Diffusion in Fe-Ni PM alloys: microstructure and DICTRA simulations

Tomas Gomez-AceboFrancisco Castro

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

• Introduction – Ni in steels• Microstructure of sintered Fe-Ni alloys• Kinetic modelling

– Kirkendall porosity

• Diffusion at high pressures

Contents

CALPHAD XL, Rio de Janeiro, 22-29/95/2011 2

• Tendency to reduce (and avoid) the use of Ni• … but it is essential in powder metallurgy

• Better understand the role of Ni diffusionduring sintering

• Model the diffusion process and Ni homogenization

Objectives

CALPHAD XL, Rio de Janeiro, 22-29/95/2011 3

[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]

Ni in steels

CALPHAD XL, Rio de Janeiro, 22-29/95/2011 4

• 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

Experimental procedure

CALPHAD XL, Rio de Janeiro, 22-29/95/2011 5

SEM micrographs from the Nickel powder used

Commercial powder grade

Nickel carbonyl powder

6CALPHAD XL, Rio de Janeiro, 22-29/95/2011

1000 °C – 0 min 1120 °C – 0 min 1120 °C – 15 min

Microstructures after quenching

• 10% Ni + 0.6% graphite + (Fe-0.8Mo) bal.

• Microstructural progress showing formation of “Nickel-rich” areas– Notice constrained shrinkage due to dual particle size distributions– First, grain boundary diffusion

7CALPHAD XL, Rio de Janeiro, 22-29/95/2011

Kinetic data in Fe-Ni alloys

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

0

1

2

3

4

5

6

7

8

9

10

11

10-15

DC(F

CC,N

I,NI,F

E)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

MOLE_FRACTION NI

Interdiffusion coefficient at 1120 °C (MOBFE1)

0

1E-14

2E-14

3E-14

4E-14

5E-14

6E-14

7E-14

0 20 40 60 80 100

D

D-Fe

D-Ni

Intrinsic diffusion coefficients at 1200 °C (Landolt-Börnstein)

Mo: 0.53

Fe: 53.10

Ni: 46.37

Mo: 0.7

Fe: 99.3

Ni: 0

Mo: 0.72

Fe: 96.14

Ni: 3.14

EDS analyses10%Ni + 0.6%C + (Fe-0.8Mo) bal., 1120 °C – 15min

9

0

10

20

30

40

50

60

70

80

90

100

WEI

GHT

-PER

CENT

NI

0 5 10 15 20 25 30 35 40

10-6DISTANCE

TIME = 0,1,10,100,1000,10000,100000,1000000

1000 s = 16 min

• Guillet constitutionaldiagram for Ni steels(1910)

• Compositions in wt-%• Still used

Guillet constitutional diagram

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

0

5

10

15

20

25

30

MAS

S_PE

RCEN

T NI

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

MASS_PERCENT C

DATABASE:TCFE6 N=1, P=1E5, T=973;

FCC_A1CEMENTIT+FCC_A1

BCC_A2+CEMENTIT

700 °C

0

5

10

15

20

25

30

MAS

S_PE

RCEN

T NI

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

MASS_PERCENT C

( ) DATABASE:TCFE6 N=1, P=1E5, T=1273;

FCC_A1

CEMENTIT+FCC_A1

1000 °C

Sintered at 1120 °C for 30 minfollowed by furnace cooling to RT (10 h)

CALPHAD XL, Rio de Janeiro, 22-29/95/2011 11

Sintered at 1120 °C for 30 min followed by slow cooling to 283 °C

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

Illustration of chemical gradients thus leading to different transformation products

10%Ni, 0.6%C,

(Fe-0.8Mo) bal

• Ni-Fe diffusion couple• Heating 20 °C/s to 1120

°C

Calculated diffusion profile

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

950

1000

1050

1100

1150

1200

T (º

C)

0 500 1000 1500

time [s]

A B

0

10

20

30

40

50

60

70

80

90

100

WEI

GHT

-PER

CENT

FE

-12 -9 -6 -3 0 3 610-6

z [m]

A (1120 °C, t=0)

B (1120 °C, 15 min)

Kirkendallplane

0

10

20

30

40

50

60

70

80

90

100

WEI

GHT

-PER

CENT

FE

-12 -9 -6 -3 0 3 610-6

z [m]

A (1120 °C, t=0)

B (1120 °C, 15 min)

Kirkendallplane

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

1120 °C – 15min

• Diffusion couple Ni-Fe, 1120 °C, 15 min

• Simulation: TCFE6 + MOBFE1

Isothermal diffusion

15CALPHAD XL, Rio de Janeiro, 22-29/95/2011

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ato

mic

frac

tion

Ni

-12 -10 -8 -6 -4 -2 0 2 4 610-6

z [m]

Ni Fe

• Velocity of the atomic planes in the lattice-fixed frame of reference

• Two velocity peaks

Velocity of the atomic planes

16CALPHAD XL, Rio de Janeiro, 22-29/95/2011

( )

( )z

xV

DD

JJJVv

m

∂∂

−=

=+−=

Ni

mFeNi

VaFeNi

1''

''

0

2

4

6

8

10

12

14

10-11

v [m

/s]

-12 -10 -8 -6 -4 -2 0 2 4 610-6

z [m]

Ni Fe

0

5

10

15

20

25

10-3

Max

imum

por

e fra

ctio

n

-12 -10 -8 -6 -4 -2 0 2 4 610-6

z [m]

Maximum pore fraction(model of Höglund & Agren, 2005)

17

-12

-9

-6

-3

0

3

6

9

12

15

d(-J

Va)/d

z

-12 -10 -8 -6 -4 -2 0 2 4 610-6

z [m]

Ni Fe

Derivative of the vacancy flux

zv

VzJ

m ∂∂

−=∂−∂ 1)( Va

Ni Fe

∫ ∂−∂

=t

dtzJVy

0

VamVa

)(

Va

Va

1 yyf p −

=

(Only for positive values of the integrand)

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

PRESSURE EFFECT ON FE-NI DIFFUSION

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

• 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

Pressure dependence on diffusion

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

Activation volume

VPSTUSTHG ∆+∆−∆=∆−∆=∆

TVGV

∂∆∂

=∆ Activation volume

For interstitials: MVV =∆ Migration volume

VPQQQMRTRTMRT

RTRTQMM

ii

iii

mgmgiii

∆+=

=−=∴

=ΓΓ

−=

0

0

0

MQln)ln(

magnetic-nonfor 1;1exp

Qi0: for 1 bar

20CALPHAD XL, Rio de Janeiro, 22-29/95/2011

• 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)

Experimental data

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

• Preliminary assessment results:– V(fcc&Fe,Fe)=13.2E-06 m3/mol– V(fcc&Ni,Ni)=0.91E-06 m3/mol– V(fcc&Fe,Ni)=5.9E-06 m3/mol– V(fcc&Ni,Fe)=4.1E-06 m3/mol

Diffusion profiles at 1, 12 and 23 GPa

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

0

10

20

30

40

50

60

70

80

90

100

ATO

MIC

-PER

CENT

FE

-300 -200 -100 0 100 200 300 400 500

DISTANCE (um)

0

10

20

30

40

50

60

70

80

90

100

ATO

MIC

-PER

CENT

FE

-150 -100 -50 0 50 100 150 200 250

DISTANCE (um)

0

10

20

30

40

50

60

70

80

90

100

ATO

MIC

-PER

CENT

FE

-150 -100 -50 0 50 100 150 200 250

DISTANCE (um)

1GPa, 1280C, 6h 1GPa, 1150C, 18h

1GPa, 1420C, 2h

12GPa, 1600C, 2h

12GPa, 1500C, 2h

12GPa, 1600C, 10h

12GPa, 1600C, 0.5h

23GPa, 1600C, 6h 23GPa, 1700C, 6h

Interdiffusion coeff. at 1, 12 and 23 GPa

-15.0

-14.5

-14.0

-13.5

-13.0

-12.5

-12.0

LOG

DC(F

CC,N

I,NI,F

E)

0 10 20 30 40 50 60 70 80 90 100

MOLE_PERCENT FE

-15.0

-14.5

-14.0

-13.5

-13.0

-12.5

-12.0

LOG

DC(F

CC,N

I,NI,F

E)

0 10 20 30 40 50 60 70 80 90 100

MOLE_PERCENT FE

-15.0

-14.5

-14.0

-13.5

-13.0

-12.5

-12.0

LOG

DC(F

CC,N

I,NI,F

E)

0 10 20 30 40 50 60 70 80 90 100

MOLE_PERCENT FE

23CALPHAD XL, Rio de Janeiro, 22-29/95/2011

23GPa, 1600C, 6h 23GPa, 1700C, 6h

1GPa, 1280C, 6h 1GPa, 1150C, 18h

1GPa, 1420C, 2h

12GPa, 1600C, 2h

12GPa, 1500C, 2h

12GPa, 1600C, 10h

12GPa, 1600C, 0.5h

• (On-going work)• Study of Ni diffusion in Fe powders• Modelling the pressure effect on diffusion

Summary and conclusions

24CALPHAD XL, Rio de Janeiro, 22-29/95/2011

THANK YOU!(and see you at Calphad 2013

in San Sebastian, Spain)