High Throughput Analysis of Multicomponent Diffusion Data

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High Throughput Analysis of Multicomponent
Diffusion Data

• C. E. Campbell and W. J. Boettinger
• National Institute of Standards and Technology
• Gaithersburg, MD 20899
• J-C. Zhao
• General Electric Company Global Research
• Schenectady, NY

• Need for Multicomponent Diffusion Data
  Simulations
• Review of Multicomponent Diffusion Basics
• Structure of Diffusion Mobility Database
• Optimization to obtain mobility parameters
• from measured diffusion coefficients (normal
  approach)
• from measured diffusion profiles (new work)

TMS Fall Meeting 2003 The Accelerated
Implementation of Materials Processes
November 11, 2003
This work was partially funded by the GE-led
DARPA AIM program
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AIM Strategy
R88
Ni
NiAl
W
Ta
Rapid Experiments Diffusion Multiples g ?
Experiments Characterization Grain Size
Experiments Characterization
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AIM Precipi-Calc simulation of multi-modal gsize
distribution for Rene-88

• Validated against GE-Interrupt cooling
  experiments
• GE-AE proprietary data
• Literature data Mao (2001)
• Thermodynamics Thermo-tech
  Ni-Data
• Diffusion NIST Ni-mobility database
• Thermal profile DEFORM simulation of blank disk
• Assume 3D spherical particle need to add elastic
  energy effects
• t lt 100 s low nucleation rate
• 100 s lt t lt 150 s Primary g is formed
• 150 s lt t lt 350 s Primary g grows
• 400 s Secondary g precipitates
• 500 s Tertiary g precipitates

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Multicomponent Diffusion
Review
Ficks first law for Flux, Ji
Ficks second law
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Multicomponent Diffusion Database Structure

• Inputs
• Calphad Thermodynamics
• Diffusion experiments (unary, binary, ternary
  systems)
• Tracer diffusivity,
• Intrinsic diffusivity,
• Interdiffusion coefficients/Marker motion
• Optimize value of mobilities, Mi , for all
  binaries consistent with available data
• Composition and Temperature-dependent
• Consistent with estimates of Metastable end
  members e.g., FCC W
• Optimized using code, DICTRA (Parrot)
• Add terms if necessary to fit ternary data,
  etc.

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Optimization of Experimental Diffusion
Coefficients
Experimental diffusion data
Calculate diffusion Coefficients D f(c,T)
Mobility Mf (c,T)
Ni - Al
Diffusion profile ? Diffusion Coefficient
T 1150 C
Composition
Log (Mobility)
T 1050 C
T 950 C
Distance
Composition
For a binary
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Examples of Optimized Binary Interactions
Ni-Al-Cr-Co-Fe-Hf-Nb-Mo-Re-Ta-Ti-W
Previous assessments Ni-Al-Cr Engström and
Ågren, Z. Metallkd. 87 (1996) 92.
Ni-Al-Ti Matan et al., Acta mater., 46
(1998) 4587. Ni-Cr-Fe
Jönsson, Z. Metallkd 85 (7)502-509,
1994. Current assessments Ni-Co,
Ni-Hf,Ni-Mo, Ni-Nb,Ni-Re, Ni-Ta, Ni-Ti, Ni-W
Co-Cr, Co-Mo
C. E. Campbell, W. J. Boettinger, U. R. Kattner,
Acta Mat, 50 (2002) 775
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Optimization of Ni-W
Interdiffusion data
Data from Monma et. Al., JIM, 28 (1964) 197.
Tracer diffusivity data
Data from Karuanaratne et al., Mater. SciEng.
281 (2000) 229.
Data from Monma et. Al., JIM, 28 (1964) 197.
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Challenge Analysis of Diffusion Multiples
/Multicomponent Diffusion Cannot determine
diffusion coefficients from experimental data
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Example René-88/IN-100 1000 h at 1150 C

• At 1150 C equilibrium
• phase fractions
• René-88 fg 1
• IN-100 fg 0.638 fg 0.362

Additional gg GE couples analyzed René-95/
René-88 ME3/IN718 IN100/ME3 U720/IN718 IN100/
René-88 René-95/U720 IN718/IN100 U720/ME3
René-95/IN718 ME3/ René-95 ME3/
René-88 IN100/U720
Experimental data from J. C. Zhao, GE-GR,
Schenectady, NY
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Diffusion Database Optimization Scheme
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Test Example Binary Ni-Co
Interdiffusion Coefficient obtained by
Boltzmann-Matano method
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Programming Elements and Inputs

• Error Definition

• Wi(z) Weighting function
• Currently set to equal 1

• z0 Error associated with location of Matano
  plane

a
b

• Change selected mobility parameters

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Ni-Co Optimization Results
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Optimization Results Diffusion Coefficient
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Ternary Example Ni-5.13Al-9.77Cr/Ni-2.39Al-19.3
4Cr (at.)
For a single couple cannot determine the
interdiffusion coefficients using the BM method
T 1100 C t 1000 h
T 1100 C t 1000 h
Reference
Reference
Binary interactions zeroed
Binary interactions zeroed
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Diffusion Database Optimization Scheme
Diffusion Mobility Database
Run DICTRA (via python)
Thermodynamic Database
Compare composition profiles
Change Mi Run new simulation
Input Experimental File (Composition Profiles)
Calculate Error (via Mathematica)
1 couple 2 profiles
Minimize Error f(Mi)
Changing 9 binary interactions
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Optimization Results 9 parameters
T 1100 C t 1000 h
T 1100 C t 1000 h
Reference
AlAlCr335000 CrAlCr 487000
NiAlCr211000 AlAlNi-166517 CrAlNi-118000
NiAlNi-23068 AlCrNi-53200 CrCrNi-68000
NiCrNi-81000
Binary Interactions zero
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Goal Ni/Rene-88

• Optimization strategy
• Ni end-member term
• Ti, Nb
• Ni binary interactions
• Ni-Ti Ni-Nb
• Ni-Cr Ni-Al
• Ni ternary interactions
• Ni-Al-Cr
• Ni-Al-Ti
• Ni-Cr-Nb

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Diffusion Database Optimization Scheme
1 couple 7 profiles
Changing 2 binary end members 2 binary
interactions
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Ti Profile from Ni/Rene-88
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Summary

• Multicomponent Ni-base diffusion mobility
• Based on optimization of available diffusion
  coefficient data
• Comparison of simulation results with experiments
  shows good agreement
• Optimization based on composition profiles
• Method
• Relates profiles to mobility parameters
• Provides ability to asses error associated with
  mobility parameters
• Examples
• Binary Ni-Co (1 couple, fixed T,1 profile, 4
  parameters, z0)
• Ternary Ni-Al-Cr (1 couple, fixed T, 2 profiles,
  9 parameters)
• Multicomponent Ni/Rene88 (1 couples, fixed T, 7
  profiles, 4 parameters, z0)
• Improved optimization strategy needed
• Multicomponent single phase (Need to consider
  more than 1 couple)
• Multicomponent multiphase
• Programming additions needed
• Weighting functions
• Other error definitions