1. A Kinetic Monte Carlo Study Of Ordering in a Binary Alloy Group 3: Tim Drews (ChE) Dan Finkenstadt (Physics) Xuemin Gu (MSE) CSE 373/MatSE 385/Physics 363 Final Project University of Illinois at Urbana-Champaign December 14, 2000

2. Code Introduction Main part of project: development of Kinetic Monte Carlo (KMC) code to simulate ordering in a binary superalloy Equilibrium simulations that compute a vacancy pathway through the bulk alloy Simulated alloy: similar to Fe-Al Exhibits three phase behavior: 1.B2 ordered phase 2.A2 disordered phase 3.A2+B2 mixed phase Compared the results to phase diagrams from the literature Developed data analysis code to compute various order parameters Developed many visualization techniques to determine the phase of the alloy

3. Kinetic Monte Carlo Method Move Nearest Neighbor Sites 01 1 2345678 Jump Frequency and Potential Function where

4. Phase Diagrams Theoretical Simulated with Grand Canonical MC Simulations Reproduced from A Monte-Carlo Study of B2 Ordering and Precipitation Via Vacancy Mechanism in B.C.C. Lattices. Athenes, M., Bellon, P., Martin, G., and Haider, F. Acta Metallurgica. Vol. 44, No. 12, pp. 4739-4748, 1996.

5. BCC Lattice Bulk BCC Lattice Two Simple Cubic Lattices a sublattice (arbitrary)  sublattice (arbitrary)

6. 64 Cell Cubic Lattice - Disordered A2 Phase T = 1000 K u 1 = -0.04 1*10 7 MC Steps c B = 0.25  sublattice  sublattice  2 plot

7. 32 Cell Cubic Lattice - High and Low Order B2 Phase  sublattice  sublattice  2 plot T = 700 K MC steps = 1*10 7 u 1 = -0.04 c B = 0.25 T = 700 K MC steps = 1*10 7 u 1 = -0.04 c B = 0.50

8. 64 Cell Cubic Lattice - High Order B2 Phase  sublattice  sublattice  2 plot T = 700 K u 1 = -0.04 1*10 7 MC Steps c B = 0.45

9. 16, 32, and 64 Cell Cubic Lattice - High Order B2 Phase  sublattice  sublattice  sublattice  sublattice  sublattice  sublattice 1*10 7 MC steps 1*10 6 MC steps T = 700 K u 1 = -0.04 c B = 0.45

10. 32 Cell Cubic Lattice - Mixed A2+B2 Phase  sublattice  sublattice  2 plot T = 200 K u 1 = -0.04 1*10 7 MC Steps c B = 0.25

11. Conclusions KMC code can generate expected equilibrium phase behavior, for a given temperature and concentration, provided enough MC steps are taken for the given simulation cell size Observed dynamic growth and ageing Did not distinguish phase transitions Could do this by computing total free energy and looking for kinks in the free energy diagram Could also look for critical slowing down or finite-size scaling phenomena Did not vary the activation energy Done by Athenes, et al., and this energy was found to have a significant effect Can be readily done with this code