3D KMC Simulation in the Annealed Binary and Ternary Alloy Systems Xuan Zhang, Mengqi Huang Dept. of MatSE and Dept. of NPRE, UIUC May 11, 2010

Motivation Binary thin film alloy (Cu-Nb): large Nb precipitates ( > 40 nm) at 600C [1] Ternary thin film alloy (Cu88.5W1.5Nb10): thermal annealing at two different temperature, different structures are observed in XRD: Solution: a simplified model, using KMC simulation to study the evolution of precipitates. Knowledge we know: Below 600 C, W is immobile in bulk Cu At 600 C, W starts to be mobile Nb is mobile at both of the temperatures Mobility of W is the key point! [1] E. Botcharova etc. Journal of Alloys and Compounds 356 (2004) 157-163

KMC flowchart: start Parameter input Initial configuration done. N = 643 atoms Only one vacancy: Initial configuration done. Calculate jumping probabilities. : thermal transition rate of the vacancy jumping to the nn sites. Choose a jump. nstep Update configuration. Configuration output; analysis output. End.

KMC parameters Eorder Ecoh EVf ESaddle Binary system A90 B10 Ordering energy Cohesive energy Vac. formation energy Saddle point energy Eorder Ecoh EVf ESaddle Binary system A90 B10 Ternary system A89 B10 C1 [2]J. M. Roussel and P. Bellon, Physical Review B 63(2001) 184114

KMC parameters -- EVf Time scale T (℃) 100 300 400 500 A 6.9E11 6.7E5 821 2.0E16 4.6E8 3.6E6 1E5

Part 1. Average particle size VS real time Binary A90 B10 Ternary A89 B10 C1 Ternary system has much smaller precipitates than binary system. The lower the temperature, the more time it will take to form precipitates the same size as of the higher temperature.

Part 2. important parameter -- ESaddle x Saddle point energy: determine atom’s mobility Decreasing the mobility of atom C by increasing ECSaddle The Five Frequency Model[3]: - Assume an infinite dilute solution A-C - Get the exchanging rate between vacancy and neighboring atoms. A B w2: the frequency of B atom-vacancy exchanges [3] J. Philibert, Atom movements: diffusion and mass transport in solids, Monograph de Physique F-91944, France 1991

Histogram of (C)n at different ECSaddle T = 300 C

Part 3.Simulation of experimental conditions (ECS=-9.2eV) Three different conditions: annealing temp (C) Amount of B in matrix Amount of C in matrix 1 300 5% 69% 2 300+500 <13% <50% 3 500 <11% <41% 300 C 300 C + 500 C 500 C

Conclusions Ternary alloy will have much smaller precipitates than binary alloy for all the temperatures. The saddle point energy of C atom plays a key role in simulation. By simulating the experimental conditions, main features are obtained, and a qualitative explanation is given; however, more data is needed to make it convincing enough.