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Title: Development and Application of Composition-Dependent Diffusion Databases: Solid State Diffusion


1
Development and Application of Composition-Depende
nt Diffusion Databases Solid State Diffusion
Carelyn E. Campbell National Institute of
Standards and Technology Metallurgy
Division Gaithersburg, MD 20899
  • Motivation
  • Multicomponent Diffusion Basics
  • Development and Structure of a Diffusion
    Mobility Database
  • Validation of Database
  • Applications using Diffusion Mobility Databases

Constructing Kinetic Databases
April 20, 2004
This work was partially funded by the GE-led
DARPA AIM program
2
Types of Problems of Interest Diffusion
Controlled
3
Diffusion in Binary Alloys
Ficks first law for Flux, J
Ficks second law (conservation of mass)
If D is independent of composition
Simple solutions
4
What is needed to simulate multicomponent
diffusion?
At each grid point for each time step for a given
temperature profile.
René-N4
René-N5
g
g
5
Atomic Mobility
6

Diffusion in Multicomponent Solids
To describe the flux of atoms in the presence of
a driving force (composition gradient) and
assuming the vacancy concentration is in
thermodynamic equilibrium
Lattice fixed frame of reference
Note Tracer diffusivity is given by where
and is not dependent on the thermodynamics
Volume fixed frame of reference
where
Chemical (interdiffusion coefficient)
References Borgenstam et. al., J. Phase
Equilibria, 21 (2000) 269. Andersson and
Ågren, J. Appl. Phys. 72 (1992) 1350. Ågren, J.
Phys. Chem. Solids, 43 (1982) 421.
Ågren, J. Phys. Chem. Solids, 43 (1982) 385.
7
Concentration Dependent Diffusion Coefficients
Thermodynamic factor
Note that tracer diffusivity is not dependent on
thermodynamics.
8
Diffusion Database Development
  • Inputs
  • Thermodynamics (CALPHAD approach)
  • 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)

is exponentially dependent on composition
and
9
Thermodynamic AssessmentCALPHAD Approach
Experimental phase diagram Thermochemical data
Determine Gibbs Energy G f(x,T,P)
Calculated phase diagram
TltTE
L
a
b
Gibbs Energy
Composition
10
Assessment of Diffusion Mobilities
For a binary
11
Examples of Fits for Binary Interactions
Ni-Al-Cr-Co-Fe-Hf-Nb-Mo-Re-Ta-Ti-W (-C)
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-Fe-Cr Jönsson, Z. Metallkde. 86 (1995) 686.
Ni-Fe-Cr-C Jönsson, Z. Metallkde. 85 (1994)
502. Current assessments Ni-Co, Ni-Hf, Ni-Mo,
Ni-Nb, Ni-Re, Ni-Ta, Ni-Ti,Ni-W, Co-Cr, Co-Mo,
Fe-Al, Fe-Co C. E. Campbell, W. J.
Boettinger, U. R. Kattner, Acta Mat, 50 (2002)
775, C. E. Campbell, J-C. Zhao, M. Hnery, J.
Phase Equilibria Diffusion, 25, (2004) 6.
12
Assessment of Ni-W
Interdiffusion data
Tracer diffusivity data
13
Diffusion Correlation at Melting Temperature
  • For a pure metal

Element Crystal Structure TM, K TM, K (fcc) TM, K (fcc) (Kaufman) Activation Energy (J/mole) -Q/RTM (fcc) (SGTE) -Q/RTM (fcc) (Kaufman)
Ni fcc 1728 1728 1725 -287000 20.0 20.0
Al fcc 933.5 933.5 931 -142000 18.3 18.4
Cr bcc 2133 1475 860 -235000 19.2 32.9
Co hcp 1770 1768 1768 -286175 19.5 19.5
Hf hcp 2504 1952 2076 -235350 14.5 13.6
Mo bcc 2895 1740 1530 -254975 17.6 20.0
Nb bcc 2468 1300 1170 -274328 25.4 28.2
Re hcp 3459 3084 2830 -382950 14.9 16.3
Ta bcc 3296 1416 1540 -268253 22.8 20.9
Ti hcp 1946 900 1421 -256900 34.3 21.7
W bcc 3695 2229 2230 -311420 16.8 16.8
14
Comparison with Ni-Co-Cr-Mo Data at 1300 oC
Composition (Atomic Percent) Ni balance Composition (Atomic Percent) Ni balance Composition (Atomic Percent) Ni balance
Cr Co Mo Measured Calculated NIST Thermotech Calculated NIST Thermotech

24.2 24.1 7.4 7.51.5 10.2 10.7
22.7 24.5 7.4 9.7 1.9 10.1 10.6
20.8 25.0 7.4 9.9 2.0 9.85 10.3
18.4 25.6 7.2 10.1 2.0 9.56 10.0
15.2 25.8 7.4 8.2 1.6 9.35 9.74
10.8 26.2 7.4 6.9 1.4 8.95 9.25
6.4 27.1 7.7 6.4 1.3 8.4 8.59
3.2 47.9 7.7 6.8 1.4 4.94 5.03

26.8 1.7 6.6 8.9 1.8 10.3 10.3
26.5 4.4 6.4 6.0 1.2 9.61 9.78
26.3 7.4 6.6 4.8 1.0 8.96 9.22
25.8 19.8 7.1 3.7 0.7 7.01 7.53
25.8 21.4 7.1 4.2 0.8 6.83 7.58
25.9 16.2 7.1 3.3 0.7 7.47 7.93

22.2 3.7 6.2 -2.0 0.4 -2.26 -4.69
6.5 23.9 7.6 -1.7 0.3 -2.37 -2.27
Diffusion coefficients calculated using the
different thermodynamic databases and a fixed
diffusion mobility database.
Heaney and Dayananda. Metall. Trans. 17A
(6)983-989, 1986.
15
René-N4/René-N5 at 1293 C for 100 h
Experimental work performed by T. Hansen, P.
Merewether, B. Mueller, Howmet Corporation,
Whitehall, MI.
16
Analysis of Diffusion Multiples /Multicomponent
Diffusion
Experimental data from J-C. Zhao, GE Global
Research
17
René-88/IN-100 1000 h at 1150 C
Experimental data from J-C. Zhao, GE Global
Research
18
IN-718/IN-100 1000 h at 1150 C
Experimental data from J-C. Zhao, GE Global
Research
19
IN-718/IN-100 1000 h at 1150 C
1000 h
100 h
1000 h
1 h
10 h
100 h
1 h
10 h
20
AIM Strategy
R88
Ni
NiAl
W
Ta
Rapid Experiments Diffusion Multiples g ?
Experiments Characterization Grain Size
Experiments Characterization
21
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

22
Transient Liquid Phase Bonding
T 1315 C Time 900 s Ni-10.3Al/Ni-10B/Ni-10.3Al
T 1315 C
Thermodynamics Diffusion mobilities
Mole Fraction B
microstructure evolution
Mole Fraction Al
C. E. Campbell and W. J. Boettinger, Metall.
Materials Trans., 31A, 2000, 2835.
23
Solidification of Rene-N4Rene-N4
(Ni-9Cr-7Co-3.6Al-1.3Mo-0.4Nb-3.8Ta-4.1Ti-5.75W
wt. )
  • Solidification paths
  • Lever L? L g ? g ? g g
  • Scheil
  • L ? L g ? L g g
  • ? L g g s
  • ? L g g s BCC
  • ? L g s BCC h
  • ? L g s BCC h B2
  • ? L g s BCC h B2 m
  • DICTRA
  • Cooling rate 1 K/s
  • l/2 20 mm
  • Microstructure Evolution

Lever
Scheil
DICTRA
Fraction Solid
t 0 s
L
g
0 s lt t lt 130 s
L
Temperature (K)
g
130 s lt t lt 135 s
g
gg
135 s lt t lt 620 s
Thermodynamics Ni-Data, Thermotech Diffusion
Ni-Mob, NIST
After 620 s, s phase forms
20 mm
24
Solidification of Rene-N4Phase Fraction
Evolution
t 935 s (700 K)
t 935 s (700 K)
t 500 s (1135 K)
Phase Fraction g
Phase Fraction s
t 300 s (1335 K)
t 750 s (885 K)
t 150 s (1485 K)
t 620 s (1015 K)
t 135 s (1500 K)
Distance (mm)
Distance (mm)
25
Incipient Melting Temperature
  • Simulation Setup
  • Used composition and phase fractions from
    solidification calculation.
  • Assume linear heating rates beginning at 700 K
  • Assume g and s fraction are in equilibrium with
    g matrix at each grid point.
  • Assume incipient melting occurs at the center
    between dendrites.

26
Diffusion Database CenterC. E. Campbell, U.R.
Kattner, C. Beauchamp, K. Dotterer, H. Gates, S.
Tobery, L. Souders
c
  • Goal To make the NIST paper-based diffusion
    database center publicly available.
  • Convert to a searchable electronic form to be
    access over the internet
  • Motivation
  • Industrial and academic support GE 5K
    initiation
  • Center represents an unique collection
    summarizing the diffusion work between 1965-1980
  • Task
  • Need to enter 25000 bibliographic and diffusion
    system cards
  • Convert paper documents to electronic documents
  • Develop searchable database
  • Accomplishments
  • Developed database entry strategy
  • Entered bibliographic cards
  • Purchase high speed scanner and software

27
Other databases
  • TCS Alloy mobility database (v2.0, 1999).It is
    the most general alloy mobility database, within
    a framework of 75 elements. It can be used for
    steels/Fe-alloys, some Ni-based alloys, some
    Al-based alloys and more.
  • Bishop Dilute Al-alloy mobility database (v1,
    1995).It contains mobility data for dilute
    Al-based alloys, within a framework of 30
    elements.
  • Oikawa Dilute Fe-alloy mobility database (v1,
    1995).It contains mobility data for dilute
    Fe-based alloys, within a framework of 28
    elements.
  • Friberg Dilute Fe-alloy mobility database (v1,
    1995). It contains mobility data for dilute
    Fe-based alloys, within a framework of 16
    elements. It can be used for dilute Fe-alloys.

Available from ThermoCalc Software AB
28
Summary/Future Work
  • Diffusion mobility databases
  • Based unary, binary, and ternary tracer,
    intrinsic, and chemical diffusivities
  • Dependent on available thermodynamic databases
  • Extrapolate to n-component systems
  • Need unstable end-members
  • NIST-NiMOB (Ni (fcc) diffusion mobility database
  • FCC phase only (Ni-rich alloys)
  • 13 components
  • Applications (Ni-base superalloys, steels, Al
    alloys, solders)
  • Transient Liquid Phase Bonding
  • Heat Treatment Optimization
  • Solidification
  • Future Work
  • Diffusion order phases
  • Optimization of mobility parameters directly
    from experimental data
  • Charged ions Oxide phases (Höglund
    Thermo-Calc Software AB)

29
Diffusion in Ordered Phases
  • Expansion to Multicomponent systems Helander and
    Ågren, (Acta Mater., 1999, 47, 1141.)

DQ DQdis DQord
contribution to activation energy for
component k as a result of the ordering of i-j
atoms
From Shankar and Seigle, Metall. Trans. 9A,
(1978) 1476.
30
Diffusion Database Optimization Scheme
31
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

32
Mobility Description Ni-W
  • FCC_A1 Mobility of Ni
  • MQ(FCC_A1,NIVA0) -2870069.8T
  • MQ(FCC_A1,WVA0) V1RTLN(V2)
  • MQ(FCC_A1,NI,WVA0) V3V4T
  • FCC_A1 Mobility of W
  • MQ(FCC_A1,NIVA0) V5RTLN(V6)
  • MQ(FCC_A1,WVA0) V7RTLN(V8)
  • MQ(FCC_A1,NI,WVA0) V9V10T

33
Cu-Sn Intermetallic Growth
Time 0 s
9Cu 6Sn(l) ? Cu3Sn Cu6Sn5
Cu Concentration
Distance
Time gt 0 s
h
e
Cu Solid Solution
Sn Solution
34
Cu-Sn Intermetallic Growth
35
Solid-State Reactions in a Binary A-B System
A B AB
AB
A
B
Diffusion control
Interface control
Relaxation control
Mixed transport interface control
36
Definitions
Coefficient General Notation Mobility Notation
Tracer Diffusivity
Intrinsic Diffusivity (partial chemical)
Chemical Diffusivity (Interdiffusion) (binary) are related by the velocity of Kirkendall frame,
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