This document summarizes research on the diffusion of nickel (Ni) in iron-nickel (Fe-Ni) powder metallurgy alloys under various conditions. Microstructures of sintered Fe-Ni alloys showed the formation of Ni-rich areas over time. Kinetic modeling of Ni diffusion was performed using thermodynamic and kinetic simulation software. The simulations matched experimental diffusion profiles and indicated the presence of a Kirkendall plane. The maximum pore fraction model was also applied. Experimental diffusion data under high pressure (1-23 GPa) was presented and preliminary activation volumes were estimated from the pressure-dependent diffusion coefficients.

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)
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 8

9. EDS analyses
10%Ni + 0.6%C + (Fe-0.8Mo)
bal., 1120 °C – 15min
TIME = 0,1,10,100,1000,10000,100000,1000000
100
90
80
70
WEIGHT-PERCENT NI
60
50
40
1000 s = 16 min
30
Mo: 0.7
20
Fe: 99.3 10
Ni: 0 0
0 5 10 15 20 25 30 35 40
-6
10 DISTANCE
Mo: 0.72 Mo: 0.53
Fe: 96.14 Fe: 53.10
Ni: 3.14 Ni: 46.37
9

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
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 10

11. Sintered at 1120 °C for 30 min
followed by furnace cooling to RT (10 h)
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 11

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
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 12

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]
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 13

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]
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 14

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
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 18

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
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 19

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
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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)
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 21

22. Diffusion profiles at 1, 12 and 23 GPa
100 100
90 1GPa, 1150C, 18h 90 12GPa, 1500C, 2h
80
1GPa, 1280C, 6h 80 12GPa, 1600C, 0.5h
1GPa, 1420C, 2h 12GPa, 1600C, 2h
70
ATOMIC-PERCENT FE
70
ATOMIC-PERCENT FE
12GPa, 1600C, 10h
60 60
50 50
40 40
30 30
20 20
10 10
0 0
-150 -100 -50 0 50 100 150 200 250 -300 -200 -100 0 100 200 300 400 500
DISTANCE (um) DISTANCE (um)
100
• Preliminary assessment results:
90
23GPa, 1600C, 6h
80 23GPa, 1700C, 6h
V(fcc&Fe,Fe)=13.2E-06 m3/mol
70
ATOMIC-PERCENT FE
60
–
– V(fcc&Ni,Ni)=0.91E-06 m3/mol
50
40
30
20
– V(fcc&Fe,Ni)=5.9E-06 m3/mol
10
0
– V(fcc&Ni,Fe)=4.1E-06 m3/mol
-150 -100 -50 0 50 100 150 200 250
22
DISTANCE (um)
CALPHAD XL, Rio de Janeiro, 22-29/95/2011

23. Interdiffusion coeff. at 1, 12 and 23 GPa
-12.0 -12.0
1GPa, 1150C, 18h 12GPa, 1500C, 2h
1GPa, 1280C, 6h 12GPa, 1600C, 0.5h
-12.5 -12.5
1GPa, 1420C, 2h 12GPa, 1600C, 2h
12GPa, 1600C, 10h
LOGDC(FCC,NI,NI,FE)
LOGDC(FCC,NI,NI,FE)
-13.0 -13.0
-13.5 -13.5
-14.0 -14.0
-14.5 -14.5
-15.0 -15.0
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100
-12.0 MOLE_PERCENT FE MOLE_PERCENT FE
23GPa, 1600C, 6h
-12.5
23GPa, 1700C, 6h
LOGDC(FCC,NI,NI,FE)
-13.0
-13.5
-14.0
-14.5
-15.0
0 10 20 30 40 50 60 70 80 CALPHAD XL, Rio de Janeiro, 22-29/95/2011
90 100
23
MOLE_PERCENT FE

24. Summary and conclusions
• (On-going work)
• Study of Ni diffusion in Fe powders
• Modelling the pressure effect on diffusion
CALPHAD XL, Rio de Janeiro, 22-29/95/2011 24

25. THANK YOU!
(and see you at Calphad 2013
in San Sebastian, Spain)