1. 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

2. 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)

3. 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.

4. 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)

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

6. 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.

7. Part 2. important parameter -- ESaddlex
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

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

9. 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
<13%
<50% 3
500
<11%
<41%
300 C
300 C C
500 C

10. 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.