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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
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