CALPHAD Printed
in
pp.
vol.7, No.4, tne USA.
317-326,
1983 (c)
A THERMODYNAMIC EVALUATION
Jan-Olof Div. Royal
ABSTRACT.
A new evaluation of the subregular model. A set dividual phase is given. lattice model.
OF THE
Andersson
IRON -
TUNGSTEN
0364-5916183 $3.00 + .OO 1983 Pergamon Press Ltd.
SYSTEM
and Per Gustafson
of Physical Metallurgy Institute of Technology S-100 44 Stockholm
Fe-W system has been made using a magnetic multi-sublattice of parameter values describing the Gibbs energy of each The treatment of the u phase is based upon a three-sub-
in-
Introduction Several thermodynamic evaluations of the phase relationships in the iron-tungsten system have been presented during the last few years (l-5). In general, simplified descriptions of the intermetallic phases have been used. No one has taken into account the nonstoichiometric existence range of the intermetallic 1~ phase. The thermodynamics of the so called Laves phase has not been incorporated in earlier work. The accepted phase diagram (6) is mainly based on experimental investigations by Sinha and Flume-Rothery (7) who used a combination of thermal analysis, microscopy, X-ray and dilatometric methods to determine phase boundaries in the iron-rich half of the system. Kirchner et al (1) performed some experimental work together with their theoretical analysis. Their experiments were mainly designed to determine the bcc/fcc and bee/u equilibrium. The phase boundaries between bee and the u phase have also been investigated by Abrahamson and Lopta (8), Reuth (g), and Takayama et al (10). In particular, Takayama tested but did not verify a suggested abnormal change of the solubitity of tungsten in bee in equiliAbrahamson and Lopta (8) also determined brium with the Laves phase below the Curie temperature. Contrary to the detailed knowledge of the the composition of bee at these low temperatures. iron-rich part of the phase diagram the knowledge of the solubility limit of iron in the tungThe values given by Hansen (11) are taken from fairly old insten-rich bee phase is very poor. vestigations
by
Sykes
Information
on
(12,13). the
bcc/fcc
equilibria
has
been
published
those are Hillert et al (lb), Fischer et al (15) and its phase boundaries have been examined by Schneider Rothery (7) who confirmed the existence of a minimum
by various
Kovacova and Kralik and Vogel (17) and on the liquidus at
other
authors
among
(16). The liquid and by Sinha and Humelow tungsten concentra-
tions. Supplementary details of the thermodynamic properties of the liquid was recently published by lguchi et al (18) who carried out a few enthalpy measurements at 1873 K. In a new book by Ortrud Kubaschewski (19) the experimental data on the iron-tungsten system is reviewed. She suggested the existence of a sigma phase at high temperatures although the experimental evidence of a sigma phase at high temperatures although the experimental evidence is rather weak. there are some thermochemical measurements of the Gibbs energy of formation for the In addition, intermetallic
phases
made
by
Rezukhina
Thermodynamic
(22).
A new thermodynamic in this model the
scribed
by
site-fractions
the
site in
model fraction
fraction, each
and
model
for
Kashina ferrite,
(20)
and
February
denoted
sublattice
16,
and
(21). liquid
for phases of sites is
with several sublattices has recently been developed in each subiattice occupied by a component is dei in sublattice s. The sum of the by yi for component
by definition
equal
contribution to the Gibbs energy due to magnetic ordering Hillert and Jar1 (24). The Curie or NtSel temperature and entered as functions of the composition.
Received
Kleykamp
austenite
1983
317
to in the
one.
The model can also handle a the form suggested by lnden (23) average magnetic moment per atom
and are
318
J-O. ANDERSSON and P. GUSTAFSON
The Gibbs energy for the bee (ferrite), system can all be described with one
sten
fee
(austenite)
sublattice
and
and the
liquid
model
Gm=y~eoG~e+yWoGW~RT(y~elny~e+yW~nyW)+y~eyWL~e
The
lattice temperature
stability of bee iron relative to of 1043 K and the average magnetic o bee G Fe
The
phase
_ ‘G;zC
= 1462.4
-
+ 1.15TlnT
-
given
in
to
by 2igren 2.22 for
0.00064T2
J/mol
_ 0 fee GFe
= -11274
Bee tungsten was chosen as standard liquid tungsten was taken from the oGl iq W
Nesor
lattice
(25) with pure bee
a Curie iron, 12)
2. oGTiq Fe
The
iron-tung-
Agren (25). Followof 67 K and a numerical values
stability of liquid iron relative to fee iron was also taken from fee iron was treated as antiferromagnetic with a Neel temperature moment of 0.7. These values are so low that they do not affect the eq.
the
(1)
ing ref. 26 magnetic
in
.W+GT
fee iron was estimated moment per atom set
8.282T
phases
yields:
stability
of
fee
+
163.878T
-
22.02TlnT
+ 0.0041755T2
state for pure tungsten. SETE databank for elements
The Gibbs energy and substances
_ oGbcc W
J/mol
tungsten
= 35397
relative
to
-
9.6197‘
bee
tungsten
was
(3)
J/mol of formation (27).
for
(41 taken
from
Kaufman
and
(3). oGfcc W 1 is
_ oGbcc W
= 10460
+ 0.62761
J/m01
(5)
an
interaction parameter where the comna separates two components that interact This parameter can be concentration dependent according to a Re,$ichThe y fractions are here identical to the ordinary mole fractions. Gm is the are thus defined for completely contribution due to the magnetic ordering. The values of”GFe Lacking experimental infor~t~on on the composition dependence d i sordered paramagnet ic states. of the magnetic transition temperature and on the magnetic moment in the Fe-W system, straight lines were chosen to represent the values between the pure elements. The values for pure iron used by Hgren (25) were accepted and for pure tungsten the values were put to zero due to its paramegnatic nature. The magnetic effect on the Gibbs energy could then be calculated by inserting the values for the Curie temperature and the average magnetic moment per atom in the ex:r!etWei?azz.sublattice. Kister polynomial.
pressions
proposed
by
Hillert
and
Jar1
Thermodynamic There
is
overwhelming
experimental
(24). model
for
evidence
the for
intermetallic the
existence
phases of
two
intermetallic
phases
in the Fe-W system. One of them, the i_t phase, has a measurable range of existence. For this phase a thermodynamic model was now applied which is based upon its crystal structure by taking It has a rhombohedral crystal structure into account the number of atoms in each sublattice. containing 13 atoms per unit cell (28). The atoms are distributed among five groups of sites There is experimental information indicating that two of with 1,6,2,2 and 2 atoms per sublattice. these are occupied by iron, one by tungsten and two by a mixture of iron and tungsten. The same situation is found in the Fe-MO system and it lead Fernandez Guillermet (29) to describe the ii It yields the following expression, phase with a three-sublattice model Fe7M2(Fe,Mj4. Gu = y3 OGp m Fe Fe:W:Fe
30 P + ‘W GFe:W:W
3 + 4RT(yFelny:,
+ y:lny:)
+ ~~~~~~~~~~~~~~~
(6)
The parameter ‘Gu iron in the first, is the Gibbs energy of formation of a u phase wit D tungsten in the %&&eand iron in the third sublattice. The parameter >EeIX:W tj :;;t;;;r-~-~~~ sponding quantity when there is tungsten in the third sublattcce. The y site fractions in the third sublattice. In the following thermodynamic F?eZmen t ! he interaction parameter in the u phase was assumed.to be zero because the information on the IJ phase is not sufficient for determining its value. The phase which appears below about 1330 K is of the hexagonai Laves type. Its range of existence is not known and it was treated as a stoichiometric phase Fe2W. To represent this phase in the thermodynamic calculations a two-sublattice model was used where the first sublattice has two sites occupied by iron and the second sublattice has one site occupied by tungsten
THERMODYNAMICSOF THE IRON - TUNGSTEN SYSTEM
red
The sigma phase in the evaluation.
was
assumed
to
be metastabie
Selected
in
the
binary
Fe-W
319
system
and
was
not
conside-
data
The following selected set of experimental data was processed in PARROT, a newly developed thermodynamic optimization program (30,31) in order to obtain the best possible set of thermodynamical parameters for describing the phase diagram. The liq/!~/bcc three-phase temperature was placed at 1910 + 7 K by Sykes (7) in agreement with experimental results by Schneider (17) and Sykes (13). The composition of the liquid in this three-phase equilibrium was taken from Schneider (17), and the composition of the tungsten-rich bee phase was taken from Sykes (13). The composition of the u phase in this equilibrium was not included in the optimization. A few of the liquidus and solidus determinations at low tungsten content made by Sinha (7) were used in order to fit the minimum in the liquidus. The enthalpy measurements in the liquid at 1873 K made by lguchi et al (IS) were accepted with a suggested experimental error of 15 percent. The temperature for the three-phase equilibrium liq/bcc/p was placed 1823 + 5 K according to Sinha (7) although Schneider (17) and Sykes (13) reported a temperature 20 K lower. All three compositions at this equilibrium seem to be reasonably well established by Sinha (7) and their values were accepted. The solubility of tungsten in Fe-rich bee phase at temperatures between 873 and 1573 K has been determined with rather good accuracy by Kirchner et al (1) and Takayama et al (10). A selected set of their experimental tie-lines was used in the optimization procedure. The bee/p tie-lines measured by Takayama et at (10) probably give too much tungsten in the p phase and therefore only the bee end point of the tie-lines was used. The temperature for the three-phase equilibrium bcc/Laves/u is 1333 i 20 K according to Sinha (7). Sykes (13) reported that the temperature should be close to 1313 K. This temperature is not important for the rest of the optimization and the value of 1333 K was accep.ted. The two-phase field between austenite and ferrite has been thoroughly investigated by Kirchner et al (1) and by Fischer et al (15). The work of Hiilert et al (14) was of a more preliminary type. The proposed ~ximum tungsten content of the so called y-loop is lower for Fischer and Hillert than for Kirchner. In the later work a very carefully controlled isothermal equilibration heat treatment was used while Fischer used a The tie-lines published by Kirchner et al (1) more uncertain dynamic heat treatment technique. were thus accepted and used together with a single tie-line from Hillert et al (14) to optimize the bccifcc phase boundaries. Results
of
optimization
In the early stage of the present evaluation it was intended to use only regular-solution parameters but it was soon realized that a subregular-solution parameter in bee was needed in order to reproduce the low solubility of iron on the tungsten-rich side at high temperatures. During the optimizing procedure the main effort was focused on obtaining good agreement between the experimental three-phase equilibria at ,823 and 1910 K and the corresponding values obtained In order to succeed it was necessary to include a subregular-solution parameter by calculations. On the other hand there were not in the interaction energy expression for the liquid phase. enough data for evaluating its temperature dependence. It was thus treated as temperature independent. All the parameter values obtained in the present assessment are summarized in Table I and the complete phase diagram is presented in Fig. 1. Comparisons with the experimental data are given in the following diagrams. As shown in Figs. 2 and 3 the calculated phase diagram is information given by Sinha (7) and Schneider (17). in excellent agreement with the experimental Fig. 3 shows that the calculated iron-rich limit of the u phase is in good agreement with data by Sinha (7). Fig. 2 shows that it is also in fair agreement with a value given by Kirchner et al (I) at 1573 K. At 1373 K it falls between the values given by Kirchner et al (I) and Takayama et al (to). The Gibbs energy of formation for the Laves phase was adjusted to make the threedependence of the Laves phase phase equilibrium bcc/Laves/p appear at 1333 K. The temperature 4 shows the solubilities of the u was adjusted to make it stable down to at least 500 K. Fig. They are in very good agreement with the experimental information and Laves phases in bee iron. At lower temperatures the deviations given by Takayama et al (10) at medium high temperatures. become larger. This is a well known phenomenon and might be due to the slow equilibration at low The liquidus and solidus determinations by Sinha (7) are plotted in Fig. 5. The temperatures. scatter of the data is rather large and the measured melting point of pure iron is about 5 K too low, The temperatures at low tungsten contents should thus be adjusted to allow a correct The tungsten content at the temperature comparison between calculated and measured values. minimum can be directly compared with the value suggested by Sinha (7), xW=O.O44. The calculation gives the value 0.047 which is within a reasonable accuracy. The calculated SO called y-loop
is
plotted
in
Fig.
6
together
with
some experimental
information.
The
calculated
J-O. ANDERSSON and P. GUSTAFSON
FIG. 1 The complete Fe-W phase diagram according to the present evaluation. The greek letters @., Y and h are used to denote the bee,
0
0.20
0.40 MOLE-FRACTION
0.60
0.80
0.20 MOLE-FRACTION
Laves
phases.
1.00
FIG. 2 Part of the Fe-W phase diagram according to the present evaluation values
0.10
and
W
m SCHNEIDER 8 ABRAHAMSON A KIRCHNER
0
fee
0.30 w
0.40
0.50
together with experimental of phase boundaries.
THERMODYNAMICSOF THE IRON - TUNGSTEN SYSTEM
FIG. 3 Part of the Fe-W phase diagram according to the present evaluation together with experimental information on phase boundaries.
0
0.10
0.20
0.30
MOLE-FRACTION
1700
2 z-I “,
I w 5 az z a lo F +
0.40
0.50
W
_
1600
.-
1500
.
1400..
.
1300
1200
Q+ ABRAHAMSON
1100
1000 I X
800
u
0
FIG. 4 The solubilities of the u and Laves phases in the bee phase according to the present evaluation and previous experiments.
-r
A
BCCLAVES
KIRCHNER TAKAYAMA
BCCDIU BCC /LAVES
TAKAYAMA SINHA
BCC/!‘tU
.
-.
I 0.02
0.04 MOLE-FRACTION
0.06 U
0.08
0.10
321
322
J-O.
ANDERSSON and
P.
GUSTAFSON
1 825 m SINHA
LIO-BCC
1 820 z >
izi xl 815 t
Comparison mental and and liquidus
w
.a
rich
51 810 3
alloys
FIG. 5 between the expericalculated solidus of bee in ironwith
tungsten.
LL
I-
1 805
I.
1800+ 0
0.04
0.08 MOLE-FRACTION
0.12
0.16
c 0.20
W
1900 1800
m
KIRCHNER
1700 1600
FIG. The ted
1000 900 0
5.00
10.00 MOLE-FRACTION
is.00 W *103
20.00
25.00
experimental y-loop in
6 the
and calculaFe-W system.
THERMODYNAMICS OF 'THEIRON - TUNGSTEN SYSTEM
0
KLEYKAMP
323
C2i >
FIG. 7 The assessed Gibbs energy of fornmtion for the u phase in the Fe-W system together with the results of previous calculations and experiments. The curve from the present work refers to Fe0.6Wo.4*
CALCULATIONS:
ROB
+ x
-500, 1400
1200
I000
TEMPERATUE
0 -
I
13
-50
A
KIRCHNER KAUFMAN UHRENIUS
I600
1800
(5) 2000
KELVIN
4
t
FROM EXPERIMENTS: ._
EI REZUKHINA o KLEYKAMP
c20> (21)
’
FIG. 8 The assessed Gibbs energy of formation for the Laves phase in the Fe-W system together with some experimental values. The curve from the present work refers
-504 1000
. 1200
1400
TEMPERATURE
1600 KELVIN
1600
c 2000
to
Feo.667Wo.333’
P. GUSTAFSON
J-O. ANDEKSSON and
324
two-phase field is completely consistent with the though the maximum tie-line was given less weight is some thermochemical information available from
one determined by Kirchner et al (1) even than the others during the optimization. There experiments which was not used in the optimienergy of formation for the u and Laves Rezukhina (20) and Kleykamp (21) gave the Gibbs A comparison between their experimental reobtained directly through emf measurements. and the results of various calculations is made in Figs. 7 and 8.
zation. phases sults
All grams
calculated
in
Figs.
three-phase
equiiibrium
temperatures
and
compositions
are
given
in
the
dia-
2-6. Discussion
Most of the experimental compositions reported for the p phase fall at about 40 atomic percent W which corresponds to Fe W . In some discussions (6,7) this has been considered as the it is recognized that the u phase has a crystal structure center of the existence range 2 1? bough may seem confusing and the lack of clarity may be caused by the fact corresponding to Fe W . This that Arnfelt and WeZ6 tgren published their classical paper on the p phase in Swedish with a short English summary (28). They reported compositions in the range 40 to 46 atomic percent and the upper limit corresponds to the ideal composition of Fe W . The model used in the present evalua86 tion alsohas Fe W as the upper limit and it is intere tlng to note that the mere application of composition approach 46 atomic percent at low temperatures althis model Imakeg @he calculated though all experimental values used in the assessment were much lower. Arnfelt and Westgren (28) mentioned that technicai ferro-tungsten with 85 weight percent tungsten at low temperatures consists of bee tungsten and Laves phase but no u phase. This result could easily be included in the present assessment by making the Laves phase more stable at low temperatures. However, this was n8t done, partly because Arnfelt and Westgren (28) did not suggest any value for the three-phase equilibrium temperature, Laves/u/bcc. Another reason was the suspicion that the impurities in technical ferro-tungsten may have been responsible for the absence It
of
the
u phase.
is
interesting
to
compare
the
Gibbs
energy
of
formation
of
the
the Fe-W and Fe-MO systems. The recent assessment of the Fe-MO system A comparison of the results with the same methods as the present work. obtained from emf measurements, gives the same picture in both systems. satisfactory but the experimental information falls consistently above See Figs. 7 and 8 in the present work and Figs. 10 and 11 in the Fe-MO system at1 the experimental and calculated values fat1 within the error (20) experimental uncertainty. On the other hand, Kleykamp (21) claims certainty is much smaller which is surprising in view of the fact that Fe-MO system was considerably larger than Rezukhina’s.
intermetallic
phases
in
(29)
was made with the experimental information, The agreement is rather the calculated curves. report. For the Fe-W bar given by Rezukhina’s that his experimental unhis uncertainty in the
The Fe-W and Fe-MO phase diagrams are very similar apart from the presence of the R and u phases at a high temperature range in the Fe-MO system. Another difference is to be found in the extension of the bee MO and W phases. At low temperatures the solubility of iron is much lower in tungsten than in molybdenum. At high temperatures, solubility in tungsten shows a retrograde behaviour whereas the solubility in molybdenum shows an opposite effect. The retrograde behaviour is common among systems with one high-melting element. The difference in behaviour between the Fe-W and Fe-MO systems is probably closely related to the difference in the metastable bee miscibility gap. In the Fe-MO system this gap closes at a temperature of about 1800 K but in the Fe-W system it is stable to much higher temperatures. Acknowledgements The structive
authors criticism
diagrams Division
in of
The
wish
to express and for the
this report have Physical Metallurgy
work
was
supported
their gratitude help received
been
by
calculated (32).
The
Swedish
to during with
Board
Prof. the
Mats Hillert preparation
a computer
for
program
Technical
43: 5.
G. L. L. 8. B.
Kirchner, Kaufman Kaufman Uhrenius Uhrenius,
H. Harvig and B. Uhrenius. Met. Trans. and H. Nesor, Met. Trans. 6A (1975) 2123. and H. Nesor, Calphad 2 (1979) 55. and L. Kaufman, Calphad 3 (1979) 223. Calphad (1980) 4 178.
4
(1973)
for useful advice, this paper. All
POLY developed
Development.
References 1. 2.
of
1059.
at
conphase the
THERMODYNAMICSOF THE IRON - TUNGSTEN SYSTEM
6.
R.
Hultgren,
P.
Desai,
0.
Hawkins,
dynamic Properties of Binary A.K. Sinha and W. Hume-Rothery, ;:
9. 10. 11. 12.
13. 14. 15. 16. 17. 18. TV. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. TABLE
M.
Gleiser
and
Al 10~s. American J. Iron Steel
K.
Society Inst.
Kelley,
325
Selected
Values
of
the
Thermo-
for Metals 1973. 205 (1967) 1145.
Abrahamson and S.L. Lopata, Trans. AIME 236 (1966) 76. AIME 215 (1959) 216. Reuth, Trans. T. Takayama, Y.W. Myeong and T. Nishizawa, Trans. Japan Inst. of Metals 22 (1981) 315. McGraw-Hill New York 1958. M. Hansen, Constitution of Binary Alloys, W.P. Sykes, Trans. AIME 73 (1926) 968. W.P. Sykes and K.R. Horn, Trans. AIME 105 (1933) 198. H. Hiilert, T. Wada and H. Wada, J. iron Steel Inst. 205 (1967) 539. W.A. Fischer, F. Lorenz, H. Fabritius and D. Schegel, Arch. Eisenh.w. 41 (1970) 489. E.P.
C.
K. R.
Kovacova Schneider
and F. Kralik, and R. Vogel,
Y. Iguchi, S.
Kovove Arch.
Materialy Eisenh.w.
11 (1973) 93. 26 (1955) 483. to Hagane 68 (1982) 633. Nobori, K. Saito and T. Fuwa, Tetsu Iron-Binary Phase Diagrams. Springer-Verlag New York (1982) J. Chem. Thermodynamics 8 (1976) 519. and T.A. Kashina,
0. Kubaschewski, T.N. Rezukhina H. Kleykamp, J. Less-Common Metals 71 (1980) 127. B. Sundman and J. Agren, J. Phys. Chem. Solids 42 (1981) 297. G. Inden, Proc. Calphad V, 1976, p 111.4. M. Hillert and M. Jar-l, Calphad 2 (1978) 22.7. J. Agren, Met. Trans. 10A (1979) 1847. S. Hertzman and B. Sundman, Calphad 6 (1982) 67. SGTE databank 1982. Compiled by I. Ansara. H. Arnfelt and A. Westgren, Jernkontorets Annaler 19 (1935) 185. A. Fernandez Guillermet, Calphad 6 (1982) 127. Internal report 039 Div. Phys. Met., Royal Inst. Techn, B. Jansson, Internal report 040 Div. Phys. Met., Royal Inst. Techn. B. Jansson, internal report 019 Div. Phys. Met., Royal inst. Techn. B. Jansson,
I
Summary
of
Stockholm, Stockholm, Stockholm,
p.
164.
Sweden. Sweden.
Sweden.
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 IN M3 THE EXCESS ENERGY MODEL USED IS 1, REDLICH-KISTERPOLYNOM FE W
STATE: FCC STATE: BCC
FCC SUBLATTICE 1, SITES: ELEMENTS: FE W
MASS: 5.5847E-03 MASS: 1.8385E-03
7
THIS PHASE IS FERROMAGNETIC THE MAGNETIC CONTRIBUTION TO GIBBS ENERGY IS DESCRIBED BY T=TEMF/Tc R*TEMP*ln( betha + 1 1 * f(T), f(T) FOR T c 1 = - 8.60346-01 * T **( -1) + l.OOOOE+OO - 1.7450E-01 * T **f 3 f - 7,7550E-03 * T **( 9 ) - 1.745OE-03 * T **( 15) AND FOR T >= 1 = - 4,2690E-02 * T **( -5) - 1.3550E-03 * T **c-15) - 2.8460E-04 * T **(-25) THE ANTI-FERROMAGNETICFACTOR: -3 G$O(FE) - G§O(FE) : 0.0 Tc!$OfFE)= - 2.010E+OZ BG§G(FE) = - 2.100E+OO G§O(W) - G$O(W) : 1,0460E+o4 + 6.276E-01 * T **( 1 ) Tc§O(W) = 0.0 BO$OtFCC>(W) : 0.0 _____ G§D(FE,W) 1:3.22648+04 - 6.4172E+OO * T **( 1 f
326
J-O. ANDERSSONand P. GUSTAFSON
BCC SUBLATTICE 1, SITES: 1 ELEMENTS:FE W THIS PHASE IS FERROMAGNETIC THE MAGNETICCONTRIBUTION TO GIBBS ENERGYIS DESCRIBEDBY T=TEMF/Te R~TEMPuln(betha + 1 ) * f(T), f(T) FOR T c 1 = - 9,0530E-01* T N*( -1 ) + 1.0000E+OO- 1.53001%01* T **( 3 ) - 6.80003-03* T **( 9 ) - ?.5300E-03* T **( 15) AND FOR T >= 1 E - 6,4170E-02* T **( -5 ) - 2.0370E-03* T **(-15) - 4.270OE-04* T **(-25) THE ANTI-~ERR~GNETI~ FACTOR: -1 G§O(FE)- G§O(FE)= 1.46243+03- 8.2820E+OO* T **( 1 ) + l.l500E+OO* T * LN( T ) - 6.4DOO~-04* T **( 2 ) Tc§O(FE) = l.O43E+03 BO§O(FE) = 2.2203+00 G$O(W)- G$O(W)= 0.0 Tc§O(W)= 0.0 BO§O(W)= 0.0 w_..-G§O(FE,W) = 4.52073+04- 1.8501E+OO* T **( 1 ) G§l(FE,W) = - 1,3409E+O4 LIQUID SUBLATTICE 1, SITES: 1 ELEMENTS:FE W G§O(FE) - G$O(FE)= - l.l274E+04+ 1.63883+02ffT **( 1 ) - 2.203OE+Ol* T * LN( T ) + 4.17553-03* T **( 2) G~O(W) - G§0(W)= 3.5397E+04- 9,61903+00* T **( 1 I m--mG§O(FE,W) = 1.99873+04+ 6.827E-01* T **( 1 ) G§l(FE,W) = - 1.20903+04 MU-PHASE SUBLATTICE 1, SITES: 7 ELEMENTS,FE SUBLATTICE 2, SITES: 2 ELEMENTS:W S~LATTICE 3, SITES: 4 ELEMENTS:FE W G~O(FE:W:FE)-7.0*G§O~FCC>(FE)(FE) = 6.2374E+04 G§O~MU-PHASE~(FE:W:W~-7.O*G~OCFCC>(FE)-2.O*G~O(W)-4.G~G~G(W) = - 6.52508+04 + 2.53203+01l T **( I 1 LAVES-PHASE SUBLATTICE 1, SITES: 2 ELE~NTS: FE SUBLATTICE 2, SITES: 1 ELEMENTS:W G§O(FE:W) - Z.O*GSO(FE) - GSo(W) = - 1.4911E+04+ 6.0000E+OO* T **( 1 )