Microsegregation Formation in Al–Cu Alloy under Action of Steady Magnetic Field

Abstract

The effect of a steady magnetic field (SMF) on microsegregation in the Al-4.5mass%Cu alloy during equiaxed solidification was investigated experimentally. It was found that the amount of microsegregation increased with increasing the SMF intensity at the same cooling rate. The variation of the microsegregation level with the SMF intensity at different cooling rates showed the consistent tendency. The effect of the change in various factors such as diffusivity in the solid phase, dendrite coarsening and undercooling on the microsegregation behavior was analyzed. The reduction of diffusivity in the solid phase in the SMF increased the microsegregation level. The increase in average nucleation undercooling of primary Al phase in the SMF, which was examined by the differential thermal analysis (DTA), led to decrease the amount of microsegregation. The enhancement of coarsening kinetics in the SMF increased the microsegregation level. Under the combined action of various factors, it was found that the increase in microsegregation in the range of the cooling rates under investigation was mainly attributed to the increase of the secondary dendrite arm spacing (SDAS) and the decrease in solid diffusion coefficient induced by the SMF.

1. Introduction

Microsegregation in as-cast alloys caused by non-equilibrium solidification is the inhomogeneity of solute concentration between the dendrite core and the interdendritic region, which results in poor performance such as low impact toughness and bad corrosion resistance. The microsegregation formation has been intensively investigated theoretically and experimentally and its mechanism in normal solidification conditions has been fully understood.^1,2,3) Various techniques like diffusion annealing,⁴⁾ rapid solidification⁵⁾ and the solidification processing under external fields⁶⁾ have been proposed to reduce or eliminate microsegregation during alloy solidification. Among those methods, the steady magnetic field (SMF) is frequently used to control macro/micro segregation with the aid of certain magnetic effects. Utech and Chedzey almost simultaneously found the SMF could eliminate the solute band during semi-conductor crystal growth.^7,8) Youdelis et al. observed that the effective partition coefficient in the Al–Cu alloy increased in the magnetic field at low growth rates and low concentrations and they thought the phenomena was ascribed to the diffusion inhibition in the magnetic field to a great extent.⁹⁾ Recently, Li et al. found that the solid solubility increased with increasing the SMF intensity during directional solidification of the alloys and speculated that the reduction of microsegregation was attributed to the thermoelectric magnetic force and the thermoelectric magnetic convection.⁶⁾ Song et al. observed that the magnetic field enlarged the carbon solubility limit of ferrite in the Fe-0.027mass%C alloy and they believed that the introduction of SMF increased the driving force of the phase transformation from austenite to ferrite.¹⁰⁾ Those studies demonstrated the SMF modified microsegregation during alloy solidification. Unfortunately, the previous studies hardly took into account the effect of the change in factors influencing microsegregation in the SMF, thus it was difficult to clarify the nature of the change in microsegregation. In fact, the SMF has been found to affect diffusivity,¹¹⁾ undercooling,¹²⁾ melt flow,¹³⁾ etc. Therefore, it is necessary for exactly predicting microsegregation formation in the SMF to consider the combined action of the change in various factors.

The objectives of the present work are twofold. The first one is to experimentally examine the degree of microsegregation in the Al-4.5mass%Cu alloy solidified with and without a SMF. The second one is to predict microsegregation formation in the SMF based on the numerical model developed by Voller.¹⁴⁾

2. Experimental Procedure

The Al-4.5mass%Cu alloy was prepared by melting high-purity metals Al (99.99%) and Cu (99.99%) in a vacuum induction furnace. The ingot was annealed for 80 h at 530°C in order to ensure the homogeneity of concentration of the ingot. Composition measurements and microstructure observation were carried out in different positions (upper, middle and lower) of the annealed ingot, it was found that the non-equilibrium second phase was basically dissolved in the Al matrix and the actual compositions in different positions were 4.45±0.11 mass%. The annealed ingot was cut into two kinds of cylindrical samples with different dimensions. The first one was 4 mm in diameter and 4 mm in length, which was used to detect the change in undercooling by differential thermal analysis (DTA). The second one was 6 mm in diameter and 8 mm in length, which was used for the microstructure observation and the composition measurement. In DTA runs, the sample was placed in a corundum crucible and heated to 750°C at the rate of 10°C·min⁻¹, held for 30 min and then cooled to room temperature in high pure Ar atmosphere. Only one sample for all runs was used in order to eliminate the effect of the impurities on undercooling. DTA runs were repeated five times in the same conditions. From DTA curves, the degrees of nucleation undercooling for primary Al phase in different conditions were obtained. Detailed DTA apparatus in the SMF was depicted elsewhere.¹⁵⁾ Similar to the DTA experiments, the second kind of samples were solidified in graphite crucibles at different cooling rates in various SMF intensities. The sketch of the experimental apparatus for solidification in the SMF is shown in Fig. 1. The sample was placed in the central region with a uniform magnetic field intensity and a homogeneous temperature. The SMF was generated by a superconducting magnet and its intensity could be adjusted from 0T to 8T. The temperature was monitored by a K-type thermocouple with an accuracy of ±1°C.

Fig. 1.

Schematic representation of the experimental apparatus: (1) temperature recorder; (2) temperature controller; (3) thermocouple; (4) SiC heating tube; (5) sample; (6) superconducting magnet.

The microstructures of the solidified samples after grinding and polishing were observed using a scanning electron microscope (SEM). The amount of the non-equilibrium eutectic and the secondary dendrite arm spacing (SDAS) were obtained by the software, Image J. The SDASs more than 20 from different positions in each specimen were measured, and their average values were taken as the SDAS.

3. Microsegregation Model

The one-dimensional (1-D) microsegregation model developed by Voller et al.¹⁴⁾ is utilized to predict the microsegregation behavior in the SMF. In this model, the following assumptions are included: (a) mass diffusion in the liquid is complete, i.e. the solute concentration in the liquid phase is uniform at any point in time; (b) local equilibrium is maintained at the solid-liquid interface; (c) the liquidus and solidus (in mass fraction) are straight; (d) the temperature between the dendritic arms is uniform at any point in time owing to the relatively rapid rate of heat diffusion; (e) 1-D plate-like dendritic morphology is used to describe the microstructure. Owing to the symmetry and simplicity of the plate-like dendritic morphology, the curvature and end effects can be neglected. It has been evidently demonstrated that with only few exceptions e.g. sudden changes of the cooling rate or strong forced convection, this simple geometry is adequately applicable to solidification processes of the majority of alloy systems.¹⁶⁾ Thus, the effect of the difference dimension on the numerical results can be ignored in this work. The main part in the model is the solute balance in the half dendrite arm spacing, which can be given as   

$${\int }_0^{x_s}{C}_{s}dx+\left(x_0-x_s\right)C_l=x_0{C}_0$$(1)

where x_s is the length of the solid phase, x₀ is the original length of the half-arm spacing domain, C_s, C_l and C₀ denote the concentrations in the solid phase, the liquid phase and the initial alloy, respectively. For the sake of simplicity, calculation is run with dimensionless space and time variables   

$$\eta =x/X_{final},\mathrm{\hspace{0.17em} }\tau =t/t_{final}$$(2)

where $X_{final}=0.5M{t}_{final}^{1/3}$ and $t_{final}=\frac{T_L-T_{eu}}{v}$ are SDAS and solidification time at the final solidification point, respectively, M is coarsening coefficient, T_L is liquidus temperature, T_eu is eutectic temperature, v is cooling rate. In the dimensionless form of the differentiation with respect to τ, Eq. (1) can be transformed into:   

$$\begin{array}{l}{\int }_0^{{\eta }_s}\frac{\partial C_s}{\partial \tau }d\eta +\left(k-1\right)C_l\frac{d{\eta }_s}{d\tau }+\left({\eta }_0-{\eta }_s\right)\frac{d{C}_l}{d\tau }+\\ \left(C_l-C_0\right)\frac{d{\eta }_0}{d\tau }=0\end{array}$$(3)

The back diffusion in solid is governed by   

$$\frac{\partial C_s}{\partial \tau }=\alpha \frac{{\partial }^2{C}_s}{\partial {\eta }^2}$$(4)

where $\alpha =\frac{D_s{t}_{final}}{X_{final}^2}$ is a Fourier number and D_s is the solid diffusion coefficient, Eq. (4) can be calculated by a deforming finite difference method.

The secondary dendrite coarsening process can be described as   

$${\eta }_0={\tau }^n$$(5)

where n is a coarsening exponent and it is equal to 1/3.

The set of differential Eqs. (3), (4), (5) is main governing equations for the microsegregation model. They can be solved by using a time marching numerical solution with the initial conditions η_s=0, C_l=C₀, and $\partial C_s/\partial \eta {|}_{\eta =0}=0$. More details regarding the model are given in Reference.¹⁴⁾

In consideration of the SMF effects on some factors influencing microsegregation, the change in solid diffusivity and the dendrite coarsening has been incorporated into the Voller’s microsegregation model.

4. Results and Discussion

As is known, the non-equilibrium solidified structures of the Al-4.5mass%Cu alloy consist of primary α-Al phase and interdendritic Al–Al₂Cu eutectic. The amount of the non-equilibrium eutectic reflects the severity of microsegregation. The extent of microsegregation in two extreme cases can be predicted using the lever rule and Scheil model, respectively, whereas the quantity generally lies somewhere in between during real solidification, which depends on solidification conditions. In this work, in addition to the cooling rate, the SMF was also applied to solidification process to observe its effect on microsegregation. Figure 2 shows the microstructures of the Al-4.5mass%Cu alloy solidified at the cooling rate of 1°C·min⁻¹ in different SMFs. In all cases, the solidified structures consist of primary α-Al phase (dark part) and non-equilibrium Al₂Cu phase (bright part). The non-equilibrium eutectic which consists of α-Al phase and Al₂Cu phase is lamellar structure, as shown in Fig. 2(e).

Fig. 2.

BSE images of microstructures of the Al-4.5mass%Cu alloy solidified in different magnetic fields at cooling rate of 1°C·min⁻¹, (a) 0T, (b) 2T, (c) 4T, (d) 5T.

In order to further quantify the extent of microsegregation in different conditions, the amount of the non-equilibrium eutectic was extracted from microstructures using quantitative image analysis. Figure 3 shows the amount of the non-equilibrium eutectic with and without the SMFs at different cooling rates. It is seen that the amount of the non-equilibrium eutectic overall increases with the SMF intensity at the same cooling rate. This means that the microsegregaion is aggravated in the SMF. It also should be noted that in the absence of the SMFs Fig. 3 also demonstrates that the relationship between the microsegregation level and the cooling rate obeys general law, i.e. the higher the cooling rate is, the larger the microsegregation level is in the range of the cooling rates under investigation, which was testified by previous studies.^3,5)

Fig. 3.

The amount of the non-equilibrium eutectic in different SMF intensities at different cooling rates. (Online version in color.)

It is well known that microsegregation is affected by various factors like back diffusion,⁹⁾ undercooling,¹⁷⁾ coarsening kinetics¹⁸⁾ and solid/liquid phase equilibrium.¹⁹⁾ Therefore, the change in microsegregation may be attributed to the variation of one or more above factors in the SMF. In the following sections, the effect of the SMF on those factors influencing microsegregation is discussed in three aspects separately: (1) only changing the solid diffusivity, (2) only changing the coarsening kinetics, (3) the undercooling effect on microsegregation behavior. Further, the resulting microsegregation level in the SMF is calculated using the microsegregation model developed by Voller et al.¹⁴⁾

Firstly, the solid-state back diffusion is one of important factors influencing the microsegregation, which is beneficial to reducing the microsegregation level. In the case of negligible solid diffusion, the amount of microsegregation predicted by the Scheil model is the maximum. Brody et al. firstly took into account contribution of the back diffusion to microsegregation and proposed an analytic model of microsegregation.²⁰⁾ Then Clyne et al. further improved it.²⁾ Thereafter, almost all microsegregation models incorporated the back diffusion.^21,22) It is easily understood that the change in diffusivity in the solid phase modifies the extent of microsegregation as well. Some studies showed that the SMF inhibited diffusivity in alloys.^11,23) For example, Youdelis et al. found that the diffusivity in the Al–Cu alloy was reduced by approximately 25% in the SMF of 3T. Therefore, the amount of the non-equilibrium eutectic of the Al-4.5mass%Cu alloy with and without a 3T SMF can be compared, the following values are used in the calculation without a SMF, k=0.17, C_eut=33.2 mass%, D_s=1.2×10⁻¹² m²s⁻¹.²⁴⁾ In the SMF of 3T, D_s decreased by 25%¹¹⁾ and the other parameters are kept the same values. The results are shown in Fig. 4. It is seen that the decrease in solid diffusivity in the SMF results in a larger amount of the non-equilibrium eutectic compared to those without a SMF.

Fig. 4.

The amounts of the non-equilibrium eutectic with and without a 3T SMF at different cooling rates. (Online version in color.)

Secondly, the dendrite coarsening also exerts an important effect on microsegregation formation. On one hand, The smaller the SDAS is, the shorter the back diffusion path is and the more significant the effect of the back diffusion on microsegregation is.²⁵⁾ On the other hand, coarsening process can dilute the concentration in the liquid phase and thus reduce the amount of second phase.²⁶⁾ From solidified microstructures (Fig. 2), the average SDAS can be obtained, as shown in Fig. 5(a). The dependence of the SDAS on the solidification time still obeys the cubic law. From the slopes, a higher SMF intensity significantly leads to a faster coarsening rate. In addition, the SDAS decreases with increasing cooling rate regardless of the SMF, the effect of the SMF on the SDAS is not obvious at the relatively high cooling rate, while it increases with the SMF intensity at low cooling rates, i.e., the dendrite coarsening is enhanced by the SMF. In the coarsening model developed by Kattamis and Flemings, the relationship of the SDAS and the local solidification time is given by:²⁷⁾   

$$\lambda =M{t}^{1/3}$$(6)

in which M is the coarsening coefficient, λ is the SDAS and $t=\frac{T_L-T_{eu}}{v}$ is the local solidification time.

Fig. 5.

The SDAS is plotted against the cubic root of the local solidification time (a) and the variation of the coarsening coefficient with the SMF intensity (b). (Online version in color.)

By linear fitting, the coarsening coefficients can be obtained in different SMF intensities (Fig. 5(b)). It is found that the coarsening coefficient increases with the SMF intensity and the value under 0T is in good accordance with Kirkwood’s work.²⁸⁾ Concerning the influence of dendrite coarsening on microsegregation, the ripening stage is expected to result in reduction of microsegregation, while the coalescence stage should have little effect.²⁷⁾ However, the enhancement of dendrite coarsening which enlarges the final SDAS leads to increase the back diffusion paths and thus the extent of microsegregation. The effect of dendrite coarsening on microsegregation seems to be smaller compared to the effect of back diffusion.²⁷⁾ Taking into account the change in the coarsening coefficient, it is found that the amount of the non-equilibrium eutectic increases with increasing coarsening coefficient, as shown in Fig. 6.

Fig. 6.

The amount of the non-equilibrium eutectic is plotted against the cooling rate in different SMF intensities. (Online version in color.)

Finally, the degree of undercooling is another important factor influencing microsegregation. It has been shown that the nucleation undercoolings of metal and alloy melts were modified in the SMF.^29,30,31) In order to observe the change in undercooling, the nucleation temperatures of the Al-4.5mass%Cu alloy melt with and without the SMFs were measured using DTA. Figure 7 displays the variation of the nucleation temperatures with the different SMF intensities. It is obvious that the average nucleation temperature decreases with increasing the SMF intensity, i.e., the average degree of undercooling increases with the SMF intensity. Although the nucleation undercooling is not the growth undercooling, it is approximately equal to the growth undercooling at the initial stage of solidification. Wang et al. investigated the effect of the nucleation undercooling on microsegregation and found that the solute concentration in the initial solid phase gradually increased as the nucleation undercooling increased.³²⁾ This indicated the increase in the nucleation undercooling led to reducing the microsegregation level. Additionally, a larger growth undercooling also reduces microsegregation at low and intermediate cooling rates.¹⁷⁾ Unfortunately, the effect of the SMF on growth undercooling is still unknown. Further experimental measurement for growth undercooling is in progress. In this work, the effect of change in growth undercooling in the SMF on microsegregation is not considered.

Fig. 7.

Nucleation temperatures of the Al-4.5mass%Cu alloy melt measured by DTA is plotted against the SMF intensity. (Online version in color.)

It should be pointed out that the effect of the SMF on the equilibrium solidus and liquidus of the Al–Cu alloy is negligibly small.³³⁾ Therefore, the solidus and liquidus without a SMF is used for the calculation of microsegregation.

From preceding analysis, the factors influencing microsegregation are changed in the SMF to different extents. It follows that the microsegregation formation in the SMF is affected by the variety of the magnetic effects. The combined action of the change in factors in the SMF affects the resulting microsegregation behavior. Considering the limit of Voller’s model and above-mentioned analysis, the following extra assumptions are made for the modified model: a) only the change in back diffusion and coarsening kinetics are incorporated into the microegregation model, b) owing to lack of diffusion coefficients in various SMF intensities, the diffusion coefficient in 3T given by Youdelis et al. is assumed to be applicable to other SMF intensities in this work, c) the effect of undercooling is not under consideration. Based on the above assumptions, the amount of microsegregation in the SMF can be calculated using relevant parameters in Table 1. Figure 8 compares the experimental and calculated microsegregation levels in different conditions.

Table 1. Parameters of the Al-4.5mass%Cu alloy for the numerical calculation in different conditions.

Parameters	Cooling rate (°C·min−1)	B=0T	B=2T	B=4T	B=5T
Ds(m2·s−1)		1.2×10−12	8.96×10−13	8.96×10−13	8.96×10−13
M (μm·s−1/3)		9.47	10.31	11.83	15.73
$\alpha =\frac{D_s{t}_{final}}{X_{final}^2}$	1	0.121	0.077	0.058	0.033
	2.5	0.089	0.056	0.043	0.024
	5	0.071	0.045	0.034	0.019
	FC*	0.044	0.028	0.021	0.012

*  FC denotes furnace cooling which is approximately equal to 20°C·min⁻¹ at liquidus temperature (In the case of furnace cooling, the cooling rate gradually decreased from a given temperature to room temperature. The temperature data showed that the cooling rate decreased from 20°C·min⁻¹ at liquidus temperature to 18.2°C·min⁻¹ at solidus temperature. Since this model cannot calculate microsegregation in the case of varying cooling rate, the cooling rate at liquidus temperature is used for simplicity).

Fig. 8.

Comparison of the calculated and experimental results of the amount of the non-equilibrium eutectic in different magnetic field conditions. (Online version in color.)

From Fig. 8, it is found that the extent of microsegregation increases when applying the SMFs. The experimental and calculated results are in good agreement. Therefore, it could be concluded that the increase of the SDAS and the reduction of diffusivity in the solid phase in the SMF are mainly responsible for the increase of microsegregation since both of them increase microsegregation. However, the absolute amount of microsegregation between experimental and calculated results shows some discrepancy, which possibly is caused by the following reasons: (1) the variation of the solid diffusion coefficient with SMF intensity remains unknown, whereas we assumed that the decrement of diffusion coefficient remained the same in several SMF intensities for calculation; (2) the undercooling effect was not taken into account in this model though the SMF exerted a significant effect on the nucleation undercooling; (3) the liquid phase was assumed to be homogenously mixed in Voller’s model. However, the liquid phase probably is not homogeneous due to magnetic suppression to convection and the solute diffusion in the liquid phase is also not under consideration; (4) phase diagram calculation was not coupled in the calculation, instead, liquidus and solidus were assumed to be straight; (5) there was a deviation in experimental measurement for the non-equilibrium eutectic. Thus, a more precise model is necessary in future work.

5. Conclusion

The effect of the SMF on microsegregation in the Al-4.5mass%Cu alloy during equiaxed solidification was studied experimentally. The amount of microsegregation was found to increase with increasing the SMF intensity. The effect of the change in various factors such as diffusivity in the solid phase, coarsening kinetics and undercooling influencing microsegregation in the SMF was analyzed. Considering contribution of the change in back diffusion and coarsening kinetics, a numerical model was used to predict the change in microsegregation in the SMF. The calculated results overall coincided with the experimental observations. It is necessary for fully predicting microsegregation in the SMF to develop a more exact numerical model.

Acknowledgement

This work was supported by the Natural Science Foundation of China (Nos. 51401116, 51690162, U1560202) and the United innovation program of shanghai commercial aircraft engine (AR910, AR911).

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