Phase-Field Modeling of Technical Alloy Systems Problems and Solutions

Transcription

1 Thermo-Calc User Meeting, Sept , Aachen Phase-Field Modeling of Technical Alloy Systems Problems and Solutions B. Böttger ACCESS e.v., RWTH Aachen University, Germany

2 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

3 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

4 Introduction: Phase-Field Simulation of Complex Technical Microstructures Goal: Simulation of microstructure formation during phase transformations in technical alloys Challenges: complex alloys complex morphologies carbon steel Fe C Si Mn P S Al Cr Cu Mo N Ti Ni equiaxed microstructure Bal. 0,225 0,078 1,66 0,012 0,0015 1,526 0,021 0,019 0,0053 0,0024 0,0038 0,021 complex thermodynamics Al piston alloy complex processes die casting pragmatic phase-field approach

5 Introduction: Pragmatic Phase-Field Approach What is a pragmatic phase-field approach? multiphase-field model which allows simulation on µm scale online-coupling to off-the-shelf thermodynamic and diffusion databases advanced thermal coupling to external process conditions pragmatic simulation strategy (calibration, simplifications) robust multi-purpose code (no dedicated solutions) MICRESS : MICRostructure Evolution Simulation Software

6 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

7 Phase-Field Model Diffuse interface, described by the phase-field parameter f: The order parameter f = f (x,t) corresponds to a density function for the phase state. h is the interface thickness (numerical parameter) h

8 The Multiphase-Field Model f 1 N f f f fc ( n,n ) K ( f, f, f, f ) f h, f c Vector order parameter f f c : pair interaction energies : chemical free energy f f f f : interfacial growth operator what is pragmatic? bulk thermodynamic data are used only for the chemical free energy f c f is a function of c, not of c! coupling to arbitrary thermodynamic databases possible!

9 Multiphase-Field Model: Phase-Field Equation Multiphase-field equation: f n * * f 2 f f 2 f 2h 2 f f 2 n J h f f G dual interface terms double_obstacle higher interface terms multi_obstacle chemical driving force h = interface thickness = interfacial mobility (anisotropic) = interfacial energy (anisotropic) G = driving force Steinbach et al; Physica D 1996 Tiaden et al. Physica D 1998 Steinbach, Pezzolla; Physica D 1999 Eiken, Böttger, Steinbach; Phys. Rev. E 2006

10 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

11 Phase-Field and Thermodynamics: Quasi-Equilibrium phase-field simulation: f are additional conditions! minimization of the chemical free energy G f f f k ~ k f c f f at constant phase fractions f gives: df k k k df c c, ~ k k dc dc G k c k c c G, k k c and c are calculated iteratively including the mass balance: f f c k k f c f c k c k

12 Phase-Field and Thermodynamics: Multiphase Quasi-Equilibrium Multiphase-field method: additional phases are included into the iteration process: f Phase Phase Phase G G c k c k c k c k iteration for N phases: G f f k ~ k df df k k ~ k df c c,..., dc k dc k dc k fi i k i c c k consistent quasi-equilibria for all phase pairs

13 Use of Thermodynamic Data in MICRESS M I C R E S S time loop nucleation model Tund Tcrit? CALPHAD database multiphase-field solver f (x,t) ( K wg ) multicomponent diffusion solver c ( x,t ) f D c temperature solver Thermo-Calc

14 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

15 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

16 a) Stoichiometric Phases problems in several places: a) composition cannot be used as a condition! use arbitrary activity for calculation of H or D G α β b) quasi-equilibrium: use condition for other phase quasi-equilibrium calculation starting from c k α k k k 2-phases.: c ( c f c ) / f only one phase can be stoichiometric for each element c) phase-field equation: possible violation of physical composition range 0< c α <1! restriction of phase-field increment restriction of time step k k k f c c f c, k k f ( 1 c ) f ( c 1) ( ck 1) stoichiometric phases are automatically detected by MICRESS phases with small solubility range should also be treated as stoichiometric

17 Example1: Alloy KS1295 (Al-Si-Fe-Ni-Cu-Mg-Zn), Comparison to Quantitative Metallography * ** databases: TTAL5, MOBAL1 * Mg 2 Si + Al 5 Cu 2 Mg 8 Si ** Al 3 Ni collaboration with Kolbenschmidt/Germany and University of Manchester

18 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

19 Composition Sets in many databases (e.g. TTNI7), identical thermodynamic descriptions are used for several phases! G LIQUID FCC_A1 #1: FCC #2: Ti(N,C) #3: Nb(C,N) calculation of quasi-equilibrium (parallel tangents in Gibbs energy diagram) gives several solutions! composition the composition sets are only distinguished by the start values for numerical iteration for numerical reasons, composition can switch between different phases! in phase-field simulation, switching is not allowed because phase identity is linked to objects or grid points in MICRESS, user-defined concentration limits can be used, as Calphad does not give support

20 Example 2: Equiaxed Solidification Microstructure of IN718 Laves NbC Nb δ TiN Laves NbC Ti δ (Ni,Cr) 3 B 2 TiN h fcc (Ni,Cr) 3 B 2 h fcc

21 Example 3: Columnar Ni-Base Microstructure before and after Diffusion Heat Treatment before : Ti after: Ti before after before after

22 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

23 Charged Species additional electroneutrality condition: Example Slag: Ca 2+, Si 4+, Al 3+, O 2- element composition as condition would not work! How can it work? a) treatment as stoichiometric phase (even if not true!) composition is not used as condition but: only possible if no interaction to other stoichiometric phases are needed! b) use composition of uncharged species, example: CaO, SiO 2, Al 2 O 3 may not be possible for all phases c) if elements with more than one oxidation state are present in phase extra degree of freedom compensates electroneutrality condition! Examples: - O 2 diffusion through Co 1-δ O membrane - ionic liquid in system Ag-Cu-O

24 Example 4: O 2 diffusion through Co 1-δ O membrane 1 p O 2 < 1 p O 2 O 2 (g) VA Co 3+ v O 2 (g) ½ O 2 +2 Co 2+ 2 Co 3+ + O 2- O Co (1-δ) O Membrane Co 3+ ½ O 2 +2 Co 2+ membrane is moving in oxygen pressure gradient morphological instability?

25 Example 4: O 2 diffusion through Co 1-δ O membrane Can be treated in MICRESS as a ternary system ABC: membrane: A(O 2- = 0.5at%), B(Co) and C(VA) gas phase is considered as a dissolution of A(O 2 ) in C(vacuum) construction of a linearized phase diagram using experimental concentration of vacancies: m A /m B = c V /c O 2 = const M. Martin, Materials Science Reports 7 (1991) 1-86.

26 Example 4: O2 diffusion through Co1-δO membrane: MICRESS results gas A=0.01 B=0 CoO A=0.5 B= gas A=0.1 B=0 x(b)

27 Example 4: O 2 diffusion through Co 1-δ O membrane: MICRESS results gas CoO gas A=0.01 A=0.5 A=0.1 B=0 B= B=0 x(b)

28 Example 4: O 2 diffusion through Co 1-δ O membrane: Experimental results Membrane is moving towards higher chemical potential of O 2 : M. Martin, Materials Science Reports 7 (1991) 1-86.

29 Example 4: O 2 diffusion through Co 1-δ O membrane: Experimental results Formation of morphological instability: M. Martin, Materials Science Reports 7 (1991) 1-86.

30 Example 4: O 2 diffusion through Co 1-δ O membrane: Experimental results Finally break-through towards the oxygen-rich side: M. Martin, Materials Science Reports 7 (1991) 1-86.

31 Example 4: Ag-Cu-O system, Ag8Cu Brazing with Contact to Air Al 2 O 3 brazed with Ag8Cu at: 970 C 1150 C Al 2 O 3 Al 2 O 3 Ag CuO CuO (Cu,Al)O Ag What happens during solidification? Which is the role of Cu for wetting?

32 Phase Diagram of Ag-Cu-O Species: Cu 2+, Cu +, Ag +, O 2-, VA Reference: Assal, J.; Hallstedt, B.; Gauckler, L.J., J. Phase Equilib., 19, , 1998

33 MICRESS Simulation: First Results and Comparison to DSC Experiment ionic liquid #1 (c Ag = 0.98) ionic liquid #2 (c Ag = 0.36) virtual DSC O 2 gas (0.21 atm) L1CuO+Ag CuO L2L1+CuO fcc (Ag)

34 Outline 1. Introduction 2. Pragmatic Multi-Phase-Field Model 3. Coupling to Thermodynamic Data: Quasi-Equilibrium 4. Specific Problems and Solutions 5. Conclusion a) Stoichiometric Phases b) Composition Sets c) Charged Species

35 Conclusion MICRESS is a software for simulation of technical alloys as it uses a pragmatic phase-field model and robust coupling to arbitrary Calphad databases Specific solutions for topics like stoichiometric phases or composition sets are needed Simulation of charged species is possible under certain conditions, as shown for the system Ag-Cu-O

36 Thank you for your attention!