Derivation of TTT diagrams with kinetic Monte-Carlo simulations

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Gertrude Blankenship
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1 Derivation of TTT diagrams with kinetic Monte-Carlo simulations A. Gupta, B. Dutta, T. Hickel, J. Neugebauer Department of Computational Materials Design Düsseldorf, Germany 15. September, 2016 BRITS Workshop, Dresden, September 2016

2 2 TTT-Diagram : Blueprint for heat treatment Al-based Alloys Heat Treatment Sketch: Fe-C TTT-diagram Precipitation hardening Solid solution annealing Precipitation Kinetics Precipitation Finer precipitates Coarse precipitates TTT-Diagrams Resulting Microstructure Final Product

kmc Methodology Starting configuration Harmonic Transition State Theory r htst = Γ 0 e 2E b List all the possible jumps Assign a transition rate r to each jump k B T Choose a jump k

3 kmc Methodology Starting configuration Harmonic Transition State Theory r htst = Γ 0 e 2E b List all the possible jumps Assign a transition rate r to each jump k B T Choose a jump k Execute and update configuration N R = ) r n n11 k21 k ) r n ρ 1 R ) r n n11 n11 E b = E 0 + n E bond Linear Bond-Cutting Model Update simulation time t = t + t t = ln (ρ 2 ) R While t < t #$% 3

4 Precipitate formation (T = 400K, supercell 25x25x25, E bond 0.1 ev) t 1 t 2 t T = 0 t J 0.1 µs t Q 1 µs t 3 How does this precipitation kinetics varies with temperature? t 4 t R 3 µs 4

Size distribution of precipitates (Low T) Initial stage of transformation q Decrease in gas phase concentration q Smearing towards larger particle sizes Simulation Parameters: 400

5 Size distribution of precipitates (Low T) Initial stage of transformation q Decrease in gas phase concentration q Smearing towards larger particle sizes Simulation Parameters: 400 K, 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev Later stage of transformation q Smaller precipitates dissolves and leads to the growth of large precipitate q Ostwald ripening 5

How does this transition from low to high T varies?

6 Size distribution of precipitates (High T) 700 K 750 K Ø Gas phase concentration remains constant Ø No precipitate growth observed How does this transition from low to high T varies? Simulation Parameters: K, 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev 6

7 Evolution of largest precipitate (n max ) Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev log(t) (seconds) n eq (T) Sudden drop (T 700 K) T 0.2 c q As the temperature, n max q The fluctuations increase with the temperature Temperature (K) 7

8 Nucleation stage 8 Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev q As T increases: - the duration of nucleation stage increases. - the critical nuclei size increases. We know precipitate size à remaining gas phase

9 Evolution of the gas phase 9 Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev ØWith increasing temperature, gas phase amount increase à Entropy dominates at high temperatures Ø Fluctuations increase with increasing temperature

10 Advancement Factor X(t) : Degree of Transformation 10 c m t = 0 initial conc. of solute in the matrix c m t remaining solute conc. at time t c m t equilibrium conc. of solute atoms Ø X(t) = 1 means end of transformation process Ø Equilibrium value of 1 is reached Ɐ T. Ø As T increases, total time for completion decreases à signifies the speed up with increasing temperature.

11 Gas Phase Concentration: Analytical vs Calculated = Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev ØFinite size effect observed (real system C N = 6) ØShaded area : no stable precipitates observed 11

12 Obtaining Time Scale : Statistics 12 Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev ØProcess repeated for different T and N c. TTT Diagrams

Calculated TTT Diagrams Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev E bond = 0.1 ev Kinetics Driving force E bond = 0.2 ev -10-9.5-9 -8.5-8 -7.5 log(t) (seconds) -8.

13 Calculated TTT Diagrams Simulation Parameters: 25x25x25 supercell E bond = 0.1 ev, E 0 = 0.3 ev E bond = 0.1 ev Kinetics Driving force E bond = 0.2 ev log(t) (seconds) log(t) (seconds) Ø No clusters observed at temperatures beyond 675 K. ØIs there a relation between Nose T and T asym? E bond = 0.3 ev log(t) (seconds) 13

14 14 Relationship between nose temperature T n and T asymp Ø Linear relation is obtained between T n and T asymp Ø Ignoring the intercept (150), y = 0.63x reflects the asymmetric nature of C-shape of the TTT diagrams around the nose. Ø Entropy only dominates at high temperatures which might explain this asymmetry

asymptotic temperature Outlook q Extension to realistic binding energies and Al-Sc alloy q Effect of strain on the

15 Conclusions 15 q Equilibrium size of the precipitate decreases with temperature due to entropy domination q Finite-size effects observed q Upper TTT curve challenging-no stable precipitates q Relationship b/w nose and asymptotic temperature Outlook q Extension to realistic binding energies and Al-Sc alloy q Effect of strain on the precipitation kinetics within a combined EAM-cluster expansion-kmc formalism (in collaboration with Prof. Mark Asta, UC Berkeley)

16 16 THANK YOU FOR YOUR ATTENTION q Financial support from DFG under SPP-1713 Priority Program Strong coupling of thermo-chemical and thermo-mechanical states in applied materials is highly acknowledged.

Molecular Dynamics Simulations of Fusion Materials: Challenges and Opportunities (Recent Developments)

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