Thermodynamic properties of the CrFe system

CALPHAD Vol. 11, No. 1, pp. 83-92, Printed in the USA.

0364-5916/87 $3.00 t .OO

1987

(c) 1987 Pergamon

THERMODYNAMIC PROPERTIES

Jan-Olof Division Royal S-100

ABSTRACT A revised thermodynamic major improvements are: improved description of ties of bee and a lower the Gibbs energy in each

OF THE Cr-Fe

Journals

Ltd.

SYSTEM

Andersson and Bo Sundman of Physical Metallurgy Institute of Technology 44 Stockholm, Sweden

assessment of the Cr-Fe system is presented. Some of the Altered composition dependence of the Curie temperature, the bee/sigma phase equilibrium and thermodynamic properminimum of the gamma loop. A set of parameters describing phase is given.

Introduction The thermodynamic evaluation of the binary system Cr-Fe made by Hertzman and Sundman (1) gives a thorough presentation of the available experimental data and thermodynamic models used in the Cr-Fe system. Recently, the thermodynamic properties of pure chromium was reassessed and it was decided to recommend a melting point 47 K higher than before. It thus appeared necessary to reassess the Cr-Fe system and at the same time take the opportunity to improve on some flaws in earlier descriptions. The present assessment is based on the evaluation by Hertzman and Sundman but does not use so called “lattice stabilities” for the phases of pure element state. Instead the Gibbs energy values for pure Cr and Fe presented by Andersson (2) and Fernandez Guillermet and Gustafson (3) are used. These new values derive from heat capacity and enthalpy measurements.

Bee and

liquid

phases

The effect of alloying on the magnetic properties of bee was evaluated by Hertzman and Sundman. Their description of the composition dependence of the critical temperature was mainly based on experimental information derived from dilatometric studies (4,s). t!ewer experimental information by Downie and Martin (6) concerning CP measurements in the binary system shows a considerably higher critical temperature than the values trusted by Hertzman It is also in agreement with similar data from Backhurst (7) which were disreand Sundman. These valves are now accepted and the Curie line was thus garded by Hertzman and Sundman. the average magnetic monent now had to raised in the center of the Cr-Fe system. Furthermore, be slightly adjusted to conform with for the smaller magnetic moment used for pure bee chromium by Andersson, The new magnetic parameters are given in Appendix I. The Gibbs energy equations for bee and liquid used by Hertzman and Sundman were again applied, Gm = x

m

Cr

'G

re the excess only appears

Cr

+ ‘Fe

energy in the

+ RT(xCrlnxCr OG Fe EG is expressed as ex!ression for bee.

+ xFelnxFe)

(1)

+ EG + GE m

a Redlich-Kister

polynomial

and

the

magnetic

term

There are several independent measurements of activities at various temperatures between 1173 and 1973 K (n-13). Unfortunately the measured values show a considerable scatter and the accuracy claimed by different authors using similar techniques is between a few percent and more than 20 percent.

Received

28 February

1986

83

J.-O.

84

The

assessment

of

the

bee

ANDERSSON and B. SIJNDMAN

and

liquid

phases

was

carried

out

with

a computer-operated

optimization program (14) using the available activity information with a more appropriate error estimation (10-Zll%f, together with enthaipy measurements by Dench (15), Normanton (16), lguchi (17) and Batal in et al. (18) and the liquidus-solidus determinations made by Schurman (19) and Kunrat et al. (20). Fig. 1 shows the calculated equilibria between bee and liquid together with available experimental information (4, 19-22). The values obtained for the regular solution parameters of both phases are given below: otl

iquid Cr.Fe oL bee Cr,Fe

Fig, 2 gives phase relative to satisfactory.

=

-14550

=

20500

+ 6.65

T

9.68

T

-

a comparison between pure Fe in the liquid

the measured and calculated enthalpy state and pure Cr in the bee state.

of The

the liquid agreement

is

Considerable effort was then put into the incorporation in the optimization procedure experimental values by Giilliams (Z3,24) and Vintaykin (25) and others (26-30) on the bee finally it was accepted that miscibility gap, the top part of which is metastable. tiowever, was not possible to make this information consistent with the earlier mentioned thermochemitwo very recent experimental report5 were cal and phase equilibrium data. At this stage, that the maximum temperature is higher found. The result by Vilar and Cizeron (31) indicates than reported earlier and the result by Kuwano (32) even raises the maximum temperature by about 100 K. Uhen the bee miscibility gap was calculated from the above assessment, it was found to be consistent with the result by Vilar and Cizeron and the result of the assessment was thus accepted. Fig. 3 shows a calculation of the metastable part of the miscibility gap together with experimental information from refs. 23-32.

2150

uid Adcock * Sopi d Adcock 0 ti uid Putman a Sopi d Heilawell ALiquid Hcllawell Q)Liquid Kunrat x Tie-lines Schurmexm

f I

2100 2050

1950 a a

w CL

s

W t--

1900 1850 1800 1750 t 1700

4 0

0.1

0.2

0.3

0.4

0.5

MOLE-FRACTION FIG.

0.6

0.7

0.8

0.9

c 1.0

CR

1

Experimental and calculated bccltiquid equilibrium. The calculated and experimental results are in close agreement at lower chromium content. At higher content the experimentalists report considerable difficulties due to oxidation and evaporation of chromium.

of it

5000

l

+ 4500 _.

+ Batalin * spchi

1873K 186311

4000 __ FIG.

3500

2

A comparison between the measured and calculated enthalpy of the 1iquid phase relative to pure Fe in the 1 iquid state and pure Cr in the bee state.

3000 2500

2000 1500 1000 500 0 0

0.20

0.10

0.30

MOLE-FRACTION

0.40

1

0.50

CR

FIG.

3

Experimental and catculated bcc/bcc miscibility gap. Reported exper imentat thermochemical data and phase boundaries could not be represented simultaneously around the maximum temperature. As a way out of this inconsistency it was decided to trust the thermochemical data rather than the phase boundary determinations. In a later stage af the assessment the reports by Vilar and Kuwano was found.

550 500 2 0.3

0.4

0.5

MOLE-FRACTION

0.6 CR

0.

J.-O.

86

ANDERSSON and B. SUNOMAN

70 65 FIG.

60

4

A compa r i son between experimental information on heat capacity for some ailoys between 3.0 and 16.1 percent Cr and the result of the present assessment. The calculated curve is 9.4 percent Cr. The assessment was carried out without using the experimental informat ion.

1100

900

700

t 300

1500

t 700

TEMPERATURE-KELVIN

50.0

1

I

I

t FIG.

5

Experimental and calculated heat capacity in bee at 44 mole-percent Cr. The experimental points were not in the optimization procedure. The only piece of information used was the Curie temperature.

45.0

40.0

35.0

t 30.0

J +

25 04 400

4 *

+

Dow-b Cro.47sFeo.525

* Dow&?

Cr0.434Fe0.566 0 Backhurst Cro.&@eo.$j6 i

600

800

TEMPERATURE-KELVIN

1000

I.

1200

t 400

87

THERMODYNAMIC PROPERTIES OF THE Cr-Fe SYSTEM

The

presented

assessment

was

on CR for some alloys. A comparison present assessment is given in Figs. 3.0 and 16.1 a calculated curve for 44 percent Cr and experimental data surprisingly good.

carried

out

without

using

the

experimental

information

between such information on C and the result of the 4 and 5. Fig. 4 gives data fgr some alloys between Fig. 5 gives the calculated result for 9.4 percent Cr. In both cases the agreement is for similar compositions.

FCC phase The

gamma loop

calculated

by Hertzman

and

Sundman

from

their

assessment

is

in

good

agree-

ment with experimental data around the maximum chromium content but the congruent minimum is To avoid this discrepancy the description of pure placed at least 20 K too high in temperature. fee chromium (33) could be changed or the regular interaction parameters in both fee and bee could be adjusted or a subregular fee interaction parameter could be introduced. The first two methods were tested by Hertzman and Sundman without much success. Within the SGTE organization there have been discussions whether the metastable melting point of fee Cr was correctly estimated by Kaufman (33) when he evaluated the lattice stability value which has been in general use. From work done on the binary Cr-Ni system by Chart and Dinsdale (34) it seems that it should be considerable higher and at least 1400 K. Recently SGTE requested Saunders (35) to make a review of binary Cr systems with fee stabilizing elements. From that information and from arguments concerning the entropy of fusion he now suggests a revised value. His new value was accepted in view of the difficulties otherwise encountered in the Cr-Ni system. The following difference in molar Gibbs energy for pure fee Cr was used (where hbcc represents a non-magnetic bee chromium phase). GfCC Cr

_ Ghbcc Cr

=

7284 +

0.163T

The experimental data on the fee phase in the Cr-Fe system considered most important were tie-lines by Nishizawa (36) and Kirchner (371, and DTA measurements by Baerlecken (38). It was found that a small positive subregular parameter was sufficient to tower the minimum point but instead the slope of the high temperature equilibrium bcc/fcc was changed and even a maximum could be obtained. This is in contradiction to the measurements of Bearlecken. A reasonable compromise was obtained with a subregular parameter of 1410 J/mol resulting in an almost horizontal slope at high temperature and a minimum temperature of about 1126 K. Fig. 6 shows the recalculated gamma loop together with experimental information from the literature (36-41). The parameters obtained are given below: E

Gm =

~~~~~~(10833 - 7.477T + 1410(xcr - xFe))

The magnetic properties little or no influence

of the fee phase were neglected on the thermodynamic properties

Sigma

J/no1

in this assessment as above room temperature.

they

have

phase

In order to introduce the sigma phase in the calculations one must relate its Gibbs energy to the reference used for pure Cr and Fe, the so called SER reference state. A way to do this could be to fit experimental heat capacity measurements to a polynomial in temperature, integrate it to obtain Gibbs energy and evaluate an enthalpy and entropy of formation at 298.15 K. Unfortunately the only experimental information in the literature (6,7,15,42) concerns the heat of transformation from sigma phase to bee within a small temperature range and a very limited composition range. this is not a sufficient basis for the evaluation of thermochemical properties of sigma phase. Instead an approach suggested by Andersson et al. (43) could be used where the atoms in different sublattices are compared with atoms in bee or fee structures. A sublattice with a coordination number 12 is aprroximated as an fee lattice and a sublattice with a coordination number of 14 and higher as a bee lattice (with 8 nearest neighbours and 6 close next nearest neighbours). Sigma phase has a unit cell with 30 atoms, 10 of which have 12 nearest neighbors, 4 have 15 and 16 have 14. Experimentally the 10 sites with least neighbors are preferentially occupied in this case Fe, and the 4 sites by B atoms, with most neighbors by A atoms, in this case

J.-O.

88

ANOERSSON and B. SUNOMAN

FIG.

z

1700

2

1600

E zI

1500

? E

1400

i w

1300

-

1200

.

1

t

0.04

0

0.08

0. I2

0. I6

0.20

CR

MOLE-FRACTION

FIG.

1050 z 2 w Y

wI S P

a z 0.

z P

6

Experimental and calculated bcc/fcc equilibrium. A lower value for the minimum temperature around 8% chromium would increase the slope of at the phase boundary high temperature.

. ..

1000

..

950

..

900

..

650

..

800

..

750

..

700 ‘1 0

.

7

Experimental and calcu-- lated bee/sigma equi Iibrium. The sigma phase is slightly shifted to _higher chromium content at the three-phase tem__ perature compared to earl ier assessments. This was necessary in -- order to describe the experimental heat of transformation from mm sigma to bee phase.

.

+ Pomep BastJen

* Hertzman Sundman r

0.1

0.2

0.3

0.4

0.5

MOLE-FRACTION

0.6

CR

0.7

0.8

0.9

1.0

THE~ODY~~IC

Cr,

whereas

both

elements

mix

on

the

PROPERTIES OF THE

16

remaining

sites

and

Cr-Fe

SYSTEM

allowing

89

a variation

in

compo-

In most systems the sigma phase falls within these limits sition of a binary sigma phase. of composition. However, there are strong indications in some hi-base systems that some of the sites with 12 neighbors can also be occupied by A atoms. To be able to treat such cases the model previously discussed by Andersson et al. will now be modified by reserving only 8 sites with 12 neighbors for B type atoms. In fact, of the 10 sites 8 belong to one sublattice and 2 belong to another but it is not easy to find a reason why the latter one should be less suitable to type B atoms. Instead, it should be emphasized that the present model has been defined by convenience. It yields the following expression, G s i gna= 3 0 GFe-Cr*Cr+yFe sigma 3 0 G~e~Cr~Fei’8RT~yCrlnYCr~y~elny~e)~yCryFeL~e~Cr~Cr sigma 3 3 3 3 3 3 m YCr . . . .

sigma

*

*

f Fe (61

3 y

where represents mole fractions on all the sites where both types of atoms can go, so three sublattices are considered and, in keeping to the called site fractions. Formally, basic idea of Andersson et al., we shall compare one with an fee lattice and the other two with a bee lattice. The Gibbs energy of sigma phase with the third sublattice filled with Fe wilt thus be represented by an expression, 0

The term, with third

sigma GFe:Cr:Fe

applsifataon DGP .Cr.Fe, a po?+notiral sublattice

(7) of

this expression does not involve any approximation has been added. It is hoped that this term is small the Gibbs energy of of few terms. In the same way, filled with Cr will be represented by,

0 sigma GFe:Cr:Cr The parameters netic bee state.

+ 22 hbcc G

is

the

o hbcc GCr

Gibbs

because the extra and can be treated sigma phase with the

sigma + DGFe:Cr:Cr

energy

of

the

(8) pure

component

in

an

hypothetical

non-mag-

In order to describe the heat of transformation from sigma to bee, measured by Dench (l5), Backhurst (7) and Martens and Duwez (42), the value 1450 J/mol was chosen at the congruent maximum temperature given by Pomey and Bastien (44). The eutectoid temperature where sigma phase disappears was estimated by Williams and Paxton (23) to 793 K and this value was accepted as an upper limit for this temperature. These two pieces of information were not used in the earlier assessment of Fe-Cr by Hertzman and Sundman. Additional experimental information used was the two tie-lines at 973 K on each side of the sigma phase measured by Hertzman and Sundman (l), a chromium content in the sigma phase at the maximum point (44) and an estimated composition at the eutectoid temperature, To zv$$n a reaszpzsse fit to these data a linearly temperature dependent polynomial for DG [e&g: Fe had to be used. During the optimization procedure it was found tha and DGFe:Cr:Fr same tempera ure dependence could be used in both polynomials. The result of the optimization is presented in Fig, 7 as a recalculated phase diagram together with some of the experimental information. It gave the following parameter values, sigma = +117300 Fe:Cr: Fe sigma DG = +92300 Fe:Cr:Cr DG

-

95.96T

(9)

95.96T

(10)

Discussion At the final stage all parameters except those for sigma phase were refined in a single run using all experimental data. This last optimization did not change any parameter much and the resulting sum of squares was 585 using 334 pieces of experimental information. One should bear in mind that this included ali the somewhat contradictory activity information. The recalculated phase diagram with these final parameters is shown in Fig. 8. It of sigma was later

is interesting to phase. Kubaschewski changed by Muller

compare earlier thermochemical predictions and Chart (45) estimated a eutectoid and Kubaschewski (46) to 713 K and this

of the stability range temperature of 733 K. It value has been accepted in

J.-O.

90

ANDERSSON and B. SUNDMAN

2200 2050 1900 1750 I600 450 300 150

I000 850 700 2

0.3

0.4

B.5

flULE-FR&~T~~~ FIG.

0.6

0.7

8-8

e-9

I.8

CR

8

The complete Fe-Cr diagram. 1ine is ferromagnetic.

The bee phase below

the

dashed

some phase diagram compilations (47,481 and calculations (49) and also by Hertzman and Sundman (1). With the sublattice model for sigma phase and the heat of transformation (7,15,42) applied the assessment ptaces the eutectoid temperature close to the experimenat the congruent point, tal value by Wittiams and Paxton (23)* Further calculations indicated that it is difficult to shift this temperature to the lower value suggested by Hutler and Kubaschewski without considerable error in the heat of transformation. The large difference between the experimental and calculated solid/liquid equilibrium at high chromium content can be explained by the experimental difficulties occurring at elevated temperatures described by Adcock (4). He reports a boiling point at slightly below 2173 K and a melting point of 2103 K. This is almost 700 t: and 80 K below the accepted values. It should also be noted that his experiments are in general agreement with later determinations and calAt higher chromium contents, he reports culations at less than 30 mole percent chromium. increasing experimental difficulties. dure,

All are

parameters summarized

used, taken in Appendix

from I.

the

literature

and obtained

from

the optimization

proce-

THE~~~Y~MIC

PROPERTIES OF THE Cr-Fe

SYSTEM

Acknowledgement The authors wish to express gratitude to Prof. Mats Hillert for useful advice, constructive criticism and for the help received during the preparation of this paper. All optimiaations and diagram calculations were carried out with the two computer programs, PARROT and THERMO-CALC, developed at the Oivision of Physical Metallurgy (50,51). The work was financially supported by The Swedish Board for Technical Development.

References 1. 2. :: Z: 3: 9. 10. 11. 12. 13. 14. 15. 16, 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. ::: 33. 34. ;z: 37. 38. z: 41. 42. 43. 44. 45. 46.

S. Hertzman and B. Sund~n, Calphad 6 (1982) p 67. J-O Andersson, Int. J. Thermophys 6 (1285) p 411. A. Fernandez Guillermet and P. Gustafson, High Temp.-High Press. 16 (1985) p 591. F. Adcock, J. iron Steel Inst. 124 (1931) p 99. M. Failot, Phys. 1l:e ser 6 (1936) p 99. O.B. Downie and J.F. Martin, J. Chem. Thermodyn. 16 (1984) p 743. I. Backhurst, J. iron and Steel Inst. 189, (1958) p 124. Y. Jeannin, C. Hannerskantz and F. Richardson, Trans. AiME 227 (1963) p 300. 0. Kubaschewski and G. Heymer, Acta Met. 8 (1960) p 416, P.C. Lidster and H-B. Bell, Trans. AIME 245 (1969) p 2273. C.L. McCabe, R.G. Hudson and H.W. Paxton, Trans. AIME 212 (1958) p 102. R.B. Reese, R.A. Rapp and G.R. St. Pierre, Trans. AIME 242 (1968) p 1717. J. Vrestai, J. Tousek and A. Rek, Kovove Materialy 16 (1978) p 393. B. Jansson, TRITA-MAC-234 April 1984, Div. Phys. Met., Royal Inst. Techn. Stockholm, Sweden. W. A, Oench, Trans. Faraday Sot., 59 (1963) p 1279. A.S, Normanton, R.H. Moore and B.B. Argent, Met. Sci. 10 (1976) p 207. Y. iguchi, S. Nobori, K. Saito and T. Fuwa, Tetsu-to-Hagane 68 (1982) p 623. G-1. Batalin, V.P. Kurach and V.S. Sudavtsova, Zh. Fizz, Khim. 58 (1984) (2) p 481, E. Schurman and J. Brauckmann, Arch. Eisen. 48 (1977) p 3. 5.M. Kunrat, M. Chochol and J-F. Elliott. Met. Trans. 15 (1985) p 663, J.W. Putman, R.D. Potter, M.J. Grant, Trans. ASM 43 (l?r;l) p 824, A. Hellawell, W. Home-Rothery, Phil. Trans. Roy. Sot. London, Ser. A, 249 (1957) p 417, R.0, Williams and H.W. Paxton, J. Iron Steel Inst. 185 (1957) p 358. R.0, Wi 1I iams. Trans. AIME 212 (1358) p 497. E.2, Vintaykin, V.Y. Koiontsov and E.A. Medvedev, Russ, Met. 4 (1969) p 109. E.J. Dulis, V.K. Chandhok and J. Hirth, Trans. ASM 54 (1961) p 456. 0. Chandra and L.H. Schwartz, Met. Trans. 2 (1971) p 511, T. de Nys and P.M. Gielen, Met. Trans. 2, 1971, p 1473, Y. Imai, M. lzumiyama and T. Masumoto, Sci. Rep. Res., Inst. Tohoku Univ. Ser. A, 18 (1966f P 56. R. Lagneborg, Trans. ASM 60 (1967) p 67. R. Vilar and G. Cizeron, Mem. Etud. Sci. Rev. Met. 79 (1982) p 687. H. Kuwano, Trans. Japan Inst. Metals 26 (1985) p 473. Phase Stability in Metals and Alloys, P.S. Rudman, J. Stringer, R-1. Jaffe, L. Kaufman, eds. McGraw-Hilt, NY 1967, T. Chart and A. Dinsdale, Priv. corn. N. Saunders, Priv. corn. Rep. 4602, Swedish Board for Technical Development, Stockholm 1266. T. Nishizawa, G. Kirchner, T. Nishizawa and 3. Uhrenius, Met. Trans. 4 (1973) p 167. E. Baerlecken, W.A. Fischer and K. Lorenz, Stahl u Eisen 81 (1961) p 768. T. Nishizawa and A. Chiba, Trans. JIM (1975) p 767. P. Poyet, P. Guiraldenq and J. Hochman, Rev. Met. 69 (1972) p 772. K. Bungardt, E. Kunze and E. Horn, Arch. Eisen. 29 (1258) p 193. AINE 206 (1256) p 614. H. Martens and P. Ouwez, Trans. H. HiItert, B. Jansson and B. Sundman, J-O Andersson, A. Fernandez Guillermet, Accepted Acta Met. 36 (1986). 6. Pomey and P. Bastien, Rev. Met. 53 (1956) p 147. 0. Kubaschewski and T.G. Chart, J. Institute of Metals, 93 (1964-65) p 329. F. Muiler and 0. Kubaschewski, High Temp. High Press. I (1969) p 543.

91

J.-O. ANDERSSON and B. SUNDMN

92

47. 0. Kubaschewski,

Iron Binary Phase diagrams, Springer-Verlag Berlin/Heidelberg 1982. 48. V.G. Rivlin, Int. Met. Reviews 26 ('98') p 269. 49. P. Spencer, C. Allibert, C. Bernard and D. Nussler, Proc. Calphad VIII Stockholm

50. 51.

1979 p 207. 8. Sundman, B. Jansson,

B. Jansson and J-O Andersson, Calphad 9 (1985) p 153. Internal report 040 Div. Phys. Met., Royal Inst. Techn.

APPENDIX o hbcc G Cr

_ HSER Cr

I

Summary

of

parameters

-1.47721

_ HSER Fe

G

fee _ HSER Fe Fe

10-8,3+77358.5T-1

for Ttl811 103',-'

-237.57+132.416T-24.6643Tln(T)-3.75752 -5.89269

G

for T>1811

10s3T2

10-8T3+77358.5T-'

for T>1811

-27098.266+300.25256T-46Tln(T)+2.78854 0

for ~>2180 10v3T2

-25384.451+299.31255T-46Tln(T)+2.2960305 0

R=8.31448)

for T<2180 1032T-g

+1224.83+124.134T-23.5143Tln(T)-4.39752 -5.89269

and

Sweden.

10s3T2

'0-6T3+139250T-1

= -34864+344.18T-50Tln(T)-2.88526 o hbcc G Fe

(in SI units

= -8851.93+157.48T-26.908Tln(T)+1.89435

Stockholm,

103',-'

for T>1811

fee

oGliquid Cr

for T<2180 for ~>2180

oGliquid Fe

for T<1811 for T>l811

sigma G Fe:Cr:Cr oGsigma Fe:Cr:Fe o bee LCr,Fe 0

oLliquid Cr,Fe 0 fee L Cr,Fe lLfCC Cr,Fe GP f(t)

+205oo-9.681 -14550+6.657 -'0833-7.477T +1410 RTln(B+l)f(t),

-o.go530t-1+'.o-o.153T3-6.8 -6.417

Bbcc Tbcc C

T=T/T~

,0-2~-5-2.037

1D-3.rg-1.53

'O-3~-'5-4.278

10-3-r'5

,0-4~-25

for TCl for T>l

2.22XFe_0.008xcr-XCrXFe0.85 '043XFe -3'l.5xCr+XCrXFe('65D+550(xCr-xFe))

When the calculated T is less perimental N&e1 tempesature.

than

zero

the value

should

be divided

by -1 to obtain

the ex-