Diffusion of carbon in substitutionally alloyed austenite

S. S. BABU#, H. K. D. H. BHADESHIAUniversity of Cambridge/JRDC, Department of Materials Science and Metallurgy, Pembroke Street, CambridgeCB2 3QZ, UK

where k and h are the Boltzmann and Planckconstants, respectively, W is the number of octa-hedral interstices around a single such interstice,~F* is an activation free energy, r m is an activitycoefficient and), is the distance betwe-en (002)austenite planes. <1'= 1- exp(-wy/kT); Wy is thenearest neighbour carbon-carbon interactionenergy in austenite. () is the ratio of the number ofcarbon atoms to the total number of solvent atoms,given by () = xl/(1 - Xl)' Bhadeshia [6] found~F* /k = 21230 K and In {r m/).2} = 31.84.

It clearly is possible for the same equation to beused for austenite containing substitutional solutesas well as carbon, if the sole effect of the substitu-tional solute is to influence the activity of thecarbon. The purpose of this work was to demon-strate that this is indeed the case, using publisheddata [7].

These data reveal quite significant changes in themobility of carbon as a function of the substitutionalsolute; some of the data are listed in Table I forillustration purposes. For example, nickel and alu-minium have a rather small effect when comparedwith plain carbon steel, whereas chromium andmolybdenum tend to reduce the diffusivity.

The effects clearly are significant and wereanalysed using the Siller and McLellan model. Theactivity coefficient for carbon in alloyed austenitewas calculated using the quasichemical thermody-namic model developed in [8]. In this, the activity ofcarbon depends on the partial molar enthalpy ofsolution of carbon in austenite (38575 Jmol-l), andon the partial non-configurational entropy of solu-tion of carbon in austenite (13.48 J mol-l K-1) [8].In addition, there is a carbon-carbon interactionenergy which depends on the substitutional solute aswell, and was obtained from [9]. This model isrestricted to small concentrations, but diffusion dataover the following concentrations (wt %) were

"'.

It is well known that the diffusion coefficient D ofcarbon in austenite varies with the concentration ofcarbon [1,2]. In a previous analysis, it was demon-strated that a theory due to Siller and McLellan[3,4] can adequately explain the experimental datafor Fe-C alloys in the austenitic condition over awide range of concentration and temperature.

The theory represents D in a way which iscompatible with both the kinetic and thermody-namic behaviour of carbon in austenite. There aretwo important factors: the concentration depend-ence of the activity of carbon in austenite [1,2] andthe existence of a finite repulsive interaction be-tween nearest neighbouring carbon atoms situated inoctahedral sites [5]. Smith [2] has demonstrated thatthe composition dependence of activity cannot aloneaccount for D. Siller and McLellan realized that therepulsive forces between neighbouring carbon atomsshould influence diffusivity by acting to reduce theprobability of interstitial site occupation in thevicinity of a site already containing a carbon atom.In a concentration gradient, a carbon atom attempt-ing random motion therefore 'sees' an exaggerateddifference in the number of available sites in theforward and reverse direction, so that diffusiondown the gradient is enhanced. On this basis, Sillerand McLellan obtained

D{Xl' T} = (kT/h) (exp {- ~F*/kT})()..2/3rm)11{8}

. (1)

with

~=1+ar

W(l + 0)- (O.5W + 1)0 + (O.25W2 + O.5W) (1 - <1»02 ]

1 daY+ (1 + 0) - - 1-

ar dO

TABLE I Selected coefficients for the diffusion of carbon in austenite. The data for the alloy steels are from [7] whereas those for theplain carbon steel are from [6]

D (1000 °C)(107 cm2 S-I)

D (1100 °C)

(107 cm28-1)

D (1200 °C)(107 cm2 S-I)x Wt%X Wt%C

2.212.650.411.853.92.7

6.126.541.195.019.36.6

14.8514.052.81

11.616.714.4

-Ni

Cr

Mo

Co

AI

-42.51.5560.7

"Now at the Oak Ridge National Laboratories, TN, USA.

314 0261-8028 @1995Chapman & Hall

nevertheless investigated: Ni (4, 9.5), Mn (l),.Co(6), Cr (1,2.5,7), Mo (0.9, 1.55), VV (0.5, 1.05,1.95), Si (1.6, 2.55) and Al (0.7,1.7,2.45). Data forthree different carbon concentrations (0.2, 0.4,0.7 wt %) were available in each case.

The results are illustrated in Figs 1-8. The modelin general gives good results, the most severediscrepancies being found for chromium steels. Thealloys studied [7] were checked to be fully austeniticat the temperature where the measurements weremade, by comparison against published phase dia-grams [10]. There is a slight danger of alloy carbideformation for the Fe-O. 7C- 7 .0Cr wt % alloy at1000 °C, but in all other cases, the alloys should befully austenitic. It also cannot be argued that it is the

Figure 4 Comparison of the calculated and measured diffusivitiesfor Fe-Al-C alloys.

10-51 ' """', ' "'.7~

/'"?00 CD0 0

00,

";-(/)N

'E2

Q1"CQ)-."

"5(.)

"'CijU

0 ,

y./ Tungsten

10-7 H""'" . . . . . . . . I .". . . . ...,10-7 10-6 10-5

Measured D (cm-2 S-1)

Figure 5 Comparison of the calculated and measured diffusivitiesfor Fe-W-C alloys.

Figure 1 Comparison of the calculated and measured diffusivitiesfor Fe-Mn-C alloys.

10-5/,," """"1 "';;;;""

';-(1)N

'EB

Q 10-b

"C

<11-.!P.:J.2cou

,/

/9'

/' Nickel./

Figure 6 Comparison of the calculated and measured diffusivitiesfor Fe-Cr-C alloys. The discrepancy increases with the chro-mium concentration.

10-/1/, """,1 """,,-h10-7 10-6 10-5

Measured 0 (cm-2s-1)

Figure 2 Comparison of the calculated and measured diffusivitiesfor Fe-Ni-C alloys.

315

10-

Colin Humphreys for the provision of laboratoryfacilities. HKDHB's contribution was under theauspices of the' Atomic Arrangements: Design andControl Project' which is a collaborative venturebetween the University of Cambridge and theResearch and Development Corporation of Japan.

Figure 8 Comparison of the calculated and measured diffusivitiesfor Fe-Co-C alloys.

strong carbide-forming elements which give thelargest discrepancies, since the molybdenum dataare well predicted. Indeed, silicon which is not acarbide former in steels has a (smaller) discrepancywhich is similar to that of chromium. The reason forthe large chromium discrepancy is therefore notclear and warrants experimental investigation.

References1. R. P. SMITH, J. Arner. Chern. Soc. 68 (1946) 1163.2. R. P. SMITH, Acta Metall. 1 (1953) 579.3. R. H. SILLER and R. B. McLELLAN, Trans. Met. Soc.

A/ME 24S (1969) 697.4. R. H. SILLER and R. B. McLELLAN, Metall. Trans. 1

(1970)985.5. R. B. McLELLAN and W. W. DUNN, J. Phys. Chern.

Solids 30 (1969) 2631.6. H. K. D. H. BHADESHIA, Met. Sci.15(1981)477.7. M. A. KRISHTAL, "Diffusion processes in iron alloys",

Israel program for scientific translations, Jerusalem, 1970(1963) pp. 90-133.

8. H. I. AARONSON, H. A. DOMIAN and G. M. POUND,Trans. Met. Soc. A/ME 236 (1966) 753.

9. H. K. D. H. BHADESHIA: Met. Sci. 15 (1981) 178.10. B. UHRENIUS, in "Hardenability concepts with applica-

tions to steels", edited by D. V. Doane and J. S. Kirkaldy(TMS-AIME, Warrendale, PA, 1978) pp. 28-81.

AcknowledgementsThe authors are grateful to the Ministry of Educa-tion, Taiwan for financial support and to Professor

Received 8 Augustand accepted 17 October 1994

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