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Rapid solidification of undercooled nickel-aluminium melts
Materials Science and Engineering, A178 (1994) 305-307
305
Rapid solidification of undercooled nickel-alumimum melts M. Barth, B. Wei*, D. M. Herlach and B. Feuerbacher Institut fi'ir Raumsimulation, DLR, D-51140 Krln (Germany)
Abstract
Melts of Nij(~_,-AI, of different compositions (x=20.2, 25, 26.25 and 30.8) were undercooled up to 250 K by the application of the electromagnetic levitation technique. The crystal growth velocities were measured as a function of undercooling using a high speed photosensing device for time-resolved measurements of temperature during recalescence. The structures of the as-solidified samples were investigated by optical microscopy and X-ray diffraction. The results of the growth velocity measurements were analysed within current theories of dendrite growth with special emphasis placed on non-equilibrium solidification due to disorder trapping during rapid solidification of intermetallic phases. The structure investigations in combination with growth velocity measurements allow for a detailed analysis with respect to the identification of primary phases solidified in the different alloys.
1. Introduction
Investigations of rapid solidification of intermetallic compounds have attracted much interest. Rapid solidification is a promising tool to entrap disorder during solidification of intermetallics which in turn may improve the mechanical properties of such materials. In particular, the alloy system Ni-AI has been widely studied in this respect [1, 2]. Laser surface melting and resolidification experiments have clearly shown the complete entrapment of disorder in the intermetallic y' phase (Ni~A1) [3]. Here, the pulsed laser resolidification experiments constrain externally large solidification velocities. Partial disorder entrapment has been found in melt-spun ribbons [4] and drop tube processed droplets of Ni-Ai [5]. An alternative way to produce large solidification rates even at moderate cooling rates is the method of largely undercooling the melt before solidification, generating a high driving force for crystallization owing to the large difference in Gibbs' free energy accumulated in front of the solid-liquid interface. In the present work the electromagnetic levitation technique is applied to undercool the samples with an extra benefit that rapid solidification of the undercooled drops is directly observed by time-resolved temperature measurements during undercooling and solidification. This allows for direct investigations of crystal growth velocities as a function of undercooling and their effects on microstructure development. The
results are interpreted within current theories of dendritic growth taking into account non-equilibrium at the solid-liquid interface. This analysis in combination with structure investigations of the as-solidified samples give detailed insight into phase formation in undercooled Ni-A1 melts rapidly solidified.
2. Experimental details
The alloys of Ni-AI were prepared by inductively premelting the constituents, all of purity better than 99.998%, in the levitation coil. The concentrations were chosen such that they correspond to the limit of equilibrium solubility of A1 in solid solution of Ni (x = 20.2 at.% A1) and to the limit of equilibrium solubility of Ni in NiA1 (x = 30.8 at.% A1). In addition, a eutectic alloy of composition x = 25 at.% A1 and a peritectic composition x = 26.25 at.% AI were prepared. Undercooling experiments were performed in an electromagnetic levitation chamber described in detail elsewhere [6]. The crystal growth velocity was determined as a function of undercooling using a high speed photosensitising device for time-resolved measurements of rapid temperature rise during recalescence (time resolution better than 1 us) [7]. The structure of the as-solidified samples was investigated by optical microscopy and X-ray diffraction (Cu Ka radiation).
3. Results and discussion *On leave from Northwestern Polytechnical University, Xi'an 710071, China. 0921-5093/94/$7.00 SSDI 0921-5093(93)04552-S
Figure l shows the crystal growth velocity as a function of undercooling for all alloys investigated. Maxi© 1994 - Elsevier Sequoia. All rights reserved
306
M. Barth et aL / Rapid solidification of undercooled Ni-Al
mum undercoolings A T -~ 250 K have been achieved. The measured growth velocities of Ni79.sA120.2 and Ni75A125 range up to maximum values of 13.5 m s -1 while the growth velocities of the Ni73.75AI26.25 and Ni69.2A130.8 alloys are remarkably reduced with maximum growth velocities in the range of 2.5 m s-1. The dendrite growth velocity of y-Ni solid solution was calculated by applying the model developed by Boettinger et al. [8] and using characteristic data of the alloys as given in Table 1. According to this theory the bath undercooling A T is expressed by the sum (1)
A T = A T t + A T r + A T k + AT~
with ATt, ATr, ATk, and ATe the thermal, curvature, kinetic, and constitutional undercoolings respectively. Non-equilibrium at the solid-liquid interface is taken into consideration by the kinetic undercooling A T k and by a velocity-dependent partition coefficient [9]. In particular, the kinetic undercooling is inferred from
exp
RTTL ] J
(2)
where A G is the Gibbs free energy change per mole of material solidified, AHr is the heat of fusion of the alloys and TL is the liquidus temperature. R denotes the gas constant. The kinetic prefactor Vc corresponds to the speed of sound Vs -~ 4000 m s- 1 (in the case of collision-limited growth) or to the diffusive speed V o ~ D/2. ~ 20 m s- 1 (in the case of short-range diffusion-limited growth) with D the diffusion coefficient and 2 an interatomic spacing [10]. The full line in Fig. 1 is calculated for Ni79.sA120.2 if Vc= Vs is assumed. There is agreement between the theoretical prediction and the experimental results. The V= V(AT) relation of NiTsA125 behaves in an analogous way. Because of the similarity of V(AT) of
these both alloys to V(AT) of pure Ni [11] it is concluded that the measured velocity reveals growth of y-Ni solid solution in both samples. In contrast, the much reduced growth velocities in Ni73.75Al26.25 and Ni69.2A130.s can only be fitted if Vc = VD is supposed. This means that in these alloys growth is short-range diffusion limited, causing an equivalent high interface undercooling. Such a behaviour is characteristic for growth of a solid having chemical order, as in an ordered intermetallic compound [10]. In this case the atoms must sort themselves out onto the various sublattices. Therefore, the analysis of the results of these both alloys may indicate growth of intermetallic fiNiAl (b.c.c. structure) or 7'-Ni3A1 (f.c.c. structure). According to the equilibrium phase diagram of Ni-A1 [12] only fl-NiA1 can solidify at compositions x~>30 at.% A1. On the contrary, the measured growth velocities for both alloys Ni73.75AI26.25 and Ni69.eA130.8 do not differ within the experimental scatter. From this fact and from the observation that optical micrographs reveal massive segregation even in Ni73.75A126.e5 it is concluded that fl-NiA1 primarily solidifies in both alloys. This assumption is supported if a lower nucleation threshold for the b.c.c, in comparison with the f.c.c. structural phase is postulated as suggested by the negentropic model of Thompson [13], favouring the solidification of b.c.c, fl-NiAl phase in the undercooled melt. The structure analysis of the as-solidified alloys after large undercooling reveals y'-Ni3A1 phase in Ni75A125 and Ni73.75AI26.25 alloys while the Ni69.2AI30.8 alloy structure consists of a mixture of y'-Ni3A1 and fl-NiAl phases. These results in combination with the analysis of the growth velocities can be explained if it is assumed that the y'-Ni3AI intermetallic phase is formed in a secondary peritectic reaction step such as fl + L ~ y'. The intermetallic 7' phase is not completely ordered in Ni73.75A126.25 but contains some degree of disorder. The order parameter r/is estimated by X-ray diffraction. The X-ray diffraction intensities I of one superlattice (110) and the corresponding fundamental
TABLE 1. Characteristicthermodynamicdata of the investigatedalloysused for the calculationof dendrite growth velocities Parameter
Symbol
Units
Heat of fusion Specificheat
AHf Cp~
kJ m o l - 1 jK-1 mol-1
S l o p e of liquidus Partition coefficient
mL kE
- K (at,%)-
Diffusioncoefficient Thermal diffusivity Interracial energy
D a a
m2s-1 m 2 s-1 jm-2
Valuesfor the followingphases
1
y phase
fl phase
16 40 4.1 0.81 6 x l 0 -9 6 x 1 0 -6 0.43
16 40 7.5 0.79 6x10-9 6 x 10 -6 0.35
M. Barth et al. •
r
Ni
-
x
,
1
at%
AI
,
i
/
•
i
/
"~2
'~ 8
,
theory
/
,
Rapid solidification of undercooled Ni-A 1
t
o •
--=:--
i
*
/
Oo
o° o
& • /
0~
L0
o
80
_
120
AT [K]
u x : 308ot% • x = 2625 at%
160
200
2L0
ox: 25ot% * × = 20.2 at%
Fig. 1. Dendrite growth velocity V is a function of undercooling
A T as measured for four differently concentrated Ni-A1 alloys: Ni69.2AI~I,~ (~), Ni7375AI2625 (u), NiT~AI25(0), and Niy9.sA1211. z (o). - - , predictions of dendrite growth theory for V(A T ) of Niyg.sAI202assuming primary solidification of ),-Ni solid solution and an interface undercooling given by collision-limited growth; , theoretical calculations of V ( A T ) for Ni69.2A130.8assuming that the kinetic undercooling of primarily solidifying NiAI intermetallic phase is diffusion controlled.
307
the as-solidified samples leads to the conclusion that ~/-Ni3AI phase is formed in a secondary peritectic reaction according to fl + L ~ ~' containing a partly disordered L12 structure. No direct entrapment of disorder, however, in the solidification of the NiAI intermetallic phase was observed as may be indicated by a discontinuity in the slope of the V(AT) relation predicted by theory [14]. Apparently, the undercooling was not large enough to produce critical growth velocities of the order of 40 m s-~ necessary for disorder entrapment in NiAI intermetallic phase [15]. On the contrary, the critical growth velocity for disorder trapping in v'-Ni)A1 intermetallic phase is about 4 m s-~ [3] and, hence, much smaller than in the case of NiAI. However, in the present investigations no primary solidification of f-Ni3Al could be identified in the alloys prepared according to an equilibrium phase diagram which may have some uncertainties with respect to the formation of intermetallic phases [16].
Acknowledgments (220) peak are determined using as a reference the ratio 1 ( 1 1 0 ) / 1 ( 2 2 0 ) = 0 . 2 8 in the case of complete order ( r/= 1 ) and the expression [4]
Y/-
3
I[•(220)
One of the authors (B.W.) wants to thank the Alexander yon Humboldt-Stiftung for financial support of the present work.
References x 0.28J
(3)
Here, xBAt is the fraction of A1 atoms in sublattice B of the L 12 structure. The determination of r/according to eqn. (3)leads to r/= 0.29 independent of undercooling. Apparently, the moderate cooling rate of about 102 K s- ~ of the levitation experiments was sufficient to avoid complete reordering of the ~' phase during the peritectic reaction. The order parameter r/is increased by thermally annealing one of the as-solidified samples for 4 h at temperatures of 1373 K leading to t/= 0.57 and to a sharpening of the superlattice peak owing to the growth of antiphase domains.
4. Conclusions In summary, crystal growth velocity has been measured as a function of undercooling on levitation-processed drops of Ni-AI alloys of different compositions. T h e experimental results are analysed within dendrite growth theory indicating primary solidification of ~-Ni solid solution in alloys of Ni79.sA1202 and NivsA125 with an interface undercooling determined by collisionlimited growth while in alloys of Niv3.vsA126.25 and Ni(~,)2AI3~.~ primary solidification of fl-NiAl phase is found with diffusion-controlled growth. The combination of this analysis with structure investigations of
1 R.G. Rowe, A. I. Taub and F. H. Froes, in R. Mehrabian and P. A. Parrish (eds.), Rapid Solidification Processing: Principles and Technologies IV, Claitor's, Baton Rouge, LA, 1988, p. 149. 2 C.C. Koch, Mater. Res. Soc. Syrup. Proc., 39 (t985) 397. 3 J. A. West, J. T. Manos and M. J. Aziz, Mater. Res. Soc. 5~vmp. Proc., 20 ( 1991 ) 213. 4 A.R. Yavari and B. Bochu, Philos. Mag. A, 59 (1989) 697. 5 S. C. Sharma, D. M. Herlach and P. E Sinha, Scr. Metall. Mater., 28(1993) 1365. 6 D. M. Herlach, R. Willnecker and E Gillessen, in Y. D. Guyenne (ed.), Proc. Vth Eur. Symp. on Materials Science under Microgravity, Schloss Elmau, 1984, p. 399. 7 E. Schleip, R. Willnecker, D. M. Herlach and G. R Grrler, Mater. Sci. Eng., 98 (1988) 39. 8 W. J. Boettinger, S. R. Coriell and R. Trivedi, in R. Mehrabian and R A. Parrish (eds.), Rapid Solidification Proce~sing: Principles and Technologies IV, Claitor's, Baton Rouge, LA, 1988, p. 13. 9 M.J. Aziz, J. Appl. Phys., _53(1982) 1158. 10 M.J. Aziz and W. J. Boettinger, to be published. 11 R. Wfllnecker, D. M. Herlach and B. Feuerbacher, Phys. Rev. Lett., 62 (1989) 2707. 12 T. B. Massalski, Binary Alloy Phase Diagrams, American Society for Metals, Metals Park, OH, 1986. 13 C.V. Thompson, Ph.D. Thesis, Harvard University, 198 I. 14 W. J. Boettinger and M. J. Aziz, Acta Metall., 37 (1989) 3379. 15 M.J. Aziz, personal communication, 1992. 16 K. Hilpert, D. Kobertz, V. Venugopal, M. Miller, H. Gerads, F. J. Bremer and H. Nickel, Z. Natufforsch. A, 42 (1987) 1327.
305
Rapid solidification of undercooled nickel-alumimum melts M. Barth, B. Wei*, D. M. Herlach and B. Feuerbacher Institut fi'ir Raumsimulation, DLR, D-51140 Krln (Germany)
Abstract
Melts of Nij(~_,-AI, of different compositions (x=20.2, 25, 26.25 and 30.8) were undercooled up to 250 K by the application of the electromagnetic levitation technique. The crystal growth velocities were measured as a function of undercooling using a high speed photosensing device for time-resolved measurements of temperature during recalescence. The structures of the as-solidified samples were investigated by optical microscopy and X-ray diffraction. The results of the growth velocity measurements were analysed within current theories of dendrite growth with special emphasis placed on non-equilibrium solidification due to disorder trapping during rapid solidification of intermetallic phases. The structure investigations in combination with growth velocity measurements allow for a detailed analysis with respect to the identification of primary phases solidified in the different alloys.
1. Introduction
Investigations of rapid solidification of intermetallic compounds have attracted much interest. Rapid solidification is a promising tool to entrap disorder during solidification of intermetallics which in turn may improve the mechanical properties of such materials. In particular, the alloy system Ni-AI has been widely studied in this respect [1, 2]. Laser surface melting and resolidification experiments have clearly shown the complete entrapment of disorder in the intermetallic y' phase (Ni~A1) [3]. Here, the pulsed laser resolidification experiments constrain externally large solidification velocities. Partial disorder entrapment has been found in melt-spun ribbons [4] and drop tube processed droplets of Ni-Ai [5]. An alternative way to produce large solidification rates even at moderate cooling rates is the method of largely undercooling the melt before solidification, generating a high driving force for crystallization owing to the large difference in Gibbs' free energy accumulated in front of the solid-liquid interface. In the present work the electromagnetic levitation technique is applied to undercool the samples with an extra benefit that rapid solidification of the undercooled drops is directly observed by time-resolved temperature measurements during undercooling and solidification. This allows for direct investigations of crystal growth velocities as a function of undercooling and their effects on microstructure development. The
results are interpreted within current theories of dendritic growth taking into account non-equilibrium at the solid-liquid interface. This analysis in combination with structure investigations of the as-solidified samples give detailed insight into phase formation in undercooled Ni-A1 melts rapidly solidified.
2. Experimental details
The alloys of Ni-AI were prepared by inductively premelting the constituents, all of purity better than 99.998%, in the levitation coil. The concentrations were chosen such that they correspond to the limit of equilibrium solubility of A1 in solid solution of Ni (x = 20.2 at.% A1) and to the limit of equilibrium solubility of Ni in NiA1 (x = 30.8 at.% A1). In addition, a eutectic alloy of composition x = 25 at.% A1 and a peritectic composition x = 26.25 at.% AI were prepared. Undercooling experiments were performed in an electromagnetic levitation chamber described in detail elsewhere [6]. The crystal growth velocity was determined as a function of undercooling using a high speed photosensitising device for time-resolved measurements of rapid temperature rise during recalescence (time resolution better than 1 us) [7]. The structure of the as-solidified samples was investigated by optical microscopy and X-ray diffraction (Cu Ka radiation).
3. Results and discussion *On leave from Northwestern Polytechnical University, Xi'an 710071, China. 0921-5093/94/$7.00 SSDI 0921-5093(93)04552-S
Figure l shows the crystal growth velocity as a function of undercooling for all alloys investigated. Maxi© 1994 - Elsevier Sequoia. All rights reserved
306
M. Barth et aL / Rapid solidification of undercooled Ni-Al
mum undercoolings A T -~ 250 K have been achieved. The measured growth velocities of Ni79.sA120.2 and Ni75A125 range up to maximum values of 13.5 m s -1 while the growth velocities of the Ni73.75AI26.25 and Ni69.2A130.8 alloys are remarkably reduced with maximum growth velocities in the range of 2.5 m s-1. The dendrite growth velocity of y-Ni solid solution was calculated by applying the model developed by Boettinger et al. [8] and using characteristic data of the alloys as given in Table 1. According to this theory the bath undercooling A T is expressed by the sum (1)
A T = A T t + A T r + A T k + AT~
with ATt, ATr, ATk, and ATe the thermal, curvature, kinetic, and constitutional undercoolings respectively. Non-equilibrium at the solid-liquid interface is taken into consideration by the kinetic undercooling A T k and by a velocity-dependent partition coefficient [9]. In particular, the kinetic undercooling is inferred from
exp
RTTL ] J
(2)
where A G is the Gibbs free energy change per mole of material solidified, AHr is the heat of fusion of the alloys and TL is the liquidus temperature. R denotes the gas constant. The kinetic prefactor Vc corresponds to the speed of sound Vs -~ 4000 m s- 1 (in the case of collision-limited growth) or to the diffusive speed V o ~ D/2. ~ 20 m s- 1 (in the case of short-range diffusion-limited growth) with D the diffusion coefficient and 2 an interatomic spacing [10]. The full line in Fig. 1 is calculated for Ni79.sA120.2 if Vc= Vs is assumed. There is agreement between the theoretical prediction and the experimental results. The V= V(AT) relation of NiTsA125 behaves in an analogous way. Because of the similarity of V(AT) of
these both alloys to V(AT) of pure Ni [11] it is concluded that the measured velocity reveals growth of y-Ni solid solution in both samples. In contrast, the much reduced growth velocities in Ni73.75Al26.25 and Ni69.2A130.s can only be fitted if Vc = VD is supposed. This means that in these alloys growth is short-range diffusion limited, causing an equivalent high interface undercooling. Such a behaviour is characteristic for growth of a solid having chemical order, as in an ordered intermetallic compound [10]. In this case the atoms must sort themselves out onto the various sublattices. Therefore, the analysis of the results of these both alloys may indicate growth of intermetallic fiNiAl (b.c.c. structure) or 7'-Ni3A1 (f.c.c. structure). According to the equilibrium phase diagram of Ni-A1 [12] only fl-NiA1 can solidify at compositions x~>30 at.% A1. On the contrary, the measured growth velocities for both alloys Ni73.75AI26.25 and Ni69.eA130.8 do not differ within the experimental scatter. From this fact and from the observation that optical micrographs reveal massive segregation even in Ni73.75A126.e5 it is concluded that fl-NiA1 primarily solidifies in both alloys. This assumption is supported if a lower nucleation threshold for the b.c.c, in comparison with the f.c.c. structural phase is postulated as suggested by the negentropic model of Thompson [13], favouring the solidification of b.c.c, fl-NiAl phase in the undercooled melt. The structure analysis of the as-solidified alloys after large undercooling reveals y'-Ni3A1 phase in Ni75A125 and Ni73.75AI26.25 alloys while the Ni69.2AI30.8 alloy structure consists of a mixture of y'-Ni3A1 and fl-NiAl phases. These results in combination with the analysis of the growth velocities can be explained if it is assumed that the y'-Ni3AI intermetallic phase is formed in a secondary peritectic reaction step such as fl + L ~ y'. The intermetallic 7' phase is not completely ordered in Ni73.75A126.25 but contains some degree of disorder. The order parameter r/is estimated by X-ray diffraction. The X-ray diffraction intensities I of one superlattice (110) and the corresponding fundamental
TABLE 1. Characteristicthermodynamicdata of the investigatedalloysused for the calculationof dendrite growth velocities Parameter
Symbol
Units
Heat of fusion Specificheat
AHf Cp~
kJ m o l - 1 jK-1 mol-1
S l o p e of liquidus Partition coefficient
mL kE
- K (at,%)-
Diffusioncoefficient Thermal diffusivity Interracial energy
D a a
m2s-1 m 2 s-1 jm-2
Valuesfor the followingphases
1
y phase
fl phase
16 40 4.1 0.81 6 x l 0 -9 6 x 1 0 -6 0.43
16 40 7.5 0.79 6x10-9 6 x 10 -6 0.35
M. Barth et al. •
r
Ni
-
x
,
1
at%
AI
,
i
/
•
i
/
"~2
'~ 8
,
theory
/
,
Rapid solidification of undercooled Ni-A 1
t
o •
--=:--
i
*
/
Oo
o° o
& • /
0~
L0
o
80
_
120
AT [K]
u x : 308ot% • x = 2625 at%
160
200
2L0
ox: 25ot% * × = 20.2 at%
Fig. 1. Dendrite growth velocity V is a function of undercooling
A T as measured for four differently concentrated Ni-A1 alloys: Ni69.2AI~I,~ (~), Ni7375AI2625 (u), NiT~AI25(0), and Niy9.sA1211. z (o). - - , predictions of dendrite growth theory for V(A T ) of Niyg.sAI202assuming primary solidification of ),-Ni solid solution and an interface undercooling given by collision-limited growth; , theoretical calculations of V ( A T ) for Ni69.2A130.8assuming that the kinetic undercooling of primarily solidifying NiAI intermetallic phase is diffusion controlled.
307
the as-solidified samples leads to the conclusion that ~/-Ni3AI phase is formed in a secondary peritectic reaction according to fl + L ~ ~' containing a partly disordered L12 structure. No direct entrapment of disorder, however, in the solidification of the NiAI intermetallic phase was observed as may be indicated by a discontinuity in the slope of the V(AT) relation predicted by theory [14]. Apparently, the undercooling was not large enough to produce critical growth velocities of the order of 40 m s-~ necessary for disorder entrapment in NiAI intermetallic phase [15]. On the contrary, the critical growth velocity for disorder trapping in v'-Ni)A1 intermetallic phase is about 4 m s-~ [3] and, hence, much smaller than in the case of NiAI. However, in the present investigations no primary solidification of f-Ni3Al could be identified in the alloys prepared according to an equilibrium phase diagram which may have some uncertainties with respect to the formation of intermetallic phases [16].
Acknowledgments (220) peak are determined using as a reference the ratio 1 ( 1 1 0 ) / 1 ( 2 2 0 ) = 0 . 2 8 in the case of complete order ( r/= 1 ) and the expression [4]
Y/-
3
I[•(220)
One of the authors (B.W.) wants to thank the Alexander yon Humboldt-Stiftung for financial support of the present work.
References x 0.28J
(3)
Here, xBAt is the fraction of A1 atoms in sublattice B of the L 12 structure. The determination of r/according to eqn. (3)leads to r/= 0.29 independent of undercooling. Apparently, the moderate cooling rate of about 102 K s- ~ of the levitation experiments was sufficient to avoid complete reordering of the ~' phase during the peritectic reaction. The order parameter r/is increased by thermally annealing one of the as-solidified samples for 4 h at temperatures of 1373 K leading to t/= 0.57 and to a sharpening of the superlattice peak owing to the growth of antiphase domains.
4. Conclusions In summary, crystal growth velocity has been measured as a function of undercooling on levitation-processed drops of Ni-AI alloys of different compositions. T h e experimental results are analysed within dendrite growth theory indicating primary solidification of ~-Ni solid solution in alloys of Ni79.sA1202 and NivsA125 with an interface undercooling determined by collisionlimited growth while in alloys of Niv3.vsA126.25 and Ni(~,)2AI3~.~ primary solidification of fl-NiAl phase is found with diffusion-controlled growth. The combination of this analysis with structure investigations of
1 R.G. Rowe, A. I. Taub and F. H. Froes, in R. Mehrabian and P. A. Parrish (eds.), Rapid Solidification Processing: Principles and Technologies IV, Claitor's, Baton Rouge, LA, 1988, p. 149. 2 C.C. Koch, Mater. Res. Soc. Syrup. Proc., 39 (t985) 397. 3 J. A. West, J. T. Manos and M. J. Aziz, Mater. Res. Soc. 5~vmp. Proc., 20 ( 1991 ) 213. 4 A.R. Yavari and B. Bochu, Philos. Mag. A, 59 (1989) 697. 5 S. C. Sharma, D. M. Herlach and P. E Sinha, Scr. Metall. Mater., 28(1993) 1365. 6 D. M. Herlach, R. Willnecker and E Gillessen, in Y. D. Guyenne (ed.), Proc. Vth Eur. Symp. on Materials Science under Microgravity, Schloss Elmau, 1984, p. 399. 7 E. Schleip, R. Willnecker, D. M. Herlach and G. R Grrler, Mater. Sci. Eng., 98 (1988) 39. 8 W. J. Boettinger, S. R. Coriell and R. Trivedi, in R. Mehrabian and R A. Parrish (eds.), Rapid Solidification Proce~sing: Principles and Technologies IV, Claitor's, Baton Rouge, LA, 1988, p. 13. 9 M.J. Aziz, J. Appl. Phys., _53(1982) 1158. 10 M.J. Aziz and W. J. Boettinger, to be published. 11 R. Wfllnecker, D. M. Herlach and B. Feuerbacher, Phys. Rev. Lett., 62 (1989) 2707. 12 T. B. Massalski, Binary Alloy Phase Diagrams, American Society for Metals, Metals Park, OH, 1986. 13 C.V. Thompson, Ph.D. Thesis, Harvard University, 198 I. 14 W. J. Boettinger and M. J. Aziz, Acta Metall., 37 (1989) 3379. 15 M.J. Aziz, personal communication, 1992. 16 K. Hilpert, D. Kobertz, V. Venugopal, M. Miller, H. Gerads, F. J. Bremer and H. Nickel, Z. Natufforsch. A, 42 (1987) 1327.