A thermodynamic evaluation of the iron — vanadium system

CALPHAD Printed

in

~1.7, No.4, the USA.

PP.

305-315,

1983

A THERMODYNAMIC

EVALUATION

Div. Royal

ABSTRACT.

0364-5916/83 (c)

OF THE

IRON -

VANADIUM

$3.00

Pergamon

1983

+ .OO

Press

Ltd.

SYSTEM

Jan-Olof Andersson of Physical Metallurgy Institute of Technology S-100 44 Stockholm

A new evaluation of the Fe-V system subregular model. A set of parameter vidual phase is given. The treatment model. The transition between paragreat influence on the coexistence

has been made using a magnetic multi-sublattice values describing the Gibbs energy of each indiof the a phase is based upon a three sublattice and ferromagnetic ferrite is found to have a boundaries of ferrite and u phase.

Introduction Thermodynamic descriptions of the phase relationships in the iron-vanadium system have It is well known that the contribeen presented several times during the last few years (l-4). bution from the ferromagnetic transition to the total Gibbs energy of substitutional iron-rich alloys should not be neglected but even recent investigations are based on descriptions of thermodynamic models not capable of treating the ferromagnetic part of the Gibbs energy. Spencer and Putland (1) measured the enthalpy of formation for bee alloys at 1623 K and assessed the a/bee equilibrium. Kubaschewski et al (2) evaluated activities in the liquid phase at 2193 K and presented a phase diagram for the liquid/bee equilibrium. Uhrenius (3) considered the so called y loop. Hack et al (4) reanalysed the data from Spencer and Putland (l),and Kubaschewski et al (2) together with new information on the u phase and evaluated a set of thermodynamic parameters for the description of the o/bee equilibrium and the liquid/bee equilibrium. So far, no one has assessed the complete phase diagram with all its stable phases. The present work will involve liquid, fee, paramagnetic and ferromagnetic bee and u phases. It does not consider chemical ordering of the bee at high vanadium contents and low temperatures. Thermodvnamic

(5).

A new In this

thermodynamic model the

model fraction

model

for phases with several sublattices of sites in each sublattice occupied

has by

recently been developed a component is described

by the site fraction, denoted by y? for component i in sublattice s. The sum of site fractions The model can also handle a contribution to in each sublattice is by definitio; equal to one. where the Curie or Neel temperature and the average the Gibbs enerqy due to magnetic ordering, magnetic moment oer atom may depend on the composition. The Gibbs vanadium system

energy can all

~~ = is zyyoy. dered,

for be

the bee described

yFeoGFe

+ yvoGV

(ferrite), with +

one

fee (austenite) sublattice and

RT(yFelnYFe + Yv'VV)

the contribution due to the magnetic the ‘G values are As a consequence paramagnetic staies. The y fractions

The CI phase has a complex tetragonal crystal structure The atoms are distributed among five groups of sites information indicating that lattice. There is experimental one by vanadium and two by a mixture of iron and vanadium lest possible way a three-sublattice model was adopted for

February

16,

phases yields:

+ YFeYVLFe,V +

in

the

iron-

Gt

(1)

ordering in the pure elements as well as in the defined for the pure elements in completely disorare here identical to the ordinary mole fractions.

(6,7).

Received

and liquid the model

1983

305

containing 30 atoms per unit cell with 2,4,8,8 and 8 atoms per subtwo of these are occupied by iron, To describe this in the simp(7). the

a phase.

It

yields

the

following

306

J-O.

expression

for G;

the

Gibbs

305

= yFe

energy

GFe:V:Fe

per

mole

of

+ YpGye:V:V

ANDERSSON

formula

units

+ T6RT(y~elny~e

IS the Gibbs energy ~~~a~~~~~e~h~~~~~~~ea~d iron in the third energy of a u phase with iron in the first, teraction parameter and the comma separates the third one. The variables yFe and y are sent assessment the interaction parame Y er in was not sufficient information to determine

(30

atoms):

+ YiTny:)

(2)

+ Y~,Y$~e:V:Fe,V

of formation of a CI phase wit& iron in the first, sublattice. The parameter G is the Gibbs Fe.V:yo vanadium in the second and third. is a the components that interact in theF%XeFEd K lattice, the site fractions in that sublattice. In the prethe u phase was assumed to be zero because there more than the ‘G parameters.

in-

The contribution to the Gibbs energy due to the magnetic ordering for a phase will now be evaluated with a method recently used by Hertzman and Sundman (8) in an assessment of the Fe-Cr system. They gave the Gibbs energy of formation and the lattice stabilities of phases with respect to completely disordered, paramagnetic states of the elements. The following formula was

used

to

calculate

the

magnetic

ordering G

contribution:

mo = RTln(B+l) m

f(r)

where T is T/Tc, 8 is the average magnetic moment per atom of the alloy in Bohr magnetons and Tc is the critical temperature for magnetic ordering in kelvin. The function f(T) was described with an approximation of Inden’s (8) treatment, suggested by Hillert and Jarl (10). The composition dependence of Tc and b will be expressed as symmetrical power series in the y fractions, Tc’YFeoTcFe+YVoTcV+YFeYV(TcDFe,V+(YFe-YV)TclFe,V O=Y The

parameters

were

evaluated

to

FeoaFe

make

Tc

Ferrite The composition many authors (11-17). determined by these

+(YFe-YV)2Tc2Fe,V+(YFe-YV)3Tc3Fe,V) ’

yVoRV

and

(3 vary

and

u phase

(4) (5)

+ ‘FeYVBoFe,V according

dependence of the Curie temperature Fig. 1 shows the Curie temperature authors. The points in the diagram

to

the

experimental

information.

in ferrite has been investigated by at various vanadium contents as it is indicate a maximum in the Curie tempera-

ture and a vanadium content above which all alloys are non-magnetic. According to Pataud (16) this point is around 78 atomic percent vanadium. Alikhanov et al (17) failed to reveal any ferromagnetic or antiferromagnetic ordering in pure vanadium single crystals and it may seem reasonable to quess that all alloys with more than 78 atomic percent vanadium have Tc and R equal to zero. However, it is not possible to describe such a behaviour with eq. 4 and 5. Instead a least square fit of the experimental points to eq. 4 was made under the condition that only pure vanadium is non-magnetic. The error made in the magnetic contribution to the Gibbs energy at the high vanadium contents is negligible. square fit. The average magnetic moment tions. The experimental data were taken with the fitted curve.

iron 2.22

The lattice stability was estimated by Agren for pure iron. oGbcc Fe

Bee vanadium was bee solid solution land (1) at 1623

The plotted curve per atom was least from refs. 12,18,15

of completely disordered, (20) with Tc=1043 K and

_ ‘G;;’

= 1462.4

-

8.282T

the

in Fig. 1 represents square fitted under and

paramagnetic average

+ 1.15TlnT

-

are

plotted

bee magnetic

in

-

x~~(H;~-~H;~)

-

0.00064~~

x~(H~~-~H~~~)

Fig.

iron relative moment per

-

least same condi2 along

to fee atom set

J/mol

chosen as standard state for pure vanadium. The excess enthalpy alloys was evaluated from experimental information given by K and Malinsky and Claisse (21) at 1400 K. measured EHm = H m

the the

HP

parameter Spencer and

to

(6) for Put-

(7)

The adjusted data were least square fitted to a two-parameter Redlich-Kister polynomial. The resulting curve is plotted in Fig. 3 together with the experimental information. The entropy part of the excess Gibbs energy could be derived, by combining the enthalpy measurements with the Gibbs energy determinations made by Myles and Aldred (22) and Saxer (23), but this was not

fCCFE>~l043 1350

TCCFE,V>B~-110 TCCFE,V3t=3075 TCCFE, V32=8%8 TCCFE, Y>3=-2169

1200 1: 2 1050 = z 900 rJ

FIG. t The Curie temperature bee alloys according rimental information matical representation.

750

g

7 z 600 cc w

of Fe-V to expeand mathe-

450 8”. w 300 z 2 150

2

0 0

0.2

0.4

0.6

0.8

MOLE-FRACTION V

:

2.50-

4

t BCFE+2.22

I;;

2.25

Z

BCFE, VW-G?. 215

:! u

2.00

is 2

1.75

if i

1 .50

.

o NEVfTT ALORED A RADHAKRISHNA

FlG. 2 magnetic moment per atom expressed as number of Bohr magnetons in Fe-V bee alloys according to experimental information and mathematical representation.

The average

1.25

E

1.00

g z z

0.75 0.50

s 0.25 CE 0.00 %

0.2

0.4

%.$

MUL~-FRA~T~~~

V

O.B

t .%

308

done (2) the

J-O.

due

to

some

reservations

and Hack et al lattice stability

(4).

to

Instead parameters

the

ANDERSSON

reliability

of

a computer-operated for the a phase

the

results

raised

by Kubaschewski

et

al

optimizing program (24) was used, by which and the entropy part of the excess Gibbs energy

for the bee phase were optimized with respect to the information on the given by Hack et al (4). The limited information on the phase boundaries In the literature there are three different suggestions 27 was not used.

bee/o phase boundaries from refs. 25, 26 and of the vanadium content

and temperature for the congruent transformation of u phase to ferrite. Hansen (15) proposes ~“‘0.5 and Ttl473 K. Spencer and Putland (1) found the temperature 1431 K The information presented by Hack et al (4) indicates a maximum temperature between 1473 K and 1523 K and the vanadium content a little less than 0.5. Due to this descrepancy between different authors the maximum point cannot on the congruent

be used as a strong point was that the

condition temperature

in the optimizing should be less

process. than 1523

The only K and the

condition vanadium

put con-

tent approximately 0.5, The computer program was not capable to use conditions defined in such a way. instead Hans&n’s values were used as starting values and during the optimization they were allowed tb vary rather freely. The obtained u phase field is shown in Fig. 4 together with various experimental data. The iron-rich side of the coexistence boundaries shows an excellent agreement and the vanadium-rich side is acceptable. The maximum point fell at 1516 K and x,=0.476. This procedure yielded the following parameters for the bee and u phases.

obbcc = -23980 Fe,V 1 Lbcc = 8020 Fe,V OGU Fe:V:V

-

26°G;;C

-

4°G;CC

OGU Fe:V:V

-

0 fee 10 GFe

-

20°GFc Austeni

Following ref. 8 fee iron was treated and a magnktic’m+oment of 0.7. These values values given in eq. 6. The lattice stability from Kaufman and Bernstein (28). 0

The two-phase Fischer‘et al

field (29)

fee GV

-

+ 4.5197T

JlmOi

2.5202T

J/mol

t

= -131858

(3)

c 25.9081T

= -244885

-

62.1823~

J/mol

(10)

J/mol

(11)

te

as antiferromagnetic with a Neel temperature of 67 K are so low that they do not affect the numerical for fee vanadium relative to bee vanadium was taken

OG;’

=

go00

+

3‘556T

(l-2)

J/m01

between austenite and ferrite has been investigated and by Kirchner and Gemmel (30). The minimum on the

experimentally o-loop suggested

by by

The tie-lines measured by Kirchner et al (30) were put into (15)’ had been disregarded. This procedure made it possible to determine a regular soluthe compute’r optimizing program. tion parameter which describes the phase boundaries with good accuracy. The parameter value is given below.

Hansen

fee LFe,V Fia. due

5 i’s a olot of to reff 29 and

.’

the 30.

recalculated

-18180

=

phase

J/mol

+ 1.16T

boundaries

together

with

(13) the

experimental

information

Liquid The

phase

stability 0~1 iq Fe

and the

for.liquid rrielting

vanadium ooint (2202

of t

o$:C it K)

liquid

relative

iron

= -11274

+ l63.878T

was evaluated listed in ref.

OGiiq _ V

to

from 27 >A.

o G bee V

the

-

fee

22.02TlnT

enthalpy

= 21500

iron

-

was

taken

from

+ 0.0041755T2 of

9.763T

melting

J/mol

given

ref.

20

J/mol by

Smith

(14) (31)

and

(15)

The earljer experimental information on the liquidus and solidus curves has been discussed by Hansen (15) who concluded that there is a minimum on the liquidus. More recent information from Heilawell and Hume-Rothery (33) confirms the existence of the minimum. In the thermodynamic evaluationof the liquid Xansen’s estimation of the minimum point was accepted. Together with

THERMODYNAMICSOF THE IRON - VANADIUM SYSTEM

I= s :

h

-300 -400

FIG. 3 The excess enthalpy of Fe-V bee alloys according to experimental information and calculated from the excess Gibbs energy.

-500

si -600 I

t *

UJ

-700

* L&l CA

-688

x w

-900

t

-l08p! 0

0.2

0.4

0.6

MOLE-FRACTION

1700

1608

+

GREENFIELD

x

MARTENS

+

HANSEN

sl6ma tie-Itme

0.8

t .0

Y

m REF

4 olfo

Q REF

4 olfo+clgm

A

REF

4 sigma

I500 1400

FIG. 4 The o/ferrite equilibrium in the Fe-V phase diagram according to the present calculation and experimental information.

.

788 0.2

0.4 MOLE-FRACTION

0.6 V

6.8

I .B

309

J-O.

310

1900

@J KIRCHNER

ANDERSSON

GEMMEL

I800 5 > i

1700 FIG. 5 The austenite/ferrite equilibrium in the Fe-V phase diagram according to the present calculation and experimental information.

1600

I: 5 l-

1500

s w

1400

% g

1300 1200 1100 1000 0

5

10 (POOLE-FRACTION

2150

cl HANSEN

1iq

a HANSEN

rot

A

2100

HELLAWELL

+ HELLAWELL x

2050

FURUKAUA

e FURUKAWA

15

20

25

v) w 103

1 iq sol

I iq sol FIG. 6 The liquid/ferrite equilibrium in the Fe-V phase diagram according to the present calculation and experimental information.

1700

1 0

0.2

0.4 MOLE-FRACTION

0.6 V

0.6

c 1.0

THERMODYNAMICS

0.9

Q

ACTIVITY

OF THE IRON - VANADIUM

311

SYSTEM

IRON

0.7 0.6 Comparison Pr l-l

0.5

= c

0.4

2

FIG. 7 between

activities

in the liquid at 2193 K according to experiments and the oresent calculation.

0.3

0

0.2

0.4

0.6

MOLE-FRACTION

2200

0.0

I .0

VV

+--+----+----+-

2050 1900 1750 5

1600

> J 2

1450

FIG. 8 The complete Fe-V phase diagram according to the present evaluation. The notation p~1 and fa represent paramagnetic and ferromagnetic bee, respectively. Chemical ordering at high vanadium content is neglected.

,: “,

1300

z z0

1150

5 *

1000 850 700

MOLE-FRACTION

V

J-O.

312

ANDERSSON

1700

500 400 300

2

1100

2 &J r

1000

:

900

800 700

I

0

0.2

.I

\

I .

I.

0.4

MOLE-FRACTION

0.6

V

FIG. 9 The stable (full line) and metastable (dashed I ine) equilibrium between paramagnetic and ferromagnetic bee in the Fe-V phase diagram.

\.

0.8

c

1.0

THERMODYNAMICSOF THE IRON - VANADIUM SYSTEM

liquidus/solidus evaluate

the

determinations thermodynamic

of

iron-rich

properties

of

melts the

made

liquid.

by Hellawell

Recently

313

there

Furukawa

are

and

enough

Kato

(34)

data made

to some

experiments with vanadium-rich melts. This information was not used in the evaluation. The interaction energy in the liquid was evaluated with the optimizing computer program. The main optimizing effort was focused on obtaining a congruent point as near to the one given by Hansen as In order to achieve this a two-parameter polynomial had to be used. The final values possible. of the parameters are given below. 0~1 iq Fe,V

= -31915 1Cl iq Fe,V

+ 3.951T

J/m01

= 14560

Theagreementbetween the experimental points and calculated liquidus and solidus lines is demonstrated in Fig. 6. As mentioned in the introduction Kubaschewski et al (2) has measured the Fe and V activities in the liquid at 2193 K. That information was not included in the present 7. The agreement is surprisingly good assessment but is compared with calculated values in Fig. and it was concluded that there was no need to modify the optimization by including the activity information. Discussion The complete phase diagram according to the present assessment is presented in Fig. 8. As al ready demonstrated, it is in excellent agreement with the experimental information available. An interesting feature is the strong bend of the left-hand leg of the bee/a two-phase field is due to the effect of the ferromagnetic transition to below a temperature of about 1000 K. It stabilize the bee phase below the Curie temperature. Unfortunately, there is no experimental A similar magnetic effect is present in information which can be used to test this prediction. the Fe-Cr system, where it contributes to the appearance of a bee miscibility gap. It would result in a bee miscibility gap in the present system as well but it will only be metastable. It is shown in Fig. 9. The phase diagram obtained from the present assessment is very similar to the one calculated by Hack et al (4). However it should be emphasized that the present evaluation only uses 13 parameters which can be varied in order to give agreement with the experimental information on the phase equilibria and thermochemical properties of the binary system whereas Hack et al The low number of parameters used 26. The reason why they used so many is not completely clear. which was sufficient in the present work does not seem to be due to the separate description of the magnetic effect because that effect is mainly important at low temperatures where there The explanation comes partly from the use of a new model for is no experimental information. the u phase which only required 4 parameters whereas Hack et al used 12 parameters, 2 of which refer to pure Fe and were taken from a previous study of other systems. Conclusions It may be concluded that the magnetic effect introduces important modifications in the phase boundaries below the magnetic transition line but not at higher temperatures. The introduction of a three-sublattice model for the o phase has reduced the number of adjustable pararequired for a satisfactory description of that phase, from 12 to 4. meters, Acknowledgements Mats Hillert for useful advice, conauthor wishes to express his gratitude to Prof. structive criticism and for the help received during the preparation of this paper. The author is also indebted to Dr. Bo Sundman for his interest in this work, for helpful suggestions and All phase diagrams in this report for his continuous refinement of the optimization program. were calculated with a computer program developed by Bo Jansson at the Division of Physical Metallurgy (35). All least square fits were made by a general least-square fitting program also developed at the Division of Physical Metallurgy (36). The

The

work

was

sponsored

by

the

Swedish

Board

for

Technical

Development.

References P.J.

Spencer

1. 2.

0.

3.

23. B. Uhrenius,

and

Kubaschewski,

F.H. Putland, H. Probst and

Trita-Mac-0217,

J. Iron Steel K.H. Geiger,

1977,

Stockholm,

Z.

Inst. 211 (1973) Physikalische Sweden.

293. Chemie

Neue

Folge

104

(1977)

314

J-O. ANDERSSON

K.

4.

Hack,

H.D.

Nussler,

P.J.

Spencer

and

G.

Inden,

Proc.

CALPHAD

VIII,

Stockholm,

Sweden

(1979) P 244.

B. Sundman and J. Agren, J. Phys. Chem. Solids 42 ,(1981) 297. S.H. Algie and E.O. Hall, Acta Cryst. 9 (1966) 289. A.K. Sinha, Ed. B. Chalmers, J.W. Christian and T.B. Massalski, 15 (1972) 104. B. Sundman and S. Hertzman, Calphad 6 (1982) 67. G. Inden, Proc. Calphad V, 1976, p 111.4. M. Hillert and M. Jarl, Calphad 2 (1978) 227. A. Mustaffa and D.A. Read, J. Magnetism and Magnetic Materials M. Fallot, Annales de Physique 6 (1936) 305. 27 (1978) 423. H. Claus, Solid State Communications

65: 7. 8. 9. 10. 11. 12. 13.

14. 15. 16. 17.

Progress

5 (1577)

in Materials

Science

345.

L. Edlund, Metals Handbook, ASM, 1948 p 1219. Constitution of Binary Alloys, McGraw-Hill, New York 1958. M. Hansen, P. Pataud, J. Physique colloque C4 supp. 35 (1574) 189. R.A. Alikhanov, V.N. Zui, G.E. Karstens and L.S. Smirnov, Fiz. Met. Metalloved.

(USSR)

44

(1977) 652.

18. M.V. Nevitt and A.T. Aldred, J. Applied Physics 34 (1963) 463. J. Brown and F. Kajzar, J. Phys. F:Metal Phys. 7 (1977) 2583. 19. P. Radhakrishna, 1OA (1575) 1847. 20. J. Agren, Met. Trans. and F. Claisse, J. Chem. Thermodynamics 5 (1973) 911. 21. I. Malinsky J. Phys. Chem. 68 (1964) 64. 22. K.M. Myles and A.T. Aldred, 23. 24. 25. 26. 27. 28. 29. 30.

::: ::: 35.

R.K. Saxer, Thesis, Ohio State Univ., 1562. B. Sundman, Thesis, Royal Inst. Techn. Stockholm, Sweden 1981. P. Greenfield and P.A. Beck, Trans. AIME 200 (1554) 253. H. Martens and P. Duwez, Trans. ASM 44 (1552) 484. Z. Jin, Scandinavian J. Metallurgy 10 (1981) 297. L. Kaufman and H. Bernstein, Computer Calculations of Phase Diagrams p 184 Academic Press, New York and London 1570. A. Fischer,K. Lorenz, H. Fabritius and 0. Schlege, Arch. EisenhLittenw. 41 (1870) 485. G. Kirchner and G. Gemmel, Report. Div. of Physical Metallurgy. Royal Inst, Techn. Stockholm, Sweden, 1570. J.F. Smith, Bulletin of Alloy Phase Diagrams 2 (1981) 40. Melting Points of Elements, Bulletin of Alloy Phase Diagrams 1 (1580) 146. A. Hellawell and W. Hume-Rothery, Phil. Trans. Roy. Sot. London, A245 (1557) 417. T. Furukawa and E. Kato, Tetsu to Hagane 61 (1975) 3050. B. Jansson, Internal report 019, Div. of Physical Metallurgy, Royal Inst, Techn. Stockholm, Sweden 1575.

36. J-O. Andersson Techn. TABLE

1

and B. Sundman, Stockholm, Sweden 1982.

Internal

Summary

of

report

037,

Div.

of

Physical

Metallurgy,

parameters

PARAMETER OUTPUT FROM GIBBS ENERGY SYSTEM DEVELOPED AT ROYAL INSTITUTE OF TECHNOLOGY DIVISION OF PHYSICAL METALLURGY, STOCKHOLM, SWEDEN ALL DATA IN SI UNITS PER MOLE FORMULA. ENERGIES IN JOULE, VOLUME 1, REDLICH-KISTER POLYNOM THE EXCESS ENERGY MODEL USED IS WEIGHT: 5.585E-03 FE STATE: FCC WEIGHT: 5.094E-03 STATE: BCC V BCC SUBLATTICE 1, SITES: 1 ELEMENTS: FE V THIS PHASE IS FERROMAGNETIC THE MAGNETIC CONTRIBUTION TO GIBBS ENERGY IS DESCRIBED BY R*TEMP*ln( betha + 1 ) * f(T), T=TEMP/Tc f(T) FOR T < 1 = - 9.0530E-01 * T *"(-1) + l.OOOOE+OO - 1.5300E-01 * T **(3) - 6.8000E-03 * T **(9) - 1.5300E-03 * T **cl51

IN

M3.

Royal

Inst.

THE~oDyN~Ics

OF THE IRON - VANADIUM

SYSTEM

AND FOR T >-_ 1 = - 6.41703-02 * T l*(-5) - 2.0370E-03 * T **(-15) - 4.2780E-04 * T **(-25) THE ANTI-FERROMAGNETICFACTOR: -1 G!jOcBCC>(FE)- G§O(FE) = 1.462403+03 - 8.28208+00 * T **(1) + l.l500E+OO * T * LN(T) - 6.4000E-04 * T **(If TcBO(FE) = l.O430E+03 BO§O(FE) = 2.22003+00 G$O(V) - G§O(V) = 0.0 G§O(FE,V) = - 2.3980E+O4 + 4.5197OEiOO * T "(1) G$l(FE,V) z 8.0200E+03 + 2.52020E+OO * T *Y(l) Tc§O(FE,V) = - l.lOOOE+02 Tc§WBCC>(FE,V) = 3.07503+03 Tc§2(FE,V) = 8.08ooE+o2 Tc$3cBCC>(FE,V) : - 2.1690E+03 BO§O(FE,V) = - 2.2600E+OO FCC SUBLATTICE 1, SITES: 1 ELEMENTS: FE V THIS PHASE IS FERRO~GNET~C THE MAGNETIC CONTRIBUTION TO GIBBS ENERGY IS DESCRIBED BY T=TEMF/Tc R*TEMP*ln( betha + 1 ) * F(T), f(T) FOR T < 1 = - 8.6034OE-01 * T **f-l) + l.OOOOE+OO - 1.7450E-01 * T ""(3) - 7.7550E-03 * T **(9) - 1.74503-03 * T **(15) AND FOR T >= 1 ::- 4.269OE-02 * T **i-5) - 1.3550E-03 * T "*(-15) - 2.8460$-04 * T **(-25) THE ANTI-FERROMAGNETICFACTOR: -3 G§O(FE)= 0.0 Tc§O(FE) = - 2.0lOOE+02 BO§O(FE) = - 2.1000E+OO G§O(V) - G!$O(V)= 9.0000E+03 + 3.55603+00 * T **(I) G§O~FCC>(FE,V) = - 1_818OE+o4 + 1.1600E+OO * T **( 1 ) LIQUID SUBLATTICE 1, SITES: 1 ELEMENTS: FE V G$O(FE) - G$O(FE) = - 1.127403+04 + 1.638780E+02 * T **(l) - 2.2030E+Ot * T * LN(T) + 4.17550E-03 * T **(1) G§OfV) - G§O(V) = 2.1500Ec04 - 9.7630E+OO * T **(l) G§O(FE,V)I - 3,19150E+04 + 3.9510E+OO * T **(I) G§l(FE,V)= 1.4560E+o4 SIGMA SUBLATTICE 1, SITES: 10 ELEMENTS: FE SUBLATTICE 2, SITES: 4 ELEMENTS: V SUBLATTICE 3, SITES: 16 ELEMENTS: FE G~O(FE:V:FE)-~~*G~~~FE)-~*G§O~BCC~(V)-Y~~G§O~FCC~(FE) = - 1.3185803+05+ 2.5980903+01 * T **(l) G~O(FE:V:V)-l0~G~O(FE)-4*G~O~BCC~(V)-16*G~O~BCC~(V) = - 2.4488503+05 - 6.2182303+01 * T **(I)

315