shows that the macrosegregation formed under a transverse magnetic ?eld and the segregation region increases with the increase of magnetic ?eld intensity.The above results indicate that a transverse magnetic ?eld has affected the distribution of the Pb solute at the crucible scale.

Fig.5(a)shows the microstructures during decreasing the magnetic ?eld from 0.5T to 0T after the steady-state growth for 60mm with the magnetic ?eld.Fig.5(b)shows the transverse microstructures at various positions corresponding to Fig.5(a).It is evident that the Sn-dendrite clusters on the left side of crucible under the magnetic ?eld,and then the clustering dendrites extend to the center of the crucible gradually during decreasing the magnetic ?eld process.Fig.5(c)shows the microstructure evolu-tion in increasing the magnetic ?eld.It can be seen that along with the re ?nement of the dendrite,the dendrite clusters toward the left side of crucible during increasing the magnetic ?eld.The above result further proves that the application of a transverse magnetic ?eld during directional solidi ?cation has signi ?cantly affected the solidi ?cation structure.

4.Discussions

The above results may be attributed to the formation of the interdenritic thermoelectric magnetic convection (TEMC)in the

mushy zone during directional solidi ?cation under a static mag-netic ?eld.It is well known that,in any material,a temperature gradient ?T produces a Seebeck electromotive force S ?T ,where S is the thermoelectric power of the material [10].Fig.6(a)illustrates the principal of Seebeck effect where temperature differences are converted to electricity.It is composed of two electrically conducting materials:one n-type and the other p-type.They are joined at the top by a metal (black bar)to make a junction.When the junction is instead heated,both types of carriers conduct heat to the cold base and a voltage difference is generated at the two base electrodes.If two doped semiconduct-ing materials joined together,the thermoelectric current will ?ow from the n-type material to the p-type at the heater junction.As the thermoelectric power (S )of the liquid phase is large than the solid phase (S L 4S S )[11],a simple analogy was gained:the liquid phase in the mushy zone can be considered as p-type and the solid phase will be n-type.Thus,the current as shown in Fig.6(b)will form.The Seebeck electromotive force (E S )between the solid and melt during directional solidi ?cation can be directly expressed by the equation:E S ?ηsl G T

e1T

where n sl is the effective liquid/solid thermoelectric power differ-ence and G T is the temperature gradient.In order to con ?rm the existence of the liquid/solid thermoelectric power difference during directional solidi ?cation of the Sn –Pb alloys,we have measured in-situ the Seebeck thermoelectric force of the Sn-20wt%Pb alloy.The basic principle of the interfacial thermo-electric measurement using the Seebeck technique was schemati-cally presented in Fig.7(a).The details of the principle had been discussed in Refs.[12,13].Fig.7(b)shows the Seebeck response obtained for the Sn-20wt%Pb alloy at a growth speed of 5m m/s.One can learn that a plateau is obtained on the Seebeck curve

to

500μm

500μm

Fig.5.Structure evolution in the directionally solidi ?ed Sn-20wt%Pb alloy at a growth speed of 2μm/s during decreasing and increasing the magnetic ?eld.(a)Longitudinal microstructures in decreasing the magnetic ?eld from 0.5T to 0T;(b)transverse microstructures corresponding to (a);and (c)longitudinal microstructures in increasing the magnetic ?eld from 0T to 0.5T.

D.Du et al./Journal of Crystal Growth 402(2014)319–324

322

indicate establishment of steady state,and then the signal drops to a new steady state when the furnace translation is shut off.The magnitude of signal drop,E S ,corresponds directly to the effective liquid/solid thermoelectric power difference (ηsl ).This indicates that there indeed exists a liquid/solid thermoelectric power difference during directional solidi ?cation of the Sn-20wt%Pb alloy.Therefore,it is reasonable to attribute the modi ?cation of the solidi ?cation structure during directional solidi ?cation in the magnetic ?eld to the thermoelectric magnetic effects.

Generally,for vertical Bridgman crystal growth of the Sn –Pb hypoeutectic alloys with the melt above the crystal,the heavier species Pb migrates down to the protruding liquid/solid interface due to the gravitational force.Since the solidi ?cation temperature decreases as the local concentration of the heavier species Pb increases,the solidi ?cation temperature for a Pb-rich melt at the ampoule wall is lower than that for the Sn-rich melt at the centerline,leading to a crystal –melt interface which is far more protruding than the local isothermal surfaces,as shown in Fig.6(c).However,when a transverse magnetic ?eld is applied during directional solidi ?cation,the unidirectional TEMC and the corre-sponding recirculation loops will be induced,as shown in Fig.6(d).They will cause the heavier species Pb migrates along the direction of the TEMC and lead to the formation of the sloping interface.

The effect of the convection on the dendrite/cell spacing has ever been studied.Lehmann et al.[14]proposed relating the primary arm spacing to ?ow velocity U which is parallel to the

primary arm as follows:

λ?λ0

???????????????????

?1teU =R T

p e2T

where λ0is the primary spacing without convection,U velocity

and R growth speed.This expression shows that convection reduces the primary arm spacing.Similarly,as the application of the magnetic ?eld during directional solidi ?cation induces the TEMC,the magnetic ?eld will decrease the cell/dendrite spacing.The mushy zone length,d ,is de ?ned as the distance between the tip and the root of a dendrite https://www.360docs.net/doc/634086438.html,ing the constitutional supercooling criterion for binary alloy systems in the absence of convection,d is given by d %m eC E àC 0T=G

e3T

where C E is eutectic composition,m the liquidus slope,C 0the composition of the alloy and G is the temperature gradient.It is not dif ?cult to understand that the interdendritic TEMC enhances the rate of heat-transfer and increases the temperature gradient (G ).Therefore,the decrease in the mushy zone length under a magnetic ?eld may be attributed to the enhancement of the heat-transfer rate caused by the interdendritic TEMC.

In our previous studies [9],it has been found that the value of the TEMC increases to a maximum when the magnetic ?eld reaches a critical value and then decreases as the magnetic ?eld still increases.This critical magnetic ?eld is determined by the

T+T

P

G

N

ΔΔFig.6.Schematic sketch of the TEMC and its effect on the solidi ?cation structure during directional solidi ?cation of the Sn-20wt%Pb alloy under a transverse magnetic ?eld.(a)Seebeck effects;(b)TE current and TEMC near the liquid/solid interface;(c)natural convection in the case of no ?eld and its effect on the distribution of the solute and the solid –liquid interface shape (symbols ‘t’and ‘à’indicate excess and de ?ciency of Pb solute);and (d)solute segregation and the formation of the slopping interface caused by the TEMC.

D.Du et al./Journal of Crystal Growth 402(2014)319–324323

Hartmann number (Ha )Ha ?eσ=ρνT1=2BR

e4T

where νand R ,respectively,denote the kinematic viscosity and typical length scale.The value of Ha corresponding to the critical magnetic ?eld is about 10[15].Here,the critical magnetic ?eld for the interdendritic TEMC during directional solidi ?cation of the Sn –Pb alloys was evaluated.The physical properties used in the

evaluations are presented in Table 1.Evaluation results reveal that the critical magnetic ?eld is about 1.5T for the Sn –Pb alloys.This means that value of the interdendritic TEMC increases with the increase of the magnetic ?eld intensity when the applied magnetic ?eld is less than 1.5T.The dendrite spacing and the mushy zone length decrease as the magnetic ?eld when the applied magnetic ?eld is less than 1.5T (see Figs.1and 3).5.Conclusions

The effect of a transverse magnetic ?eld on the solidi ?cation structure in the directionally solidi ?ed Sn –Pb alloys was studied and the results obtained are summarized as follows:

1.The magnetic ?eld modi ?ed the shape of the liquid/solid interfaces and dendrite morphology and caused the formation of the sloping liquid/solid interfaces.

2.The magnetic ?eld decreased the mushy zone length and the dendrite spacing.The above effect was enhanced with the increase of the magnetic ?eld when the applied magnetic ?eld is less than 0.6T.

3.The Seebeck thermoelectric force (E S )at the liquid/solid inter-face of the Sn-20wt%Pb alloy was measured in-situ and the results indicated that the value of the Seebeck thermoelectric force is about 1m V.

4.The above results may be attributed to the interdendritic thermoelectric magnetic convection (TEMC)in the mushy zone.

Acknowledgments

This work is supported partly by the European Space Agency through the Bl-inter 09_473220,National Natural Science Founda-tion of China (Nos.51271109and 51171106),and the Program for Professor of Special Appointment (Eastern Scholar)at Shanghai Institutions of Higher Learning.References

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.

0.6

0.81.01.21.41.6

1.8

2.0

Time (Min)

S e e b e c k S i g n a l (μV )

Fig.7.(a)An illustration of the principle of interfacial thermoelectric measurement using the Seebeck technique and (b)Seebeck response obtained for the Sn-20wt%Pb alloy directionally solidi ?ed at a growth speed of 5μm/s.

Table 1

Physical properties of the Sn –Pb alloys used in the evaluation [14].Properties

Magnitude

Electrical conductivity of solid Sn (σS ,Ωà1m à1)

6.3?106Electrical conductivity of liquid (σL ,

Ωà1m à1)

7?106

Thermoelectric power of liquid (S L ,νK à1)(553K)à0.109?10à6Thermoelectric power of solid Sn (S S ,νK à1)(456K)

à0.219?10à6

Temperature gradient (G ,K m à1)78?102Kinematic viscosity (ν,m s à1) 1.34?10à7Density (ρ,kg m à3)

7.7?103

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