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Analysis of Diffusion Path and Interdiffusion Microstructure
Y. Wang and J. E. MorralDepartment of Materials Science and Engineering
The Ohio State University
Work Supported by NSFNIST Diffusion Workshop
April 19-20, 2005, Gaithersburg, MD
Outline• Discontinuities in interdiffusion microstructure and “horns”
in the diffusion path• Motion of Type-0 boundaries and its effect on the shape
of diffusion path• Variation in microstructure and diffusion path caused by
deviation from local-equilibrium conditions and by precipitate coarsening
• Special points on the phase diagram that act as “strange attractors” of the diffusion paths
• Development of various morphological instabilities including concentration-gradient induced rafting
These phenomena are associated with intimate thermodynamic and kinetic coupling in multi-component diffusion and interactions between interdiffusion and microstructural evolution in multi-phase regions
Understanding the “Horns” in Diffusion Path
Horns predicted by DICTRA and Phase Field simulations
Schwind, Helendar and Argren, Scripta mater. 2001 Wu, Morral and Wang, Acta mater. 2001
A-B-C Model System
• Elements A and B form ideal solution while elements A and C or B and C form regular solutions
A B
C
’
Free energy model
Gm RT XA ln XA XB ln XB XC ln Xc I XA XC XB XC
Linear Diffusion Path
dc d
2
dJd
dc 2dc 1
dJ2
ddJ1
d
J1 D11c1
J2 D21c1
D21 RTc 2 A B
D11 RT B c1 A B
B=5.0 C=1.0 A=5.0
Single-Horn Diffusion Path
J1 D11c1
J2 D21c1
D21 RTc 2 A B
D11 RT B c1 A B
B=1.0 C=5.0 A=10.0(1)
(2)
Single-Horn Diffusion Path
12
34
1
2
3 4
dc 2dc 1
dJ2
ddJ1
d
Double-Horn Diffusion Path
0.000 0.001 0.002 0.003 0.004
0.00E+000
2.00E-010
4.00E-010
6.00E-010
8.00E-010
1.00E-009
1.20E-009
JM(A
l)
Distance x(m)
20.0 20.2 20.4 20.6 20.8 21.015
16
17
18
19
20
21
C(C
r)
C(Al)
0.000 0.001 0.002 0.003 0.004
0.00E+000
5.00E-010
1.00E-009
1.50E-009
2.00E-009
JM(C
r)
Distance x(m)
Interpretation of Simulation Results
'<<'<+
=0.0
=2000.0
B=10.0 C=5.0 A=1.0
c1 = 25 at%, c2 = 40 at% c1 = 32 at%, c2 = 60 at%
JA
JB
net flux of (A+B)
(2)
(1)
Simulations have stimulated the development of theoretical understanding and new theoretical principles have guided the interpretation of simulation results
Wu, Morral and Wang, Acta mater. 49, 3401 – 3408 (2001)
Yong-Ho Sohn and M. Dayananda
+/+ Couple
>+
=0.0
=2000.0
B=1.0 C=5.0 A=10.0
c1 = 25 at%, c2 = 40 at% c1 = 32 at%, c2 = 60 at%
(2)
(1)
JAJB
net flux of (A+B)
Wu, Morral and Wang, Acta mater. 49, 3401 – 3408 (2001)
= 0
= 100
= 2000
Moving Type 0 Boundary
4608x64 size simulation, 1024x256 size output
1=1.0 2=5.0 3=10.0
• Ppt and Type 0 boundary migrate as a results of Kirkendall effect
• Type 0 boundary becomes diffuse
• Kirkendall markers move along curved path and marker plane bends around precipitates
K. Wu, J. E. Marrol and Y. Wang, Acta mater. 52:1917-1925 (2004)
Size and position changes during
interdiffusion
Diffusion path: comparison with 1D simulation
Exp. Observation by Nesbitt and Heckel
Interdiffusion Microstructure in NI-Al-Cr Diffusion Couple0 hr
4 hr
25 hr
320m
100 hrat 1200oC
Ni-Al-Cr at 1200oC
• Free energy data from Huang and Chang
• Mobilities in from A.EngstrÖm and J.Ågren
• Diffusivities in from Hopfe, Son, Morral and Roming
200m
XCr =0.25, XAl=0.001
Annealing time: 25 hours
(a)
(b)
(c)
Effect of Cr content on interface migration
320m
Ni-Al-Cr at 1200oC
(d)
b ca d
Exp. measurement by Nesbitt and Heckel
Diffusion path and recess rate - comparison with experiment
Annealing time: 25 hours
(a)
(b)
Effect of Al content on interface migration
320m
ab
Interpretation of Phase Field Simulation - Effect of Coarsening
t = 0
t = 25h
t = 100h
Effect of Pure Coarsening
t = 0
t = 100h
t = 200h
Interpretation of Phase Field Simulation - Effect of Coarsening
A.EngstrÖm, J. E. Morral and J.ÅgrenActa mater. 1997
Interpretation of Phase Field Simulation - Deviation from Local Equilibrium Condition
0.15
0.20
0.10
e0025.mov e0045.mov
Lawrence A. Carol, Michigan Tech. 1985
“strange attractors” of the diffusion paths
Concentration-Gradient Induced Rafting
Hazotte and Lacaze, Scripta metall.
Aging of initially as cast alloy (1100oC for 1500 hr.)
Interdendritic zone
Secondary dendritic arm
Secondary dendritic armDendritic core
Interdiffusion Induced Rafting = 0
= 40
= 220
= 400
Initial Configuration
Misfitting particle Stress-free particles
No interdiffusion With interdiffusionNo interdiffusion With interdiffusion
B=5.0 C=1.0 A=5.0
left: XB=0.125, XC=0.489right: XB=0.6 XC=0.1
Summary – Predicting of Interdiffusion Microstructure
• DICTRA and Phase Field share the same thermodynamic and diffusivity databases
• DICTRA directly outputs diffusion path on phase diagram and runs on PC, but is an1D program, assumes local-equilibrium, treats precipitates as point sources or sinks, and is accurate when most diffusion occurs in a single, matrix phase, no metastable states, and for limited boundary conditions
• Phase Field directly outputs microstructure, does not require local-equilibrium, can treat diffusion couples of different matrix phase, is able to consider a wide variety of boundary conditions, and allows for studies of effects of precipitates morphology on interdiffusion and interdiffusion on microstructural evolution. But many critical issues remain•Computation efficiency•How to determine accurately the average compositions in the two-phase regions
•How to analyze the diffusion path using statistically meaningful microstructures and computationally tractable system sizes without artificial Gibbs-Thompson effect
• Incorporation of nucleation – work in progress
Phase Field Equations
XB
t M11 B A M12 C A
XC
t M21 B A M22 C A
B A BB A
B 2 112 XB 212
2 XC
C A CB A
B 2 212 XB 2 22
2 XC
Mij - chemical mobilities
ij - gradient coefficients
I - atomic mobilities
- molar density
Diffusion equations
Thermodynamic parameters
Kinetics parametersM11 XB 1 XB 2B XBXCC XB XA A M12 M21 XB XC 1 XB B 1 XC C XA A M22 XC XBXC B 1 XC 2C XC XA A
Effect of Gradient Term
3c
J
B A BB A
B 2 112c1 212
2c2