Directional solidification and characterization of the Cd Sn eutectic alloy

Journal of Alloys and Compounds 431 (2007) 171 179 Directional solidification and characterization of the Cd Sn eutectic alloy E. Çadırlı a,, H. Kaya a,m.gündüz b a Niğde University, Faculty of Arts and Sciences, Department of Physics, Niğde, Turkey b Erciyes University, Faculty of Arts and Sciences, Department of Physics, Kayseri, Turkey Received 9 May 2006; received in revised form 17 May 2006; accepted 18 May 2006 Available online 23 June 2006 Abstract The Cd 67.8 wt.% Sn eutectic alloy was prepared by melting together appropriate amounts of cadmium and tin (both of 99.99% purity) in a graphite crucible in a vacuum melting furnace. Then, this eutectic alloy was poured into graphite crucibles in a hot filling furnace and the samples were solidified. These samples were directionally solidified upward with different growth rate ranges (8.1 165 m/s) at a constant temperature gradient G (4.35 K/mm) in the Bridgman type directional solidification furnace. The lamellar spacings were measured using directional solidified samples. The variations of λ with respect to V were determined by using linear regression analysis. The dependence of lamellar spacings λ on undercooling, T, was also analysed. The variations of T with V (at constant G) were investigated. According to these results, it has been found that with the increasing values of V, λ decreases, whereas, T increases for a constant G. λ 2 V, Tλ and TV 0.5 values were determined by using λ, T and V values. The results obtained in this work have been compared with the Jackson Hunt eutectic theory and experimental results studied by Borland and Elliott, Clark and Elliott for the same alloy system, and also the similar alloy systems studied by Çadırlı and Gündüz, Kaya et al. 2006 Elsevier B.V. All rights reserved. Keywords: Crystal growth; Mechanical alloying; Undercooling; Directional solidification; Eutectic microstructure 1. Introduction In the past few decades, considerable effort has been focused on developing advanced material for technological applications. Solidification behaviour and structural characteristics of eutectic alloys in many systems continue to attract interest because of their influence on the properties and performance of materials containing eutectic constituents. Eutectic alloys are the basis of many engineering materials [1 4]. This has led to an extensive theoretical and experimental study of the relationship between microstructure and solidification conditions [5 37]. A eutectic reaction can be defined as the instance where two (or more) distinctively different solid phases simultaneously solidify from the parent liquid, i.e., liquid +. This is a complex process involving interactions of, among others, heat and mass transfer. Directional solidification of binary or pseudo-binary eutectics, may result in regular structures of fibrous or lamellar type. When two solid phases and grow from a liquid of eutectic composition C E, the average undercooling T at the interface results from three contributions. T = T E T L = T c + T r + T k (1) where T is the average interface undercooling, T E the eutectic temperature, T L the local interface temperature, and T c, T r, T k are the chemical, capillary, and kinetic undercoolings respectively. For regular metallic eutectic systems, however, T k can usually be neglected when compared to T c and T r. The and lamellae grow under steady state conditions with a build up of B atoms in the liquid ahead of the phase and the lateral transfer of solute to ensure steady state growth. One of the most significant theoretical studies is the Jackson and Hunt (J H) theory of the eutectic structures [12]. The J H theory [12] gives the following relationship between the undercooling T, the growth rate V and the lamellar spacing λ for an isothermal solidification front as, Corresponding author. Tel.: +90 388 2252164; fax: +90 388 2250180. E-mail address: ecadirli@gmail.com (E. Çadırlı). 0925-8388/$ see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.05.073 T = K 1 Vλ + K 2 λ (2)

172 E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 where K 1 and K 2 can be calculated from phase diagram and thermodynamic data. They are given by, K 1 = mpc o f f D K 2 = 2mδ i ( Γi sin θ i m i f i (3) ), i =, (4) where m = m m /(m + m ) in which m and m are the slopes of the liquidus lines of the and phases at the eutectic temperature, C o the difference between the composition in the and the phase, f and f are the volume fractions of and phases, respectively. Γ i is the Gibss Thomson coefficient, D solute diffusion coefficient for the melt, θ and θ are the groove angles of /liquid phases and /liquid phases at the three-phase conjunction point (Appendix A). These thermodynamic data concerning Cd Sn eutectic alloy are given in Appendix B. The parameter δ is unity for the lamellar growth. For lamellar eutectic the parameter P is defined as [12], P = 0.3383(f f ) 1.661 (5) Investigation of Eq. (2) gives the relationship between the extremum lamellar spacing λ, V and T as, λ 2 e V = K 2 (6.a) K 1 Tλ e = 2K 2 (6.b) T 2 V = 4K 1K 2 (6.c) A well known conjecture of this criterion is the minimum undercooling arguments. This indicates that the spacing λ, as indicated in Fig. 1, will be the operating point of spacing selection [26]. The experimentally confirmed inter-relationship between the lamellar spacing λ, growth rate V and the undercooling T in eutectic system implies that a mechanism is available for changing the lamellar spacing when the growth rate and/or T vary. Fig. 1a shows the variation of the undercooling with lamellar spacing according to the minimum undercooling criterion. In Fig. 1, λ e is the extremum lamellar spacing obtained from Eqs. (6.a) (6.c), λ m is the minimum lamellar spacing, λ M is the maximum lamellar spacing both measured on the longitudinal section of the samples and λ a is the average lamellar spacing measured on the transverse section of the samples. When λ is smaller than λ e, the growth will be unstable and when λ is smaller than λ m an overgrowth occur (Fig. 1b) and also when λ becomes greater than the λ M, tip splitting occurs (Fig. 1c) [10]. So that lamellar spacing λ for the steady growth must satisfy λ m < λ a < λ M conditions. For eutectic growth, the T V λ relationships can be predicted by the Jackson Hunt (J H) [12] and Trivedi Magnin Kurz (TMK) [13] theories. It is clear that the maximum spacing must be greater than twice the minimum spacing (λ M 2λ m ), otherwise the new lamella can not catch up [10]. Most studies [12 20] have shown that lamellar terminations are constantly created and move through the structure during eutectic growth. The presence and movement of faults and fault Fig. 1. (a) The schematic plot of average undercooling T vs. lamellar spacing λ for a given growth rate V. The stable and unstable regions, as predicted by the Jackson Hunt theory. (b) The readjustment of local spacing by the positive terminations. (c) The readjustment of local spacing by the negative terminations. lines provide by means of which lamellar spacing changes can occur in response to growth rate fluctuations or a small growth rate change. As can be seen from Fig. 1b and c, in this respect, the role of lamellar faults, and in particular lamellar terminations (positive and negative terminations), has been emphasised [21 23]. The aim of the present work is to experimentally investigate the dependence of the lamellar spacing λ on the solidification parameters (V, T) at a constant temperature gradient and also find out the effect of V on T and to compare the results with the previous experimental results and the existing theories. 2. Experimental procedure The eutectic samples (Cd 67.8 wt.% Sn) were prepared by melting weighed quantities of Cd and Sn of (>99.99%) high purity metals in a graphite crucible which was placed into the vacuum melting furnace [24]. After allowing time for melt homogenisation, the molten alloy was poured into 13 graphite crucibles (250 mm in length 4 mm i.d. and 6.35 mm o.d.) in a hot filling furnace. Then, each specimen was positioned in a Bridgman type furnace in a graphite cylinder (300 mm in length 10 mm i.d. and 40 mm o.d.). After stabilizing the thermal conditions in the furnace under an argon atmosphere, the specimen was growth by pulling it downwards at various growth rates (8.1 165.0 m/s, G constant) by means of different speeded synchronous motors. After 100 120 mm steady state growth of the samples, they were quenched by pulling them rapidly into the water reservoir (see Fig. 2). After metallographic process including mechanical and electropolishing techniques, the microstructures of the specimens were revealed.

E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 173 Fig. 2. Bridgman type directional solidification furnace and its equipments. Microstructures of the specimens were photographed from both transverse and longitudinal sections by means of scanning electron microscopy (SEM) (Fig. 3). 2.1. The measurement of lamellar spacings λ, temperature gradient, G, growth rates, V and the calculation of undercooling, T The lamellar spacings (λ a,λ a,λ m and λ M ) were measured from the photographs (Fig. 3) with a linear intercept method [25]. Where λ a and λ a, λ m, λ M have been measured from transverse and longitudinal sections, respectively. The values of λ a, λ a, λ m and λ M are given in Table 1 and Fig. 4 as a function of V. at a constant G. K-type thermocouples were used for measurement of temperature gradient and growth rate during solidification. All the thermocouple leads were taken to data-logger and computer (see Fig. 2). The thermocouples were both recorded simultaneously for measurement of the temperature gradients on the solid/liquid interface in the liquid by means of data-logger. The details of measurements of G and V are given in refs. [8,24,33 35]. The minimum undercooling values, T, were obtained from Eqs. (6.b) and (6.c) and the detailed T λ curves (Fig. 5) which were plotted by using experimental V and G values with the system parameters K 1, K 2. 3. Result and discussion Cd Sn eutectic specimens were unidirectionally solidified with a constant G (4.35 K/mm), and different V (8.1 165.0 m/ Table 1a The values of lamellar spacings λ, growth rate V and undecooling T for the directionally solidified Cd Sn eutectic system and experimental relationships between λ V and λ T for different V at a constant G (4.35 K/mm) Solidification parameters Lamellar spacings G (K/mm) V ( m/s) T (K) λ e ( m) λ a ( m) λ a ( m) λ m ( m) λ M ( m) 4.35 ± 0.1 8.1 0.41 2.16 ± 0.20 2.19 ± 0.21 2.93 ± 0.27 2.61 ± 0.25 3.59 ± 0.33 16.0 0.58 1.54 ± 0.14 1.67 ± 0.15 2.21 ± 0.22 2.02 ± 0.20 2.77 ± 0.25 41.5 0.93 0.96 ± 0.08 1.05 ± 0.09 1.47 ± 0.15 1.28 ± 0.13 1.94 ± 0.17 82.3 1.32 0.68 ± 0.06 0.76 ± 0.08 1.02 ± 0.09 0.92 ± 0.08 1.39 ± 0.14 165.0 1.86 0.48 ± 0.04 0.51 ± 0.04 0.71 ± 0.06 0.61 ± 0.05 0.89 ± 0.07 The relationships k 1 V 0.50 k 2 V 0.50 k 3 V 0.48 k 4 V 0.46 k 5 V 0.47 k 6 V 0.45 Constant (k) Correlation coefficients (r) k 1 = 0.144 (K m 0.50 s 0.50 ) r 1 = 0.999 k 2 = 4.91 ( m 1.50 s 0.50 ) r 2 = 0.999 k 3 = 6.60 ( m 1.48 s 0.48 ) r 3 = 0.998 k 4 = 8.63( m 1.46 s 0.46 ) r 4 = 0.996 k 5 = 9.55 ( m 1.47 s 0.47 ) r 5 = 0.990 k 6 = 10.28 ( m 1.45 s 0.45 ) r 6 = 0.982 λ: The values of the lamellar spacing obtained from the transverse section of the samples. λ * : The values of the lamellar spacing obtained from the longitudinal section of the samples.

174 E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 Fig. 3. Variation of lamellar spacings at the constant G (4.35 K/mm) and different V of the directionally solidified Cd Sn eutectic alloy (a) longitudinal section, (b) transverse section (V = 8.1 m/s), (c) longitudinal section, (d) transverse section (V = 41.5 m/s), (e) longitudinal section and (f) transverse section (V = 165.0 m/s). s) in order to see the effect of V on the lamellar spacings, λ and the undercooling, T. As can be seen from Fig. 3 during eutectic growth, a large number of eutectic grains can be formed. All grains seem to be oriented parallel to growth direction but usually differed in rotation about the growth axis. The normal of the and planes must be parallel to the polished longitudinal plane [24], however these are not always possible. When the normal of the and planes are not parallel to the longitudinal Table 1b Comparison of the experimental results with the theoretical predictions for Cd 67.8 wt.% Sn eutectic system for different V at a constant G (4.35 K/mm) Dependence of λ on T Dependence of T on V λ e T (K m) λ a T (K m) λ a T (K m) λ2 e V (J H) ( m3 /s) λ 2 a V ( m3 /s) λ 2 a V ( m3 /s) TV 0.50 (K m 0.50 s 0.50 ) 0.89 0.90 1.20 37.79 38.90 69.75 0.144 0.89 0.97 1.28 37.95 44.84 78.16 0.145 0.89 0.98 1.37 38.25 46.05 89.34 0.143 0.90 1.00 1.35 38.06 47.76 84.90 0.146 0.89 0.95 1.32 38.02 42.56 82.10 0.145 0.89 0.96 1.30 38.01 44.02 80.85 0.144 λ m T = 1.16 λ2 m V = 64.05 λ M T = 1.67 λ2 M V = 134.93 The bold values are averaged values.

E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 175 Fig. 4. (a) Variation of lamellar spacings as a function of V at a constant G (V = 4.35 K/mm), (b) comparison of the experimental values with the values obtained by J H eutectic theory for the Cd Sn eutectic alloy. plane, the lamellar spacings λ * observed on the longitudinal plane give larger value than the lamellar spacings λ from the transverse polished plane (Appendix A). As can be seen from Tables 1a and 1b, even some of the λ m values can be higher than the average λ a values. In a longitudinal view, the lamellar spacing seems to be different in each grain because they were cut under different angles θ, to the polished surface. θ a values can be obtained by using the measured λ a and λ a values from Tables 1a and 1b (θ a = 42.7 ± 2.2 ). For that reason, longitudinal sections are inadequate for evaluation of the lamellar spacing without the geometrical correction. It was observed that some Fig. 5. (a) The variation of the calculated T values with the lamellar spacing λ at a constant temperature gradients, G (4.35 K/mm) (higher magnification views of the minimum undecoolings are presented in the inset). (b) The variation of the undercooling T as a function of V at constant G (4.35 K/mm). of the eutectic grains increased with the increasing growth rate for the longitudinal section but the transverse section. So λ a values measured on the transverse section of the sample are more reliable. The results in this work have been compared with the results of the similar works and the values calculated from J H theory [8,19,24,26,27,34,35] and these results are given in Appendix C. For eutectic and near-eutectic composition alloys, the fluidflow effect is negligible [28]. Although fluid-flow doesn t exist

176 E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 in thin samples (<1 mm i.d.), Its effect is small in the bulk samples. Because the density of the liquid also depends on the solute concentration, the rejection of solute modifies the density field within solute layer. If the solute layer is heavier than the solvent (as in Cd Sn) then both the solutal and thermal buoyancy forces are parallel to the gravity vector. Under this ideal case of no horizontal variation of temperature, this arrangement is hydrostatically stable (i.e., fluid motion is negligible), and the transport of solute must be solely due to molecular diffusion along the growth direction [29]. The crucible used in this work is 4 mm inner diameter. So, the fluid-flow effect on lamellar eutectic is negligible. In addition to the above microstructural characteristics, several solidification faults like layer mismatches and lamellar termination were observed. As can be seen from Fig. 1b, the boundary tilts toward the lamella side and a pocked range will appear in liquid in the front of the L interface with finally a new lamella growing in the pocked and a positive termination forming. By this dynamic mechanism, the local spacing will decrease (λ m ). The boundary tilts toward the lamella side and the local L interface disappear with the lamella being overlapped by two neighbour lamella (a negative termination) [21 23]. Despite this microstructures that changed by positive and negative termination mechanism λ m,λ M values were measured as accurately as possible on each specimens. 3.1. The effect of the growth rate on the lamellar spacings Variation in lamellar spacings, λ with V at constant G (4.35 K/mm) are given in Table 1b and shown in Fig. 4a. The variations of λ versus V is essentially linear on the logarithmic scale. As can be seen from Table 1b and Fig. 4a and b, the data form straight lines, the linear regression analysis gives the proportionality equation as, λ = k 2 V n (for the constant G) (7) The values of n exponent for λ e,λ a,λ a,λ m and λ M are equal to 0.50, 0.48, 0.46, 0.47 and 0.45, respectively. It is apparent that the dependence of λ values on the growth rate exponent (average 0.47) was found to be close to the value predicted by J H eutectic theory (0.50). This exponent value ( 0.47) is in good agreement with 0.50 and 0.52 values obtained by Liu [38] for Pb Sn eutectic system and Ravishankar et al. [39] for MnBi Bi eutectic system. Besides, the exponent value ( 0.47) smaller than value of 0.66 obtained by Baragor et al. [40] for Bi Pb eutectic. The experimental measurements in the Cd Sn eutectic system obey the relationships λ 2 V = constant for a constant G, {λ 2 e V = 38.01 m3 /s (calc.), λ 2 a V = 44.02 m3 /s, λ 2 a V = 80.85 m 3 /s, λ 2 m V = 64.05 m3 /s, λ 2 M V = 134.93 m3 /s}. The experimental value (44.02) is very close to value (38.01) calculated from J H eutectic theory. The value of 44.02 m 3 /s is very close to values of (34.6, 34.7, 33.8, 35.10 and 40.61 m 3 /s) obtained by Clark and Elliott [41] and Borland and Elliott [42] for Cd Sn eutectic system, Jordan and Hunt [43],Çadırlı and Gündüz [8] for Pb Sn eutectic system and Kaya et al. [35] for Sn Zn eutectic system, respectively. The λ 2 a V value (44.02 m3 /s) is slightly higher than the results (21.1, 21.8, 23.7 and 19.6 m 3 /s) obtained by Trivedi et al. [19], Moore and Elliot [26], Çadırlı et al. [34] for Pb Cd eutectic system and Whelan and Haworth [36] for Bi-Cd eutectic system respectively. The value of λ 2 a V (44.02 m3 /s) is fairly smaller than the value of 156 m 3 /s obtained by Çadırlı et al. [24] for Al Cu eutectic. As can be seen from these results and Appendix C, λ 2 V values are more closer to each other for the similar eutectic system (Cd Sn, Pb Sn, Sn Zn) than the values of the Al Cu eutectic system. So that, λ 2 V values might be depend on components of the eutectic systems. 3.2. Effect of growth rate on the minimum undercooling Fig. 5 shows the minimum undercooling T, of the solidifying interface was obtained from Eq. (6.c) and T λ curves which were plotted by using the experimental V and G values. Fig. 5a shows the relationship between T and λ for the Cd Sn eutectic system at different V, in a constant G. As can be seen from Fig. 5a the influence of V is certain on the lamellar spacing, λ, and T. T increases with the increasing V, whereas λ e decreases. Although V values increased approximately 20 times, T value increased approximately 4.5 times. Fig. 5b shows the variation of T as a function of V in a constant G. T increases with the increasing V. As can be seen from Table 1 and Fig. 5b, the dependence of T on V and λ can be given as: TV 0.50 = 0.144 K m 0.5 s 0.5 (for constant G) (8a) λ a T = 0.96 K m (for constant G) (8b) The exponent value (0.50) is in good agreement with 0.53, 0.48, 0.50 and 0.50 obtained by Gündüz et al. [33] for Al Si eutectic alloy, Çadırlı et al. [34] for Pb Cd eutectic alloy, Kaya et al. [35] for Sn Zn eutectic alloy and J H eutectic theory Eq. (6.b), respectively. The value (0.144) is in good agreement with 0.133 obtained by Borland and Elliott [42] for the same alloy system. The values of λ a T = 0.96 and TV 0.50 = 0.144 slightly lower than values of λ a T = 1.134 and TV 0.50 = 0.234 obtained by Çadırlı et al. [34] for Pb Cd eutectic and higher than the values of λ a T = 0.529 and TV 0.50 = 0.085 obtained by Kaya et al. [35] for Sn Zn eutectic system. These discrepancies in the values of TV 0.50 and λ a T might be because of the components of eutectic systems. 4. Conclusions 1. The lamellar spacing is strongly dependent on the growth rate, since an increase which occurs in growth rate causes microstructure refinement, which is shown in Table 1a. The highest lamellar spacing was obtained for 8.1 m/s (Fig. 3a and b). On the other hand, when a 165 m/s growth rate was used, the smallest lamellar spacing was obtained (Fig. 3e and f).

E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 177 2. Lamellar spacing decrease inversely as the square root of the growth rate at directionally solidified with a constant G and different V for the Cd Sn eutectic system. The relationship between them were obtained by binary regression analysis as follows: λ a = k 3 V 0.48 (for a constant G)(k 3 = 6.60 m 1.48 s 0.48 ) This exponent value is in good agreement with some other experimental works [38,39]. 3. The bulk growth rate, λ 2 av was calculated by using experimental values and found to be 44.02 m 3 /s which is slightly higher than the J H theoretical value (38.01 m 3 /s). The value of 44.02 m 3 /s is in good agreement with some other experimental studies [8,35,41 43]. 4. Effects of growth rate V on the undercooling T was examined and the relationship between them were obtained as follows, TV 0.50 = 0.144 K m 0.50 s 0.50 (for constant G). The value (0.144) is in good agreement with 0.133 obtained by Borland and Elliott [42] for the same alloy system. Fig. A.1. (a e) The schematic illustration of the lamellar spacings measurements on the longitudinal and transverse sections.

178 E. Çadırlı et al. / Journal of Alloys and Compounds 431 (2007) 171 179 5. The T increases with the increasing growth rate V for a given G, whereas λ e decreases. On the other hand λ a T value was found to be constant (0.96 K m) which is fairly close to some other results in the literature [34,35]. Acknowledgements This project was supported by State Planning Organisation of Turkey (2003K 120880-4). Authors would like to thank to State Planning Organisation of Turkey for their financial support. Appendix A Fig. A.1. Appendix B The physical parameters for Cd Sn eutectic alloy T E (K) 449 [44] m (K (wt.%) 1 ) 2.14 [44] m (K (wt.%) 1 ) 2.07 [44] C E (wt.%) 67.8 [44] C O (wt.%) 94.8 [44] f 0.284 [44] f 0.716 [44] Γ (K m) 0.175 [45] Γ (K m) 0.480 [46] θ ( ) 22.5 [45] θ ( ) 18.43 [47] D ( m 2 /s) 1000 [42] K 1 (K s/ m 2 ) 0.01177 Calculated from the physical parameters K 2 ( m K) 0.4473 Calculated from the physical parameters λ 2 V = K 2 K = 38.0034 m 3 /s 1 Calculated from the physical parameters Appendix C The values of growth rate V, temperature gradient G, lamellar spacing λ, and the experimental relationship between λ V of the directional solidification experiment for some metallic alloys Composition T E (K) Range of G (K/mm) Range of V ( m/s) Range of λ ( m) Relationships λ 2 V ( m 3 /s), TV 0.5 (K m 0.50 s 0.50 ), λ a T (K m) Ref. Cd Sn eutectic 449 4.3 8.1 165 0.51 2.19 λ 2 V = 44.02, λ 2 V = 38.01 This work, J H theory Cd Sn eutectic 449 12.0 3 14 1.6 3.4 λ 2 V = 34.6 [41] Cd Sn eutectic 449 2.0 7 84 0.64 2.22 λ 2 V = 34.7, TV 0.5 = 0.133 [42] Al Cu eutectic 821 1.10 3.84 λ 2 V = 103.0, TV 0.5 = 0.128 Pb Sn eutectic 456 0.5 50 0.55 5.4 λ 2 V = 14.6 [30] Pb Sn eutectic 456 1.1 4.7 9.6 144.9 0.49 1.90 λ 2 V = 35.1 [8] Sn Zn eutectic 471 6.5 8.3 165.1 0.50 2.21 λ 2 V = 40.6, TV 0.50 = 0.085, λ a T = 0.529 [35] Pb Cd eutectic 521 6.4 8.3 163.5 0.38 1.69 λ 2 V = 23.7, TV 0.48 = 0.252, λ a T = 1.13 [34] Pb Cd eutectic 521 7.3 10.9 0.36 13700 0.042 8.50 λ 2 V = 21.1 [19] Pb Cd eutectic 521 λ 2 V = 21.8, T e V 0.50 = 0.047 [26] Al Cu eutectic 821 18.5 26.0 1.1 25 1.82 8.68 λ 2 V = 83.0 [43] Pb Sn eutectic 456 10.0 15.0 6 17 1.41 2.37 λ 2 V = 33.8 Al Cu eutectic 821 5.8 38.0 9.5 483.2 0.57 4.04 λ 2 V = 156.0 [24] Al Cu eutectic 821 7.6 21.6 432 0.62 2.75 λ 2 V = 164.0 [25] References [1] R. Elliott, Eutectic Solidification Processing Crystalline and Glassy Alloys, Butterworths, Guilford, UK, 1983. [2] M. McLean, Directionally Solidified Materials for High Temperature Service, The Metal Society Book, 1983, p. 296. [3] D.M. Stefanescu, G.J. Abbaschian, R.J. Bayuzick, Solidification Processing of Eutectic Alloys, A Publication of the Metallurgical Society, Inc., Ohio, 1988. [4] M.C. Flemings, Solidification processing, Mc Graw Hill, NewYork, 1974. [5] J.M. Liu, Y. Zhou, B. Shang, Acta Metall. 38 (1990) 1625 1630. [6] P. Magnin, J.T. Mason, R. Trivedi, Acta Metall. 39 (1991) 469 480. [7] A. Karma, M. Plapp, JOM 56 (4) (2004) 28. [8] E. Çadırlı, M. Gündüz, J. Mater. Process. Technol. 97 (2000) 74 81. [9] Y.X. Zhuang, X.M. Zhang, L.H. Zhu, Z.Q. Hu, Sci. Technol. Adv. Mater. 2 (2001) 37 39. [10] J.D. Hunt, Sci. Technol. Adv. Mater. 2 (2001) 147 155. [11] Y.J. Chen, S.H. Davis, Acta Metall. 50 (2002) 2269 2284. [12] K.A. Jackson, J.D. Hunt, Metall. Soc. A.I.M.E. 236 (1966) 1129 1142. [13] R. Trivedi, P. Magnin, W. Kurz, Acta Metall. 35 (1987) 971 980. [14] R.M. Jordan, J.D. Hunt, J. Cryst. Growth 11 (1971) 141 146. [15] P. Magnin, W. Kurz, Acta Metall. 35 (1987) 1119 1128. [16] P. Magnin, R. Trivedi, Acta Metall. 39 (1991) 453 467. [17] W. Kurz, R. Trivedi, Metall. Trans. 22A (1991) 3051 3057. [18] V. Seetharaman, R. Trivedi, Metall. Trans. 19A (1988) 2955 2964. [19] R. Trivedi, J.T. Mason, J.D. Verhoeven, W. Kurz, Metall. Trans. 22A (1991) 2523 2533. [20] G.E. Nash, J. Cryst. Growth 38 (1977) 155 180. [21] G. Sharma, R.V. Ramanujan, G.P. Tivari, Acta Mater. 48 (2000) 875 889. [22] J.M. Liu, Mater. Sci. Eng. A 157 (1992) 73 78. [23] J.M. Liu, Z.C. Wu, Z.G. Liu, Scr. Metall. 27 (1992) 715 722. [24] E. Çadırlı, A. Ülgen, M. Gündüz, Mater. Trans. JIM 40 (1999) 989 996. [25] A. Ourdjini, J. Liu, R. Elliott, Mater. Sci. Technol. 10 (1994) 312 318. [26] A. Moore, R. Elliott, The Solidification of Metals, Joint Conference, Iron Steel Ins. Publ. 100, 167, Brighton, 1969. [27] H. Cline, Mater. Sci. Eng. 65 (1984) 93 100. [28] J.J. Favier, J. De Goer, Results Spacelab I, ESA SP-222, European Space Agency Special Publications (ESA SP), Paris, 1984, pp. 127 134. [29] P. Mazumder, R. Trivedi, A. Karma, Metall. Mater. Trans. 31A (2000) 1233 1246.

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