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Microstructure characteristics of Cu–Mn alloys during laser surface remelting
Materials Science and Engineering A 386 (2004) 367–374
Microstructure characteristics of Cu–Mn alloys during laser surface remelting Sen Yanga,b,∗ , Yunpeng Sub , Weidong Huangb , Yaohe Zhoub a
Department of Materials Science and Engineering, Inner Mongolia Polytechnic University, Hohhot 010062, PR China State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China
b
Received 28 January 2004; received in revised form 15 July 2004
Abstract Laser surface remelting experiments were conducted on Cu–26.6, 27.3 and 31.4 wt.% Mn alloys to investigate their microstructure evolution and growth rate under an ultra-high temperature gradient. The experimental results showed that the microstructure of Cu–26.6 wt.% Mn alloy changed from cell to dendrite, super-fine cell and segregation-free solid with increase of growth rate. No dendrite growth appeared in the whole range of growth rate for Cu–27.3 wt.% Mn and Cu–31.4 wt.% Mn alloys which fully grew in cellular form. The elongated cellular structure appeared before high-velocity absolute stability was reached in Cu–31.4% Mn alloy, which showed a symmetric behavior in the morphological transformation in both limits of the absolute stability and the low rate interface morphological stability. The critical rates of absolute stability for Cu–31.4, 27.3 and 26.6 wt.% Mn alloys were 113.3, 212.6 and 260.5 mm/s, respectively, which was in reasonable agreement with those predicted by M–S theory. © 2004 Elsevier B.V. All rights reserved. Keywords: Laser surface melting; Elongated cell; Absolute stability; Cu–Mn alloys
1. Introduction Solidification is one of the most important phenomena during materials processing, therefore, research on solidification phenomenon and processing theory are central to materials science and engineering and still attract materials scientists’ and physical metallurgists’ attention. In the past four decades, important advances have been made in our fundamental understanding of solidification microstructures. In the 1960s, Mullins and Sekerka [1] first described the well-known linear kinetic theory of interface stability for a dilute binary system and low Peclet number, which predicts that the probability of the high-velocity absolute stability. Since then, interface morphologic stability theory has been developed. In the 1980s, Trivedi and Kurz [2] extended the linear stability theory for ∗ Corresponding author. Present address: Department of Materials Processing, Graduate School of Engineering, Tohoku University, Aoba-yama 02, Sendai 980-8579, Japan. Tel.: +81 22 217 7353; fax: +81 22 217 7352. E-mail address: [email protected] (S. Yang).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.08.005
large Peclet numbers, while Coriell et al. [3] and Ludwig et al. [4] applied it to multi-component alloy systems. In order to investigate the microstructure evolution from low-velocity planar growth to high-velocity planar growth, many experiments have been performed in the past four decades. Although major progress on microstructure evolution has been made, theoretical and experimental research has been focused on constrained growth at low or medium growth rate and temperature gradient. Until now, there have been few experimental investigations into microstructure evolution at rapid solidification with ultra-high temperature gradient, especially near the absolutely stable point. This has mainly been due to difficulties entailed in reaching a high enough solidification rate and temperature gradient using conventional directional solidification techniques. Trivedi et al. [5] investigated the solidification microstructure in the transparent carbon–tetrabromide system at high velocities within thin cells and observed a transition from dendritic to microcellular morphology when the interface was accelerated. However, they could not reach sufficiently high velocities to
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observe the restabilization of the plane front. Ludwig and Kurz [6] observed the morphological transition from a cellular to a planar interface at high solidification velocities in the succinonitrite–argon system. Within the limits of uncertainties with respect to the materials properties and the thermal gradient, good correspondence between experimental results on plane front transition and linear stability theory existed. Boettinger et al. [7] obtained cell-free structures in rapidly solidified Ag–Cu alloys by electron beam surface remelting while Juarez-Islas et al. [8,9] reported achieving absolute stability growth in Al–Mn alloys but did not give their structure characteristics. Banded structure is a novel microstructure, which has been observed in many alloy systems, such as Al–Cu [10–12], Al–Fe [13], Al–Zr [14], Al–Pd [15], and Ag–Cu [16], prepared by various rapid solidification processes, including splat quenching, melt spinning, electron beam, and laser resolidification. Recently, several phenomenological models have been put forward to qualitatively explain the formation mechanism of banded structures [17–22]. However, several questions need to be investigated further, including (1) what parameters affect band spacing; (2) and whether a banded structure is attainable for a given alloy. Laser surface remelting has been extensively used in investigation of the microstructure evolution for its special advantages [23,24]. During laser surface remelting, there is an extremely high temperature gradient (>106 K/m) in the laser molten pool, which leads to directional growth of various microstructures. The local growth rate Vs and the corresponding microstructure can be determined directly by Vs = Vb cos θ, Vb is the scanning velocity of laser beam, and θ the angle between the scanning velocity and the normal of the solid/liquid interface. From the bottom to the top of the molten pool, the solidification rate varies from zero to a maximum, which themselves depend upon the processing parameters (laser beam scanning velocity and output power of laser). This permits the microstructure evolution to be observed, over a wide range of growth rate, in one trace. Due to the negative slope of liquidus and solidus lines, larger equilibrium distribution coefficient, and their excellent possibility of preparation, near azeotropic Cu–Mn alloys (Mn < 32.8 wt.%) were chosen as proper model alloys for the investigation of different morphologies. The aim of this paper is to investigate the microstructure evolution of Cu–Mn alloys in the whole range of growth rate using laser surface remelting, especially the microstructure characteristics near the absolute stability limit.
Table 1 Laser processing parameters (beam diameter 0.3 mm, gas flow of 5 L/min) Laser power (W)
Scanning rate (mm/s)
1500 2000 3000
5–25 25–100 100–1500
120 mm rectangular copper mould with alumina coatings. All of these alloys lie in the left of the azeotropic point of Cu–Mn binary alloy phase diagram (k < 1) [25]. In order to remove the inhomogeneities on the surface, the outer 3 mm layer of metal was machined off and specimens of 6 mm square and 30 mm long were cut from the remaining ingot for use in laser remelting. In order to minimize the reflection for the laser beam and to obtain a similar surface quality, all specimens were ground up to 800 grit SiC paper and cleaned in methanol prior to laser surface remelting. When the scanning velocity was more than 200 mm/s, the specimens were previously remelted at output power of 1500 W and scanning velocity of 24.1 mm/s with a beam diameter of 1 mm to reduce the effect of coarse base grain on the microstructures of the molten pool. 2.2. Laser processing Laser surface remelting experiments were performed on a 5 kW CO2 laser (Rofin-Sinar RS 850). The normally incident laser beam was focused to a spot diameter of 0.3 mm. During laser remelting, a continuous flow of 5 L/min of helium was blown to the melted zone to prevent heavy oxidation. Laser beam scanning velocities (Vb ) between 5.1 and 1500 mm/s were used in this study, and the detailed laser processing parameters are summarized in Table 1. 2.3. Microstructure characteristics Microstructure analysis was performed by standard metallographic techniques after sectioning the specimens and etching them in a copper–ammonium chloride solution. The longitudinal cross-sections cut along the center of the lasermelted zones were examined by SEM. After taking a transverse cross-section of the cellular structure, the cellular spacing and their distribution range were measured using a Cambridge Quantimet 500 Image Processing and Analysis System.
3. Experimental results 2. Experimental details
3.1. Microstructures of Cu–26.6 wt.% Mn
2.1. Specimen preparation
Fig. 1 shows the microstructure of as-cast Cu–26.6 wt.% Mn alloy. It can be seen that the microstructure was very coarse, and the average grain size was more than 200 m. However, after laser surface remlting, the microstructures of the molten pool were apparently refined. Fig. 2(a) is the typi-
Cu–26.6, 27.3 and 31.4 wt.% Mn alloys were prepared by vacuum induction melting 99.99 wt.% Cu and 99.9 wt.% Mn in an alumina crucible and pouring into a 20 mm × 120 mm ×
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3.2. Microstructures of Cu–27.3 wt.% Mn Fig. 3 shows the microstructures obtained for Cu–27.3 wt.% Mn alloy at growth rates of 11.0, 127.5, 187.3 and 212.6 mm/s, respectively. It can be seen that the microstructure of Cu–27.3 wt.% Mn alloy changed from cell, to superfine cell, then irregular structure, at last character-free structure (segregation-free solid solution) with increase of growth rate under ultra-high temperature gradient condition (G > 106 K/m), which resulted from absolute stability growth of the S/L (solid/liquid) interface. It is noted that dendrite growth did not appear in whole range of growth rate for this alloy; neither did banded structure near the limit of absolute stability. Fig. 1. As-cast microstructure of Cu–26.6 wt.% Mn alloy.
cal cell at growth rate of 1.36 mm/s, which directly grew from the bottom of the molten pool. With increasing growth rate, the microstructure became dendrite as shown in Fig. 2(b). The critical rate of cellular/dendritic transform was 1.85 mm/s, which was determined by experiment. With the further increase of growth rate, the microstructure transformed into cell again. Fig. 2(c) shows the typical superfine cell at a high growth rate. When growth rate was higher than 260.5 mm/s, the microstructure was of a segregation-free solid solution, as shown in Fig. 2(d).
3.3. Microstructures of Cu–31.4 wt.% Mn Fig. 4 shows the microstructures obtained for Cu–31.4 wt.% Mn alloy at various growth rates. It can be observed that the microstructures of Cu–31.4 wt.% Mn were different from those of Cu–27.3 wt.% Mn and Cu–26.6 wt.% Mn alloys. At a low growth rate, an elongated cellular microstructure was obtained, as showed in Fig. 4(a). With increase of growth rate, the microstructure changed from elongated cell to regular cell, Fig. 4(b) shows the regular cellular structure. When the growth rate increased to a certain extent, the microstructure became elongated cell (Fig. 4(c)) again. With the further increase of growth rate, the microstructure transformed into planar-like structure
Fig. 2. Microstructures of Cu–26.6 wt.% Mn alloy from the longitudinal section of the molten pool at various growth rates: (a) Vs = 1.36 mm/s; (b) Vs = 5.61 mm/s; (c) Vs = 57.4 mm/s; (d) Vs = 260.5 mm/s.
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Fig. 3. Microstructures of Cu–27.3 wt.% Mn alloy from the longitudinal section of the molten pool at various growth rates: (a) Vs = 11.0 mm/s; (b) Vs = 127.5 mm/s; (c) Vs = 187.3 mm/s; (d) Vs = 212.6 mm/s.
(shallow cell), as showed in Fig. 4(d). When growth rate was higher than 113.3 mm/s, the absolute stable planar interface was obtained, see Fig. 4(e). It can also be found that there was no dendrite growth in whole range of growth rate for this alloy, and no banded structure appeared near the limit of absolute stability.
4. Discussions 4.1. Absence of banded structure Kubin and Estrin [26] pointed out that the stability of one phase or pattern was determined by its S/L interface temperature under constrained crystal growth conditions. The phase or pattern with higher interface temperature is much more stable in dynamics than that with lower interface temperature. The S/L interface temperature of one phase or pattern as a function of growth rate and temperature gradient was called as interface response function. For a single-phase alloy, the interface response function represented the relationship between interface temperature of the different patterns with respect to the growth rate and temperature gradient. To gain a better insight into the growth mechanism, the same analysis method as used by Carrard et al. [20] has been applied as follows. Firstly, according to the rapid dendritic growth model derived by Kurz et al. [27], the dendritic tip temperature can be
given as: Td = TM + CL∗ mV −
RTM /Sf − ΓK Vs /V0
(1)
where Γ is the Gibbs–Thomson coefficient, K the curvature of the dendrite tip, mV the velocity-dependent liquidus slope defined by Boettinger et al. [28], Vs the growth rate of the S/L interface, R the gas constant, V0 the limit of crystallization, which, for pure components, has an upper limit in the order of the velocity of sound, TM the melting temperature of the pure component, Sf the molar entropy of fusion, CL∗ the liquid solute concentration at the dendrite tip, and can be evaluated from the Ivantsov solution as CL∗ = C0 /(1 − (1 − k) Iv(P)), Iv(P) = P exp(P)E1 (P) is the Ivantsov function and E1 the exponential integral function, P the Peclet number, and k the solute distribution coefficient. Secondly, the growth temperature of a single-phase plane front described by Boettinger and Coriell [29] can be given by: Tp = TM + CL∗ mV −
RTM /Sf Vs /V0
(2)
Where CL∗ = C0 /k is the concentration at the solid/liquid interface, and C0 the bulk alloy concentration. Based on the above-mentioned models, the S/L interface growth temperature can be calculated. Fig. 5 gives the calculated S/L interface temperature as a function of growth rate of Cu–27.3% Mn alloy. At steady state (low velocity), Tp
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Fig. 4. Microstructures of Cu–31.4 wt.% Mn alloy from the longitudinal section of the molten pool at various growth rates: (a) Vs = 2.19 mm/s; (b) Vs = 11.43 mm/s; (c) Vs = 85.3 mm/s; (d) Vs = 95.8 mm/s; (e) Vs = 113.3 mm/s.
corresponds to the solidus temperature for the composition C0 . At high velocity, Tp first increases due to solute trapping, reaches a maximum Tmax and then decreases because atom attachment kinetics becomes dominant. The maximum
of Tp corresponds to the limit above which the plane front becomes unconditionally stable. The growth rate VTmax corresponding to the maximum of Tp can be calculated by Eq. (3) [30]. Pi3 + Pi2 = X0 (V0 /VD )
Fig. 5. Interface response function for plane front growth Tp and cellular/dendritic growth Td .
(3)
WherePi = VTmax /VD , VD = DL /a0 , X0 the molar fraction of solute, DL the solute diffusion coefficient in liquid, and a0 the distance of the order of the thickness of the interface. When velocity Vs < Vc = GD/T0 , the limit of constitutional undercooling, the plane front growth is stable. Between Vc and the absolute stability limit, Va = T0 DL /kΓ , the plane front is morphologically unstable and is replaced by a cellular/dendritic front. Between Va and VTmax , the driving force decreases with increasing velocity, which will lead to the oscillatory instabilities known as banding [20]. In fact, the so-called banded structure was never observed in the experiments for any of the alloys. This demonstrated that the negative slope between Va and VTmax is an essential condition
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rather than a sufficient condition for the formation of banded structure. Coriell and Sekerka [17] modified M–S theory by introducing non-equilibrium effects into the linear stability analysis of the plane front and found that a cellular oscillatory instability could occur when non-equilibrium effect was taken into account. Merchant and Davis [18,31] extended the abovementioned model by taking into account the effects of growth rate on segregation coefficient and liquidus slope and using the frozen temperature approximation (FTA), and predicted the similar results to those Coriell and Sekerka did. They found that the steady-state plane front could evolve into two types of instabilities: (1) morphological instability (forming steady-state structures such as cells or dendrites) and (2) oscillatory instability. Merchant and Davis conjectured that the bands observed in the solid were the result of an interaction of the oscillatory and cellular instabilities coexist. Thus, the banded structures should occur only where the two instabilities coexist. Fig. 6 is the oscillatory and steady branches of the neutral stability curve for Cu–Mn system with the thermal gradient G = 106 K/m. The planar interface is linearly stable to the right of the curves and unstable to the left. The rightmost curve is the steady branch, while the leftmost is the oscillatory one. The vertically hatched region is the coexistence sector, only in which bands could occur. The vertical, dashed line denoted the concentration, 26.06 wt.%, above which no bands can appear. Owing to the fact that the used alloys posited in the right side of the critical composition 26.06 wt.%, therefore, no data point should posit in the coexistence region, and no bands should exist, which was consistent with the experimental results obtained. 4.2. Elongated cell Elongated cells have been observed in many kinds of alloys, such as Pb–Sn [32], Pb–Sb [33], Pb–30 wt.% Tl [34], Al–Zn [35], and so on. Previous research conducted by Tiller and Rutter [32] showed that elongated cell was firstly formed
Fig. 6. The oscillatory and steady branches of the neutral stability curve for Cu–Mn system with the temperature gradient G = 106 K/m.
when the planar interface just became unstable for Pb–Sn, Pb–Ag, and Pb–Au alloys, and the research conducted by Morris and Winegard [33] showed that the formation of elongated cell was related to anisotropy of alloys. When the crystal growth direction was oriented along or near the [1 0 0] or [1 1 1] directions, a “pocky” shape structure was formed. When crystals grew along the [1 1 0] direction, an elongated cell was formed. But in the above-mentioned experiments only solidification behavior near the limit of constitutional supercooling for some alloys was considered; it did not mean that an elongated cell would certainly appear after the planar interface became unstable too. Our experiments showed that not only could an elongated cell occur near the limits of the constitutional supercooling, but it could also occur near the limit of absolute stability. This meant that the interface morphology transformation showed symmetry to a certain degree during solidification, such as the high-velocity cellular structure corresponding to the low-velocity cellular structure, and the low-velocity planar interface corresponding to the high-velocity absolute stable planar interface. After that, the elongated cell transformed into one kind of shallow cell, and finally transformed into the absolute stable planar interface. In another word, from regular cell to the absolute stable planar interface, the solid/liquid interface experienced three steps: regular cell to elongated cell, shallow cell, and the absolute stable planar interface, which was in agreement with Ludwig’s in situ observation [36]. 4.3. Full dendrite growth Hunt and Lu [37] analyzed the diffusion field of cellular/dendritic arrays using numerical simulation, and found that the cellular structure could stably exist not only in low growth rate regions, but also in high growth rate regions. In the low growth rate region, a transition from cellular to cellular/dendritic microstructure will occur, which is the process of formation and development of sidebranches. However, in the high growth rate region, an inverse transition from cellular/dendritic to cellular microstructure will occur, which is the process of disappearance and shrinkage of sidebranches. On one hand, sidebranching is caused by the intrinsic morphological instability of the cellular tip, which is the driving force for sidebranching. On the other hand, sidebranching needs a certain time and space condition. The first sidebranch perturbation would be permitted to emerge and to develop in the local space and time interval. Under low temperature gradient and growth rate conditions, there is enough time and space for the emergence and development of sidebranches. However, given that the mushy zone will become much narrower under a high temperature gradient condition, even though the interface marginal instability has still forced the cellular tips to sidebranch at a high growth rate, yet the sidebranching will hardly emerge and develop [38]. In fact, the constitutional supercooling zone is very narrow under a high temperature gradient. Under this condition, not only cannot cellular tips advance well, but also the side perturbation in the end of cells
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is fully restrained. This will subsequently lead to that S/L interface grows in cell in the whole range of growth rate. During laser surface remelting, there existed a high temperature gradient in the molten pool, generally more than 106 K/m, and the intervals of liquidus and solidus of Cu–27.3 wt.% Mn and Cu–31.4 wt.% Mn alloy were narrower, therefore microstructures of Cu–27.3 wt.% Mn and Cu–31.4 wt.% Mn alloys grew in cell, and no dendrites appeared within whole range of growth rate. 4.4. Absolute stability M–S interface stability theory [1] predicts that there exists a critical velocity for an alloy, above which the S/L interface will become stable again and the resulting microstructure will be a segregation-free solid solution. The critical condition for this to occur is given by: Va =
T0 DL kΓ
(4)
Under rapid solidification conditions, the S/L interface is far from equilibrium, and solute atoms tend to build up in front of the S/L interface. Owing to that there is insufficient time to diffuse, these solute atoms will inevitably be captured by the rapidly advancing S/L interface, at last solidify to form the segregation-free structure. This phenomenon is termed “solute trapping”. The critical velocity to realize “solute trapping” is [39]: Vt =
DL a0
(5)
When Va < Vt , the plane front growth results in a segregation-free structure. Inversely, when Va > Vt , it is solute trapping that dominates growth. Based on these, it can be found that there exists a critical composition C0crit for an alloy, which can be easily obtained by setting Va = Vt , C0crit = k2 Γ/m(1 − k)a0 . When C0 < C0crit , absolute stability planar interface growth results in segregation-free structure. For Cu–26.6, 27.3 and 31.4 wt.% Mn alloys, the critical composition was 165%, 226%, and 1120%, respectively, which is considerably in excess of 100%. Therefore, for these three kinds of alloys, it was the absolutely stable planar interface growth at high growth rate that led to the formation of the segregation-free structure. The theoretical critical velocities to attain absolute stability for Cu–26.6, 27.3 and 31.4 wt.%
Table 2 Critical velocity of absolute stability of Cu–Mn alloys Composition (wt.% Mn)
Va (mm/s)
Va (mm/s)
Voa (mm/s)
Voa /Va
Voa /Va
26.6 27.3 31.4
116 76.2 42.1
174.1 121.9 75.9
260.5 212.6 113.3
2.25 2.79 2.45
1.49 1.74 1.36
Note: Va is the theoretical value to attain the absolutely stable planar interface growth when k = 0.5.
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Table 3 Thermophysical parameters of Cu–Mn alloys [40] Property
Value
Gibbs–Thomson coefficient, Γ (mK) Diffusion coefficient (liq.), DL (m2 s−1 )
3 × 10−7 1.75 × 10−9
Liquidus slope, m (K(wt.%)−1 ) Cu–26.6 wt.% Mn Cu–27.3 wt.% Mn Cu–31.4 wt.% Mn
−1.71 −1.92 −0.434
Distribution coefficient, k Cu–26.6 wt.% Mn Cu–27.3 wt.% Mn Cu–31.4 wt.% Mn
0.75 0.80 0.90
Mn alloys are listed in Table 2. Thermophysical parameters used for the calculation are given in Table 3. In Table 2, it can be seen that the experimentally determined values of critical velocity (Voa ) for absolutely stable planar interface growth are 2.25, 2.79 and 2.45 times higher than those (Va ) predicted by M–S theory for Cu–26.6, 27.3 and 31.4 wt.% Mn alloys, respectively. The main reason for these differences may, in part, be attributed to uncertainties in the values of k, DL and Γ . For example, when k = 0.5, the discrepancy between the observed critical velocity (Voa ) and that (Va ) predicted by M–S theory would be virtually compensated. Generally speaking, if the difference between the calculated value and the experimental one is less than one order of magnitude, one can say that the experimental result is reasonable agreement with the theoretical value. Therefore, it can be concluded that, in view of the uncertainty of the thermophysical parameters, M–S theory can reasonably predict the critical velocity of absolute stability.
5. Conclusions (1) With the increase of growth rate, the microstructure of Cu–26.6 wt.% Mn alloy evolved from planar interface to cell, dendrite, super fine cell, and featureless structure. (2) With the increase of growth rate, the microstructure of Cu–27.3 wt.% Mn alloy evolved from planar interface to cell, super fine cell, regular structure, and featureless structure. Under the high temperature gradient condition, this alloy grew in full cell, and no dendrite appeared in whole range of growth rate. (3) With the increase of growth rate, the microstructure of Cu–31.4 wt.% Mn alloy evolved from planar interface to elongated cell, regular cell, elongated cell, shallow cell, and featureless structure. It showed that solid/liquid interface morphology evolution was symmetric. (4) The featureless structure formed under laser rapid solidification condition resulted from absolutely stable planar interface growth rather than solute trapping. The observed critical velocities of absolute stability of Cu–26.6 wt.% Mn, Cu–27.4 wt.% Mn and Cu–31.4 wt.%
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Mn alloys are 260.5, 212.6 and 113.3 mm/s, respectively, which was in reasonable agreement with those predicted by M–S theory. (5) The negative slope between Va and VTmax was only an essential condition for the formation of banded structure, rather than the sufficient condition. Acknowledgements One of the authors (S. Yang) is grateful to Japan Society for the Promotion of Science for offering a JSPS fellowship. The authors would like to express their gratitude to National Science Foundation (Grant No. 59771054) for financial support. References [1] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 65 (1964) 444. [2] R. Trivedi, W. Kurz, Acta Metall. 34 (1986) 1663. [3] S.R. Coriell, G.B. McFadden, P.W. Voohees, R.F. Sekerka, J. Cryst. Growth 82 (1987) 295. [4] A. Ludwig, B. Prustal, D.M. Herlach, Mater. Sci. Eng. A 318 (2001) 337. [5] R. Trivedi, J.A. Sekhar, V. Seetharaman, Metall. Trans. A 23 (1989) 769. [6] A. Ludwig, W. Kurz, Acta Mater. 44 (1996) 3643. [7] W.J. Boettinger, D. Shechtman, R.J. Schaefer, F.S. Biancaniello, Metall. Trans. A 15 (1984) 55. [8] J.A. Juarez-Islas, H. Jones, W. Kurz, Mater. Sci. Eng. 98 (1988) 201. [9] J.A. Juarez-Islas, H. Jones, Acta Metall. 35 (1987) 499. [10] T. Sato, et al., J. Jpn. Inst. Met. 48 (1984) 748. [11] S.C. Gill, W. Kurz, Acta Metall. Mater. 41 (1993) 3563. [12] M. Zimmermann, et al., Mater. Sci. Eng. A 134 (1991) 1278. [13] M. Gremaud, M. Carrad, W. Kurz, Acta Metall. Mater. 38 (1990) 2587.
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Microstructure characteristics of Cu–Mn alloys during laser surface remelting Sen Yanga,b,∗ , Yunpeng Sub , Weidong Huangb , Yaohe Zhoub a
Department of Materials Science and Engineering, Inner Mongolia Polytechnic University, Hohhot 010062, PR China State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China
b
Received 28 January 2004; received in revised form 15 July 2004
Abstract Laser surface remelting experiments were conducted on Cu–26.6, 27.3 and 31.4 wt.% Mn alloys to investigate their microstructure evolution and growth rate under an ultra-high temperature gradient. The experimental results showed that the microstructure of Cu–26.6 wt.% Mn alloy changed from cell to dendrite, super-fine cell and segregation-free solid with increase of growth rate. No dendrite growth appeared in the whole range of growth rate for Cu–27.3 wt.% Mn and Cu–31.4 wt.% Mn alloys which fully grew in cellular form. The elongated cellular structure appeared before high-velocity absolute stability was reached in Cu–31.4% Mn alloy, which showed a symmetric behavior in the morphological transformation in both limits of the absolute stability and the low rate interface morphological stability. The critical rates of absolute stability for Cu–31.4, 27.3 and 26.6 wt.% Mn alloys were 113.3, 212.6 and 260.5 mm/s, respectively, which was in reasonable agreement with those predicted by M–S theory. © 2004 Elsevier B.V. All rights reserved. Keywords: Laser surface melting; Elongated cell; Absolute stability; Cu–Mn alloys
1. Introduction Solidification is one of the most important phenomena during materials processing, therefore, research on solidification phenomenon and processing theory are central to materials science and engineering and still attract materials scientists’ and physical metallurgists’ attention. In the past four decades, important advances have been made in our fundamental understanding of solidification microstructures. In the 1960s, Mullins and Sekerka [1] first described the well-known linear kinetic theory of interface stability for a dilute binary system and low Peclet number, which predicts that the probability of the high-velocity absolute stability. Since then, interface morphologic stability theory has been developed. In the 1980s, Trivedi and Kurz [2] extended the linear stability theory for ∗ Corresponding author. Present address: Department of Materials Processing, Graduate School of Engineering, Tohoku University, Aoba-yama 02, Sendai 980-8579, Japan. Tel.: +81 22 217 7353; fax: +81 22 217 7352. E-mail address: [email protected] (S. Yang).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.08.005
large Peclet numbers, while Coriell et al. [3] and Ludwig et al. [4] applied it to multi-component alloy systems. In order to investigate the microstructure evolution from low-velocity planar growth to high-velocity planar growth, many experiments have been performed in the past four decades. Although major progress on microstructure evolution has been made, theoretical and experimental research has been focused on constrained growth at low or medium growth rate and temperature gradient. Until now, there have been few experimental investigations into microstructure evolution at rapid solidification with ultra-high temperature gradient, especially near the absolutely stable point. This has mainly been due to difficulties entailed in reaching a high enough solidification rate and temperature gradient using conventional directional solidification techniques. Trivedi et al. [5] investigated the solidification microstructure in the transparent carbon–tetrabromide system at high velocities within thin cells and observed a transition from dendritic to microcellular morphology when the interface was accelerated. However, they could not reach sufficiently high velocities to
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observe the restabilization of the plane front. Ludwig and Kurz [6] observed the morphological transition from a cellular to a planar interface at high solidification velocities in the succinonitrite–argon system. Within the limits of uncertainties with respect to the materials properties and the thermal gradient, good correspondence between experimental results on plane front transition and linear stability theory existed. Boettinger et al. [7] obtained cell-free structures in rapidly solidified Ag–Cu alloys by electron beam surface remelting while Juarez-Islas et al. [8,9] reported achieving absolute stability growth in Al–Mn alloys but did not give their structure characteristics. Banded structure is a novel microstructure, which has been observed in many alloy systems, such as Al–Cu [10–12], Al–Fe [13], Al–Zr [14], Al–Pd [15], and Ag–Cu [16], prepared by various rapid solidification processes, including splat quenching, melt spinning, electron beam, and laser resolidification. Recently, several phenomenological models have been put forward to qualitatively explain the formation mechanism of banded structures [17–22]. However, several questions need to be investigated further, including (1) what parameters affect band spacing; (2) and whether a banded structure is attainable for a given alloy. Laser surface remelting has been extensively used in investigation of the microstructure evolution for its special advantages [23,24]. During laser surface remelting, there is an extremely high temperature gradient (>106 K/m) in the laser molten pool, which leads to directional growth of various microstructures. The local growth rate Vs and the corresponding microstructure can be determined directly by Vs = Vb cos θ, Vb is the scanning velocity of laser beam, and θ the angle between the scanning velocity and the normal of the solid/liquid interface. From the bottom to the top of the molten pool, the solidification rate varies from zero to a maximum, which themselves depend upon the processing parameters (laser beam scanning velocity and output power of laser). This permits the microstructure evolution to be observed, over a wide range of growth rate, in one trace. Due to the negative slope of liquidus and solidus lines, larger equilibrium distribution coefficient, and their excellent possibility of preparation, near azeotropic Cu–Mn alloys (Mn < 32.8 wt.%) were chosen as proper model alloys for the investigation of different morphologies. The aim of this paper is to investigate the microstructure evolution of Cu–Mn alloys in the whole range of growth rate using laser surface remelting, especially the microstructure characteristics near the absolute stability limit.
Table 1 Laser processing parameters (beam diameter 0.3 mm, gas flow of 5 L/min) Laser power (W)
Scanning rate (mm/s)
1500 2000 3000
5–25 25–100 100–1500
120 mm rectangular copper mould with alumina coatings. All of these alloys lie in the left of the azeotropic point of Cu–Mn binary alloy phase diagram (k < 1) [25]. In order to remove the inhomogeneities on the surface, the outer 3 mm layer of metal was machined off and specimens of 6 mm square and 30 mm long were cut from the remaining ingot for use in laser remelting. In order to minimize the reflection for the laser beam and to obtain a similar surface quality, all specimens were ground up to 800 grit SiC paper and cleaned in methanol prior to laser surface remelting. When the scanning velocity was more than 200 mm/s, the specimens were previously remelted at output power of 1500 W and scanning velocity of 24.1 mm/s with a beam diameter of 1 mm to reduce the effect of coarse base grain on the microstructures of the molten pool. 2.2. Laser processing Laser surface remelting experiments were performed on a 5 kW CO2 laser (Rofin-Sinar RS 850). The normally incident laser beam was focused to a spot diameter of 0.3 mm. During laser remelting, a continuous flow of 5 L/min of helium was blown to the melted zone to prevent heavy oxidation. Laser beam scanning velocities (Vb ) between 5.1 and 1500 mm/s were used in this study, and the detailed laser processing parameters are summarized in Table 1. 2.3. Microstructure characteristics Microstructure analysis was performed by standard metallographic techniques after sectioning the specimens and etching them in a copper–ammonium chloride solution. The longitudinal cross-sections cut along the center of the lasermelted zones were examined by SEM. After taking a transverse cross-section of the cellular structure, the cellular spacing and their distribution range were measured using a Cambridge Quantimet 500 Image Processing and Analysis System.
3. Experimental results 2. Experimental details
3.1. Microstructures of Cu–26.6 wt.% Mn
2.1. Specimen preparation
Fig. 1 shows the microstructure of as-cast Cu–26.6 wt.% Mn alloy. It can be seen that the microstructure was very coarse, and the average grain size was more than 200 m. However, after laser surface remlting, the microstructures of the molten pool were apparently refined. Fig. 2(a) is the typi-
Cu–26.6, 27.3 and 31.4 wt.% Mn alloys were prepared by vacuum induction melting 99.99 wt.% Cu and 99.9 wt.% Mn in an alumina crucible and pouring into a 20 mm × 120 mm ×
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3.2. Microstructures of Cu–27.3 wt.% Mn Fig. 3 shows the microstructures obtained for Cu–27.3 wt.% Mn alloy at growth rates of 11.0, 127.5, 187.3 and 212.6 mm/s, respectively. It can be seen that the microstructure of Cu–27.3 wt.% Mn alloy changed from cell, to superfine cell, then irregular structure, at last character-free structure (segregation-free solid solution) with increase of growth rate under ultra-high temperature gradient condition (G > 106 K/m), which resulted from absolute stability growth of the S/L (solid/liquid) interface. It is noted that dendrite growth did not appear in whole range of growth rate for this alloy; neither did banded structure near the limit of absolute stability. Fig. 1. As-cast microstructure of Cu–26.6 wt.% Mn alloy.
cal cell at growth rate of 1.36 mm/s, which directly grew from the bottom of the molten pool. With increasing growth rate, the microstructure became dendrite as shown in Fig. 2(b). The critical rate of cellular/dendritic transform was 1.85 mm/s, which was determined by experiment. With the further increase of growth rate, the microstructure transformed into cell again. Fig. 2(c) shows the typical superfine cell at a high growth rate. When growth rate was higher than 260.5 mm/s, the microstructure was of a segregation-free solid solution, as shown in Fig. 2(d).
3.3. Microstructures of Cu–31.4 wt.% Mn Fig. 4 shows the microstructures obtained for Cu–31.4 wt.% Mn alloy at various growth rates. It can be observed that the microstructures of Cu–31.4 wt.% Mn were different from those of Cu–27.3 wt.% Mn and Cu–26.6 wt.% Mn alloys. At a low growth rate, an elongated cellular microstructure was obtained, as showed in Fig. 4(a). With increase of growth rate, the microstructure changed from elongated cell to regular cell, Fig. 4(b) shows the regular cellular structure. When the growth rate increased to a certain extent, the microstructure became elongated cell (Fig. 4(c)) again. With the further increase of growth rate, the microstructure transformed into planar-like structure
Fig. 2. Microstructures of Cu–26.6 wt.% Mn alloy from the longitudinal section of the molten pool at various growth rates: (a) Vs = 1.36 mm/s; (b) Vs = 5.61 mm/s; (c) Vs = 57.4 mm/s; (d) Vs = 260.5 mm/s.
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Fig. 3. Microstructures of Cu–27.3 wt.% Mn alloy from the longitudinal section of the molten pool at various growth rates: (a) Vs = 11.0 mm/s; (b) Vs = 127.5 mm/s; (c) Vs = 187.3 mm/s; (d) Vs = 212.6 mm/s.
(shallow cell), as showed in Fig. 4(d). When growth rate was higher than 113.3 mm/s, the absolute stable planar interface was obtained, see Fig. 4(e). It can also be found that there was no dendrite growth in whole range of growth rate for this alloy, and no banded structure appeared near the limit of absolute stability.
4. Discussions 4.1. Absence of banded structure Kubin and Estrin [26] pointed out that the stability of one phase or pattern was determined by its S/L interface temperature under constrained crystal growth conditions. The phase or pattern with higher interface temperature is much more stable in dynamics than that with lower interface temperature. The S/L interface temperature of one phase or pattern as a function of growth rate and temperature gradient was called as interface response function. For a single-phase alloy, the interface response function represented the relationship between interface temperature of the different patterns with respect to the growth rate and temperature gradient. To gain a better insight into the growth mechanism, the same analysis method as used by Carrard et al. [20] has been applied as follows. Firstly, according to the rapid dendritic growth model derived by Kurz et al. [27], the dendritic tip temperature can be
given as: Td = TM + CL∗ mV −
RTM /Sf − ΓK Vs /V0
(1)
where Γ is the Gibbs–Thomson coefficient, K the curvature of the dendrite tip, mV the velocity-dependent liquidus slope defined by Boettinger et al. [28], Vs the growth rate of the S/L interface, R the gas constant, V0 the limit of crystallization, which, for pure components, has an upper limit in the order of the velocity of sound, TM the melting temperature of the pure component, Sf the molar entropy of fusion, CL∗ the liquid solute concentration at the dendrite tip, and can be evaluated from the Ivantsov solution as CL∗ = C0 /(1 − (1 − k) Iv(P)), Iv(P) = P exp(P)E1 (P) is the Ivantsov function and E1 the exponential integral function, P the Peclet number, and k the solute distribution coefficient. Secondly, the growth temperature of a single-phase plane front described by Boettinger and Coriell [29] can be given by: Tp = TM + CL∗ mV −
RTM /Sf Vs /V0
(2)
Where CL∗ = C0 /k is the concentration at the solid/liquid interface, and C0 the bulk alloy concentration. Based on the above-mentioned models, the S/L interface growth temperature can be calculated. Fig. 5 gives the calculated S/L interface temperature as a function of growth rate of Cu–27.3% Mn alloy. At steady state (low velocity), Tp
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Fig. 4. Microstructures of Cu–31.4 wt.% Mn alloy from the longitudinal section of the molten pool at various growth rates: (a) Vs = 2.19 mm/s; (b) Vs = 11.43 mm/s; (c) Vs = 85.3 mm/s; (d) Vs = 95.8 mm/s; (e) Vs = 113.3 mm/s.
corresponds to the solidus temperature for the composition C0 . At high velocity, Tp first increases due to solute trapping, reaches a maximum Tmax and then decreases because atom attachment kinetics becomes dominant. The maximum
of Tp corresponds to the limit above which the plane front becomes unconditionally stable. The growth rate VTmax corresponding to the maximum of Tp can be calculated by Eq. (3) [30]. Pi3 + Pi2 = X0 (V0 /VD )
Fig. 5. Interface response function for plane front growth Tp and cellular/dendritic growth Td .
(3)
WherePi = VTmax /VD , VD = DL /a0 , X0 the molar fraction of solute, DL the solute diffusion coefficient in liquid, and a0 the distance of the order of the thickness of the interface. When velocity Vs < Vc = GD/T0 , the limit of constitutional undercooling, the plane front growth is stable. Between Vc and the absolute stability limit, Va = T0 DL /kΓ , the plane front is morphologically unstable and is replaced by a cellular/dendritic front. Between Va and VTmax , the driving force decreases with increasing velocity, which will lead to the oscillatory instabilities known as banding [20]. In fact, the so-called banded structure was never observed in the experiments for any of the alloys. This demonstrated that the negative slope between Va and VTmax is an essential condition
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rather than a sufficient condition for the formation of banded structure. Coriell and Sekerka [17] modified M–S theory by introducing non-equilibrium effects into the linear stability analysis of the plane front and found that a cellular oscillatory instability could occur when non-equilibrium effect was taken into account. Merchant and Davis [18,31] extended the abovementioned model by taking into account the effects of growth rate on segregation coefficient and liquidus slope and using the frozen temperature approximation (FTA), and predicted the similar results to those Coriell and Sekerka did. They found that the steady-state plane front could evolve into two types of instabilities: (1) morphological instability (forming steady-state structures such as cells or dendrites) and (2) oscillatory instability. Merchant and Davis conjectured that the bands observed in the solid were the result of an interaction of the oscillatory and cellular instabilities coexist. Thus, the banded structures should occur only where the two instabilities coexist. Fig. 6 is the oscillatory and steady branches of the neutral stability curve for Cu–Mn system with the thermal gradient G = 106 K/m. The planar interface is linearly stable to the right of the curves and unstable to the left. The rightmost curve is the steady branch, while the leftmost is the oscillatory one. The vertically hatched region is the coexistence sector, only in which bands could occur. The vertical, dashed line denoted the concentration, 26.06 wt.%, above which no bands can appear. Owing to the fact that the used alloys posited in the right side of the critical composition 26.06 wt.%, therefore, no data point should posit in the coexistence region, and no bands should exist, which was consistent with the experimental results obtained. 4.2. Elongated cell Elongated cells have been observed in many kinds of alloys, such as Pb–Sn [32], Pb–Sb [33], Pb–30 wt.% Tl [34], Al–Zn [35], and so on. Previous research conducted by Tiller and Rutter [32] showed that elongated cell was firstly formed
Fig. 6. The oscillatory and steady branches of the neutral stability curve for Cu–Mn system with the temperature gradient G = 106 K/m.
when the planar interface just became unstable for Pb–Sn, Pb–Ag, and Pb–Au alloys, and the research conducted by Morris and Winegard [33] showed that the formation of elongated cell was related to anisotropy of alloys. When the crystal growth direction was oriented along or near the [1 0 0] or [1 1 1] directions, a “pocky” shape structure was formed. When crystals grew along the [1 1 0] direction, an elongated cell was formed. But in the above-mentioned experiments only solidification behavior near the limit of constitutional supercooling for some alloys was considered; it did not mean that an elongated cell would certainly appear after the planar interface became unstable too. Our experiments showed that not only could an elongated cell occur near the limits of the constitutional supercooling, but it could also occur near the limit of absolute stability. This meant that the interface morphology transformation showed symmetry to a certain degree during solidification, such as the high-velocity cellular structure corresponding to the low-velocity cellular structure, and the low-velocity planar interface corresponding to the high-velocity absolute stable planar interface. After that, the elongated cell transformed into one kind of shallow cell, and finally transformed into the absolute stable planar interface. In another word, from regular cell to the absolute stable planar interface, the solid/liquid interface experienced three steps: regular cell to elongated cell, shallow cell, and the absolute stable planar interface, which was in agreement with Ludwig’s in situ observation [36]. 4.3. Full dendrite growth Hunt and Lu [37] analyzed the diffusion field of cellular/dendritic arrays using numerical simulation, and found that the cellular structure could stably exist not only in low growth rate regions, but also in high growth rate regions. In the low growth rate region, a transition from cellular to cellular/dendritic microstructure will occur, which is the process of formation and development of sidebranches. However, in the high growth rate region, an inverse transition from cellular/dendritic to cellular microstructure will occur, which is the process of disappearance and shrinkage of sidebranches. On one hand, sidebranching is caused by the intrinsic morphological instability of the cellular tip, which is the driving force for sidebranching. On the other hand, sidebranching needs a certain time and space condition. The first sidebranch perturbation would be permitted to emerge and to develop in the local space and time interval. Under low temperature gradient and growth rate conditions, there is enough time and space for the emergence and development of sidebranches. However, given that the mushy zone will become much narrower under a high temperature gradient condition, even though the interface marginal instability has still forced the cellular tips to sidebranch at a high growth rate, yet the sidebranching will hardly emerge and develop [38]. In fact, the constitutional supercooling zone is very narrow under a high temperature gradient. Under this condition, not only cannot cellular tips advance well, but also the side perturbation in the end of cells
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is fully restrained. This will subsequently lead to that S/L interface grows in cell in the whole range of growth rate. During laser surface remelting, there existed a high temperature gradient in the molten pool, generally more than 106 K/m, and the intervals of liquidus and solidus of Cu–27.3 wt.% Mn and Cu–31.4 wt.% Mn alloy were narrower, therefore microstructures of Cu–27.3 wt.% Mn and Cu–31.4 wt.% Mn alloys grew in cell, and no dendrites appeared within whole range of growth rate. 4.4. Absolute stability M–S interface stability theory [1] predicts that there exists a critical velocity for an alloy, above which the S/L interface will become stable again and the resulting microstructure will be a segregation-free solid solution. The critical condition for this to occur is given by: Va =
T0 DL kΓ
(4)
Under rapid solidification conditions, the S/L interface is far from equilibrium, and solute atoms tend to build up in front of the S/L interface. Owing to that there is insufficient time to diffuse, these solute atoms will inevitably be captured by the rapidly advancing S/L interface, at last solidify to form the segregation-free structure. This phenomenon is termed “solute trapping”. The critical velocity to realize “solute trapping” is [39]: Vt =
DL a0
(5)
When Va < Vt , the plane front growth results in a segregation-free structure. Inversely, when Va > Vt , it is solute trapping that dominates growth. Based on these, it can be found that there exists a critical composition C0crit for an alloy, which can be easily obtained by setting Va = Vt , C0crit = k2 Γ/m(1 − k)a0 . When C0 < C0crit , absolute stability planar interface growth results in segregation-free structure. For Cu–26.6, 27.3 and 31.4 wt.% Mn alloys, the critical composition was 165%, 226%, and 1120%, respectively, which is considerably in excess of 100%. Therefore, for these three kinds of alloys, it was the absolutely stable planar interface growth at high growth rate that led to the formation of the segregation-free structure. The theoretical critical velocities to attain absolute stability for Cu–26.6, 27.3 and 31.4 wt.%
Table 2 Critical velocity of absolute stability of Cu–Mn alloys Composition (wt.% Mn)
Va (mm/s)
Va (mm/s)
Voa (mm/s)
Voa /Va
Voa /Va
26.6 27.3 31.4
116 76.2 42.1
174.1 121.9 75.9
260.5 212.6 113.3
2.25 2.79 2.45
1.49 1.74 1.36
Note: Va is the theoretical value to attain the absolutely stable planar interface growth when k = 0.5.
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Table 3 Thermophysical parameters of Cu–Mn alloys [40] Property
Value
Gibbs–Thomson coefficient, Γ (mK) Diffusion coefficient (liq.), DL (m2 s−1 )
3 × 10−7 1.75 × 10−9
Liquidus slope, m (K(wt.%)−1 ) Cu–26.6 wt.% Mn Cu–27.3 wt.% Mn Cu–31.4 wt.% Mn
−1.71 −1.92 −0.434
Distribution coefficient, k Cu–26.6 wt.% Mn Cu–27.3 wt.% Mn Cu–31.4 wt.% Mn
0.75 0.80 0.90
Mn alloys are listed in Table 2. Thermophysical parameters used for the calculation are given in Table 3. In Table 2, it can be seen that the experimentally determined values of critical velocity (Voa ) for absolutely stable planar interface growth are 2.25, 2.79 and 2.45 times higher than those (Va ) predicted by M–S theory for Cu–26.6, 27.3 and 31.4 wt.% Mn alloys, respectively. The main reason for these differences may, in part, be attributed to uncertainties in the values of k, DL and Γ . For example, when k = 0.5, the discrepancy between the observed critical velocity (Voa ) and that (Va ) predicted by M–S theory would be virtually compensated. Generally speaking, if the difference between the calculated value and the experimental one is less than one order of magnitude, one can say that the experimental result is reasonable agreement with the theoretical value. Therefore, it can be concluded that, in view of the uncertainty of the thermophysical parameters, M–S theory can reasonably predict the critical velocity of absolute stability.
5. Conclusions (1) With the increase of growth rate, the microstructure of Cu–26.6 wt.% Mn alloy evolved from planar interface to cell, dendrite, super fine cell, and featureless structure. (2) With the increase of growth rate, the microstructure of Cu–27.3 wt.% Mn alloy evolved from planar interface to cell, super fine cell, regular structure, and featureless structure. Under the high temperature gradient condition, this alloy grew in full cell, and no dendrite appeared in whole range of growth rate. (3) With the increase of growth rate, the microstructure of Cu–31.4 wt.% Mn alloy evolved from planar interface to elongated cell, regular cell, elongated cell, shallow cell, and featureless structure. It showed that solid/liquid interface morphology evolution was symmetric. (4) The featureless structure formed under laser rapid solidification condition resulted from absolutely stable planar interface growth rather than solute trapping. The observed critical velocities of absolute stability of Cu–26.6 wt.% Mn, Cu–27.4 wt.% Mn and Cu–31.4 wt.%
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Mn alloys are 260.5, 212.6 and 113.3 mm/s, respectively, which was in reasonable agreement with those predicted by M–S theory. (5) The negative slope between Va and VTmax was only an essential condition for the formation of banded structure, rather than the sufficient condition. Acknowledgements One of the authors (S. Yang) is grateful to Japan Society for the Promotion of Science for offering a JSPS fellowship. The authors would like to express their gratitude to National Science Foundation (Grant No. 59771054) for financial support. References [1] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 65 (1964) 444. [2] R. Trivedi, W. Kurz, Acta Metall. 34 (1986) 1663. [3] S.R. Coriell, G.B. McFadden, P.W. Voohees, R.F. Sekerka, J. Cryst. Growth 82 (1987) 295. [4] A. Ludwig, B. Prustal, D.M. Herlach, Mater. Sci. Eng. A 318 (2001) 337. [5] R. Trivedi, J.A. Sekhar, V. Seetharaman, Metall. Trans. A 23 (1989) 769. [6] A. Ludwig, W. Kurz, Acta Mater. 44 (1996) 3643. [7] W.J. Boettinger, D. Shechtman, R.J. Schaefer, F.S. Biancaniello, Metall. Trans. A 15 (1984) 55. [8] J.A. Juarez-Islas, H. Jones, W. Kurz, Mater. Sci. Eng. 98 (1988) 201. [9] J.A. Juarez-Islas, H. Jones, Acta Metall. 35 (1987) 499. [10] T. Sato, et al., J. Jpn. Inst. Met. 48 (1984) 748. [11] S.C. Gill, W. Kurz, Acta Metall. Mater. 41 (1993) 3563. [12] M. Zimmermann, et al., Mater. Sci. Eng. A 134 (1991) 1278. [13] M. Gremaud, M. Carrad, W. Kurz, Acta Metall. Mater. 38 (1990) 2587.
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