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Microstructural length scales in directionally solidified Sn-40 at.%Mn peritectic alloy containing intermetallic compounds
Intermetallics 55 (2014) 73e79
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Microstructural length scales in directionally solidified Sn-40 at.%Mn peritectic alloy containing intermetallic compounds Peng Peng a, b, *, Yanqing Su c, Xinzhong Li c, Jiangong Li a, b, Jingjie Guo c, Hengzhi Fu c a
Institute of Materials Science and Engineering, Lanzhou University, Lanzhou 730000, PR China MOE Key Laboratory for Magnetism and Magnetic Materials, Lanzhou University, Lanzhou 730000, PR China c School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 May 2014 Received in revised form 10 July 2014 Accepted 12 July 2014 Available online
Sn-40 at.%Mn peritectic alloys in which both primary and peritectic phase are intermetallic compounds were directionally solidified at different growth rates (1 mm/s~100 mm/s). Dendritic growth of primary phase has been observed even at low growth rate, and dependence of microstructural characteristic length scales on growth rate has been investigated. Liquidus slope is the dominating factor in determining non-faceted/faceted solid/liquid morphology. Experimental results show that: l1 ¼ 229.64v0.20, l2 ¼ 33.337v0.34, l3 ¼ 39.90v0.378, R ¼ 16.90v0.384. Besides, both l1/l2 and l1/l3 vary greatly with increasing growth rates while l2/R ranges from 2 to 2.3 with increasing growth rate. Both the peritectic reaction and solute distribution of intermetallic compounds during solidification influence these length scales. A modified solute distribution coefficient which is appropriate for intermetallic compounds makes calculation agree reasonably well with experimental results. The value of l1 is influenced more by solute distribution of intermetallic compounds, while growth of l2, l3 and R are more significantly influenced by the peritectic reaction. © 2014 Elsevier Ltd. All rights reserved.
Keywords: A. Intermetallics B. Nucleation and growth D. Microstructure
1. Introduction Dendrite morphology has been commonly observed in many peritectic alloys [16]. The dendrite microstructure is generally described by length scales such as primary/higher order dendrite arm spacing (l1, l2, l3) and dendrite tip radius (R) which have been characterized as functions of dendrite tip growth rate, solute concentration, temperature gradient [710]. In peritectic solidification, dendrites of primary phase often grow in a complex matrix of peritectic phase over an extensive range of growth rates. As a result, investigation on dependence of microstructural characteristic length scales on solidification processing parameters such as growth rate is expected in peritectic systems. The primary (l1) and secondary dendrite arm spacing (l2) have been studied in many peritectic alloys such as CueZn alloys [3,11]. D. Ma et al. [11] proposed that the values of lv1/2 for peritectics are generally two orders of magnitude higher than those for eutectics. They also held that the arm coarsening for primary phase should be * Corresponding author. School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, PR China. Tel.: þ86 931 2166588. E-mail address: [email protected] (P. Peng). http://dx.doi.org/10.1016/j.intermet.2014.07.009 0966-9795/© 2014 Elsevier Ltd. All rights reserved.
suppressed by the formation of peritectic phase surrounding the primary phase [11], which has been confirmed [3]. However, there has been no research on tertiary dendrite arm spacing or dendrite tip radius in peritectic alloys; neither did the relations between these characteristic length scales, which are insufficient to describe microstructural characteristic length scales in peritectic systems. For intermetallic compounds with nil [12,13] or narrow [4,5] solubility, they usually exhibit faceted solid/liquid interfaces. But it has been confirmed that the faceting behavior may depend upon growth temperatures as well as compositions [14]. It has also been observed that dendritic morphology of intermetallic compounds exist in some alloy systems in the case of very large undercooling [6,15]. However, dendritic growth of intermetallic compounds has never been comprehensively analyzed, neither microstructural characteristic length scales of dendrites nor relations between them. In the present work, SneMn peritectic alloy where both primary phase and peritectic phase are intermetallic compounds was chosen, and microstructural length scales at the solid/liquid interface were measured and compared with theoretical predictions in directionally solidified samples. For this alloy, dendritic growth of primary phase was observed. The occurrence of dendritic growth of
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the intermetallic compound was analyzed, and influence of peritectic reaction on characteristic length scales was investigated. 2. Experimental procedures 2.1. Sample production process The Sn-40 at.%Mn alloy from pure Mn and Sn (99.9%) was induction melted. As-cast rods of 3 mm in diameter and 110 mm in length were machined from the ingot by a spark machining. Experiments consisting of melting followed by directional solidification were carried out in a Bridgman-type furnace which is composed of a resistance furnace, a water cooled liquid metal bath filled with a liquid GaeIneSn alloy, and an adiabatic zone which is located between the heater and the cooler. For each experiment, the furnace was heated to 900 C to melt the alloy, and then was held there for 30 min to homogenize the melt. Solidification of Sn40 at.%Mn peritectic alloy was carried out at different growth rates (1, 3, 5, 10, 30, 50 and 100 mm/s) under a constant temperature gradient (40 K/mm) in the Bridgman-type apparatus. With a predetermined distance of 30 mm reached, the samples were quenched into liquid GaeIneSn alloy quickly to preserve the solid/ liquid interface. As the growth distance in the present work is larger than three times of the distance before initiation of steady-state growth [16], the influence of the solidification fraction (pulling distance) on l1, l2, l3 and R can be neglected. 2.2. Measurement of temperature gradient and characteristic length scales The samples were 99.99 pct pure alumina crucibles of 4/5.5 mm diameter (insider/outside diameter) and length of 150 mm. Temperature profiles were measured using PtRh30-PtRh6 thermocouple inserted down the center of the samples. During the pulling process, the thermocouple moved downwards with the sample at the same pulling velocity. The temperature gradient close to the solid/liquid interface as deduced from the temperature profiles was approximately 40 K/mm. The solidified samples were longitudinally and transversally sectioned and polished to study the solidification microstructure by optical microscope (OM) and scanning electron microscopy (SEM (Quanta-200F)). pffiffiffiffiffiffiffiffiffi The primary dendrite arm spacing was measured by l1 ¼ A=N [17], where A is the area of the transverse section and N is the number of the primary dendrites counted. In order to weaken the influence of coarsening of the secondary dendrite arm spacing to a large extent, the secondary dendrite arm spacing (l2) was measured by averaging the distance between adjacent side branches on the longitudinal section of a primary arm near the dendrite tip. In these methods, 15 values were measured for each selected position. The tertiary values were measured in longitudinal section of samples. The primary dendrite tip radius was measured by comparing the unperturbed tip region to a series of parabolas of known curvatures as described by Somboonsuk et al. [9]. The procedure involved projecting a greatly enlarged tip image from the photographic negative onto the standard parabolas and adjusting the magnification until a best fit was obtained. At least 15 readings were taken for each sample and the value of these characterization length scales were obtained from their mean value.
Fig. 1. The relevant part of SneMn binary phase diagram [15].
line. Under equilibrium solidification, Sn-40 at.%Mn alloy [18] begins at TL ¼ 745 C with a primary precipitation of Mn3Sn2 phase: L / Mn2xSn, followed by a peritectic reaction at TP ¼ 549 C: L þ Mn2xSn / MnSn2. The Mn2xSn phase changes into Mn3Sn2 phase when the temperature is below 540 C. Morphological evolution of the solid/liquid interface at different growth rates is shown in Fig. 2. It can be observed that dendritic growth of primary Mn3Sn2 phase exists, and l1 decreases as the growth rate increases. Dendritic morphology of intermetallic compounds exist in some alloy systems in the case of large cooling rate [6,17]. However, in the present work, the cooling rate is rather small. Even at the growth rate of 100 mm/s, the cooling rate during directional solidification is only 4 K/s (G$v ¼ 4 K/s). Kerr and Winegard [19] have shown that the entropy of fusion in the expression for the parameter of Jackson factor a can be replaced by the entropy of solution DSaL. Saroch et al. [20] has proposed that liquidus lines with very small slope are therefore indicative of a large temperature coefficient of DSaL, and alloys for which the solid/liquid interface compositions yield inherently low DSaL and dDSaL/dT values are not likely to exhibit faceting. dDSaL/dT can be expressed as [20]:
dDSaL 1 vDSaL 1 vDSaL ¼ þ a ma vxe mL vxae dT
(1)
where ma and mL are the slopes of the solidus and liquidus lines, respectively. dDSaL/dT is negative, and in the case of small solid solubility, ma is very large and dDSaL/dT is essentially controlled by the second term in Eq. (1). The dominating factor in the second term is the slope of the liquidus. Thus, as the liquidus slope of primary Mn3Sn2 phase is much larger than that of peritectic MnSn2 phase [18] in the vicinity of the peritectic reaction temperature TP, dendritic growth of primary Mn3Sn2 phase and faceted growth of peritectic MnSn2 phase [21] can be observed. 3.2. Primary dendrite arm spacing ll
3. Results and discussion 3.1. Microstructure of directionally solidified Sn-40 at.%Mn alloy Fig. 1 shows the equilibrium phase diagram of SneMn alloy, and the concentration in present work is shown as the dashed
Studies characterizing the variation of l1 with alloy composition, solidification rate (v), and temperature gradient (G) in the liquid involving solidification both in steady-state heat flow [7,2225] and that in unsteady-state regime [10]. Expressions of these models have been presented in our previous work on SneNi
P. Peng et al. / Intermetallics 55 (2014) 73e79
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Fig. 2. Morphological evolution of the solid/liquid interface in directionally solidified Sn-40 at.%Mn peritectic alloy: (a) v ¼ 1 mm/s, (b) v ¼ 5 mm/s, (c) v ¼ 10 mm/s, (d) v ¼ 30 mm/s, (e) v ¼ 50 mm/s, (f) v ¼ 100 mm/s.
peritectic systems [4]. These models are quite similar in form; thus, only the model proposed by Bouchard and Kirkaldy [10] is presented here for the following discussion:
l1 ¼ 120
!1=2 16ðCl 1Þ1=2 G0 εsTM D ð1 kÞml DHGv
(2)
where k is the equilibrium distribution coefficient, G is the temperature gradient, melt concentration is assumed to be equal to the initial concentration of alloy C0. The denotations of other parameters can be found in Ref. [4]. Table 1 illustrates the physical parameters used in calculations for the SneMn peritectic systems [26]. The predictions of these models are compared with our measured values in Fig. 3(a): the models discussed above show different constancies: the Hunt model [22] and the Kurz-Fisher model [7] show constancy of l1v1/4 for a given C0 whereas the Kurz-Giovanola-Trivedi [23,24] and Table 1 Physical parameters regarding peritectic reaction L þ a / b at 549 C for SneMn system. Symbol
Parameter
Value
Unit
Ref.
TL Tp TE TM C0 ma ka
Melting temperature Peritectic temperature Eutectic temperature Melting temperature of solvent Composition of a at Tp a-Liquidus slope Distribution coefficient of a Gibbs-Thomson coefficient Diffusion coefficient in liquid Scaling factor for the surface tension Liquid-solid surface energy Heat of fusion Temperature gradient
745 549 231.15 232 40 8.91 0.489 1 107 5 109 6
C C C C at.%Mn C per at.%Mn
[17] [17] [17] [17] [17] [17] [17] [22] [22] [22]
0.25 1.5 105 40
J/m2 J/kg K/mm
G
D ε
s DH G
mK m2/s
[22] [22]
Hunt-Lu [25] models indicate constancy of l1v1/2 and l1v0.59, respectively, for given C0. These models all predict large deviations from our experimental results, and none of them exhibit excellent agreement with experimental data for Sn-40 at.%Mn alloy. At the growth rate of 1 mm/s, the cell/dendrite transition can be observed in the microstructure. When the growth rate ranging from 3 mm/s to 100 mm/s, the primary dendrite arm spacing continues decreasing with increasing growth rate, and our results shows that l1 ¼ 229.64v0.20. The exponent (0.20) in present work makes a large difference among the eutectics have been reported (close to 0.5) [27,28]. It can be observed from Fig. 3(a) that significant difference exists between the experimental results and predictions by models. The experimental results are smaller than the predictions by the above models, and decrease of l1 with growth rate is more slowly. This means that the decrease of primary dendrite arm is decelerated, or deceleration in decrease of primary dendrite arm occurs. These differences arise from the following two reasons: peritectic reaction and solidification characteristic of intermetallic phases. For the former reason, peritectic reaction changes the melt concentration during dendritic growth of primary phase. During solidification of SneMn peritectic alloys, if peritectic reaction occurs, as the liquidus slope of peritectic phase is smaller than that of primary phase, Mn concentration in the melt at the solid/liquid interface decreases more slowly during solidification. And decrease of melt concentration at the solid/liquid interface of the primary dendrite arms is also decelerated. According to Eq. (2), deceleration of l1 is restricted. The latter reason is more complex. As the steady-state solute concentration can hardly be achieved [12] during growth of intermetallic compound, solute concentration continues changing during solidification of intermetallic compound. As proposed by Liu et al. [12], the solute concentration of the liquid at the interface, Cl* , varies linearly with the growth distance within the initial transient in intermetallic compounds with nil solubility. The expression of Cl* is [12]:
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Fig. 3. Variation of characterization length scales with growth rate v at a constant temperature gradient (G ¼ 40 K/mm): (a) primary dendrite arm spacing l1, (b) secondary dendrite arm spacing l2 (a) tertiary dendrite arm spacing l3, (a) dendrite tip radius R.
Cl*
v ¼ ðC0 Ca Þ x þ C0 D
(3)
where Ca is the solute concentration of primary a phase. Thus, the solute distribution in the liquid at the growing interface can not reach the steady-state unless the initial composition of the alloy equals to the composition of the intermetallic compound [12]. As the composition of the intermetallic with narrow solubility can not be equal to the initial composition of the alloy, there is no steadystate boundary layer at the solid/liquid interface front. Thus, more obvious deviation of Cl* from the initial composition of alloy can be predicted in intermetallic with narrow solubility. The theoretical models discussed above [7,10,2225] are based on the assumptions that the solute distribution coefficient k is independent of temperature and the melt concentration equals to the initial concentration of the alloy during solidification. But for concentrated alloys and alloys near intermetallic compounds, melt concentration Cl gradually deviates from C0 during solidification, accompanied by significant variation in k with temperature. Analysis by Trivedi and Kurz [29] has shown that necessary modifications in the theoretical models must be made since large variation in k with temperature. Thus, when the equilibrium distribution coefficient is not constant, a modified solute distribution coefficient k*, has been proposed [29]:
k* ¼
CS a CL a
(4)
where a is the composition at which the linear segments of the solidus and liquidus lines intersect. It can be obtained from Fig. 1 that the values of k* at TL ¼ 745 C and TP ¼ 549 C are 0.0769 and 0.0714, respectively (a ¼ 66 at.%Mn). Here the mean value of k*
(0.0742) is used for calculation, which is significantly different from k (0.489 is obtained directly through k ¼ CS/Cl at TP). It can be found from Fig. 3(a) that among these models the Hunt [22] model is most similar to experimental results except that the predictions by this model is larger. Therefore, the modified solute distribution coefficient k*, has been taken into consideration in prediction of the Hunt model. Predictions close to the experimental results can be obtained through the Hunt model with the modified solute distribution coefficient k*. Therefore, it can be concluded from Eq. (2) that solute distribution of intermetallic phase significantly influences the growth of primary dendrite arm. The deceleration of l1 with growth rate is restricted by peritectic reaction. Furthermore, the result in present work is also distinct from that in ZneCu peritectic alloy [11], in which the composition is 1.53 wt.% Cu. This can be attributed to that the solute concentration in the present work is much higher than that in ZneCu peritectic alloys [11], while the Bouchard and Kirkaldy [10] model is based on dilute solution melt. 3.3. Secondary dendrite arm spacing l2 Kattamis and Flemings [30] predicted that the secondary dendrite arm spacing l2 was proportional to the cube root of solidification time (tf). Langer and Muller-Krumbhaar [31] have predicted a scaling law between secondary dendrite arm spacing l2 and the dendrite tip radius R as l2/R ¼ 2. Trivedi and Somboonsuk [32] and Bouchard and Kirkaldy [10] also described the variation of l2 with dendrite tip growth rate, solute concentration, temperature gradient. Expressions of these models have been presented in Ref. [4]. The predictions of these models are compared with our measured values in Fig. 3(b). Our experimental results show that l2 ¼ 33.34v0.34 and it can be observed from Fig. 3(b) that none of
P. Peng et al. / Intermetallics 55 (2014) 73e79
these models exhibits excellent agreement with experimental data. The deceleration of the secondary dendrite arm spacing is close to that predicated by the commonly accepted KattamisFlemings model. However, this model predicts smaller values than our results. This can be attributed to the following two reasons. First, peritectic reaction has been confirmed to restrict the coarsening process in peritectic alloys [4,5,11], comprehensive analysis and calculation can be found in our previous work [5]. The dissolution rate of thin arms will be decelerated, leading to reduction of the coarsening degree of thick arms. Second, as the steady-state solute concentration can hardly be achieved [12] during growth of intermetallic compound, solute concentration continues increasing during solidification of intermetallic compound. Thus, the values of l2 are slightly larger than those predicted by Kattamis and Flemings [30]. If k* is taken into consideration, predictions by the models should be smaller, leading to more deviation from experimental results. Thus, the influence of solidification characteristic of intermetallic phase on l2 is not obvious.
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3.6. Relations between characterization length scales The l1/l2 ratio can be used to estimate the permeability of the mushy zone, but only limited information is available in the literature about this ratio. Cicutti and Boeri [37] developed an analytical model to estimate the l1/l2 ratio and a roughly constant value is obtained for l1/l2 ratio: l1/l2 z 2.6. This value is in consistent with the values ranging from 2 to 4 which are suggested by Wolf [38]. But it can be observed in Fig. 4(a) that the l1/l2 ratio is not constant
3.4. Tertiary dendrite arm spacing l3 Researches on transparent alloys have shown that column dendrites can adjust their primary spacing during growth without difficulty. If spacing is too large, a tertiary arm initiating from the secondary branches will catch up to the growing primary tips and becomes one of them [33]. Investigations on tertiary dendrite arms are scarce in literature and they are more commonly mentioned on steady-state growth experiments where they are observed to grow past initiating secondary branches and go on to become primary arms [34]. Grugel [35] suggested a power law correlating l3 with local solidification time (tf):
1=3 l3 ¼ 10 tf
(5)
Based on experimentally examination of both SnePb and AleCu et al. [36] proposed a 0.55 power law to charalloy, Fernando Sa acterize the tertiary spacing variation:
0:55 l3 ¼ K tf
(6)
where K is a coefficient which can be determined by regression analysis. The predictions of these models are compared with our measured values in Fig. 3(c). By linear regression analysis we can obtain thatl3 ¼ 39.90v0.378. And it can be found from Fig. 3(c) that the experimental results (l3 ¼ 4.5(tf)0.33) exhibits reasonably agreement with the Grugel model except that the constant K is different.
3.5. Dendrite tip radius R Numerous studies [22,7,31] have been carried out on the dendrite tip radius R. The expressions of these models have been summarized [4]. Our experimental results show that R ¼ 16.9v0.384 and it can be observed from Fig. 3(d) that the measured values deviate obviously from the models discussed above. Furthermore, it can be observed that the measured values decrease more slowly as compared with these models based on alloys without a peritectic reaction. Similar to what has been discussed in 3.3, this arises from peritectic reaction. Like l2, the influence of solute distribution of intermetallic phase on R is not either.
Fig. 4. Relation between characterization length scales: (a) l1/l2, (b) l1/l3, (b) l2/R.
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P. Peng et al. / Intermetallics 55 (2014) 73e79
but range from 8.1 to 16.3 with the increase of growth rate. This means that l1 decrease more slowly than l2 with increasing growth rate. Slower decrease of l1 as compared with l2 can be attributed to the following two reasons. On the one hand, as has been discussed in 3.2, peritectic reaction and non steady-state melt concentration restricts decrease of l1 with increasing growth rate. On the other hand, it has been confirmed that peritectic reaction can also retard the coarsening process in peritectic systems [3,4,11], leading to more quickly decrease of l2 with increasing growth rate. In addition, the influence of the coarsening process can not be totally neglected. Due to the coupling effect of these two aspects, the values of l1/l2 change obviously with increasing growth rate. It can be observed from Fig. 4(b) that the l1/l3 ratio is not constant but range from 7 to 12.5 with increasing growth rate, which is in sharp contrast to results in AleCu, Pb-15 wt.%Sn and Pb30 wt.%Sn alloys, which are 3.4, 5, 6, respectively [35]. This can also be attributed to peritectic reaction. On one aspect, decrease of primary dendrite arm spacing with increasing growth rate has been restricted as discussed above. On the other aspect, peritectic reaction can also retard the coarsening process of tertiary dendrites in peritectic systems [4,11], leading to more quickly decrease of tertiary dendrite arm spacing with increasing growth rate. Thus, similar to l1/l2 ratio, the values of l1/l3 ratio change obviously with increasing growth rate. A numerical analysis of the wavelength of instabilities along the sides of a dendrite was carried out by Langer and Müller-Krumbhaar [31] and they have predicted a scaling law as l2/R z 2. Results of numerous studies show that although in most cases l2/R might be constant, its value is different in different alloy systems, and ranges from 2 [33] to 4.86 [38,39]. It can be found in Fig. 4(c) that l2/ R is not constant but range from 2 to 2.3 with the increase of growth rate in our experiment. In general, this is consistent with the ratio of 2 which is predicted by Langer et al. [31]. 4. Conclusions In a Bridgman-type furnace, directional solidification on Sn40 at.%Mn peritectic alloy was carried out. Dendritic growth of primary phase has been observed even at low growth rate, and characteristic length scales of dendrites were measured and compared with theoretical predictions. 1) The relations between microstructural parameters and the solidification parameters have been obtained: l1 ¼ 229.64v0.20; l2 ¼ 33.34v0.34; l3 ¼ 39.30v0.378; R ¼ 16.90v0.384. l1/l2 and l1/l3 are not constant, which is distinct from results in alloys without a peritectic reaction. l2/R ranges from 2 to 2.3 with increasing growth rate. 2) Higher order dendrite arm spacings and dendrite tip radius are more significantly influenced by the peritectic reaction as compared with effective solute distribution of intermetallic compound. The peritectic reaction which decelerates the coarsening process can restricts the decrease of secondary and tertiary dendrite arms and primary dendrite tip radius. 3) The liquidus slope is the dominating factor determining whether faceted solid/liquid morphology exists. The effective solute distribution coefficient of intermetallic compound is distinct from the equilibrium solute distribution coefficient. Acknowledgments This project is supported by the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2014-
34),Open Project of Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University (Grant No. LZUMMM2014009), fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201416). References [1] Ding XF, Lin JP, Zhang LQ, Su YQ, Hao GJ, Chen GL. A closely-complete peritectic transformation during directional solidification of a Tie45Ale8.5Nb alloy. Intermetallics 2011;19(8):1115e9. [2] Hu D, Yang C, Huang A, Dixon M, Hecht U. Solidification and grain refinement in Ti45Al2Mn2Nb1B. Intermetallics 2012;22:68e76. [3] Ma D, Xu W, Ng SC, Li Y. On secondary dendrite arm coarsening in peritectic solidification. Mater Sci Eng A 2005;390(1e2):52e62. [4] Peng P, Li XZ, Liu DM, Su YQ, Guo JJ, Fu HZ. Characterization of microstructural length in directionally solidified Sne36 at.%Ni peritectic alloy. Trans Nonferrous Met Soc China 2012;20:302e7. [5] Peng P, Li XZ, Liu DM, Su YQ, Guo JJ, Fu HZ. Effect of peritectic reaction on dendrite coarsening in directionally solidified Sn-36 at.%Ni alloy. J Mater Sci 2012;47:6108e17. [6] Wang N, Wei B. Rapid solidification of undercooled CueGe peritectic alloy. Acta Mater 2000;48(8):1931e8. [7] Kurz W, Fisher JD. Dendrite growth at the limit of stability: tip radius and spacing. Acta Mater 1981;29:11e20. [8] Trivedi R. Interdendritic spacing: part II. A comparison of theory and experiment. Metall Mater Trans A 1984;15(6):977e82. [9] Somboonsuk K, Mason JT, Trivedi R. Interdendritic spacing: part I. experimental studies. Metall Mater Trans A 1984;15(6):967e75. [10] Bouchard D, Kirkaldy JS. Prediction of dendrite arm spacings in unsteady-and steady-state heat flow of unidirectionally solidified binary alloys. Metall Mater Trans B 1997;28(4):651e3. [11] Ma D, Li Y, Ng SC, Jones H. Unidirectional solidification of Zn-rich ZneCu peritectic alloys-II. Microstructural length scales. Acta Mater 2000;48: 1741e51. [12] Liu DM, Li XZ, Su YQ, Luo LS, Guo JJ, Fu HZ. Solute redistribution during planar growth of intermetallic compound with nil solubility. Intermetallics 2012;26: 131e5. [13] Izumi T, Nakamura Y, Shiohara Y. Crystal growth mechanism of YBa2Cu3Oy superconductros with peritectic reaction. J Cryst Growth 1993;128:757e61. [14] Yilmaz F, Elliott R. Faceting in the AleCuAl2 system. J Cryst Growth 1984;66: 465e8. [15] Zhong H, Li SM, Lü HY, Liu L, Zou GR, Fu HZ. Solidification microstructure selection of the peritectic NdeFeeB alloys. Sci China G 2007;50(4):432e41. [16] Kurz W, Fisher DJ. Fundamentals of solidification. 4th ed. Aedermannsdorf: Transactions of Technical Publications Ltd; 1989. [17] Jacobi H, Sehwerdtfeger K. Dendrite morphology of steady state unidirectionally solidified steel. Metall Mater Trans A 1976;7:811e20. [18] Stange M, Fjellvåg H, Furuseth S, Hauback BC. Crystal structure and phase relations for Mn3Sn2 and non-stoichiometric Mn2xSn. J Alloys Compd 1997;259:140e4. [19] Kerr HW, Winegard WC. Crystal growth. In: Peiser HS, editor. Oxford: Pergamon; 1967. p. 179. [20] Saroch M, Dubey KS, Ramachandrarao P. On the composition dependence of faceting behaviour of primary phases during solidification. J Cryst Growth 1993;126:701e6. [21] Peng P, Li XZ, Liu DM, Su YQ, Guo JJ, Fu HZ. Secondary dendrite arm migration caused by temperature gradient zone melting in directionally solidified Sn40 at.%Mn peritectic alloy. J Mater Res 2013;28(9):1196e202. [22] Hunt JD. Solidification and casting of metals. 1st ed. London: The Metals Society; 1979. [23] Kurz W, Giovanola B, Trivedi R. Theory of microstructural development during rapid solidification. Acta Mater 1986;34:823e30. [24] Kurz W, Giovanola B, Trivedi R. Microsegregation in rapidly solidified Ag15 wt.%Cu. J Cryst Growth 1988;91:123e5. [25] Hunt JD, Lu SZ. Numerical modeling of cellular/dendritic array growth: spacing and structure predictions. Metall Mater Trans A 1996;27:611e23. [26] Elding-Ponten M, Stenberg L, Larsson AK, Lidin S, Stashl K. Three NiAseNi2In type structures in the MneSn system. J Solid State Chem 1997;129:231e41. €yük U, Kaya H, Maras¸lı N, Kes¸liog lu K, Akbulut S. The effect of [27] Çadırlı E, Bo growth rate on microstructure and microindentation hardness in the IneBieSn ternary alloy at low melting point. J Alloys Compd 2009;470:150e6. €yük U, Engin S, Kaya H, Maras¸lı N. Effect of solidification parameters on the [28] Bo microstructure of Sne3.7Age0.9Zn solder. Mater Charact 2010;61:1260e7. [29] Trivedi R, Kurz W. Modeling of solidification microstructures in concentrated solutions and intermetallic systems. Metall Mater Trans A 1990;21A:1311e8. [30] Kattamis TZ, Flemings MC. Dendrite structure and grain size of undercooled melts. Trans Met Soc AIME 1965;233:992e1001. [31] Langer JS, Müller-Krumbhaar H. Theory of dendritic growth-I. Elements of a stability analysis. Acta Mater 1978;26:1681e7. [32] Trivedi R, Somboonsuk K. Constrained dendritic growth and spacing. Mater Sci Eng A 1984;65:65e74.
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Microstructural length scales in directionally solidified Sn-40 at.%Mn peritectic alloy containing intermetallic compounds Peng Peng a, b, *, Yanqing Su c, Xinzhong Li c, Jiangong Li a, b, Jingjie Guo c, Hengzhi Fu c a
Institute of Materials Science and Engineering, Lanzhou University, Lanzhou 730000, PR China MOE Key Laboratory for Magnetism and Magnetic Materials, Lanzhou University, Lanzhou 730000, PR China c School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 May 2014 Received in revised form 10 July 2014 Accepted 12 July 2014 Available online
Sn-40 at.%Mn peritectic alloys in which both primary and peritectic phase are intermetallic compounds were directionally solidified at different growth rates (1 mm/s~100 mm/s). Dendritic growth of primary phase has been observed even at low growth rate, and dependence of microstructural characteristic length scales on growth rate has been investigated. Liquidus slope is the dominating factor in determining non-faceted/faceted solid/liquid morphology. Experimental results show that: l1 ¼ 229.64v0.20, l2 ¼ 33.337v0.34, l3 ¼ 39.90v0.378, R ¼ 16.90v0.384. Besides, both l1/l2 and l1/l3 vary greatly with increasing growth rates while l2/R ranges from 2 to 2.3 with increasing growth rate. Both the peritectic reaction and solute distribution of intermetallic compounds during solidification influence these length scales. A modified solute distribution coefficient which is appropriate for intermetallic compounds makes calculation agree reasonably well with experimental results. The value of l1 is influenced more by solute distribution of intermetallic compounds, while growth of l2, l3 and R are more significantly influenced by the peritectic reaction. © 2014 Elsevier Ltd. All rights reserved.
Keywords: A. Intermetallics B. Nucleation and growth D. Microstructure
1. Introduction Dendrite morphology has been commonly observed in many peritectic alloys [16]. The dendrite microstructure is generally described by length scales such as primary/higher order dendrite arm spacing (l1, l2, l3) and dendrite tip radius (R) which have been characterized as functions of dendrite tip growth rate, solute concentration, temperature gradient [710]. In peritectic solidification, dendrites of primary phase often grow in a complex matrix of peritectic phase over an extensive range of growth rates. As a result, investigation on dependence of microstructural characteristic length scales on solidification processing parameters such as growth rate is expected in peritectic systems. The primary (l1) and secondary dendrite arm spacing (l2) have been studied in many peritectic alloys such as CueZn alloys [3,11]. D. Ma et al. [11] proposed that the values of lv1/2 for peritectics are generally two orders of magnitude higher than those for eutectics. They also held that the arm coarsening for primary phase should be * Corresponding author. School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, PR China. Tel.: þ86 931 2166588. E-mail address: [email protected] (P. Peng). http://dx.doi.org/10.1016/j.intermet.2014.07.009 0966-9795/© 2014 Elsevier Ltd. All rights reserved.
suppressed by the formation of peritectic phase surrounding the primary phase [11], which has been confirmed [3]. However, there has been no research on tertiary dendrite arm spacing or dendrite tip radius in peritectic alloys; neither did the relations between these characteristic length scales, which are insufficient to describe microstructural characteristic length scales in peritectic systems. For intermetallic compounds with nil [12,13] or narrow [4,5] solubility, they usually exhibit faceted solid/liquid interfaces. But it has been confirmed that the faceting behavior may depend upon growth temperatures as well as compositions [14]. It has also been observed that dendritic morphology of intermetallic compounds exist in some alloy systems in the case of very large undercooling [6,15]. However, dendritic growth of intermetallic compounds has never been comprehensively analyzed, neither microstructural characteristic length scales of dendrites nor relations between them. In the present work, SneMn peritectic alloy where both primary phase and peritectic phase are intermetallic compounds was chosen, and microstructural length scales at the solid/liquid interface were measured and compared with theoretical predictions in directionally solidified samples. For this alloy, dendritic growth of primary phase was observed. The occurrence of dendritic growth of
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the intermetallic compound was analyzed, and influence of peritectic reaction on characteristic length scales was investigated. 2. Experimental procedures 2.1. Sample production process The Sn-40 at.%Mn alloy from pure Mn and Sn (99.9%) was induction melted. As-cast rods of 3 mm in diameter and 110 mm in length were machined from the ingot by a spark machining. Experiments consisting of melting followed by directional solidification were carried out in a Bridgman-type furnace which is composed of a resistance furnace, a water cooled liquid metal bath filled with a liquid GaeIneSn alloy, and an adiabatic zone which is located between the heater and the cooler. For each experiment, the furnace was heated to 900 C to melt the alloy, and then was held there for 30 min to homogenize the melt. Solidification of Sn40 at.%Mn peritectic alloy was carried out at different growth rates (1, 3, 5, 10, 30, 50 and 100 mm/s) under a constant temperature gradient (40 K/mm) in the Bridgman-type apparatus. With a predetermined distance of 30 mm reached, the samples were quenched into liquid GaeIneSn alloy quickly to preserve the solid/ liquid interface. As the growth distance in the present work is larger than three times of the distance before initiation of steady-state growth [16], the influence of the solidification fraction (pulling distance) on l1, l2, l3 and R can be neglected. 2.2. Measurement of temperature gradient and characteristic length scales The samples were 99.99 pct pure alumina crucibles of 4/5.5 mm diameter (insider/outside diameter) and length of 150 mm. Temperature profiles were measured using PtRh30-PtRh6 thermocouple inserted down the center of the samples. During the pulling process, the thermocouple moved downwards with the sample at the same pulling velocity. The temperature gradient close to the solid/liquid interface as deduced from the temperature profiles was approximately 40 K/mm. The solidified samples were longitudinally and transversally sectioned and polished to study the solidification microstructure by optical microscope (OM) and scanning electron microscopy (SEM (Quanta-200F)). pffiffiffiffiffiffiffiffiffi The primary dendrite arm spacing was measured by l1 ¼ A=N [17], where A is the area of the transverse section and N is the number of the primary dendrites counted. In order to weaken the influence of coarsening of the secondary dendrite arm spacing to a large extent, the secondary dendrite arm spacing (l2) was measured by averaging the distance between adjacent side branches on the longitudinal section of a primary arm near the dendrite tip. In these methods, 15 values were measured for each selected position. The tertiary values were measured in longitudinal section of samples. The primary dendrite tip radius was measured by comparing the unperturbed tip region to a series of parabolas of known curvatures as described by Somboonsuk et al. [9]. The procedure involved projecting a greatly enlarged tip image from the photographic negative onto the standard parabolas and adjusting the magnification until a best fit was obtained. At least 15 readings were taken for each sample and the value of these characterization length scales were obtained from their mean value.
Fig. 1. The relevant part of SneMn binary phase diagram [15].
line. Under equilibrium solidification, Sn-40 at.%Mn alloy [18] begins at TL ¼ 745 C with a primary precipitation of Mn3Sn2 phase: L / Mn2xSn, followed by a peritectic reaction at TP ¼ 549 C: L þ Mn2xSn / MnSn2. The Mn2xSn phase changes into Mn3Sn2 phase when the temperature is below 540 C. Morphological evolution of the solid/liquid interface at different growth rates is shown in Fig. 2. It can be observed that dendritic growth of primary Mn3Sn2 phase exists, and l1 decreases as the growth rate increases. Dendritic morphology of intermetallic compounds exist in some alloy systems in the case of large cooling rate [6,17]. However, in the present work, the cooling rate is rather small. Even at the growth rate of 100 mm/s, the cooling rate during directional solidification is only 4 K/s (G$v ¼ 4 K/s). Kerr and Winegard [19] have shown that the entropy of fusion in the expression for the parameter of Jackson factor a can be replaced by the entropy of solution DSaL. Saroch et al. [20] has proposed that liquidus lines with very small slope are therefore indicative of a large temperature coefficient of DSaL, and alloys for which the solid/liquid interface compositions yield inherently low DSaL and dDSaL/dT values are not likely to exhibit faceting. dDSaL/dT can be expressed as [20]:
dDSaL 1 vDSaL 1 vDSaL ¼ þ a ma vxe mL vxae dT
(1)
where ma and mL are the slopes of the solidus and liquidus lines, respectively. dDSaL/dT is negative, and in the case of small solid solubility, ma is very large and dDSaL/dT is essentially controlled by the second term in Eq. (1). The dominating factor in the second term is the slope of the liquidus. Thus, as the liquidus slope of primary Mn3Sn2 phase is much larger than that of peritectic MnSn2 phase [18] in the vicinity of the peritectic reaction temperature TP, dendritic growth of primary Mn3Sn2 phase and faceted growth of peritectic MnSn2 phase [21] can be observed. 3.2. Primary dendrite arm spacing ll
3. Results and discussion 3.1. Microstructure of directionally solidified Sn-40 at.%Mn alloy Fig. 1 shows the equilibrium phase diagram of SneMn alloy, and the concentration in present work is shown as the dashed
Studies characterizing the variation of l1 with alloy composition, solidification rate (v), and temperature gradient (G) in the liquid involving solidification both in steady-state heat flow [7,2225] and that in unsteady-state regime [10]. Expressions of these models have been presented in our previous work on SneNi
P. Peng et al. / Intermetallics 55 (2014) 73e79
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Fig. 2. Morphological evolution of the solid/liquid interface in directionally solidified Sn-40 at.%Mn peritectic alloy: (a) v ¼ 1 mm/s, (b) v ¼ 5 mm/s, (c) v ¼ 10 mm/s, (d) v ¼ 30 mm/s, (e) v ¼ 50 mm/s, (f) v ¼ 100 mm/s.
peritectic systems [4]. These models are quite similar in form; thus, only the model proposed by Bouchard and Kirkaldy [10] is presented here for the following discussion:
l1 ¼ 120
!1=2 16ðCl 1Þ1=2 G0 εsTM D ð1 kÞml DHGv
(2)
where k is the equilibrium distribution coefficient, G is the temperature gradient, melt concentration is assumed to be equal to the initial concentration of alloy C0. The denotations of other parameters can be found in Ref. [4]. Table 1 illustrates the physical parameters used in calculations for the SneMn peritectic systems [26]. The predictions of these models are compared with our measured values in Fig. 3(a): the models discussed above show different constancies: the Hunt model [22] and the Kurz-Fisher model [7] show constancy of l1v1/4 for a given C0 whereas the Kurz-Giovanola-Trivedi [23,24] and Table 1 Physical parameters regarding peritectic reaction L þ a / b at 549 C for SneMn system. Symbol
Parameter
Value
Unit
Ref.
TL Tp TE TM C0 ma ka
Melting temperature Peritectic temperature Eutectic temperature Melting temperature of solvent Composition of a at Tp a-Liquidus slope Distribution coefficient of a Gibbs-Thomson coefficient Diffusion coefficient in liquid Scaling factor for the surface tension Liquid-solid surface energy Heat of fusion Temperature gradient
745 549 231.15 232 40 8.91 0.489 1 107 5 109 6
C C C C at.%Mn C per at.%Mn
[17] [17] [17] [17] [17] [17] [17] [22] [22] [22]
0.25 1.5 105 40
J/m2 J/kg K/mm
G
D ε
s DH G
mK m2/s
[22] [22]
Hunt-Lu [25] models indicate constancy of l1v1/2 and l1v0.59, respectively, for given C0. These models all predict large deviations from our experimental results, and none of them exhibit excellent agreement with experimental data for Sn-40 at.%Mn alloy. At the growth rate of 1 mm/s, the cell/dendrite transition can be observed in the microstructure. When the growth rate ranging from 3 mm/s to 100 mm/s, the primary dendrite arm spacing continues decreasing with increasing growth rate, and our results shows that l1 ¼ 229.64v0.20. The exponent (0.20) in present work makes a large difference among the eutectics have been reported (close to 0.5) [27,28]. It can be observed from Fig. 3(a) that significant difference exists between the experimental results and predictions by models. The experimental results are smaller than the predictions by the above models, and decrease of l1 with growth rate is more slowly. This means that the decrease of primary dendrite arm is decelerated, or deceleration in decrease of primary dendrite arm occurs. These differences arise from the following two reasons: peritectic reaction and solidification characteristic of intermetallic phases. For the former reason, peritectic reaction changes the melt concentration during dendritic growth of primary phase. During solidification of SneMn peritectic alloys, if peritectic reaction occurs, as the liquidus slope of peritectic phase is smaller than that of primary phase, Mn concentration in the melt at the solid/liquid interface decreases more slowly during solidification. And decrease of melt concentration at the solid/liquid interface of the primary dendrite arms is also decelerated. According to Eq. (2), deceleration of l1 is restricted. The latter reason is more complex. As the steady-state solute concentration can hardly be achieved [12] during growth of intermetallic compound, solute concentration continues changing during solidification of intermetallic compound. As proposed by Liu et al. [12], the solute concentration of the liquid at the interface, Cl* , varies linearly with the growth distance within the initial transient in intermetallic compounds with nil solubility. The expression of Cl* is [12]:
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Fig. 3. Variation of characterization length scales with growth rate v at a constant temperature gradient (G ¼ 40 K/mm): (a) primary dendrite arm spacing l1, (b) secondary dendrite arm spacing l2 (a) tertiary dendrite arm spacing l3, (a) dendrite tip radius R.
Cl*
v ¼ ðC0 Ca Þ x þ C0 D
(3)
where Ca is the solute concentration of primary a phase. Thus, the solute distribution in the liquid at the growing interface can not reach the steady-state unless the initial composition of the alloy equals to the composition of the intermetallic compound [12]. As the composition of the intermetallic with narrow solubility can not be equal to the initial composition of the alloy, there is no steadystate boundary layer at the solid/liquid interface front. Thus, more obvious deviation of Cl* from the initial composition of alloy can be predicted in intermetallic with narrow solubility. The theoretical models discussed above [7,10,2225] are based on the assumptions that the solute distribution coefficient k is independent of temperature and the melt concentration equals to the initial concentration of the alloy during solidification. But for concentrated alloys and alloys near intermetallic compounds, melt concentration Cl gradually deviates from C0 during solidification, accompanied by significant variation in k with temperature. Analysis by Trivedi and Kurz [29] has shown that necessary modifications in the theoretical models must be made since large variation in k with temperature. Thus, when the equilibrium distribution coefficient is not constant, a modified solute distribution coefficient k*, has been proposed [29]:
k* ¼
CS a CL a
(4)
where a is the composition at which the linear segments of the solidus and liquidus lines intersect. It can be obtained from Fig. 1 that the values of k* at TL ¼ 745 C and TP ¼ 549 C are 0.0769 and 0.0714, respectively (a ¼ 66 at.%Mn). Here the mean value of k*
(0.0742) is used for calculation, which is significantly different from k (0.489 is obtained directly through k ¼ CS/Cl at TP). It can be found from Fig. 3(a) that among these models the Hunt [22] model is most similar to experimental results except that the predictions by this model is larger. Therefore, the modified solute distribution coefficient k*, has been taken into consideration in prediction of the Hunt model. Predictions close to the experimental results can be obtained through the Hunt model with the modified solute distribution coefficient k*. Therefore, it can be concluded from Eq. (2) that solute distribution of intermetallic phase significantly influences the growth of primary dendrite arm. The deceleration of l1 with growth rate is restricted by peritectic reaction. Furthermore, the result in present work is also distinct from that in ZneCu peritectic alloy [11], in which the composition is 1.53 wt.% Cu. This can be attributed to that the solute concentration in the present work is much higher than that in ZneCu peritectic alloys [11], while the Bouchard and Kirkaldy [10] model is based on dilute solution melt. 3.3. Secondary dendrite arm spacing l2 Kattamis and Flemings [30] predicted that the secondary dendrite arm spacing l2 was proportional to the cube root of solidification time (tf). Langer and Muller-Krumbhaar [31] have predicted a scaling law between secondary dendrite arm spacing l2 and the dendrite tip radius R as l2/R ¼ 2. Trivedi and Somboonsuk [32] and Bouchard and Kirkaldy [10] also described the variation of l2 with dendrite tip growth rate, solute concentration, temperature gradient. Expressions of these models have been presented in Ref. [4]. The predictions of these models are compared with our measured values in Fig. 3(b). Our experimental results show that l2 ¼ 33.34v0.34 and it can be observed from Fig. 3(b) that none of
P. Peng et al. / Intermetallics 55 (2014) 73e79
these models exhibits excellent agreement with experimental data. The deceleration of the secondary dendrite arm spacing is close to that predicated by the commonly accepted KattamisFlemings model. However, this model predicts smaller values than our results. This can be attributed to the following two reasons. First, peritectic reaction has been confirmed to restrict the coarsening process in peritectic alloys [4,5,11], comprehensive analysis and calculation can be found in our previous work [5]. The dissolution rate of thin arms will be decelerated, leading to reduction of the coarsening degree of thick arms. Second, as the steady-state solute concentration can hardly be achieved [12] during growth of intermetallic compound, solute concentration continues increasing during solidification of intermetallic compound. Thus, the values of l2 are slightly larger than those predicted by Kattamis and Flemings [30]. If k* is taken into consideration, predictions by the models should be smaller, leading to more deviation from experimental results. Thus, the influence of solidification characteristic of intermetallic phase on l2 is not obvious.
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3.6. Relations between characterization length scales The l1/l2 ratio can be used to estimate the permeability of the mushy zone, but only limited information is available in the literature about this ratio. Cicutti and Boeri [37] developed an analytical model to estimate the l1/l2 ratio and a roughly constant value is obtained for l1/l2 ratio: l1/l2 z 2.6. This value is in consistent with the values ranging from 2 to 4 which are suggested by Wolf [38]. But it can be observed in Fig. 4(a) that the l1/l2 ratio is not constant
3.4. Tertiary dendrite arm spacing l3 Researches on transparent alloys have shown that column dendrites can adjust their primary spacing during growth without difficulty. If spacing is too large, a tertiary arm initiating from the secondary branches will catch up to the growing primary tips and becomes one of them [33]. Investigations on tertiary dendrite arms are scarce in literature and they are more commonly mentioned on steady-state growth experiments where they are observed to grow past initiating secondary branches and go on to become primary arms [34]. Grugel [35] suggested a power law correlating l3 with local solidification time (tf):
1=3 l3 ¼ 10 tf
(5)
Based on experimentally examination of both SnePb and AleCu et al. [36] proposed a 0.55 power law to charalloy, Fernando Sa acterize the tertiary spacing variation:
0:55 l3 ¼ K tf
(6)
where K is a coefficient which can be determined by regression analysis. The predictions of these models are compared with our measured values in Fig. 3(c). By linear regression analysis we can obtain thatl3 ¼ 39.90v0.378. And it can be found from Fig. 3(c) that the experimental results (l3 ¼ 4.5(tf)0.33) exhibits reasonably agreement with the Grugel model except that the constant K is different.
3.5. Dendrite tip radius R Numerous studies [22,7,31] have been carried out on the dendrite tip radius R. The expressions of these models have been summarized [4]. Our experimental results show that R ¼ 16.9v0.384 and it can be observed from Fig. 3(d) that the measured values deviate obviously from the models discussed above. Furthermore, it can be observed that the measured values decrease more slowly as compared with these models based on alloys without a peritectic reaction. Similar to what has been discussed in 3.3, this arises from peritectic reaction. Like l2, the influence of solute distribution of intermetallic phase on R is not either.
Fig. 4. Relation between characterization length scales: (a) l1/l2, (b) l1/l3, (b) l2/R.
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P. Peng et al. / Intermetallics 55 (2014) 73e79
but range from 8.1 to 16.3 with the increase of growth rate. This means that l1 decrease more slowly than l2 with increasing growth rate. Slower decrease of l1 as compared with l2 can be attributed to the following two reasons. On the one hand, as has been discussed in 3.2, peritectic reaction and non steady-state melt concentration restricts decrease of l1 with increasing growth rate. On the other hand, it has been confirmed that peritectic reaction can also retard the coarsening process in peritectic systems [3,4,11], leading to more quickly decrease of l2 with increasing growth rate. In addition, the influence of the coarsening process can not be totally neglected. Due to the coupling effect of these two aspects, the values of l1/l2 change obviously with increasing growth rate. It can be observed from Fig. 4(b) that the l1/l3 ratio is not constant but range from 7 to 12.5 with increasing growth rate, which is in sharp contrast to results in AleCu, Pb-15 wt.%Sn and Pb30 wt.%Sn alloys, which are 3.4, 5, 6, respectively [35]. This can also be attributed to peritectic reaction. On one aspect, decrease of primary dendrite arm spacing with increasing growth rate has been restricted as discussed above. On the other aspect, peritectic reaction can also retard the coarsening process of tertiary dendrites in peritectic systems [4,11], leading to more quickly decrease of tertiary dendrite arm spacing with increasing growth rate. Thus, similar to l1/l2 ratio, the values of l1/l3 ratio change obviously with increasing growth rate. A numerical analysis of the wavelength of instabilities along the sides of a dendrite was carried out by Langer and Müller-Krumbhaar [31] and they have predicted a scaling law as l2/R z 2. Results of numerous studies show that although in most cases l2/R might be constant, its value is different in different alloy systems, and ranges from 2 [33] to 4.86 [38,39]. It can be found in Fig. 4(c) that l2/ R is not constant but range from 2 to 2.3 with the increase of growth rate in our experiment. In general, this is consistent with the ratio of 2 which is predicted by Langer et al. [31]. 4. Conclusions In a Bridgman-type furnace, directional solidification on Sn40 at.%Mn peritectic alloy was carried out. Dendritic growth of primary phase has been observed even at low growth rate, and characteristic length scales of dendrites were measured and compared with theoretical predictions. 1) The relations between microstructural parameters and the solidification parameters have been obtained: l1 ¼ 229.64v0.20; l2 ¼ 33.34v0.34; l3 ¼ 39.30v0.378; R ¼ 16.90v0.384. l1/l2 and l1/l3 are not constant, which is distinct from results in alloys without a peritectic reaction. l2/R ranges from 2 to 2.3 with increasing growth rate. 2) Higher order dendrite arm spacings and dendrite tip radius are more significantly influenced by the peritectic reaction as compared with effective solute distribution of intermetallic compound. The peritectic reaction which decelerates the coarsening process can restricts the decrease of secondary and tertiary dendrite arms and primary dendrite tip radius. 3) The liquidus slope is the dominating factor determining whether faceted solid/liquid morphology exists. The effective solute distribution coefficient of intermetallic compound is distinct from the equilibrium solute distribution coefficient. Acknowledgments This project is supported by the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2014-
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