The Influence of Magnetic Order to Crystal Nucleation

Transcription

1 Sino-German Workshop on EPM, Shanghai University October 11 th -1 th, 004 The Influence of Magnetic Order to Crystal Nucleation Sven Reutzel 1,, Dirk Holland-Moritz, Matthias Kolbe, Dieter M. Herlach 1 Ruhr-University Bochum, Germany German Aerospace Center (DLR), Cologne, Germany Corresponding Author: sven.reutzel@dlr.de Tel.: +49 (0) Fax: +49 (0)

2 Overview I Motivation 1 Thermodynamics of Undercooled Metallic Melts Classical Nucleation Model 3 Magnetic Influence on Nucleation II Thermonetic Analyses 1 Method of Measurement Experiments on Co, Co-Pd and Co-Au III Résumé 1 Experimental Results Modification of Existing Classical Nucleation Model

3 Motivation 1 st Order Phase Transition: Solid Liquid Driving Force to Nucleation G(p,T) = G liquid G solid T L G liquid Metastable Stable Liquid Gibbs Free Energy G G G solid T G solid G liquid Temperature T Metastable Regime of Undercooled Liquid

4 Motivation Activation Energy for Nucleation: G 16 σ = π 3 ( 3 G V ) + G* G Cluster Nucleus r* σ r - G V Gibbs Free Energy Difference G V L mol S G G = V Solid-Liquid Interfacial Energy σ(t) Sf T = α (N V ) A mol 1 3 [Spaepen, Acta Acta Metall. 3, 3, (1975) 79] 79] Crystal Nucleation Rate: I SS = k V e G * f( θ ) k T B Nucleation Event: I SS (T N ) V t N 1

5 Motivation Undercooling of Co-Pd Alloys by Different Processing Techniques: Differential Thermal Analysis Electronetic Levitation [Wilde, PhD-thesis, Technical University Berlin (1997)] [Herlach et al., J.Non-Cryst.Sol (1999) 71] 1768 K T L Temperature T 30 K T C T = T L -T N T S T N calculated Nucleation Temperature: DTA EML Co-concentration [at%]

6 Motivation Electronetic Levitation of Co-Pd Melts Nucleation Statistics Observation of Magnetically Induced Crystallisation [Schenk et al., Europhys. Lett. 50, 3, (000), 40] [Holland-Moritz et al., MRS Proceedings 580, (000), 393] T T L T T L -T C Symmetry axis T C Attractive Interaction Increase of Magnetic Order while Approaching Curie-Temperature T C! [Platzek et et al., al., Appl. Appl. Phys. Phys. Lett., Lett., (1994) 173] 173]

7 Thermonetic Analyses Sketch of Constructed Faraday-Balance [Reutzel, Herlach, Adv. Eng. Mat. 3, 1-, (001), 65] z Micro Scale y x Gradient Coil Graphite Tube Control Unit Polecap Thermocouple Polecap Sealed Crucible: Specimen Glas Flux Embedding Magnetic Force Equation H ( T ) = µ 0 ρ V H χ(t ) z FZ 0 const. const.

8 Thermonetic Analyses Front View of Constructed Faraday-Balance Technical Data: Resolution µg at 0 g Load Temperature Range 300 K < T < 000 K Magnetic Field H 1. T

9 Thermonetic Analyses Calibration on Cobalt Molecular Field Theory M(T,H eff ) = M 0 (T, H 0 + λ M(T)) Spontaneous Magnetisation [10 3 ka/m] 0,6 0,4 0, λ = H 0 = 0 T C N g µ 3k B B J(J+ 1) H 0 = 1 T 0, T C = 1394 K, J = S = ½, g =.17, N = 1.61 [Trebble, Craig, Magnetic Materials, Wiley-Interscience (1969)] Temperature [K]

10 Thermonetic Analyses Inverse Susceptibility of Cobalt 1 χ = N µ 3k 0 B eff µ T = 1 T C Release of Latent Heat T L = 1763 K Inverse Susceptibility χ -1 [10 6 kg/m³],0 1,5 1,0 0,5 T N = 1486 K T CS = (1400 ± 3) K T CL = (1394 ± 1) K T = 77 K +5 K/min Effective Magnetic Moments µ effs = (3.18 ± 0.06) µ B µ effl = (3.15 ± 0.06) µ B [Reutzel, Herlach, TMS Proceedings, EPD Congress, (00), 609] 0, µ effs = 3.1 µ [Kamp, Methfessel, B LAM Temperature [K] 6 Proceedings, µ effl = 3.05 µ B 1, (1986), 575]

11 Thermonetic Analyses Completely Miscible Alloy System Co-Pd Inverse Magnetic Susceptibility of Co 8 Pd 18 Inverse Suszeptibilität χ -1 [10 6 kg/m³] 3 1 T CS = 1306 K T CL = 164 K T L = 165 K Co 100-x Pd x Alloy Melts: T N = 1407 K Increasing Co-Content Decrease of (T CS -T CL ) 3 K/min T = 18 K Temperatur [K] µ effs = (.98 ± 0.01) µ B µ effl = (.85 ± 0.01) µ B Co-Content [at.%] T CS -T C L [K] 4 6 [Reutzel, PhD-thesis, Ruhr-University Bochum, 00]

12 Thermonetic Analyses Eutectic Alloy System Co-Au Equilibrium Phase Diagram Temperature [ C] 1495 C 4 C (αco) (εco) T Eut = C ~ 4 C L (Au) C 1700 Undercooling Levels on Co-Au Alloy Melts [ Wilde, PhD-thesis, Technical University Berlin, 1997] T N Nucleation Temperature (DTA using Glass Flux) Cobalt [at.%] Temperature [K] αco Cobalt [at.%] 70 T L T/ ~ 0.1 TL T Eut

13 Thermonetic Analyses Eutectic Alloy System Co-Au Magnetic Effects on Crystallisation? Temperature [K] 1700 αco 1500 T L T C (Au,αCo) Co [at%] T Eut 70 Assumption: Curie-Temperature of of Undercooled Liquid Triggers Nucleation..?

14 Thermonetic Analyses Eutectic Alloy System Co-Au Inverse Magnetic Susceptibility of Co 90 Au 10 Inverse Susceptibility χ -1 [10 6 kg/m³] 1 0 T L C T N T (Au,αCo) C T ~ 50 K T L cooling -5 K/min heating +5 K/min Temperature [K]

15 Thermonetic Analyses Eutectic Alloy System Co-Au Inverse Magnetic Susceptibility of Co 100-x Au x Alloys Inverse Susceptibility χ -1 [10 6 kg/m³] 3 1 T C L decrease T L decrease Temperature [K] x = 0 x = x 10 = x = 010 x = 0

16 Thermonetic Analyses Magnetic Properties of Undercooled Co-Au Alloys [Reutzel, Herlach, Mat. Sci. Eng. A, , (004), 55] µ effl = effl 3. µ B 1700 µ effl = effl.83 µ B Temperature [K] αco 1500 T L T C (Au,αCo) T T L T L L C ~ T C L T Eut Co [at%] 70

17 Résumé Activation Energy [Holland-Moritz, Spaepen Phil. Mag. 84, 10 (004) 957 ] G = 16 ( σ + σ π 3 ( G + G V 3 ) V, ) Broken-Bond Model: Molecular Field Theory: Ordered Cluster (fcc) V L,S G = H -T S L,S Melt (111)-Surface, Z fcc = 1 3 Missing Nearest Neighbour Atoms! H L,S G V H Surface = 3 H 1 Atom S L,S σ = σ ( H Atom ) T S C T L C V σ 1% σ G 15% G V (T N ) G* Lowered by Magnetic Contribution!

18 Résumé I Precise Detection of Magnetic Properties of Undercooled Co and Co-Pd- & Co-Au-Alloy Melt at Elevated Temperatures! II Detected Curie-Temperatures of Liquid Phase of Cobalt and of Co-Pd- & Co-Au-Alloy Systems Correspond to Maximum Undercooling Levels III Crystal Nucleation in Undercooled Liquid Affected by Onset of Magnetic Ordering IV Formulation of Extended Nucleation Model Useful to Describe Limited Experimental Undercooling Levels

19 Acknowledgement Contributors G.P. Görler T. Volkmann Project Funded by Deutsche Forschungsgemeinschaft