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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

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high throughput analysis of multicomponent diffusion data

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

slide2

Material Models

Thermo-Calc

DICTRA

Precipi-Calc

g’ Fast Track

Grain size

Property Models

Yield Strength

UTS

Creep

Fatigue

Crack Growth

AIM Strategy

R88

Ni

NiAl

W

Ta

Rapid Experiments

Diffusion Multiples

g  Experiments & Characterization

Grain Size Experiments & Characterization

slide3

Particle Distribution

Mean <R>

Primary g’

Temp. profile

Volume Fraction

Total # Particles/m3

AIM Precipi-Calc simulation of multi-modal g’size 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 < 100 s low nucleation rate
  • 100 s < t < 150 s Primary g’ is formed
  • 150 s < t < 350 s Primary g’ grows
  • 400 s Secondary g’ precipitates
  • 500 s Tertiary g’ precipitates
multicomponent diffusion

Multicomponent diffusion matrix for

René-88 composition using NIST database

René-88 at 1100 °C (x 10-14 m2/s)

Simulations need to compute the diffusion

matrix for each composition encountered in

diffusion profile at each time step.

Approach enables efficient data storage

Multicomponent Diffusion

Review

Fick’s first law for Flux, Ji

Fick’s second law

multicomponent diffusion database structure
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.
optimization of experimental diffusion coefficients

Simulate diffusion process

Compare experimental

and calculated D

Estimate Mobility

Adjust Mobility

Optimization of Experimental Diffusion Coefficients

Experimental

diffusion data

Calculate diffusion

Coefficients D = f(c,T)

Mobility M=f (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:

examples of optimized binary interactions ni al cr co fe hf nb mo re ta ti w

Ni-Co Interdiffusion

Interdiffusionwith Ni

Data from Ustad and Sorum, Phys. Stat. Sol. A 285 (1973) 285.

Calculated

T = 1000 oC

1400 oC

Log (D) m2/s

1325 oC

Log (D) m2/s

1250 oC

1200 oC

1160 oC

Data from Komai et al., Acta. Mater., 46, (1998) 4443.

Data from Karunaratne et al., Mater. Sci. Eng., A281 (2000) 229.

Atomic Percent Ni

Weight Fraction

Examples of Optimized Binary InteractionsNi-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

optimization of ni w

Activation energies in the fcc phase

Self activation energies

Optimized parameters

Optimization of Ni-W

Interdiffusion data

Data from Monma et. Al., JIM, 28 (1964) 197.

Tracer diffusivity data

Data from Karuanaratne et al., Mater. Sci&Eng.281 (2000) 229.

Data from Monma et. Al., JIM, 28 (1964) 197.

slide9

Diffusion Multiple

1 Sample  8 Diffusion Couples

R88

IN718

R95

IN100

ME3

R88/R95 R88/IN718

R88/ME3 R88/IN100

R95/IN718 R95/ME3

IN718//IN100 ME3/IN100

Experimental data provides composition and

phase fraction profiles as functions of distance.

Is it possible to directly relate composition profiles to mobility parameters?

Challenge: Analysis of Diffusion Multiples /Multicomponent DiffusionCannot determine diffusion coefficients from experimental data
example ren 88 in 100 1000 h at 1150 c

g

g+g

g

g+g´

René-88

IN-100

g

g

g

R88

g

IN100

R88

g

g

IN100

g

René-88

IN-100

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 g+g’ 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

diffusion database optimization scheme

Diffusion Mobility

Database

Run DICTRA

(via python)

Thermodynamic

Database

Compare composition profiles

Change Mi and z0, Run new simulation

Input Experimental File

(Composition Profiles)

Calculate Error

(via Mathematica)

Minimize Error f(Mi)

Diffusion Database Optimization Scheme
test example binary ni co
Test Example: Binary Ni-Co

Interdiffusion Coefficient obtained by Boltzmann-Matano method

programming elements and inputs

Shift Matano

interface

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
ni co optimization results

Initial Parameters

Initial

Optimized

Optimized Parameters

Distance shift z0= -1.58 mm

Ni-Co: Optimization Results
optimization results diffusion coefficient

Initial Parameters

NIST MOB - Initial

Optimized

Optimized Parameters

GE Experimental data

BM analysis

Distance shift z0= -1.58 mm

Optimization Results: Diffusion Coefficient
ternary example ni 5 13al 9 77cr ni 2 39al 19 34cr at
Ternary Example:Ni-5.13Al-9.77Cr/Ni-2.39Al-19.34Cr (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

diffusion database optimization scheme17
Diffusion Database Optimization Scheme

Diffusion Mobility

Database

Run DICTRA

(via python)

Thermodynamic

Database

Compare composition profiles

Change MiRun new simulation

Input Experimental File

(Composition Profiles)

Calculate Error

(via Mathematica)

1 couple

2 profiles

Minimize Error f(Mi)

Changing 9 binary interactions

optimization results 9 parameters

Optimized

AlAlCr= 341099 CrAlCr= 397756 NiAlCr=265578

AlAlNi= -175812 CrAlNi=-117332 NiAlNi=-24037

AlCrNi= -58013 CrCrNi=-62614 NiCrNi=-89378

Optimization Results: 9 parameters

T = 1100 °C

t = 1000 h

T = 1100 °C

t = 1000 h

Reference

AlAlCr=335000 CrAlCr= 487000 NiAlCr=211000

AlAlNi=-166517 CrAlNi=-118000 NiAlNi=-23068

AlCrNi=-53200 CrCrNi=-68000 NiCrNi=-81000

Binary Interactions zero

goal ni rene 88
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
diffusion database optimization scheme20

Diffusion Mobility

Database

Run DICTRA

(via python)

Thermodynamic

Database

Compare composition profiles

Change Mi and z0, Run new simulation

Input Experimental File

(Composition Profiles)

Calculate Error

(via Mathematica)

Minimize Error f(Mi)

Diffusion Database Optimization Scheme

1 couple

7 profiles

Changing 2 binary end members

2 binary interactions

ti profile from ni rene 88

Initial Ni-MOB

= -386325

=-81000

=-367650

=-68000

Optimized

= -367867

=-93125

=-327697

=-70015

z0= +7.5 mm

Experiment

4 parameters optimized

Initial Ni-MOB

  • Need to consider additional parameters:
    • Other binary interactions
    • Ternary interactions
Ti Profile from Ni/Rene-88
summary
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