NIST Workshop:High Throughput Analysis of Multicomponent Multiphase

Diffusion DataFebruary 7-8, 2006

Carelyn Campbell&

Bill Boettinger

Metallurgy Division

Why a Workshop on Diffusion?

• Consensus of NIST Workshop held March 21-22, 2002 Computational Thermodynamics and Diffusion Modeling- Promotes continuing interest in thermodynamic databases

• Metallurgy Division participation in DARPA/AIM/GE program on Turbine Disks

• NIST interest in Combinatorial (High Thoughput) Measurement Methods

• Existence of legacy Diffusion in Metals Data base at NIST ( J. R. Manning)

Goals

Improve communication between experts in multicomponent diffusion measurement, analysis and simulation.

Establish the most efficient method for extracting diffusion data (diffusion coefficients, fluxes, marker location) from multicomponent diffusion couple experiments.

Provide a forum to solve common diffusion software execution problems.

Agree on a common diffusion mobility data base assessment procedure.

Establish a general approach to data handling and diffusion modeling in ordered phases.

Develop standard problems and web site for inter-laboratory comparison of diffusion simulation methods and data extraction techniques

AgendaTuesday, February 7, 2006

8:30- 9:00 Introduction (Coffee and bagels)

9:00 –9:30 Review of action items from last workshop

9:30-10:00 Diffusion Barriers: Overview (Boettinger, Perepezko)10:00-10:30 Diffusion Barriers: Experimental Examples (Sohn, Josell)

10:30-10:45 Break

10:45-11:15 Review of Horn Formation (Morral) 11:15-11:45 1-D Multiphase Diffusion Simulations (Larsson)

12:00-1:00 Lunch

AgendaTuesday afternoon

1:00-1:30 Hot topics in Grain Boundary Diffusion (Mishin) 1:30 –1:45 Discussion1:45 - 2:15 Kirkendall effect in two phase systems (Boettinger) 2:15 – 2:45 Onsager relations and Kirkendall shift as a cross effect (Ågren)2:45 – 3:00 Break3:00 –3:30 Partial Thermodynamic Properties of γ'-(Ni,Pt)3Al and γ-(Ni,Pt,Al) in the Ni-Al-Pt-O system

(Copland) 3:30-4:00 Review and Assessment of Diffusion in B2 and γ’ (L12) Phase (Campbell)4:00-4:30 Oxide Modeling (Höglund) 4:30-5:00 First Principle Calculations (Liu)

6:00 Dinner: Café Mileto

Wednesday February 8

9:00-9:30 RPI Teaching Modules (Lupulescu)9:30-10:30 DICTRA Discussion: (Reference Frames, Comparisons with MultiDiflux,

Order diffusion models, other suggestions)10:30-10:45 Viewpoint Discussion (Perepezko)10:45-11:30 Open discussion11:00 –12:00 Action items

Lunch/Adjourn

DefinitionsCoefficient General Notation DICTRA notation

Tracer Diffusivity

IntrinsicDiffusivity

(partial chemical)

(binary)are related by the

velocity of Kirkendall frame,

ChemicalDiffusivity

(Interdiffusion)

ABBA DxDxD +=~

( ) m

n

i j

iiikikkj V

xMxxD ∑

= ∂∂

−=1

µδ

⎥⎦

⎤⎢⎣

⎡∂∂

+=N

DD ii loglog1* γ

DDi~ and

MVaVJv −=

factorn correlatio cubic diamondfor 1/8 and BCC and FCCfor 1

parameter lattice frequencyvibration ~

expexp~ 2*

====

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆+∆−⎟⎟

⎠

⎞⎜⎜⎝

⎛ ∆+∆=

f

a

kTHH

kSSfaD

mVa

fVa

mVa

fVa

i

β

υ

βν

j

kkVakkj

i

cMcD

∂∂

=µ

kk RTMD =*

RTRTGM kVa

k1exp

*2

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−= νδ

⎟⎠⎞

⎜⎝⎛ −

=RT

QDD exp0

Further testing and refinement of database using GE Diffusion Couple Data (FY 2003)

• Binary Couples– Single phase couples

• at 1100 °C for 1000 h : Ni/Co– Multiphase couples

• at 1100 °C for 1000 h : Co/Cr, Co/Mo, Co/Nb, Co/W, Cr/Ta, Cr/W, Cr/Mo, Ni/W, Ni/Ta, Ni/Mo, Ni/NiAl(1150 °C)

• at 850 °C for 4000 h: Ni/W, Co/Fe, Cr/Mo, Cr/Co, Mo/Fe• at 700 °C for 4000 h: Fe/Co, Mo/Cr

• Multicomponent Couples – Single Phase γ

• at 1150 °C for 1000 h: René88 /IN718 and Ni/René88– γ / γ+γ’ or γ+γ’ / γ+γ’ at 1150 °C for 1000 h

• 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

– γ / B2 or γ+γ’ /B2• at 1150 °C for 1000 h: NiAl/ René-88, NiAl/Ta• at 850 °C for 4000 h: NiAl/ René-88, NiAl/Ta

– TCP Couples: (Rene88-X)• at 1150 °C for 1000 h: X= Ta, W• at 850 °C for 4000 h: X=Ta, W, Co, Cr, Fe, Mo, Ni, Ti• at 700 °C for 4000 h: X=Co, Cr, Fe, Mo

Couples from UCF and RPI

• NiAl/Superalloy (UCF)– CM247/NiAl– GTD11/NiAl– IN738/NiAl– IN939/NiAl– Waspalloy/NiAl

• FeCrAl-Single Phase BCC (RPI)– X2/X3: Fe-18.5Cr-2.5Al/Fe-15.8Cr-35.7Al (at.%)– X5/X10: Fe-18.8Cr-25.8Al/Fe-20.6Cr-9.51Al (at.%)– X4/X6: Fe-5.7Cr-28.1Al/Fe-30.5Cr-18.7Al (at.%)

Multicomponent Mobility Database for FCC phase of SuperalloysCampbell, Boettinger & Kattner, Acta Mat.50 (2002) 775-792.

Reduced (n-1)Diffusion Matrix at 1293 °C

40.370.083.022.160.055.062.081.141.562.2357.625.694.494.435.163.123.050.076.026.024.053.033.068.031.085.074.005.2427.066.025.031.045.017.036.055.057.7426.0280.033.849.225.891.993.821.367.1337.526.469.910.783.155.567.525.800.1737.1122.5351.4950.5143.4234.3483.3493.135.119

+−−−−−−−+++++++++++++++−++++++++−−−−+−−−++++−+−−−−−−−−+−

++++++++

WTiTaNbMoCrCoAl

WTiTaNbMoCrCoAl

René-N4 (x10-14 m2/s) Ni = solvent

59.076.011.039.051.454.057.018.187.075.786.064.017.498.033.003.032.051.008.025.059.236.032.075.019.013.025.071.7905.130.030.035.084.137.287.052.11.26270.107.086.089.681.1378.022.025.602.2123.415.421.987.311.595.464.2756.822.2751.687.5063.4844.2542.3351.646.3392.1316.93

+−−−−−−−++++−++−−−+−−−−−−−−+−−−−++++++++−−−+−+−+−−−−+−

+++−+++

WTaReMoHfCrCoAl

WTaReMoHfCrCoAl

René-N5 (x10-14 m2/s)

René-88/IN-100; 1000 h at 1150 °C

0

0.05

0.1

0.15

0.2

-400 -200 0 200 400

Mas

s Fr

actio

n in

FC

C (G

amm

a)

Distance ( m)Rene-88 IN100

T = 1150 oC t = 1000 h

Co

Cr

WAlNb

Mo

Ti

Experimental data from J-C. Zhao, GE Global Research

René-88/IN-100; 1000 h at 1150 °C

10

12

14

16

18

-400 -200 0 200 400

Ato

mic

Per

cent

Co

Distance (µm)

Co content of γ’

Co content of γ

Average Co content

René-88 IN-100

γ γ+γ′

IN-718/IN-100; 1000 h at 1150 °C

IN718 IN100

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-1200 -800 -400 0 400 800 1200 1600 2000

Phas

e Fr

actio

n (G

amm

a P

rime)

Distance ( m)IN718 IN100

T = 1150 oCt = 1000 h

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-2000 -1500 -1000 -500 0 500 1000 1500 2000

Phas

e Fr

actio

n M

C c

arbi

de

Distance ( m)IN718 IN100

T = 1150 oCt = 1000 h

IN-718/IN-100; 1000 h at 1150 °C

0

0.05

0.1

0.15

0.2

-1200 -800 -400 0 400 800 1200

Mas

s Fr

actio

n in

FC

C p

hase

Distance ( m)

FeCr

Co

Nb

Mo

Al

Ti

T = 1150 oCt = 1000 h

IN718 IN100

Comparison of DICTRA and MultiDiflux Results for Ni/René-88

•Symbols = GE exp. Data

•Solid lines = DICTRA simulation (only uses initial compositions as inputs)

•Dashed lines = MultiDiflux (uses experimental profiles as input)

0.0

0.050

0.10

0.15

0.20

-1000 -500 0 500 1000

Mol

e Fr

actio

n

Distance ( m)

Cr

Co

Nb

Al

MoW

Ti

T = 1150 °C t = 1000 h

0.0

0.010

0.020

0.030

0.040

-1000 -500 0 500 1000

Mol

e Fr

actio

n

Distance ( m)

Nb

Al

Mo

W

Ti

Comparison of DICTRA and MultiDiflux Results for Ni/René-88

( ) ( )[ ]( ) ( )[ ] ( )1,...,2,1

~~

21

1

121

, −=−

−=

∑−

=∆ ni

xcxc

xcxcDD

i

n

jjj

nij

effci

-∞ (Ni) to 0 (x10-15m2/s) 0 to + ∞ (R88) (x10-15m2/s)

Component MultiDiflux DICTRA MultiDiflux DICTRA

8.71 12.3 5.21 10.8

15.5 12.9 16.9 11.9

48.4 39.7 37.7 40.6

6.52 10.6 7.19 9.92

48.9 34.0 31.5 33.7

1.05 3.06 1.72 1.56

42.8 35.3 46.5 58.0

effCoD~

effCrD~

effTiD~

effMoD~

effNbD~

effWD~

effAlD~

Comparison of Al Diffusion Coefficients for Ni/René-88

2.0 10-14

3.0 10-14

4.0 10-14

5.0 10-14

6.0 10-14

7.0 10-14

8.0 10-14

9.0 10-14

-1500 -1000 -500 0 500 1000 1500

Inte

rdiff

usio

n C

oeffi

cien

t (m

/s2)

Distance ( m)Ni R88

effAlD~MultiDiflux,

DICTRA, AlAlD ,~

DICTRA, AlAlD ,~

Diffusion Database CenterC. E. Campbell, U.R. Kattner, C. Beauchamp, K. Dotterer, H. Gates, S. Tobery

Goal: To make the NIST paper-based diffusion database center publicly available.

Convert to a searchable electronic form to be access over the internet

Task:• Need to enter bibliographic and diffusion system cards• Convert paper documents to electronic documents • Develop searchable database

Motivation • Industrial and academic support: GE $5K initiation • Center represents an unique collection summarizing the diffusion work between 1965-1980

Accomplishments (2006)• Developed database entry strategy• Entered 14000 bibliographic and system cards• Database available online

Diffusion Database CenterC. E. Campbell, U.R. Kattner, C. Beauchamp, K. Dotterer, H. Gates, S. Tobery, L. Souders

Web site: http://winweb.nist.gov/diffusion/

Goal: To make the NIST paper-based diffusion database center publicly

available.

Current tasks:• Testing implementation • Scanning unpublished reports

Can search by author or diffusion element

Ternary A-B-C SystemIn the lattice fixed frame of reference, assuming a substitutional solid solution for a given phase:

RTRTGMM kVa

kkVa1exp0 ⎟

⎠⎞

⎜⎝⎛ ∆−

=

Assume: 10 =kM

Then the activation energy, Qk:

excessVaCCVaC

VaBCVaB

VaACVaACVa

excessVaCBVaC

VaBBVaB

VaABVaABVa

excessVaCAVaC

VaBAVaB

VaAAVaAAVa

GGyxGyxGyxG

GGyxGyxGyxG

GGyxGyxGyxG

∆+∆+∆+∆=∆

∆+∆+∆+∆=∆

∆+∆+∆+∆=∆

:::*

:::*

:::*

Note xi = mole fraction of component iyi = site fraction of component i

on a given sublattice

Since this is a substitutional solid solution with no interstitials, yVa = 1 :

Concentration variables: kNTPj

jn

jjj

k

m

kk N

VVandVx

xVxc

,,

1

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

===

∑=

Where xk is the mole fraction of component k, Vj is the partial molar volume and Nj is the number of moles of component k.

Assume all the substitutional components have the same partial molar volume: then for the A-B-C system:sj VV = sCsBsAm VxVxVxV ++=

Ternary A-B-C SystemCBAVa

n

kk JJJJJ ++=−=∑

=1

In the lattice fixed frame of reference:

∑∑−

== ∂

∂

∂∂

−=∂

∂−=

1

11

n

j

j

j

kkk

n

j

jkj

ik z

cc

Lzc

DJ µ

j

kkVaVak

j

kkkkj

i

cMyc

cLD

∂∂

=∂∂

=µµ Note yVa =1 and for simplicity drop the Va

from MkVa = Mk

m

ii V

xc =

CCCC

BBBB

AAAA

MxLMxLMxL

===

C

CCCCC

i

B

CCCCB

i

A

CCCCA

i

C

BBBBC

i

B

BBBBB

i

A

BBBBA

i

C

AAAAC

i

B

AAAAB

i

A

AAAAA

i

cLD

cLD

cLD

cLD

cLD

cLD

cLD

cLD

cLD

∂∂

=∂∂

=∂∂

=

∂∂

=∂∂

=∂∂

=

∂∂

=∂∂

=∂∂

=

µµµ

µµµ

µµµ

Ternary A-B-C SystemIn the volume-fixed frame of reference: ( ) sCBAk

n

kk VJJJVJ ⋅++==∑

=

01

( )

∑

∑∑

∑∑ ∑∑

=

==

== ==

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=′

∂∂

−=∂∂′−=

∂

∂−=

∂

∂

∂∂′−=

∂∂′−=

n

iij

m

ikikkj

m

n

i j

iiikik

n

i j

ikikj

n

j

jkj

n

i

n

j

j

j

iki

n

i

ikik

LVVxL

Vx

Mxxc

LD

zc

Dzc

cL

zLJ

1

11

11 11

δ

µδµ

µµ

knkjnkj DDD −=Reduce diffusivities when Vk= Vs: ∑

−

= ∂

∂−=

1

1

n

j

jnkjk z

cDJ

Or

( )[ ] ∑ ∑ ∑∑

∑∑∑

∑

= = ==

= ==

=

′⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∂∂′=

∂−∂′′=

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=′⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=′′

⎥⎦

⎤⎢⎣

⎡∇⎟⎟

⎠

⎞⎜⎜⎝

⎛−∇′′−=

n

i

n

i

n

rkr

m

r

j

ii

j

iki

n

i j

nmiikikj

jrm

jkjk

n

j

n

r m

riirkj

n

j m

iiijki

n

in

m

iikik

LVV

cx

cL

cVVLD

LVV

xVVxL

VVxL

VVLJ

1 1 11

1 11

1

µµµµ

δδδ

µµ

Recall that the Gibbs–Duhem equations provides that: ∑=

=∂∂n

i j

ii c

x1

0µ thus, ∑= ∂

∂′=n

i j

ikikj c

LD1

µ

kVaVakkk MycL =

See next page for expansion

Equ

ival

ent f

orm

s

Ternary A-B-C( ) m

n

i j

iiikik

n

i j

ikikj V

xMxx

cLD ∑∑

== ∂∂

−=∂∂′−=

11

µδµ

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( ) mC

CCCCm

C

BBBCm

C

AAACCC

mB

CCCCm

B

BBBCm

B

AAACCB

mA

CCCCm

A

BBBCm

A

AAACCA

mC

CCCBm

C

BBBBm

C

AAABBC

mB

CCCBm

B

BBBBm

B

AAABBB

mA

CCCBm

A

BBBBm

A

AAABBA

mC

CCCAm

C

BBBAm

C

AAAAAC

mB

CCCAm

B

BBBAm

B

AAAAAB

mA

CCCAm

A

BBBAm

A

AAAAAA

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

Vx

MxxVx

MxxVx

MxxD

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

∂∂

−+∂∂

−+∂∂

−=

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

µµµ

101

101

100

010

010

010

001

001

001

Relation between Intrinsic and Interdiffusion CoefficientsFrom Sohn and Dayananda (Met. Mat. Trans 33A (2002) 3375)

DICTRA notation: ∑

=

−=n

k

nkj

ii

nij

inij DxDD

1

~

∑=

−=n

k

nkji

nij

nij DNDD

1

~

fraction atom

(reduced)t coefficiendiffusion intrinsic

tcoefficiension interdiffu~

=

=

=

i

nij

nij

N

D

DPublished notation:

Example: ( )CCA

iCBA

iCAA

iA

CAA

iCAA DDDxDD ++−=~

( ) ( )

( ) ( ) ( )[ ]( ) ( ) ( ) ( )[ ]

[ ]CCA

iCBA

iCAA

imA

CAA

iCAA

CCi

CAi

BCi

BAi

ACi

AAi

mAACi

AAiC

AA

CCi

CAi

BCi

BAi

ACi

AAi

mAC

AAmA

A

AAmA

CAA

CCi

BCi

ACi

C

AAmACA

iBA

iAA

i

A

AAmA

CAA

j

kkkkj

i

C

CCC

C

BBB

C

AAAmA

A

CCC

A

BBB

A

AAAmA

CAA

ACAACAA

DDDVxDD

DDDDDDVxDDD

DDDDDDVxx

MVxx

MVxD

DDDx

MVxDDDx

MVxD

xMxDNote

xMx

xMx

xMxVx

xMx

xMx

xMxVxD

DDD

++−=

−+−+−−−=

−+−+−−∂∂

−∂∂

=

⎥⎦

⎤⎢⎣

⎡−−−

∂∂

−⎥⎦

⎤⎢⎣

⎡−−−

∂∂

=

∂∂

=

⎥⎦

⎤⎢⎣

⎡∂∂

−∂∂

−∂∂

−−⎥⎦

⎤⎢⎣

⎡∂∂

−∂∂

−∂∂

−=

−=

~iesdiffusivit reduce of in terms Rewrite

~

~

~

11~

~

µµ

µµ

µ

µµµµµµ

CCi

CAiC

CAi

BCi

BAiC

BAi

ACi

AAiC

AAi

kni

kjin

kji

DDD

DDD

DDD

DDD

−=

−=

−=

−=

Note:

(see previous slide for expansion of DAA and DAC)

NIST participation in GE-AIM (DARPA) Programγ’ Precipitation Model

Experimental diffusion data(Binary data)J.C. Zhao, GE-CRDNIST Diffusion Data Center

Multicomponent diffusion dataB. Mueller, HowmetJ-C. Zhao, GE-CRD

Lattice parametersQuestek

Diffusion MobilityDatabase NIST

Thermodynamic DatabasesThermotech,UW, NIST

γ′ precipitationQuestek, GE

Models for mechanical propertiesGE

NIST also providing guidance on γ′precipitation modeling, simplecoding for thermodynamic calculations, modeling interfacial energies.

Linear cooling rate 0.2 °C/s

Rene-88