Interfacial Pattern Formation During Rapid Phase Transformations in a Binary System
Final Report Abstract
Solidification of alloys often occurs under conditions far from thermodynamic equilibrium. This process of "rapid solidification" requires special concern beyond the conventional formulations of piecewise linear non-equilibrium thermodynamics. The microstructures and thus the properties of the resulting solids are largely determined by the pattern-forming processes during solidification. Theoretical and experimental work was performed. An alloy system Co-Cu has been analysed in a region of miscibility gap with separation of the undercooled melt into the Co-rich and Cu-rich liquids. Phase separation of undercooled and quenched specimens of Co50Cu50 alloy have been investigated experimentally using electromagnetic levitation technique, quenching onto a Pb-solder coated copper chill substrate and splat quenching methods. A variety of microstructures has been observed. It is found that quenching of the liquid samples with the cooling rate ? 106 K/s leads to a freezing of microstructure of primarily spinodally decomposed liquids. The composition of the Co-rich phase measured by TEM-EDS is Co71.7Cu28.3 and the Cu-rich phase is Co26.8Cu73.2 respectively. These compositions are inside the spinodal region and close to the calculated spinodal boundary in the phase diagram of the Co-Cu system. The solidification velocity as a function of undercooling has been measured for the Co81.2Cu18.8 composition. The data has been analysed within the Galenko and Danilov model using a kinetic growth coefficient of µ=0.22 m/Ks. Two different morphologies of the Co-rich phase have been observed. They attributed to the transition in the dendrite growth kinetics from diffusionally and thermally controlled to only thermally controlled growth. On the numerical simulation level, pattern formation was investigated through phase-field model and boundary-integral technique. Our work first consisted in solving the problem of dendritic growth along an interface using the boundary-integral technique (sharp interface approach). The presence of a triple junction was found to provide a selection mechanism and, in this frame, a eutectoid dendritic growth was studied. Secondly we focused on peritectic, eutectic and monotectic alloys. Prior to the beginning of this project, some substantial analytical development of the theory of liquid-film-migration (LFM) had been made. Using this frame, we investigated numerically this phenomenon in the peritectic system using the phasefield method. This method has the advantage to pick up only dynamically stable steady states. The LFM was found to be the generic process for isothermal transformations only above the peritectic temperature Tp. Finally, we focused on the isothermal solidification of monotectic alloys showing a phase separation of the liquid phase like in Co-Cu system. Along the liquidliquid interface, the solidification is found to take place through an assymetric dendritic growth, obtained by means of phase-field method and sharp-interface method. From a single liquid phase, the solidification takes the form of a lamellar structure that is often obtained experimentally, but it can also consist in a LFM process where the stable liquid separates the metastable liquid and the solid. Outlook for future work and possible applications: • Measurements of thermo-physical properties for the Co-Cu alloy in the vicinity of critical point (around critical concentration and critical temperature), especially below and at the critical temperature; • Experimental investigations of phase separation including the complete scenario of phase separation in the alloy (binodal and spinodal decompositions); Verification of the theoretical models for phase separation in comparison with the obtained scenario, • Experimental tests for the transition from the diffusion-controlled to diffusionless dendritic growth together with the appearance of grain-refined effect in the Co82.2Cu18.8 alloy; • Tests of theoretical models for single dendritic growth and two-phase-mushy zone in comparison with presently obtained dendritic growth kinetics in the Co82.2Cu18.8 alloy. • Numerical investigation of the dendritic solidification along the liquid-liquid interface (publication in preparation). • Numerical investigation of the influence of the diffusion in the second liquid phase in a more systematic way. Indeed, a broad spectrum of different patterns is expected in monotectic systems.
Publications
- (2007) Analysis of dispersion relation in spinodal decomposition of a binary system, Philosophical Magazine Letters, 87(11), 821-827
P. Galenko, V. Lebedev
- (2007) Experimental test for hyperbolic model of spinodal decomposition in a binary system, Letters to Journal of Experimental and Theoretical Physics, 86(7), 527-529
P. Galenko, V. Lebedev
- (2007) Modeling of non-equilibrium effects in spinodal decomposition of a binary system, EUROMAT-2007,Nürnberg (D)
P. Galenko, V. Lebedev
- (2007) Non-equilibrium effects in rapid solidification and spinodal decomposition, Liquid and Amorphous Metals (LAM-13), Ekaterinburg (Russia)
P. Galenko, D. Herlach
- (2007) One test for a hyperbolic model of spinodal decomposition in a binary system, Experiments in Space and beyond (dedicated to J.C. LEGRO), Brussels (Belgium)
P. Galenko, D. Herlach, V. Lebedev
- (2007) Supersymmetry model of a binary mixture with noise of the diffusion flux, Physics Letters A, 365 358–363 (2007)
A. Olemskoi, P. Galenko, A. Shmatko
- (2007), invited lecture, Spinodal decomposition in a binary system as a fast phase transition, Interdisciplinary Workshop: Recent trends in phase-field theory. Institut Henri Poincaré, Paris (France)
P.K. Galenko
- (2007), Local non-equilibrium effect on spinodal decomposition in a binary system, JETC-IX: Joint European Thermodynamic Conference Saint-Etienne: Ecole Nationale Superieure des Mines
P. Galenko, V. Lebedev
- Velocity Selection Problem in the Presence of the Triple Junction, Phys. Rev. Lett. 99, 105701 (2007)
E.A. Brener, C. Hueter, D. Pilipenko, D.E. Temkin
- (2008) Local nonequilibrium effect on spinodal decomposition in a binary system, The International Journal of Thermodynamics, 11(1), 21–28
P. Galenko, V. Lebedev
- (2008) Modelling of memory effects in spinodal decomposition. MRS – Materials Research Society Symposia “Computational Materials Design via Multiscale Modeling”, Boston (USA)
N. Lecoq, H. Zapolsky, P. Galenko
- (2008) Temperature at the front of a moving two-phase zone in a supercooled binary mixture, Transactions of the Udmurt State University: PHYSICS, 4, 57-66
P. K. Galenko, D.E. Temkin
- (2008): Phase separation in undercooled and quenched Co-Cu melts, 13th International Conference on Rapidly Quenched and Metastable Materials, Dresden (D)
E. Davydov, P.K. Galenko, D.M. Herlach, M. Kolbe, D.E. Temkin
- DPG meeting 2008, Berlin
G. Boussinot
- invited lecture, Theoretical modelling of patterns in rapid solidification and spinodal decomposition. Phase-field-Simulations: Materials Science meets Biology and Medicine International Focus Workshop (Dresden, November 12 - 14, 2008)
P. Galenko
- (2009) Deterministic and stochastic phenomenological models in spinodal decomposition of a binary system, Progress in Physics of Metals [Uspekhi Fiziki Metallov], 10, 27-102
D. Kharchenko, P. Galenko, and V. Lebedev
- (2009) Evolution of the structure factor in a hyperbolic model of spinodal decomposition, The European Physical Journal ST, 177, 165
N. Lecoq, H. Zapolsky, P. Galenko
- (2009) Kinetic contribution to the fast spinodal decomposition controlled by diffusion, Physica A 388, 3113
P. Galenko and D. Jou
- (2009) Phase-field modeling of rapid solidification: solute trapping and diffusionless crystal growth, 2nd Symposium on Phase-Field Modeling in Materials Science, Rolduc Abbey, (Holland)
E. Abramova, D. Danilov, P. Galenko, V. Lebedev
- (2009), invited lecture, Application of the fast transition model to the process of phase separation by spinodal mechanism, EUROTHERM Seminar Nr.84, Namur (Belgium)
P. Galenko
- 2nd Symposium on Phase-field modelling in Material Science (PF09), Rolduc Abbey, Kerkrade, Netherland, August 2009
G. Boussinot
- 5th International conference on Diffusion in Liquids and Solids, Roma, Italy, June 2009
E.A. Brener
- DPG meeting 2009, Dresden
G. Boussinot
- GDR ‘Transdiff’ meeting, Grenoble, France, April 2009
G. Boussinot
- (2010) Spinodally decomposed patterns in rapidly quenched Co-Cu melts: experiments and modelling, 14thLiquid and Amorophous Metals (LAM-14), Rome (Italy)
E. Davydov, P.K. Galenko, D.M. Herlach, M. Kolbe, N. Wanderka
- Kinetics of isothermal phase tranformations above and below the peritectic temperature : Phase-field simulations, Acta Materialia 58, 1750 (2010)
G. Boussinot, E.A. Brener, D.E. Temkin
- Kinetics of isothermal phase tranformations by phase-field simulations : an analogy between the peritectic and monotectic systems, Defect and Diffusion Forum, Vols 297-301, Trans Tech Publications, Switzerland (2010)
G. Boussinot, E.A. Brener, D.E. Temkin
- SPP 1296 Kick-Off meeting, Aachen, January 2010
G. Boussinot
