DICTRA and Diffusion Assessments

• Diffusion Mobility Assessment: Optimization• Simulation of Diffusion Controlled

Transformations

High Throughput Analysis of Multicomponent Multiphase Diffusion Data

March 27-28, 2003

What is needed to simulate multicomponent diffusion?

René-N4 René-N5

� �

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

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WTiTaNbMoCrCoAl

WTiTaNbMoCrCoAl

René-N4 (x10-14 m2/s) at 1293 °C

Diffusion matrix

�

Thermodynamics

����

�+L L

�+��+P+B2�+��

+P

�+��+B2

�+B2

�+B2+L

B2+L

�+P+B2

René-N4

Need efficient data storage

At each grid point for each time step for a given temperature profile.

Multicomponent Thermodynamics:Calphad Approach

Calculated phasediagram

Experimental phase diagramThermochemical data

Determine Gibbs EnergyG = f(x,T,P�

A B

TE

�

Liquid

�

Tem

pera

ture

CompositionA B

TE

�

Liquid

�

Tem

pera

ture

Composition

�

�

L

Gib

bs E

nerg

y

Composition

T<TE

G G G Gideal excess�� � �

0

Binaries Ternaries Quaternaries nth ordersystems

Diffusion Database Development� 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. kjiijki xxxTB )(

kk RTMD �*

� � 1 and , whereexp �����

���

� �� �

�

iiiii

i MTcfQRTQ

RTMM

)()(1 1

0 TAxxTQxQn

p

n

qp

n

q

pqiqp

pipi � ��

� � �

���

Assessment of Diffusion Mobilities

Estimate MobilitySimulate diffusion processCompare experimental

and calculated D Adjust Mobility

Experimental diffusion data Mobility M=f (c,T) Calculate diffusion

Coefficients D = f(c,T)

Distance

Com

posi

tion

Diffusion profile � Diffusion Coefficient

Composition

Log

(Mob

ility)

T = 1150 °C

T = 1050 °C

T = 950 °C

Ni - Al

� � 1 and , whereexp �����

���

� �� �

�

iiiii

i MTcfQRTQ

RTMM

� �...)()( ,2,,��������ji

ijiji

ijiji

ijijij

iiii CccBccAccQcQc�

-15

-14.5

-14

-13.5

-13

-12.5

-12

0 0.05 0.1 0.15 0.2

log

D� (

m2 /s

)

Mole Fraction Al

1000°C

1050°C

1100°C

1250°C

Data from Yamamoto et. al. (1980)Assessment by Engström and Ågren (1996)

QFor a binary:

Assessment of Ni-W

-15.5

-15

-14.5

-14

-13.5

-13

-12.5

5.8 10-4 6 10-4 6.2 10-4 6.4 10-4 6.6 10-4 6.8 10-4 7 10-4 7.2 10-4 7.4 10-4

x(w)=.017

x(w)=.053

x(w)=.092

Log

D* (F

CC

,Ni)

(m2 /s

)

(1/Temperature) (K)

Ni-1.7W (at.%)

Ni-5.3W (at.%)

Ni-9.2W (at.%)

1340 1290 1242 1197 1155 1116 107813941451Temperature ( oC)

-16

-15.5

-15

-14.5

-14

-13.5

6.2 10-4 6.4 10-4 6.6 10-4 6.8 10-4 7 10-4 7.2 10-4 7.4 10-4

x(w)=.017

x(w)=0.053

w(w)=.092

Log

D*

(FC

C,W

) (m

2 /s)

(1/Temperature) (K)

Ni-1.7 W

Ni-5.3 W

Ni-9.2 W

1340 1290 1242 1197 1155 1116 1078Temperature ( oC)

-18

-17

-16

-15

-14

-13

0 0.02 0.04 0.06 0.08 0.1

Log

D (I

nter

diffu

sion

) m2 /s

Mass Fraction W

900 oC

1100 oC

1000 oC

1200 oC

1300 oC

WNiNiWNi

WNiW

NiNiNiNi AxxQxQxQ ,0*

����

WNiWWNi

WWW

NiWNiW AxxQxQxQ ,0*

����

Activation energies in the fcc phase

Self activation energiesOptimized parameters

Trac

er d

iffus

ivity

dat

aInterdiffusion data

Mobility Description Ni-W

• FCC_A1: Mobility of Ni– MQ(FCC_A1,NI:VA;0) = -28700+69.8*T– MQ(FCC_A1,W:VA;0) = V1+R*T*LN(V2)– MQ(FCC_A1,NI,W:VA;0) = V3+V4*T

• FCC_A1: Mobility of W– MQ(FCC_A1,NI:VA;0) = V5+R*T*LN(V6)– MQ(FCC_A1,W:VA;0) = V7+R*T*LN(V8)– MQ(FCC_A1,NI,W:VA;0) = V9+V10*T

Ni-W : DOP file• $$ Data from Momma et al, J. Japan Inst. Metals, 28 (1964) 197-200.• $$ Measured diffusivity in Ni-W alloys with Ni-63 and W-185

• TABLE_HEAD 655• CREATE_NEW_EQ @@, 0• CHANGE_STATUS COMP Ni,W=ENT• CHANGE_STATUS PHASE FCC_A1=ENT 1• S-COND X(W)=.017• S-COND P=101325 N=1 T=@1• EXPERIMENT LOGDT(FCC,NI)=@2:.05• TABLE_VALUES

• $$Ni-5W• $$ Temp(K) Log(DT)• 1668 -12.57675413• 1623 -12.82973828• 1579 -13.07058107• 1530 -13.49485002• 1478 -13.8827287• 1433 -14.1739252• 1369 -14.74714697• TABLE_END

Ni-W Interdiffusion: DOP file• TABLE_HEAD 325• CREATE_NEW @@,0• CHANGE_STATUS COMP NI,W=ENT• CHANGE_STATUS PHASE FCC_A1=ENT 1• S-COND w(W)=@1• S-COND N=1 P=101325 T=1273• EXPERIMENT LOGDC(FCC,W,W,NI)=@2:.1• TABLE_VALUES

• $$ 1000 C• $$ w(W) logD• 0.00E+00 -16.18708664• 5.00E-03 -16.15490196• 1.00E-02 -16.09691001• 1.50E-02 -16.04575749• 2.00E-02 -16.00877392• :• 9.00E-02 -15.76955108• 9.50E-02 -15.75696195• 1.00E-01 -15.74472749• TABLE_END

Optimization= = OPTIMIZING VARIABLES = =AVAILABLE VARIABLES ARE V1 TO V50

3.15926361E+00-9.70151891E+04-9.70151891E+04-9.70248906E+4V9

1.19007328E+012.18664263E-042.18664263E-042.18664263E-04V8

1.02636444E+01-3.11392279E+05-3.11392279E+05-4.11423418E+5V7

4.48683550E-012.79975794E-052.79975794E-052.80004792E-05V6

1.95885497E-02-2.82130025E+05-2.82130025E+05-2.82130025E+05V5

1.44758232E+001.75718445E+051.75718445E+051.7573601E+05V3

6.01374702E+004.78304593E-044.78304593E-044.78352423E-04V2

3.85216307E-01-6.28250129E+05-6.28250129E+05-6.28250129E+05V1

Rel. Stand. DevScaling FactorSTART ValueValue

NUMBER OF OPTIMIZING VARIABLES: 8ALL OTHER VARIABLES ARE FIX WITH THE VALUE ZEROTHE SUM OF SQUARES HAS CHANGED FROM 5.19453290E+02 TO 5.1944291E+02DEGREES OF FREEDOM 109. REDUCED SUM OF SQUARES 4.76554396E+00

Optimization Results: Tracer Diffusivity

Difference/ Error

DifferenceAcceptable error

Optimized Value

Experimental Quantity

0.94404.72E-25.0E-02-14.70LOGDT(FCC_A1,NI)=-14.75

-0.642-3.2E-25.0E-02-14.21LOGDT(FCC_A1,NI)=-14.17

-3.2E-2-1.59E-35.0E-02-13.88LOGDT(FCC_A1,NI)=-13.88

-0.826-4.13E-25.0E-02-13.54LOGDT(FCC_A1,NI)=-13.49

-3.170-0.15855.0E-02-13.23LOGDT(FCC_A1,NI)=-13.07

-2.788-0.13945.0E-02-12.97LOGDT(FCC_A1,NI)=-12.83

-2.814-0.14075.0E-02-12.72LOGDT(FCC_A1,NI)=-12.57

Extrapolation to Higher Order Systems

AlAlAlCr

CrAlNi

NiAlAl

AlAlCrCr

CrCrNi

NiCrCr

AlCrNiNiCrAlNiCrNi

NiCrNiAl

AlNiCr

CrNiNi

NiNiNi

AlAlAlCr

CrAlAl

AlAlCrCr

CrCrCr

AlAlAlNi

NiAlAl

AlAlNiNi

NiNiNi

CrCrCrNi

NiCrCr

CrNiNiCrNiCr

CrNiNi

NiNiNi

xQxQxQQ

xQxQxQQ

xxxBxxAxQxQxQQ

xQxQQ

xQxQQ

xQxQQ

xQxQQ

xQxQQ

xxAxQxQQ

����

����

������

���

���

���

���

���

����

Ternaryinteraction

Binaryinteraction

Ni-Cr

Ni-Al

Cr-Al

Ni-Cr-Al

Examples of Fits for Binary InteractionsNi-Al-Cr-Co-Hf-Nb-Mo-Re-Ta-Ti-W

-17.5

-17

-16.5

-16

-15.5

-15

-14.5

-14

0 0.02 0.04 0.06 0.08 0.1

Ti

Ta

W

Re

-14.5

-14

-13.5

-13

-12.5

-12

0 20 40 60 80 100

Atomic Percent Ni

1400 oC

1325 oC

1250 oC

1200 oC

1160 oC

Ni-Co Interdiffusion

Log

(D) m

2 /s

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

Log

(D) m

2 /sWeight Fraction

Interdiffusion with Ni

Data from Karunaratne et al., Mater. Sci. Eng., A281 (2000) 229.Data from Komai et al., Acta. Mater., 46, (1998) 4443.

T = 1000 oC

Previous assessments: Ni-Al-Cr Engström and Ågren, Z. Metallkd. 87 (1996) 92.

Ni-Al-Ti Matan et al., Acta mater., 46 (1998) 4587.

Current assessments: Ni-Co, Ni-Hf,Ni-Mo, Ni-Nb,Ni-Re, Ni-Ta, Ni-Ti,Ni-W, Co-Cr, Co-MoC. E. Campbell, W. J. Boettinger, U. R. Kattner, Acta Mat, 50 (2002) 775

Diffusion Correlation at Melting Temperature

18�

�

MRTQ

� For a pure metal

13.614.5-235350207619522504hcpHf

16.816.8-311420223022293695bccW

21.734.3-25690014219001946hcpTi

20.922.8-268253154014163296bccTa

16.314.9-382950283030843459hcpRe

28.225.4-274328117013002468bccNb

20.017.6-254975153017402895bccMo

19.519.5-286175176817681770hcpCo

32.919.2-23500086014752133bccCr

18.418.3-142000931933.5933.5fccAl

20.020.0-287000172517281728fccNi

-Q/RTM (fcc) (Kaufman)

-Q/RTM(fcc)

(SGTE)

ActivationEnergy (J/mole)

TM, K (fcc)(Kaufman)

TM, K (fcc)

TM, KCrystal Structure

Element

Comparison with Ni-Co-Cr-Mo Data at 1300 oC*

Diffusion coefficients calculated using the different thermodynamic databases and a fixed diffusion mobility database.

-2.27

-4.69

7.93

7.58

7.53

9.22

9.78

10.3

5.03

8.59

9.25

9.74

10.0

10.3

10.6

10.7

-2.37-1.7 ± 0.37.623.96.5

-2.26-2.0 ± 0.46.23.722.2

7.473.3 ± 0.77.116.225.9

6.834.2 ± 0.87.121.425.8

7.013.7 ±0.77.119.825.8

8.964.8 ±1.06.67.426.3

9.616.0 ± 1.26.44.426.5

10.38.9 ± 1.86.61.726.8

4.946.8 ± 1.4 7.747.93.2

8.46.4 ± 1.3 7.727.16.4

8.956.9 ± 1.47.426.210.8

9.358.2 ± 1.67.425.815.2

9.5610.1 ± 2.07.225.618.4

9.859.9 ± 2.07.425.020.8

10.19.7 ± 1.97.424.522.7

10.27.5±1.57.424.124.2

CalculatedNIST Thermotech

Measured Mo CoCr

Composition (Atomic Percent)Ni = balance

NiCrCrD~

NiCoCoD~

CoNiCrD~

smDNiij

21410�

~

†Heaney and Dayananda Metall. Trans. A, 1986, 17A, 983.

Co-Nb at 1100 C for 1000 h

0

0.01

0.02

0.03

0.04

0.05

-400 -350 -300 -250 -200 -150 -100 -50 0

GE Data (Nb)

DICTRA 1

DICTRA 2

Mol

e Fr

actio

n N

b

Distance (�m)

T = 1100 oC

Mobility of Nb in fcc Co not evaluated in diffusion database

0

0.2

0.4

0.6

0.8

1

-400 -300 -200 -100 0 100 200 300 400

Nb: GE Data

DICTRA: FCC phase

Mol

e Fr

actio

n N

b

Distance (�m)

T = 1100 oC

A+B*erf[(x-C)/(4Dt)^0.5]A = 0.026B = 0.025C = -47 �m

D = 2.13 x10-15 m2/s

FCC

smNbxDFCCCoMo

2141026.1]1.)([~�

���

Based on this result re-evaluate mobility parameter(MQ(FCC_A1&Nb,Co:V;0)] = -275333+R*T*LN(7.6071E-05)

smNbxDFCCCoMo

2151023.2]1.)([~�

���

smNbxDFCCCoMo

2141026.1]1.)([~�

���

(MQ(FCC_A1&Nb,Co:V;0) =-255333+R*T*LN(7.6071E-05)

DICTRA*Diffusion Controlled Transformations

• 1-D finite difference solution to diffusion equations• Variable self-adjusting mesh• Volume fixed reference frame• Vacancy and interstitial diffusion• Can solve problems with planar layers of

– single phase material – multiphase material (matrix and dispersed phase)

• describes suitable average concentration of multiphase mixture• assumes diffusion only in the matrix phase• assumes phase fraction of dispersed phase is small• assumes the composition of the dispersed phase is given by

local equilibrium for average concentration* from the Division of Physical Metallurgy, The Royal Institute of Technology, Stockholm, Sweden.

René-N4/René-N5 at 1293 °C for 100 h

0

0.02

0.04

0.06

0.08

0.1

0.12

-1000 -500 0 500 1000

Mas

s Fr

actio

n

Distance (�m)

Cr

Co

W

Ta

Al

TiMo

Re

HfNb

� Databases used– Thermodynamics:

Thermotech– Diffusion mobilities:

NIST Ni-mob

René-N4 René-N5

� �

6.35 mm 6.35 mm

Double geometric grid: 200 points

Experimental work performed by T. Hansen, P. Merewether, B. Mueller, Howmet Corporation, Whitehall, MI.

Porosity Prediction

-0.1

-0.05

0

0.05

0.1

-0.0004 -0.0002 0 0.0002 0.0004

Distance (m)

� �zJVa�

��

10 h

100 h

Rene-N4 Rene-N5

200 �m

N4 N5

Back scatter image; 100 h

0- +Predicted position for

maximum pore formationMaximum gives location of pore formation.

René-88/IN-718; 1000 h at 1150 °C

0

0.05

0.1

0.15

0.2

-500 0 500 1000

Mas

s Fr

actio

n

Distance (�m)

Cr

Co

Fe

Nb

Mo

TiAl

W

At 1150 °C equilibrium phase fractions

• René-88: f�

= 1• IN-718: f

�= 1

René-88 IN-100

4 mm 4 mm

Experimental data from J. C. Zhao, GE-CRD, Schenectady, NY

Applications of Diffusion Database

• Prediction of �� precipitation: GE-AIM program: – Composition and volume of ��� is key to predicting many of mechanical properties

• Back diffusion during solidification: Howmet

• Protective coatings: Howmet• B2/Rene-N5 diffusion simulations

•B2 layer dissolves, forms �� layer

• Heat treatment optimization: avoiding incipient melting.

Transient Liquid Phase Bonding

T = 1315 °C; Time 900 sNi-10.3Al/Ni-10B/Ni-10.3Al

0.00 0.04 0.08 0.120.00

0.05

0.10

0.15

0.20

LL ��������

L��� �����

L ���

Mole Fraction Al

T = 1315 °C

50 �m

Ni-Al Ni-Al

�

L� ���� ���

Thermodynamics &Diffusion mobilities

Mol

e Fr

actio

n B

microstructureevolution

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Rapid quench experimentsSlow cooled experimentsPrediction after isothermal holdPrediction with cooling

�Time (s)

Join

t wid

th (�

m)

0.00 0.02 0.04 0.06 0.08 0.10 0.120.000

0.002

0.004

0.006

0.008

0.010

Mole Fraction Al

Mol

e Fr

actio

n B

L + �

���

�

t = 1 st = 900 s

t = 1800 s

t = 3600 s

L ���� �

L �

L �

� ��� �

Time = 0 s

Time = 1 s

Time = 900 s

Time = 3600 s

C. E. Campbell and W. J. Boettinger, Metall. Materials Trans., 31A, 2000, 2835.

Heat Treatment Optimization:Solidification of Ni-11Al-4.5Ta (at.%)

L

L�

�����’9.5�m

t = 0 s

0 s < t < 4 s

t > 4 s

• Microstructure evolution

Solidification assumptions

• Cooling rate = 8K/s; • �/2 = 9.5 �m

0

0.05

0.1

0.15

0.2

0.25

0 0.05 0.1 0.15 0.2

Mol

e Fr

actio

n Al

Mole Fraction Ta

�'

B2

�

Ni3Ta�

DICTRA solidification path�' is a dispersed phase in �

T�= 8 K/s

Solidification Path

Thermodynamics: Ni-Data, ThermotechDiffusion: Ni-Mob, NIST

Incipient Melting Temperature

1635

1640

1645

1650

1655

1660

1665

0.0001 0.001 0.01 0.1 1 10 100 1000

(K/s)-1

Inci

pien

t Mel

ting

Tem

pera

ture

(K)

1000 (K/s) 100 (K/s)

1 (K/s) 0.01 (K/s)

Ni-11Al-4.5Ta (at.%)

Simulation Setup• Used composition and phase fractions from solidification calculation.

• Assume linear heating rates beginning at 800 K

• Assume �’ fraction is in equilibrium with � matrix at each grid point.

• Assume incipient melting occurs at the center between dendrites.

��

10 (K/s)

T�1

TE

TSolidus

Tsolvus (�/�’)

Heating Rate 100 K/s, TIM= 1655 K

Optimized Heat Treatment

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2 4 6 8

Distance (�m)

Phas

e Fr

actio

n �’

t = 0 s

800 s

855 s

1000 s

1200 s800

1000

1200

1400

1600

0 200 400 600 800 1000 1200

Tem

pera

ture

(K)

Time (s)

For Ni-11Al-4.5Ta alloy solidified at 8 K/s

� Heat from 800 K to 1655 K at 1 K/s

� Hold at 1655 K until t = 1325 s (t = 470 s)

Homogenous microstructure

Next step: Multicomponent simulation, optimization, experimental verification