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
•
Ternary thin film alloy (Cu88.5W1.5Nb10): thermal annealing at two different
temperature, different structures are observed in XRD:
10
4
600C_2hr
Cu
600C_2hr_700C_2hr
Knowledge we know:
700C_2hr
counts
10
3
10
2
10
1
Nb
[1]
 Below 600 C, W is immobile in bulk Cu
W
 At 600 C, W starts to be mobile
 Nb is mobile at both of the temperatures
Mobility of W is the key point!
10
0
36
38
40
42
44
46
2
• Solution: a simplified model, using KMC simulation to study the
evolution of precipitates.
[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: X VKMC  1 / 643  3.8 10 6
  1 /  vi
Calculate jumping
probabilities.
Choose
a jump.
Update
configuration.
Configuration output;
analysis output.
End.
 vi
nstep
i
: thermal transition
rate of the vacancy jumping
to the nn sites.
• Ordering energy
KMC parameters
• Cohesive energy
• Vac. formation energy
• Saddle point energy
Eorder
Binary
system
A90 B10
Ternary
system
A89 B10 C1
Ecoh
EVf
ESaddle
coh
order
E AB
 0.0553eV [2] E A  4.34eV
f
E AV
 1.28eV
E AS  10.217eV
EBcoh  4.34eV
f
EBV
 1.28eV
EBS  10.217eV
f
E AV
 1.28eV
E AS  10.217eV
f
E BV
 1.28eV
E BS  10.217eV
f
ECV
 1.28eV
ECS  10.217eV
order
E AC
 0.1659eV

order
E AB
 0.0553eV

E
order
BC
 0eV
E
coh
A
 4.34eV
E
coh
B
 4.34eV
coh
C
 4.70eV
E
 9.8eV
 9.5eV
 9.2eV
[2]J. M. Roussel and P. Bellon, Physical Review B 63(2001) 184114
KMC parameters -- EVf
• Time scale
GV
S
HV
)  exp( V )  exp(
)
RT
R
RT
HV
 exp(
)
RT
1.28eV
 exp(
)
T (eV )
X Veq  exp(
X VKMC
t real (T )
 eq
t KMC
X V (T )
t
real
X VKMC  1 / 643  3.8 10 6
X VKMC KMC
(T ) 
t
 At KMC
eq
XV
T (℃)
100
300
400
500
A
6.9E11
6.7E5
1.5E4
821
EVf  1.28eV
A
2.0E16
4.6E8
3.6E6
1E5
EVf  1.60eV
Part 1. Average particle size VS real time
1000
1000
100 K
300 K
400 K
500 K
<n>
10000
<n>
10000
100 C
300 C
400 C
500 C
100
10
0
10
10
4
8
10
10
Real time [s]
12
Binary A90 B10
10
16
100
10
0
10
10
4
10
8
10
12
10
16
Real time [s]
Ternary A89 B10 C1
ECsaddle  10.217eV
• 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
0
•
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
Ei
x
- Get the exchanging rate between vacancy and neighboring atoms.
A
B
w2
•
Eis
w2: the frequency of B atomvacancy exchanges
10
12
10
10
10
8
10
6
10
4
10
2
-10.2 -10.0
-9.8
-9.6
-9.4
saddle
EC
[3] J. Philibert, Atom movements: diffusion and mass transport in solids,
Monograph de Physique F-91944, France 1991
-9.2
Histogram of (C)n at different ECSaddle
T = 300 C
400
400
-10.22eV
Count
350
300
300
250
250
50
50
0
0
40
80
120
0
0
20
40
(C)n
400
60
80
-9.5eV
300
250
250
50
50
0
0
20
40
60
(C)n
80
100
120
120
-9.2eV
350
300
100
(C)n
400
350
Count
-9.8eV
350
0
0
20
40
60
(C)n
80
100
120
Part 3.Simulation of experimental conditions (ECS=-9.2eV)
Three different conditions:
10
4
10
3
600C_2hr
Cu
600C_2hr_700C_2hr
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%
counts
700C_2hr
10
2
10
1
10
0
Nb
36
38
W
40
42
2
300 C
300 C + 500 C
500 C
44
46
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.