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Undercoolability of pure Co and Co-based alloys
Journal of Non-Crystalline Solids 250±252 (1999) 271±276
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Undercoolability of pure Co and Co-based alloys D.M. Herlach a,*, D. Holland-Moritz a,b, Th. Schenk a,b, K. Schneider a, G. Wilde a, O. Boni c, J. Fransaer c, F. Spaepen c b
a Institut f ur Raumsimulation, Deutsches Zentrum f ur Luft- und Raumfahrt, D-51170 K oln, Germany Institut f ur Experimentalphysik/Festk orperphysik, Ruhr-Universit at Bochum, D-44780 Bochum, Germany c Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
Abstract The undercooling of Co and Co±Pd melts is investigated using both electromagnetic levitation and melt ¯uxing. These techniques, designed to reduce heterogeneous nucleation from container walls, surface oxides or inclusions, produced large undercoolings that approach the Curie temperatures (Tc ) of the samples. The results are analysed within classical nucleation theory, incorporating the speci®c conditions of undercooling techniques and the composition dependence of the nucleation frequency. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Alloys of Co±Pd have recently attracted attention because drops about 6 mm in diameter were undercooled to their Curie-temperatures, Tc , of the paramagnetic±ferromagnetic transition showing an attractive interaction with an external Co±Sm magnet while still in the liqud state [1]. Recently, even undercoolings of a Co80 Pd20 alloy melt below Tc were reported for droplets with diameters of 1.5 to 2 mm using a miniaturized electromagnetic levitation device [2]. The magnetic susceptibility in the liquid state was measured on levitated undercooled samples applying a modi®ed Faraday balance for contactless measurements [3]. These measurements reveal a Curie±Weiss behaviour of the undercooled melt and similar magnetic moments in liquid and solid state were observed. From the temperature dependence of the recipro-
* Corresponding author. Tel.: +49 2203 601 2332; fax: +49 2203 61768; e-mail: [email protected]
cal susceptibility the Curie-temperatures of liquid, Tc (l) and solid, Tc (s), Co80 Pd20 are inferred. Tc (l) is approximately 20 K below Tc (s). The dierence between Tc (l) and Tc (s) is independent on the Pdconcentration of Co100ÿx Pdx alloys in the range 15 < x < 30 [4]. When the temperature of the undercooled melt is approaching Tc (l), the magnetization steeply rises [3]. An equivalent increase of other physical properties have been observed in Co80 Pd20 alloys. The speci®c heat of droplets with a mass of 400 mg undercooled in a ¯ux medium (Duran glass) to Tc (s), (DT 335 K) [5,6] shows a cusp-like increase. Also the electrical resistivity of bulk samples 7 mm in diameter undercooled (DT 345 K) by an electromagnetic levitation device for containerless processing in space (TEMPUS) during NASA's spacelab mission MSL1 increases if temperature is approaching Tc (s) caused by spin-¯ip scattering [7]. All of these measurements indicate the onset of ferromagnetic ordering in the liquid state as the undercooling temperature approaches the Tc . However, no undercooling of Co±Pd alloy below
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Tc (l) was reported, with only one exception [2], despite the application of dierent techniques. In particular, to test the in¯uence of sample size on the maximum undercoolability, droplets of dierent diameters of Co80 Pd20 were produced by dispersing a melt in a drop-tube producing droplets ranging from 200 lm to 1 mm in diameter. Subsequently, an ensemble of variously sized droplets was embedded in a Duran glass slag and undercooled by a dierential heat ¯ow calorimeter (DSC) [8]. The DSC trace shows dierent crystallization events and a `cut-o temperature' was observed corresponding to an undercooling of DT 345 K Tl ÿ Tc (s) beyond which all droplets were crystallized including also droplets with a mass of less 50 lg [8]. In the present work we study the maximum undercoolability of Co100ÿx Pdx (0 6 x 6 50) alloys as a function of concentration using both electromagnetic levitation and melt ¯uxing. The results are analysed and discussed within classical nucleation theory. 2. Experimental The Co±Pd alloys were melted from the elements Co (99.998%) and Pd (99.9%) in an arc furnace under Ar atmosphere. Samples approximately 1 g in mass were prepared for levitation experiments and for the ¯uxing experiments. An ultra high vacuum (UHV) chamber was used to containerlessly process bulk samples in diameter of about 6±7 mm by electromagnetic levitation. The UHV chamber was evacuated to a pressure of 10ÿ7 mbar before back®lling with He± 5%H2 -cooling gas of purity better than 99.9999% passing through a puri®cation system (Oxysorb) and a liquid nitrogen cold trap. A two colour pyrometer was used to measure the temperature of the sample. The absolute accuracy of the temperature measurements was 5 K. Cooling rates ranged between 10 and 40 K/s. The reader is referred for more details about the levitation chamber to Ref. [9] and the procedure of undercooling experiments on Co±Pd alloys to Ref. [10]. Comparative undercooling experiments were conducted on pure Co. Samples with diameter
between 2 and 3.3 mm (40±170 mg) were surrounded by a borosilicate glass ¯ux and melted in a fused silica crucible by resistive heating in a vacuum chamber that was back®lled with argon. The temperature was monitored by a thermocouple placed right above the sample. The temperature measurement was calibrated by measuring the melting temperatures of Ag, Cu, Si, Ni and Co under the same conditions. The borosilicate ¯ux was chosen among other oxide glasses because it combined chemical stability with a suciently low viscosity at the temperatures of interest. 3. Results Fig. 1 shows the Co-rich side of the phase diagram of Co±Pd. The liquidus (TL ) and solidus temperatures (TS ) were measured by DSC and are represented by lines labelled and ´, respectively. They are taken from Ref. [8] and are located on the temperature scale by about 30 K higher in comparison with those of Ref. [11]. The line labelled + shows the Tc (s) of solid Co±Pd alloys as a function of concentration as also determined from DSC measurements [8]. The full dots give the results of undercooling experiments on samples of about 1 g in mass encased in a duran glass slag while the open squares correspond to the results on levitation experiments on samples of comparable mass. Within the uncertainty of temperature measurements, levitation and ¯ux experiments lead to the same maximum undercoolings. It is obvious, however, that at concentrations in the range 15±30 at.% Pd the nucleation temperatures approach the line of Tc (s). However, in none of the undercooling experiments nucleation temperature below the Tc of the liquid ferromagnet were observed. This situation is even true for very small droplets of Co75 Pd25 (cf. diamond in Fig. 1) with a mass of only 50 lg of each undercooled in duran glass when taking into account the Tc of the undercooled liquid being about 20 K less than Tc (s) [4]. The closed square corresponds to the maximum undercooling, DT 380 K, observed on pure Co droplets with sizes of 2±3.3 mm (40±170 mg) using borosilicate glass as a ¯uxing medium. Electromagnetic levitation of 6 mm drops yields maximum
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Fig. 1. Co-rich side of the Co±Pd phase diagram. The liquidus (TL ) and solidus (TS ) temperatures as well as the Tc (s) of solid samples are taken from Ref. [8]. The closed and open dots show undercoolings obtained by ¯uxing and levitation experiments (0.5±1 g). The square gives the undercooling of pure Co (170 mg) in a borosilicate ¯ux and the diamond represents undercooling of very small particles (50 lg) of Co75 Pd25 in a duran ¯ux [8]. The solid lines labelled f(h) correspond to the prediction of nucleation theory assuming catalytic potency factors of f(h) 0.34 and f(h) 0.28.
undercoolings of about 350 K (cf. open square) [12]. Measurements of the magnetic susceptibility on liquid pure Co above and below its melting temperature indicate that the Tc of solid and liquid Co are comparable, Tc (l) Tc (s) [13] with Tc (s) 1394 K [11].
with go 0.004 Pas for pure Co [15], B 2000 K [16] and Tog the ideal glass transition temperature which is approximated by Tog 0.35 TL [17]. The activation energy DG for the formation of a critical nucleus is given by DG
4. Analysis and discussion For an analysis of the undercooling results we refer to classical nucleation theory [14]. Accordingly, the steady state nucleation rate, Iss , is expressed as kB T nNL DG f # : 1 exp ÿ Iss 3pg T a3o kB T For homogeneous nucleation n 1 and f(h) 1 while for heterogeneous nucleation n 10ÿ13 and f(h) < 1. ao 2.3 ´ 10ÿ10 m denotes an interatomic distance and NL Avogadro's number. kB is Boltzmann's constant. The temperature dependence of the viscosity is approximated by the Vogel±Fulcher±Tammann Ansatz B 2 g T go exp ÿ T ÿ Tog
16 r3 p f h 3 DG2v
3
with DGv the Gibbs Free Energy dierence which is calculated using the model by Dubey and Ramachandrarao [18] DT 2 DT ; 4 1ÿ DGv DSf DT ÿ Dcp 6T 2T where DSf is the entropy of fusion and Dcp the dierence of speci®c heat between solid and liquid at the melting temperature with DSf 7.47 J/(mol K), Dcp 5 J/(mol K) for Co82 Pd18 and DSf 7.23 J/(mol K), Dcp 6 J/(mol K) for Co50 Pd50 , respectively, [17]. The comparison with values of DGv as determined from the measured speci®c heat values shows, that the agreement is well within the con®dence range of the experimental data [8]. The interfacial energy, r, is determined using the negentropic model [19,20]
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DSf T 1=3
2=3
NL V m
5
with a 0.86 for fcc structure and Vm 7.23 ´ 10ÿ6 m3 /mol the molar volume of Co [15]. Applying Eqs. (1)±(5) the nucleation rate, Iss , is computed for Co±Pd alloys an example of which is shown in Fig. 2 for the alloy Co82 Pd18 both for homogeneous nucleation (solid line) and heterogeneous nucleation (dashed line). As reported previously [10], the solid solution Co±Pd crystallizes very rapidly from the undercooled melt. As an example, the Co82 Pd18 alloy shows a maximum growth velocity at an undercooling of 325 K of 35 m/sec, i.e. the sample in size of 6 mm is fully crystallized within a time period of 200 ls. This also means that one nucleation event is sucient to initiate solidi®cation. Under such circumstances, the relation holds [14] Iss Vt 1
6
with V the volume of the sample and t the observation time which can be directly taken from the measured temperature-time pro®le. Eq. (6) is drawn as a straight line in Fig. 2. The intersection point of this line with the nucleation curve de®nes the maximum undercooling to be expected with V
and t the experiment parameters. The closed dot gives the undercooling result of a levitation experiment on a 6 mm drop, DT 335 K. The heterogeneous nucleation curve is computed such that it is in agreement with this experimental result using the catalytic potency factor, f(h), as the ®tting parameter, yielding f(h) 0.28. The products of chemical reactions of the hot liquid with oxygen impurities within the environmental gas atmosphere may act as a possible source for heterogeneous nucleation sites. There are three Co oxides: CoO (TL 2083 K), CoO4 (TL 1173 K) and Co2 O3 (TL 673 K) [21]. In the temperature range of liquid and undercooled Co base alloys only CoO is stable. It dissolves, however at high temperatures, T > 2000 K, and is reduced by hydrogen. The solubility of O2 in Co and Pd is less than 0.4 at.%. PdO already dissolves at temperatures T 1143 K. The limit of undercoolability by homogeneous nucleation is inferred to be DT 475 K at an experiment time t 100 s. If the droplet diameter is decreased from 6 to 1.5 mm an extension of the undercooling of 10 K is expected provided all other experiment conditions are kept unchanged. A larger undercooling, DT 425 K, may be obtainable if the droplet size is further decreased to
Fig. 2. Nucleation rates calculated for homogeneous nucleation (solid line) and heterogeneous nucleation (dashed line). The heterogeneous nucleation was determined such that it is in agreement with the experiment (solid dot). The maximum undercoolings are given for dierent conditions. For comparison the Tc (s) of the alloy is drawn.
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60 lm and the experiment time is shortened from 100 to 1 s by e.g. a greater cooling rate. The maximum undercoolings are calculated as a function of concentration for Co±Pd alloys assuming that f(h) 0.28 and d 6 mm and t 100 s remain constant. The results of the calculations are plotted in Fig. 1. Surprisingly, the curve computed with f(h) 0.28 only describes the undercooling result of the Co82 Pd18 alloy. If the catalytic potency factor is changed to f(h) 0.34 the undercooling results on Co±Pd alloys of concentrations of x > 30 at.% Pd are in agreement with the analysis but not in the concentration range x < 30 at.% Pd. Obviously, the catalytic potency factor changes continuously in the concentration range from 0 to 30 at.% Pd. Such a behaviour is unusual for a solid solution such as Co±Pd. For instance, in the system Cu±Ni (complete miscibility in solid and liquid but Tc much less than for the Co±Pd alloys) undercooling experiments indicate one unique potency factor, f(h), over the entire concentration range of the alloy system independently on the undercooling technique, in case of droplet dispersion f(h) 0.16 [22] and in case of levitation f(h) 0.19 [23].
magnetostriction) in¯uences undercooling and the onset of magnetic ordering may stimulate crystal nucleation in Co100ÿx Pdx alloys in the concentration range 0 < x < 30.
5. Conclusions
References
The undercoolability of pure Co and Co±Pd alloys has been studied as a function of composition and under dierent experimental conditions. Levitation and ¯uxing was applied to undercool samples of about 1 g in mass. Similar undercoolings were observed independent of the technique. For comparison, smaller drops of pure Co in mass of 170 mg were undercooled in a boronsilicate ¯ux. Here, an undercooling to and even slightly below the Tc of the solid material was measured. The experimental results were analysed within nucleation theory. The analysis shows an unusual behaviour in the concentration range from 0 to 30 at.% Pd such that the nucleation rates cannot be described by heterogeneous nucleation with one unique catalytic potency factor. The crystallization temperatures of the undercooled melt almost coincide with the Tc of the alloys in this composition range. One may speculate that magnetic eects (eg.
[1] C. Platzek, D.M. Nottho, G. Herlach, D. Jacobs, K. Maier, Appl. Phys. Lett. 65 (1994) 1723. [2] T. Albrecht, C. B uhrer, M. F ahnle, K. Maier, D. Platzek, J. Reske, Appl. Phy. A 65 (1997) 215. [3] J. Reske, D.M. Herlach, F. Keuser, K. Maier, D. Platzek, Phys. Rev. Lett. 75 (1995) 737. [4] D. Platzek, PhD thesis, Ein ¯ ussiger Ferromagnet: Untersuchungen mit mikroskopischen Sonden, University Bonn, 1997. [5] G. Wilde, G.P. G orler, R. Willnecker, J. Non-Cryst. Solids 205±207 (1996) 317. [6] G. Wilde, G.P. G orler, R. Willnecker, Appl. Phys. Lett. 69 (1996) 2995. [7] G. Loh ofer, I. Egry, Workshop on Nucleation and Thermophysics, Bad Honnef, 1998. [8] G. Wilde, PhD thesis, Technical University Berlin, 1997. [9] D.M. Herlach, R. Willnecker, F. Gillessen, in: Proceedings of the Fifth European Sympsosium on Materials Sciences Under Microgravity, ESA SP-222, Elmau, 1984, p. 399. [10] T. Volkmann, G. Wilde, R. Willnecker, D.M. Herlach, J. Appl. Phys. 83 (1998) 3028. [11] T.B. Massalski (ed.), Binary Alloy Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1996.
Acknowledgements Support by the Deutsche Forschungsgemeinschaft within contract no He 1601/5, Ho 1942/2 and Wi 1350/3 is gratefully acknowledged. The work at Harvard was supported by the National Aeronautics and Space Administration under Contract No. NAG8 1256. O.B. is an undergraduate student in Materials Engineering, at the Technion, Israel. Her summer work at Harvard was supported through the REU program of the Harvard MRSEC, supported by the National Science Foundation under contract number DMR -94-00396. The authors thank G.-P. G orler, T. Volkmann and R. Willnecker for helpful discussions. One of the authors (D.M.H.) expresses his gratitude to Professor Frans Spaepen for his kind hospitality during a 4 months stay at Harvard.
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[12] J. Schade, A. McLean, W.A. Miller, in: Undercooled Alloy Phases, E.W. Collings, C.C. Coch (Eds.), Metall. Soc., Warrendale, 1986, p. 233. [13] G. Urbain, E. Ubelacker, Adv. Phys. 16 (1967) 429. [14] J.W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed., Chap. 10, Pergamon, Oxford, 1975. [15] Smithells, Metals Reference Book, E.A. Brandes (Ed.), Butterworths, London, 1983. [16] L. Battezzati, C. Antonione, T. Mariono, J. Mater. Sci. 24 (1989) 2324.
[17] G. Wilde, G.P. G orler, R. Willnecker, Appl. Phys. Lett. 68 (1996) 2935. [18] P. Ramachandrarao, Key Eng. Mater. 13±15 (1987) 195. [19] F. Spaepen, Acta Metall. 23 (1975) 729. [20] F. Spaepen, R.B. Meyer, Scripta Metall. 10 (1976) 257. [21] E. Fromm, E. Gebhardt (Eds.), Gase und Kohlensto in Metallen, Springer, Berlin, 1976. [22] R.E. Cech, D. Turnbull, J. Met. 191 (1951) 242. [23] R. Willnecker, D.M. Herlach, B. Feuerbacher, Mater. Sci. Eng. 98 (1988) 85.
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Undercoolability of pure Co and Co-based alloys D.M. Herlach a,*, D. Holland-Moritz a,b, Th. Schenk a,b, K. Schneider a, G. Wilde a, O. Boni c, J. Fransaer c, F. Spaepen c b
a Institut f ur Raumsimulation, Deutsches Zentrum f ur Luft- und Raumfahrt, D-51170 K oln, Germany Institut f ur Experimentalphysik/Festk orperphysik, Ruhr-Universit at Bochum, D-44780 Bochum, Germany c Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
Abstract The undercooling of Co and Co±Pd melts is investigated using both electromagnetic levitation and melt ¯uxing. These techniques, designed to reduce heterogeneous nucleation from container walls, surface oxides or inclusions, produced large undercoolings that approach the Curie temperatures (Tc ) of the samples. The results are analysed within classical nucleation theory, incorporating the speci®c conditions of undercooling techniques and the composition dependence of the nucleation frequency. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Alloys of Co±Pd have recently attracted attention because drops about 6 mm in diameter were undercooled to their Curie-temperatures, Tc , of the paramagnetic±ferromagnetic transition showing an attractive interaction with an external Co±Sm magnet while still in the liqud state [1]. Recently, even undercoolings of a Co80 Pd20 alloy melt below Tc were reported for droplets with diameters of 1.5 to 2 mm using a miniaturized electromagnetic levitation device [2]. The magnetic susceptibility in the liquid state was measured on levitated undercooled samples applying a modi®ed Faraday balance for contactless measurements [3]. These measurements reveal a Curie±Weiss behaviour of the undercooled melt and similar magnetic moments in liquid and solid state were observed. From the temperature dependence of the recipro-
* Corresponding author. Tel.: +49 2203 601 2332; fax: +49 2203 61768; e-mail: [email protected]
cal susceptibility the Curie-temperatures of liquid, Tc (l) and solid, Tc (s), Co80 Pd20 are inferred. Tc (l) is approximately 20 K below Tc (s). The dierence between Tc (l) and Tc (s) is independent on the Pdconcentration of Co100ÿx Pdx alloys in the range 15 < x < 30 [4]. When the temperature of the undercooled melt is approaching Tc (l), the magnetization steeply rises [3]. An equivalent increase of other physical properties have been observed in Co80 Pd20 alloys. The speci®c heat of droplets with a mass of 400 mg undercooled in a ¯ux medium (Duran glass) to Tc (s), (DT 335 K) [5,6] shows a cusp-like increase. Also the electrical resistivity of bulk samples 7 mm in diameter undercooled (DT 345 K) by an electromagnetic levitation device for containerless processing in space (TEMPUS) during NASA's spacelab mission MSL1 increases if temperature is approaching Tc (s) caused by spin-¯ip scattering [7]. All of these measurements indicate the onset of ferromagnetic ordering in the liquid state as the undercooling temperature approaches the Tc . However, no undercooling of Co±Pd alloy below
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Tc (l) was reported, with only one exception [2], despite the application of dierent techniques. In particular, to test the in¯uence of sample size on the maximum undercoolability, droplets of dierent diameters of Co80 Pd20 were produced by dispersing a melt in a drop-tube producing droplets ranging from 200 lm to 1 mm in diameter. Subsequently, an ensemble of variously sized droplets was embedded in a Duran glass slag and undercooled by a dierential heat ¯ow calorimeter (DSC) [8]. The DSC trace shows dierent crystallization events and a `cut-o temperature' was observed corresponding to an undercooling of DT 345 K Tl ÿ Tc (s) beyond which all droplets were crystallized including also droplets with a mass of less 50 lg [8]. In the present work we study the maximum undercoolability of Co100ÿx Pdx (0 6 x 6 50) alloys as a function of concentration using both electromagnetic levitation and melt ¯uxing. The results are analysed and discussed within classical nucleation theory. 2. Experimental The Co±Pd alloys were melted from the elements Co (99.998%) and Pd (99.9%) in an arc furnace under Ar atmosphere. Samples approximately 1 g in mass were prepared for levitation experiments and for the ¯uxing experiments. An ultra high vacuum (UHV) chamber was used to containerlessly process bulk samples in diameter of about 6±7 mm by electromagnetic levitation. The UHV chamber was evacuated to a pressure of 10ÿ7 mbar before back®lling with He± 5%H2 -cooling gas of purity better than 99.9999% passing through a puri®cation system (Oxysorb) and a liquid nitrogen cold trap. A two colour pyrometer was used to measure the temperature of the sample. The absolute accuracy of the temperature measurements was 5 K. Cooling rates ranged between 10 and 40 K/s. The reader is referred for more details about the levitation chamber to Ref. [9] and the procedure of undercooling experiments on Co±Pd alloys to Ref. [10]. Comparative undercooling experiments were conducted on pure Co. Samples with diameter
between 2 and 3.3 mm (40±170 mg) were surrounded by a borosilicate glass ¯ux and melted in a fused silica crucible by resistive heating in a vacuum chamber that was back®lled with argon. The temperature was monitored by a thermocouple placed right above the sample. The temperature measurement was calibrated by measuring the melting temperatures of Ag, Cu, Si, Ni and Co under the same conditions. The borosilicate ¯ux was chosen among other oxide glasses because it combined chemical stability with a suciently low viscosity at the temperatures of interest. 3. Results Fig. 1 shows the Co-rich side of the phase diagram of Co±Pd. The liquidus (TL ) and solidus temperatures (TS ) were measured by DSC and are represented by lines labelled and ´, respectively. They are taken from Ref. [8] and are located on the temperature scale by about 30 K higher in comparison with those of Ref. [11]. The line labelled + shows the Tc (s) of solid Co±Pd alloys as a function of concentration as also determined from DSC measurements [8]. The full dots give the results of undercooling experiments on samples of about 1 g in mass encased in a duran glass slag while the open squares correspond to the results on levitation experiments on samples of comparable mass. Within the uncertainty of temperature measurements, levitation and ¯ux experiments lead to the same maximum undercoolings. It is obvious, however, that at concentrations in the range 15±30 at.% Pd the nucleation temperatures approach the line of Tc (s). However, in none of the undercooling experiments nucleation temperature below the Tc of the liquid ferromagnet were observed. This situation is even true for very small droplets of Co75 Pd25 (cf. diamond in Fig. 1) with a mass of only 50 lg of each undercooled in duran glass when taking into account the Tc of the undercooled liquid being about 20 K less than Tc (s) [4]. The closed square corresponds to the maximum undercooling, DT 380 K, observed on pure Co droplets with sizes of 2±3.3 mm (40±170 mg) using borosilicate glass as a ¯uxing medium. Electromagnetic levitation of 6 mm drops yields maximum
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Fig. 1. Co-rich side of the Co±Pd phase diagram. The liquidus (TL ) and solidus (TS ) temperatures as well as the Tc (s) of solid samples are taken from Ref. [8]. The closed and open dots show undercoolings obtained by ¯uxing and levitation experiments (0.5±1 g). The square gives the undercooling of pure Co (170 mg) in a borosilicate ¯ux and the diamond represents undercooling of very small particles (50 lg) of Co75 Pd25 in a duran ¯ux [8]. The solid lines labelled f(h) correspond to the prediction of nucleation theory assuming catalytic potency factors of f(h) 0.34 and f(h) 0.28.
undercoolings of about 350 K (cf. open square) [12]. Measurements of the magnetic susceptibility on liquid pure Co above and below its melting temperature indicate that the Tc of solid and liquid Co are comparable, Tc (l) Tc (s) [13] with Tc (s) 1394 K [11].
with go 0.004 Pas for pure Co [15], B 2000 K [16] and Tog the ideal glass transition temperature which is approximated by Tog 0.35 TL [17]. The activation energy DG for the formation of a critical nucleus is given by DG
4. Analysis and discussion For an analysis of the undercooling results we refer to classical nucleation theory [14]. Accordingly, the steady state nucleation rate, Iss , is expressed as kB T nNL DG f # : 1 exp ÿ Iss 3pg T a3o kB T For homogeneous nucleation n 1 and f(h) 1 while for heterogeneous nucleation n 10ÿ13 and f(h) < 1. ao 2.3 ´ 10ÿ10 m denotes an interatomic distance and NL Avogadro's number. kB is Boltzmann's constant. The temperature dependence of the viscosity is approximated by the Vogel±Fulcher±Tammann Ansatz B 2 g T go exp ÿ T ÿ Tog
16 r3 p f h 3 DG2v
3
with DGv the Gibbs Free Energy dierence which is calculated using the model by Dubey and Ramachandrarao [18] DT 2 DT ; 4 1ÿ DGv DSf DT ÿ Dcp 6T 2T where DSf is the entropy of fusion and Dcp the dierence of speci®c heat between solid and liquid at the melting temperature with DSf 7.47 J/(mol K), Dcp 5 J/(mol K) for Co82 Pd18 and DSf 7.23 J/(mol K), Dcp 6 J/(mol K) for Co50 Pd50 , respectively, [17]. The comparison with values of DGv as determined from the measured speci®c heat values shows, that the agreement is well within the con®dence range of the experimental data [8]. The interfacial energy, r, is determined using the negentropic model [19,20]
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DSf T 1=3
2=3
NL V m
5
with a 0.86 for fcc structure and Vm 7.23 ´ 10ÿ6 m3 /mol the molar volume of Co [15]. Applying Eqs. (1)±(5) the nucleation rate, Iss , is computed for Co±Pd alloys an example of which is shown in Fig. 2 for the alloy Co82 Pd18 both for homogeneous nucleation (solid line) and heterogeneous nucleation (dashed line). As reported previously [10], the solid solution Co±Pd crystallizes very rapidly from the undercooled melt. As an example, the Co82 Pd18 alloy shows a maximum growth velocity at an undercooling of 325 K of 35 m/sec, i.e. the sample in size of 6 mm is fully crystallized within a time period of 200 ls. This also means that one nucleation event is sucient to initiate solidi®cation. Under such circumstances, the relation holds [14] Iss Vt 1
6
with V the volume of the sample and t the observation time which can be directly taken from the measured temperature-time pro®le. Eq. (6) is drawn as a straight line in Fig. 2. The intersection point of this line with the nucleation curve de®nes the maximum undercooling to be expected with V
and t the experiment parameters. The closed dot gives the undercooling result of a levitation experiment on a 6 mm drop, DT 335 K. The heterogeneous nucleation curve is computed such that it is in agreement with this experimental result using the catalytic potency factor, f(h), as the ®tting parameter, yielding f(h) 0.28. The products of chemical reactions of the hot liquid with oxygen impurities within the environmental gas atmosphere may act as a possible source for heterogeneous nucleation sites. There are three Co oxides: CoO (TL 2083 K), CoO4 (TL 1173 K) and Co2 O3 (TL 673 K) [21]. In the temperature range of liquid and undercooled Co base alloys only CoO is stable. It dissolves, however at high temperatures, T > 2000 K, and is reduced by hydrogen. The solubility of O2 in Co and Pd is less than 0.4 at.%. PdO already dissolves at temperatures T 1143 K. The limit of undercoolability by homogeneous nucleation is inferred to be DT 475 K at an experiment time t 100 s. If the droplet diameter is decreased from 6 to 1.5 mm an extension of the undercooling of 10 K is expected provided all other experiment conditions are kept unchanged. A larger undercooling, DT 425 K, may be obtainable if the droplet size is further decreased to
Fig. 2. Nucleation rates calculated for homogeneous nucleation (solid line) and heterogeneous nucleation (dashed line). The heterogeneous nucleation was determined such that it is in agreement with the experiment (solid dot). The maximum undercoolings are given for dierent conditions. For comparison the Tc (s) of the alloy is drawn.
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60 lm and the experiment time is shortened from 100 to 1 s by e.g. a greater cooling rate. The maximum undercoolings are calculated as a function of concentration for Co±Pd alloys assuming that f(h) 0.28 and d 6 mm and t 100 s remain constant. The results of the calculations are plotted in Fig. 1. Surprisingly, the curve computed with f(h) 0.28 only describes the undercooling result of the Co82 Pd18 alloy. If the catalytic potency factor is changed to f(h) 0.34 the undercooling results on Co±Pd alloys of concentrations of x > 30 at.% Pd are in agreement with the analysis but not in the concentration range x < 30 at.% Pd. Obviously, the catalytic potency factor changes continuously in the concentration range from 0 to 30 at.% Pd. Such a behaviour is unusual for a solid solution such as Co±Pd. For instance, in the system Cu±Ni (complete miscibility in solid and liquid but Tc much less than for the Co±Pd alloys) undercooling experiments indicate one unique potency factor, f(h), over the entire concentration range of the alloy system independently on the undercooling technique, in case of droplet dispersion f(h) 0.16 [22] and in case of levitation f(h) 0.19 [23].
magnetostriction) in¯uences undercooling and the onset of magnetic ordering may stimulate crystal nucleation in Co100ÿx Pdx alloys in the concentration range 0 < x < 30.
5. Conclusions
References
The undercoolability of pure Co and Co±Pd alloys has been studied as a function of composition and under dierent experimental conditions. Levitation and ¯uxing was applied to undercool samples of about 1 g in mass. Similar undercoolings were observed independent of the technique. For comparison, smaller drops of pure Co in mass of 170 mg were undercooled in a boronsilicate ¯ux. Here, an undercooling to and even slightly below the Tc of the solid material was measured. The experimental results were analysed within nucleation theory. The analysis shows an unusual behaviour in the concentration range from 0 to 30 at.% Pd such that the nucleation rates cannot be described by heterogeneous nucleation with one unique catalytic potency factor. The crystallization temperatures of the undercooled melt almost coincide with the Tc of the alloys in this composition range. One may speculate that magnetic eects (eg.
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Acknowledgements Support by the Deutsche Forschungsgemeinschaft within contract no He 1601/5, Ho 1942/2 and Wi 1350/3 is gratefully acknowledged. The work at Harvard was supported by the National Aeronautics and Space Administration under Contract No. NAG8 1256. O.B. is an undergraduate student in Materials Engineering, at the Technion, Israel. Her summer work at Harvard was supported through the REU program of the Harvard MRSEC, supported by the National Science Foundation under contract number DMR -94-00396. The authors thank G.-P. G orler, T. Volkmann and R. Willnecker for helpful discussions. One of the authors (D.M.H.) expresses his gratitude to Professor Frans Spaepen for his kind hospitality during a 4 months stay at Harvard.
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