Thermodynamics of the Fe-Cr-C System at 985 K H. WADA Carbon solubility and the composition of carbides in the Fe-Cr-C system up to 8.07 pct Cr were measured at 985 K by CH4/H2 gas equilibration. An iron-carbon binary alloy was included in the equilibration as a reference material. The chromium-carbon interaction in c~-phase was analyzed by the central atoms model. The Wagner interaction coefficient was determined as e c~ = - 7 2 -+ 2, a significantly higher negative value than in austenitic alloy. The activity coefficient of carbon in a-Fe was determined as log qS~ = 3.617, which supports the values reported by Swartz and by Chipman. The carbide phase was analyzed as a regular solution of two component carbides, FeC~ and CrC,. M7C3 carbide was present in the carbon activity range up to ac = 0.8, while M3C carbide was present at higher carbon activities. Partitioning of chromium between a and the carbide phases was measured. The standard Gibbs energies of formation of the two component carbides and the interaction energy parameters were determined for both M y C 3 and M3C carbides.
I.
INTRODUCTION
THE stability of carbides in ferritic steels is an important fundamental feature of the steel. For instance, hydrogen attack is known to be caused by a reaction between hydrogen and carbon in steel to form methane. Hydrogen can also decarburize steel. Hydrogen attack can be prevented by selecting alloying elements such as chromium and molybdenum so that carbides possess adequate stability. Thermodynamic evaluation of carbide activity with relation to the concentrations of alloying elements in ferrite and carbide phases are useful for a quantitative analysis of hydrogen attack. Thermodynamic properties of the Fe-Cr-C system in the ferritic temperature range have not been established, because of experimental difficulties due to the low carbon content of ferrite and long equilibration time necessary to reach equilibrium. Kuo ~ measured the equilibrium between a and M3C carbide while Jellinghaus and Keller 2 measured the equilibrium, mainly with M23C6 and M7C3 carbides. Carbon contents and Cr partitioning between a and carbide phases were measured in these works. Small and Ryba 3 analyzed these experimental results by an analytical method developed by Darken, under the following assumptions: (a) the activity of Cr in the a-Fe-Cr binary alloy can be expressed as a regular solution, (b) the carbide phase is an ideal solution of the component carbides, FeCx and CrC~. They evaluated the carbon activity and computed the standard Gibbs energies of formation of Cr3C2, CrvC3, and Cr23C6. Sharma et al. 4 measured Cr partitioning between a and y, a and M3C, and 3' and M3C in the vicinity of the eutectoid temperature. They analyzed their data by a modified regular solution model developed by Hillert and Staffansson. 5 Waldenstr6m and Uhrenius 6 and Lundberg et al. 7 computed the phase diagram of the Fe-Cr-C system based on the Hillert-Staffansson model with thermodynamic parameters derived from available information for the system. They proposed isothermal sections of the Fe-Cr-C system in the temperature range of 873 to 1373 K. Because iron and iron alloys transform from paramagnetic to ferromagnetic near their Curie temperature, H. WADA is Associate Research Scientist, Department of Materials and Metallurgical Engineering, University of Michigan, Ann Arbor, MI 48 [09. Manuscript submitted November 5, 1984. METALLURGICAL TRANSACTIONS A
it may not be appropriate to extrapolate thermodynamic properties of the paramagnetic form linearly to the ferromagnetic form. For this reason experimental studies below the Curie temperature are needed. The effect of ferromagnetism on the thermodynamic properties of iron alloys is largely unknown. In this study, the equilibrium carbon solubility and Cr partitioning were measured for known carbon activity at 985 K, and thermodynamic parameters were evaluated for the a-Fe-Cr-C system. The activity of carbon was determined from the CH4/H2 gas ratio as well as from the carbon content in a-Fe which was included in the equilibration. II.
EXPERIMENTAL PROCEDURE
A. Materials
Six Fe-Cr alloys were perpared in the composition range from 0.2 to 8 wt pct Cr. The alloys were melted in an induction furnace in fused alumina crucibles under an argon3 pct H2 gas flow. Starting materials were Ferrovac E iron and a metallic Cr powder having the purities shown in Table I. The melted alloys were siphoned into 9 mm ID quartz tubes, then quenched in water. The rods were cold rolled into 0.5 mm foils and cut into 100 mm long specimens. The pure iron specimens used as a reference material were cold rolled from Ferrovac E iron. B. Equilibration with CH4/H: Gas Mixtures
The experimental procedure is outlined schematically in Figure 1. Alloy specimens were equilibrated with the CH4/H2 gas mixtures at 985 K. Two each of the six Fe-Cr alloys (wt pct Cr: 0.2, 0.73, 1.32, 2.09, 4.93, and 8.07) and Table I.
Material Ferrovac E iron
Chromium
Purity of Metallic Materials
Purity, Wt Pct 99.97 0.00015 N2 0.0012 02 99.9 0.003 N2 0.08 02
Source Crucible Steel
Ventron Co.
VOLUME 16A. AUGUST 1985-- 1479
Fe and Fe-Cr Alloys Equilibration with fixed ratio CH4/H 2 gas mixture at 985K
Fe-C
Fe-Cr-C
Determination of a C from
(wt% C)tota I by LECO CS-244
CH4/H 2 gas ratio and (wt% C)F e by LECO CS-244
Microstructure examination for carbide precipitation by SEM
I
[
f
No carbide precipitation I
[ (wt% Cr)~ by EPMA
Carbide precipitation
]
Carbide
I extraction
from matrix
I
[
t atrix]
I
I (Wt% Cr)a by EPMA Zand AAS
--
"1
(Cr/Fe)carbid e by EDX of extraction carbon replica
F
i
Carbide identification[ by X-ray diffraction l
l
Fig. 1--Outline of experimental procedure.
one or two Fe specimens were placed in a mullite boat. The specimens were separated by 1 mm diameter alumina rods studded on the boat. Figure 2 shows the equilibrium apparatus. After the boat was located at the end of the reaction tube, the tube was purged with argon gas. The boat was pushed into the hot zone of the furnace under the argon gas flow by an alumina rod attached to the boat by a Me wire. The specimens were held at approximately 1120 K in hydrogen for 2 to 3 hours before a fixed ratio CH4/H2 gas mixture was introduced, and the temperature was adjusted to the equilibration temperature. At the end of equilibration, the boat was withdrawn to the end of the reaction tube and quenched with helium gas. The three-zone horizontal resistance furnace used has a 13 cm constant temperature zone 1480 VOLUME16A, AUGUST 1985
(-+0.5 K) controlled to +-1.0 K with a solid-state temperature controller. The temperature was measured with a Pt/Pt- 10 pct Rh thermocouple calibrated against the melting points of gold and silver. Three high-purity CH4/H2 mixtures were used, containing 8.5, 10.51, and 20.03 pct CH4. Desired CH4/H2 ratios were obtained by mixing pure H2 with one of these three mixed gases under controlled flow rates, using constantpressure-head flowmeters. The flow rates were calibrated for the CH4/H2 mixed gases and for H2 by a soap bubble method at room temperature. The H2 was purified through three columns containing heated platinized asbestors, Mg(C104)~ and P~O~. The CH4/H2 mixed gas was purified by an ascarite column in addition to these three columns. METALLURGICAL TRANSACTIONS A
R
A
l
t I
H
R
B
M
IF
S
"-0
A: Mullite reaction tube B: Boat C: Alumina tube H: Helium gas inlet [: Gas inlet O: Gas outlet M: Molybdenum wire R: Radiation shields (Alumina) S: Skids (Alumina) T, Pt-Pt.tO% Rh lhermocouple Fig. 2--Reaction tube arrangement.
The total flow rate of the gases was maintained between 110 to 240 cc per minute, depending on the carbon activity and the original CH4/H2 mixed composition. The activity of carbon was determined according to the following reaction: C + 2H2(g) -- CH4(g)
K1 = P c n J [ P . ~ " ac]
[1]
where ac is the activity of carbon referred to graphite as the standard state. The equilibrium constant K~ was obtained as a function of temperature in previous studies. 8'9"t° The total carbon content of each specimen was analyzed by the LECO CS-244 C/S analyzer. Each specimen was cut into small pieces before analysis; two to four analyses were performed for each alloy. Contamination of specimen surfaces was carefully avoided, because the accuracy of carbon analysis of low-carbon specimens is limited by contamination rather than by the capability of the analytical instrument. The carbon analysis was based on calibration curves prepared from standard samples. A standard sample having a carbon content close to that of the specimen was determined after every three specimen analyses. C. Analytical Metallography
Microstructures of specimens were examined for carbide precipitation by a SEM (Hitachi S-520). The chromium content in the c~-matrix was measured by an EPMA (ARL EMX-SM) and by an atomic absorption spectrometer. Specimens containing considerable amounts of carbides were usually analyzed by the latter method. For the EPMA analysis, a calibration line was prepared for each measurement with several standard Fe-Cr alloys as: wt pct Cr/wt pct Fe = kc~ve[(l - Io)c,/(I - I0)F,]
[2]
where (1 - 10)c, and (I - 10)Feare measured intensities of Cr K~ and Fe Kc~ lines, and k is a constant determined from METALLURGICALTRANSACTIONSA
standard analyses. Several Fe-Cr standard alloys were prepared from pure Fe and Cr metals. Three to four standard alloys, whose compositions covered the anticipated range of the Cr content in the c~-matrix, were chosen as standards for each EPMA analysis. The correlation factor for the standard analysis was generally higher than 0.99. The measurement was repeated 7 to 8 times on each specimen, and the standards analyses were repeated during the specimen analyses. Chromium and iron ratios in the precipitated carbides were determined with an energy-dispersive X-ray spectrometer (EDX) in SEM. Two Fe-Cr alloys, 9.07 and 11.70 wt pct Cr and pure Cr, were used as standards. Selected specimens were analyzed by a TEM (JEOL TEM100 CX) with extraction carbon replicas using beryllium grids. Pure Cr and Fe deposited by vaporization on thin graphite foils supported by beryllium grids were used as standards. The Cr/Fe ratios were calculated by Eq. [2] with kc,Fe = 0.90 at 100 KeV. D. Carbide Extraction
Specimens containing precipitated carbides were decomposed by H3PO4 (2:1) solution at room temperature. ~ A known amount of finely cut and ultrasonically cleaned specimen was decomposed in argon.~2 During the decomposition, ultrasonic vibration was applied in 1 rain./ 30 min. cycles and temperature was monitored. Decomposed specimens were filtered through 0.2/~m millipore filters. Chromium and iron contents in the filtered solutions were determined by an atomic absorption spectrometer and by the 1,10 phenanthroline method, respectively. To minimize the interference from iron, ~3 a nitrous oxide-acetylene flame and a single Cr lamp were used for the atomic absorption analysis at a wave length of 357.9 A. Standard solutions were prepared from Fe and Cr stock solutions to have approximately the same Cr/Fe ratios and the same phosphoric acid concentrations as the sample solutions. The extracted carbides were analyzed by X-ray diffraction. VOLUME16A.AUGUST1985--1481
III. EXPERIMENTAL RESULTS AND DISCUSSIONS A. Equilibrium Carbon Contents
The total carbon contents in Fe-Cr-C alloys are summarized in Table II. The units of the carbon contents are wt pct. Since the Fe-Cr-C alloy contains both interstitial (C) and substitutional (Cr) alloying elements, lattice concentration units are used for analyzing the results. The units are defined as follows: Yc ~ N c / N , = Xc/3(1 - Xc) Yc : m c / N v = Xc/(3 - 4Xc)
[3]
Eq. [3] is introduced because the number of interstitial sites is three times the number of substitutional sites in the bcc lattice. The total carbon contents in the equilibrated specimens are plotted against chromium contents in Figures 3 and 4. Figure 3 shows the relation in the range where carbides are presented, while Figure 4 shows the relation in the range where no carbides existed, only a phase being present. The chromium contents of a-phase, (Y~), are shown by arrows in Figure 4. The carbon content in a-phase, (y~), in equilibrium with carbides, was estimated in Figure 4 at the lowest (Y~0 for each carbon activity level. These equilibrium carbon contents are listed in Table III.
and Ear : NcffNs = Xcff(1 - Xc) Yr~ = NF~/Ns = XFe/(1 - Xc)
[41
where N o No, and NFe: number of C, Cr, and Fe atoms; Nl, Ns, and Nv: number of interstitial sites, substitutional sites, and vacancies on interstitial sites; X o Xc~, and Xve: atom fractions of C, Cr, and Fe, respectively. The factor 3 in
Table II. Activity of Carbon ac 0.11
Equil. Time Hours 169.3
0.22
725.0
0.49
503.0
0.80
552.5
0.90
1.08
B. a-Fe-C
Figure 5 shows the relationship between the carbon content and ac in a-Fe. The logarithm of Yc at 985 K is expressed by a straight line as:
[5]
log Yc = log ac - 3.617
Experimental Results of Equilibration at 985 K Total Carbon Contents, Wt Pct C x 102
Wt Pct Cr
0.0
0.20
0.73
1.32
0.170 0.172 0.180 0,300 0.337 0,372
0.196 0.190
0.220 0.240
0.335 0.337
0,390 0.390
0.570 0.600 0.596
2.35 2.82 2.79
0.890 0.920
1.28
1.45 1.50
3.17 3.95 4.20
574.0
0.760 0.690 0.870 1.15 1.24 1.38 1.40
504.0
1.66
2.20 2.20
Table III.
41.4 42.8 47.4
2.09
10.6 11.8 11.7 11.9 19.5 19.8 20.5 35.6 35.8
15.9 16.8 17.6
I10.0 111.0 102.9 103.3 135.0 135.0
102.0 105.0
4.93
8.07
29.2 33.2
117.0 118.0 119.0
65.4 66.0 69.2 87.2 87.1 85.3 167.0 165.9
170.6 178.4 191.2
160.0 160.0
Experimental Results of Ferrite Phase Analysis
Yc × 104 (Average) ac
YCr × 10z
0.0
0.11 0.265 0.22 0.522 0.49 1.18 0.80 1.92 0,90 2.17 1.08 2.57 * Estimated according to Ycr. ** The lowest Yc~among shown in Figure 4 with arrows.
1482--VOLUME 16A, AUGUST 1985
0.215
0.784
0.30 0.60 1.37 2.25
0.40 0.90 2.0
y~ X 104*
Y~; x 102.*
1.21 2.04 3.03
1.21 0.79 0.61 0.56 0.20
3.02
METALLURGICAL TRANSACTIONS A
10.O
I
1
I
I
I
1
I
]
]
I
I
l
~
90 80
7.0 60
I
I
]
I
I
15
1.6
17
0c:0.49
°~ 5.0 40
30
20
10 I
°o
o.L 0.2 0.3 o 4
05
0.6 0 7
08
09
~.0
1.1
12
I 3
1.4
wt%C Fig. 3 - - T o t a l carbon contents in Fe-Cr-C alloys at 985 K.
,
i
!
aC=I.08 t~ Clc=0.80
The activity coefficient of carbon is defined as: log qSc = log ac - log Yc = log qS~ + log ~bCc [6] where qSc c is a function of Yc. From Eqs. [5] and [6],
3.6
c=o.9o
7~
log 4~ = 3.617 and log Oc = 0
ac=049
3.~ J~ " ~ ' ~ Y ~ /
~
ac=0.22
4.0 4
O I
4.2 CIc=O 11
e
4.z
•
461
0
The equilibrium constant and the solubility of carbon in c~-Fe have been reported by several investigators. Diinwald and Wagner ~4 measured the carbon content in equilibrium with CO/CO2. Smith 8 studied extensively the equilibrium with CH4/H2 and CO/CO2 mixtures. Swartz 9 also investigated the equilibrium with CH4/H2 as well as CO/CO2 mixtures. McLellan and Dunn 15JrJ7 determined carbon solubility in a-Fe and also analyzed previous work including that by Schiirmann et al. ~8 Chipman]9 proposed equations for the activity of carbon and the solubility of graphite in c~-Fe based on a comprehensive review of the Fe-C system. Lobo and Geiger t° recently measured carbon solubility in ~-Fe with CH4/H2 mixtures, employing a Cahn RG Electrobalance. Swartz9 reported the activity of carbon as log ac(0.001 wt pct C) = 24,000/RT - 12.72 [8] Chipman t9 expressed the activity coefficient of carbon, tO~, as log qJ~ = log ac - log Xc/[1 - Xc] = 5 , 5 5 0 / T - 2.49
'
_L 05
i
Ycr x 102
, 10
,
I 1.5
Fig. 4 - - Solubility of carbon in a-phase of Fe-Cr-C alloys at 985 K.
METALLURGICAL TRANSACTIONS A
[7]
[9]
The values of log ~b~ = 3.612 and 3.622 are obtained at 985 K from Eqs. [8] and [9], respectively. The present result, 3.617 in Eq. [7], is in good agreement with these
VOLUME t6A, AUGUST 1985-- 1483
I
I
I
I
The carbon activity in a-phase can be expressed with the central atoms model as:
2.5
In ac = In Yc + ln(37~) + 2z In Acc + 2Z In Acrc [10]
Fe-C
2.0
/
//
A c c = Yc" hcc Ac~c = 1/[1 - YCr" ")~2rC]
[11]
where Acc and Ac~c are parameters representing interactions between C-C and Cr-C atoms, respectively. These values are related to the Wagner interaction coefficients as: 21
// 1.5
O
where 7~ is Henry's law constant, Acc and A¢~c are the Lagrange parameters, and Z and z are the numbers of substitutional and interstitial nearest neighbors to interstitial sites: Z = 2 and z = 4 for ferrite. In a dilute solution, Acc and Ac~c can be simplified as:
ecc = (0 In Cbc/OXc)xc~o = 4(1 + 2Acc)/3
X
e cr = (0 In Cbc/OXcr)xc~o = 4Ac~c h
[12]
The activities of carbon are equal in equilibrated Fe-C and Fe-Cr-C alloys,
I
ac(Fe-C) = ac(Fe-er-C)
[13]
Combining Eqs. [10], [11], and [13], the carbon solubilities in these two systems are expressed as:
1.0
// /
0.5
{yc(Fe-Cr-C)/yc(Fe-C)} v4 x e {2[yc(ve-cr-cl-ycIFe'c)]xcc} -
/
= -Ycr" Aoc
•
...... ~--:
,
:
0
1 [14]
Since the activity coefficient of carbon in a - F e is independent of the carbon content, Acc becomes practically zero in a-Fe, so Eq. [14] is further simplified as
Chipman
exp{2[yc(Fe-Cr-C) - yc(Fe-C)]Acc} = 1.
: Swartz Lobo and G e i g e r
----o---: P r e s e n t work
0 i
-
I
I
I
I
0.25
0.50
0.75
1.0
tic Fig. 5--Solubility of carbon in e-Fe at 985 K.
values. The values obtained from the measurements of Lobo and Geiger ]° and Dunn and McLellan ]7 are significantly higher than the present result. The graphite solubility estimated from their activity coefficients are Yc = 0.00019 and 0.00020, respectively. These values are much lower compared with 0.00024, 0.00025, and 0.00024 calculated by Eqs. [7],[8], and [9], respectively.
From the averaged values of yc(Fe-C) according to Eq. [5], and the measured values ofyc(Fe-Cr-C) including estimated values at phase boundary, y~, the value of Ac~c is computed as: hc~c = - 1 8 . 1 -+ 0.3
[15]
Figure 6 shows the relationship of Eq. [14]. The Wagner interaction coefficient is calculated as: E CCr =
- 7 2 _+ 2
[16]
The solubility of carbon in the a-phase of Fe-Cr-C alloys was expressed as: log Yc = log ac - 3.617 + 31.35Ycr
[17]
The Wagner interaction coefficient is ecc = 4/3 from Eq. [ 12]. The effect of interaction coefficient on the carbon content at the highest carbon solubility in this study, yc = 3 x 10 -4 at ac = 1.08, is approximately 3.6 x 10 -7, which is much smaller than the experimental accuracy.
C. Ferrite Phase in Fe-Cr-C Alloys Since a-phase of the Fe-Cr-C alloys in this study is a dilute solution of both C and Cr, the central atoms model, generalized by Foo and Lupis, z° Lupis, 21 and Enomoto 22 is suitable for analyzing the results.
1484--VOLUME 16A, AUGUST 1985
D. Ferrite + Carbide Region in Fe-Cr-C Alloys The results of carbide phase analyses are summarized in Table IV. Figures 7(a) and (b) show the SEM microstructures of the 1.32 pct Cr alloys equilibrated at ac =
METALLURGICAL TRANSACTIONS A
!
!
I
O
o X
'-" 1.5
o/
I
I
"-
1 (a)
? Y. t-.,,a
0.5
/
0 ¥
i
o
I
i
I
0.5
I
1.0
Ye,
x
1.5
10 2
Fig. 6--Effect of chromiumon activity of carbon in a-phase of Fe-Cr-C alloys at 985 K.
0.22 and 1.08, respectively. Carbides are precipitated only on grain b o u n d a r i e s in the s p e c i m e n e q u i l i b r a t e d at ac = 0.22, while carbides are precipitated both on grain boundaries and inside of grains in the specimen equilibrated at ac = 1.08. The carbides were identified as M7C 3 for ac = 0.22 and M3C for ac = 1.08 by X-ray diffraction.
(b) Fig. 7 - - Microstructuresof Fe-1.32 wt pct Cr alloy equilibratedat 985 K: (a) at ac = 0.22, (b) at ac = 1.08.
Table IV. Experimental Results of Carbide Phase Analysis
'ac
Wt Pct Cr
Carbide Species
0.11 0.22
no carbide precipitation 1.32 M7C3 2.09 M7C3
0.49
2.09 4.93 8.07 0.73 2.09 4.93
0.80
0.90
1.08
2.09 0.20 0.73
1.32 METALLURGICAL TRANSACTIONS A
M7C3 M7C3 M7C3
M7C3 M7C3 M7C3
M7C3, M3C M3C M3C
(Wt Pct Cr)c (Wt Pct Cr + Wt Pct Fe)c
(Wt Pct Cr)~
71.2, 70.9 72.4, 70.8
1.17 1.13
57.0, 54.8 56.7 56.5 38.7 40.2, 40.2 48.7
0.74 0.85 0.79 0.57 0.59 0.57
23.9, 10.9 6.8 6.7, 4.5, 4.7, 5.8, 4.3 6.8
0.56 0.20 0.19
VOLUME 16A, A U G U S T 1985-- 1485
Fig. 8--Microstmcture and Cr X-ray image of Fe-2.09 wt pct Cr alloy equilibrated at 985 K and ac = 0.49.
Fig. 9--Microstmcture and Cr X-ray image of Fe-2.09 wt pct Cr alloy equilibrated at 985 K and ac
Figure 8 shows the SEM microstructure and Cr X-ray image of the 2.09 pct Cr specimen equilibrated at ac = 0.49. A higher Cr content in the carbides identified as M7C3 is shown in the map. Figure 9 shows the SEM microstructure and Cr X-ray map of ~he same alloy equilibrated at ac = 0.9. The specimen contained both M7C3 and M3C carbides, identified by X-ray diffraction and Murakami's reagent. All specimens equilibrated at ac = 0,9 contained both M7C3 and M3C carbides, although the relative amounts of these two carbides varied between specimens. Figure 10 shows a typical energy spectrum of Cr K s and Fe K s obtained from a carbon extraction replica of M7C 3 carbide precipitated in the Fe-1.32 pct Cr specimen equili-
t486--VOLUME 16A. AUGUST1985
= 0.9.
brated at ac -- 0.22. The Cr/Fe ratio was determined from the spectrum using k = 0.90. Figure 11 shows a typical energy spectrum of the M3C carbide extracted from the 2.09 pct Cr specimen shown in Figure 9. A value of atom fraction of Cr in carbide, XC~, was determined for each carbon activity level from atomic ratio of Cr and Fe, Rcrre, and Cr and C, Rc~c, which was determined from the total carbon contents in the a + carbides region shown in Figure 3 as follows: XCr = [Rc,F# × Rc,c]/[Rc~F~ × Rc~c + Rc~F~ + Rc~c]. Then values of X C~ and X c were determined from x C~ accordingly.
METALLURGICALTRANSACTIONS A
II
I, I
1"
I m
l
]
[
I
80 °•
// 70
T
/ //
//
: Present work, 9 8 5 K Jellinghous and Keller, 9 7 3 K re:Small and Ryba (Kuo, 9 7 3 K ) x : Shormo, et al, 9 7 5 K ..... WoldenstrOm and Uhrenius
r/
g
50
-/'--
+ (.)
40
7.06
O~
Ii
:
:
a
;~
;
',,.,/V 5.41
Cr K~
5.45
*
¢.
:
L 6,40
Cr K~ Fe K~
(Fe,Cr)TC3
/.
o
°"
=.
Ii
/
ID
X3
:-
I,
:
Fe K~
Energy ~
Fig, 1 0 - - E n e r g y spectrum of MTC~ carbide precipitated in Fe- l 32 wt pct Cr alloy at ac = 0.22.
O
:30
20 III
I
I
i
(Fe,Cr)3C
mA
10
0
0
I 1.0
1 2.0
! 3.0
I 4.0
I 5.0
(wt % Cr) a Fig. 1 2 - - C h r o m i u m partition between o~ and carbides of Fe-Cr-C alloys at 985 K.
Relationship between (wt pct CrL and [(wt pct Cr)/ (wt pct Cr + wt pct Fe)]ca~b~a~is shown in Figure 12 and compared with other studies. Chromium partitioning to M 7 C 3 carbide was higher in the present study than that reported by Jellinghaus and Keller.-' The partitioning of Cr between a and M3C carbide was close to that observed by Kuo ~ and lower than that of Sharma et al. 3 although both investigations were made at 973 K. The free energy of a solid-solution carbide (Fe, Cr)C~ is expressed by a regular solution model 5'23 as:
T $
I,..4
+ R~yC~ In YCe + yC in YCr] + AMcYc~YC~
I $
l:P
I, !
•
,
.
B
;' ",_I.
i
:
:
i
*
4
.!
[18]
where G ~eC~and G ~rC~ are the standard Gibbs energies of formation of the component carbides, AMc, is an interaction energy parameter of MC,, and x is 3/7 for M 7 C 3 and I/3 for M3C carbide. The partial molar free energies of the component carbides are given as: GFec~ = G~ + xGc = G~:<~ + RT In yC
CrNFer FeN Energy
C "~ + (Yc0"AMcx [19]
and - -
Fig. I l - - E n e r g y spectrum of M,C carbide precipitated in Fe-2.09 wt pct Cr atloy at ac = 0.9.
METALLURGICAL TRANSACTIONs A
GCrC~ = Gcr +
- -
o
xGc = Gcrcx + RT In yC C -t- ( y Fe)-A MC.x
[2ot
VOLUME 16A, AUGUST 1985-- 1487
Since the a-phase is a dilute solution of Cr and C, Raoult's law can be assumed for the activity of Fe, which refers to pure a-Fe as the standard state. Because the a-phase and the carbide phase are in equilibrium and graphite is taken as the standard state of carbon activity for both phases, ~-c = ~-~ = RT in Y~e
[21]
Gc = RT in ac
[22]
and
Combining Eqs. [19], [21], and [22], RT[ln(1 - Y~)/(1 - YcC~)+ x In ac] = (YCr)2AMc~ q-
G °v¢c~ [23]
Equation [23] is a reasonable approximation to Eq. [19], and useful for estimating the parameters G~ec~ and AMCx directly from experimental results. The partial molar free energy of Cr in Eq. [20] is calculated as follows: g g = -Gc~ o = RT In ac~ Cr = RT[ln Y~ + In "/c~ + ec~Yc~ + e~y~]
[24]
where the activity of Cr is referred to a-Cr, and e~r is Cr-C interaction being calculated from Eq. [16], ec~ = [0(ln ~c~)rc~o/Oyc]yc-,o = 3e c~ O
I25]
Cr
The values of 7c~ and ec~ represent the thermodynamic properties of the c~-Fe-Cr alloys. These values are calculated from the equations derived by Enomoto 22based on the compilation of the excess free energy of mixing reported by Kaufman and Nesor 24 as y ~ = 5.965 and eCr~= - 3 . 6 1 for 985 K. The activity coefficient of Cr in the a-Fe-Cr alloys calculated with these values agrees with the value used by Small and Ryba. 3 Combining Eqs. [20], [24], and [25], the standard Gibbs energy of formation of CrC, is rewritten as:
study. These values are compared with other studies in Table V. The standard Gibbs energy of formation of CrC3, was evaluated as -20,190 J/mol Cr from the equation by Small and R y b a / They calculated G~c3n as a function of temperature from 600 to 973 K from their analysis of the experimental data of Jellinghaus and Keller] combined with published free-energy functions. Waldenstr6m and Uhrenius 6 selected the temperature dependences of G~c3, and G~ec317according to the same data as Small and Ryba, assuming that AMC3n w a s independent of temperature. These temperature-dependent lines of Gc~c3,7 are shown in Figure 13, together with experimentally determined lines 25-28and a line evaluated by S t o r m s . 29 The present result is close to the value measured from CH4/H2 equilibrium, 28 and the lines evaluated by Waldenstr6m and Uhrenius 6 and b y S t o r m s . 29
The same comparison is shown in Figure 14 for G~cv3. The present results show a reasonably good agreement with others. WaldenstrSm and Uhrenius 6 computed the temperature dependence of G~rc~/3 from available information on Cr partitioning between cementite and the e~ or y phase, and the value of AMcv3 was obtained at 1273 K. Sharma et al. 4 proposed an equation for G~rcl/3 as a function of temperature under an assumption that AMC1/3 = 0. The value of G~c~zv3calculated with their equation is much lower than other values shown in Figure 14. The values of the interaction energy parameters obtained in this study are approximately twice those used by Waldenstr6m and Uhrenius in their computation of the FeCr-C system. Note that they selected their temperaturedependent parameters so that they could cover a broader temperature range. The values of the standard Gibbs energies of formation of FeC3,7 and FeC ~3 carbides agree with those of Waldenstr6m and Uhrenius and of Chipman.
R T [ l n y ~ + ln(yUyc~) + x in ac + ec~Y~ + 3eC~y~] c~ o - (1 - Yc0"AMcx = Goc.~
[26]
The standard Gibbs energies of formation and the interaction energy parameters were determined as: MC3/7 carbide G~ee3/7 =
4,220 -2--310
J/tool Fe
G~rc3/7 =
- 2 4 , 3 9 0 ± 540
J/mol Cr
AMC3/7 =
1,660 ± 780
J/tool M
[27]
o
J/mol Cr
AMCtJ3 = 4,100 ± 2,000
J/mol M
[28]
Since the experimentally determined Cr partitionings between the a-phase and the MC~,3 carbide phase by Kuo agree with the present results, Kuo's results were incorporated in the calculation of G~ecv3 and AMcv3. The parameters determined for the MC3/7 carbide phase showed smaller uncertainties than those for the MC1/3 carbide phase in this
1488--VOLUME 16A, AUGUST 1985
The thermodynamic properties of the Fe-Cr-C system were determined for ferrite and carbide phases from equilibrium with CH4/Hz at 985 K. The resuIts for a-phase are summarized as follows: l. The interaction parameter of Cr for C was determined as:
2. The Wagner interaction coefficient was determined as: e c r = - 7 2 -+ 2. 3. The activity coefficient of carbon in a-Fe is independent of carbon concentration, and the carbon solubility in or-phase of Fe-Cr-C alloys was expressed as:
J/mol Fe
Gc~cv3 = - 1 4 , 5 0 0 -4- 3,400
SUMMARY
Ac~c = - 1 8 . 1 ± 0.3.
MCI/3 c a r b i d e
G~ecl/3 = 530 ± 60
IV.
log Yc = log ac - 3.617 + 31.35Ycr. The carbide phase was analyzed by a regular solution model with component carbides, FeCx and CrCx. The results include the following: 4. The standard Gibbs energies of formation were determined for FeC3/7, FeCv3, CRC3/7, and CrCv3 carbides. 5. The interaction energy parameters of the regular solution model were determined for MC3, and MCv3 carbides. METALLURGICAL TRANSACTIONS A
Table V.
Comparison of Thermodynamic Parameters at 985 K, J/mol of Metal
Ref. 3
Ref. 4
Ref. 6
G °FeC317
G~,qn
4,900 -23,490 780 - 15,210 750 1,790
-20,190 -36,000
AMC3n
AMCI/3
Ref. 19
0
4,220 -24,390 530 - 14,500 1,660 4,100
530
i
i
Present Work
I
i
.~
Small ani:l Ryba
!
K I eykamp
-2 Tanaka, et al Alekseev and Shvartsman
Waldenstr6m and Uhrenius
5 E -.)
Storms
-2 o o~
K u l k a r n i and W o r r e l l
o: Preset work -3( I
!
I
I
700
I
|
900
1000
I
800
Temperature,
K
Fig. 13--Standard free energy of formation of CRC3,7 carbide. !
!
©:Kunitake
e: K u o - H u l t g r e n
-10
o : L e i b e r , et al ©
c3
x: S a t o - N i s h i z a w a
E
m=
-15
L=
ot~
8
L9
8
- - : W a l d e n st r6m-Uhrenius zx P r e s e n t Work I
800
t
i
900 Temperature.
1000 K
Fig. 14--Standard free energy of formation of CrC,3 carbide. METALLURGICAL TRANSACTIONS A
VOLUME 16A, AUGUST 1985-- 1489
ACKNOWLEDGMENTS The author acknowledges the support of the National Science Foundation under Grant DMR-8105026. Assistance in the laboratory work by B. M. Davis, and helpful discussions with Dr. T. Wada and Dr. W.C. Leslie are appreciated.
REFERENCES 1. K. Kuo: J. Iron Steel Inst., 1953, vol. 173, p. 363. 2. W. Jellinghaus and H. Keller: Arch. Eisenhiittenw., 1972, vol. 13, p. 319. 3. M. Small and E. Ryba: Metalt. Trans. A, 1981, vol. 12A, p. 1389. 4. R, C. Sharma, G.R. Purdy, and J.S. Kirkaldy: Metall. Trans. A, 1979, vol. 10A, p. 1119. 5. M. Hillert and L I. Staffansson: Acta Chem. Scand., 1970, vol. 24, p. 3618. 6. M. WaldenstriSm and B. Uhrenius: Scand. J. Mat., 1977, vol. 6, p. 202; TRITA-MAC-0100, Oct. 1976. 7. R. Lundberg, M. Waldenstr/Sm, and B. Uhrenius: CALPHAD, 1977, vol. 1, p. 159. 8. R. R Smith: J. Am. Chem. Soc., 1946, vol. 68, p. 1163; Trans. TMSAIME, 1962, vol. 224, p. 105. 9. J.C. Swartz: Trans. TMS-AIME, 1967, vol. 239, p. 68; 1969, vol. 245, p. 1083. 10. J.A. Lobo and G.H. Geiger: Metall. Trans. A, 1976, vol. 7A, p. 1347. 11. K. Narita, H. Hara, A. Miyamoto, and H. lwakiri: Tetsu-to-Hagand, 1974, vol. 13, p. I962. 12. I. Taguchi: Japan Analyst, 1973, vol. 22, p. 359.
1490--VOLUME 16A, AUGUST 1985
13. "Atomic Absorption Spectrometric Analyses of Iron, Steel and Iron Ore", Iron Steel Inst., Japan, 1974. 14. D~inwald and C. Wagner: Z. Anorg. AUgem. Chem., 1931, vol. 199, p. 321. 15. R.B. McLeUan: Trans. TMS-A1ME, 1965, vol. 233, p. 1664. 16. R.B. McLeUan and W.W. Dunn: Metall. Trans., 1970, vol. 1, p. 535. 17. W.W. Dunn and R.B. McLellan: Metall. Trans., 1971, vol. 2, p. 1079. 18. E. Schiirmann, T. Schmidt, and F. Titlmann: Giesserei-Forschung, 1967, vol. 19, p. 35. 19. J. Chipman: Metall. Trans., 1972, vol. 3, p. 55. 20. E.H. Foo and C. H. P. Lupis: Acta Metall., 1973, vol. 21, p. 1409. 21. C.H.P. Lupis: "Chemical Thermodynamics of Materials", NorthHolland, Elsevier, NY, 1983. 22. M. Enomoto: Tetsu-to-Hagan(, 1983, vol. 69, p. 1336. 23. M. Hillert, T. Wada, and H. Wada: J. Iron Steel Inst., 1967, vol. 205, p. 539. 24~ L. Kaufman and H. Nesor: CALPHAD, 1978, vol. 2, p. 55, p. 81; p. 117, p. 295, p. 325; 1979, vol. 3, p. 45. 25. H. Kleykamp: Ber. Bunsenges. Phy. Chem., 1969, vol. 73, p. 354. 26. H. Tanaka, Y. Kishida, A. Yamaguchi, and J. Moriyama: J. Japan Inst. Metals, 1971, vol. 35, p. 523. 27. A.D. Kulkami and W.L. Warrell: Metall. Trans., 1972, vol. 3, p. 2363. 28. V.I. Alekseev and L. A. Shvartsman: Fiz. Metal. Metalloved., Akad. Nauk SSSR, 1961, vol. 11, p. 545. 29. E.K. Storms: "The Refractory Carbides", Academic Press. NY, 1967, p. 102. 30. T. Kunitake: Trans. Japan Inst. Metals, 1966, vol. 7, p. 253. 31. K. Kuo and A. Hultgren: Jernkont. Ann., 1951, vol. 135, p. 449. 32. E Leiber, W. Kock, and E. Schiirmann: Arch. Eisenhiittenw., 1971, vol. 42, p. 106. 33. T. Sato and T. Nishizawa: J. Japan Inst. Metals, 1955, vol. 19, p. 385.
METALLURGICAL TRANSACTIONS A
