Modelling of Kinetics in Multi- Component, Multi-Phase, Multi- Particle Systems: Application E. Kozeschnik J. Svoboda F.D. Fischer Institute for Materials Science, Welding and Forming, Graz University of Technology Materials Center Leoben, Austria Academy of Sciences, Brno, Czech Republic Institute of Metal Physics, University of Mining, Leoben, Austria Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Austria Institute of Mechanics, University of Mining, Leoben, Austria

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Contents Model formulation Computer Implementation Algorithm flow-chart Application to –Nucleation, growth and coarsening of cementite in steel –TTP Diagram for gamma_prime in Ni-base –Complex experimental tool steel

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, The modeling team ( )... J. Svoboda –Academy of Sciences, Czech Republic, CZ F.D. Fischer –Institute of Mechanics, University of Leoben, A E. Kozeschnik B. Sonderegger (2004-) –Institute for Materials Science, Welding and Forming, Graz University of Technology, A Task: Model development and implementation for precipitation kinetics in multi-component, multi-phase, multi-particle systems

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Idea … System with spherical precipitates of different size, composition and phase type in multi-component matrix. Evolution equations from Onsager thermodynamic extremal principle: System develops with constrained maximum Gibbs Free Energy dissipation.

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Model formulation: Growth … Gibbs Free Energy Maximum Gibbs Free Energy Dissipation with constraint

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Gibbs Free Energy dissipation … 1.Diffusion through matrix 2.Interface movement 3.Diffusion in precipitates

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Results: Growth Linear system of equations in, and :

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Multi-component nucleation

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Thermo-Kinetic software: MatCalc Equilibrium (CALPHAD) Diffusion (MOBILITY) Phase trans- formations E. Kozeschnik, B. Buchmayr, “MatCalc – A simulation tool for multicomponent thermodynamics, diffusion and phase transformation kinetics”, in: ‘Mathematical Modelling of Weld Phenomena 5’, Institute of Materials, London, Book 734, 2001;349.

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Software implementation Overall composition Matrix phase Precipitate 1 Precipitate 2 Precipitate 3 … Microstructure - f(t,T) dislocation density grain size sub-grain size … Precipitate props , k, M intf nucleation site(s) … + NRXCXC X Cr X Fe … 1e124e e135e e136e ……… bulk dislocations grain boundaries sub-grain boundaries other particles

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Calculation: flow-chart Pre-Proc.: Initialize and set up parameters for all precipitates Nucleation? Add precipitate class Growth Evaluate Dissolution? Remove prec. class next time step Post-Proc.: Evaluate results

Example I Nucleation – Growth - Coarsening

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Start MatCalc... Live demo... Cementite precipitation in Fe-0.1%C 100 precipitate classes Automatic interfacial energy

Example II TTP-diagram

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik,  ’-precipitation in Ni-base alloy Ni-13at%Al 200 classes  =17 mJ/m 2 Cooling rates: 0,01 – 1000 °/s

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, e01e11e21e31e4 time [s]  ’-precipitation in Ni-base alloy 0.1% 1% 10% 25% 50% 75%

Example III Complex systems...

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, A Comprehensive Treatment of Precipitation Kinetics in Complex Materials B. Sonderegger 1,6,M. Bischof 2, E. Kozeschnik 1 H. Leitner 2, H. Clemens 2, J. Svoboda 4, F.D. Fischer 3,5 1: Institute for Materials Science, Welding and Forming, Graz, University of Technology, Austria 2: Dept. of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Austria 3: Institute of Mechanics, Montanuniversität Leoben, Austria 4: Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech Republic 5: Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Leoben, Austria 6: Materials Center Leoben, Leoben, Austria Presentation given at „Solid-solid Phase Transformations in Inorganic Materials“, Phoenix, AZ, USA, 2005

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Outline Introduction Experimental Numerical Results Conclusion ! !

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Outline Complex material Experimental Results Improved Understanding of Precipitation Kinetics Numerical Simulations

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Introduction Precipitation Hardening in Steels Carbides,Nitrides Intermetallic Phases (e.g maraging steels) Testmelt

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Testmelt CCrMoVNiAlCoSiMnFe bal Composition (at%) Carbides (MC, M 2 C, M 3 C, M 6 C, M 23 C 6 ) Intermetallic Phases (NiAl, B2 ordering)

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Experimental Investigations Casting, Austenitising, HT Up to 10000min APFIM SANS TEM M. Bischof et al.: „An advanced approach to the characterisation of precipitates in steels“, 4:45pm, Room Pueblo/Sonora

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Experimental - Numerical Numerical Simulation: APFIM SANS TEM “MatCalc—a simulation tool for multicomponent thermodynamics, diffusion and phase transformation kinetics.” Kozeschnik E, Buchmayr B., Mathematical mod. of weld phenomena 5. London Institute of Materials; p. 349– 61

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Simulation Starting Conditions Database: extended TCFE3+Mobility Chemical Composition (10 Elements) Phases: MC, M 2 C, M 3 C, M 6 C, M 23 C 6, NiAl Matrix: Grain Size, Subgrain Size etc. (Number of Nucleation sites) Interfacial Energies Chemical driving forces Chemical potentials Exact Heat Treatment conditions from casting to annealing (610°C, up to 10000min (167h)) Calculated from thermodyn. Databases

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Equilibrium Analysis Precipitates after austenitising (990°C) Precipitates after HT (10000min) (610°C) MX M6CM6CM6CM6C M 2 C?M2CM2C M 23 C 6 NiAl No M 3 C Decrease of G(M 6 C): G=G [J/mol]

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Calculation with improved database Improved Database M 6 C: 1,5mol%, d=580nm MX: 0,2mol%, d=60 nm M 2 C: very few primary G(M 6 C)=G [J/mol]

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Identification of Precipitates cast + austHT NiAl MX M2CM2C Cementite M 23 C 6 M6CM6C : too small SANS (HT 10000min)

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, M 23 C 6 : nucleation too fast r stays too small f growing too fast Variation of G? Correction of  ! Increase of  Lower Nucleation Rate Slower increase of f Faster increase of r Matrix Parameters? cast + austHT Identification of Precipitates

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik,  (M 23 C 6 ) All numerical results agree with experimental findings (within statistical errors) HT

IWS, Graz University of Technology, Austria / Materials Center LeobenE. Kozeschnik, Summary and Conclusions Simulated full heat treatment of a very complex system (10 Elements, 6 phases) Correct Equlibrium Calculations Very good results of kinetic simulation Fit of 2 parameters were sufficient to meet ~ single measurement points Experiments get easier to interpret Simulation results get improved Further development of thermodynamic databases