Journal of Crystal Growth 322 (2011) 84–90
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Formation of the solidified microstructure in Mg–Sn binary alloy J.W. Fu, Y.S. Yang n Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 October 2010 Received in revised form 25 February 2011 Accepted 14 March 2011 Communicated by M. Rettenmayr Available online 21 March 2011
The solidified microstructures in Mg–3Sn and Mg–5Sn (wt%) alloys were investigated experimentally. For Mg–3Sn, secondary and ternary dendrite arms grow rapidly from a-Mg equiaxed dendrites in a certain direction. When Sn content is increased to 5%, developed secondary and ternary dendrite arms in the upstream direction in the center of the sample do not occur. Formation of this microstructure characteristic was discussed in terms of cooling rate, force caused by fluid flow, and dendrite growth behavior of Mg–Sn alloy. The model for growth restriction factor (GRF) has been further discussed by considering the growth behavior of a dendrite tip, which reveals the relationship between GRF and dendrite growth rate. The relationship between GRF and constitutional undercooling was discussed during dendrite growth. The deviation of growth direction from o 1 0 1¯ 0 4 crystal direction has been analyzed by fluid flow during solidification. & 2011 Elsevier B.V. All rights reserved.
Keywords: A1. Dendrites A2. Growth from melt B1. Mg–Sn alloy
1. Introduction More and more efforts have been devoted to develop magnesium alloys as structural materials to decrease the weight to strength ratio to improve the fuel efficiency and minimize environmental degradation due to their lowest density among the commercially available structural metals and the excellent specific strength [1–8]. In addition, magnesium alloys usually have good castability and machinability, making them quite suitable for applications as casting alloys [9]. Among all the magnesium alloys, Mg–Sn system is considered as a potential for precipitation strengthening of Mg alloys and for application at elevated temperatures since the main precipitate phase, Mg2Sn, has a high melting temperature of about 1043 K, a high temperature property superior to that of the AZ alloys is anticipated [10–12]. Mg–Sn system has a higher eutectic temperature, compared with the most widely used Mg–A1 and Mg–Zn systems. The solubility of Sn in a-Mg solid solution drops sharply from 14.85 wt% at the eutectic transformation temperature 561 1C to 0.45 wt% at 200 1C. This provides an important basis for improving the mechanical properties of Mg–Sn alloys through ageing [13]. Recently, a series of investigations on the microstructures and properties of Mg–Sn alloys has been conducted. The microstructures, tensile properties, and indentation creep resistance of the as-cast Mg–5Sn alloy were studied by Liu et al. [14,15]. It was suggested that Mg–5%Sn has a good creep resistance and they attributed this to the presence of thermally stable Mg2Sn particles
n
Corresponding author. Tel.: þ86 24 23971728; fax.: þ 86 24 23844528. E-mail address:
[email protected] (Y.S. Yang).
0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2011.03.026
in Mg–5%Sn alloy. Additions of Zn and Zn þNa to an age hardenable Mg–1.3 at%Sn alloy have been examined [16]. It was found that Zn additions resulted in a substantial increase (300%) in the hardening increment after aging at 200 1C but the time to peak hardness was relatively unaffected. Wei et al. [17,18] studied the microstructure and compressive creep behaviors of Mg–Sn and Mg–Sn–La alloys. They found that the compressive creep resistance of aging-treated Mg–5 wt%Sn alloy is much better than that of as-cast alloy due to the dispersive distribution of Mg2Sn phase in the aging-treated Mg–5 wt% Sn alloy and the creep resistance of La-containing Mg–Sn alloys is much better than that of as-cast Mg–5Sn alloy owing to the formation of fine feather-shaped, rodlike and massive secondary phases in Mg–Sn–La alloys. Kang et al. [19] reported that the creep resistance of Mg–Sn based alloys can be improved by the formation of Mg2Sn nano-particles and the morphology of Mg2Sn nano-particles was determined by cooling rate, occurrence in the form of rod-type Mg2Sn particles at high cooling rates, and polygonal particles at low cooling rates. From the above results, it is clear that at present the investigations on Mg–Sn alloys are mainly focused on the properties and few investigations referring to the solidified microstructure formation have been reported. More attention should be paid to the solidified microstructure because the properties of Mg–Sn alloys are fundamentally determined by their as-cast microstructures, which are basically depended on the alloy compositions and the solidification conditions. In this work, Mg–Sn melt was cast into a water-cooled copper mold with a wedge shaped slot to investigate the effect of cooling rates on the solidified microstructure. Novel solidified microstructures are observed in Mg–Sn alloys. A model for growth restriction factor has been developed, which confirms that the product of growth restriction factor and the
J.W. Fu, Y.S. Yang / Journal of Crystal Growth 322 (2011) 84–90
85
dendrite growth rate is a constant. The formation of the solidified microstructure in binary Mg–Sn alloys is discussed in terms of the nucleation and growth theories.
2. Experimental procedure In this study, Mg–3Sn and Mg–5Sn (wt%) alloys were used. The alloys were prepared with high-purity Mg (99.99%) and Sn (99.99%) in an induction furnace under a pure argon atmosphere. In the experiments, the alloys were heated to 720 1C in an induction furnace. After heating and stabilization at 720 1C for 30 min, the melt was cast into a symmetrical water-cooled copper mold to form a wedge shaped sample with the 1.5–10.0 mm thickness, 60 mm width, and 120 mm length. Fig. 1 schematically illustrates the casting procedure of the experiments. The microstructures in different thickness are representative of corresponding solidification conditions since the cooling rate continuously increases from the thickest to the thinnest part of the sample. Therefore, effect of cooling rate on the solidified microstructures of Mg–Sn alloys can be revealed using this experimental apparatus. The solidified samples were sectioned longitudinally and etched with 1.0% oxalic acid reagent after being mechanically ground and polished for microstructure observation. The solidification microstructures were analyzed by optical microscopy (OM). The phase identification and the crystallographic orientations were determined by a Rigaku D/max-2400PC X-ray diffractometer using Cu Ka working at a voltage of 56 kV and current of 182 mA.
Fig. 2. Microstructure of Mg–3Sn alloy composed of coarse a-Mg equiaxed dendrites with fine secondary and ternary arms in the center and fine columnar a-Mg dendrites in the surface layers of the sample.
3. Results 3.1. Microstructure morphology The solidification microstructure of Mg–3%Sn alloy with the thickness of 6.0 mm, where the cooling rate is lower compared with the thinner section of the sample, is shown in Fig. 2. It can be seen that the microstructure is composed of coarse a-Mg equiaxed dendrites in the center of the sample and fine columnar a-Mg dendrites in the surface layers of the sample. The growth of coarse a-Mg equiaxed dendrites is dissymmetrical and the size of the a-Mg dendrites, with developed and fine secondary and ternary arms in a certain direction, in the center of the sample varies greatly, as shown in Fig. 3. With the increase of cooling rate, the coarse a-Mg equiaxed dendrites with developed and fine secondary and ternary arms gradually disappear and the microstructure is composed of entire columnar coarse a-Mg dendrites when the thickness of the sample reaches 2.0 mm, as shown in Fig. 4. This means that higher cooling rate can avoid the formation
Fig. 1. Schematic illustration of the experimental process with a water-cooled copper mold.
Fig. 3. a-Mg equiaxed dendrites in the center of the Mg–3Sn alloy sample indicating rapid growth of fine secondary and ternary arms in a certain direction.
Fig. 4. Microstructure of Mg–3Sn alloy solidified at higher cooling rate without coarse a-Mg equiaxed dendrites in the center of the sample.
86
J.W. Fu, Y.S. Yang / Journal of Crystal Growth 322 (2011) 84–90
of the coarse a-Mg equiaxed dendrites with developed and fine secondary and ternary arms. When the Sn content is increased to 5%, the coarse a-Mg equiaxed dendrites with developed secondary and ternary arms disappear in the center of the sample with the thickness of 6.0 mm, as shown in Fig. 5. The microstructure consists of coarse columnar a-Mg dendrites with secondary arm in the center of the sample and fine a-Mg columnar dendrites in the surface layers of the sample. The secondary arm of a-Mg columnar dendrites is not developed and the ternary arms do not occur any more. Compared with the microstructure of Mg–3%Sn alloy, the microstructure of Mg–5%Sn alloy in the center of the sample is more uniform and this size characteristic is in agreement with the normal ingot microstructure. This result indicates that alloy composition has an important effect on the solidified microstructure characteristic of Mg–Sn binary alloys. Required microstructures can be obtained by adjusting alloy compositions and the solidification parameters.
Mg–5Sn alloy on the section parallel to the thickness direction of the sample. From XRD analyses, it is known that the microstructure of Mg–5Sn alloy is composed of a-Mg phase and Mg2Sn phase, though Mg2Sn phase is low in volume fraction. The crystal orientation can also be determined by XRD analysis. Based on the XRD result, it is apparent that crystallographic orientation is also changed under different solidification conditions for Mg–5Sn alloy. There are three strong peaks in the center of the sample and there are two strong peaks in the surface layers of the sample. The first, second, and the third strongest peaks correspond to (1 0 3), (1 1 0), and (1 0 1) crystal plans, respectively, in the center of the sample. The strongest peak is changed to (1 0 1) crystal plan, and the second strongest peak is changed to (1 0 3) crystal plan in the surface layers of the sample. The peak of (1 0 0) crystal plan is very weak in the sample compared with the strongest peaks.
3.2. Phase constitutions and growth direction of a-Mg
4. Discussion
In order to identify the phase constitutions in Mg–Sn alloys, XRD analyses were conducted. Fig. 6 shows the XRD result of
4.1. Effect of cooling rate Solidification microstructures depend not only on the alloy compositions but also on the processing parameters such as the cooling rate, or melt undercooling prior to solidification [20,21]. According to classical nucleation theory (CNT) [22], formation of a nucleus with a critical size from the undercooled melt depends on the competition between the driving force for the phase transformation from liquid to solid (the volume free energy) and the barrier resulting from the energy that is required for forming a new interface. The free energy barrier to form a spherical critical nucleus on a heterogeneous substrate can be expressed as 16p s3 DG ¼ ð1Þ f ðyÞ 3 DG2m
Fig. 5. Microstructure of Mg–5Sn alloy where secondary arms of a-Mg equiaxed dendrites become shorter compared with the microstructure of Mg–3Sn alloy and the developed ternary arms do not occur due to the increase of GRF.
Fig. 6. X-ray diffraction patterns in the center and in the surface layers of the sample for Mg–5Sn alloy.
where s is the interface energy of the new interface, DGm ¼ ðDHm =Tm ÞDT is the Gibbs free energy difference per unite volume between liquid and solid, DHm is the latent heat of fusion per unite volume, Tm is the melting temperature of the pure component, DT is the undercooling of the melt, and f(y) is a catalytic potency factor in the case of heterogeneous nucleation. From Eq. (1), it is apparent that nucleation in the undercooled melt becomes easy on increasing the melt undercooling DT, which increases linearly with the cooling rate [23]. For Mg–3Sn alloy in present experiments, the formation of coarse a-Mg dendrites in the center is mainly accounted for low cooling rate and finer columnar dendrites in the surface layers of the sample is related to high cooling rate and directional heat extraction. It is noted from Figs. 2 and 3 that the size of a-Mg in the center of the sample varies greatly, consisting of coarse a-Mg equiaxed dendrites and finer dendrite arms from a-Mg in Mg–3Sn alloy. The formation mechanism of this non-uniform microstructure should be examined based on both nucleation and growth theories. From nucleation theory, it is clear that the nucleation frequency in the center of the sample is very low because the undercooling in the section has not reached the critical values required for abundant nuclei of a-Mg owing to low cooling rate and the release of the latent heat from the growing grain. Thus, the number of nucleus with the size larger than the critical value is very small in the center of the sample, resulting in the formation of coarse a-Mg equiaxed dendrites. The occurrence of plenty of finer dendrite arms from a-Mg equiaxed dendrites in the center of the sample results from the rapid growth of the secondary and ternary arms from the coarse a-Mg equiaxed dendrites. Compared with nucleation, the undercooling required for growth of a nucleus is very small. Therefore, once the radius of
J.W. Fu, Y.S. Yang / Journal of Crystal Growth 322 (2011) 84–90
the embryo exceeds a critical size, it will grow rapidly in the undercooled melt, where the undercooling is less than the required nucleation undercooling. 4.2. Formation mechanism of the developed dendrite characteristic Different solute elements have variant effects on the growth behavior of the nucleated grains and the subsequent nucleation process [24–28]. This effect can be considered in terms of growth restriction factor (GRF). Addition of solute elements generates constitutional undercooling within a diffusion layer ahead of the advancing solid/liquid interface, which restricts grain growth since solute diffusion occurs slowly, thus limiting the growth rate of the alloys. In addition, further nucleation events occur in front of the interface (in the diffusion layer) because nuclei in the constitutionally undercooled zone are more likely to survive and be activated since constitutional undercooling is a major driving force for nucleation. Growth restriction factor for a binary alloy can be written as [24] GRF ¼ mL C0 ðk0 1Þ
ð2Þ
where mL is the slope of liquidus line (assumed to be straight line). The growth restriction factor was originally derived by Maxwell and Hellawell [29] by solving the diffusion equation of a spherical growth. The growth parameter was shown as S¼
2DTC mL C0 ðk0 1Þ þ DTC ðk0 1Þ
V¼
ADL ðDTC Þ2 GmL C0 ðk0 1Þ
dendrite can be expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ¼ l ¼ 2p
G
The value of GC can be obtained from the solute flux balance at the interface DL
@C ¼ VðCL CS Þ @x
where V is the growth rate, A is a constant, DL is the solute diffusion coefficient in the liquid, and G is the Gibbs-Thompson parameter. However, Eqs. (3) and (4) cannot reveal the direct relationship between the growth restriction factor and the growth rate due to the existence of constitutional undercooling term. We then tried to develop a model to determine the direct relationship between growth restriction factor and the growth rate by considering the growth of a dendrite tip. Taking account into surface tension at the solid/liquid interface, Millus and Sekerka [31] proposed the interface stability theory by solving the diffusion equations assuming a slight sinusoidal perturbation at the interface. The change rate of the perturbation amplitude can be written as V V e_ =e ¼ o ð5Þ ðGo2 GL þ mL GC Þ m L GC DL where e_ ¼ de=dt, e is the amplitude of perturbation, GC is the concentration gradient in the liquid at the solid/liquid interface, o ¼ 2p=l is the perturbation frequency, l is the perturbation wavelength, o ¼ V=2DL þ ½ðV=2DL Þ2 þ o2 0:5 is a function of o and DL, and GL is the temperature gradient in the liquid. Based on LMK marginally stable theory [32], the tip radius of a dendrite should be close to the shortest perturbation wavelength l. In order to obtain the critical stable wavelength l, the third term on the right-hand-side pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiof Eq. (5) is set to be equal to zero, giving l ¼ 2p G=ðmL GC GL Þ. Therefore, the tip radius of a
ð7Þ
where CL and CS are the liquid and solid concentration at the interface, respectively. From Eq. (7) we can obtain the expression of GC as GC ¼
V C ð1k0 Þ DL L
ð8Þ
For dendrite growth, CL can be given as CL ¼
C0 1IvðpÞð1k0 Þ
ð9Þ
where Iv(p) is Ivantsov’s solution and p ¼RV/2DL is solutal Pe´clet number. At dendrite growth region, temperature gradient in the liquid has little effect on the tip radius of a dendrite [33]. Furthermore, the terms Iv(p) can be ignored due to small tip radius during dendrite growth. Substituting Eqs. (8) and (9) into Eq. (7) with GL-0 and Iv(p)-0, the relationship between growth rate and tip radius can be obtained as
ð3Þ
ð4Þ
ð6Þ
mGC GL
VmL C0 ðk0 1Þ ¼ VQ ¼
where DTC is constitutional undercooling available to the alloy. Based on Eq. (3), Maxwell and Hellawell [29] inferred that the growth restriction factor (mLC0(k0 1)) is inversely proportional to the growth rate during dendrite growth by neglecting the DTC term in Eq. (3), thus limiting the grain size. Later, by assuming that constitutional undercooling is dominant, Hunt [30] also developed an equation of the form:
87
4p2 DL G R2
ð10Þ
Thus, the model for growth restriction factor has been established, as shown in Eq. (10). From Eq. (10) it is apparent that the growth restriction factor, Q, is inversely proportional to the growth rate during dendrite growth for a given binary alloy for a certain stable tip radius of the dendrite. Compared with Eqs. (3) and (4) developed by Maxwell and Hellawell [29] and Hnut [30], Eq. (10) clearly exhibits the relationship between the growth restriction factor and the dendrite growth rate without the occurrence of the constitutional undercooling term. This equation can give a better understanding why growth restriction factor can be used to determine the effect of solute element on the grain size. Therefore, the growth behavior of a dendrite can be characterized by the growth restriction factor for an alloy. From Eq. (10), assuming that the liquid diffusion coefficient and Gibbs-Thompson coefficient are constant, the product of Q and V is dependent on the tip radius of the dendrite. This is in good agreement with the theory of Langer [34]. Though there is no constitutional undercooling term in Eq. (10), it does not mean that GRF is independent of constitutional undercooling. The constitutional undercooling can be given as
DTC ¼ mL ðC0 CL Þ
ð11Þ
Substituting Eq. (9) into (11), we can obtain
DTC ¼ Q ½29,30
1 1=IvðpÞ1 þ k0
ð12Þ
For paraboloid dendrite growth, Iv(p) can be replaced with O, the solute supersaturation. Thus, constitutional undercooling can be given by the following:
DTC ¼ Q
1 1=O1 þk0
ð13Þ
Solute supersaturation, which represents the driving force for the diffusion of solute at the dendrite tip in an alloy, is in proportion to the growth rate of a dendrite at a given tip radius. According to Eq. (13), when the value of GRF is increased, the value of supersaturation will be decreased under a given constitutional undercooling, which leads to the decrease of the growth
88
J.W. Fu, Y.S. Yang / Journal of Crystal Growth 322 (2011) 84–90
rate. Thus, Eq. (13) reveals the relationship between growth restriction factor and constitutional undercooling. Growth restriction factor and growth rate is influenced by the constitutional undercooling during dendrite growth. Based on the binary phase diagram, some GRFs for Mg–Sn, Mg–Sr, Mg–Al, Mg–Zn alloys have been calculated [26], as listed in Table 1. It is noted from Table 1 that the GRF value for Sn element is the lowest compared with those for Sr, Al, Zn elements. This indicates that Sn element has the weakest growth restriction capability, resulting in rapid growth of secondary and ternary arms from coarse a-Mg equiaxed dendrites in the undercooled melt where the undercooling required for nucleation is not satisfied. Thus, the non-uniform microstructure, coarse a-Mg equiaxed dendrites and finer secondary and ternary dendrite arms, is formed. The formation process can be schematically illustrated in Fig. 7. At the initial stage, some primary arms of a-Mg equiaxed dendrites protrude into the undercooled melt and secondary and ternary dendrites have a tendency to rapid growth due to the constitutional undercooling ahead of the solid/liquid interface, as shown in Fig. 7(a). With the increase of the protruded length into the undercooled melt, the growth rate of secondary and ternary dendrites enhances owing to higher undercooling, as shown in Fig. 7(b). Finally, coarse a-Mg equiaxed dendrites with
Table 1 Slope of the liquidus line (mL), equilibrium partition coefficient (k0), and growth restriction parameter mL(k0 1) for some alloying elements in magnesium. Element
mL
k0
mL(k0 1)
Sn Sr Al Zn
2.41 3.53 6.87 6.04
0.39 0.006 0.37 0.12
1.47 3.51 4.32 5.31
finer secondary and ternary dendrite arms in a certain direction are formed, as shown in Fig. 7(c). From Eq. (2), it is known that the value of GRF increases with increasing alloy composition. The growth of secondary or ternary dendrite arm from a-Mg dendrites becomes difficult at higher GRF value. For the present experiments, the developed secondary and ternary dendrite arms of a-Mg equiaxed dendrites in the center of the sample disappear when the Sn content comes to 5%, as shown in Fig. 5.
4.3. Morphology and solidification direction of a-Mg Another characteristic of Fig. 3 is the asymmetric growth of
a-Mg equiaxed dendrites, with fine secondary and ternary arms growth in a certain direction. This should be interpreted in terms of fluid flow in the melt during solidification and the growth direction of the fine secondary and ternary arms should be antiparallel to the flow direction and is called upstream growth, as shown in Fig. 7. It is known that the difference in temperature or concentration can cause natural convection in the melt. In addition, some residual momentum, resulting from the pouring process, still exists in the melt during solidification. The growth of fine secondary and ternary arms in the upstream direction, caused by flow of melt, can be easily understood when the interaction between melt flow and dendrite growth behavior is taken into account. It is well known that the solute concentration at the solid/liquid interface is enriched and the growth proceeds when the enriched solutes are transferred to the liquid. The growth rate can be accelerated when the enriched solute at the solid/liquid interface is flushed to the liquid rapidly by the flow of melt. Furthermore, according to the constitutional undercooling theory rapid heat extraction, caused by flow of melt, can also accelerate the growth of the fine secondary and ternary arms.
Fig. 7. Schematic illustration of the formation of fine secondary and ternary arms from coarse a-Mg equiaxed dendrites in the upstream direction (a) the initial stage where secondary or ternary dendrite has a tendency to rapid growth, (b) occurrence of rapid growth of the secondary and ternary arms due to large constitutional undercooling ahead of the solid/liquid interface, (c) final a-Mg equiaxed dendrites with developed secondary and ternary dendrite arms in the upstream direction.
J.W. Fu, Y.S. Yang / Journal of Crystal Growth 322 (2011) 84–90
The growth of the fine secondary and ternary arms in the direction of upstream accelerates, which caused the occurrence of the developed secondary and ternary arms in the direction anti-parallel to the flow of the melt. Based on the solidified microstructures in the present experiments, it can be deduced that we can obtain refine microstructures of Mg–Sn alloy by eliminating the primary coarse dendrites and leaving the developed refiner secondary or ternary arms, by controlling the solidification parameters. For polycrystalline alloys, anisotropy, which is resulted from different atomic densities in different orientations, is an important characteristic. According to Wulf theorem [35], crystal will adjust its shape to make the total interface energy minimum when the interface equilibrium is achieved. Thus, during solidification solute atoms tend to deposit on the crystal plane with lowest atomic density and the growth rate of the crystal direction perpendicular to the lowest atomic density plane is the fastest. This crystal direction is called preferred growth direction in solidification. For magnesium, which is a typical closed-packed hexagonal structure, the preferred growth direction is o1 0 1¯ 04. However, it is found that the growth directions are affected by other factors during solidification. It has been shown that the [1 1 1] crystal direction tends to orient along the solidification direction for Al–Cu alloy under a high magnetic field during directional solidification [36]. The authors attributed this to the Lorentz forces caused by the interaction between thermoelectric (TE) current and the imposed magnetic field (B). For the present experimental results, as shown in Fig. 6, the growth directions are not the preferred growth direction in the microstructure and have been deflected to other directions. This deflection of growth direction should be caused by the twist due to the force caused by flow of the melt. The convection and residual momentum can cause flow of the melt and the evidence of flow of melt can be clearly shown in Fig. 3. In addition, the other evidence can be found from Fig. 8, where some primary dendrite arms have been broken from a-Mg equiaxed dendrites, which confirms that strong flow of melt should exist during solidification in the center of the sample. This strong flow can alter the growth direction of a-Mg equiaxed dendrites during growth, and the intensity of (1 0 0) crystal plan, which is perpendicular to the preferred growth direction o1 0 1¯ 04, is not the strongest peak in the XRD analysis any more, as shown in Fig. 6. The solidification direction in different sections of the sample is varying. The difference in the growth direction between the center and the surface layers can be interpreted in terms of the magnitude of the force caused by the flow in the melt. Based on the
89
microstructure of Fig. 8, where the primary arm can be broken, it can be inferred that the force caused by the flow is very strong. This result can be understood by considering the solidification process of Mg–Sn alloys. The melt adjacent to the wall of the copper mold solidifies rapidly due to high heat extraction, which results in the rapid decrease in the viscosity of the melt and the force caused by flow is decreased consequently. The flow caused by natural convection and the residual momentum is transferred to the center of the sample, resulting in the strong flow in the center.
5. Conclusions Effects of solidification parameters, including cooling rate and alloy composition, on the solidified microstructures of Mg–Sn alloys have been examined experimentally. The model for growth restriction factor has been further discussed by considering the growth behavior of a dendrite tip, which confirms that the product of the growth restriction factor and the dendrite growth rate is a constant for a given stable tip radius of the dendrite. The relationship between growth restriction factor and constitutional undercooling was revealed during dendrite growth. When the value of GRF is increased, the value of growth rate will be decreased under a given constitutional undercooling. The experimental results show that, for Mg–3Sn alloy, in the middle zone of the sample, secondary and ternary arms grow rapidly from coarse a-Mg dendrites due to low cooling rate and small growth restriction factor of Sn in Mg–Sn alloy. The asymmetry growth of a-Mg equiaxed dendrites in Mg–3Sn alloy is caused by the fluid flow in the melt during solidification and the growth direction of the fine secondary and ternary arms should be the upstream direction. When the Sn content is increased to 5%, rapid growth of secondary and ternary arms in the upstream direction in the center of the sample do not occur any more due to high GRF. The growth direction is transformed from o1 0 1¯ 0 4 crystal direction due to the force caused by fluid flow during solidification.
Acknowledgment This work was financially supported by the National Natural Science Foundation of China (no. 50974114). References
Fig. 8. Microstructure of Mg–3Sn alloy in the center of the sample with the break of primary arm from a-Mg equiaxed dendrites (indicated by arrows), confirming the existence of strong flow of melt during solidification.
[1] C. Zhang, D. Ma, K.S. Wu, H.B. Cao, G.P. Cao, S. Kou, Y.A. Chang, X.Y. Yan, Intermetallics 15 (2007) 1395. [2] S. Harosh, L. Miller, G. Levi, M. Bamberger, J. Mater. Sci. 42 (2007) 9983. [3] A. Kozlov, M. Ohno, R. Arroyave, Z.K. Liu, R. Schmid-Fetzer, Intermetallics 16 (2008) 299. [4] H. Cao, C. Zhang, J. Zhu, G. Cao, S. Kou, R. Schmid-Fetzer, Y.A. Chang, Acta Mater. 56 (2008) 5245. [5] H. Cao, C. Zhang, J. Zhu, G. Cao, S. Kou, R. Schmid-Fetzer, Y.A. Chang, Scripta Mater. 58 (2008) 397. [6] H.K. Lim, D.H. Kim, J.Y. Lee, W.T. Kim, D.H. Kim, Mater. Lett. 62 (2008) 2271. [7] D. Qiu, M.X. Zhang, J.A. Taylor, P.M. Kelly, Acta Mater. 57 (2009) 3052. [8] H.K. Lim, D.H. Kim, J.Y. Lee, W.T. Kim, D.H. Kim, J. Alloy Compd. 468 (2009) 308. [9] D.H. Kang, S.S. Park, N.J. Kim, Mater. Sci. Eng. A 413–414 (2005) 555. [10] T.T. Sasaki, K. Oh-ishi, T. Ohkubo, K. Hono, Scripta Mater. 55 (2006) 251. [11] M. Zhang, W.Z. Zhang, G.Z. Zhu, Scripta Mater. 59 (2008) 866. [12] T.T. Sasaki, J.D. Ju, K. Hono, K.S. Shin, Scripta Mater. 61 (2009) 80. [13] H.M. Liu, Y.G. Chen, Y.B. Tang, S.H. Wei, G. Niu, J. Alloy Compd. 440 (2007) 122. [14] H.M. Liu, Y.G. Chen, Y.B. Tang, D.M. Huang, G. Niu, Mater. Sci. Eng. A 437 (2006) 348. [15] H.M. Liu, Y.G. Chen, Y.B. Tang, S.H. Wei, G. Niu, Mater. Sci. Eng. A 464 (2007) 124. [16] C.L. Mendis, C.J. Bettles, M.A. Gibson, C.R. Hutchinson, Mater. Sci. Eng. A 435–436 (2006) 163.
90
J.W. Fu, Y.S. Yang / Journal of Crystal Growth 322 (2011) 84–90
[17] S.H. Wei, Y.G. Chen, Y.B. Tang, H.M. Liu, S.F. Xiao, G. Niu, X.P. Zhang, Y.H. Zhao, Mater. Sci. Eng. A 492 (2008) 20. [18] S.H. Wei, Y.G. Chen, Y.B. Tang, X.P. Zhang, M. Liu, S.F. Xiao, Y.H. Zhao, Mater. Sci. Eng. A 508 (2009) 59. [19] D.H. Kang, S.S. Park, Y.S. Oh, N.J. Kim, Mater. Sci. Eng. A 449–451 (2007) 318. [20] J.W. Fu, Y.S. Yang, J.J. Guo, J.C. Ma, W.H. Tong, J. Cryst. Growth 311 (2008) 132. [21] J.W. Fu, Y.S. Yang, J.J. Guo, W.H. Tong, Mater. Sci Technol. 24 (2008) 941. [22] J.W. Christian, The Theory of Transformations in Metals and Alloys, Pergamon, Oxford, 1975. [23] H. Mizukami, T. Suzuki, T. Umeda, W. Kurz, Mater. Sci. Eng. A 173 (1993) 363. [24] M. Easton, D. Stjohn, Metall. Mater. Trans. A 1999 (1613) 30. [25] M. Easton, D. Stjohn, Metall. Mater. Trans. A 1999 (1625) 30.
[26] [27] [28] [29] [30] [31] [32] [33]
Y.C. Lee, A.K. Dahle, D.H. Stjohn, Metall. Mater. Trans. A 31 (2000) 2895. M. Easton, D. Stjohn, Acta Mater. 2001 (1867) 49. H. Xu, L.D. Xu, S.J. Zhang, Q. Han, Scripta Mater. 54 (2006) 2191. I. Maxwell, A. Hellawell, Acta Metall. 23 (1975) 229. J.D. Hunt, Mater. Sci. Eng. 65 (1984) 75. W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35 (1964) 444. ¨ J.S. Langer, H. Muller-Krumbhaar, J. Cryst. Growth 42 (1977) 11. W. Kurz, D.J. Fisher, Fundamentals of Solidification, Trans Tech Aedermannsdorf, Switzerland, 1984. [34] J.S. Langer, Science 243 (1989) 1150. [35] G. Wulf, Z. Kristallogr. 34 (1901) 449. [36] X. Li, Y. Fautrelle, Z. Ren, Acta Mater. 56 (2008) 3146.
