Enhanced Dendrite Coarsening and Microsegregation in Al­Cu Alloy under a SteadyMagnetic Field

Shengya He+1, Tongjun Zhan+1, Chuanjun Li+2, Weidong Xuan, Jiang Wang and Zhongming Ren+2

State Key Laboratory of Advanced Special Steel & Shanghai Key Laboratory of Advanced Ferrometallurgy & School of Materials Scienceand Engineering, Shanghai University, 200444, Shanghai, P. R. China

The final mechanical properties of alloys are significantly influenced by the secondary dendrite arm spacing (SDAS). The application of asteady magnetic field (SMF) during solidification is a novel method to control the SDAS, however, the nature of the change in SDAS under anSMF is still an open question. In this work, dendrite coarsening in the Al­4.5mass%Cu alloy in an SMF and its effect on microsegregation wereinvestigated experimentally by the quenching technique. The coarsening experiments showed that the SDAS increased in an SMF, which wasmainly attributed to the thermoelectric magnetic convection (TEMC) while the change in solid/liquid interfacial tension in the SMF played anadverse role. Further, the variation of the microsegregation level in the SMF was examined by composition measurements. It was shown that thesegregation ratio increased in the SMF, which could be ascribed to the reduction of diffusivity in the solid phase and the enlargement of SDAS inthe SMF. Using a modified analytical model developed by Voller, the microsegregation levels with and without an SMF were predicted, whichwas in agreement with the experimental results. [doi:10.2320/matertrans.M2019057]

(Received February 27, 2019; Accepted June 28, 2019; Published August 25, 2019)

Keywords: dendrite coarsening, microsegregation, convection, magnetic field, solidification

1. Introduction

Dendrite coarsening significantly affects the final secon-dary dendritic arm spacing (SDAS) and thus has a crucialinfluence on microsegregation, which directly decides themicrostructure and the final mechanical properties.1) It isgenerally believed that coarsening can be realized by twomain mechanisms: 1) the dissolution of small dendrite arms,which benefits the growth of bigger adjacent arms, i.e.ripening; 2) the coalescence of side-branches due topreferential deposition of solid on certain regions along thesolid-liquid interface, i.e. coalescence.2) In early studies,3­5)

the influence of coarsening on microsegregation wasgenerally believed to be negligible. However, someliteratures also showed that this effect should be taken intoaccount. For example, Kirkwood et al. found that thecoarsening of dendrite always had a pronounced influenceon the extent of microsegregation in Al­Cu alloys.6)

Mortensen pointed out that coarsening would lead to anoverestimation of the reduction in microsegregation if itwas assumed that ripening proceeded throughout solid-ification.7) Kraft and Chang draw a conclusion that thedendrite coarsening should be considered in some particularsituations.8) Voller found that the predicted microsegregationwas in good agreement with experiments in considerationof coarsening.9) These studies demonstrated that dendritecoarsening is one of the most significant factors influencingmicrosegregation.

Over the past decades, a steady magnetic field (SMF) hasbeen widely applied to materials processing owing to itscontactless interaction and various magnetic effects. There-into, it has been reported that the SMF had a pronouncedeffect on microsegregation during alloy solidification. Zhanget al. found that the extent of microsegregation of Ti andMo in superalloy DZ417G decreased by about 28% and 40%,

respectively, with a 6T magnetic field.10) Li et al. revealedthat the solid solubility of Cu in ¡-Al phase was promoted inan SMF during directional solidification of Al­Cu alloys.11)

Hou et al. indicated that the SMF refined cells/dendritesand reduced microsegregation of Ni­Mn­Ga alloy.12) In ourrecent work, it was found that the extent of microsegregationin the Al­4.5mass%Cu alloy increased in the SMF.13) Theseinvestigations have showed that the SMF leads to a changein microsegregation. However, up to now, few studies havefocused on the effect of the change in dendrite coarsening inthe SMF on microsegregation.

In fact, it has been found that the SMF can modify thedendrite morphology significantly. Moreau et al. observedthat dendrites were well-developed under an SMF of 0.55 T,they believed that the thermoelectric magnetic convection(TEMC) induced by the SMF caused melt flow within themushy zone and in turn enhanced coarsening of the dendriticstructure.14) Tewari found that the arrays of cellular dendriteswere deformed under a transverse SMF.15) Li et al. reportedthat TEMC could cause the liquid-solid interface uneven andbreak the cellular morphology during directional solid-ification.16) Zhong et al. observed that tertiary dendrites ofAl­4.5mass%Cu alloy changed into a pinwheel-like patternwhen its growth direction was parallel to the directions ofthe SMF and the temperature gradient.17) These investiga-tions imply that the SMF possibly modifies the coarsening ofdendrites. Nevertheless, there has been no study concerningcoarsening kinetic in an SMF up to now.

Therefore, the aims of this work are, on the one hand, toexperimentally investigate the change in coarsening kineticsin an SMF and its effect on microsegregation, on the otherhand, to predict the microsegregation formation in the SMFusing a modified numerical model proposed by Voller9) inconsideration of coarsening.

2. Experimental Procedure

The Al­4.5mass%Cu alloy used in present work was+1Graduate Student, Shanghai University+2Corresponding authors, E-mail: cjli21@shu.edu.cn, renzm2201@163.com

Materials Transactions, Vol. 60, No. 9 (2019) pp. 1921 to 1927©2019 The Japan Institute of Metals and Materials

prepared from high-purity Al (99.999%) and Cu (99.999%)in a vacuum induction furnace. The alloy melt was cast torods by vacuum suction casting, from which cylindricalsamples with the dimension of ¯6 © 8mm were obtained. Aseries of coarsening experiments were performed with andwithout an SMF. The superconducting magnet could generatean axial SMF up to 5T. The sample in a graphite crucible wasplaced in the central region of the magnet, i.e. approximatelyuniform magnetic field region. During the coarseningexperiments, the sample was firstly heated to 700°C at aconstant rate of 10°Cmin¹1, held for 20mins, and thencooled at a constant rate of 0.3°Cmin¹1. The temperatures ofthe sample and the furnace were monitored by two K-typethermocouples with an accuracy of «1°C. Afterwards, thesample was quenched into water at different temperatures.The experimental apparatus is shown in Fig. 1.

The quenched samples were sectioned both parallel andperpendicular to the magnetic field direction. After ground,polished and etched with a 2.5% HNO3 + 1.5% HCl + 1%HF + 95% H2O solution by volume, the microstructures ofquenched samples were observed by optical microscopy(OM) and scanning electron microscopy (SEM). More than20 SDASs at different positions in each sample weremeasured by the software, Image J and their average valuewas taken as the SDAS. The extent of microsegregationwas characterized by composition profiles across the dendritecore, which was performed by using an energy dispersespectroscopy (EDS) equipped in the SEM.

3. Model Description

In this work, the microsegregation level is calculated usingthe numerical model proposed by Voller,9) which incorporatesdendrite coarsening and solid back diffusion. In this model,main assumptions are made as follows: 1) the liquid phase is

completely mixing; 2) local interfacial equilibrium applies; 3)the liquidus and solidus lines are straight; 4) the temperaturein volume domain is constant due to fast heat diffusion; 5)dendrite morphology is simplified as 1-D plate-like becauseall complicated curvature and end effects are neglected.18)

Figure 2 schematically shows the solute distribution ina calculation volume. The characteristic length of thecalculation domain is half SDAS which increases assolidification proceeds. The solid concentration Cs increaseswith the movement of solid/liquid interface and liquidconcentration Cl keeps constant during time interval dt. Themass balance must be satisfied with advance of the solid-liquid interface.Z xs

0

Csdxþ ðx0 � xsÞCl ¼ x0C0 ð1Þ

where x0 is the original volume element length, xs is thelength of solidified solid phase. The coarsening kinetics canbe described as:19)

X ¼ 2x0 ¼ Mt1=3 ð2Þ

t ¼ TL � Teuv

ð3Þ

where X is the SDAS, M is the coarsening coefficient, t isthe local solidification time, and TL, Teu and v are liquidustemperature, eutectic temperature and cooling rate, respec-tively. Here, the dimensionless space and time variables areintroduced, which can be expressed as © = x/Xfinal and ¸ =t/tfinal, the subscript “final” indicates the final solidificationpoint.

Since the solute concentration in the solid and SDAS varywith time, eq. (1) can be transformed into a differential formwith respect to ¸:Z ©s

0

@Cs

@¸d©þ ðk� 1ÞCl

d©sd¸

þ ð©0 � ©sÞdCl

d¸

þ ðCl � C0Þd©0d¸

¼ 0 ð4Þ

where k is the equilibrium partition coefficient. The backdiffusion in the solid is governed by:

@Cs

@¸¼ ¡

@2Cs

@©2ð5Þ

where ¡ ¼ 4Dstfinal=X2final is a Fourier number, Ds is the solid

diffusion coefficient. Equation (5) can be calculated by adeforming finite difference method.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Fig. 1 Sketch of the experimental apparatus: (1) temperature recorder;(2) temperature controller; (3) thermocouple; (4) SiC heating tube; (5)sample; (6) superconducting magnet; (7) quenching pool; (8) circulatingwater system.

Fig. 2 The schematic diagram of one volume element during solidification.

S. He et al.1922

The set of eqs. (1)­(5) are main governing equations forthe microsegregation model. The finite difference solutioncan be obtained using a time marching numerical solutionwith the initial conditions: ©s = 0, Cl = C0, and @Cs/@©«©=0 =0. More details can be referred to Ref. 9).

4. Results and Discussion

In order to investigate the effect of the SMF on dendritecoarsening, a series of coarsening experiments have beenperformed. Figure 3 shows the longitudinal microstructuresof the Al­4.5mass%Cu alloy quenched at various temper-atures with and without an SMF, the transverse

microstructures are similar. It can be seen that the micro-structure consists of the primary ¡-Al phase (bright parts)and quenched residual liquid (dark parts). As the quenchingtemperature decreases, the dendrites gradually grow and theamount of the residual liquid phase decreases. The SDASincreases as the quenching temperature decreases. Thedendritic morphologies in both conditions show theconsistent variation with the quenching temperature. Also,it is apparent that the dendrites under a 5 T SMF are coarsercompared to that under 0 T. From the dendrite morphology,the average SDASs in given conditions can be obtained. Thelocal solidification time t can be calculated through eq. (3)with replacement of Teu by Tquench which is the quenchingtemperature. Figure 4 indicates that the variation of dendriticarm spacing with local solidification time follows theclassical cubic law (eq. (2)). The coarsening coefficientscan be calculated using eq. (2), listed in Table 1. Thecoarsening coefficient without an SMF is in accordance withKattamis’s work.20) The value of M is larger in 5 T. It followsthat the application of the SMF of 5T enhances the dendritecoarsening. Meanwhile, it should be noticed in Fig. 4 that theSDASs seem to be identical when the quenching temperatureis above 590°C. This is because that the dendritic growth isinterrupted at initial stage while the SMF has no enough timeto affect its coarsening process.

Based on the dissolution of small arms from their tips,Kirkwood proposed a simple model to quantitively describethe coarsening of secondary dendritic arm.21) In his model,coarsening coefficient is presented as:

M ¼ � 128·DLTmHmLð1� kÞ

lnðce=c0Þðce � c0Þ

� �1=3

ð6Þ

Fig. 3 Longitudinal microstructures of the Al­4.5mass%Cu alloyquenched at different temperatures with and without an SMF, to whichthe samples were cooled at the rate of 0.3°Cmin¹1, (a) 0 T, 580°C; (b) 0T,570°C; (c) 0 T, 560°C; (d) 0 T, 550°C; (e) 5T, 580°C; (f ) 5 T, 570°C;(g) 5 T, 560°C; (h) 5T, 550°C.

Fig. 4 SDAS is plotted against the cubic root of local solidification timewith and without an SMF in the condition of ¹0.3°Cmin¹1.

Table 1 Coarsening coefficient M in the Al­4.5mass%Cu alloy with andwithout an SMF.

Enhanced Dendrite Coarsening and Microsegregation in Al­Cu Alloy under a Steady Magnetic Field 1923

in which DL is the liquid diffusion coefficient, · is liquid-solid interface free energy per unit area, k is the equilibriumpartition coefficient, Tm is the melting point, H is heat offusion, mL is liquidus slope and ce is the eutecticconcentration. For a given alloy composition in the conditionof gravity environment without external applied physicalfields such as high pressure, strong electric/magnetic fieldsetc., the values of k, Tm, H, mL and ce is certain accordingto the equilibrium phase diagram at a constant pressure. Inaddition, it should be emphasized that the equilibriumliquidus and solidus are not influenced by the applicationof an SMF.22) Hence, M varies with parameters of · and DL,i.e., M = f (·,DL). Since the coarsening coefficient dependson multiple factors, the change in coarsening coefficient in anSMF probably stems from a change in one or more abovefactors, which will be discussed in the following.

Firstly, liquid-solid interface free energy per unit area isequivalent to surface tension. It has been found that surfacetension of several materials can be modified under the actionof an SMF.23,24) Based on the magnetic dipole model,25) theSMF can induce an additional surface tension £B ¥ AijB2/4¬®0, in which B is the magnetic field intensity, ¬ is thecurvature, ®0 is the magnetic permeability of vacuum, Aij isthe interaction factor at an interface. The value of Aij isassociated with the magnetic susceptibilities of materials » onboth sides of the interface with i indicating the melt and jindicating the contact material. If 0 < »i < »j, then Aij < 0.25)

For paramagnetic Al­4.5mass%Cu alloy, the magneticsusceptibilities of the solid ¡-Al and the melt are in arelationship of 0 < »melt < »¡-Al.26­28) Thus, it can be deduced£B < 0, which signifies that the SMF reduces the solid/liquid

surface tension. However, this is contradictory to theexperimental observation that the coarsening coefficient Mincreases under an SMF. Therefore, it is reasonably inferredthat the change in solid/liquid surface tension in an SMF isnot the dominant factor.

The change of diffusivity in the liquid phase also modifiesthe coarsening kinetics. In the SMF, the rates of masstransport probably are different from the case without anSMF owing to a combined effect of thermoelectric magneticconvection (TEMC)11,29­31) and magnetic suppression.32­35)

In the following, the effect of the SMF on melt flow and thuson mass transport will be estimated.

A 3D numerical simulation of TEMC and magneticsuppression during equiaxed solidification is carried outusing the commercial finite element software COMSOLMultiphysics. For simplicity, one dendritic tip is selected ascontrolled domain (see Fig. 5(a)­(b)). It is worth pointing outthat natural convection induced by gravity and heat exchangeis ignored. The electric current is constructed based on Ohm’slaw. The contributions of electric field, TE effect andmagnetic suppression are coupled as follows:

~| ¼ · ~Eþ ·~u� ~B� ·S ~G ð7Þwhere ~|, ·, ~E, S, ~B, ~u and ~G, respectively, denote the electriccurrent density, the electrical conductivity, the electrical field,the absolute thermoelectric coefficient of the conductingmedium, the magnetic field intensity, the velocity of the fluidflow and the temperature gradient. For equiaxed dendriticgrowth (k < 1), heat and mass are rejected into the melt, thetemperature gradient near a dendritic tip is generally high.36)

The value of mean temperature gradient near the dendritic

Fig. 5 3D numerical simulation of TEMC near the solid/liquid interface (a) schematic diagram of an equiaxed dendrite; (b) geometry ofsimulation domain with a radius of 25 µm; (c) distribution of TE current near the dendritic tip; (d) pattern of the TEMC (m s¹1) aroundthe dendritic tip in 5T.

S. He et al.1924

tip can be estimated via famous Lipton-Glicksman-Kurz(LGK) model,37) which is expressed as:

G ¼ V�H

2acpð8Þ

where V is the interface growth rate, ¦H is the latent heat, ais the thermal diffusivity and cp is the specific heat. Manystudies have cited this relation to deduce the temperaturegradient near the solid/liquid interface.38,39)

Assuming that the fluid is incompressible, the fluid flowcan be governed by the Navier-Stokes equation:

@ðµ~uÞ@t

þ µð~u � r~uÞ ¼ �rpþ ®r2~uþ ~|� ~B ð9Þ

together with the continuity equation:

~r � ~u ¼ 0 ð10Þwhere µ, p and ® are the density, the pressure and thekinematic viscosity, respectively. For the initial conditionsof the TEMC numerical simulation, the initial value of flowvelocity was set to be zero, all surfaces were set to be zeroelectric potential and the liquid was initially stationary. Forthe boundary conditions of the TEMC numerical simulation,slip boundary condition was applied on boundary I, whileboundaries II, III, and IV were to set to be no-slip boundarycondition (see Fig. 5(b)), adiabatic boundary conditions weregiven on the sidewall of the model. More details regardingthe equations and corresponding initial and boundaryconditions are described in previous publication.40) Thephysical parameters used for the simulation are list inTable 2.

Figure 5(c) depicts the distribution of TE currents near adendritic tip. It can be seen that the direction of TE currentgradually becomes parallel to z-axis, far from the dendritictip, which implies that the Lorentz force will be onlygenerated in the liquid around the dendritic tip when avertical SMF is applied. Figure 5(d) presents the pattern ofthe TEMC near the dendrite tip. The maximum magnitude

of flow velocity reaches 8 © 10¹5m s¹1. The TEMC willmotivate an intense stir, and thus accelerate the masstransportation in the melt. Garandet et al. supposed that theadditional convective contribution to mass transportationcould be simply added to the liquid diffusion term, which canbe written as:48)

Deff ¼ D 1þ 1

4H2 u2

D2

� �ð11Þ

where Deff is the apparent liquid diffusion coefficient, D is theactual liquid diffusion coefficient, H is characterizing length,u is flow velocity. Taking D = 5.59 © 10¹9m2 s¹1,49) H =10¹4m, u = 8 © 10¹5m s¹1 yields an apparent diffusioncoefficient of 8.45 © 10¹9m2 s¹1. The liquid diffusioncoefficient increases by 51.2% under the action of TEMC.Therefore, it is reasonable to deduce that TEMC can promotethe effective liquid diffusion near the dendritic tip. As aconsequence, the dendrite coarsening is accelerated in anSMF.

In order to testify the effect of change in coarseningkinetics on microsegregation, the extents of microsegregationwith and without an SMF are characterized and thencompared. The Cu composition measurements were carriedout across five dendrites per sample along the measured linewhich is 200 µm below the dendritic tip. The step lengthbetween measured points was 2 µm. Figure 6 shows theposition of composition measurement and the concentrationprofiles across the dendrite. It is clearly seen that regardlessof an SMF the Cu concentration increases from the dendriticcore to the interdendritic region, which reflects the character-istic of non-equilibrium solidification. In 5 T, the minimumsolubility of Cu atom in ¡-Al phase decreases significantly.The same tendency is found in other quenching conditionsas well. It follows that an SMF results in a highermicrosegregation.

It is known that the microsegreagtion is influenced byvarious factors such as undercooling, dendritic coarseningand solid back diffusion.50) The change in microsegregation

Table 2 Physical parameters of Al­4.5mass%Cu alloy used in the simulation.

Enhanced Dendrite Coarsening and Microsegregation in Al­Cu Alloy under a Steady Magnetic Field 1925

can be ascribed to the combined action of those factors.Therefore, it is necessary to consider the possible effect ofchange in each factor under an SMF. A larger undercoolingcan significantly suppress the formation of non-equilibriumsecondary phase and reduce microsegregation.6,51,52) In ourprevious work, the nucleation undercoolings in Al­Cu alloyswere found to increase with increasing SMF intensity.53,54)

However, the increase in undercooling induced by a 5 T SMFis not large enough to alter the microsegregation. Addition-ally, it has been demonstrated that the SMF could modifythe solid diffusivity.55­58) Therefore, the inhibition of solid-state diffusivity in an SMF must lead to an increase inmicrosegregation. Finally, change in SDAS during solid-ification will influence microsegregation. A larger SDAS willincrease the solid back diffusion path and thus the extent ofmicrosegregation.

To calculate microsegregation in the SMF, the changes inabove factors are incorporated into Voller’s model9) and someadditional assumptions have been made: a) the effect ofchange in undercooling is ignored; b) the solid-state diffusioncoefficient D0

s in 5 T is assumed to be equal to the value givenby Youdelis et al.55) since the dependence of the diffusioncoefficient on SMF intensity is still unknown. In order tocharacterize the microsegregation, the segregation ratio SR isemployed, which is defined as the ratio of the maximumsolute concentration Cmax

s in the ¡-Al phase to the minimumconcentration Cmin

s , i.e. SR ¼ Cmaxs =Cmin

s .8) In calculations,fraction solid fs is calculated at corresponding quenchingtemperature by the following relationship,47)

Tquench ¼ Tm þmLC0ð1� fsÞk�1 ð12Þwhere Tm is the melting temperature, mL is liquidus slopeand C0 is origin composition of alloy. Figure 7 compares

segregation ratios between calculations and experiments withand without 5 T. Obviously, the segregation ratio in the SMFis larger than that without an SMF, and the calculations arein well agreement with experiments, which possibly becausethe solid-state diffusion coefficient in 5 T approximates to thevalue measured by Youdelis et al. in 3 T.55) Indeed, furtherinvestigation on solid diffusion of Al­Cu under an SMF isneeded in the future. Considering the contributions fromvarious factors, it is inferred that the enhanced dendritecoarsening aggravates the microsegregation level togetherwith the inhibition of solid-state diffusivity in the SMF.

5. Conclusion

The dendrite coarsening and its effect on microsegregationin Al­4.5mass%Cu alloy in 5T were investigated. It wasfound that the SMF enhanced the dendrite coarsening, thiswas due to the enhanced mass transport induced by theTEMC near the dendritic tip, while the reduction of solid/liquid surface tension in an SMF played a minor negativerole. It was experimentally showed that the extent ofmicrosegregation increased in the SMF of 5T. Consideringthe combined contributions of various factors, it could beconcluded that the aggravation of microsegregation mainlyoriginated from the enhanced dendrite coarsening and theinhibition of solid-state diffusivity. A modified numericalmodel was used to predict microesegregation. The calcu-lations coincided with experimental results.

Acknowledgement

This work was supported by Shanghai Pujiang TalentsProgram (18PJ1403700), the Joint Funds of the NationalNatural Science Foundation of China (Nos. U1560202,51604171 and 51690162), the Shanghai Municipal Scienceand Technology Commission Grant (No. 17JC1400602),National Science and Technology Major Project “Aeroengineand Gas Turbine” (2017-VII-0008-0102) and the ChinaScholarship Council Funds (No. 201806890052).

Fig. 6 (a) Backscattered electron (BSE) image of Al­4.5mass%Cu alloysolidified at the cooling rate of 0.3°Cmin¹1 with an SMF quenching at550°C, and (b) the distribution of Cu composition along the directionperpendicular to the secondary dendritic arms in the sample quenched at550°C.

Fig. 7 Comparisons of segregation ratios between calculations andexperiments with and without 5T. The following parameters are usedfor calculations: Ds = 1.5 © 10¹13m2 s¹1,59) D0

s ¼ 1:125� 10�13

m2 s¹1,55) Tm = 933.6K, mL = ¹2.6K (mass%)¹1,47) k = 0.169) and C0 =

4.5mass%.

S. He et al.1926

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