thermodynamics of carbon in nickel, iron-nickel and iron-chromium-nickel alloys

Thermodynamics of Carbon in Nickel, Iron-Nickel and Iron-Chromium-Nickel Alloys

K. NATESAN AND T. F. KASSNER

I r o n - n i c k e l a l l oys with 8 and 16 wt pc t n icke l and i r o n - c h r o m i u m - n i c k e l a l l o y s with 8 pc t n i cke l and c h r o m i u m contents in the r a n g e of 2 to 22 pc t we re e q u i l i b r a t e d with i r on and n icke l in f lowing CH4-H 2 gas m i x t u r e s and in s e a l e d c a p s u l e s under p a r t i a l vacuum at t e m - p e r a t u r e s be tween 700 and 1060~ Carbon a c t i v i t i e s in t hese a l loys w e r e e s t a b l i s h e d f r o m the ca rbon concen t r a t i ons in the n i cke l by apply ing H e n r y ' s law to the so lub i l i t y of ca rbon in n icke l that was d e t e r m i n e d in the t e m p e r a t u r e r a n g e of 500 to 1000~ F i r s t - o r d e r f r e e - e n e r g y i n t e r ac t i on p a r a m e t e r s we re used to r e l a t e the ca rbon a c t i v i t i e s to compos i t i on and t e m p e r a t u r e in the s i n g l e - p h a s e aus t en i t i c F e - N i and F e - C r - N i a l l oys . An e x p r e s s i o n was a l so deve loped to eva lua te ca rbon a c t i v i t i e s in F e - C r - N i a l loys in the r e g i o n of h igher c h r o - mium contents (>4 wt pct) that r e s u l t in a t w o - p h a s e aus t en i t e plus c a r b i d e mix tu r e at t he se t e m p e r a t u r e s .

I R O N - b a s e a l loys with v a r i a t i o n s in the c h r o m i u m and n icke l concen t r a t i ons fo rm the b a s i s of a number of aus t en i t i c s t a i n l e s s s t e e l s that have ex t ens ive h igh- t e m p e r a t u r e app l i ca t ion in t u rb ine s , s t e a m g e n e r a t o r s , and p ip ing in e l e c t r i c power gene ra t i ng p l an t s ; in gas c r a c k i n g and r e f o r m i n g f a c i l i t i e s in the p e t r o l e u m r e - f ining i ndus t ry ; and in s o d i u m - c o o l e d f a s t - b r e e d e r nu- c l e a r r e a c t o r s for the fuel c ladding, hea t e x c h a n g e r s , p iping, va lve s , and v a r i o u s s t r u c t u r a l components . A l - though the e n v i r o n m e n t a l condi t ions a r e v a s t l y d i f f e r - ent in t hese app l i ca t i ons , the m a t e r i a l s in g e n e r a l change in m i c r o s t r u c t u r e and compos i t ion , p r i m a r i l y in the nonme ta l l i c e l e m e n t s such as ca rbon , n i t rogen , and boron , a f t e r l o n g - t e r m s e r v i c e at high t e m p e r a - t u r e s . The r e l a t i o n s h i p be tween the compos i t i on , m i - c r o s t r u c t u r e and m e c h a n i c a l p r o p e r t i e s of t h e s e m a t e - r i a l s has been the sub jec t of n u m e r o u s inves t iga t ions . l -*~ The i m p o r t a n c e of the ca rbon and n i t rogen contents in t h e s e s t e e l s on the m i c r o s t r u c t u r a l s t a b i l i t y n-~4 and the m e c h a n i c a l behav io r ~-9 is a l so wel l r e c o g n i z e d . F r o m a knowledge of the t h e r m o d y n a m i c and k ine t i c behav io r of t he se e l e m e n t s in the p a r t i c u l a r e n v i r o n - ment and in the a l l oys , i t is p o s s i b l e to d e t e r m i n e the su i t ab i l i t y of the m a t e r i a l s for h i g h - t e m p e r a t u r e s e r - v ice . This a p p r o a c h has been used to ana lyze c a r b u r i - z a f i o n - d e c a r b u r i z a t i o n phenomena that involve a u s t e n - i t i c s t a i n l e s s s t e e l s in sod ium h e a t - t r a n s p o r t s y s t e m s of nuc l ea r r e a c t o r s . ~%18 F o r th is p u r p o s e , ca rbon a c - t i v i t y - c o n c e n t r a t i o n r e l a t i o n s h i p s have been g e n e r a t e d for F e - C r - 8 wt pc t Ni a l loys with c h r o m i u m contents be tween 0 and 22 wt pc t in the t e m p e r a t u r e r a n g e of 725 to 1060~ The e x p e r i m e n t a l data , which were ob- t a ined at t e m p e r a t u r e s c o n s i d e r a b l y lower than those r e p o r t e d in the l i t e r a t u r e , wi l l be useful in e s t a b l i s h i n g quant i t a t ive p r e d i c t i o n s of the c a r b u r i z a t i o n - d e c a r b u r i - za t ion behav io r of aus t en i t i c s t a i n l e s s s t e e l s under d i f - f e r en t e n v i r o n m e n t a l condi t ions .

K. NATESAN and T. F. KASSNER arc Metallurgists with the Mate- rials Science Division, Argonne National Laboratory, Argonne, Ill. 60439.

Manuscript submitted March 6, 1973.

EXPERIMENTAL PROCEDURE

Appara tus

M e a s u r e m e n t s of ca rbon ac t i v i t y in the i r o n - b a s e a l - loys w e r e made by equ i l i b ra t i ng foi l s a m p l e s in CI-I4-H a gas m i x t u r e s of a f ixed compos i t i on . The ca rbon a c t i v i - t i e s in t hese m a t e r i a l s a s a function of t e m p e r a t u r e and ca rbon concen t r a t i on we re b a s e d upon two p r e m i s e s : f i r s t , the E l l io t t and G l e i s e r 17 t abu la t ion of the Nat iona l Bureau of S tanda rds (NBS) is e q u i l i b r i u m da ta for the r e a c t i o n

Cgraphite + 2H2 = CH4, [1]

where the e q u i l i b r i u m cons tan t (Keq = PC H 4/P~I 2 a C) i s r e p r e s e n t e d by

pa AG ~ = - R T I n ( P c H 4 / H2aC) = - 2 1 , 5 5 0 + 26.16T

[2] and second ly , c a rbon a c t i v i t i e s e s t a b l i s h e d f r o m c a r - bon concen t r a t i ons in e q u i l i b r a t e d n icke l fo i l s and the app l i ca t ion of H e n r y ' s law to the so lub i l i ty of c a r b o n in n icke l . The l a t t e r a p p r o a c h was inc luded b e c a u s e i t is known tha t the compos i t i on of CH4-H z gas m i x t u r e s can be inf luenced by m o i s t u r e con tamina t ion , and some d i f f icu l ty could r e s u l t in the d e t e r m i n a t i o n of ca rbon a c t i v i t i e s in the m a t e r i a l s s o l e l y f r o m the gas c o m p o - s i t ion . The d e s i r e d ca rbon a c t i v i t i e s a t each t e m p e r a - tu re we re e s t a b l i s h e d by con t ro l l ing the flow r a t e of u l t r a p u r e hydrogen and one of s e v e r a l mixed g a s e s with 0.1, 1.0, and 5.0 pc t methane in hydrogen , which c o r r e s p o n d e d to gas r a t i o s c a l c u l a t e d us ing Eq. [2]. The ca rbon concen t r a t i ons in foi l s p e c i m e n s of h igh- p u r i t y n i cke l we re used to d e t e r m i n e the ac tua l c a rbon a c t i v i t i e s ob ta ined in these e x p e r i m e n t s .

The equ i l i b r a t i on e x p e r i m e n t s were conducted in a f i v e - z o n e p la t inum-wound fu rnace that conta ined four 25 m m outs ide d i a m (OD) quar tz r e a c t i o n tubes . The s a m p l e s w e r e a t t ached to a 5 m m OD the rmocoup l e wel l p r o v i d e d in the c e n t e r of the r e a c t i o n tube that was c l o s e d at the bo t tom. The mixed gas e n t e r e d th rough ano the r 5 m m OD quar tz tube a t t ached to the ins ide of the r e a c t i o n tube, p a s s e d through the s a m p l e

METALLURGICAL TRANSACTIONS VOLUME 4, NOVEMBER 1973-2557

section, and exited at the top. The t empera tu re in the vicini ty of the samples was control led within •176

Carbon-ac t iv i ty measurements were also made by enclosing spec imens of var ious i ron -chromium-n icke l al loys with a carbon ]"source in evacuated quartz capsules and then annealing the capsules until carbon equi- l ibr ium was achieved in al l specimens. The carbon ac - t ivi ty at tained within each capsule was determined from the final carbon content of the nickel and Fe-Ni al loys included in the capsules . In these exper iments , the equi l ibr ium carbon concentrat ions in the al loys were de te rmined by specif ic CO/CO2 ra t ios es tabl ished by the carbon source .

Carbon-solubi l i ty values in nickel were also de te r - mined in the t empera tu re range of 500 to 1000~ by equil ibrat ing h igh-pur i ty nickel foils with graphite rods in a flowing CHa-H ~ gas mixture whose composit ion yielded a unit carbon act ivi ty. At t empera tu res between 800 and 1000~ high-pur i ty iron was included in these exper iments ; upon equil ibrat ion, the carbon concentrations were found to be in agreement with the repor ted graphi te -so lubi l i ty data, which indicated the val idi ty of the exper imental methods.

Mater ia l s and Analysis Procedure

The F e - C r - N i al loys were a rc melted from Armco iron, h igh-pur i ty nickel and chromium in a 75 pct He- 25 pct Ar a tmosphere at a reduced p r e s s u r e of 400 Tor t . The cast ings were extruded, ro l led and/or swaged to the des i r ed th icknesses . All samples were solution annealed at 1025~ for 1 h p r io r to use in the carbon equil ibrat ion exper iments . The composit ions of the foil specimens of iron, nickel, and the i ron-base al loys used in the ca rbon-ac t iv i ty measurements a re given in Table I. Inasmuch as the t empera tu re in the gas-phase equil ibrat ion exper iments ranged between 500 and 1000~ ma te r i a l s of seve ra l th icknesses were requi red to minimize the t ime for 99 pct equil ibrat ion, pa r t i cu l a r ly at the lower t empera tu re s . Mater ia ls of the following th icknesses were used: iron, 10 and 30 mi ls ; nickel, 2, 5, and 12 mi l s ; Fe-8 wt pct Ni, 2 and 10 mi ls ; Fe-16 wt pct Ni, 2 mi l s ; and F e - C r - 8 wt pct Ni al loys, 1, 2, and 5 mi ls . The ca rbon-source s am- ples , requi red for the capsule equi l ibrat ion exper i - ments, were obtained by carbur iz ing iron, nickel, and

Table I. Composition of Iron, Nickel, and Iron-Base Alloys (Concentrations are given in wt pct)

Alloy Cr Ni C N O Fe

Fe <0.004 0.012 0.002 0.001 <0.007 Bal*t Ni-270 <0.001 Bal* 0.002 0.00t <0.005 <0.01 Fe-8 wt pct Ni <0.01 7.99 0.002 <0.001 0.016 Bal* Fe-16wtpctNi <0.001 15.87 0.003 <0.001 0.008 Bal* Fe-8 wt pct Ni-2 wt pct Cr 1.96 7.92 0.002 <0.001 0.010 Bal* Fe-8 wt pct Ni-4 wt pct Cr 3.89 7.86 0.004 <0.001 0.010 Bal* Fe-8 wt pct Ni-8 wt pct Cr 7.90 7.90 0.004 <0.001 0.013 Bal* Fe-8wtpctNi-12wtpctCr 11.96 7.96 0.003 <0.001 0.012 Bal* Fe-8wtpctNi.15wtpctCr 14.74 7.82 0.003 <0.001 0.013 Bal* Fe-8 wt pct Ni-18 wt pct Cr 17.74 7.92 0.003 0.002 0.008 Bal* Fe-8 wt pct N1-22 wt pct Cr 21.86 7.92 0.003 0.002 0.009 Bal*

*Bal indicates balance; spectrographic analyses for Mn, Mo, Si, Nb, Ti, Zr, V, Co, Cu indicated <0.01 wt pct.

tManganese concentration in high-purity iron was 0.05 wt pct.

Fe-Ni al loys in CHa/H 2 a tmospheres between 800 and 1000~

The foil specimens were analyzed for carbon using a LECO low-carbon combustion analyzer that had a sensi t ivi ty of ~ 5 tzg of carbon for a 1-g sample. The analyzer was ca l ibra ted with a s e r i e s of NBS i ron- carbon al loy s tandards over the range of carbon values for the specimens in each run; a minimum of two analyses was made on each specimen. An examination of the F e - C r - N i foils by optical and scanning e lec t ron mi - croscopy ensured that the specimens were equi l ibrated in thei r ent i re c ros s section. The accuracy of carbon analyses was • pct for carbon concentrat ions above ~0.05 wt pct and • pct at carbon levels of ~0.005 wt pct in the ma te r i a l s .

EXPERIMENTAL RESULTS AND DISC USSION

The resu l t s for the solubi l i ty of carbon in nickel at t empera tu re s between 500 and 1000~ shown in Fig. 1, a re in good agreement with the higher t empera tu re measurements of Wada e t al . 19 and Smith. 2~ The com- bined data for the graphite solubi l i ty in nickel over the t empera tu re range of 500 to 1200~ can be r ep resen ted by the re la t ion

CNi (wt pct) = 12.4 exp ( - 5160/T). [3]

The resu l t s of other inves t iga tors 21-25 were included in Fig. 1 for comparison. Wada et al . provided pos s i - ble explanations for the somewhat l a rge r carbon solu- b i l i ty values obtained in the other h igh- tempera ture investigations.a~- 2s

Z o m I:E < (..)

T E M P E R A T U R E , *(3 1200 I I 0 0 I 0 0 0 9 0 0 8 0 0 7 '00 6 0 0 50(

0 .8 - I I I I I I I I __

- - - - DUNN et al. \ NICKEL SCHENCK et al

. , ~ L A N D E R e t o1." ~ , , . 0 WADA et ol.

" ~ x SMITH ~ 1 ~ a RAO & NI CHOLSON ~ "~"%.. z~ �9 ALCOCK 8, STAVROPOULOS

- ' ~ . , ~ PRESENT WORK 0.I_-- "\,\ _

C ~ ~ I 6 0 / T ) " ~ �9

0.01 4

- - A - -

0.003 I I I I I I I 0.7 0.8 0.9 1.0 I.I 1.2 1.3

IO~/T, OK -I F i g . 1 - - T e m p e r a t u r e d e p e n d e n c e of the s o l u b i l i t y of c a r b o n in n i c k e l .

2558-VOLUME 4, NOVEMBER 1973 METALLURGICAL TRANSACTIONS

Carbon Act iv i ty in I r o n - N i c k e l Al loys

The c a r b o n ac t iv i ty a s a funct ion of c a rbon concen- t r a t i o n for F e - 8 wt pc t Ni and F e - 1 6 wt pc t Ni a l loys was d e t e r m i n e d in the t e m p e r a t u r e r ange of 700 and 1060~ by equ i l i b ra t i ng in CH4-H~ gas m i x t u r e s . The ca rbon a c t i v i t i e s * in the a l loys we re ob ta ined f rom

*Carbon activities in this paper are based upon a graphite standard state.

ca rbon concen t r a t i ons in n icke l s p e c i m e n s that were inc luded in the equ i l i b ra t i on e x p e r i m e n t s and f rom ap - p l i ca t ion of H e n r y ' s law to the ca rbon so lub i l i ty in n i cke l at v a r i o u s t e m p e r a t u r e s f rom Eq. [3]. The r e - su l t s a r e p r e s e n t e d in F ig . 2 for the F e - 8 wt pc t Ni and F e - 1 6 wt pct Ni a l l oys .

CARBON, wt % ' 0.Ii 0.21 Oi~ 0,41 0.51 0.61 017 018 019

1.0

0.8 - 800~

,oo-c/ / . _ / / . -

/ / / o _ z 05- / / / .-8~%., _ ~ ~ / / ~ - o 0.3-

02 - ! ~

0 .1 -

O O.OI O.02 O!O3 OI.o4

CARBON MOLE FRACTION e)

CARBON, ppm 200 400 6OO 800 100012OO IqO01600 1800 ;~300 25L I I I I I I I I I I I !

o

/ ~..700e c Fe-16w, % Ni

o oF / - / oo.c -

I i" / !o,51 J 7 ~%oo'r _ I / / /

F/// o

OilZ I I I I 0 0.00~ 0.004 0.006 0.008 0.010

CARBON MOLE FRACTION (b)

Fig. 2--Carbon activity-concentration relationship for the F e - 8 wt pct Ni and Fe-16 wt pct Ni alloys at 700, 800, and 900~

The effect of n i cke l on the ac t i v i t y of c a rbon in F e - N i -C a l loys was d e t e r m i n e d f r o m the da ta us ing a f i r s t - o r d e r f r e e - e n e r g y i n t e r a c t i o n p a r a m e t e r to obta in a r e l i a b l e e x t r a p o l a t i o n of the c a r b o n - a c t i v i t y r e s u l t s to o the r t e m p e r a t u r e s and a l loy c ompos i t i ons . The ca rbon ac t i v i t y (acFeNiC) in the t e r n a r y s y s t e m can be wr i t t en a s

(FeNiC) a C = y(C FeNiC) NC, [4]

where

(c FeNiC) = Raoul t ian a c t i v i t y coef f ic ien t for carbon 7 in an F e - N i - C a l loy ,

N c = mole f r a c t i o n of c a rbon in an F e - N i - C a l loy ,

and the ac t i v i t y c o e f f i c i e n t y(C FeNiC) is g iven by

in ~(C FeNiC) = In y(C FeC) + ENiNNi , [5]

where

~FeC) = Raoul t ian ac t iv i ty coef f ic ien t for c a rbon Y in an F e - C b i n a r y a l loy ,

E~ i = f r e e - e n e r g y i n t e r ac t i on p a r a m e t e r for n icke l on ca rbon

\ ~ / N F e ..). 1 '

and

NNi , NFe = mole f r a c t i o n s of n icke l and i ron in the a l loy .

Resu l t s of d i f fe ren t i n v e s t i g a t o r s 28-3~ for the v a r i a - t ion of the ac t i v i t y coef f ic ien t of ca rbon in aus t en i t e with ca rbon concen t ra t ion in the F e - C b i n a r y s y s t e m a r e shown in Fig . 3. The c u r v e s at 700~ w e r e e x t r a p - o l a t ed f r o m the h igher t e m p e r a t u r e data . Since t h e r e is no b a s i s fo r s e l e c t i n g the r e s u l t s of a p a r t i c u l a r in-

va lue s of In y(FeC) f rom the v a r i o u s s t u d - ves t iga t ion , k ~

Y

_=

CARBON, wt % 0.1 0.2 0 5 0 4 0 5 0.6 0 7 0 8 0 9 I0 II 1.2

3.4" I I [ I I .~-IP) I e [ I ( I I --~ 3 6 ~ t 7 0 0 C

3 2 ~ } 8oo ~ -

3.c ~ : ' ~ J

" }900%

. ~ ~ ~':~

'0 0.01 0 0 2 003 0 0 4 0 0 5 C A R B O N M O L E F R A C T I O N

Fig . 3 - -The ac t iv i ty coeff ic ient of carbon in F e - C aus teni te as a function of carbon concen t ra t ion obtained f r o m the r e su l t s of d i f ferent i nves t iga to r s . 26-3~


ies were ave raged to obtain the dashed curves in Fig. 3 which can be r ep re sen t ed by the equation

In y{cFeC)=ln ( 1 ~ C ) + ( 1 1 . 9 2 - 6330~(T/\I-----Z~C/NC "~

5100 - 1.845 + T [6 ]

The r e su l t s of the different inves t igators a re in good ag reemen t ; for example, the exper imenta l ly de te rmined carbon act ivi t ies a re within =L10 and ~:2 pct of the va l - ues computed using Eq. [6] for carbon mole f rac t ions of 0.001 and 0.05, respec t ive ly , at 900~ By combining Eqs. [5] and [6], a genera l i zed mathemat ica l re la t ion can be obtained for the ca rbon-ac t iv i ty coefficient as a function of carbon concent ra t ion in i ron -n icke l - ca rbon al loys at var ious t e m p e r a t u r e s . The t empera tu re dependence of in terac t ion p a r a m e t e r e Ni, shown in Fig. 4, was obtained f rom a l e a s t - s q u a r e s analys is of the r e - sults of this work and the data in the l i t e ra ture and can be r ep resen ted by the re la t ion

7600 ~ N i = _ 2 . 2 + T [7 ]

Therefore, the carbon activity in the ternary Fe-Ni-C system becomes

N c 6330 N c

5100 - ( 2 . 2 - 7600 1.845 + T - T / NNi

[8] The carbon-activity values calculated using Eq. [8] are compared, in Fig. 5, with the experimental data generated in the present work and those available in the lit- erature 1~'2~ for the t e m pe ra t u r e range of 700 to 1060~

Using the notation of Lupis and Elliott , 32,33 the t e m - pe ra tu re dependence of E Ni can be wri t ten in t e r m s of f i r s t - o r d e r enthalpy Ni (TNi C, and entropy C , coeff icients

E Ni= 7/Ni ffNi R T R [ 9 ]

?7 Ni and a Ni a re independent of t empera tu re , a plot

of e Ni vs 1 /T should resu l t in a s t ra ight line. As shown in Fig. 4, this is the case within exper imenta l sca t te r of the r e su l t s of the va r ious invest igat ions. Therefore , the enthalpy and ent ropy interact ion p a r a m e t e r s for the effect of nickel on carbon in Fe -Ni -C al loys a re

7]C Ni = 15,100 c a l / m o l e (63,180 jou les /mole ) [10]

and

aNi = 4.35 eu (18.2 jou le s /mole -K) . [11]

Carbon Activity in I r o n - C h r o m i u m - N i c k e l Alloys

The carbon ac t iv i ty -concen t ra t ion re la t ionships for the Fe-8 wt pct Ni and Fe-16 wt pct Ni al loys and the carbon-so lubi l i ty values in nickel were used to es tab- l ish carbon act iv i t ies in F e - C r - 8 wt pct Ni al loys whose ch romium content ranged between 2 and 22 wt pct. The re la t ion between the ca rbon and ch romium concen t ra - t ions in these a l loys is shown in Figs. 6 and 7 by the t soact lv i ty l ines that were genera ted over a wide range

of carbon activities at temperatures between 725 and 1060~ It is evident from these figures that the carbon concentration increases with an increase in chromium content of the Fe-Cr-8 wt pct Ni alloy for a given carbon activity and temperature. Furthermore, an increase in the chromium content of the alloy results in precipitation of carbide phases, particularly at lower temperatures and high carbon activities.

The influence of chromium on the carbon activity in these quarternary alloys can be evaluated by applying the interaction-parameter concept to the experimental data at low carbon activities and low chromium concentrations. The carbon activity in the Fe-Cr-8 wt pct Ni- C alloy, a (C FeCrSNiC), can be expressed as

a ~FeCr8NiC)= y~FeCr8NiC)Nc = ~Fe8NiC)yCrNc '

[12] where

~FeCrSNiC) = Raoultian act ivi ty coeff icient for c a r - bon in the q u a r t e r n a r y alloy;

(c Fe8NiC) = Raoultian act ivi ty coeff icient for c a r - Y bon in the Fe-8 wt pct Ni-C al loy and given by Eq. [6];

C c r = Raoultian act ivi ty coeff icient fo r c a r - bon that r esu l t s f r o m chromium addition to the al loy;

and

N C = mole f rac t ion of carbon in t he alloy.

Therefore , f rom Eq. [12]

/ (FeCrSNiC)

I

where In ~C Cr is a function of the mole f rac t ion of ch ro - mium in the alloy.

T E M P E R A T U R E , ~ 1200 ~00 ~000 900 soo 700

9.0 I

8.0 m

m 7.0

6 . 0 B

5 . 0 - -

4"0 I

5.0

0.6

I I [ r I GREENBANK

0 BODSWORTH, el oi. 0 HECKLER 8~ WlNCHELL 0 SMITH o SCHENCK ond KAISER v WADA, el ol �9 PRESENT WORK

~*= -2 24 7600 T

0.7

T

I I o.8 0.9 I.o ~.l 103/T, OK "l

Fig. 4--Temperature dependence of the free-energy interaction parameter for nickel on carbon in Fe-Ni-C alloys.


1.0

0 . 9 -

0 . 8 -

>- 0.7- I - > m

t - O . 6 - (D <~

0 . 5 - z 0 rn 0.4-- fig < o

0 . 3 -

0 . 2

0.I

O f

0

~ t 0.9

O8 >- I-- 07 I

~ 0 6

O 5 z

m ~ 0 4 C12 ~ o3

0 2

0.1

0.1

C A R B O N , wt % 0.2 ~ 3 0 . 4 0 . 5 0 .6 O~ I I I I I I

/ / F e - 8 w t % N i

/ /

/ /

/ /

/

/ o /

/ /

/ /

/ /

/

u /

O 750~ GREENBANK

�9 700~ PRESENT WORK

----700~ Eq (8) /

I 0,01

CARBON

I I 0 .02 0 . 0 5

M O L E F R A C T I O N

(a)

OI 0.2 0 3 0 4 I I I I

Fe -8wt % Ni

/

�9 / d �9 /

CARBON, wt %

0.5 0.6 0.7 0.8 09 1.0 I I I I I I

/ - /

y / _

/ / _

/ 4 / 0 - -

/ A �9 /

z~ 925~ BODSWORTH et al

o 900~ GREENBANK I

�9 900~ PRESENT WORK!

- - - - 900~ Eq (8)

0 I i I I I I 0 0.01 0"02 0 03 0 04 0.05

CARBON MOLE F R A C T I O N

N- l--

t.-- L) <

z

0.I 0.2 0.3 0

t 0.8--

0 7 - -

0E--

0 5 - - /

o 4 - ~iVoo /

0 3 - ~ , / ~

02- ~,,@ o., y

v I I 0 001

CARBON

0 4

0.3 >.- I-- > I--

z 0.2 0 3 r,," <~ o

I I I

OI

Ol 02 I I

CARBON,wt % 04 05 0.6 07 0.8 09 Io

I I I I o I I i / a /

/ F e - 8 w t % Ni /

/ a / / a

? / , -

y,/~ o _ / #

/ / _

----800~ Eq (81

a 850~ BODSWORTH et at-

~ 825~ GREENBANK

o 800~ WADA et ol

v 800~ HECKLER BWlNCHE~L

�9 800~ PRESENT WORK

/

/ I I I 0.02 0 .03 0 0 4

MOLE FRACTION

(a)

CARBON, w t % 03 04 05 06 07

I I 1 I I

Fe - 8wt % Ni / - / /

/ / / o/o/

/

,ooo-c-~ y~Df' ,oso'c--~x,,/' y

//?/ / / / V IO00"C SMITH

J / 0 I000 ~ SCHENCK & KAISEI

J ,x 1050 ~ BODSWORTH et ol /aO~',Z~ ' o 1050 ~ GREENBANK -

,/7 �9 IOOO ~ // I I0600C.] PRESENT WORK

/ /~ l ~---- Eq (8 )

I I [ 0 010 0 020 o 030

CARBON MOLE FRACTION

Co) W)

Fig. 5--Carbon activity--concentration relationship in Fe-8 wt pct Ni alloy at 700, 800, 900, 1000, and 1050~

The carbon-ac t iv i ty coef f i c ient that r e s u l t s f r o m the addition of c h r o m i u m to the F e - N i - C al loy was eva lu- ated as a function of the c h r o m i u m m o l e fract ion of the a l loy f r o m the exper imenta l i soac t iv i ty l ines p r e s e n t e d in Figs . 6 and 7 at the var ious t e m p e r a t u r e s , and the r e s u l t s are g iven in Fig. 8. It should be noted that the va lues of in y ~ r at high c h r o m i u m concentrat ions do not r e p r e s e n t true act iv i ty coe f f i c i ents for carbon b e - cause of the fact that the al loy is c o m p o s e d of a two- phase mix ture of carbide and austeni te . However , at low c h r o m i u m concentrat ions (i .e. , 0 to 4 wt pct), the carbon-ac t iv i ty coef f i c ient in the s i n g l e - p h a s e austen-

METALLURGICAL TRANSACTIONS

i t ic a l loys can be re la ted to the c h r o m i u m mole f r a c - t ion by

aNcr [14]

where

E Cr = free-energy interaction parameter for chro-

mium on carbon, and NCr = mole fraction of chromium in the alloy.

VOLUME 4, N O V E M B E R 1 9 7 3 - 2 5 6 1

0 m r r

L~

!

�9 0 0 8 7

0 0 . 037

0 0 . 006

i0 ~

io -2

163 o 4

1 T 1 ~ I 725 ~

I I ,0 !

i0 ~

Io-' o (23 ne

io-3!

I T r I I I i a ~ 800 ~

�9 0 1 0

o 0 053

o 0 020 / ~ e -

o 0 018

o 0,6 . . . . , - / - - o o 0,2 . A d 7" z'! n 0 008

8 12 16 20 24 I I I ] ~ i ~ I I ] I CHROMIUM wt % 4 8 12 16 20 24

' CHROMIUM, wt %

(a) (b)

Fig. 6--Isoact ivi ty l ines for carbon in F e - C r - 8 wt pct Ni alloys at 725 and 800~

!

,o ' I ' 1 ' I ' I ' I I ~

age r 9 0 0 o c

�9 O. 196 o 0 .078 . I o ,, o.o6~ / Jo o o.ozr . ~ - / . ~

o o ~ " ~ 1 7 6 1 7 6

~ Id' "

%,111,I, [ IlL 4 8 12 16 2 0 2 4

CHROMIUM, wt %

(a)

Fig. 9 shows t i e interaction parameter ~Cr as a function of temperature obtained from the present work, which can be represented by the expression

00 10'

z" z" o o m m E E (.j r

16' !0 -2

10~" 0 4 8 12 16 20 2410-3

CHROMIUM, wt %

(b)

Fig. 7-- Isoact iv i ty l ines for carbon in F e - C r - 8 wt pot Ni a l - loys at 900, 1000, and 1060~

C Cr = 2 4 . 4 3 8 , 4 0 0 [ 1 5 ] T

As before, the temperature dependence of e Cr can be written in terms of f irst-order enthalpy ~?~r and en-


2 4 CHROMIUM,

8 12 15 wt %

18 22

8. L

Z

} co

u- t_~

Z

cO ,

t

%

CHROMIUM MOLE FRACTION

Fig. 8--The effect of chromium on the activity coefficient of carbon in F e - C r - 8 wt pct Ni-C alloys at var ious t empera tu re s .

TEMPERATURE, ~

I100 I000 900 850 800 750 ] I 1 I I I 1

.--J -15 -

-13 --

- I - -

(3(j klJ - , - -

- 5 - -

- 3 ..... O 7 0 8 3 - I O ' 9 I O

IO /T,~K

F i g . 9 - - T e m p e r a t u r e dependence o f the f r e e - e n e r g y i n t e r a c - t i o n pa rame te r for chromium on carbon in F e - C r - 8 wt pct Ni-C alloys with low chromium concentrat ions .

aCr t ropy C , coefficients whose values a re

~/Cr = _ 76,300 ca l /mole ( - 319,240 joules /mole)

and [16]

t7 Cr = - -48 .5 eu ( - -202 .9 j o u l e s / m o l e - K ) [17]

In addition to evaluating the thermodynamic in terac- tion p a r a m e t e r s for carbon f rom the exper imental data at low carbon activit ies and low chromium contents in the alloys, it is also desi rable to obtain an express ion that re la tes the carbon activit ies to the carbon and chromium concentrations over the entire range of

chromium contents (0 to 22 wt pet) and t empera tu res (725 to 1060~ investigated in this work. For this purpose, yCcr in Eq. [14] was expressed as

In yC Cr = ECrNcr ~-" ~c~Cr ~T2~'Cr ' [18]

and pCr was evaluated as a function of t empera tu re to r ep resen t the data in Fig. 9. It should be noted that p c Cr in Eq. [18] has no direct thermodynamic signifi- cance, since the alloy at the high chromium levels is composed of a two-phase (carbide + austenit~) mixture. The value of pc Cr evaluated at var ious t empera tu res is plotted in Fig. 10 and can be expressed by the relat ion

p C r = _ 9 6 . 8 + 84 ,800 [19] T

Therefore , the carbon activity in the quar te rnary F e - C r - N i - C sys tem in the composition range of 0 to 16 wt pct Ni and 0 to 22 wt pct Cr becomes

NC (11.92 6330 N c In a(cFeCrNiC) = ln ( I_---Z-~C ) + - ----~) (1---Z--~C )

- 1.845 + ~ - - ~ NNi

+ (24.4 38,400) N C r T

- (96 ,4 , ,00) I 01 T

The carbon-act iv i ty values calculated using Eq. [20] are compared, in Fig. 11, with the exper imenta l data generated in the presen t work (Figs. 6 and 7) at t e m - pe ra tu res of 725, 800, 900, and 1000~ It is evident froth these f igures that there is good agreement between the carbort-act ivi ty values calculated f rom Eq. [20] and the exper imenta l data points.

For compar ison of these resul ts with data in the l i t- e ra ture , it is useful to re la te the carbon' activity to the alloy composition in weight percent unit's given by Eq. [21].

TEMPERATURE, ~

I IOO IOOO 900 850 800 750 1 I ] [ I I

-35 - -

- 3 0 - -

-25 --

~cL(~_ 20 _

-15 --

Cr = - 9 6 8 + 8 4 8 0 0 / T

-10 - -

-~7 J I , I I I 08 103/T, OK_109 I 0

Fig. 10- -Tempera ture dependence of the s econd -o rde r coeff i - cient in Eq. [18] that is used to desc r ibe the effect of ch ro - mium on the carbon-act iv i ty coefficient in F e - C r - 8 wt pet Ni-C alloys with chromium contents up to 22 wt pet.


CARBON, wt % O.01 O I I O

' ' ' ''"I l , , , l,,,] , l , l,,~,]

I __ 7 2 5 ~ I I wt % C r

o o / / / /

>- ~ ,8 / / / / F ~ z2 o//~ / /

- - = - - Eq ( 2 0 ) / / /~" IF / "~ / ~ / / / o / / / < / / /

/ / / / / /

~,6 ~ / / / / / / ~ / / / / / . F~/~ _. / . / � 9 ,.

~ 7 / 7 / , / 4 / / l � 9 / I l l

i 0 - ~ / I I I I I l l l l - - I t I I l l l l 1 I I I1 16 4 tO -~ 16 2


(~)

CARBON, wt % 001 0.I I0

l I I I I I r ] I I I I I I I I ] I I I , I t l t l J

16'

IO"

F-

0 <~

Z

IO -2

(D

~d a id 4

900 ~ wt % Cr

- - O O A 2

- �9 15 - �9 18 - i 22 _ Eq (2o)

I i / / / / .

A / / ~,/ / i / i i / i

A,'/ //C

/ / / / / / . / o{/ ~," ./ , , I / .

/ / / / / / / / / / / /

/ ~ / ' / / ~-- o~ / o / . / - - / / / /

- / / / / / / - / ~ / / ~ / " / ' / / . / _~

id a tO 2 iO' CARBON MOLE FRACTION

Id' >- I-- > I --

,,~

Z o ~= io-2 L)

io- a id 4

CARBON, wt % O,Ol o I I o

�9 I I I l l l I t I I I l t t t I t I I ~1~,, I t

_ 8 O O O 0 1 I

wt %Ct : o / / / / /

. ,o / / / / ; - , ,, / / . / ~ ' . Z /

�9 2}. / / / / / / - - ~q~2o) / . . / - - / / / _ /

o ~ / 0 / ./ / y ~ _ z r ~ ; { / / / -

U ~ / # / ' / // / / / / / / /

iff a Id 2 a6' CARBON MOLE FRACTION

(b)

b-

I - (.)

Z 0

,o "2

,j

CARBON, wt % 0.01 O I I 0

l r i i i t l I i I I i i l l l I I i I i l i l t I

10OO =C

o A

i 0 - j - - o - �9

10"3164

I I wt % Cr

i / / / / / . / / / / , / / _ ,2 / / / . / / . / / / ,s ,o .~/ ~ o / ~r �9 ,,e

/

- - - E0, o, /

/ / / / / / /

I l l , l l t l i i L IIKlll ~ i i l l Id 3 Id z Id'


(c) (d) Fig. l l - - T h e carbon act ivi ty-concentrat ion relat ionship in F e - C r - 8 wt pct Ni-C alloys at 725, 800, 900, and 1000~ The dashed lines in this f igure were calculated using Eq. [20].

In a(cFeCrNiC) = In (0 .048 pct C) + (0 .525 - --~/300 ~ pct C

+ (0.248 - 404 ~ / pct Cr

- (0.0102 9.422) pct Cr 2. [21] T

Carbon-activity data obtained by a number of investi- gators 29'3~ for Fe -Cr -C alloys with chromium contents between 3.35 and 5.00 wt pct at 1000 to 1050~ are replotted in Fig. 12 after converting their carbon activities to a common Fe-C baseline (Le., the f irst four te rms in Eqs. [20] and [21]) that was used in this work.

The carbon activity-concentration relationships calculated using Eq. [20] for an Fe-4 wt pct Cr alloy at 1000 and 1050~ indicated by the dashed lines in this figure, are in good agreement with the results of Bodsworth et al . , a~ Brigham and Kirkaldy, a4 Wada et al. , a7 and Greenbank. 3a

Greenbank 3~ equilibrated a number of Fe-Cr-Ni alloys with iron in methane-hydrogen gas mixtures at temperatures between 900 and 1050~ The chromium and nickel content of the alloys and the carbon concentrations after equilibration are given in Tables II and III as well as the carbon content of the iron that was included in each run. The carbon activities obtained from the carbon concentrations in iron and the Fe -Cr - Ni alloys using Eq. [21] are in excellent agreement for


Table II. Comparison of Carbon Activities from Eq. [21] Based Upon the Carbon Concentrations in Iron and Fe-Cr-Ni Alloys of Different Composition

Equilibrated at 900~ from the Work of Greenbank 39

Composition of Equilibrated Fe-Cr-Ni-C Alloys

Pct Cr PctNi Pct C

Carbon Acuvity Carbon Concentration

in Iron, Pet C a Fe a (FeCrNi)

4.10 0.60 0.200 0.138 0.084 0.082 3.12 1.62 0.177 0.138 0.084 0.084 2.22 2.54 0.158 0.138 0.084 0.086 1.41 3.61 0.135 0.138 0.084 0.083 0.53 4.52 0.117 0.138 0.084 0.081 4.10 0.60 0.607 0.422 0.277 0.279 3.12 1.62 0.543 0.422 0.277 0.285 2.22 2.54 0.483 0.422 0.277 0.286 1.41 3.61 0.431 0.422 0.277 0.286 0.53 4.52 0.382 0.422 0.277 0.283 4.10 0.60 2.24 1.070 0.837 1.60 3.12 1.62 1.745 1.070 0.837 1.27 2.22 2.54 1.345 1.070 0.837 1.14 1.41 3.61 1.097 1.070 0.837 0.870 0.53 4.52 0.979 1.070 0.837 0.852 8.52 1.04 0.105 0.038 0.023 0.025 6.04 3.09 0.070 0.038 0.023 0.025 4.67 4.88 0.052 0.038 0.023 0.023 2.70 7.03 0.038 0.038 0.023 0.023 1.00 8.61 0.024 0.038 0.023 0.018 8.52 1.04 0.364 0.122 0.074 0.092 6.04 3.09 0.213 0.122 0.074 0.077 4.67 4.88 0.173 0.122 0.074 0.079 2.70 7.03 0.127 0.122 0.074 0.078 1.00 8.61 0.098 0.122 0.074 0.076 8.52 1.04 1.090 0.420 0.276 0.336 6.04 3.09 0.680 0.420 0.276 0.280 4.67 4.88 0.549 0.420 0.276 0.277 2.70 7.03 0.427 0.420 0.276 0.284 1.00 8.61 0.342 0.420 0.276 0.283

0 02

i 035-- %Cr T *C

V 4 I0 IOO0 0 4 O0 I000 0 5 o0 Iooo o 385 I000

0 3 0 - - 0 400 iooo zx 3 35 1050 o 4 35 1050

- - - - 4 0 0

025 --

>-

> ozo L.)

Z 0

015 <~ r

0 I0

0O5

CARBON, wt % 0 4 06 08 I0

I I I I

SCHENCK 81 KAISER BRIGHAM 8L KIRKALDY FLENDER S WEVER BUNGARDT et al WADA et al / - - BOOSWORTH et al / / GREENBANK "/ A/ V Eq (201 / / /

/ ~ /

i 1 ~ I o

- - i / / I o - - I

iooo * c - . . . ~ / ~ . j ~ l o 5 o *c

- J / o - / / v

_ / / o

/o, 'o //r o / /

i

/ I I I I 001 002 O05 0 0 4

CARBON MOLE FRACTION 005

F i g . 1 2 - - C o m p a r i s o n o f c a r b o n - a c t i v i t y r e s u l t s f r o m th i s w o r k w i t h data in the l i t e r a t u r e 2g,a~ f o r F e - C r a l l o y s w i t h 3 . 3 5 t o 5 . 0 w t p c t C r at 1000 and 1 0 5 0 ~

Table III. Comparison of Carbon Activities from Eq. [21] Based Upon the Carbon Concentrations in Iron and Fe-Cr-Ni Alloys of Different

Composition Equilibrated at 1050~ from the Work of Greenbank ~

CompositionofEquflibrated Fe-Cr-Ni-CAlloys

Pct Cr PctNi Pct C

Carbon Activity Carbon Concentration

Fe ac(FeCrNi) in Iron, Pct C a C

4.10 0.60 0.116 0.082 0.030 0.033 3.12 1.62 0.103 0.082 0.030 0.033 2.22 2.54 0.091 0.082 0.030 0.032 1.41 3.61 0.080 0.082 0.030 0.030 0.53 4.52 0.071 0.082 0.030 0.029 4.10 0.60 0.308 0.230 0.088 0.092 3.12 1.62 0.278 0.230 0.088 0.093 2.22 2.54 0.260 0.230 0.088 0.095 1.41 3.61 0.229 0.230 0.088 0.091 0.53 4.52 0.211 0.230 0.088 0.091 4.10 0.60 0.602 0.460 0.189 0.198 3.12 1.62 0.546 0.460 0.189 0.197 2.22 2.54 0.493 0.460 0.189 0.193 1.41 3.61 0.450 0.460 0.189 0.191 0.53 4.52 0.411 0.460 0.189 0.188 4.10 0.60 1.380 1.092 0.542 0.571 3.12 1.62 1.275 1.092 0.542 0.572 2.22 2.54 1.195 1.092 0.542 0.577 1.41 3.61 1.098 1.092 0.542 0.565 0.53 4.52 1.020 1.092 0.542 0.559 8.52 1.04 0.122 0.066 0.024 0.023 6.04 3.09 0.109 0.066 0.024 0.028 4.67 4.88 0.086 0.066 0.024 0.027 2.70 7.03 0.061 0.066 0.024 0.024 1.00 8.61 0.050 0.066 0.024 0.023 8.52 1.04 0.450 0.223 0.085 0.094 6.04 3.09 0.346 0.223 0.085 0.096 4.67 4.88 0.290 0.223 0.085 0.096 2.70 7.03 0.230 0.223 0.085 0.094 1.00 8.61 0.191 0.223 0.085 0.091 8.52 1.04 0.790 0.419 0.170 0.182 6.04 3.09 0.606 0.419 0.170 0.182 4.67 4.88 0.511 0.419 0.170 0.179 2.70 7.03 0.415 0.419 0.170 0.178 1.00 8.61 0.347 0.419 0.170 0.173 8.52 1.04 1.150 0.509 0.212 0.295 6.04 3.09 0.725 0.509 0.212 0.226 4.67 4.88 0.625 0.509 0.212 0.227 2.70 7.03 0.510 0.509 0.212 0.225 1.00 8.61 0.420 0.509 0.212 0.214

14.65 15.53 0.130 0.062 0.023 0.019 14.65 15.53 0.375 0.109 0.040 0.056 14.65 15.33 0.400 0.131 0.049 0.060 14.65 15.33 0.960 0.203 0.077 0.172

carbon concentrat ions in the a l loys be low ~ 1.0 wt pet. These r e s u l t s further indicate that the interact ion e f - fec t of c h r o m i u m and n icke l on the carbon act iv i ty in F e - C r - N i a l loys and i ts var iat ion with t e m p e r a t u r e have been adequately e x p r e s s e d by Eqs. [20] and [21] for c h r o m i u m and n icke l concentrat ions in the range of 0 to 22 and 0 to 16 wt pet, r e s p e c t i v e l y .

ACKNOWLEDGMENTS

The Jones and Laughlin Steel Corporat ion and the A r m c o Steel Corporat ion supplied s o m e of the a l loys used in this work. The Mater ia l s Sc ience Div i s ion Fabr icat ion Technology Group cas t s o m e of the a l loys and produced the foi l s p e c i m e n s . D. L. Rink a s s i s t e d with the e x p e r i m e n t a l program. This work was p e r - f o r m e d under the ausp ices of the U. S. Atomic Energy C o m m i s s i o n .

M E T A L L U R G I C A L T R A N S A C T I O N S V O L U M E 4, N O V E M B E R 1 9 7 3 - 2 5 6 5

REFERENCES

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3. R. Nakagawa and Y. Otoguro: Tetsu-To-Hagane, 1961, vol. 47, p. 1169. 4. Y. Kawabe, R. Nakagawa, and T. Mukoyama: Trans. Iron SteelInst. Jap.,

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10. J. T. Barnby and F. M. Peace: ActaMet., 1971, vol. 19, p. 1351. 11. R. Stickler and A. Vinckier: Trans. ASM, 1961, vol. 54, p. 362. 12. H. F. Ebling and M. A. Scheil: Advances in the Technology o/Stainless Steels

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242, p. 2129. 22. H. Schenck, M. G. Frohberg, and E. Jaspert: Arch. Eisenh~ttenw., 1965, vol.

36, p. 683. 23. J. J. lander, H. E. Kern, and A. L. Beach: s Appl. Phys., 1952, vol. 23, p. 1305. 24. K. K. Rao and M. E. Nicholson: Trans. TMS-AIME, 1963, vol. 227, p. 1029. 25. C. B. Alcock and G. P. Stavropoulos: Trans. Inst. Mining Met., Section C,

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242, p. 1135. 31. A. J. Heckler and P. G. WincheU: Trans. TMS-AIME, 1963, vol. 227, p. 732. 32. C. H. P. Lupis and J. F. EUiott: Trans. TMS-AIME, 1965, vol. 233, p. 820. 33. C. H. P. Lupis and J. F. EUiott: ActaMet., 1966, vol. 14, p. 529. 34. R. J. Brigham and J. S. Kirkaldy: Trans. TMS-AIME, 1963, vol. 227, p. 538. 35. H. Flender and H. Wever: Arch. Eise~mttenw., 1963, vol. 34, p. 727. 36. IC Bungardt, H. Preisendanz, and G. Lehnert: Arch. Eisenhfatenw., 1964, vol.

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2 5 6 6 - V O L U M E 4, NOVEMBER 1973 M E T A L L U R G I C A L TRANSACTIONS

thermodynamics of carbon in nickel, iron-nickel and iron-chromium-nickel alloys

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