horn formation on multiphase diffusion paths
DESCRIPTION
NIST Diffusion Workshop February 7-8, 2006. HORN FORMATION ON MULTIPHASE DIFFUSION PATHS. John Morral and Yunzhi Wang Department of Materials Science and Engineering The Ohio State University Columbus, Ohio 43210. OUTLINE. Horn definition Importance of horns Seminal paper - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/1.jpg)
HORN FORMATION ON MULTIPHASE DIFFUSION PATHS
John Morral and Yunzhi Wang
Department of Materials Science and EngineeringThe Ohio State University
Columbus, Ohio 43210
NIST Diffusion WorkshopFebruary 7-8, 2006
![Page 2: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/2.jpg)
OUTLINE
• Horn definition• Importance of horns• Seminal paper• Theoretical basis for single Horns• Numerical example• Horns in Ni-Cr-Al• Conclusions
![Page 3: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/3.jpg)
Horn definition
“Sharp deviations (singularities) in zigzag diffusion paths”
20
25
30
10 15 20 25 30
Al (at %)
Cr (at %)
’
0
15
5
10
Hopfe, William D. and J. E. Morral. Acta Metall. et Mater. 42 (1994) 3887-3894.
horns on a diffusion path
(variable [D])
zigzag diffusion path (constant [D])
![Page 4: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/4.jpg)
Why Horns are important
They can lead to the formation of brittle intermetallic compounds at bond interfaces
layer
![Page 5: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/5.jpg)
1994 Phase Transformation Meeting
![Page 6: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/6.jpg)
DICTRA Finite Difference Simulation of a Diffusion Couple
Anders Engstrom, J.E. Morral and John Ågren. Acta Mater. 45 (1997) 1189-1199.
![Page 7: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/7.jpg)
Seminal paper on Horns
![Page 8: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/8.jpg)
Types of Horns
“Double Horn”DICTRA simulation
“Single Horn”Analytical, Perturbation
method solution
![Page 9: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/9.jpg)
Deviation from the linear zigzag path that isn’t a horn
Exceptional CaseNumerical simulation
![Page 10: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/10.jpg)
Comparison of two numerical simulations
M. Schwind, T. Helander, J. Agren, Scripta Mater. 44 (2001) 415-421
Single HornLinear variation
of D with concentration
No HornParabolic variation
Of D with concentration
10
01D
![Page 11: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/11.jpg)
M. Schwind, T. Helander, J. Agren, Scripta Mater. 44 (2001) 415-421
10
01D
Single HornLinear variation
of D with concentration
No HornParabolic variation
Of D with concentration
Path with no horn is smooth when the composition jump at the initial interface is removed
![Page 12: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/12.jpg)
Theoretical Basis for Single Horns
The continuity equation is the key
x
J
t
C ii
iC iJ
dx
ppti
pptmatrixi
matrixi CfCfC
d
dJ
d
Cd ii 2
1
1
n
j
jiji
CDJ
![Page 13: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/13.jpg)
Theoretical Basis for Single Horns
d
dJ
d
Cd 2
d
dJ
d
Cd ii 2
Cd
Predicted by theory
Cd
Not predicted by theory
![Page 14: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/14.jpg)
Numerical example of the of the A-B-C system
(d)
Flux profile
Concentrationprofile
K. Wu, J.E. Morral and Y. Wang, submitted to Acta Mater, Jan. 2006
d
dJ
d
Cd ii 2
![Page 15: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/15.jpg)
DICTRA Simulations of Ni-Cr-Al+ diffusion paths
“On diffusion paths with ‘horns’…” H. Yang, J.E. Morral, Y. Wang, Acta Mater. 53 (2005) 3775-3781
![Page 16: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/16.jpg)
DICTRA simulations of Ni-Cr-Al+ diffusion couples
Simulations by Dr. Ximiao Pan 2006
Diffusion Path Flux Profiles
![Page 17: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/17.jpg)
Numerical simulations of Ni-Cr-Al+ diffusion paths
0.160.1650.170.1750.180.1850.190.1950.2
0.205
0.17 0.19 0.21 0.23 0.25
0.2
0.201
0.202
0.203
0.204
0.205
0.184 0.185 0.186 0.187 0.1880.16
0.161
0.162
0.163
0.164
0.165
0.234 0.235 0.236 0.237 0.238
Simulations by Dr. Ximiao Pan 2006
![Page 18: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/18.jpg)
“New model”simulations of Ni-Cr-Al+ diffusion paths
Simulations by Henrik Larsson - 2006
![Page 19: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/19.jpg)
CONCLUSIONS
• Only single horns are predicted by the diffusion equation for multiphase diffusion couples if the diffusivity varies with composition.
• The exception is that no horns will form if the diffusivity doesn’t vary at x = 0.
• Double horns occur in DICTRA simulations, but their origin is unknown.
![Page 20: HORN FORMATION ON MULTIPHASE DIFFUSION PATHS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814743550346895db4801e/html5/thumbnails/20.jpg)
THE END