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▲465The Journal of The South African Institute of Mining and Metallurgy VOLUME 105 REFEREED PAPER AUGUST 2005

Introduction

Co-Fe-C alloys find applications in manymetallurgical processes such as welding andindustrial diamond synthesis. In highpressure-high temperature (HPHT) diamondsynthesis, it is generally agreed that diffusionis the dominant transport mechanism by whichcarbon is transported through the molten metalto the growing diamond crystal. In diamondsynthesis, the diffusion of carbon through themetal, both in the solid and molten states, isbelieved to be probably the rate-determiningstep for the growth of diamonds1. The study ofpressure effects on rate-limited processes is ofgreat importance and very often unique fordirectly determining the volume changesassociated with these processes. Pressureinfluences various parameters such astransformation temperatures, phase stability,transport mechanisms and the kinetics ofapproach to equilibrium, such that the extentand type of transformation in a variety of alloysystems can be altered by altering thepressure1.

Very little data exists on the influence ofpressure on the diffusion of carbon in the Co-Fe-C system2,3 both in the solid and liquidstates. Borimskii et al.’s work3, at a pressureof 50 kbar, in the temperature range1100–1400°C and covering Fe-Co alloyscontaining up to 70% Co was the only workknown to the authors on carbon diffusion athigh pressure in a cobalt-rich Fe-Co alloy,albeit in the molten state. Their results suggestthat the diffusion coefficient of carbon in themolten alloys at high pressure is approxi-mately one order of magnitude lower than thatin similar melts at atmospheric pressure.However, they concluded that this reductionwas not directly related to high pressure. Theeffect of pressure on the diffusion coefficient ofcarbon in Co-Fe-C alloys cannot be fullyassessed from these investigations due todifferences in experimental technique andpressures employed.

The metallography of Co-Fe alloys treatedat high pressures has received very littleattention. Metallographic studies can providemuch needed information on the stability ofphases at different temperatures andpressures.

This study aimed at measuring the solidstate diffusion of carbon in the Co-5% Fe-Csystem at high pressures and at studying thephase diagram of the Co-5% Fe-C system atsuch high pressures and the resultingmicrostructures. The microstructures, phasecomposition and identity of the phases werestudied by metallography, X-ray diffractionand X-ray spectral microanalysis oflongitudinal sections of diffusion samples.

Experimental procedureDiffusion experiments at atmospheric pressure

Solid state diffusion of carbon in theCo-5% Fe-C system at high pressure:metallography and phase equilibriumby M. Sibanda*, R.H. Eric†, and A. Koursaris†

Synopsis

The diffusion of carbon in Co-5%Fe alloy was studied in a belt-type pressure system at temperatures of up to 1330˚C and pressloads or nominal pressures of 7 020 tons or 42±3 kbar. Underthese conditions, this alloy is in the solid state. Discs of graphiteand prealloyed Co-5%Fe were used to make up the diffusioncouple. The diffusion coefficient increased with increasing pressload due to the tendency of the low density graphite to dissolvein the metallic phase reducing the overall volume and increasingthe density of the system. Furthermore, inhomogeneous plasticdeformation may have promoted diffusion by creating defects inthe alloy. Diffusion couples treated at atmospheric pressureexhibited graphite particles in the metal, while those treated athigh pressures exhibited carbide in the form of Widmanstattenlaths. Carbon analyses indicated increased carbon solubilitywith increasing pressure. This was confirmed from calculatedhigh-pressure phase diagrams.

* National Research Foundation–Innovation Fund.† School of Process and Materials Engineering,

University of the Witwatersrand, Wits, South Africa.© The South African Institute of Mining and

Metallurgy, 2005. SA ISSN 0038–223X/3.00 +0.00. Paper received Jun 2004; revised paperreceived Mar. 2005.

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressure

were carried out in an argon atmosphere using an A DSP1503P Fritsch Sintering Press in the temperature range1300–1310°C. This press was equipped with a vacuum andinert gas hood and a three-phase temperature control device,comprising three pyroscopes positioned 120° apart. Thesamples were heated by resistance heating and thetemperature was measured by the pyroscopes by convertingthe infrared radiation emitted by the sample to an electricalsignal related to temperature. At the end of the experiments,the temperature was allowed to decrease to room temperatureon average, over a period of 300 seconds, by force-coolingwith argon gas.

High-pressure experiments were carried out in a belt-typeapparatus of the type used for HPHT diamond synthesis4.Such a belt-type apparatus comprises a die in the form of acylindrical bore and two opposed anvils shaped in the form oftruncated cones. In use, these cones are supported at theopposed openings of the bore, with an appropriate gasketsuch as talc, pyrophyllite or mixtures thereof, provided at theopenings to allow for high pressures to be achieved.

A 10.6 mm thick layer of high purity graphite discs witha diameter of 59.8 mm and an average individual discthickness of 0.8 mm, was placed on a 10.6 mm thick layer ofpre-alloyed Co-5% Fe metal discs to form the diffusion couple(Figure 1). A 2 mm thick pyrophyllite ceramic pad was placedbeneath the metal layer. Another 10.5 mm thick layer of highpurity graphite discs was placed under the pyrophylliteceramic pad. The second layer of graphite discs was used tomaintain capsule stiffness and also to minimize metaldeformation.

The pyrophyllite ceramic pad served as a diffusion barrierbetween the metal and the bottom graphite layer. Thegraphite-metal-graphite stack was inserted into apyrophyllite ceramic tube having an inner diameter of 60 mm. The pyrophyllite ceramic tube was sealed with 2 mmthick pyrophyllite ceramic pads. Tantalum cups were placed

on both ends of the pyrophyllite ceramic tube and a tantalumsheet wrapped round the pyrophyllite ceramic tube. This wasinserted into a hollow KBr salt tube, which acted as apressure transmitting medium. The tantalum cups and thetantalum sheet together provided an encapsulating mediumfor the ‘reaction volume’ due to tantalum’s high meltingpoint and its electrical conductivity.

The reaction volume as described above was inserted intoa pyrophyllite ceramic outer tube of outside diameter equal tothe press die bore diameter. The ends of this outer tube weresealed with thin mild steel discs. The reaction volume wasthen annealed for 18000s in a belt-type press for the HPHTexperiments using a resistance heater sleeve. Severaldiffusion anneals were carried out at different temperaturesand loads/pressures. At the end of each anneal, the currentwas turned off, thereby initiating a temperature drop, whilemaintaining high load/pressure. The load was then reducedto zero in about twenty minutes.

Cylinders 22 mm in diameter were cut longitudinally byelectro-diamond machining of the annealed diffusioncouples. These were used for various analytical proceduresincluding carbon analyses and metallographic examination.Carbon content and hence diffusion depth, the extent towhich the carbon had diffused from an interface into themetal, was determined by a glow discharge optical emissionspectroscope5 using the following parameters: 1200 Vregulated voltage, 120 mA current, preburn time of 6 secondsand a sputtering rate of 0.036 mg s-1. The carbon contentanalysis method used had a spatial resolution of 2 µm.Three carbon diffusion profiles were obtained for eachsample to ensure reproducibility, and the carbon solubilitywas determined as the maximum carbon content measured.Longitudinal sections through the couples were prepared formetallographic examination and studied using optical andscanning electron microscopes.

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466 AUGUST 2005 VOLUME 105 REFEREED PAPER The Journal of The South African Institute of Mining and Metallurgy

Figure 1—Arrangement of a diffusion couple used in the determination of carbon diffusion in the Co-5%Fe alloy at high pressure

Results

Carbon diffusion in Co-5% Fe alloy

Carbon diffusion coefficients were determined from concen-tration-penetration depth profiles (Figure 2) by solving Fick’ssecond law6.

[1]

for the following conditions:

where t is the time in seconds, D is the diffusion coefficient(cm2 s-1), x is the depth in cm and cs and c0 are the carbonconcentrations at the metal surface and initial carbon contentof the metal, respectively. Since the carbon concentration atthe far end of the metal layer remained unchangedthroughout the experiments, the diffusion couple wasassumed to be semi-infinite. For the above initial andboundary conditions, Fick’s second law has the followingsolution for a semi-infinite couple

[2]

where A is a constant and c is the measured carbon concen-tration. The diffusion coefficients were determined from theslope of linear plots of ln (c-c0) vs x2, (Figure 3). Thelinearity of these plots indicates that the chosen solution toFick’s second law adequately describes the experimentalcarbon distribution in the Co-5% Fe alloy studied. Thediffusion coefficient values at atmospheric pressure and1290, 1310 and 1330°C and different press loads aresummarized in Table I. These results show that, in the Co-5%Fe alloy investigated, the diffusion coefficient of carbonincreased with increasing press load and temperature.

Metallography The atmospheric and high pressure Co-5% Fe samples wereexamined using optical and scanning electron microscopy.The sections were etched in 3% nital. An intimate bond wasfound to have formed at the graphite-metal interface. Thealloy exhibited a carbon depleted zone about 0.2 mm thick atits interface with the graphite layer in all HPHT samples,Figure 4. An explanation for the existence of this zone isprovided below. The diffusion depth increased withincreasing press load for a given temperature, as can be seenfrom Figure 2. In all HPHT samples, the diffusion zone wascomprised of two distinct areas: (i) a primary zone of varying

c c Ax

Dto− = − exp ( )2

4

c c x t

c c x t

c c x t

xx t

o

s

o

= > =( )= > >( )= = ∞ >( )

= > =( )

and c

0 0

0 0

0

0 0 0

,

,

,

,∂∂

∂∂

∂∂

2

2

2

2

c

tD

c

x=

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressureTransaction

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▲467The Journal of The South African Institute of Mining and Metallurgy VOLUME 105 REFEREED PAPER AUGUST 2005

Figure 2—Carbon concentration-depth profiles in Co-5%Fe at (a) 1290 °C and (b) 1330°C

Table I

Carbon diffusion coefficient in the Co-5%Fe alloy

Temperature (°C) Diffusion coefficient x 10-6 (cm2 s-1)

6020 tonne 6520 tonne 6620 tonne 6820 tonne 7020 tonne Pressure Atm.

1290 0.800 0.838 0.986 1.060 1.101 -1310 - - - - - 1.010–1.1101330 0.899 1.000 1.002 - 1.137 -

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressure

depth located adjacent to the carbon depleted zone andcharacterized by a Widmanstatten pattern, Figure 5, and (ii)a secondary zone further from the interface, showing grainboundary carbide and graphite precipitates in the metallicmatrix.

Samples treated at ambient pressure exhibited graphiteparticles in the metallic matrix, Figure 6. There was noevidence of carbide precipitation.

The increase in the width of the diffusion zone withincreasing press load supports the experimentally determineddiffusion coefficient values. The extent of the primary zoneincreased with increasing pressure, also indicating morerapid diffusion at higher pressures. This was furtherconfirmed by its absence in samples treated at atmosphericpressure.

EDS analyses, Figure 7, showed that the Widmanstatten

pattern is a carbide, probably of the type (Fe1-x Cox)3 C7. Thiscarbide structure was well defined, starting at the grainboundaries and penetrating the grains on selected crystallo-graphic planes. EDS spectra of different phases in the alloyare shown in Figure 7. These indicate a higher carboncontent in the carbide laths compared to the grain boundary.Microhardness tests on longitudinal sections showed that theprimary zone was much harder than the secondary zone.This can be attributed to the presence of the Widmanstattencarbide laths in the primary zone.

Scanning electron microscopy showed that the carbidelaths had a fairly regular spacing and that they wereinterrupted along their length by fine particles of graphite,Figures 8 and 9. There was a reduced amount ofWidmanstatten carbide in the vicinity of the graphiteparticles.

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468 AUGUST 2005 VOLUME 105 REFEREED PAPER The Journal of The South African Institute of Mining and Metallurgy

Figure 3—Plots of lnc vs x2 (where c is the carbon concentration and x is the depth) for carbon diffusion in Co-5% Fe at (a) 1290°C and (b) 1330°C andvarious press loads

Figure 4—Micrograph of diffusion zone showing a carbon depleted band (top). Etched, 3% Nital, 50X

Phase equilibrium in the Co-5%Fe-C system

The Co-Fe-C phase diagram for a 5%Fe alloy was calculatedat atmospheric pressure and pressures up to 45 kbar, Figure 10, using Thermo-Calc®, a software system developedat the Royal Institute of Technology (Stockholm), for thermo-chemical equilibrium calculations, comprising modules forequilibrium calculations, phase diagram calculations andtabulations of thermochemical quantities. Thermo-Calc® usesa data bank of assessed thermochemical data and models forthe phases in the system. In this case, the calculations weredone using a proprietary high pressure high temperaturetransition metals-carbon database. This phase diagram isvery similar to that of the binary Co-C system8. Increases inpressure lead to (i) an increase in carbon solubility in theaustenitic or face centred cubic (fcc) phase, (ii) a shift of theliquidus and solidus lines upwards, (iii) an increase in theeutectic temperature and eutectic carbon content from 1315°Cand 0.99wt-% at ambient pressure to 1420°C and 1.8wt-% at

45 kbar. The combined effect of factors (i), (ii) and (iii) is toexpand the austenitic or face centred cubic (fcc) phaseregion.

The eutectic temperature of the Co-5% Fe-C system atambient pressure was experimentally determined, by meltingthe Co-5% Fe alloy in the presence of graphite, and found tobe between 1315 and 1320°C.

The measured and calculated carbon solubilities in theaustenitic or face centred cubic (fcc) phase at ambientpressure and 1310°C were 0.73 and 0.88%C, respectively.The corresponding values at 45 kbar and 1330°C were 1.28and 1.58%C. The relationship between the calculated carbonsolubility in the austenitic or face centred cubic (fcc) phaseand pressure was linear, Figure 11. The carbon solubilitieswere determined from the measured maximum carboncontents at the graphite-metal interface or ‘zero’ diffusiondepth from the carbon concentration-depth profiles similar tothose shown in Figure 2.

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressureTransaction

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▲469The Journal of The South African Institute of Mining and Metallurgy VOLUME 105 REFEREED PAPER AUGUST 2005

Figure 5—Widmanstatten carbide laths and spheroidal carbide particles in the Co-5% Fe matrix. Etched, 3% Nital, 500X

Figure 6—Micrograph of a sample treated at atmospheric pressure showing graphite in a metallic matrix. Etched, 3% Nital, 500X

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressure

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470 AUGUST 2005 VOLUME 105 REFEREED PAPER The Journal of The South African Institute of Mining and Metallurgy

Figure 7—Semi-quantitative EDS spectra showing carbon concentrations in (a) the carbide laths, (b) the matrix and (c) the grain boundary carbide

Figure 8—Back scattered scanning electron microscope image showing graphite nodules, Widmanstatten carbide, grain boundary carbide, and darkplatelets on the grain boundary and in the carbide laths. Etched, 3% Nital, 8000X

0.0 0.5 1.0 1.5 2.0Energy (keV)

(a)

(c)

(b)

2.0

1.5

1.0

0.5

0.00.0 0.5 1.0 1.5 2.0

Energy (keV)

FeCocps cpsFeCo2.0

1.5

1.0

0.5

0.0

0.0 0.5 1.0 1.5 2.0Energy (keV)

cpsFeCo

1.5

1.0

0.5

0.0

Discussion

The observed increase in diffusion coefficient of carbon withincreasing pressure is interesting. Cox and Homan2 foundthat the diffusion coefficient of carbon in α-iron decreasedunder conditions of hydrostatic pressure. This was attributedto a volume decrease due to reduced interatomic distancesand elimination of microvoids.

In the present experiments, the pressure conditions wereprobably not purely hydrostatic. Such conditions can beexpected to generate defects in the lattice9,10, due to plasticdeformation. Defects could very well provide sites and pathsfor diffusing solute atoms, thereby potentially enhancing the

diffusion process. Thus, at high pressures, diffusion will tendto decrease due to lattice contraction and increase due toincreased lattice defects. The tendency of the system toreduce its volume and thereby increase its density wouldtend to enhance carbon solubility and diffusivity in the metal.A higher density would be obtained at high pressure andtemperature by reducing the volume of graphite, i.e., bydiffusion of carbon into the alloy. Maintaining a highpressure and reducing the temperature would favour theexsolution of carbon as carbide. Reducing the pressure andthe temperature, would favour the exsolution of carbon asgraphite. These effects can be expected from a considerationof the Le Chatelier principle.

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressureTransaction

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▲471The Journal of The South African Institute of Mining and Metallurgy VOLUME 105 REFEREED PAPER AUGUST 2005

Figure 9—Back scattered scanning electron microscope image showing graphite particles in the matrix and in association with Widmanstatten and grainboundary carbide. Etched, 3% Nital, 1000X

Figure10—The Co-5% Fe-C phase diagram at different pressures

Solid state diffusion of carbon in the Co-5% Fe-C system at high pressure

The increased width of the diffusion zone with increasingpressure shows clearly that diffusion was enhanced at highpressures. The Widmanstatten carbide laths formed duringcooling under high pressure are also a clear indication of thestabilizing effect of pressure on the denser phase. In contrast,in experiments conducted under ambient pressure, onlygraphite was obtained despite the high quenching rates.

The formation of graphite particles on the carbide lathsand in the matrix, during cooling, suggests a strong tendencyof the system to form the equilibrium phases. These graphiteparticles appear to have been the result of the decompositionof the mixed carbide. Their mode of occurrence suggests thatsmall cracks formed in the carbide laths providing suitablesites for the nucleation of the graphite. Such cracks may alsoenhance decomposition of the carbide due to void formation,and a balance between carbide and graphite is thereforeobtained.

The Widmanstatten carbide formed due to a reduction incarbon solubility during cooling. The carbide laths nucleate atgrain boundaries and grow rapidly along preferred crystallo-graphic planes in order to reduce supercooling of the solidsolution and bring it closer to equilibrium.

The carbon depleted zone described in this study hasbeen observed before11 in diffusion experiments but has notbeen explained. This zone is related to the cooling of thecouple and superzaturation of the diffusion zone in carbon.The carbon in the zone adjacent to the graphite diffuses backto, and re-deposits on the graphite leaving the zone depletedin carbon. Material further away becomes supercooled andprecipitates carbide laths. These phenomena are analogous tothe precipitation of ferrite adjacent to graphite in graphiticcast irons and pearlite further away from the graphite due tosupercooling of the austenite. The Widmanstatten patternformed in the diffusion zone is characteristic of supercooledmaterial.

There are appreciable deviations between the measuredand calculated carbon contents of the austenite at 1310 and1330°C and pressures of one atmosphere and 45 kbar. Thesemay be due to inaccuracies in the experimental results or topossible inadequacies of the model used in the calculations.

The exact values of carbon solubility at different temper-atures and pressures will probably not be known until furtherexperimental results on the Co-5% Fe-C system becomeavailable.

Conclusions

The diffusivity and solubility of carbon in a Co-5% Fe alloyincreased with increasing press load or pressure andtemperature as a result of volume reduction at high pressload and due to plastic deformation of the alloy.

Cooling of diffusion couples under high pressurestabilized the denser carbide phase in the alloy. Coolingunder ambient pressure stabilized the graphite phase.

Calculations showed that pressure expands the austeniticor face centred cubic (fcc) phase region in the Co-5% Fe-Csystem and increases carbon solubility in the alloy.

The measured solubilities of carbon in the austenite atpressures of one atmosphere and 45 kbar and temperaturesof 1310 and 1330°C differed appreciably from the calculatedvalues.

References

1. KIMSTACH, G.M. Metalloved. Term. Obrab. Met, 1991, no. 8, pp. 6–7.2. COX, J.F. and HOMAN, C.G. Physical Review B, vol. 5, no. 12, 1972,

p. 4755.3. BORIMSKII, A.I., DELEVI, V.G., BAGNO, N.G., NAGORNY, P.A., and

TRUNEVICH, L.V. Sverkhtverdye Materialy, 1993, no. 4, vol. 15, pp. 11.4. GIARDINI, A.A. and TYDINGS, J.E. The American Mineralogist, 1962, vol. 47,

p. 1393.5. PHILIBERT, J. Atom Movements, Les editions de Physique, 1991, France.6. CRANK, J. The Mathematics of Diffusion, London, Oxford University Press,

1970.7. PAVEL, E. et al., Physica B, vol. 175, 1991, pp. 354.8. HANSEN, M. Constitution of Binary Alloys, McGraw-Hill Book Company,

USA , 1958.9. GERTSRIKEN, S.D. and PRYANNISHNIKOV, M.P. Ukr. fiz. zhurnal, vol. 3, 1958,

no. 2.10. GERTSRIKEN, S.D. and YA. I. DEKHTYAR, Solid State Diffusion in Metals and

Alloys, State Publishing House for Physical Mathematical Literature,Moscow , 1960.

11. BRAMLEY, A. Iron and Steel Institute; Carnegie Memorial Scholarships, vol. 15, 1926, pp. 155. ◆

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Figure 11—Plots of calculated eutectic temperature and carbon solubility in the Co-5% Fe-C system against pressure