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Diffusion in Fe-Ni PM alloys: microstructure and DICTRA simulations
1. Diffusion in Fe-Ni PM alloys:
microstructure and DICTRA simulations
Tomas Gomez-Acebo
Francisco Castro
CALPHAD XL, Rio de Janeiro, 22-29/95/2011
2. Contents
• Introduction – Ni in steels
• Microstructure of sintered Fe-Ni alloys
• Kinetic modelling
– Kirkendall porosity
• Diffusion at high pressures
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3. Objectives
• Tendency to reduce (and avoid) the use of Ni
• … but it is essential in powder metallurgy
• Better understand the role of Ni diffusion
during sintering
• Model the diffusion process and Ni
homogenization
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4. Ni in steels
[W.C. Leslie, Met. Trans., vol.3, 1972, pp 5-26]
• Does not form any carbides hence remains in solution
strengthening ferrite
• Lowers critical cooling rate
• Grain refiner
• In combination with Cr, produces steels with greater hardenability,
higher impact strength and fatigue resistance than can be achieved
in carbon steels.
• The notch toughness of ferritic steels can be improved by grain
refinement and by additions of Ni.
• In the alloy steels, nickel is the most common of the alloying
elements used to lower the transition temperature
• Nickel is the only element in the periodic table that increases
toughness of Fe alloys
• Pt, Ni, Ru, Rh, Ir and Re
[de Retana A.F et al., Metal Progress, Sept., 100, 105, 1971]
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5. Experimental procedure
• Powder mixtures as multiple diffusion couples
– Fe-0.8 Mo, powder 60 µm
– Ni: 2-6 wt-%, powder 0.5-7 µm
– C (graphite): 0.2 wt-%
• Thermodynamic and kinetic modelling
– Mo not considered
– C: problems in calculations. Skipped
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6. SEM micrographs from the Nickel powder used
Commercial powder grade
Nickel carbonyl powder
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7. Microstructures after quenching
• 10% Ni + 0.6% graphite + (Fe-0.8Mo) bal.
1000 °C – 0 min 1120 °C – 0 min 1120 °C – 15 min
• Microstructural progress showing formation of “Nickel-rich”
areas
– Notice constrained shrinkage due to dual particle size distributions
– First, grain boundary diffusion
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8. Kinetic data in Fe-Ni alloys
11 7E-14
10 D
6E-14
9 D-Fe
D-Ni
8 5E-14
DC(FCC,NI,NI,FE)
7
4E-14
6
5 3E-14
4
2E-14
3
2
1E-14
1
-15
10
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 40 60 80 100
MOLE_FRACTION NI
Interdiffusion coefficient at Intrinsic diffusion coefficients at
1120 °C (MOBFE1) 1200 °C (Landolt-Börnstein)
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10. Guillet constitutional diagram
• Guillet constitutional
diagram for Ni steels
(1910)
• Compositions in wt-%
• Still used
( )
DATABASE:TCFE6 DATABASE:TCFE6
N=1, P=1E5, T=1273; N=1, P=1E5, T=973;
30 30
25
1000 °C 25
700 °C
CEMENTIT+FCC_A1
20
MASS_PERCENT NI
20
MASS_PERCENT NI
CEMENTIT+FCC_A1
FCC_A1
15 FCC_A1 15
10 10
5 5
0 BCC_A2+CEMENTIT
0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
MASS_PERCENT C MASS_PERCENT C
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11. Sintered at 1120 °C for 30 min
followed by furnace cooling to RT (10 h)
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12. Sintered at 1120 °C for 30 min followed by slow
cooling to 283 °C
10%Ni, 0.6%C,
(Fe-0.8Mo) bal
Illustration of chemical gradients thus leading to
different transformation products
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13. Calculated diffusion profile
• Ni-Fe diffusion couple
100
90 A (1120 °C, t=0)
• Heating 20 °C/s to 1120 80
°C 70
WEIGHT-PERCENT FE
60
50
1200
40 B (1120 °C, 15 min)
1150 A B
30
1100
T (ºC)
1050
20
Kirkendall
1000
10 plane
0
950
-12 -9 -6 -3 0 3 6
0 500 1000 1500 -6
10 z [m]
time [s]
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14. 100
90 A (1120 °C, t=0)
80
70
WEIGHT-PERCENT FE
1120 °C – 15min
60
50
40 B (1120 °C, 15 min)
30
20
Kirkendall
10 plane
0
-12 -9 -6 -3 0 3 6
-6
10 z [m]
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15. Isothermal diffusion
1.0 • Diffusion couple Ni-Fe,
Ni Fe
0.9
1120 °C, 15 min
0.8
0.7
• Simulation: TCFE6 +
MOBFE1
Atomic fraction Ni
0.6
0.5
0.4
0.3
0.2
0.1
0
-12 -10 -8 -6 -4 -2 0 2 4 6
-6
10 z [m]
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 15
16. Velocity of the atomic planes
14 • Velocity of the atomic
Ni Fe
12
planes in the lattice-
10
fixed frame of reference
= −( J ' Ni + J 'Fe ) = J Va
8
v
v [m/s]
Vm
6
1 ∂xNi
4 = (D' Ni − D'Fe )
Vm ∂z
2
-11
• Two velocity peaks
10
0
-12 -10 -8 -6 -4 -2 0 2 4 6
-6
10 z [m]
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 16
17. Maximum pore fraction
(model of Höglund & Agren, 2005)
15 25
12
Ni Fe Ni Fe
20
9
Maximum pore fraction
6
15
d(-JVa)/dz
3
0
10
-3
-6
5
-9 -3
10
-12 0
-12 -10 -8 -6 -4 -2 0 2 4 6 -12 -10 -8 -6 -4 -2 0 2 4 6
-6 -6
10 z [m] 10 z [m]
Derivative of the vacancy flux yVa
fp =
∂ (− J Va ) 1 ∂v 1 − yVa
=−
∂z Vm ∂z
∂ (− J Va )
t
yVa = Vm ∫ dt (Only for positive values of the integrand)
0
∂z
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18. PRESSURE EFFECT ON FE-NI
DIFFUSION
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19. Pressure dependence on diffusion
• Diffusion coefficient decreases with increasing
pressure
– Traditional model: relate to the melting point
diffusivity
– Melting point increases with pressure
– Same diffusivity at same homologous
temperature, T/TM
• Activation volume
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20. Activation volume
∆G = ∆H − T∆S = ∆U − T∆S + P∆V
∂∆G Activation volume
∆V =
∂V T
For interstitials: ∆V = V M Migration volume
Qi 1 mg
M i = M exp −
i
0
Γ; mg Γ = 1 for non - magnetic
RT RT
∴ RT ln( RTM i ) = RT ln M i0 − Qi = MQ
Qi = Q + P∆V
i
0
Qi0: for 1 bar
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 20
21. Experimental data
• Diffusion couples Fe-Ni
– P up to 23 GPa
– T=1280 – 1700 °C
• [Goldstein, Trans. Metall. Soc. AIME, 233 (1965) 812]
• [Yunker, Earth and Planetary Sci. Lett., 254 (2007) 203]
• Thermodynamic and mobility data:
– TCFE6 and MOBFE1 (modified introducing the pressure
term in mobility)
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24. Summary and conclusions
• (On-going work)
• Study of Ni diffusion in Fe powders
• Modelling the pressure effect on diffusion
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