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Thermodynamic assessment of the CoFeGd systems
Journel of
AH~) COM~)UHDS ELSEVIER
Journal of Alloys and Compounds 226 (1995) 33--45
Thermodynamic assessment of the Co-Fe-Gd systems Zi-Kui Liu a, Weijing Zhang b, Bo Sundman
a
"Department of Materials Science and Engineering, Royal Institute of Technology, S-I O044 Stockholm, Sweden b Department of Materials Science and Engineering, Universityof Science and Technology, Beijing, Beijing 100083, People's Republic of China Received 14 October 1994
Abstract
The thermodynamic properties of the ternary Co--Fe--Gdsystem are investigated,based on the three binary systems, i.e. Co-Fe system by Fern~dez Guillermet, and Co-Gd and Fe-Gd from the present work. The assessment is carded out by means of the computer programs PARROTand THERMO-CALC,using models for the Gibbs energy of individual phases. The ternary system contains eight different intermetallic compounds and they are all treated as line compounds. Good agreement is obtained between the calculation and experimental results in the two binary systems and the ternary system. Keyword~.:Thermodynamic properties; Binary systems
1. Introduction
Intermetallic compounds formed between rare earth and transition metals, especially 3d elements, are of particular interest regarding their magnetic properties [ 1] and their reversible absorption of hydrogen gas at room temperature and nearly atmospheric pressure [2]. However, there have been few thermodynamic studies of rare earth-transition metal alloys and experimental data are scarce, though it is undoubted that self-consistent thermodynamic descriptions of alloy systems will greatly help in alloy design and processing. The phase diagram, which is a presentation of the thermodynamic properties of the alloy system, is used extensively in the field of metallurgy and materials science. The importance of phase diagrams and the thermodynamic properties of alloy systems is reflected in the numerous compilations of phase diagrams and thermodynamic data. However, there is usually no check of consistency between the thermodynamic data and the suggested phase diagrams. Thermodynamic modelling is necessary if we want to couple phase diagram and thermodynamics. It is the only method by which various types of experimental information can be compared and by which the description of all the thermodynamic properties of a system can be optimized. This method is often referred to as the CALPHAD (calculation of phase diagram) method [3]. In this method, the thermodynamic 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved
SSD10925-8388(95)01578-7
properties of the alloy systems are analyzed using thermodynamic models for the Gibbs energy of individual phases. The models involve adjustable parameters that are evaluated from the experimental thermodynamic and phase diagram information. This is made possible by increasingly powerful computers and computer programs. When a consistent description of the thermodynamic properties of the alloy system is obtained, in principle, any kind of diagrams of interest can be calculated, which is outside the capacities of the ordinary compilations. The present work deals with the evaluation of the thermodynamic properties of the Co-Fe--Gd system, where some important thermodynamic quantities have been measured in the Co-Gd and Fe-Gd binary systems, such as the enthalpy formation of.intermetallic compounds and the heat of mixing in the liquid phase. An assessed thermodynamic description of the Co-Fe--Gd system will be useful for the evaluation of other rare earth-transition metal alloy systems for which there is less experimental information.
2. Thermodynamic models
The Gibbs energy of individual phases is described by sublattice models [4] relative to the so-called 'standard element reference' (SER), i.e. the enthalpies of the pure elements in their defined reference phase at 298.15 K.
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
34
518 11 692 (_1 A = 112----5+ 15 975 ~p
2.1. Liquid, fc.c., b.c.c, and h.c.p, phases The liquid, tic.c, b.c.c, and h.c.p, phases are treated by one sublattice model which is equivalent to a substitutional model with the Gibbs energy expressed as 4'_ o 4' o G m - XFe G Fe + X c o
4' Gco +
E
4' Gm+
rng
~_
4" Gm
i 4"
4' ~,xixjTci4'j + XrzeXcoXodTcFe,
i
i
i
+ XcoXcd~'_~L~co. Cd(XCo-- XCd)
(8)
Co, C d
i
+ XF~XcoXcdLF~c,Co,Cd
(2)
where LFe. 4" Co, L~o.ca and LF,. co are the binary interaction parameters, and L~,, co, co is the ternary interaction parameter set to be zero, as a result of a lack of experimental data. /-~,, Co is taken from Fern~dez Guillermet's assessment [ 6]. Lc~o.Cd and L~,cd are to be evaluated in the present work. L ~ can be temperature dependent and two terms are usually sufficient, i.e.
(:3)
L~=a+bT
The magnetic contribution to the Gibbs energy in f.c.c., b.c.c. and h.c.p, phases (mgG~m) is described by
mgGOm=RTln(/3+ 1)f("r)
X~
f(~-)=1 1.140p + 497~p-I
79 :~---~))/A + 135 + (5)
for ~-< 1 and .rf(.'r) = - (~0 + ~"r-15 + 21.1_~)/A
(9)
+ ~ x : f l ~ ,4"j + XF~XcoXcd/3F~, 4" Co. Cd
i
i,j
where °Tcf and °/3/~ are unary quantities and Tc~j and/3~j are the binary quantities. The Fe-Gd and Co-Gd binary quantities, i.e. TcF~. 4' Cd and flF~. 4' ca , and the ternary quantities, i.e. 4' 4' T~Fe,Co.Cd and/3F~, co. Gd, are set to zero, as a result of a lack of experimental data and extremely low solubilities. No ternary interactions are included, for the same reason.
There are seven stable intermetallic compounds in the CoGd system and four in the Fe-Gd system, i.e. C017Gd2, C05Gd, C07Gd2, C03Gd, C02Gd, C03Gd4 and CoGd3, and FelTGd2, Fe23Gd6, FeaGd and Fe2Gd. No ternary compound has been reported. All the intermetallic compounds are modelled by a two-sublattice model, with the transition metal elements on one sublattice and the rare earth element on the other sublattice, i.e. MaGdB, where M is used as an abbreviation for a mixture of Co and Fe. As a result of a lack of experimental measurements, it is assumed that the NeumannKopp rule applies for the heat capacity, i.e. A Cp = 0. Thus, the Gibbs energy per mole of formula unit MAGdB can be expressed as GMAGdB __ • Og'2MAGdB d.. • 0t'2MAGdB m - - Y F e ~JFe:Gd ~ Y C o ~-~Co:Gd
(4)
where ~"is defined as T/T~, with T¢ the critical temperature for magnetic ordering, i.e. the Curie temperature (T~) for ferromagnetic ordering and the Nrel temperature (TN) for antiferromagnetic ordering;/3 is a quantity related to the total magnetic entropy and, in most cases, is set equal to the Bohr magnetic moment per mole of atoms, f('r) represents the polynomials obtained by Hillert and Jarl [7] based on the magnetic specific heat of iron, i.e. 474(1
/34' = Ex/°/3
2.2. Intermetallic compounds
+ XF~XCd~,iL~o, c~(XF, -- XCd) i i
for ~-> 1, where
E X i o Tci4, +
(1)
G m - XFeXCoE L F , . Co(XF~-- Xco)
_~'79~ --1
and p depends on the structure; p = 0.4 for a b.c.c, structure and p = 0.28 for the others. T~ and/3 are described by Zc4' =
where °G/* is the molar Gibbs energy of the element i ( i - Fe, Co, Gd) with the structure ~b in a non-magnetic state, from the work of Dinsdale [ 5]. EG~mis the excess Gibbs energy, expressed in Redlich-Kister polynomials as E
(7)
]
0 4' XGd G G d
+ RT(XF, In XFe+ Xco In Xco + xco In XCd) +
_ 1~
(6)
+ mgaMaCdB+ ART{yFe ln(yF¢) + Yco ln(Yco) }
(10) O/'~MAGdB - - A 0g'~hbcc - - lqDOt"2hhcp __ a
VFe:Gd
•"
"-'~
u "-'Gd -- "1 + biT
( 11 )
bET
(12)
0/'7_MAGdB __ A0/'Thhcp - - D0/2_hhcp - - ~ + UCo:O d .'~ U C o u "JGd --~2
Here, °GFc:Ca represents the Gibbs energy of formation of a compound with all sites on the first sublattice filled with Fe and all sites on the second sublattice filled by Gd. °Gco:Gd has a similar meaning but for Co. °G~C, ° G ~ and °Gc~o~p are the Gibbs energies of the respective pure elements in a hypothetical non-magnetic b.c.c, or h.c.p, structure. YFc and Yco are the so-called site fractions and represent the mole fractions of Fe and Co in the first sublattice respectively. The parameters a/and b/, with i being 1 or 2, should be evaluated separately in the Co-Gd and Fe-Gd systems. When there are measurements of the heat capacity, more terms may be added, i.e.
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
35
Table 1 Invariant reactions in the Co-Gd system Reaction
T, K (xgqo)
b.c.c. ~ h.c.p. liq. + h.c p. ~ CoGd3 liq. -o Co3Gd4+ CoGd3 liq. + Co:~Gd~ Co3Gd4 liq. + Co:~Gd--, Co2Gd liq. + Co-,Gd2-o Co3Gd liq. + Co:~Gd"-*C07Gd2 liq. + Co 7Gd2~ C05Gd liq. --*Co ,TGd2 liq. ~ CojTGd2+ f.c.c. CsGd --~Col7Gd2+ C07Gd2 f.c.c. --*h.c.p.
Present work
Buschowand van derGoot [9]
Ge et M.[10]
1262(0.025) 1053(0.261) 918(0.368) 943(0.391) 1388(0.555) 1549(0.703) 1570(0.741) 1619(0.820) 1658(0.895) 1643(0.933) 1123 695
1053
1053 918(0.358) 943 1389 1550 1568 1623 1643 1614(0.925) 1123 -
O['TMAGdB _ A O / ' T h b c c _ / ~ / " 2 _ h h c p 'J Fe:Gd za UFe u *.JGd
=a+bT+cTln(T)
+dT2 + e T - l + f T -3
(13)
All intermetallic compounds are ferromagnetic except CoGd 3. As a first approximation, the magnetic contribution to the Gibbs energy mgamMaGdBis described by mg
GM mA G d B = R T I n ( / 3 + 1)f(~-)
(14)
with f(~-) from Eqs. ( 5 ) - ( 7 ) , though Eqs. ( 5 ) - ( 7 ) were derived for iron. Tc and/3 are taken from the measured critical temperature and the mean Bohr magnetic moment per mole of formula unit. In the ternary system, they can be represented by TcMAGdB --. 7" M A G d B -L. x, T M A G d B - - Y F e -t c F e : G d - - Y C o x c C o : G d
i
MAGdB
+ yFeYCo)"~. Tcco. Ve:~d(YFe--YCo)
i
(15)
i
..a_., Fe:Gd /31VIAGdB_- -.Y F e / J/~MAGdB
f~MAGdB
--YCobJCo:Gd
i
MAGdB
q- YFeYCoE fl~o. Fe:Gd(YFe-- YCo)'
(16)
i
3. Experimental information 3.1. C o - G d system
The phase diagram of the C o - G d system was measured by Novy et al. [8] and Buschow and van der Goot [9], and more recently by Ge et al. [ 10], as discussed by Okamoto [ 11 ]. The results of Novy et al. are quite different from those of the studies in Refs. [9,10], so are not used in the present work. The last two investigations [ 9,10] gave the same kind of phase relationships, i.e. two eutectic reactions, congruent melting of Co17Gd2 and incongruent melting of all other
(0.358) 938(0.365) 1388 1548 1573 1628 1658 1638(0.925) -
compounds. Co5Gd is unstable at low temperatures, and decomposes into Co,7Gd2 and CoTGd2 at about 850 °C. Both CosGd and Co27Gd/were reported to have a certain homogeneity region at high temperatures [9,10], but they are treated in the present work as stoichiometric compounds, because of limited information. Table 1 lists the various reaction temperatures and the composition of the liquid phase, together with the calculated values from the present work. The heat of mixing in the liquid phase at 1823 K was measured by Nikolaenko and Turchanin [ 12] for the entire composition range. The enthalpies of formation of the compounds were measured by various authors [ 13-15], with the most complete set being that by Colinet and coworkers [ 15,16], which is used in the present assessment. The heat capacities of CosGd and Co2Gd were measured by Keller et al. [17] and Leghari [18] in the temperature ranges 5-300 K and 300-473 K respectively. However, Leghari's measurements are not used in evaluating the properties of Co2Gd, for the reason given later. The measurements by Keller et al. are used to evaluated the entropy of formation of CosGd and some low temperature coefficients in the heat capacity expression. Baricco et al. [ 19] measured the heat capacity of Co36.8Gd63.2 in the temperature range 800-980 K, which is a mixture of Co3Gd 4 and CoGd3 below 910 K, and liquid above 910 K. There are numerous magnetic measurements of the compounds. The interest of the present work is the critical magnetic ordering temperature and the Bohr magnetic moment. The values measured by Burzo [20] and Lemaire [21,22] are presented in Table 2, and those by Burzo are used. 3.2. F e - G d system
The F e - G d system was included by Kubaschewski [ 23 ] in the compilation of iron-binary phase diagrams with four intermetallic compounds. In the work by Novy et al. [24], seven intermetallic compounds were detected, which were not confirmed by the other measurements by Copeland et al.
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
36
Table 2 Measured T¢ (K) and/3 (P,R) values in the Co--Gd system
Burzo [ 20] Lemaire [21,22]
T¢ /3 T¢ /3
CoGd 3 a
Co3Gd4
Co2Gd
Co3Gd
Co7Gd2
CosGd
Col7Gd 2
130 a 21.5 a -
233 26.0 -
395 4.95 404 4.9
611 2.3 612 2.2
767 2.6 775 1.65
1020 1.4 1008 1.2
1222 14.1 1209 14.4
a CoGd3 is antiferromagnetic and its TN and/3 values need to be multiplied by - 3 when put into the PARROTprogram. Table 3 Invariant reactions in the Fe-Gd system Reaction
T, K ( ~ q )
b.c.c. ~ f.c.c. + liq. liq. + f.c.c. ~ Fe17Gd 2 liq. + FelTGd2 ---~Fe23Gd6 liq. + Fe23Gd 6 ~ Fe3Gd liq. + FeaGd ~ Fe2Gd liq. ~ FeaGd + h.c.p. b.c.c. ~ h.c.p. + liq. f.c.c. +FelTGd2 ~ b.c.c.
Present work
Refs. [27,28]
Ref. [25]
Ref. [26]
1653 (0.910) 1604(0.881 ) 1556(0.766) 1429 ( 0.523 ) 1355 (0.440) 1105 (0.264) 1512(0.040 b) 1197 c
1653 + 10 1608 + 10 1553 + 10 1433 + 10 1353 + 10 1103 + 7 _ 1205 4-5
1661 1593
1587
1423 a 1353 1118
1446 ~ 1334
1183
a The intermetallic compound Fe23Gd6 was not detected.
~x~ = 0.0044. ~ x ~ =0.998 717, x ~ : = 0.999 724. Table 4 Measured T¢ (K) and/3 (/~B) values in the Fe-Gd system
Tc /3
3.3. Co-Fe-Gd system
Fe2Gd
Fe3Gd
Fe23Gd6
FelTGd2
782 3.35
728 1.6
468 14.8
472 21.2
[25], Spedding et al. [26] and Savitsky and coworkers [27,28]. In the work by Copeland et al. and Spedding et al., only three intermetallic compounds were found, i.e. Fe17Gd2, Fe3Gd and Fe2Gd. Another compound (Fe4Gd) was detected by Novy et al. and Savitsky et al. [28], but Novy et al. presented a congruent melting of the compound and Savitsky et al. an incongruent melting. In line with the other Fe-Re systems, this phase was given the formula Fe23Gd6, with an incongruent melting, as suggested by Kubaschewski. Table 3 depicts the various reaction temperatures and compositions of the liquid phase, together with the calculated values from the present work. The heat of mixing in the liquid was measured by Nikolaenko and Nosova [29] at 1850 K. The enthalpies of formation of Fel7Gd2, Fe3Gd and Fe2Gd are taken from the work by Colinet et al. [ 16]. The heat capacity of Fe2Gd was measured in the temperature range 15-300 K by Germano and Butera [30], from which its entropy at 298 K can be evaluated. The magnetic properties of the compounds were reviewed by Wallace and Segal [ 31 ], from which the critical magnetic ordering temperatures and the atomic Bohr magnetic moments are taken (see Table 4).
The only available experimental information on the phase equilibria in the literature is the isothermal section at 1323 K, measured by Atiq et al. [ 32], in which the solubility limits of the compounds M23Gd6, MsGd and MTGd2 in the ternary system were reported. For MGd3, Poldy and Taylor [33] mentioned that the solubility limit of Fe in (Co~ _y,Fey)Gd3 is y=0.1. Upon further addition of iron, other phases appeared. However, Poldy and Taylor did not identify what the other phases are, but only mentioned the presence of gadolinium, based on the observation of a magnetic transition at 270 K, which is the Curie temperature of metallic gadolinium. Furthermore, they did not mention at what temperature the solubility limit is located, though it was pointed out in a later report [34] that the magnetic properties do not change after annealing at 700 K and the X-ray photographs were taken at 300 K. The magnetic properties have been investigated by several authors. Belov et al. [35] measured the Curie temperature and the Bohr magnetic moment of (Coo.l,Feo.9)2Gd, and Burzo [36] measured the Bohr magnetic moment of the pseudo-binary system Fe2Gd-Co2Gd. Hubbard and Adams [ 37 ] presented the Bohr magnetic moment measurements of (Co~-x,Fex) 5Gd with x = 0-1. The Curie temperatures of the pseudo-binary system Fe~7Gd2-Co~TGd2 were measured by Chen et al. [38].
37
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33--45 0
[
-4 -5 E
-6
-~o5
-8
I
I
works by minimizing an error sum, where each of the selected data values is given a certain weight. The weight is chosen by personal judgment, and changed by trial and error during the work, until most of the selected experimental information is reproduced within the expected uncertainty limits. All the thermodynamic calculations are carried out by means of the THERMO-CALCprogram [40].
[
ikolaenko et al.(1989)
i
~6 - 2
4.1. F e - G d and C o - G d systems
z~
N-xc- -i 0
\f
_~ -'4
|
/
The two binary systems Fe-Gd and Co--Gd are investigated separately. Because the f.c.c, structure is not stable for pure Gd, its lattice stability has to be estimated. In the work by
t-
"E -'6 LU
-!8
4O
--r'!O 0
0.2
i 0.4
i 0.6
i 0.8
1.0
I
I
I
3O
~: 25 )
20
I
&15 O
ANikolaenkoet a1.(1989) /
-1 O
I
I
35
Xco Fig. 1. Heat of mixing in the liquid of the Co-Gd system at 1823 K: A, measured by Nikolaenko and Turehanin [ 12]; - - , calculated from the present thermodynamicdescriptionof the Co-Gd system.
I
A
10
-2
A
E
"--~
-3-
o5 --= ._x -4-
0
o -5-
I
[
500
1000 T,K
1500
2000
Fig. 3. Calculated heat capacityof CosGd ( - - ) comparedwith the experimental measurementsof Kelleret al. 117] (A).
>,
'~ -'3A UJ
50
-7-
i
i
t 500
i 1000
45-
-8
0
I
!
I
I
0.2
0.4
0.6
0.8
1.0
40-
XF e
Fig. 2, He.atof mixing in the liquid of the Fe--Gd system at 1859 K: A, measuredby Nikolaenkoand Nosova [29 ] ; - - , calculatedfromthe present thermodyaamicdescription of the Fe-Gd system.
4. Evaluation of the thermodynamic parameters Most of the experimental information mentioned above is selected in the evaluation of thermodynamic model parameters. For the magnetic properties, the Tc and /3 values are simply taken from the experimental measurements in two binary systems. All the Tc co. Fe:Cdand/3Co, Fe:~dterms in Eqs. (15) and (16) are set equal to zero in the present work, as a result of a lack of experimental information. The optimization is achieved by means of the PARROT program [39], which can take various kinds of experimental data. The program
3530-
o E
25-
& O
2015 10 50
0
1500
T,K Fig. 4. Calculated heat capacityof Co=Gd ( - - ) comparedwith the experimental measurementsof Germanoand Butera [30] (A).
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
38
50
i
Orfcc
i ........
, .."
L
40
_Orhcp
t-,Co:G d --
_Orhcp
L,Co:G d --
(18)
-- 106 J m o 1 - 1
s.-,Fc:G d - -
- ...........
....,'
45
_Orbcc
t-,Co:G d --
......
In the F e - G d system, certain solubilities are allowed in the f.c.c, and b.c.c, structures, to treat the decrease in the reaction
...........
.."r'Y'"
I
0
I
I
I
AColinet et a1.(1986) E]Schott et al.(1986) <~Deodhar et a1.(1975)
c-
-6 35 E '-3 & o 30
-4-
E
-6-
E
-8-
25
E LLo
20
i 500
0
"5
i 1000
1500
>, Q..
/
d,present work
~-5
o
/ /
/
-10-12 -
-14-16-
T,K t-
Fig. 5. Calculated heat capacity of Fe2Gd, compared with the experimental measurements (A) of Leghari [18]. The full curve represents the Neu-
tu -18 -20
mann-Kopp rule which was selected in the present work.
0 50 45 ¸
I
I
I
I
I
[
I
0.2
0.4
0.6
0.8
1.0
Xco
I
Fig. 7. Calcu~_atedenthalpy of formation in the Co-Gd system with various experimental measurements superimposed: A, Ref. [ 16] ; I-q,Ref. [ 14] ; O, Ref. [13]; ~ C%Gd, present work. Note that CosGd is not stable at 298 K.
AGds3.20036.8, Baricc0 et a1.(1987)
40-
0
P
x/
t
I
I
eo0.ar et al I197 /
5 35E & O 30-
/
-2 o
E
-4
E
-6
o
-6-
"D
25u.. 20
700
I
I
I
I
750
800
850
900
950
>, -10 -
T,K Fig. 6. Calculated heat capacity of Co36.sGd63.2 ( - - ) which is a mixture of CoGd3 and C03Gd4, compared with the experimental measurements of Baricco et ai. [ 19].
~
m
-12 -14
Fern~tndez and Guillermet and Huang [41], the lattice stabilities for the high melting temperature b.c.c, metals V, Nb and Ta were estimated, and the enthalpy and entropy differences between the f.c.c, and h.c.p, structures were found as 4000 J m o l - ~ and 0.7 J m o l - ~ K - ~ respectively. In line with their analysis, the following lattice stability is chosen: O(7_fccvGd= O a h e l ~ +
5000
J mol - 1
(17)
No solubility is assumed in the f.c.c., b.c.c, and h.c.p. phases in the C o - G d system, or in the h.c.p, phase in the F e Gd system, which is realized by assigning a large positive interaction parameter, i.e.
i
0
0.2
014
0J6
018
1.0
XFe Fig. 8. Calculated enthalpy of formation in the Fe-Gd system with various experimental measurements superimposed: I-q,Ref. [ 13]; A, Ref. [ 16].
Table 5 Estimated Tc (K) and/3 (/zB) values in the Fe-Gd and Co-Gd systems
Tc /3
Co23Gd~
FeGd 3
Fe3Gd4
Fe7Gd2
FesGd
836 7.97
476 9.16
681 10.57
560 4.23
470 4.86
Zi-Kui Liu et aL / Journal of Alloys and Compounds 226 (1995) 33-45
39
Table 6 Thermodynamic parameters obtained in present work (in SI units) F e - G d system Liquid
b.c.c.
f.c.c.
°L~q~c,a = - 27625 + 17.869T IL~q~c~ = 14594 -- 8.894T (Fe,Gd)l ° L ~ c ~ = - 28758 + 38.096T (Fe,Gd)l 30231
°L~ee~, Gd =
h.c.p.
(Fe,Gd)l o / . ~ p = 1000000
Fe,TGd: Fe23Gd6 Fe3Gd Fe2Gd FesGd Fe7Gd2 FeGd3 Fe3Gd4
0
C o - G d system Liquid
617Gd2 G~F~:GO -- 1 7 ° G ~ - 2 ° G ~ d = - 228222 + 98.884T O,'~0f~hb¢.c hop '-'F¢:Ga --'--' ~'~ - - "*K0~2tl'-'~a - -~ ...... 182.333T 0 Fe3C,d 0 b¢C - - 0 hcp __ GF,:Gd--3 C,F~ G~d -- - 6 1 3 9 3 + 2 6 . 2 1 4 T 0 FeZGd bee GFe:Gd 2 0 G~F¢ -- 0 ~ d hop -- - 4 6 8 2 9 + 6 3 . 2 9 5 T - 5 . 9 1 7 T I n 0 FezC-d 0 Fel7Gd2 Fe23Gd6 GF~:Gd=0.125 GF~:c,a + 0 . 1 2 5 0 GFe:C,a +6802 0 e7C~12 Fe23Gd6 G~F~:GO = 0.2 0 GFo:~ + 0.8 0 G Fe3Gd ~ : ~ + 6240 0 FeGO3 Fc2Gd hhcp aFe:Gd = 0.5 0 Gv~:c~ + 2.5 0 Gc, a + 12903 orz.~c,,u_ ~ ~ot-z_v~c,a a_ 1 . 5 o ~ o p + 13102 ~Fo:Gd • .--' L/Fe:Gd O/'~Pe23Gd6
--
--
A.
__
--
T - 3 5 3 1 2 1 T - 1 - 9 4 4 6 3 5 4 2 T -3
--
°L~q~ca = - 136388 + 3 2 4 . 4 4 4 T - 34.273T In T IL~q~Go = -- 9689
b.c.c.
( Co,Gd ) 1 °L~oC,Od = 1000000
f.c.c.
(Co,Gd)I ° L ~ . ca = 1000000
h.c.p.
(Co,Gd) 1 ° L ~ ca = 1000000
Col7Gd: Co5Gd Co7Gd2 Co3Gd Co2Gd CoaGd4 CoGda
0
Co23Gd6
A q / ~ 7 ~
ot 7Gd2 lflacp G~co:~ - 170 G ~ o - 2 0 Gc~ = -282208+88.842T osGd 0 p 0 hhcp G~co:c~ - 5 G ~ - Gc,a = - 108678 + 3 7 . 5 4 8 T - 0.74263T In T - 4 2 4 4 0 6 E 5 T - l 0~Co: r : c oC~I ~ _ .~o~r~p _ ,~ 0,-:_hr~p_ _ 202973 + 65.526T / VCo ~ vC~ I -0
0
o~Gd 0 hiacp __ G~co:c,a - 30 ~ Gc~ - - 94127 + 30.262T o2Gd - - 0 - - 0 hhop __ G~co:c,a 2 ~ Goa - - 6 5 8 5 3 + 1 8 . 8 6 4 T 0.r:co~c,~ ao_,,-~op_ A0r:_~p- _ 126432 + 1 2 3 . 3 9 4 T - 11.257T In T 0
~ C o : G d
J
~ C o
~
0
~ C ~
oGd3 0 G~co:c,aG~o-3
0
o23Cn:16 o7Gd2 G~co:~ - 1.3333 0 Gc~:Ga + 2.3333 0 G~F~:Gd + 207624
~
__
op
--
0
__
- -50065+62.515T-6.4326TIn
T
5GO
Table 7 Invariant reactions on liquidus in the C o - F e - G d system
J
200O
T (K)
xl~q
x~
1800-
Liq. Liq. Liq. Liq. Liq.
915 940 1465 1481 1497
0.331 0.197 0.467 0.551 0.0816
0.635 0.695 0.203 0.194 0.279
1600-
T (K)
x~cq o
~
Liq. Liq. Liq. Liq.
943 1325 1462 1500
0.232 0.263 0.405 0.434
0.676 0.488 0.209 0.139
M2Gd + MGd 3 M3Gd + M2Gd MtvGd2 + M3Gd f.c.c. + Mt7Gd2
I
I
J
[
I
I
/
fcc
1200,¢,
1000800-
Equilibrium + + + +
1400-
I-"
Table 8 M i n i m u m or m a x i m u m points on liquidus in the Co-Fe,-Gd system
I
liquid
Reaction --, M2Gd + M3Gd4 + MGda ---*b.c.p. + M2Gd + MGd3 + MTGd2 ~ MtTGd2 + M3Gd + MsGd --~ MlTGd2 + MTGd2 + M17Gd2 + M23Gd6 ~ M3Gd
I
temperature of b.c.c. + l i q . - f.c.c, and the increase in the reaction temperature of Fe17Gd2~f.c.c.~b.c.c. with the addition of Gd [ 28 ].
600-
bcc
4002000
0 0'1 012 013 014 o'.s 016 o'.7 0.8 0'.9 1.0 XCo
Fig. 9. Co--Fe phase diagram calculated from the thermodynamic data by Fem(mdez Guillermet [ 6].
40
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
L
2000-
L
I _ _ L _ _
The heat capacity measurements of the CosGd and Fe2Gd compounds are used to evaluated the parameters c, e and f i n Eq. (13) (Figs. 3 and 4). Fig. 5 depicts the heat capacity measurements of Co2Gd by Leghari [ 18 ] and two calculated curves. The dotted line is obtained by fitting the measurements, and the solid line is from the Neumann-Kopp rule. As can be seen, the dotted curve is much higher than the solid curve. Thus, the Gibbs energy difference between the two curves increases with the temperature. The Co2Gd described by the dotted curve becomes too stable at high temperature with respect to the liquid phase, in comparison with other
1800
zN3uschowet a1.(1969) 1600
. • , ~ A
1400 1200 1000 800 600
1
[ I I Co5Gd AEvaluatedfrom Keller et a1.(1974)
I
A
400 0
0.2
0.4
0.6
0.8
1.0
XCo Fig. 10. Calculated Co-Gd phase diagram from the present thermodynamic
description, with the experimentallymeasurements (A) by Buschowand van der Goot [9] included.
"7, ',C "7, -6 -1 E
E
1900
I
I
I
ABuschow et a1.(1969)
1800
-4
liquid
1700
-2
O9 <1 -3
I
-5 0
i
i
i
I
0.2
0.4
0.6
0.8
XCo
1600
Fig. 12. Calculated entropy of formation in the Co43d system: A, Ref. [ 17] ; Fq, present work.
c~
1500
O
1900
c~
1400
0.5
t
I
o 0
G I
I
I
0.6
0.7
0.8
o 0
I
I
ASavitskii et al.(1963) *Savitsky et a1.(1969)
1800
/
1300
1.0
~/~
1 700 0.9
1.0
/
1600
~bcc
XCo Fig. 11. Enlarged upper part of Fig. 10.
Similar optimization procedures are followed in both binary systems, except that the o/.,~ Odand °L~Coo terms have to be evaluated in the Fe-Gd system. The interaction parameters in the liquid phase are evaluated first, by fitting the heat of mixing (Figs. 1 and 2) and the equilibrium temperatures between liq. ** h.c.p, in the Fe-Gd system and those of liq. ** b.c.c., liq. ** f.c.c, and liq. ** h.c.p, in the Co--Gd system. In the Co-Gd system, the T In(T) term is introduced to fit the heat capacity of the liquid measured by Baricco et al. [ 19], which is about 41 J K - ~ per mole of atoms at about 975 K. The intermetallic compounds are then investigated one after another.
--~
1500
j /,
liquid
1400 1300
E
1200 1100-
-:.•
,L,
~'K. ~
_ _ •
.,.
O00- hop 900 0
LL Ui 0.2
, 0.4
~-
I
0.6
0.8
1.0
XFe Fig. 13. Calculated Fe-Gd phase diagram from the present thermodynamic description, with the experimental measurements by Savitsky and coworkers included: A, Ref. [27]; *, Ref. [28].
41
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45 r
1900
I
I
Copelandeta1.(1962) E]solidus Oqneltni g~DTA +liquidus
1800 1700 1600
During optimization, the failure to achieve a satisfactory representation of certain selected data leads to changes in the model parameters of the phases previously determined. The final set of thermodynamic model parameters is obtained by including all selected experimental information at the same time in the optimization.
I
. ~
.~ -"'-7
"my
1500
4.2. Co-Fe-Gd system
v"
1400
C [] V
1300
Because FesGd, Fe7Gd2, Fe3Gd4, FeGd3 and C023Gd6 are not stable as binary compounds, their lattice stabilities and magnetic properties need to be evaluated. However, because of very limited experimental information, the interaction parameters and the lattice stabilities cannot be evaluated at the same time. In the present work, the interaction parameters in the intermetallic compounds are tentatively set as equal to
1200 1100 1000 9OO
I
0.2
0
0.4
I
I
0.6
0.8
1.0
WFe Fig. 14. Calculated Fe--Gd phase diagram from the present thermodynamic description, with the experimental measurements by Copeland et al. [25] included: r-i, solidus; <>, melting; V, DTA; +, liquidus.
1700
I
I
xl "7 o E
1600
i
15O0 140(I
AFe2GdGermanoetal.(1981)
03
0 -1 -2 -3 -4 -5 -6
1300
-7 0
I
I
I
I
0.2
0.4
0.6
0.8
",..
1200
1.0
XFe Fig. 16. Calculated entropy of formation in the Fe-Gd system: A, Ref. [30].
1100 980
E-3
I 985
I
990
)95
1000
0.9"0Abcc
XFe Fig. 15. Enlarged fight-hand part of Fig. 13, with the ot-y loop superimposed.
compounds described by the Neumann-Kopp rule. Therefore, these measurements are not used in the present work. The heat capacity of Co36.8Gd63.2 in the solid state, measured by Baricco [ 19] is a combination of those of Co3Gd4 and CoGd3. To define the individual contributions uniquely, it is assumed that the ACp value in per mole of atoms is the same for both phases. Fig. 6 presents the experimental measurements with the calculated one. The coefficient a in Eq. (11) is determined by the enthalpy of formauon of the compounds. The experimental measurements by Colinet and Pasturel [ 16] are well reproduced (Figs. 7 and 8). The coefficient b is mostly determined by the incongruent melting temperature of the compound.
0.8 0.7
0.6~~M3Gd4
'cc 2 ;\ 0
0.2
0.4
0.6
0.8
Fig. 17. Liquidus projection of the Co-Fe-Gd system.
1.0
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33--45
42
1800
I
I
I
I
I
Furthermore, from the measurements by Atiq et al. [ 32], one finds that the substitution limits of Co by Fe in CosGd and C07Gd2 at 1323 K are 0.16 and 0.12, respectively, which are not very far away from 0.1, as would be found with the structural stability rule just mentioned, taking into account the effect of the temperature. Thus, it is tentatively suggested here that the substitution limit of Co by Fe in Co3Gd4 is also around 0.1 at 700 K. Under such an approximation, the two three-phase equilibria involving M3Gd4 and MGd3 at 700 K are obtained as h.c.p.+M2Gd+MGd3 and M2Gd+ M3Gd4 + MGd3, respectively, because the three-phase equilibrium h.c.p. + M3Gd4 + MGd3 should not exist. The Tc and/3 values of these unstable phases are estimated by a linear combination of the properties of two neighboring stable phases (see Table 5).
I
.//~fcc+bcc
1700 1600 1500
V 1400 1300
MaGd+M2Gd
1200 1100-
cp+MGd3
1000900
0
011
012
MGd3+M3Gd 4
013 0.14 015
016
0.7 5. Discussion
Fig. 18. Liquidus projection of the Co-Fe-Gd system with the temperature on the vertical axis.
1.0 0.9 0 . 8 ~
T=1323K
0.7 0.6
o.°S .;Z7
0 2
//~@'~
0.1 ' ' - ~
0 A..... 0
+, 1"12...... 3-" J
~ ~
~Gd+U"Gd' rn~d'+M"G
The thermodynamic description of the Co--Fe-Gd system obtained in the present work is presented in Table 6. The Co-Fe binary phase diagram is presented in Fig. 9 for the reader's convenience, calculated from the thermodynamic data assessed by Fern~dez Guillermet [6]. Fig. 10 depicts the Co-Gd phase diagram calculated from the present work. A satisfactory agreement with the measurements by Buschow and van der Goot [9] can be observed from the upper part of the diagram enlarged in Fig. 11. The satisfactory agreement between the calculations and experiments can also been seen from Figs. 1, 3, 6 and 7. Fig. 12 shows the calculated entropy of formation in the Co-Gd system, noting that CosGd is not stable at 298 K. The calculated Fe-Gd binary phase diagram is presented in Figs. 13 and 14 from the present thermodynamic description of the system, in comparison with the measurements by Savitsky and coworkers [27,28] and Copeland et al. [25] respectively. The calculations agree better with the measurements by Savitsky and coworkers than with those by Cope-
Fig. 19. Isothermal section of the Co--Fe43d system at 1323 K.
1.0 zero. The lattice stabilities of FesGd, Fe7Gd2 and Co23Gd6 are then evaluated from the three-phase equilibria at 1323 K, as measured by Atiq et al. [32], with respect to two neighboring stable phases. The lattice stabilities of FeaGd4 and FeGd3 can only be deduced from the work by Poldy and Taylor [33,34]. The substitution limit of Co by Fe in CoGd3 is taken as 0.1 at 700 K from their experimental observation. They further satisfactorily interpreted their results in terms of the structural stability rule, which states, "if a stable structure exists for which the Fermi energy lies above the 3d electron energy band, then any change which leads to the Fermi level intersecting the 3d band will probably cause the structure to become unstable". They also applied this structural stability rule to the substitution limit of Ni by Fe in Gd3Ni and that of Ni by Cu in GdNi2, achieving satisfactory agreement [42].
0.9/~ 0.8 0.7 0.6
T=700K
0' 0.4 "ed.~:~i;~G'J3 VM'G'+M.G<~'~
o.,g,/f/ /+,o../7't oo,
0
0.2
0.4
0.6
0.8
1.0
XCo Fig. 20. Isothermal section of the Co-Fe-Gd system at 700 K.
43
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45 I
1800
I
I
in the figure. It can be seen that the temperature has a minimum for the three-phase equilibria liq. +MaGd+M2Gd, liq. + M~7Gd2+ M3Gd and liq. + f.c.c. + MlTGd2, and maximum for liq. + M2Gd + MGd3. The temperatures and the liquid compositions of these points are presented in Table 8. It should be pointed out that there is uncertainty over the two four-phase equilibria close to the Gd comer, as a result of the arbitrary setting of the substitute limits of Co by Fe in M3Gd4 and MGd3. In Fig. 20, one notices that MI7Gd2 is only stable in the composition range close to the Fe-Gd and CoGd binary sides, but not in the middle. This will be discussed further later. With the thermodynamic description of the Co-Fe-Gd system obtained, one can now make relevant calculations for
I
liquid
1600 -
co
1400 M17Gd2
1200 I.-" 1000 800 600 400 -
I
1580
200 o
I
I
I
o,
liquid+M5Gd//
1560
///
1540 I
1800 1600 [
I
~
I
I
,,¢,, I.-" 1520
liquid
1400
~~
1500 7Gd2+M3Gd// /
1200-
MFGd2
liquid+M~/
_
1480
I.--" 10001460
800-
I w Ij
0
..,,-~2..-.3--
,
0.2
0.4
irl
f
0.6
1.0
0.8
XCo/(Xco+XFe)
600-
Fig. 23. Enlargementof the upperpart of Fig. 22.
40020'3
--
I
i
I
r
0.2
0.4
0.6
0.8
XCo/(Xco+XFe)
0.26 1.0
I
I
~ T =
I
I
M3Gd 1500K M7G 2d
0.24
Fig. 22. Verticalsectionof MTGd2. land et al. It should be noted that Copeland et al. did not follow their results when drawing the phase diagram themselves. In Fig. 15, the enlarged phase diagram close to the Fe side is presented with the a - y loop superimposed by dotted lines. Fig. 16 depicts the calculated entropy of formation in the system, with the measurement by Germano and Butera [30] included. The liquidus projection (Figs. 17 and 18) and the isothermal sections at 1323 K (Fig. 19) and 700 K (Fig. 20) are calculated and compared with the experimental information available. The invariant reactions on the liquidus are listed in Table 7. Fig. 18 is also the liquidus projection, but with the temperature plotted on the vertical axis. The phases in equilibrium with the liquid phase in various curves are presented
I
0.22 .~ 0.20 0.18
~
M5Gd
0.16 0.14 0.58
I
I
I
0.60
0.62
0.64
I
0.66
XCo
0.68
0.70
Fig. 24. Part of the isothermalsectionof the Co-Fe--Gdsystemat 1500 K.
44
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
practical interest. As examples, Figs. 21 and 22 depict the pseudo-binary system of Fel7Gd2-Col7Gd2 and the vertical section of M7Gd2. The upper part of Fig. 22 is enlarged in Fig. 23. It can be seen that the b.c.c, phase appears at low temperatures in both diagrams. The reason is the negative interaction parameter between Fe and Co in the b.c.c, phase in the Fe-Co binary system, i.e. /ff~Co:Cd= - 23 669 + 103.9627T- 12.7886T ln(T) J molwhile it is set equal to zero in the Fe17Gd2---Co17Gd2pseudobinary system. However, to make M17Gd2 stable in the middle of the pseudo-binary system at low temperatures, an inter. parameter of/_~, M 17Gd2 action Co:Cd----"-- 350 000 J mol- 1 is needed. One would also have to introduce z'Fe, r ~ BCo:Gd for M2Gd and MaGd to make them stable over the entire composition range between the Fe-Gd and Co-Gd binaries. However, there is no experimental information to support this modification, except magnetic measurements by Chen et al. [38] in the pseudo-binary system, but Chen et al. did not examine the microstructure of their specimens. Thus, we feel that such modification should be carried out later, when there is more convincing experimental evidence. In both diagrams in Figs. 21 and 22, one notices several occasions where a phase boundary separates a three-phase field and a one-phase field, but this does not violate the phase rule and can be understood by examining the isothermal section shown in Fig. 20. For example, let us consider the Fe17Gd2---Co17Gd2 pseudo-binary system at 700 K. From the Fe-Gd binary side, M~TGd2 one-phase state is stable until the b.c.c., Mx7Gd2 and M3Gd three-phase equilibrium triangle is reached. With a further increase in the Co content, one enters into a three-phase equilibrium field. However, in calculating the pseudo-binary system, the Gd content cannot be exactly on the pseudo-binary plane. As can be seen from Fig. 20, one will then obtain very different diagrams, depending on if the Gd content is slightly higher or lower than that on the pseudo-binary plane. This problem has been discussed in detail by Huang et al. [43]. In the present plotting, all the lines which are not exactly on the pseudo-binary plane are excluded to give a simple picture of the pseudo-binary system and the vertical section. This is why there are phase boundaries separating a three-phase field and a one-phase field. It should be mentioned that the boundary between M7Gd2 and liq. + M7Gd2 in Fig. 23 cannot be calculated by normal phase diagram mapping, but has to be calculated separately by only considering the two-phase equilibrium between the liquid and M7Gd2 phases. This can be understood by examining the isothermal section at 1500 K, for example, as shown in Fig. 24. The calculated phase boundary in the normal phase diagram mapping would represent either liq. + M3Gd + MTGd2 or liq. + MsGd + M7Gd2, while the experimentally observed boundary in the vertical section would be neither of these, but the point A in Fig. 24, which
is represented by the phase boundary in Fig. 23 for various temperatures.
6. Conclusions The thermodynamic properties of the Co--Fe--Gd system are evaluated from the experimental information available in the literature, based upon the three binary systems, i.e. CoFe, Co-Gd and Fe-Gd. The properties of the Co-Gd and FeGd systems are evaluated in the present work. With the thermodynamic description available, one can now make various calculations of practical interest.
Acknowledgements One of the authors (WZ) is grateful for financial support by the NSFC (China) and thanks the Tm~RMO-CALCproject for his visit to the Royal Institute of Technology, during which the main part of the present work was conducted. The authors are grateful to Prof. John/~gren for encouragement and support during this work.
References [ 1] K.H.J. Buschow, Rcp. Prog. Phys., 40 (1977) 1179-1256. [2] K.H.J. Buschow, Mater. Res. Bull., 19 (1984) 935-943. [3] L. Kaufman and H. Bemstein, Computer Calculation of Phase Diagrams, Academic Press, New York, 1970. [4 ] M. Hillert and L.-I. Staffansson, Acta Chem. Scand., 24 ( 1970 ) 36183626. [5] A.T. Dinsdale, CALPHAD, 15 (1991) 317-425. [6] A. Fermtndez Guillermet, High Temp. High Pressure, 19 (1987) 477499. [7] M. Hillert and M. Jarl, CALPHAD, 2 (1978) 227-238. [8] V.F. Novy, R.C. Vickery and E.V. Kleber, Trans. Metall. Soc. AIME, 221 (1961) 588-590. [9] K.H.J. Buschow and A.S. van der Goot, J. Less-Common Met., 17 (1969) 249-255. [10] W.Q. Ge, C.H. Wu and Y.C. Chuang, Z. Metallkd., 83 (1992) 300303. [11] H. Okamoto, J. Phase Equil., 13 (1992) 673-674. [ 12] I.V. Nikolaenko and M.A. Turchanin, Rasplavy, 5 (1989) 77-79. [ 13] S.S. Deodhar and P.J. Ficalora, High Temp. Sci., 8 (1976) 185-193. [ 14] J. SchoU and F. Sommer, J. Less-Common Met., 119 (1986) 307--317. [15] C. Colinet, A. Pasturel and K.H.J. Buschow, Metall. Trans. A, 18 (1987) 903-907. [16] C. Colinet and A. Pasturel, CALPHAD, 11 (1987) 323-324. [ 17] D.A. Keller, S.G. Sankar, R.S. Craig and W.E. Wallace, Am. Inst. Phys. Conf. Proc., 18 (1974) 1207-1211. [18] S.B.K. Leghari, J. NaturalSci. Math., 29 (1) (1989) 69--85. [19] M. Baricco, C. Antonions and L. Battezzati, Scr. Metall., 21 (1987) 849-852. [20] E. Burzo, Phys. Rev. B, 6 (1972) 2882-2887. [21] R. Lemalre, Cobalt, 32 (1966) 132-140. [22] R. Lemaire, Cobalt, 33 (1966) 201-211. [23] O. Kubaschewski, IRON-Binary Phase Diagrams, Springer, Berlin, 1982. [24] V.F. Novy, R.C. Viekery and E.V. Kleber, Trans. Metall. Soc. AIME, 221 (1961) 580-585.
Zi-Kui Liu et aL / Journal of Alloys and Compounds 226 (1995) 33~15 [25] M.I. Copeland, M. Krug, C.E. Armantrout and H. Kato, USBur. Mines, Rep. Invest., 5925 (1962). [26] F. Spedding, A. Daane, B. Beaudry, I. Haefling, F. Hunter, M. Michel, H. Rider, F. Smidt, R. Valletta and W. Wunderlin, U.S. Atom. Energy Commun., 1S-700 (1963) C15. [ 27 ] E.M. Savitskii, V.F. Terekhova, 1.V. B urov and O.D. Chistyakov, Russ. J. Inorg. Chem., 6 (1961) 883-885. [28] E.M. Savitsky, V.F. Terekhova, R.S. Torchinova, I.A. Markova, O.P. Naumkin, V.E. Kolesnichenko and V.F. Stroganova, Proc. Conf. Les Elements des Terres Rares, Paris-Grenoble, 5-10 May 1969, Vol. 1, pp. 49-60. [29] I.V. Nikolaenko and V.V. Nosova, Soy. Prog. Chem., 55 (2) (1989) 30-33. [30] D.J. Germano and R.A. Butera, J. Solid State Chem., 37 ( 1981 ) 383389. [31] W.E. Wallace and E. Segal, Rare Earth lntermetallics, Academic Press. New York, 1973. [32] S. Atiq, R.D. Rawlings and D.R.F. West, J. Mater. Sci. Lett., 9 (1990) 518-519. [33] C.A. Poldy and K.NR. Taylor, J. Less-Common Met., 27 (1972) 9597.
45
[34] C.A. Poldy and K.N.R. Taylor, J. Phys. F, 3 (1973) 145-156. [35] K.P. Belov, V.A. Vasil'kovkskii, N.M. Kovtun, A.K. Kupriyanov and S.A. Nikitin, JETP Lett., 20 (1974) 304-305. [36] E. Burzo, J. Phys. Coll. C5, 40 (1979) 184-185. [37] W.M. Hubbard and E. Adams, J. Phys. Soc. Jpn., 17 (BI) (1962) 143-146. [38] H. Chen, W.-W. Ho, S.G. Sankar and W.E Wallace, J. Magn. Magn. Mater., 78 (1989) 203-207. [39] B. Jansson, Evaluation of parameters in thermochemical models using different types of experimental data simultaneously, Trita-Mac-0234, Royal Institute of Technology, Stockholm, 1984. [40] B. Sundman, B. Jansson and J.-O. Andersson, CALPHAD, 9 (1985) 153-190. [41] A. Fernfmdez Guillermet and W. Huang, Z. Metallkd., 79 (1988) 8895. [42] C.A. Poldy and K.N.R. Taylor, Phys. Status Solidi A, 18 (1973) 123128. [43] W. Huang, M. Hillert and X. Wang, Thermodynamic assessment of the Cao-MgO-SiO2 system, Trita-Mac-0530, Royal Institute of Technology, Stockholm, 1993, Metall. Mater Metall. (1995) in press.
AH~) COM~)UHDS ELSEVIER
Journal of Alloys and Compounds 226 (1995) 33--45
Thermodynamic assessment of the Co-Fe-Gd systems Zi-Kui Liu a, Weijing Zhang b, Bo Sundman
a
"Department of Materials Science and Engineering, Royal Institute of Technology, S-I O044 Stockholm, Sweden b Department of Materials Science and Engineering, Universityof Science and Technology, Beijing, Beijing 100083, People's Republic of China Received 14 October 1994
Abstract
The thermodynamic properties of the ternary Co--Fe--Gdsystem are investigated,based on the three binary systems, i.e. Co-Fe system by Fern~dez Guillermet, and Co-Gd and Fe-Gd from the present work. The assessment is carded out by means of the computer programs PARROTand THERMO-CALC,using models for the Gibbs energy of individual phases. The ternary system contains eight different intermetallic compounds and they are all treated as line compounds. Good agreement is obtained between the calculation and experimental results in the two binary systems and the ternary system. Keyword~.:Thermodynamic properties; Binary systems
1. Introduction
Intermetallic compounds formed between rare earth and transition metals, especially 3d elements, are of particular interest regarding their magnetic properties [ 1] and their reversible absorption of hydrogen gas at room temperature and nearly atmospheric pressure [2]. However, there have been few thermodynamic studies of rare earth-transition metal alloys and experimental data are scarce, though it is undoubted that self-consistent thermodynamic descriptions of alloy systems will greatly help in alloy design and processing. The phase diagram, which is a presentation of the thermodynamic properties of the alloy system, is used extensively in the field of metallurgy and materials science. The importance of phase diagrams and the thermodynamic properties of alloy systems is reflected in the numerous compilations of phase diagrams and thermodynamic data. However, there is usually no check of consistency between the thermodynamic data and the suggested phase diagrams. Thermodynamic modelling is necessary if we want to couple phase diagram and thermodynamics. It is the only method by which various types of experimental information can be compared and by which the description of all the thermodynamic properties of a system can be optimized. This method is often referred to as the CALPHAD (calculation of phase diagram) method [3]. In this method, the thermodynamic 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved
SSD10925-8388(95)01578-7
properties of the alloy systems are analyzed using thermodynamic models for the Gibbs energy of individual phases. The models involve adjustable parameters that are evaluated from the experimental thermodynamic and phase diagram information. This is made possible by increasingly powerful computers and computer programs. When a consistent description of the thermodynamic properties of the alloy system is obtained, in principle, any kind of diagrams of interest can be calculated, which is outside the capacities of the ordinary compilations. The present work deals with the evaluation of the thermodynamic properties of the Co-Fe--Gd system, where some important thermodynamic quantities have been measured in the Co-Gd and Fe-Gd binary systems, such as the enthalpy formation of.intermetallic compounds and the heat of mixing in the liquid phase. An assessed thermodynamic description of the Co-Fe--Gd system will be useful for the evaluation of other rare earth-transition metal alloy systems for which there is less experimental information.
2. Thermodynamic models
The Gibbs energy of individual phases is described by sublattice models [4] relative to the so-called 'standard element reference' (SER), i.e. the enthalpies of the pure elements in their defined reference phase at 298.15 K.
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
34
518 11 692 (_1 A = 112----5+ 15 975 ~p
2.1. Liquid, fc.c., b.c.c, and h.c.p, phases The liquid, tic.c, b.c.c, and h.c.p, phases are treated by one sublattice model which is equivalent to a substitutional model with the Gibbs energy expressed as 4'_ o 4' o G m - XFe G Fe + X c o
4' Gco +
E
4' Gm+
rng
~_
4" Gm
i 4"
4' ~,xixjTci4'j + XrzeXcoXodTcFe,
i
i
i
+ XcoXcd~'_~L~co. Cd(XCo-- XCd)
(8)
Co, C d
i
+ XF~XcoXcdLF~c,Co,Cd
(2)
where LFe. 4" Co, L~o.ca and LF,. co are the binary interaction parameters, and L~,, co, co is the ternary interaction parameter set to be zero, as a result of a lack of experimental data. /-~,, Co is taken from Fern~dez Guillermet's assessment [ 6]. Lc~o.Cd and L~,cd are to be evaluated in the present work. L ~ can be temperature dependent and two terms are usually sufficient, i.e.
(:3)
L~=a+bT
The magnetic contribution to the Gibbs energy in f.c.c., b.c.c. and h.c.p, phases (mgG~m) is described by
mgGOm=RTln(/3+ 1)f("r)
X~
f(~-)=1 1.140p + 497~p-I
79 :~---~))/A + 135 + (5)
for ~-< 1 and .rf(.'r) = - (~0 + ~"r-15 + 21.1_~)/A
(9)
+ ~ x : f l ~ ,4"j + XF~XcoXcd/3F~, 4" Co. Cd
i
i,j
where °Tcf and °/3/~ are unary quantities and Tc~j and/3~j are the binary quantities. The Fe-Gd and Co-Gd binary quantities, i.e. TcF~. 4' Cd and flF~. 4' ca , and the ternary quantities, i.e. 4' 4' T~Fe,Co.Cd and/3F~, co. Gd, are set to zero, as a result of a lack of experimental data and extremely low solubilities. No ternary interactions are included, for the same reason.
There are seven stable intermetallic compounds in the CoGd system and four in the Fe-Gd system, i.e. C017Gd2, C05Gd, C07Gd2, C03Gd, C02Gd, C03Gd4 and CoGd3, and FelTGd2, Fe23Gd6, FeaGd and Fe2Gd. No ternary compound has been reported. All the intermetallic compounds are modelled by a two-sublattice model, with the transition metal elements on one sublattice and the rare earth element on the other sublattice, i.e. MaGdB, where M is used as an abbreviation for a mixture of Co and Fe. As a result of a lack of experimental measurements, it is assumed that the NeumannKopp rule applies for the heat capacity, i.e. A Cp = 0. Thus, the Gibbs energy per mole of formula unit MAGdB can be expressed as GMAGdB __ • Og'2MAGdB d.. • 0t'2MAGdB m - - Y F e ~JFe:Gd ~ Y C o ~-~Co:Gd
(4)
where ~"is defined as T/T~, with T¢ the critical temperature for magnetic ordering, i.e. the Curie temperature (T~) for ferromagnetic ordering and the Nrel temperature (TN) for antiferromagnetic ordering;/3 is a quantity related to the total magnetic entropy and, in most cases, is set equal to the Bohr magnetic moment per mole of atoms, f('r) represents the polynomials obtained by Hillert and Jarl [7] based on the magnetic specific heat of iron, i.e. 474(1
/34' = Ex/°/3
2.2. Intermetallic compounds
+ XF~XCd~,iL~o, c~(XF, -- XCd) i i
for ~-> 1, where
E X i o Tci4, +
(1)
G m - XFeXCoE L F , . Co(XF~-- Xco)
_~'79~ --1
and p depends on the structure; p = 0.4 for a b.c.c, structure and p = 0.28 for the others. T~ and/3 are described by Zc4' =
where °G/* is the molar Gibbs energy of the element i ( i - Fe, Co, Gd) with the structure ~b in a non-magnetic state, from the work of Dinsdale [ 5]. EG~mis the excess Gibbs energy, expressed in Redlich-Kister polynomials as E
(7)
]
0 4' XGd G G d
+ RT(XF, In XFe+ Xco In Xco + xco In XCd) +
_ 1~
(6)
+ mgaMaCdB+ ART{yFe ln(yF¢) + Yco ln(Yco) }
(10) O/'~MAGdB - - A 0g'~hbcc - - lqDOt"2hhcp __ a
VFe:Gd
•"
"-'~
u "-'Gd -- "1 + biT
( 11 )
bET
(12)
0/'7_MAGdB __ A0/'Thhcp - - D0/2_hhcp - - ~ + UCo:O d .'~ U C o u "JGd --~2
Here, °GFc:Ca represents the Gibbs energy of formation of a compound with all sites on the first sublattice filled with Fe and all sites on the second sublattice filled by Gd. °Gco:Gd has a similar meaning but for Co. °G~C, ° G ~ and °Gc~o~p are the Gibbs energies of the respective pure elements in a hypothetical non-magnetic b.c.c, or h.c.p, structure. YFc and Yco are the so-called site fractions and represent the mole fractions of Fe and Co in the first sublattice respectively. The parameters a/and b/, with i being 1 or 2, should be evaluated separately in the Co-Gd and Fe-Gd systems. When there are measurements of the heat capacity, more terms may be added, i.e.
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
35
Table 1 Invariant reactions in the Co-Gd system Reaction
T, K (xgqo)
b.c.c. ~ h.c.p. liq. + h.c p. ~ CoGd3 liq. -o Co3Gd4+ CoGd3 liq. + Co:~Gd~ Co3Gd4 liq. + Co:~Gd--, Co2Gd liq. + Co-,Gd2-o Co3Gd liq. + Co:~Gd"-*C07Gd2 liq. + Co 7Gd2~ C05Gd liq. --*Co ,TGd2 liq. ~ CojTGd2+ f.c.c. CsGd --~Col7Gd2+ C07Gd2 f.c.c. --*h.c.p.
Present work
Buschowand van derGoot [9]
Ge et M.[10]
1262(0.025) 1053(0.261) 918(0.368) 943(0.391) 1388(0.555) 1549(0.703) 1570(0.741) 1619(0.820) 1658(0.895) 1643(0.933) 1123 695
1053
1053 918(0.358) 943 1389 1550 1568 1623 1643 1614(0.925) 1123 -
O['TMAGdB _ A O / ' T h b c c _ / ~ / " 2 _ h h c p 'J Fe:Gd za UFe u *.JGd
=a+bT+cTln(T)
+dT2 + e T - l + f T -3
(13)
All intermetallic compounds are ferromagnetic except CoGd 3. As a first approximation, the magnetic contribution to the Gibbs energy mgamMaGdBis described by mg
GM mA G d B = R T I n ( / 3 + 1)f(~-)
(14)
with f(~-) from Eqs. ( 5 ) - ( 7 ) , though Eqs. ( 5 ) - ( 7 ) were derived for iron. Tc and/3 are taken from the measured critical temperature and the mean Bohr magnetic moment per mole of formula unit. In the ternary system, they can be represented by TcMAGdB --. 7" M A G d B -L. x, T M A G d B - - Y F e -t c F e : G d - - Y C o x c C o : G d
i
MAGdB
+ yFeYCo)"~. Tcco. Ve:~d(YFe--YCo)
i
(15)
i
..a_., Fe:Gd /31VIAGdB_- -.Y F e / J/~MAGdB
f~MAGdB
--YCobJCo:Gd
i
MAGdB
q- YFeYCoE fl~o. Fe:Gd(YFe-- YCo)'
(16)
i
3. Experimental information 3.1. C o - G d system
The phase diagram of the C o - G d system was measured by Novy et al. [8] and Buschow and van der Goot [9], and more recently by Ge et al. [ 10], as discussed by Okamoto [ 11 ]. The results of Novy et al. are quite different from those of the studies in Refs. [9,10], so are not used in the present work. The last two investigations [ 9,10] gave the same kind of phase relationships, i.e. two eutectic reactions, congruent melting of Co17Gd2 and incongruent melting of all other
(0.358) 938(0.365) 1388 1548 1573 1628 1658 1638(0.925) -
compounds. Co5Gd is unstable at low temperatures, and decomposes into Co,7Gd2 and CoTGd2 at about 850 °C. Both CosGd and Co27Gd/were reported to have a certain homogeneity region at high temperatures [9,10], but they are treated in the present work as stoichiometric compounds, because of limited information. Table 1 lists the various reaction temperatures and the composition of the liquid phase, together with the calculated values from the present work. The heat of mixing in the liquid phase at 1823 K was measured by Nikolaenko and Turchanin [ 12] for the entire composition range. The enthalpies of formation of the compounds were measured by various authors [ 13-15], with the most complete set being that by Colinet and coworkers [ 15,16], which is used in the present assessment. The heat capacities of CosGd and Co2Gd were measured by Keller et al. [17] and Leghari [18] in the temperature ranges 5-300 K and 300-473 K respectively. However, Leghari's measurements are not used in evaluating the properties of Co2Gd, for the reason given later. The measurements by Keller et al. are used to evaluated the entropy of formation of CosGd and some low temperature coefficients in the heat capacity expression. Baricco et al. [ 19] measured the heat capacity of Co36.8Gd63.2 in the temperature range 800-980 K, which is a mixture of Co3Gd 4 and CoGd3 below 910 K, and liquid above 910 K. There are numerous magnetic measurements of the compounds. The interest of the present work is the critical magnetic ordering temperature and the Bohr magnetic moment. The values measured by Burzo [20] and Lemaire [21,22] are presented in Table 2, and those by Burzo are used. 3.2. F e - G d system
The F e - G d system was included by Kubaschewski [ 23 ] in the compilation of iron-binary phase diagrams with four intermetallic compounds. In the work by Novy et al. [24], seven intermetallic compounds were detected, which were not confirmed by the other measurements by Copeland et al.
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
36
Table 2 Measured T¢ (K) and/3 (P,R) values in the Co--Gd system
Burzo [ 20] Lemaire [21,22]
T¢ /3 T¢ /3
CoGd 3 a
Co3Gd4
Co2Gd
Co3Gd
Co7Gd2
CosGd
Col7Gd 2
130 a 21.5 a -
233 26.0 -
395 4.95 404 4.9
611 2.3 612 2.2
767 2.6 775 1.65
1020 1.4 1008 1.2
1222 14.1 1209 14.4
a CoGd3 is antiferromagnetic and its TN and/3 values need to be multiplied by - 3 when put into the PARROTprogram. Table 3 Invariant reactions in the Fe-Gd system Reaction
T, K ( ~ q )
b.c.c. ~ f.c.c. + liq. liq. + f.c.c. ~ Fe17Gd 2 liq. + FelTGd2 ---~Fe23Gd6 liq. + Fe23Gd 6 ~ Fe3Gd liq. + FeaGd ~ Fe2Gd liq. ~ FeaGd + h.c.p. b.c.c. ~ h.c.p. + liq. f.c.c. +FelTGd2 ~ b.c.c.
Present work
Refs. [27,28]
Ref. [25]
Ref. [26]
1653 (0.910) 1604(0.881 ) 1556(0.766) 1429 ( 0.523 ) 1355 (0.440) 1105 (0.264) 1512(0.040 b) 1197 c
1653 + 10 1608 + 10 1553 + 10 1433 + 10 1353 + 10 1103 + 7 _ 1205 4-5
1661 1593
1587
1423 a 1353 1118
1446 ~ 1334
1183
a The intermetallic compound Fe23Gd6 was not detected.
~x~ = 0.0044. ~ x ~ =0.998 717, x ~ : = 0.999 724. Table 4 Measured T¢ (K) and/3 (/~B) values in the Fe-Gd system
Tc /3
3.3. Co-Fe-Gd system
Fe2Gd
Fe3Gd
Fe23Gd6
FelTGd2
782 3.35
728 1.6
468 14.8
472 21.2
[25], Spedding et al. [26] and Savitsky and coworkers [27,28]. In the work by Copeland et al. and Spedding et al., only three intermetallic compounds were found, i.e. Fe17Gd2, Fe3Gd and Fe2Gd. Another compound (Fe4Gd) was detected by Novy et al. and Savitsky et al. [28], but Novy et al. presented a congruent melting of the compound and Savitsky et al. an incongruent melting. In line with the other Fe-Re systems, this phase was given the formula Fe23Gd6, with an incongruent melting, as suggested by Kubaschewski. Table 3 depicts the various reaction temperatures and compositions of the liquid phase, together with the calculated values from the present work. The heat of mixing in the liquid was measured by Nikolaenko and Nosova [29] at 1850 K. The enthalpies of formation of Fel7Gd2, Fe3Gd and Fe2Gd are taken from the work by Colinet et al. [ 16]. The heat capacity of Fe2Gd was measured in the temperature range 15-300 K by Germano and Butera [30], from which its entropy at 298 K can be evaluated. The magnetic properties of the compounds were reviewed by Wallace and Segal [ 31 ], from which the critical magnetic ordering temperatures and the atomic Bohr magnetic moments are taken (see Table 4).
The only available experimental information on the phase equilibria in the literature is the isothermal section at 1323 K, measured by Atiq et al. [ 32], in which the solubility limits of the compounds M23Gd6, MsGd and MTGd2 in the ternary system were reported. For MGd3, Poldy and Taylor [33] mentioned that the solubility limit of Fe in (Co~ _y,Fey)Gd3 is y=0.1. Upon further addition of iron, other phases appeared. However, Poldy and Taylor did not identify what the other phases are, but only mentioned the presence of gadolinium, based on the observation of a magnetic transition at 270 K, which is the Curie temperature of metallic gadolinium. Furthermore, they did not mention at what temperature the solubility limit is located, though it was pointed out in a later report [34] that the magnetic properties do not change after annealing at 700 K and the X-ray photographs were taken at 300 K. The magnetic properties have been investigated by several authors. Belov et al. [35] measured the Curie temperature and the Bohr magnetic moment of (Coo.l,Feo.9)2Gd, and Burzo [36] measured the Bohr magnetic moment of the pseudo-binary system Fe2Gd-Co2Gd. Hubbard and Adams [ 37 ] presented the Bohr magnetic moment measurements of (Co~-x,Fex) 5Gd with x = 0-1. The Curie temperatures of the pseudo-binary system Fe~7Gd2-Co~TGd2 were measured by Chen et al. [38].
37
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33--45 0
[
-4 -5 E
-6
-~o5
-8
I
I
works by minimizing an error sum, where each of the selected data values is given a certain weight. The weight is chosen by personal judgment, and changed by trial and error during the work, until most of the selected experimental information is reproduced within the expected uncertainty limits. All the thermodynamic calculations are carried out by means of the THERMO-CALCprogram [40].
[
ikolaenko et al.(1989)
i
~6 - 2
4.1. F e - G d and C o - G d systems
z~
N-xc- -i 0
\f
_~ -'4
|
/
The two binary systems Fe-Gd and Co--Gd are investigated separately. Because the f.c.c, structure is not stable for pure Gd, its lattice stability has to be estimated. In the work by
t-
"E -'6 LU
-!8
4O
--r'!O 0
0.2
i 0.4
i 0.6
i 0.8
1.0
I
I
I
3O
~: 25 )
20
I
&15 O
ANikolaenkoet a1.(1989) /
-1 O
I
I
35
Xco Fig. 1. Heat of mixing in the liquid of the Co-Gd system at 1823 K: A, measured by Nikolaenko and Turehanin [ 12]; - - , calculated from the present thermodynamicdescriptionof the Co-Gd system.
I
A
10
-2
A
E
"--~
-3-
o5 --= ._x -4-
0
o -5-
I
[
500
1000 T,K
1500
2000
Fig. 3. Calculated heat capacityof CosGd ( - - ) comparedwith the experimental measurementsof Kelleret al. 117] (A).
>,
'~ -'3A UJ
50
-7-
i
i
t 500
i 1000
45-
-8
0
I
!
I
I
0.2
0.4
0.6
0.8
1.0
40-
XF e
Fig. 2, He.atof mixing in the liquid of the Fe--Gd system at 1859 K: A, measuredby Nikolaenkoand Nosova [29 ] ; - - , calculatedfromthe present thermodyaamicdescription of the Fe-Gd system.
4. Evaluation of the thermodynamic parameters Most of the experimental information mentioned above is selected in the evaluation of thermodynamic model parameters. For the magnetic properties, the Tc and /3 values are simply taken from the experimental measurements in two binary systems. All the Tc co. Fe:Cdand/3Co, Fe:~dterms in Eqs. (15) and (16) are set equal to zero in the present work, as a result of a lack of experimental information. The optimization is achieved by means of the PARROT program [39], which can take various kinds of experimental data. The program
3530-
o E
25-
& O
2015 10 50
0
1500
T,K Fig. 4. Calculated heat capacityof Co=Gd ( - - ) comparedwith the experimental measurementsof Germanoand Butera [30] (A).
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
38
50
i
Orfcc
i ........
, .."
L
40
_Orhcp
t-,Co:G d --
_Orhcp
L,Co:G d --
(18)
-- 106 J m o 1 - 1
s.-,Fc:G d - -
- ...........
....,'
45
_Orbcc
t-,Co:G d --
......
In the F e - G d system, certain solubilities are allowed in the f.c.c, and b.c.c, structures, to treat the decrease in the reaction
...........
.."r'Y'"
I
0
I
I
I
AColinet et a1.(1986) E]Schott et al.(1986) <~Deodhar et a1.(1975)
c-
-6 35 E '-3 & o 30
-4-
E
-6-
E
-8-
25
E LLo
20
i 500
0
"5
i 1000
1500
>, Q..
/
d,present work
~-5
o
/ /
/
-10-12 -
-14-16-
T,K t-
Fig. 5. Calculated heat capacity of Fe2Gd, compared with the experimental measurements (A) of Leghari [18]. The full curve represents the Neu-
tu -18 -20
mann-Kopp rule which was selected in the present work.
0 50 45 ¸
I
I
I
I
I
[
I
0.2
0.4
0.6
0.8
1.0
Xco
I
Fig. 7. Calcu~_atedenthalpy of formation in the Co-Gd system with various experimental measurements superimposed: A, Ref. [ 16] ; I-q,Ref. [ 14] ; O, Ref. [13]; ~ C%Gd, present work. Note that CosGd is not stable at 298 K.
AGds3.20036.8, Baricc0 et a1.(1987)
40-
0
P
x/
t
I
I
eo0.ar et al I197 /
5 35E & O 30-
/
-2 o
E
-4
E
-6
o
-6-
"D
25u.. 20
700
I
I
I
I
750
800
850
900
950
>, -10 -
T,K Fig. 6. Calculated heat capacity of Co36.sGd63.2 ( - - ) which is a mixture of CoGd3 and C03Gd4, compared with the experimental measurements of Baricco et ai. [ 19].
~
m
-12 -14
Fern~tndez and Guillermet and Huang [41], the lattice stabilities for the high melting temperature b.c.c, metals V, Nb and Ta were estimated, and the enthalpy and entropy differences between the f.c.c, and h.c.p, structures were found as 4000 J m o l - ~ and 0.7 J m o l - ~ K - ~ respectively. In line with their analysis, the following lattice stability is chosen: O(7_fccvGd= O a h e l ~ +
5000
J mol - 1
(17)
No solubility is assumed in the f.c.c., b.c.c, and h.c.p. phases in the C o - G d system, or in the h.c.p, phase in the F e Gd system, which is realized by assigning a large positive interaction parameter, i.e.
i
0
0.2
014
0J6
018
1.0
XFe Fig. 8. Calculated enthalpy of formation in the Fe-Gd system with various experimental measurements superimposed: I-q,Ref. [ 13]; A, Ref. [ 16].
Table 5 Estimated Tc (K) and/3 (/zB) values in the Fe-Gd and Co-Gd systems
Tc /3
Co23Gd~
FeGd 3
Fe3Gd4
Fe7Gd2
FesGd
836 7.97
476 9.16
681 10.57
560 4.23
470 4.86
Zi-Kui Liu et aL / Journal of Alloys and Compounds 226 (1995) 33-45
39
Table 6 Thermodynamic parameters obtained in present work (in SI units) F e - G d system Liquid
b.c.c.
f.c.c.
°L~q~c,a = - 27625 + 17.869T IL~q~c~ = 14594 -- 8.894T (Fe,Gd)l ° L ~ c ~ = - 28758 + 38.096T (Fe,Gd)l 30231
°L~ee~, Gd =
h.c.p.
(Fe,Gd)l o / . ~ p = 1000000
Fe,TGd: Fe23Gd6 Fe3Gd Fe2Gd FesGd Fe7Gd2 FeGd3 Fe3Gd4
0
C o - G d system Liquid
617Gd2 G~F~:GO -- 1 7 ° G ~ - 2 ° G ~ d = - 228222 + 98.884T O,'~0f~hb¢.c hop '-'F¢:Ga --'--' ~'~ - - "*K0~2tl'-'~a - -~ ...... 182.333T 0 Fe3C,d 0 b¢C - - 0 hcp __ GF,:Gd--3 C,F~ G~d -- - 6 1 3 9 3 + 2 6 . 2 1 4 T 0 FeZGd bee GFe:Gd 2 0 G~F¢ -- 0 ~ d hop -- - 4 6 8 2 9 + 6 3 . 2 9 5 T - 5 . 9 1 7 T I n 0 FezC-d 0 Fel7Gd2 Fe23Gd6 GF~:Gd=0.125 GF~:c,a + 0 . 1 2 5 0 GFe:C,a +6802 0 e7C~12 Fe23Gd6 G~F~:GO = 0.2 0 GFo:~ + 0.8 0 G Fe3Gd ~ : ~ + 6240 0 FeGO3 Fc2Gd hhcp aFe:Gd = 0.5 0 Gv~:c~ + 2.5 0 Gc, a + 12903 orz.~c,,u_ ~ ~ot-z_v~c,a a_ 1 . 5 o ~ o p + 13102 ~Fo:Gd • .--' L/Fe:Gd O/'~Pe23Gd6
--
--
A.
__
--
T - 3 5 3 1 2 1 T - 1 - 9 4 4 6 3 5 4 2 T -3
--
°L~q~ca = - 136388 + 3 2 4 . 4 4 4 T - 34.273T In T IL~q~Go = -- 9689
b.c.c.
( Co,Gd ) 1 °L~oC,Od = 1000000
f.c.c.
(Co,Gd)I ° L ~ . ca = 1000000
h.c.p.
(Co,Gd) 1 ° L ~ ca = 1000000
Col7Gd: Co5Gd Co7Gd2 Co3Gd Co2Gd CoaGd4 CoGda
0
Co23Gd6
A q / ~ 7 ~
ot 7Gd2 lflacp G~co:~ - 170 G ~ o - 2 0 Gc~ = -282208+88.842T osGd 0 p 0 hhcp G~co:c~ - 5 G ~ - Gc,a = - 108678 + 3 7 . 5 4 8 T - 0.74263T In T - 4 2 4 4 0 6 E 5 T - l 0~Co: r : c oC~I ~ _ .~o~r~p _ ,~ 0,-:_hr~p_ _ 202973 + 65.526T / VCo ~ vC~ I -0
0
o~Gd 0 hiacp __ G~co:c,a - 30 ~ Gc~ - - 94127 + 30.262T o2Gd - - 0 - - 0 hhop __ G~co:c,a 2 ~ Goa - - 6 5 8 5 3 + 1 8 . 8 6 4 T 0.r:co~c,~ ao_,,-~op_ A0r:_~p- _ 126432 + 1 2 3 . 3 9 4 T - 11.257T In T 0
~ C o : G d
J
~ C o
~
0
~ C ~
oGd3 0 G~co:c,aG~o-3
0
o23Cn:16 o7Gd2 G~co:~ - 1.3333 0 Gc~:Ga + 2.3333 0 G~F~:Gd + 207624
~
__
op
--
0
__
- -50065+62.515T-6.4326TIn
T
5GO
Table 7 Invariant reactions on liquidus in the C o - F e - G d system
J
200O
T (K)
xl~q
x~
1800-
Liq. Liq. Liq. Liq. Liq.
915 940 1465 1481 1497
0.331 0.197 0.467 0.551 0.0816
0.635 0.695 0.203 0.194 0.279
1600-
T (K)
x~cq o
~
Liq. Liq. Liq. Liq.
943 1325 1462 1500
0.232 0.263 0.405 0.434
0.676 0.488 0.209 0.139
M2Gd + MGd 3 M3Gd + M2Gd MtvGd2 + M3Gd f.c.c. + Mt7Gd2
I
I
J
[
I
I
/
fcc
1200,¢,
1000800-
Equilibrium + + + +
1400-
I-"
Table 8 M i n i m u m or m a x i m u m points on liquidus in the Co-Fe,-Gd system
I
liquid
Reaction --, M2Gd + M3Gd4 + MGda ---*b.c.p. + M2Gd + MGd3 + MTGd2 ~ MtTGd2 + M3Gd + MsGd --~ MlTGd2 + MTGd2 + M17Gd2 + M23Gd6 ~ M3Gd
I
temperature of b.c.c. + l i q . - f.c.c, and the increase in the reaction temperature of Fe17Gd2~f.c.c.~b.c.c. with the addition of Gd [ 28 ].
600-
bcc
4002000
0 0'1 012 013 014 o'.s 016 o'.7 0.8 0'.9 1.0 XCo
Fig. 9. Co--Fe phase diagram calculated from the thermodynamic data by Fem(mdez Guillermet [ 6].
40
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
L
2000-
L
I _ _ L _ _
The heat capacity measurements of the CosGd and Fe2Gd compounds are used to evaluated the parameters c, e and f i n Eq. (13) (Figs. 3 and 4). Fig. 5 depicts the heat capacity measurements of Co2Gd by Leghari [ 18 ] and two calculated curves. The dotted line is obtained by fitting the measurements, and the solid line is from the Neumann-Kopp rule. As can be seen, the dotted curve is much higher than the solid curve. Thus, the Gibbs energy difference between the two curves increases with the temperature. The Co2Gd described by the dotted curve becomes too stable at high temperature with respect to the liquid phase, in comparison with other
1800
zN3uschowet a1.(1969) 1600
. • , ~ A
1400 1200 1000 800 600
1
[ I I Co5Gd AEvaluatedfrom Keller et a1.(1974)
I
A
400 0
0.2
0.4
0.6
0.8
1.0
XCo Fig. 10. Calculated Co-Gd phase diagram from the present thermodynamic
description, with the experimentallymeasurements (A) by Buschowand van der Goot [9] included.
"7, ',C "7, -6 -1 E
E
1900
I
I
I
ABuschow et a1.(1969)
1800
-4
liquid
1700
-2
O9 <1 -3
I
-5 0
i
i
i
I
0.2
0.4
0.6
0.8
XCo
1600
Fig. 12. Calculated entropy of formation in the Co43d system: A, Ref. [ 17] ; Fq, present work.
c~
1500
O
1900
c~
1400
0.5
t
I
o 0
G I
I
I
0.6
0.7
0.8
o 0
I
I
ASavitskii et al.(1963) *Savitsky et a1.(1969)
1800
/
1300
1.0
~/~
1 700 0.9
1.0
/
1600
~bcc
XCo Fig. 11. Enlarged upper part of Fig. 10.
Similar optimization procedures are followed in both binary systems, except that the o/.,~ Odand °L~Coo terms have to be evaluated in the Fe-Gd system. The interaction parameters in the liquid phase are evaluated first, by fitting the heat of mixing (Figs. 1 and 2) and the equilibrium temperatures between liq. ** h.c.p, in the Fe-Gd system and those of liq. ** b.c.c., liq. ** f.c.c, and liq. ** h.c.p, in the Co--Gd system. In the Co-Gd system, the T In(T) term is introduced to fit the heat capacity of the liquid measured by Baricco et al. [ 19], which is about 41 J K - ~ per mole of atoms at about 975 K. The intermetallic compounds are then investigated one after another.
--~
1500
j /,
liquid
1400 1300
E
1200 1100-
-:.•
,L,
~'K. ~
_ _ •
.,.
O00- hop 900 0
LL Ui 0.2
, 0.4
~-
I
0.6
0.8
1.0
XFe Fig. 13. Calculated Fe-Gd phase diagram from the present thermodynamic description, with the experimental measurements by Savitsky and coworkers included: A, Ref. [27]; *, Ref. [28].
41
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45 r
1900
I
I
Copelandeta1.(1962) E]solidus Oqneltni g~DTA +liquidus
1800 1700 1600
During optimization, the failure to achieve a satisfactory representation of certain selected data leads to changes in the model parameters of the phases previously determined. The final set of thermodynamic model parameters is obtained by including all selected experimental information at the same time in the optimization.
I
. ~
.~ -"'-7
"my
1500
4.2. Co-Fe-Gd system
v"
1400
C [] V
1300
Because FesGd, Fe7Gd2, Fe3Gd4, FeGd3 and C023Gd6 are not stable as binary compounds, their lattice stabilities and magnetic properties need to be evaluated. However, because of very limited experimental information, the interaction parameters and the lattice stabilities cannot be evaluated at the same time. In the present work, the interaction parameters in the intermetallic compounds are tentatively set as equal to
1200 1100 1000 9OO
I
0.2
0
0.4
I
I
0.6
0.8
1.0
WFe Fig. 14. Calculated Fe--Gd phase diagram from the present thermodynamic description, with the experimental measurements by Copeland et al. [25] included: r-i, solidus; <>, melting; V, DTA; +, liquidus.
1700
I
I
xl "7 o E
1600
i
15O0 140(I
AFe2GdGermanoetal.(1981)
03
0 -1 -2 -3 -4 -5 -6
1300
-7 0
I
I
I
I
0.2
0.4
0.6
0.8
",..
1200
1.0
XFe Fig. 16. Calculated entropy of formation in the Fe-Gd system: A, Ref. [30].
1100 980
E-3
I 985
I
990
)95
1000
0.9"0Abcc
XFe Fig. 15. Enlarged fight-hand part of Fig. 13, with the ot-y loop superimposed.
compounds described by the Neumann-Kopp rule. Therefore, these measurements are not used in the present work. The heat capacity of Co36.8Gd63.2 in the solid state, measured by Baricco [ 19] is a combination of those of Co3Gd4 and CoGd3. To define the individual contributions uniquely, it is assumed that the ACp value in per mole of atoms is the same for both phases. Fig. 6 presents the experimental measurements with the calculated one. The coefficient a in Eq. (11) is determined by the enthalpy of formauon of the compounds. The experimental measurements by Colinet and Pasturel [ 16] are well reproduced (Figs. 7 and 8). The coefficient b is mostly determined by the incongruent melting temperature of the compound.
0.8 0.7
0.6~~M3Gd4
'cc 2 ;\ 0
0.2
0.4
0.6
0.8
Fig. 17. Liquidus projection of the Co-Fe-Gd system.
1.0
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33--45
42
1800
I
I
I
I
I
Furthermore, from the measurements by Atiq et al. [ 32], one finds that the substitution limits of Co by Fe in CosGd and C07Gd2 at 1323 K are 0.16 and 0.12, respectively, which are not very far away from 0.1, as would be found with the structural stability rule just mentioned, taking into account the effect of the temperature. Thus, it is tentatively suggested here that the substitution limit of Co by Fe in Co3Gd4 is also around 0.1 at 700 K. Under such an approximation, the two three-phase equilibria involving M3Gd4 and MGd3 at 700 K are obtained as h.c.p.+M2Gd+MGd3 and M2Gd+ M3Gd4 + MGd3, respectively, because the three-phase equilibrium h.c.p. + M3Gd4 + MGd3 should not exist. The Tc and/3 values of these unstable phases are estimated by a linear combination of the properties of two neighboring stable phases (see Table 5).
I
.//~fcc+bcc
1700 1600 1500
V 1400 1300
MaGd+M2Gd
1200 1100-
cp+MGd3
1000900
0
011
012
MGd3+M3Gd 4
013 0.14 015
016
0.7 5. Discussion
Fig. 18. Liquidus projection of the Co-Fe-Gd system with the temperature on the vertical axis.
1.0 0.9 0 . 8 ~
T=1323K
0.7 0.6
o.°S .;Z7
0 2
//~@'~
0.1 ' ' - ~
0 A..... 0
+, 1"12...... 3-" J
~ ~
~Gd+U"Gd' rn~d'+M"G
The thermodynamic description of the Co--Fe-Gd system obtained in the present work is presented in Table 6. The Co-Fe binary phase diagram is presented in Fig. 9 for the reader's convenience, calculated from the thermodynamic data assessed by Fern~dez Guillermet [6]. Fig. 10 depicts the Co-Gd phase diagram calculated from the present work. A satisfactory agreement with the measurements by Buschow and van der Goot [9] can be observed from the upper part of the diagram enlarged in Fig. 11. The satisfactory agreement between the calculations and experiments can also been seen from Figs. 1, 3, 6 and 7. Fig. 12 shows the calculated entropy of formation in the Co-Gd system, noting that CosGd is not stable at 298 K. The calculated Fe-Gd binary phase diagram is presented in Figs. 13 and 14 from the present thermodynamic description of the system, in comparison with the measurements by Savitsky and coworkers [27,28] and Copeland et al. [25] respectively. The calculations agree better with the measurements by Savitsky and coworkers than with those by Cope-
Fig. 19. Isothermal section of the Co--Fe43d system at 1323 K.
1.0 zero. The lattice stabilities of FesGd, Fe7Gd2 and Co23Gd6 are then evaluated from the three-phase equilibria at 1323 K, as measured by Atiq et al. [32], with respect to two neighboring stable phases. The lattice stabilities of FeaGd4 and FeGd3 can only be deduced from the work by Poldy and Taylor [33,34]. The substitution limit of Co by Fe in CoGd3 is taken as 0.1 at 700 K from their experimental observation. They further satisfactorily interpreted their results in terms of the structural stability rule, which states, "if a stable structure exists for which the Fermi energy lies above the 3d electron energy band, then any change which leads to the Fermi level intersecting the 3d band will probably cause the structure to become unstable". They also applied this structural stability rule to the substitution limit of Ni by Fe in Gd3Ni and that of Ni by Cu in GdNi2, achieving satisfactory agreement [42].
0.9/~ 0.8 0.7 0.6
T=700K
0' 0.4 "ed.~:~i;~G'J3 VM'G'+M.G<~'~
o.,g,/f/ /+,o../7't oo,
0
0.2
0.4
0.6
0.8
1.0
XCo Fig. 20. Isothermal section of the Co-Fe-Gd system at 700 K.
43
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45 I
1800
I
I
in the figure. It can be seen that the temperature has a minimum for the three-phase equilibria liq. +MaGd+M2Gd, liq. + M~7Gd2+ M3Gd and liq. + f.c.c. + MlTGd2, and maximum for liq. + M2Gd + MGd3. The temperatures and the liquid compositions of these points are presented in Table 8. It should be pointed out that there is uncertainty over the two four-phase equilibria close to the Gd comer, as a result of the arbitrary setting of the substitute limits of Co by Fe in M3Gd4 and MGd3. In Fig. 20, one notices that MI7Gd2 is only stable in the composition range close to the Fe-Gd and CoGd binary sides, but not in the middle. This will be discussed further later. With the thermodynamic description of the Co-Fe-Gd system obtained, one can now make relevant calculations for
I
liquid
1600 -
co
1400 M17Gd2
1200 I.-" 1000 800 600 400 -
I
1580
200 o
I
I
I
o,
liquid+M5Gd//
1560
///
1540 I
1800 1600 [
I
~
I
I
,,¢,, I.-" 1520
liquid
1400
~~
1500 7Gd2+M3Gd// /
1200-
MFGd2
liquid+M~/
_
1480
I.--" 10001460
800-
I w Ij
0
..,,-~2..-.3--
,
0.2
0.4
irl
f
0.6
1.0
0.8
XCo/(Xco+XFe)
600-
Fig. 23. Enlargementof the upperpart of Fig. 22.
40020'3
--
I
i
I
r
0.2
0.4
0.6
0.8
XCo/(Xco+XFe)
0.26 1.0
I
I
~ T =
I
I
M3Gd 1500K M7G 2d
0.24
Fig. 22. Verticalsectionof MTGd2. land et al. It should be noted that Copeland et al. did not follow their results when drawing the phase diagram themselves. In Fig. 15, the enlarged phase diagram close to the Fe side is presented with the a - y loop superimposed by dotted lines. Fig. 16 depicts the calculated entropy of formation in the system, with the measurement by Germano and Butera [30] included. The liquidus projection (Figs. 17 and 18) and the isothermal sections at 1323 K (Fig. 19) and 700 K (Fig. 20) are calculated and compared with the experimental information available. The invariant reactions on the liquidus are listed in Table 7. Fig. 18 is also the liquidus projection, but with the temperature plotted on the vertical axis. The phases in equilibrium with the liquid phase in various curves are presented
I
0.22 .~ 0.20 0.18
~
M5Gd
0.16 0.14 0.58
I
I
I
0.60
0.62
0.64
I
0.66
XCo
0.68
0.70
Fig. 24. Part of the isothermalsectionof the Co-Fe--Gdsystemat 1500 K.
44
Zi-Kui Liu et al. / Journal of Alloys and Compounds 226 (1995) 33-45
practical interest. As examples, Figs. 21 and 22 depict the pseudo-binary system of Fel7Gd2-Col7Gd2 and the vertical section of M7Gd2. The upper part of Fig. 22 is enlarged in Fig. 23. It can be seen that the b.c.c, phase appears at low temperatures in both diagrams. The reason is the negative interaction parameter between Fe and Co in the b.c.c, phase in the Fe-Co binary system, i.e. /ff~Co:Cd= - 23 669 + 103.9627T- 12.7886T ln(T) J molwhile it is set equal to zero in the Fe17Gd2---Co17Gd2pseudobinary system. However, to make M17Gd2 stable in the middle of the pseudo-binary system at low temperatures, an inter. parameter of/_~, M 17Gd2 action Co:Cd----"-- 350 000 J mol- 1 is needed. One would also have to introduce z'Fe, r ~ BCo:Gd for M2Gd and MaGd to make them stable over the entire composition range between the Fe-Gd and Co-Gd binaries. However, there is no experimental information to support this modification, except magnetic measurements by Chen et al. [38] in the pseudo-binary system, but Chen et al. did not examine the microstructure of their specimens. Thus, we feel that such modification should be carried out later, when there is more convincing experimental evidence. In both diagrams in Figs. 21 and 22, one notices several occasions where a phase boundary separates a three-phase field and a one-phase field, but this does not violate the phase rule and can be understood by examining the isothermal section shown in Fig. 20. For example, let us consider the Fe17Gd2---Co17Gd2 pseudo-binary system at 700 K. From the Fe-Gd binary side, M~TGd2 one-phase state is stable until the b.c.c., Mx7Gd2 and M3Gd three-phase equilibrium triangle is reached. With a further increase in the Co content, one enters into a three-phase equilibrium field. However, in calculating the pseudo-binary system, the Gd content cannot be exactly on the pseudo-binary plane. As can be seen from Fig. 20, one will then obtain very different diagrams, depending on if the Gd content is slightly higher or lower than that on the pseudo-binary plane. This problem has been discussed in detail by Huang et al. [43]. In the present plotting, all the lines which are not exactly on the pseudo-binary plane are excluded to give a simple picture of the pseudo-binary system and the vertical section. This is why there are phase boundaries separating a three-phase field and a one-phase field. It should be mentioned that the boundary between M7Gd2 and liq. + M7Gd2 in Fig. 23 cannot be calculated by normal phase diagram mapping, but has to be calculated separately by only considering the two-phase equilibrium between the liquid and M7Gd2 phases. This can be understood by examining the isothermal section at 1500 K, for example, as shown in Fig. 24. The calculated phase boundary in the normal phase diagram mapping would represent either liq. + M3Gd + MTGd2 or liq. + MsGd + M7Gd2, while the experimentally observed boundary in the vertical section would be neither of these, but the point A in Fig. 24, which
is represented by the phase boundary in Fig. 23 for various temperatures.
6. Conclusions The thermodynamic properties of the Co--Fe--Gd system are evaluated from the experimental information available in the literature, based upon the three binary systems, i.e. CoFe, Co-Gd and Fe-Gd. The properties of the Co-Gd and FeGd systems are evaluated in the present work. With the thermodynamic description available, one can now make various calculations of practical interest.
Acknowledgements One of the authors (WZ) is grateful for financial support by the NSFC (China) and thanks the Tm~RMO-CALCproject for his visit to the Royal Institute of Technology, during which the main part of the present work was conducted. The authors are grateful to Prof. John/~gren for encouragement and support during this work.
References [ 1] K.H.J. Buschow, Rcp. Prog. Phys., 40 (1977) 1179-1256. [2] K.H.J. Buschow, Mater. Res. Bull., 19 (1984) 935-943. [3] L. Kaufman and H. Bemstein, Computer Calculation of Phase Diagrams, Academic Press, New York, 1970. [4 ] M. Hillert and L.-I. Staffansson, Acta Chem. Scand., 24 ( 1970 ) 36183626. [5] A.T. Dinsdale, CALPHAD, 15 (1991) 317-425. [6] A. Fermtndez Guillermet, High Temp. High Pressure, 19 (1987) 477499. [7] M. Hillert and M. Jarl, CALPHAD, 2 (1978) 227-238. [8] V.F. Novy, R.C. Vickery and E.V. Kleber, Trans. Metall. Soc. AIME, 221 (1961) 588-590. [9] K.H.J. Buschow and A.S. van der Goot, J. Less-Common Met., 17 (1969) 249-255. [10] W.Q. Ge, C.H. Wu and Y.C. Chuang, Z. Metallkd., 83 (1992) 300303. [11] H. Okamoto, J. Phase Equil., 13 (1992) 673-674. [ 12] I.V. Nikolaenko and M.A. Turchanin, Rasplavy, 5 (1989) 77-79. [ 13] S.S. Deodhar and P.J. Ficalora, High Temp. Sci., 8 (1976) 185-193. [ 14] J. SchoU and F. Sommer, J. Less-Common Met., 119 (1986) 307--317. [15] C. Colinet, A. Pasturel and K.H.J. Buschow, Metall. Trans. A, 18 (1987) 903-907. [16] C. Colinet and A. Pasturel, CALPHAD, 11 (1987) 323-324. [ 17] D.A. Keller, S.G. Sankar, R.S. Craig and W.E. Wallace, Am. Inst. Phys. Conf. Proc., 18 (1974) 1207-1211. [18] S.B.K. Leghari, J. NaturalSci. Math., 29 (1) (1989) 69--85. [19] M. Baricco, C. Antonions and L. Battezzati, Scr. Metall., 21 (1987) 849-852. [20] E. Burzo, Phys. Rev. B, 6 (1972) 2882-2887. [21] R. Lemalre, Cobalt, 32 (1966) 132-140. [22] R. Lemaire, Cobalt, 33 (1966) 201-211. [23] O. Kubaschewski, IRON-Binary Phase Diagrams, Springer, Berlin, 1982. [24] V.F. Novy, R.C. Viekery and E.V. Kleber, Trans. Metall. Soc. AIME, 221 (1961) 580-585.
Zi-Kui Liu et aL / Journal of Alloys and Compounds 226 (1995) 33~15 [25] M.I. Copeland, M. Krug, C.E. Armantrout and H. Kato, USBur. Mines, Rep. Invest., 5925 (1962). [26] F. Spedding, A. Daane, B. Beaudry, I. Haefling, F. Hunter, M. Michel, H. Rider, F. Smidt, R. Valletta and W. Wunderlin, U.S. Atom. Energy Commun., 1S-700 (1963) C15. [ 27 ] E.M. Savitskii, V.F. Terekhova, 1.V. B urov and O.D. Chistyakov, Russ. J. Inorg. Chem., 6 (1961) 883-885. [28] E.M. Savitsky, V.F. Terekhova, R.S. Torchinova, I.A. Markova, O.P. Naumkin, V.E. Kolesnichenko and V.F. Stroganova, Proc. Conf. Les Elements des Terres Rares, Paris-Grenoble, 5-10 May 1969, Vol. 1, pp. 49-60. [29] I.V. Nikolaenko and V.V. Nosova, Soy. Prog. Chem., 55 (2) (1989) 30-33. [30] D.J. Germano and R.A. Butera, J. Solid State Chem., 37 ( 1981 ) 383389. [31] W.E. Wallace and E. Segal, Rare Earth lntermetallics, Academic Press. New York, 1973. [32] S. Atiq, R.D. Rawlings and D.R.F. West, J. Mater. Sci. Lett., 9 (1990) 518-519. [33] C.A. Poldy and K.NR. Taylor, J. Less-Common Met., 27 (1972) 9597.
45
[34] C.A. Poldy and K.N.R. Taylor, J. Phys. F, 3 (1973) 145-156. [35] K.P. Belov, V.A. Vasil'kovkskii, N.M. Kovtun, A.K. Kupriyanov and S.A. Nikitin, JETP Lett., 20 (1974) 304-305. [36] E. Burzo, J. Phys. Coll. C5, 40 (1979) 184-185. [37] W.M. Hubbard and E. Adams, J. Phys. Soc. Jpn., 17 (BI) (1962) 143-146. [38] H. Chen, W.-W. Ho, S.G. Sankar and W.E Wallace, J. Magn. Magn. Mater., 78 (1989) 203-207. [39] B. Jansson, Evaluation of parameters in thermochemical models using different types of experimental data simultaneously, Trita-Mac-0234, Royal Institute of Technology, Stockholm, 1984. [40] B. Sundman, B. Jansson and J.-O. Andersson, CALPHAD, 9 (1985) 153-190. [41] A. Fernfmdez Guillermet and W. Huang, Z. Metallkd., 79 (1988) 8895. [42] C.A. Poldy and K.N.R. Taylor, Phys. Status Solidi A, 18 (1973) 123128. [43] W. Huang, M. Hillert and X. Wang, Thermodynamic assessment of the Cao-MgO-SiO2 system, Trita-Mac-0530, Royal Institute of Technology, Stockholm, 1993, Metall. Mater Metall. (1995) in press.