phase stability, diffusion, kinetics and applications...introduction - boundaries in binary...
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http://174.120.122.245/program/technical-program/fundamentals-and-characterization/
Abstract deadline is Monday March 29, 2010
Call for papers
Phase Stability, Diffusion, Kinetics and Applications
Where: Houston, 2010 MS&T meetingWhen: October 18-20, 2010
Included in the symposium will be special sessions honoringAustin Chang, 2009 ASM J. Willard Gibbs Award recipientArthur Pelton, 2010 ASM J. Willard Gibbs Award recipient
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Xiaoqin Ke and John MorralDepartment of Materials Science and Engineering
The Ohio State UniversityColumbus, Ohio
MSE
DICTRA Simulations of Type 3 Boundaries Using the Homogenization Model
NIST Diffusion WorkshopMay 23-24, 2010, Gaithersburg, MD
Number of phase
changes when crossing a boundary
Diffusion couple
Type 3
x = 0
x = 0
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OUTLINE
• Introduction– Boundaries in Microstructures– Boundaries in Diffusion paths – Dictra simulations of boundaries using the
disperse system model• Dictra simulations of Type 3 boundaries
using the homogenization model• Summary
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Introduction - Boundaries in MicrostructuresA Type 3 boundary in a
Ni-Cr-Al diffusion couple
From: Lawrence A. Carol, NASA Contractor Report 174852, 1985.
Type 3 Type 1Type 0
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S.M.Merchant, M.R. Notis, J.I.Goldstein, Met.Trans 21A(1990)1901
Type 3
Introduction - Boundaries in MicrostructuresA Type 3 boundary in a
Ni-Cr-Al diffusion couple
Type 1
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T
A B
Type 2
Type 1
Type 0
Introduction - Boundaries in Binary Diffusion Paths
Can move to left or right
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Introduction - Boundaries in Ternary Diffusion Paths
A B
Type 2
Type 1a
Type 0
C
Type 1b
Can move to left or right
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’
Introduction - Boundaries in Ternary Diffusion Paths
Type 2
Type 3
A
C
B
Diffusion paths mustgo through a tie triangle corner when there is a
Type 3 boundary Can move to left or right
Can move to left or right
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S.M.Merchant, M.R. Notis, J.I.Goldstein, Met.Trans 21A(1990)1901
Type 3
Introduction - Boundaries in Ternary Diffusion Paths
Which directions are the boundaries moving?
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Diffusion Couple microstructure
Dictra simulations of boundaries using the disperse system model
Xin Qiao, M.S. 1998, Univ. Conn.
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• Homogenization functions: Hashin Shtrikman lower bounds(Wiener bounds, Hashin Shtrikman bounds, Labyrinth factor)
• Degree of implicity when integrating PDEs: 0.5(0.0 Euler forwards, 0.5 Trapezoidal rule, 1.0 Euler backwards)
• Ideal flux contribution for fluctuations in composition: 0.05 (range .01-.05)
Dictra simulations of Type 3 boundariesusing the homogenization model
Settings
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Key references on the homogenization model
AlsoMultiphase diffusion simulations in 1D using the Dictra Homogenization model
Henrik Larsson. Lars HoglundCALPHAD, 33(2009) 495-501
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X=0X=0
Dictra simulation using theHomogenization model
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6.00E-01
6.20E-01
6.40E-01
6.60E-01
6.80E-01
7.00E-01
7.20E-01
7.40E-01
7.60E-01
0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01
Unexpected shape of the diffusion path
Unexpected shape of the diffusion path
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From: Lawrence A. Carol, NASA Contractor Report 174852, 1985.
Similar diffusion path in the
region given in the NASA Report
But the microstructure shows a sharp Type 0 boundary
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Mass balance violation?
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6.30E-01
6.40E-01
6.50E-01
6.60E-01
6.70E-01
6.80E-01
6.90E-01
7.00E-01
7.10E-01
6.00E-02 8.00E-02 1.00E-01 1.20E-01 1.40E-01 1.60E-01
Extra Cr on both sides of
the initial interface
Diffusion path doesn’t cross the line between the initial alloys
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Summary
• Homogenization model successfully predicted a Type 3 boundary
• Questionable observations in homogenization model simulations- diffusion path at a Type 1a boundary- large deviations from a linear diffusion path
in a two phase region- apparent mass balance violation