Investigation of Methods for Calculation of Interdiffusion Coefficients of

Iron and Nickel Powder Mixtures

F.NAZEMI

Material Eng.Dept.

Isfahan University of Technology

Isfahan

IRAN

Faranaknazemi@Gmail.Com

Abstract. In this research, new methods were devised and investigated for calculation of interdiffusion of ironand nickel powder mixtures in porous media. We consider that two particles is like thin film in diffusioncouples and we use SEM and EDAX analysis and two mathematical methods to calculating “InterdiffusionCoefficient”. In these samples after metallography the observation with SEM show that microstructure consistsof ferrite and nickel-rich regions. Diffusion profile was established by EDAX analysis from center of grain richof nickel up to the out of its boundary and with an experimental method and spherical equation of secondFick’s law of diffusion, we obtain acceptable results for interdiffusion coefficient. We did not use otheradditional element to produce samples and our sample have 4% nickel and 0.8% Microwax in pure ironpowder (WPL200) and after mixing and compaction sintering was carried out in a mesh-belt conveyor furnacein 1120 ºC and 30 min in control endogas atmosphere. The green density of our sample is 6.8 g/cm3.

Keywords: Interdiffusion Coefficients, Powder, Nickel, Iron

1 IntroductionAlloys based on mixture of Fe and Ni powdersare common throughout powder metallurgy(P/M) 1. This alloys may seem simple,considering that the two elements are close

together in periodic table and are similarchemically, and in terms of electronic structureand atomic radius. However, the behavior of

these alloys is complex. As shown in the Fe-Ni phase diagram in Figure 1, 2 the liquidusand solidus temperatures are high, with anarrow solidification range. The face-centeredcubic crystal structure of iron (γ or austenite) is stabilized by alloying with nickel (the γ region expands with increasing nickelconcentration). Sintering techniques have beenexploited for several years in the production ofFe-Ni alloys. In mixed elemental powdersintering, there are fundamentally threeevents- particle adhesion, densification, andhomogenization. Adhesion occurs by surfacediffusion, typically during heating.Concomitant bonding without densificationprovides handling strength in the powdermass. At higher temperatures, densificationprocesses become active, leading to poreelimination via grain boundary diffusion.However, as high sintered densities areachieved the microstructure is nothomogeneous, but consists of Ni-rich islandsin the Fe-C steel matrix. During the sintering

Fig. 1: Fe -Ni binary phase diagram

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of mixed Fe-Ni powders, the adhesion,densification and homogenization events are

controlled by several

factors. In the early stage of sintering, chemicalgradients associated with mixed Ni and Fepowders improve diffusion fluxes over thoseassociated with surface energy which normallydrives single-phase sintering. Thus initialsintering can be improved significantly by theaddition of Ni. However, this chemicalgradient enhancement decreases withincreasing temperature as the concentrationgradients are eliminated.

Also, Ni enlarges the austenite zone andlowers the ferrite-to-austenite transformationtemperature. Since lattice diffusivity in face-centered cubic Fe is much lower than that thebody-centered cubic Fe, the phasetransformation lowers the sintering rate. Theconcentration of Ni in Fe increases duringsintering, inducing Ni-rich areas to transforminto austenite earlier than would occur with alow Ni content. The result is slower hightemperature densification due to the reduceddiffusion rate. Also, when Fe goes through thealpha-to-gamma transformation, there is asignificant increase in grain size. This result ina decrease in annihilation sites for vacanciesand substantial decrease in the sintering rate,which is sensitive to grain boundary area. Thusthe addition of Ni powder to Fe powderenhances early stage sintering but retards laterstage sintering. The coefficient of diffusion Feis much higher than those of Ni, leading topossible pore creation during interdiffusion.For example, raising the sintering temperaturefrom 1100 °C to 1250 °C increases theinterdiffusion coefficient of Fe into Ni by afactor of four, while that of Ni diffusion into Feincreases by only two and half times. Thedifference in diffusivity is another factor thatinfluences densification and homogenization inmixed Fe-Ni powder sintering. Thus, it isdifficult and costly to obtain a fullyhomogenized Fe-Ni alloy based on thesintering of mixed elemental powder if the Nicontent is high.5

This study measures the interdiffusioncoefficient of mixture of Fe-Ni powders thatsinter in 1120°C and 30 min time, in this studywe assume that the particles of given type arespherical and of the same size6, we can drive a

simple model that particle of Ni surroundedby Fe and during sintering gradient ofconcentration causes the interdiffusion ofthese particles so after sintering we havegrains Ni-rich areas. By using SEM andEDAX analysis and two mathematicalmethods a considerable good result nearsolid particle obtained.

2 Experimental Procedure:In this research, we use Ni and Fe powder toproduce experimental samples after mixing,compaction and sintering, cylindricalsamples prepared for metallugraphy and thisprocess was performed by optical andsecondary electron microscope.

3 Result and Discussion:Metallography indicates that these samplesincluded of ferrite, ferrite rich of nickel,minor pearllite and porosity. Figure (2) showthese regions. Also, EDAX analyses show usconcentration gradient of Nickel from ferriterich zone to Nickel poor zone.

Figure 2: Microstructure of Fe-4%Nickel by secondryelectron microscope

Bright zone: Ferrite rich of Nickle, Gray zone: α-Iron,minor pearllite, Dark zone: porosity

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(1) d=0, Center of BrightRegion

(4) d=6 μm

(2) d=2 μm(5)d=8 μm

(3) d=4 μm(6) d=10 μm

Figure 3: The results of EDAX analysis (Nickelcontents: (1)=19.205wt%, (2)=18.54wt%,

(3)=13.54wt%, (4)=6.742wt%, (5)=2.201wt%,(6)=1.459wt%)

3-1 Calculation of interdiffusioncoeficent Linear Diffusion at onecoordination3:Table 1 and 2 show the calculations and theresults of this method.

Table 1: Calculations of the experimental data for firstmethod

XXXYLnC=

Y

C=theresults of

EDAXanalysis

dd=X[μm]2

Distancefrom

assumingoriginal

d

00-1.6490.1920500

16-6.74-1.6850.185442

256-31.984-1.9990.1354164

1296-99.648-2.7680.06274366

4096-244.224-3.8160.02201648

10000-422.7-4.2270.0145910010

The results of some other analysis from thesesamples around the grain Ni rich show thesame variation, with mathematical Eq.1,Eq.2 and least square method and somelinear condition we assume two particles likethin film so diffusion could perform in onedimension and two different negative andpositive directions.

Dt

x

Dt

bctxc

4exp

2),(

20

. (1)

Dt

x

Dt

bctxc

42ln),(ln

2

. (2)

Table 2: Result of the experimental data for firstmethod

22)()( ii xxn

4.5584*10-14

])[(1

iiii yxyxna

-0.02808*108

)(1 2

iiiii yxyb xx

Not required

, t=1800 sec,Dt4

1Y=ax+ b, a=

sec109458.4

211 cm

D

After rectifying the Data

sec105992.3

211 cm

D

Fig. 4 shows the results of LnC(X,t)according X, by reactifying these data, theslope of this diagram

is better show ofDt4

1 . Rectifying take

places by continuing the first line passingfrom first data until cutting the horizontalline at -35 (μm). By adding this content to alldata, the line passing from second dataintersect the horizontal line at zero. The

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original era of diffusion can obtain accordingto this rectifying.

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 20 40 60 80 100 120

Distance X (μm)

Ln

C(X

,t)

Before rectifing After rectifying

Fig.4: Diagram of Logarithm of concentration dataaccording to square distance

3-2 Calculation of interdiffusion coeficent atspherical coordination4:By the separating variations on sphericalcoordination also we could calculateinterdiffusion coefficient of this mixture. Thesecond Fick’s law on spherical coordination atvariable conditions is like below: Eq. 3

r

c

rx

cD

t

n 22

2

. (3)

After solution of this equation we couldunderstand the relative variation ofconcentration with suitable linear condition a,b and c that are like below:

a) Diffusion from out to inside the sphere of Nito Fe

0,0,0 0 tcrr

0,,0 0 trrcc f

b) Diffusion from inside to out the sphere of Nito Fe

0,0,0 0 trrcc i

0,,0 0 trrcc f

c) In total condition

0,0,0 0 trrcc i

0,,0 0 trrcc f

In this linear condition Ci, Cf, C are initial,final and average of concentration and r0 isthe average radius of Nickel particles andwith forcing this linear condition the solutionof Fick’s equation is as below: Eq. 4

20

22

122

exp16

rDt

cc

cc

fi

f

.(4)

In this equation if the experimental time istoo long with assumeing the first serialsentence, the result of calculation of equationis like below: Eq. 5 and we could calculate“D“ with Eq.6

2

0

2

2exp

6

rDt

cc

cc

fi

f

. (5)

2

0

2

2ln

6lnln

rDt

cc

cc

fi

f

. (6)

The result of D can obtain by putting datafrom EDAX analysis and assuming time

equal 30 min and radius equal cm41010

as follow:

82 10100/6030ln4977.0

)02201.099.0/()02201.010139.0ln(

D

sec10334.11

211 cmD

4 Summary

1- By using the method of of calculationof interdiffusion coefficient LinearDiffusion at one coordination we can

obtainsec

109458.42

11 cmD

2- After rectifying data theinterdiffusion coefficient obtain

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sec105992.3

211 cm

D

3- By using Calculation of interdiffusioncoeficent at spherical coordination ofmixture of Fe-4%Ni powders that sinterin 1120°C and 30 min we can

obtainsec

10334.11211 cmD

References

[1] R. M. German, Powder Metallurgy of Ironand Steel, 1998, Wiley- Interscience, NewYork, NY.

[2] L.J. Swartzendruber, V.P. Itkin, and C.B.Alcock, Alloy Phase Diagrams, Volume 3of the ASM Handbook. 1992

[3] P.Shewmon, “Diffusion in Solids”, 2 ed.1989, Warrendale, PA: The Minerals,Metals, Materials Society.

[4] A. Sadjadi, “Diffusion in Solids”, IranUni.of Sci.and Tech., 1997

[5] H.Zhang, M.German.Randall“SinteringMIM Fe–Ni Alloys”, The InternationalJournal of Powder Metallurgy – Vol 38,NO.1, 2002

[6] P.Marsh., J.V.Wood, J.R.Moon, “Diffusionbetween high speed steel and ironpowders”, Powder Metallurgy2001,Vol.44 No.3

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