- Email: [email protected]
Thermodynamic modeling of some aluminium-rare earth binary systems: Al-La, Al-Ce and Al-Nd
Calphad, Q 2002
Pergamon
Vol. 25,
No.
4, pp. 583-597, 2001
Published by Elsevier Science Ltd 0364-5916/01/$ - see front matter
PII: SO364-5916(02)00009-3
Thermodynamic Modeling of Some Aluminium-Rare Earth Binary Systems: Al-La, Al-Ce and Al-Nd
G. Cacciamani and R. Ferro Universiti di Genova, Dipartimento di Chimica e Chimica Industriale via Dodecaneso 31 - 16146 Genova Corresponding author’s e-mail: [email protected] (Received October 16,200l) Abstract. A thermodynamic modeling and optimization of the Al-La, Al-Ce and Al-Nd systems has been carried out on the basis of the literature information available. The compound energy formalism has been used to describe the thermodynamic functions of either solution and stoichiometric phases present in the systems. Present results are discussed and compared to the previous optimizations. 0 2002 Published by Elsevier Science Ltd. Introduction The alloys of aluminium with the rare earth metals (R metals) show several interesting applications. Lanthanide additions to Al-based alloys are very effective in enhancing mechanical properties (see e.g. [OOLun]), beneficial effects on corrosion resistance have been described [97Sta], [89Jed]. A wide bibliography [98Ino, 89Cah, OOPin] is available, moreover, on the effects of rare earths in the preparation, and properties, of amorphous Al-based alloys. For a long time our team has been involved in the investigation of several groups of rare-earth alloys (and of the related systematics). As for the specific case of alloys with Al, recent contributions of ours are the following: - Contributions to the study of the alloys and intermetallic compounds of aluminium with the rare earth metals [98Sac], - Thermodynamics of homogeneous crystal nucleation in Al-R metallic glasses [98Bar]; - Systematics of lanthanide and actinide compound formation: remarks on the americium alloying behaviour [OlFer]. -The Al-Er-Mg ternary system. Part I: experimental investigation [02Sac] and Part II: thermodynamic modelling [02Cac]. Work is in progress along these lines. It seemed important, however, to have a good assessment and optimisation of the binary R-Al systems. A systematic revision of these systems has been started, beginning with the light lanthanides. Considering the R-Al systems for which experimental data are widely available, the systems La-Al, Ce-kl and Nd-Al have first been examined: they will be presented and discussed in this paper.
Literature information Al-La system Al-La phase equilibria have been mainly investigated by Buschow [65Busl], in the whole composition range, Kononenko and Golubev [90Konl on the Al-rich side up to 3 at% La, and Saccone et al. [96Sac] in the
563
584
G. CACCIAMANI
AND
R. FERRO
La rich region up to 35 at% Al. An assessment of the system was compiled by Gschneidner and Calderwood [88Gscll. The Al-La phases are listed in Table 1 together with crystallographic information. Thermodynamics has been investigated by several authors: the enthalpy of formation of one or more individual solid phases was measured, by means of calorimetric methods, by Canneri [32&n] and then by Colinet et al. [85Col], Sommer et al. 188Som1, Jung et al. 191Jun1, Meschel and Kleppa [93Mes] and, recently, by Borzone et al. [97Borl who determined the whole trend of ArH as a function of composition at 300 K by direct reaction calorimetry. Thermodynamics of the solid phases was also investigated by Kober et al. [77Kob] by e.m.f. measurements at 400 to 6OoPC.Measurements in the liquid phase were carried out by Lebedev et al. [72Leb] (activity coefficient and solubility limit in the Al rich region at 680 to 85O*C by the e.m.f. method), Esin et al. [81Esi] (La partial enthalpy of mixing at 1920 K and 0 to 46 at% La by high temperature calorimetry), Sommer et al. 188Soml (partial and integral enthalpy of mixing by calorimetry at 1200 K). Deenadas et al. [71Dee] measured the heat capacity of LaAls in the 8 to 300 K temperature range. A thermodynamic optimization of the system was carried out by Wang [94Wan], before the papers of [96Sac] and [97Borl. AI-Ce system Al-Ce phase equilibria were first investigated by Vogel [12Vog] and then by van Vucht [57Vuc], Buschow and van Vucht [ZEBUS]in the whole composition range, Kononenko and Golubev [90Kon] in the Al-rich end up to 3 at% Ce, and Saccone et al. 196Sacl in the Ce rich region up to 35 at% Al. An assessment of the system was compiled by Gschneidner and Calderwood [88Gsc2]. The AI-Ce phases are listed in Table 1 together with crystallographic information. Thermodynamics has been investigated by several authors. The enthalpy of formation of one or more individual solid phases was measured, by means of calorimetric methods, by Biltz and Pieper [24Bil], Colinet et al. [85Col], Sommer and Keita [87Som] and, finally, by Borzone et al. [91Borl who determined the whole trend of ArH as a function of composition at 300 K by direct reaction calorimetry and by Cacciamani et al. [95Cac]. Thermodynamics of the solid and/or liquid phases was also investigated by Yamshchikov et al. [77Yam] (partial properties of Ce by e.m.f. method at 700 to 900 K in the solid state and at 900-1100 K in the liquid), Esin et al. [79Esil (partial and integral enthalpy of mixing at 1870 K by solution calorimetry), Shevchenko et al. [79Shel] (activity of the elements in the liquid at 1423 to 1673 K by the Knudsen effusion method), Yamshchikov et al. [8OYam] (solubility of Ce in Al at 950 to 1130 K by e.m.f. method), Kober et al. [82Kob] (Ce partial Gibbs energy in the solid two-phase fields at 800 K by e.m.f. method), Yamshchikov et al. [83Yam] (enthalpy of dissolution of Ce in molten Al at 1013 K by calorimetry). Deenadas et al. [71Dee] measured the heat capacity of CeAls in the 8 to 300 K temperature range. Further experimental work, also in connection with the glass-forming ability of the Al-Ce alloys, was performed by Baricco et al. [93Bar] by measuring heat capacity and melting enthalpy of selected Al-Ce alloys. A first optimization of the system was carried out by Cacciamani et al. [9OCacl, followed by partial or full revisions made on the basis of new literature data [98Cacl and in order to obtain a thermodynamic description of the amorphous phase [98Barl. Al-Nd system
AI-Nd phase equilibria were first investigated by Buschow [65Bus21 in the whole composition range, by Kononenko and Golubev [90Kon] in the Al-rich side up to 6 at% Nd, and Saccone et al. [96Sac] in the Nd rich region up to 30 at% Al. Kale et al. [97Kall studied the Al-rich eutectic obtaining contradictory results with respect to [90Kon]. An assessment of the system was compiled by Gschneidner and Calderwood [~~Gsc]. The Al-Nd phases are listed in Table 1 together with crystallographic information. Thermodynamics has been investigated by several authors. The enthalpy of formation of NdAlz was measured by Colinet et al. [85Col], by Al solution calorimetry. Borzone et al. [93Bor] determined the whole trend of ArH as a function of composition at 300 K by direct reaction calorimetry. Thermodynamics of the solid and/or liquid phases was also investigated by Zviadazde et al. [76Zvi] (enthalpy of mixing of the liquid at 1250 to 1550 K by high temperature calorimetry), Kereselidze et al. [77Ker] (enthalpy of mixing by the e.m.f. method at 1033 K), Kober et al. [79Kob] (partial Gibbs energy of Nd in two-phase fields at 800 and 1000 K by the e.m.f. method), Shevchenko et al. [79She21 (partial Gibbs energy of Al in the liquid at 1700 K
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
585
by vapour pressure measurements), Kober et al. [84Kobl (partial Gibbs energy of Nd in two-phase fields at 800 K by the e.m.f. method). Deenadas et al. [71Deel measured the heat capacity of NdAls in the 8 to 300 K temperature range. The Al-Nd system was first optimized by Cacciamani et al. [93Cac] and, independently, by Clavaguera and Du [96Cla] and Wang 196Wanl. More recently the optimization by [93Cac] has been revised by [98Cac] on the basis of the new literature available, and by [98Barl in order to model the amorphous phase.
Table 1: Nomenclature and crystallographic structures of the solid phases Phase names Al-Ce
Al-La
(Al), @La) ($a) (aLa) LaAlz aLasAl 1 (3La3Ah1 LaA13 LazzAlss LaAl ___ ___ LasAl ___
(Al), (yCe) We) ___ CeAlz aCesAl 1 (3CeAh 1 CeAL ___ CeAl ___ ___ aCesA flCesA1
Al-Nd
(Al) @Nd) (aN4 NdA12 aNdsAl 1 (JNd3AllI NdA13 ___ ___ NdAl Nd2Al Nd3Al ___
Thermodynamic
The thermodynamic the following.
Pearson symbolStructure type
cF4-Cu cI2-w hP4-aLa cF24-CusMg oI28-aLasAl tIlO-AlABa hP8-NisSn hP3-AIBz oC16-AlCe oP16-AlEr 0PlZCosSi hP8-NisSn cPCAUCU,
Names used in the Appendix
fcc_Al bcc_A2 dhcp_A3’ RAlz c&All 1
PRsAll1 RA13 RzzAls3 RAl_CeAI RAl_ErAl R2Al RsAl_NisSn R3AI_AuCu3
modeling
models here adopted are summarized in the Appendix and briefly introduced in
Elements The Gibbs energy of the pure elements is referred to the enthalpy of the element in the SER (Standard Element Reference) state. The Gibbs energy functions of the pure elements were taken from the PURE database [96SGT]. Phases
The Gibbs energy of the various phases is expressed according to the compound energy formalism [OlHil]. According to this formalism, the different atoms forming the phase occupy one or more sublattices and thermodynamic quantities are expressed as a function of the site fractions. The model is suitable for the description of either stoichiometric compounds and of both disordered and ordered solutions. In general the total Gibbs energy of a phase cpis given by the sum of three contributions: G’p =
Rfe’G’P + id@ +
e”@
where the three terms assume different forms according to the kind of sublattice model adopted. Stoichiometric compounds. Stoichiometric compounds are represented with as many sublattices as the number of component elements, with only one atom type in each sublattice. In the binary case the model is (A),(B), and the three contributions to the Gibbs energy are:
586
G. CACCIAMANI
"fG'p = d(u+v)
GAsER +
AND R. FERRO
vI(u+v) GBsER + LA:B(p
0)
idG=O ‘“G=O
where L,M’ = A~G(cplis the Gibbs energy of formation of the phase referred to the SER state of the component elements. This model was adopted for most intermediate phases in the three systems. In all cases the L interaction functions were assumed to be: L=a+bT
(2)
where a and b are temperature- and composition-independent
parameters to be optimized.
Liquid and solid substitutional solutions., Substitutional solutions are represented by only one sublattice where all the atoms mix together. In the binary case (A,B) the three contributions to the Gibbs energy are: “%’ = XAGaq + xa GeV idG’p= R T [XAht.d + XB hhB)] exGq = XA
XB
&
(3)
“LA,B’ (XA- ~p.1~
where GAGand GB~are the Gibbs energies of the pure elements in the cpstructure and the L functions have the form indicated in eq. (2). This model was adopted for the liquid and for the terminal fee, bee, dhcp solutions. Ordered solid solutions. Ordered solid solutions are represented by a two sublattice model where each sublattice is preferentially occupied by a specific elements but other elements are allowed to mix in the same sublattices. A binary phase of this kind may be represented by the model &B),(A,B),, the first sublattice being mainly occupied by A and the second by B. IfyA’, yA”,ya’ and ya” are the site fractions of the elements A and B in the first (‘1 and second (“1 sublattice respectively, the fully ordered state corresponds to the conditions yA’=I, YA”=~,ya’=O, ya”=l; the fully disordered state corresponds to the condition xe = ya’ = ya” (same composition in each sublattice and in the overall phase). The contributions to the Gibbs energy are: refGcp=YA’~A” GA,A’ +y~‘ya” GA,B’ +YB’YA”GB,A’ +ya’ya” Ga,a’ idG’p= R T ‘“G’
(U/(u+V)
=_YA’_YB’_YA”
bA’
z
+YA’~A”~B”
+_YA’_YB’_YA”YB”
h(vA’)
“LA.B:A~
z
‘LA:A,B’
2~
+yB’
h(yB’)]
(YA’ -YB’)”
(YA”
“LA,B:A,B’
+ Vi(U+Vj
+YA’YB’YB”
-_YB”)’
b.4”
&
h(vA”)
“LA,B:B’
+_YB’_YA”_YB”
(YA’ -YB’)~
(YA”
x,
+yB”
(4) h(vB”)]}
(YA’ -YB’)’
“LB:A.B’
(VA”
-_YB”)’
-_YB”)~
It may be emphasized that when more atoms mix in a sublattice (see eq. (3)) “‘GV requires the Gibbs energy of the pure elements in the cp phase to be known even if it is not a stable phase for the element. Similarly, when more sublattices are used and more atoms occupy each sublattice, terms of the type GA:~’ appear in “‘CT (see (4)). They correspond to the Gibbs energies of formation of hypothetical stoichiometric compounds metastable in the system. Nevertheless they have to be evaluated in some way, together with the vL’L’parameters (which still have the form shown in eq. (2)). This model was adopted here for the Laves phase present in the three systems at the composition RAlz (R=La, Ce, Nd) in order to be compatible with the description of the same phase already adopted in several other systems, even though no information about the solubility range is reported in literature for the R-Al systems.
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE Optimization
EARTH BINARY SYSTEMS
587
procedure
It has been remarked that several properties of the rare earths present regular and smooth variations on passing from one element to the next. This is particularly true when considering the group of the trivalent rare earths (from La to Lu, except Eu and Yb) or even smaller subgroups like the light (from La to Sm) or the heavy (from Gd to Lu, except Yb) rare earths. Such behavior of the pure elements extends to their alloys and similar regularities may also be observed when considering series of R-Me binary alloys of the rare earths with the same partner Me. In the modeling and optimization of rare earth binary systems this characteristic may constitute an additional criterion for the selection of the more reliable experimental data and for the discussion of the optimization results. This implies that, if possible, at least two or three systems should be studied at the same time and the regular variation of the properties considered (in our case thermodynamics, phase diagrams, phase structures, etc.) should be verified. The present optimization and calculations have been performed by means of the Thermo-Calc software package [85Sun]. In the optimization of the three binary systems Al-La, Al-Ce and Al-Nd phases having the same crystallographic structure have been generally described by the same thermodynamic models and the same type and number of interaction parameters. In a first optimization stage all the experimental data available were used with the same optimization weight. Then, on the basis of the first optimization results and of a critical discussion of the reliability of the different literature data (intrinsic accuracy of the experimental technique employed, purity of the starting materials, check of the equilibrium state of the samples, etc.) the optimization weights of the different sources were slightly modified. Only in a few cases, experimental data were rejected and not considered for the optimization, due to their inconsistency with the majority of the other data (see the next paragraph for a detailed discussion of this point).
Results and Discussion The thermodynamic models adopted and the Gibbs energy functions for all the phases in the Al-La, Al-Ce and Al-Nd systems are summarized in the Appendix, where the underlined parameters are those optimized in this work. The calculated phase equilibria are presented and briefly discussed in the following. In general, no excess heat capacity was optimized, due to an insufficient literature information: in the case of the liquid phase, however, this is probably a too rough approximation and miscibility gaps appear in the computed liquid phase at temperatures higher than 2500-3000 K, caused by the quite large values of the entropy of mixing. Optimized low temperature phase equilibria, on the other hand, looks reasonable down to temperatures lower than 100 K. We can conclude that the results of the present optimization may be considered reliable in the 200 to 2500 K temperature range. Al-La system The optimized Al-La phase diagram is shown in Fig. 1 together with the experimental liquidus points. Optimized invariant equilibria are reported in Table 2 for easier comparison with the literature. Standard enthalpy and entropy of formation of the solid phases are shown and compared to the literature data in Fig. 2. Enthalpy, entropy and Gibbs energy of mixing at 1200 K of the liquid phase are shown in Fig. 3. Calculated values are in agreement (within the experimental uncertainties) also with the results by [72Leb] and [71Dee]. The results by [77Kob] however looks inconsistent with the other experimental data and have been rejected during the optimization. Similar inconsistencies have been observed for the data obtained from e.m.f. measurements in various R alloys. A general good agreement between experimental data and optimization results may be noticed. Small discrepancies concern type and temperature of a few invariant equilibria (peritectic instead of congruent melting of PLasAlrt, peritectic instead of peritectoidic formation of LaAlj). The experimental determination of such equilibria is very difficult, due to the reactivity of the involved elements, and, in some cases, it was carried out several years ago: for these reasons it was considered not necessary to introduce more complex thermodynamic functions in order to match more closely such uncertain experimental data.
588
G. C A C C I A M A N I A N D R. FERRO I
I
~
I
[] [65Bus1] A [90Kon] ~,[96Sac]
...,~
.~
1500
I
~
5~
"-" 1200 t.-
,.-t
Q.
E 900 -
/
,.
I--
La3AI~'~
600 (A1)
300
~
0
~
(aLa)
.1 I
I
0.6 0.4 Mole fractionLa
0.2
0.8
1.0
Fig. l: Optimized A1-La phase diagram compared to a selection of experimental points. Notice that peritectic formation of LaA13and La-rich eutectic are not resolved in the figure.
I
I
I
0
I
-6 E
-10~'~'-20-
p
I
I
016
018
-10-
~"2'
|
~
~ ~ -404
-40
[]
ttl
'"
-50 ] 0
I
~-30
E
-60
I
°
-50 &[88Som] 1200 K m[81Esi] 1920 K
0:2
0:4
o18
o:a
1.o
Mole fraction La
Fig. 2: AI-La system: enthalpy and entropy of formation of the solid phases at 300 K.
-6
0
012
014
1.0
Mole fraction La
Fig. 3: AI-La system: enthalpy, entropy and Gibbs energy of mixing of the liquid phase at 1200 K.
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
589
Similar considerations are also applicable to the optimizations of Al-Ce and AI-Nd systems, discussed here below, and other Al-R systems like Al-Sm [98Sacl, AI-SC [99Cac] and Al-Er [02Cac]. On the other hand it may be noted that, according to the assessment performed by [94Wang], where 15 optimization coefficients and Legendre polynomials up to the fifth order have been used to describe the excess Gibbs energy of the liquid phase in order to match the assessed version [89Gsc] of the phase diagram, a miscibility gap (not reported in the paper) appear at T>1500 K and thermodynamic functions of the liquid assume unrealistic trends at higher temperatures. Even in the present optimization, due to the quite large entropy contribution, a miscibility gap appear if the liquidus parameters are extrapolated at temperatures higher than 2500 K.
Table 2: Calculated invariant equilibria in the Al-La system. Composition Invariant equilibrium
Temperature 00
First Phase (At % La) 2.32 21.43
Second Phase (At % La) 21.43 21.43
Third Phase (At % La) 0.00 ___
913 1200
Liquid t) czLasAlrl + (Al) SLasAlIr H aLasAll
1.511
Liquid + LazzAls3 tj
19.00
29.33
21.43
1542
Liquid + LaAlz C) LazzA153
20.83
32.83
29.33.
1324 1445 1658
LaazAlss w LaAls + LaAl2 PLasAlrr + LazzAlss w LaAls Liquid H LaAlz
29.33 21.43 33.62
25.00 29.33 33.62
33.12 25.00 ___
1137 800.7 800.6 672
Liquid Liquid Liquid LasAl
60.31 76.69 76.71 75.00
37.69 50.00 75.00 50.00
50.00 75.00 99.99 99.99
1117
(yLa) H Liquid ‘+ @La)
99.49
94.95
99.99
+ + H t)
@LasAlrr
LaAlz H LaAl LaAl H La3Al LaxAl + (@La) LaAl + @La)
Table 3: Calculated invariant equilibria in the Al-Ce system. Composition Temperature (IQ
Invariant equilibrium
First Phase (At % Ce) 2.60 21.43
Second Phase (At % Ce) 21.43 21.43
Third Phase (At % Ce) 0.00 ___
904 1290
Liquid H aCesAltr + (Al) flCesAll1 t) aCesAl
1529 1407 1748 1116 925 930
Liquid + CeA& (3CesAllt PCe3AIrI + CeAlz t) CeAl3 Liquid t) CeAl2 Liquid + CeAlz f~ AlCe Liquid e AlCe + aCesA Liquid CJ aCesA
18.74 21.43 33.57 62.92 72.13 75.00
32.93 33.08 33.57 37.88 50.00 75.00
21.43 25.00 --_ 50.00 75.00 -__
866 523
Liquid w aCesA + ($e) aCesA w (3CesAl
86.47 75.00
75.00 75.00
99.99 ___
961
(6Ce) TV Liauid + (yCe)
98.67
92.60
99.99
590
G. C A C C I A M A N I A N D R. FERRO
1800
I
i
,.oo / 900
I
v [66Bus]
z [80Yam] A [90Kon] ~ [96Sac]
/~ / ~ . -
1500
~"
i
/
-
_ _
oT
600 L (Al) rj
30O
0
0.2
r.J
0.4
rJ I
I
0.6
0.8
1.0
Mole fraction Ce Fig. 4: Optimized AI-Ce phase diagram compared to a selection of experimental points.
0
I
I
I
I
"ot~,
-10
~
~.~oJ ~,\
~" ~" -20 E-~ "E
/
///
~.~-3o-
w w -40-
y-:[~o~,
,0
& 91Bor] x [95Cac] -60
0
0:2
014
016
0:8
"t
N c w
1.0
Mole fraction Ce
Fig. 5: AI-Ce system: enthalpy and entropy of formation of the solid phases at 300 K.
-50 -60
rq [76Zvi] 1250 K & [79Esi] 1870 K 0
012
014 016 Mole fraction Ce
018
1.0
Fig. 6: AI-Ce system: enthalpy, entropy and Gibbs energy of mixing of the liquid phase at 1200 K.
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
591
Al-Ce system
The optimized Al-Ce phase diagram is shown in Fig. 4 together with the experimental liquidus points. Optimized invariant equilibria are reported in Table 3 for easier comparison with the literature. Figs. 5 and 6 show integral thermodynamic functions of formation of the solid and liquid phases, respectively. The activity of the elements in the liquid phase at 1673 K are shown in Fig. 7 and low temperature heat capacity of CeAlz is reported in Fig. 8. The optimization results show a good agreement also with the C, data reported by [93Bar]. The e.m.f. measurements by [77Yam] and [82Kob], however, seems to be inconsistent with the other experimental data and have been rejected during the optimization. The general good agreement, within the limits of the same considerations applied to the Al-La system, between experimental and calculated values may be noticed. Present results have to be, considered an update of the optimization previously carried out by [98Cac].
Al-Nd system
The optimized Al-Nd phase diagram is shown in Fig. 9 together with the experimental liquidus points. Optimized invariant equilibria are reported in Table 4 for easier comparison with the literature. Small discrepancies may be noticed between calculation and experiments in the liquidus curve close to the Nd-rich eutectic. Figs. 10 and 11 show integral thermodynamic functions of formation of the solid and liquid phases, respectively. General considerations reported for Al-La and Al-Ce hold for Al-Nd also. The optimization results show a good agreement also with the C, data reported by [71Dee] and the partial Gibbs energy of Nd in the liquid at 1033 K measured by [77Kerl. The vapor pressure measurements by [79She2] and the e.m.f. measurements by [79Kob] and [84Kob], however, seems to be inconsistent with the other experimental data and have been rejected during the optimization. The present re-optimization of the Al-Nd system has to be considered an update of the optimization previously carried out by [98Cac]. Present results are also in quite good agreement with the optimizations by [93Cac, 96Cla, 96Wan] which, however, do not take into account the more recent literature data by [96Sac].
0.6-I
_
\
"/
0
0
0.2
0.4
0.6
0.6
1.0
Molefraction Ce Fig. 7: Al-Ce system: activity of Al and Ce in
the liquid phase at K.
0
I 50
I I I I I I 100 150 200 250 300 350 400 Temperature(K)
Fig. 8: Al-Ce system: low temperature molar heat capacity of the CeAlz phase.
G. CACCIAMANI
592
I
1800 f
(Al)
6oo
AND R. FERRO
I
I
I •.I [65Bus2] III [89Gsc] A [SOKon] 0 [96Sac] x [97Kal]
0:s
0:s
$
” /
% i
300 + 0
I
0.4
0,
1 I
Mole fraction Nd Fig. 9: Optimized
AI-Nd phase diagram compared to a selection of experimental points.
-45 -
-60 ! 0
I 0.2
I 0.4
I 0.6
I 0.6
I 1.0
Mole fraction Nd
Fig. 10: AI-Nd system: enthalpy and entropy of formation of the solid phases at 300 K.
-50
0
I 0.2
A [76Zvi] 1250 R [76Zvi] 1550 I I 0.4 0.6
K K I 0.6
1.0
Mole fraction Nd
Fig. 11: AI-Nd system: enthalpy, entropy and Gibbs energy of mixing of the liquid phase at 1500 K.
THERMODYNAMIC
MODELING
Table 4: Calculated
OF ALUMINIUM-RARE invariant
EARTH BINARY SYSTEMS
593
equilibria in the Al-Nd system. Composition
Invariant
Temperature 00
equilibrium
First Phase (At % Nd)
Second Phase (At % Nd)
Third Phase (At % Nd)
901 1214
Liquid H aNdsA1tt + (Al) fiNdsAlIt t) aNd,Alr,
2.79 21.43
21.43 21.43
0.00 __-
1496 1479 1736
Liquid + NdAlz f~ PNd3Alti BNdsAlrt + NdAlz TV NdA13 Liquid tj NdAlz
17.33 21.43 34.33
32.89 32.91 34.33
21.43 25.00 -_-
1219 1072 1046 1000 925
Liquid Liquid Liquid Liquid @Nd)
65.59 73.30 76.02 82.86 90.32
41.39 50.00 66.67 75.00 75.00
50.00 66.67 75.00 88.71 93.33
+ + + f3 ti
NdAl2 t) NdAl NdAl C) NdzAl NdsAl tj NdsAl NdsAl + ((3Nd) Nd3Al + (&Nd)
,
Final remarks
In all the calculated phase diagram the RAl2 phase show appreciable solubility ranges at high temperature, not determined in literature. These, however, have been considered realistic, and no excess parameters have been introduced to reduce them. This also in agreement with some indication coming from the analysis of ternary systems such as Al-Mg-Er [02Sac]. In some cases thermodynamic functions of the binary Al-R liquid phases have been described by means of an associate model (see, for inst. [87Soml). In the present assessment a Redlich-Kister expansion was preferred for easier extrapolation to higher order systems and because no confirmation of the existence of associate species in the liquid was found in literature. Finally we may notice smooth variations of the phase diagram shapes on passing from La to Ce to Nd (especially for La and Gel and clear similarities between the parameter values reported in the Appendix. We may also notice the large values of the entropies of formation of the solid and liquid phases. They are in agreement with the optimization results obtained for other Al-R binary systems and with first principles calculations recently performed by Asta and Ozoling 101Ast] on the Al-SC system. It will be interesting to study the trend of these parameters along the complete series of lanthanides. This will be done as soon as more R-Al systems are assessed. In the particular case of the Pr-Al system the thermodynamic optimisation will be performed when the results of some experiments in progress are available.
Acknowledgements
The authors wish to dedicate this paper to the memory of Dr. I. Ansara: his friendship and his scientific advice will be greatly missed. Italian “Consiglio Nazionale delle Ricerche” is acknowledged with thanks for the financial support given in the framework of the “Progetto Finalizzato Matriali Speciali per Tecnologie Avanzate II”.
References 12vog
24Bil 32Can 57vuc
R. Vogel, Z. Anorg. Chem., 75 (1912) 41. W. Biltz and H. Pieper, Z. Anorg. Chem., 134 (1924) 13. G. Canneri and A. Rossi, Gazz. Chim. Ital., 62 (1932) 202-211. J.H.N. van Vucht, Z. Metallkunde, 48 (1957) 253.
594 65Bus1 65Bus2 66Bus 71Dee 72Leb 76Zvi 77Ker 77Kob 77Yam 79Esi 79Kob 79Shel 79She2 80Yam 81Esi 82Kob 83Yam 84Kob 85Col 85Sun 87Som 88Gscl 88Gsc2 88Som 89Cah 89Gsc 89Jed 90Cat 90Kon 91Bor 91Jun 93Bar 93Bor 93Cac 93Mes 94Wan 95Cac 96C1a 96Sac 96SGT
G. CACCIAMANI AND R. FERRO K.H.J. Buschow, J.H.N. van Vucht, Philips Res. Rep., 20 (1965) 337-348. K.H.J. Buschow, J. Less-Common Metals, 9 (1965) 452-456. K.H.J. Buschow and J.H.N. van Vucht, Z. Metallkunde, 57 (1966) 162. C. Deenadas, A.V. Thompson, R.S. Craig, W.E. Wallace, J. Phys, Chem. Solids, 32 (1971) 18531866. V.A. Lebedev, V.I. Kober, I.F. Nichkov, S.P. Raspopin, A.A. Kalinowskii, Izv. Akad. Nauk SSSR, Metal. (1972) issue 2, 91-95. G.N. Zviadadze, L.A. Chkhikvadze, M.V. Kereselidze, Soobshch. Akad. Nauk Gruz. SSR, 81 (1976) 149. M.V. Kereselidze, G.N. Zviadadze, M.Sh. Pkhachiashvilil I.S. Omiadze, L.A. Chkhikvadze,, Soobshch. Akad. Nauk Gruz. SSR, 85 (1977) 129. V.I. Kober, I.F. Nichkov, S.P. Raspopin and V.A. Nauman, Izv. Vyssh. Uchebn. Zaved., Tsvetn. MetaU., 5 (1977) 83-86. L.F. Yamshchikov, V.A. Lebedev, V.I. Kober, I.F. Nichkov and S.P. Raspopin, Izv, Akad. Nauk. SSSR, Met., (1977) issue 5, 90-96. Yu.O. Esin, G.M. Ryss and P.V. Gel'd, Zh. Fiz. Khim., 53 (1979) 2380-2381. V.L Kober, I.F. Nichkov, S.P. Raspopin, V.M. Kuz'minykh, Termodin. Svoistva Met. Rasplavov, Mater. Vses. Soveshch. Termodin. Met. Splavov (Rasplavy), (1979) issue 4, 72-77. V.G. Shevchenko, V.I. Kononenko, A.L. Sukhman, Zh. Fiz. Khim., 53 (1979) 1351. V.G. Shevchenko, V.I. Kononenko, A.L. Sukhman, I.I. Feodoritov, Zh. Fiz. Khim., 53 (1979) 314317. L.F. Yamshchikov, V.A. Lebedev, I.F. Nichkov, S.P. Raspopin and O.K, Kokoulin, Izv. Vyssh. Uchebn. Zaved., Tsvetn. MetaU., (1980) issue 5, 50-54. Yu.O. Esin, S.P. Kolesnikov, V.M. Baev, M.S. Petrushevskii, P.V. Gerd, Russian J. Phys. Chem., 55 (1981) 893-894. V.I. Kober, I.F. Nichkov, S.P. Raspopin, A.S. Kondratov, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metali. (1982) issue 5,101-102. L.F. Yamshchikov, V.A. Lebedev, I.F. Nichkov, S.P. Raspopin, V.G. Shein, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall. (1983) issue 2, 64-66. V.I. Kober, I.F. Nichkov, S.P. Raspopin and A.G. Osval'd, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall., (1984) issue 5, 125-127. C. Colinet, A. Pasturel, K.H.J. Buschow, J. Chem. Thermodyn., 17 (1985) 1133-1139. B. Sundman, B. Jansson, J.-O. Andersson, Calphad, 9 (1985) 153-190. F. Sommer and M. Keita, J. Less-Common Met., 136 (1987) 95-99. K.A.Gschneidner Jr. and F.W.Calderwood, Bull. Alloy Phase Diagrams, 9 (1988) 686-689. K.A.Gschneidner Jr. and F.W.Calderwood, Bull. Alloy Phase Diagrams, 9 (1988) 669-672. F. Sommer, M. Keita, H.G. Krull and B. Predel, J. Less-Common Met., 137 (1988) 267-275. R.W.Cahn, Science, 341 (1989) 183. K.A. Gschneidner, Jr. and F.W. Calderwood, Bull. Alloy Phase Diagrams, 10 (1989) 28-30. J. Jedlinski, K. Godlewski, S. Mrowec, Mater. Sci. Eng., AI20 (1989) 539. G. Cacciamani, G. Borzone and R. Ferro, Anales de Fisica, B86 (1990) 160-162. V.I. Kononenko and S.V. Golubev, Izv. Akad Nauk SSSR, Met., 2 (1990) 197-199. G. Borzone, G..Cacciamani and R. Ferro, Met. Trans., A22 (1991) 2119-2123. W.-G. Jung, O.J. Kleppa and L. Topor, J. Alloys and Compounds, 176 (1991) 309-318. M. Barieco, L. Battezzati, G. Borzone, G. Cacciamani, J. Chim. Phys., 90 (1993) 261-268. G. Borzone, A.M. Cardinale, G. Cacciamani, R. Ferro, Z. Metallkunde, 84 (1993) 635-640. G. Cacciamani, G. Borzone, R. Ferro, Calphad XXII, Barcelona, 15-21/5/1993. S.V. Meschel, O.J. Kleppa, J. Alloys and Compounds, 197 (1993) 75-81. J. Wang, Calphad, 18 (1994) 269-272. G. Caeciamani, G. Borzone, R. Ferro, J. Alloys and Compounds, 220 (1995) 106-110. N. Clavaguera, Y. Du, J. Phase Equilibria, 17 (1996) 107-111. A. Saccone, A.M. Cardinale, S. Delfino, R. Ferro, Z. MetaUkunde, 87 (1996) 82-87. SGTE pure element database ver. 3.00 updated from: A.T. Dinsdale, Calphad, 15 (1991) 317425.
THERMODYNAMIC 96Wan 97Bor 97Kal 97Sta 98Bar 98Bis 98Cac
981no 98Sac 99Cac 0OLt.m OOPin OlAst OlFer OlHil 02Cac 02Sac
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
595
J. Wang, Calphad, 20 (1996) 135138. G. Borzone, A.M. Cardinale, N. Parodi, G. Cacciamani, J. Alloys and Compounds, 247 (1997) 141. G.B. Kale, A. Biswas, I.G. Sharma, Scripta Mater., 37 (1997) 999-1003. J.T. Staley, J. Liu and W.T.Hunt, Jr., Adv. Materials and Processes, 152 (1997) 17 M. Baricco, F. Gaertner, G. Cacciamani, P. Rizzi, L. Battezzati, A.L. Greer, Mat. Sci. Forum, 269. 272 (1998) 553-558. A. Biswas, I.G. Sharma, G.B. Kale, D.K. Bose, Met. Mat. Trans., B29 (1998) 309. G. Cacciamani, G. Borzone, R. Ferro in I. Ansara, A.T. Dinsdale, M.H. Rand Eds. ‘COST 507 Thermochemical database for light metal alloys’ vol. 2, Office for Official Publications of the European Communities, Luxembourg (1998) p.20 and p.75. A. Inoue in K.A. Gscneidner Jr. and L. Eyring Eds. ‘Handbook on the Physics and Chemistry of the Rare Earths’, 25 (1998) 83. A. Saccone, G. Cacciamani, D. Macci6, G. Borzone, R. Ferro, Intermetallics, 6 (1998) 201. G. Cacciamani, P. Riani, G. Borzone, N. Parodi, A. Saccone, R. Ferro, A. Pisch, R. SchmidFetzer, Intermetallics, 7 (1999) 101-108. R. Lundin, J.R. Wilson, Advanced Materials and Processes, July (2000) 52. D.H. Ping, K. Hono, A. moue, Met. Mat. Trans., A31 (2000) 607. M. Asta, y. OzolinS, Phys. Rev. B, 64 (2001) 094104. R. Ferro, G. Cacciamani, A. Saccone, G. Borzone, J. Alloys and Compounds, 320 (2001) 326-340. M. Hillert, J. of Alloys and Compounds, 320 (2001) 161-176. G. Cacciamani, A. Saccone, S. De Negri, R. Ferro, J. Phase Equilibria (to be published in Feb. 2002). A. Saccone, S. De Negri, G. Cacciamani, R. Ferro, J. Phase Equilibria (to be published in Feb. 2002).
596
G. CACCIAMANI AND R. FERRO
~J
• ~-~
o
,
,
° i
~
m i..,
~° +
~o
s
~~
I
4-
E~
+ °~
~.~= ct~
"~o~
ee~e. [.-.
~
°.
~t
+181500-42.5 T +2 GHSERLA +GHSERAL -574000+173 T ill GHSERAL+3 GHSERLA -570533+144.1 T +ll GHSERAL+3 GHSERLA -176000+50 9 T -& +3 GHSERAL+GHSERLA -46360+12 71 2’ -& +0.707 GHSERAL
G(RAlz,R:Al;O) -2 H298(SER,R;O)-H2p8(SER.Al;O)
G(aR~Alll,Al:R;O) -11 H298(SER,Al;O)-3 Hzp8(SER,R;O)
G(~IR~AI,I,AI:R;O) -11 H298(SER,Al;O)-3 HB8(SER,R;O)
G(RA&,Al:R;O) -3 H298(SER,A1;0)-H2p8(SER,R;O)
G(RzAla,Al:R;O) -0.707 HB8(SER,Al;O) -0.293 f18(sER,~;0) G(RA1 CeAl,Al:R;O) -HT8(SER 1Al.O)-HB8(SER , 7R.0) I
(Al) (Rh
(AU W3 R&_AuCu3
(AIN& R&_ Ni3Sn
(Al)(R) R3U
itAc_ErAl
(Al)(R)
RAl_CeAl
(Ahm(Rh.m
&z&3
(AIMR)
R43
(Ah(R),
P&Ah
(Ah(R)3
T +GHSERAL+3 GHSERLA
___
G(R3AI AuCu3,AI:R;O) -Hm(SER,Al;O)-3 Hzg8(SER,R;O)
-91100+28.09
---
G(R2Al,Al:R;O) -H298(SER,Al;O)-2 Hn8(SER,R;O)
G(R3AI Ni&h,Al:R;O) -e(SER,Al;O)-3 Hzp8(SER,R;O)
---
G(RAI ErAI,AI:R;O) -fP8(~~R,Ai;0bHzg8(~~~,~~0~
+GHSERAL+GHSERU
-92000+29 66 T -A
+0.293 GHSERLA
-1515OO+42 59 T -A +2 GHSERAL+GHSERLA
G(RAl,,Al:R;O) -2 HZ9S(SER,Al;O)-H2p%ER,~O)
a&Ah
+ MWOi3GHSERL4
G(RA12,R:R;O)-3 H=(SER,R;O)
@!J&(ALB
H‘=(SER,AI;O)
AI-La --__+ 15000+3GHSERAL
G(RAl,,AI:AI;Ob3
Parameters
R&
Phase Name and Model
T
T
T +GHSERAL+3 GHSERCE
-97000+21.01
+GHSERAL+3 GHSERCE
-101000+28.66
___
-_-
T +GHSERAL+GHSERCE
-86000+19.07
___
+3 GHSERAL+GHSERCE
-180000+41 28 T -&
6T +I1 GHSERAL+3 GHSERCE
-541000+104 -A
+2 GHSERCE+GHSERAL -581000+135 6T -d +I 1 GHSERAL+3 GHSERCE
+180000-30
+2 GHSERAL+GHSERCE
-150000+30 T
+15000+3GHSERCE
Parameter values Al-Ce +15000+3GHSERAL
T T
--_
T +GHSERAL+3 GHSERND
-110000+33.75
T +GHSERAL+2 GHSERND
-109500+36.86
+GHSERAL+GHSERND
-100000+32 63 T -A
_-_
___
-180000+46.76 T +3 GHSERAL+GHSERND
-527000+114 1T -A iI1 GHSERAL+3 GHSERND
+2 GHSERND+GHSERAL -548000+1314 T -A +I 1 GHSERAL+3 GHSERND
+189000-41.37
+2 GHSERALiGHSERhfD
-159000+41.37
+15000+3GHSERND
Al-Nd +15000+3GHSERAL
5
iz ;;I
cn
m z
2
I..
s
5
ki
i’
Pergamon
Vol. 25,
No.
4, pp. 583-597, 2001
Published by Elsevier Science Ltd 0364-5916/01/$ - see front matter
PII: SO364-5916(02)00009-3
Thermodynamic Modeling of Some Aluminium-Rare Earth Binary Systems: Al-La, Al-Ce and Al-Nd
G. Cacciamani and R. Ferro Universiti di Genova, Dipartimento di Chimica e Chimica Industriale via Dodecaneso 31 - 16146 Genova Corresponding author’s e-mail: [email protected] (Received October 16,200l) Abstract. A thermodynamic modeling and optimization of the Al-La, Al-Ce and Al-Nd systems has been carried out on the basis of the literature information available. The compound energy formalism has been used to describe the thermodynamic functions of either solution and stoichiometric phases present in the systems. Present results are discussed and compared to the previous optimizations. 0 2002 Published by Elsevier Science Ltd. Introduction The alloys of aluminium with the rare earth metals (R metals) show several interesting applications. Lanthanide additions to Al-based alloys are very effective in enhancing mechanical properties (see e.g. [OOLun]), beneficial effects on corrosion resistance have been described [97Sta], [89Jed]. A wide bibliography [98Ino, 89Cah, OOPin] is available, moreover, on the effects of rare earths in the preparation, and properties, of amorphous Al-based alloys. For a long time our team has been involved in the investigation of several groups of rare-earth alloys (and of the related systematics). As for the specific case of alloys with Al, recent contributions of ours are the following: - Contributions to the study of the alloys and intermetallic compounds of aluminium with the rare earth metals [98Sac], - Thermodynamics of homogeneous crystal nucleation in Al-R metallic glasses [98Bar]; - Systematics of lanthanide and actinide compound formation: remarks on the americium alloying behaviour [OlFer]. -The Al-Er-Mg ternary system. Part I: experimental investigation [02Sac] and Part II: thermodynamic modelling [02Cac]. Work is in progress along these lines. It seemed important, however, to have a good assessment and optimisation of the binary R-Al systems. A systematic revision of these systems has been started, beginning with the light lanthanides. Considering the R-Al systems for which experimental data are widely available, the systems La-Al, Ce-kl and Nd-Al have first been examined: they will be presented and discussed in this paper.
Literature information Al-La system Al-La phase equilibria have been mainly investigated by Buschow [65Busl], in the whole composition range, Kononenko and Golubev [90Konl on the Al-rich side up to 3 at% La, and Saccone et al. [96Sac] in the
563
584
G. CACCIAMANI
AND
R. FERRO
La rich region up to 35 at% Al. An assessment of the system was compiled by Gschneidner and Calderwood [88Gscll. The Al-La phases are listed in Table 1 together with crystallographic information. Thermodynamics has been investigated by several authors: the enthalpy of formation of one or more individual solid phases was measured, by means of calorimetric methods, by Canneri [32&n] and then by Colinet et al. [85Col], Sommer et al. 188Som1, Jung et al. 191Jun1, Meschel and Kleppa [93Mes] and, recently, by Borzone et al. [97Borl who determined the whole trend of ArH as a function of composition at 300 K by direct reaction calorimetry. Thermodynamics of the solid phases was also investigated by Kober et al. [77Kob] by e.m.f. measurements at 400 to 6OoPC.Measurements in the liquid phase were carried out by Lebedev et al. [72Leb] (activity coefficient and solubility limit in the Al rich region at 680 to 85O*C by the e.m.f. method), Esin et al. [81Esi] (La partial enthalpy of mixing at 1920 K and 0 to 46 at% La by high temperature calorimetry), Sommer et al. 188Soml (partial and integral enthalpy of mixing by calorimetry at 1200 K). Deenadas et al. [71Dee] measured the heat capacity of LaAls in the 8 to 300 K temperature range. A thermodynamic optimization of the system was carried out by Wang [94Wan], before the papers of [96Sac] and [97Borl. AI-Ce system Al-Ce phase equilibria were first investigated by Vogel [12Vog] and then by van Vucht [57Vuc], Buschow and van Vucht [ZEBUS]in the whole composition range, Kononenko and Golubev [90Kon] in the Al-rich end up to 3 at% Ce, and Saccone et al. 196Sacl in the Ce rich region up to 35 at% Al. An assessment of the system was compiled by Gschneidner and Calderwood [88Gsc2]. The AI-Ce phases are listed in Table 1 together with crystallographic information. Thermodynamics has been investigated by several authors. The enthalpy of formation of one or more individual solid phases was measured, by means of calorimetric methods, by Biltz and Pieper [24Bil], Colinet et al. [85Col], Sommer and Keita [87Som] and, finally, by Borzone et al. [91Borl who determined the whole trend of ArH as a function of composition at 300 K by direct reaction calorimetry and by Cacciamani et al. [95Cac]. Thermodynamics of the solid and/or liquid phases was also investigated by Yamshchikov et al. [77Yam] (partial properties of Ce by e.m.f. method at 700 to 900 K in the solid state and at 900-1100 K in the liquid), Esin et al. [79Esil (partial and integral enthalpy of mixing at 1870 K by solution calorimetry), Shevchenko et al. [79Shel] (activity of the elements in the liquid at 1423 to 1673 K by the Knudsen effusion method), Yamshchikov et al. [8OYam] (solubility of Ce in Al at 950 to 1130 K by e.m.f. method), Kober et al. [82Kob] (Ce partial Gibbs energy in the solid two-phase fields at 800 K by e.m.f. method), Yamshchikov et al. [83Yam] (enthalpy of dissolution of Ce in molten Al at 1013 K by calorimetry). Deenadas et al. [71Dee] measured the heat capacity of CeAls in the 8 to 300 K temperature range. Further experimental work, also in connection with the glass-forming ability of the Al-Ce alloys, was performed by Baricco et al. [93Bar] by measuring heat capacity and melting enthalpy of selected Al-Ce alloys. A first optimization of the system was carried out by Cacciamani et al. [9OCacl, followed by partial or full revisions made on the basis of new literature data [98Cacl and in order to obtain a thermodynamic description of the amorphous phase [98Barl. Al-Nd system
AI-Nd phase equilibria were first investigated by Buschow [65Bus21 in the whole composition range, by Kononenko and Golubev [90Kon] in the Al-rich side up to 6 at% Nd, and Saccone et al. [96Sac] in the Nd rich region up to 30 at% Al. Kale et al. [97Kall studied the Al-rich eutectic obtaining contradictory results with respect to [90Kon]. An assessment of the system was compiled by Gschneidner and Calderwood [~~Gsc]. The Al-Nd phases are listed in Table 1 together with crystallographic information. Thermodynamics has been investigated by several authors. The enthalpy of formation of NdAlz was measured by Colinet et al. [85Col], by Al solution calorimetry. Borzone et al. [93Bor] determined the whole trend of ArH as a function of composition at 300 K by direct reaction calorimetry. Thermodynamics of the solid and/or liquid phases was also investigated by Zviadazde et al. [76Zvi] (enthalpy of mixing of the liquid at 1250 to 1550 K by high temperature calorimetry), Kereselidze et al. [77Ker] (enthalpy of mixing by the e.m.f. method at 1033 K), Kober et al. [79Kob] (partial Gibbs energy of Nd in two-phase fields at 800 and 1000 K by the e.m.f. method), Shevchenko et al. [79She21 (partial Gibbs energy of Al in the liquid at 1700 K
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
585
by vapour pressure measurements), Kober et al. [84Kobl (partial Gibbs energy of Nd in two-phase fields at 800 K by the e.m.f. method). Deenadas et al. [71Deel measured the heat capacity of NdAls in the 8 to 300 K temperature range. The Al-Nd system was first optimized by Cacciamani et al. [93Cac] and, independently, by Clavaguera and Du [96Cla] and Wang 196Wanl. More recently the optimization by [93Cac] has been revised by [98Cac] on the basis of the new literature available, and by [98Barl in order to model the amorphous phase.
Table 1: Nomenclature and crystallographic structures of the solid phases Phase names Al-Ce
Al-La
(Al), @La) ($a) (aLa) LaAlz aLasAl 1 (3La3Ah1 LaA13 LazzAlss LaAl ___ ___ LasAl ___
(Al), (yCe) We) ___ CeAlz aCesAl 1 (3CeAh 1 CeAL ___ CeAl ___ ___ aCesA flCesA1
Al-Nd
(Al) @Nd) (aN4 NdA12 aNdsAl 1 (JNd3AllI NdA13 ___ ___ NdAl Nd2Al Nd3Al ___
Thermodynamic
The thermodynamic the following.
Pearson symbolStructure type
cF4-Cu cI2-w hP4-aLa cF24-CusMg oI28-aLasAl tIlO-AlABa hP8-NisSn hP3-AIBz oC16-AlCe oP16-AlEr 0PlZCosSi hP8-NisSn cPCAUCU,
Names used in the Appendix
fcc_Al bcc_A2 dhcp_A3’ RAlz c&All 1
PRsAll1 RA13 RzzAls3 RAl_CeAI RAl_ErAl R2Al RsAl_NisSn R3AI_AuCu3
modeling
models here adopted are summarized in the Appendix and briefly introduced in
Elements The Gibbs energy of the pure elements is referred to the enthalpy of the element in the SER (Standard Element Reference) state. The Gibbs energy functions of the pure elements were taken from the PURE database [96SGT]. Phases
The Gibbs energy of the various phases is expressed according to the compound energy formalism [OlHil]. According to this formalism, the different atoms forming the phase occupy one or more sublattices and thermodynamic quantities are expressed as a function of the site fractions. The model is suitable for the description of either stoichiometric compounds and of both disordered and ordered solutions. In general the total Gibbs energy of a phase cpis given by the sum of three contributions: G’p =
Rfe’G’P + id@ +
e”@
where the three terms assume different forms according to the kind of sublattice model adopted. Stoichiometric compounds. Stoichiometric compounds are represented with as many sublattices as the number of component elements, with only one atom type in each sublattice. In the binary case the model is (A),(B), and the three contributions to the Gibbs energy are:
586
G. CACCIAMANI
"fG'p = d(u+v)
GAsER +
AND R. FERRO
vI(u+v) GBsER + LA:B(p
0)
idG=O ‘“G=O
where L,M’ = A~G(cplis the Gibbs energy of formation of the phase referred to the SER state of the component elements. This model was adopted for most intermediate phases in the three systems. In all cases the L interaction functions were assumed to be: L=a+bT
(2)
where a and b are temperature- and composition-independent
parameters to be optimized.
Liquid and solid substitutional solutions., Substitutional solutions are represented by only one sublattice where all the atoms mix together. In the binary case (A,B) the three contributions to the Gibbs energy are: “%’ = XAGaq + xa GeV idG’p= R T [XAht.d + XB hhB)] exGq = XA
XB
&
(3)
“LA,B’ (XA- ~p.1~
where GAGand GB~are the Gibbs energies of the pure elements in the cpstructure and the L functions have the form indicated in eq. (2). This model was adopted for the liquid and for the terminal fee, bee, dhcp solutions. Ordered solid solutions. Ordered solid solutions are represented by a two sublattice model where each sublattice is preferentially occupied by a specific elements but other elements are allowed to mix in the same sublattices. A binary phase of this kind may be represented by the model &B),(A,B),, the first sublattice being mainly occupied by A and the second by B. IfyA’, yA”,ya’ and ya” are the site fractions of the elements A and B in the first (‘1 and second (“1 sublattice respectively, the fully ordered state corresponds to the conditions yA’=I, YA”=~,ya’=O, ya”=l; the fully disordered state corresponds to the condition xe = ya’ = ya” (same composition in each sublattice and in the overall phase). The contributions to the Gibbs energy are: refGcp=YA’~A” GA,A’ +y~‘ya” GA,B’ +YB’YA”GB,A’ +ya’ya” Ga,a’ idG’p= R T ‘“G’
(U/(u+V)
=_YA’_YB’_YA”
bA’
z
+YA’~A”~B”
+_YA’_YB’_YA”YB”
h(vA’)
“LA.B:A~
z
‘LA:A,B’
2~
+yB’
h(yB’)]
(YA’ -YB’)”
(YA”
“LA,B:A,B’
+ Vi(U+Vj
+YA’YB’YB”
-_YB”)’
b.4”
&
h(vA”)
“LA,B:B’
+_YB’_YA”_YB”
(YA’ -YB’)~
(YA”
x,
+yB”
(4) h(vB”)]}
(YA’ -YB’)’
“LB:A.B’
(VA”
-_YB”)’
-_YB”)~
It may be emphasized that when more atoms mix in a sublattice (see eq. (3)) “‘GV requires the Gibbs energy of the pure elements in the cp phase to be known even if it is not a stable phase for the element. Similarly, when more sublattices are used and more atoms occupy each sublattice, terms of the type GA:~’ appear in “‘CT (see (4)). They correspond to the Gibbs energies of formation of hypothetical stoichiometric compounds metastable in the system. Nevertheless they have to be evaluated in some way, together with the vL’L’parameters (which still have the form shown in eq. (2)). This model was adopted here for the Laves phase present in the three systems at the composition RAlz (R=La, Ce, Nd) in order to be compatible with the description of the same phase already adopted in several other systems, even though no information about the solubility range is reported in literature for the R-Al systems.
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE Optimization
EARTH BINARY SYSTEMS
587
procedure
It has been remarked that several properties of the rare earths present regular and smooth variations on passing from one element to the next. This is particularly true when considering the group of the trivalent rare earths (from La to Lu, except Eu and Yb) or even smaller subgroups like the light (from La to Sm) or the heavy (from Gd to Lu, except Yb) rare earths. Such behavior of the pure elements extends to their alloys and similar regularities may also be observed when considering series of R-Me binary alloys of the rare earths with the same partner Me. In the modeling and optimization of rare earth binary systems this characteristic may constitute an additional criterion for the selection of the more reliable experimental data and for the discussion of the optimization results. This implies that, if possible, at least two or three systems should be studied at the same time and the regular variation of the properties considered (in our case thermodynamics, phase diagrams, phase structures, etc.) should be verified. The present optimization and calculations have been performed by means of the Thermo-Calc software package [85Sun]. In the optimization of the three binary systems Al-La, Al-Ce and Al-Nd phases having the same crystallographic structure have been generally described by the same thermodynamic models and the same type and number of interaction parameters. In a first optimization stage all the experimental data available were used with the same optimization weight. Then, on the basis of the first optimization results and of a critical discussion of the reliability of the different literature data (intrinsic accuracy of the experimental technique employed, purity of the starting materials, check of the equilibrium state of the samples, etc.) the optimization weights of the different sources were slightly modified. Only in a few cases, experimental data were rejected and not considered for the optimization, due to their inconsistency with the majority of the other data (see the next paragraph for a detailed discussion of this point).
Results and Discussion The thermodynamic models adopted and the Gibbs energy functions for all the phases in the Al-La, Al-Ce and Al-Nd systems are summarized in the Appendix, where the underlined parameters are those optimized in this work. The calculated phase equilibria are presented and briefly discussed in the following. In general, no excess heat capacity was optimized, due to an insufficient literature information: in the case of the liquid phase, however, this is probably a too rough approximation and miscibility gaps appear in the computed liquid phase at temperatures higher than 2500-3000 K, caused by the quite large values of the entropy of mixing. Optimized low temperature phase equilibria, on the other hand, looks reasonable down to temperatures lower than 100 K. We can conclude that the results of the present optimization may be considered reliable in the 200 to 2500 K temperature range. Al-La system The optimized Al-La phase diagram is shown in Fig. 1 together with the experimental liquidus points. Optimized invariant equilibria are reported in Table 2 for easier comparison with the literature. Standard enthalpy and entropy of formation of the solid phases are shown and compared to the literature data in Fig. 2. Enthalpy, entropy and Gibbs energy of mixing at 1200 K of the liquid phase are shown in Fig. 3. Calculated values are in agreement (within the experimental uncertainties) also with the results by [72Leb] and [71Dee]. The results by [77Kob] however looks inconsistent with the other experimental data and have been rejected during the optimization. Similar inconsistencies have been observed for the data obtained from e.m.f. measurements in various R alloys. A general good agreement between experimental data and optimization results may be noticed. Small discrepancies concern type and temperature of a few invariant equilibria (peritectic instead of congruent melting of PLasAlrt, peritectic instead of peritectoidic formation of LaAlj). The experimental determination of such equilibria is very difficult, due to the reactivity of the involved elements, and, in some cases, it was carried out several years ago: for these reasons it was considered not necessary to introduce more complex thermodynamic functions in order to match more closely such uncertain experimental data.
588
G. C A C C I A M A N I A N D R. FERRO I
I
~
I
[] [65Bus1] A [90Kon] ~,[96Sac]
...,~
.~
1500
I
~
5~
"-" 1200 t.-
,.-t
Q.
E 900 -
/
,.
I--
La3AI~'~
600 (A1)
300
~
0
~
(aLa)
.1 I
I
0.6 0.4 Mole fractionLa
0.2
0.8
1.0
Fig. l: Optimized A1-La phase diagram compared to a selection of experimental points. Notice that peritectic formation of LaA13and La-rich eutectic are not resolved in the figure.
I
I
I
0
I
-6 E
-10~'~'-20-
p
I
I
016
018
-10-
~"2'
|
~
~ ~ -404
-40
[]
ttl
'"
-50 ] 0
I
~-30
E
-60
I
°
-50 &[88Som] 1200 K m[81Esi] 1920 K
0:2
0:4
o18
o:a
1.o
Mole fraction La
Fig. 2: AI-La system: enthalpy and entropy of formation of the solid phases at 300 K.
-6
0
012
014
1.0
Mole fraction La
Fig. 3: AI-La system: enthalpy, entropy and Gibbs energy of mixing of the liquid phase at 1200 K.
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
589
Similar considerations are also applicable to the optimizations of Al-Ce and AI-Nd systems, discussed here below, and other Al-R systems like Al-Sm [98Sacl, AI-SC [99Cac] and Al-Er [02Cac]. On the other hand it may be noted that, according to the assessment performed by [94Wang], where 15 optimization coefficients and Legendre polynomials up to the fifth order have been used to describe the excess Gibbs energy of the liquid phase in order to match the assessed version [89Gsc] of the phase diagram, a miscibility gap (not reported in the paper) appear at T>1500 K and thermodynamic functions of the liquid assume unrealistic trends at higher temperatures. Even in the present optimization, due to the quite large entropy contribution, a miscibility gap appear if the liquidus parameters are extrapolated at temperatures higher than 2500 K.
Table 2: Calculated invariant equilibria in the Al-La system. Composition Invariant equilibrium
Temperature 00
First Phase (At % La) 2.32 21.43
Second Phase (At % La) 21.43 21.43
Third Phase (At % La) 0.00 ___
913 1200
Liquid t) czLasAlrl + (Al) SLasAlIr H aLasAll
1.511
Liquid + LazzAls3 tj
19.00
29.33
21.43
1542
Liquid + LaAlz C) LazzA153
20.83
32.83
29.33.
1324 1445 1658
LaazAlss w LaAls + LaAl2 PLasAlrr + LazzAlss w LaAls Liquid H LaAlz
29.33 21.43 33.62
25.00 29.33 33.62
33.12 25.00 ___
1137 800.7 800.6 672
Liquid Liquid Liquid LasAl
60.31 76.69 76.71 75.00
37.69 50.00 75.00 50.00
50.00 75.00 99.99 99.99
1117
(yLa) H Liquid ‘+ @La)
99.49
94.95
99.99
+ + H t)
@LasAlrr
LaAlz H LaAl LaAl H La3Al LaxAl + (@La) LaAl + @La)
Table 3: Calculated invariant equilibria in the Al-Ce system. Composition Temperature (IQ
Invariant equilibrium
First Phase (At % Ce) 2.60 21.43
Second Phase (At % Ce) 21.43 21.43
Third Phase (At % Ce) 0.00 ___
904 1290
Liquid H aCesAltr + (Al) flCesAll1 t) aCesAl
1529 1407 1748 1116 925 930
Liquid + CeA& (3CesAllt PCe3AIrI + CeAlz t) CeAl3 Liquid t) CeAl2 Liquid + CeAlz f~ AlCe Liquid e AlCe + aCesA Liquid CJ aCesA
18.74 21.43 33.57 62.92 72.13 75.00
32.93 33.08 33.57 37.88 50.00 75.00
21.43 25.00 --_ 50.00 75.00 -__
866 523
Liquid w aCesA + ($e) aCesA w (3CesAl
86.47 75.00
75.00 75.00
99.99 ___
961
(6Ce) TV Liauid + (yCe)
98.67
92.60
99.99
590
G. C A C C I A M A N I A N D R. FERRO
1800
I
i
,.oo / 900
I
v [66Bus]
z [80Yam] A [90Kon] ~ [96Sac]
/~ / ~ . -
1500
~"
i
/
-
_ _
oT
600 L (Al) rj
30O
0
0.2
r.J
0.4
rJ I
I
0.6
0.8
1.0
Mole fraction Ce Fig. 4: Optimized AI-Ce phase diagram compared to a selection of experimental points.
0
I
I
I
I
"ot~,
-10
~
~.~oJ ~,\
~" ~" -20 E-~ "E
/
///
~.~-3o-
w w -40-
y-:[~o~,
,0
& 91Bor] x [95Cac] -60
0
0:2
014
016
0:8
"t
N c w
1.0
Mole fraction Ce
Fig. 5: AI-Ce system: enthalpy and entropy of formation of the solid phases at 300 K.
-50 -60
rq [76Zvi] 1250 K & [79Esi] 1870 K 0
012
014 016 Mole fraction Ce
018
1.0
Fig. 6: AI-Ce system: enthalpy, entropy and Gibbs energy of mixing of the liquid phase at 1200 K.
THERMODYNAMIC
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
591
Al-Ce system
The optimized Al-Ce phase diagram is shown in Fig. 4 together with the experimental liquidus points. Optimized invariant equilibria are reported in Table 3 for easier comparison with the literature. Figs. 5 and 6 show integral thermodynamic functions of formation of the solid and liquid phases, respectively. The activity of the elements in the liquid phase at 1673 K are shown in Fig. 7 and low temperature heat capacity of CeAlz is reported in Fig. 8. The optimization results show a good agreement also with the C, data reported by [93Bar]. The e.m.f. measurements by [77Yam] and [82Kob], however, seems to be inconsistent with the other experimental data and have been rejected during the optimization. The general good agreement, within the limits of the same considerations applied to the Al-La system, between experimental and calculated values may be noticed. Present results have to be, considered an update of the optimization previously carried out by [98Cac].
Al-Nd system
The optimized Al-Nd phase diagram is shown in Fig. 9 together with the experimental liquidus points. Optimized invariant equilibria are reported in Table 4 for easier comparison with the literature. Small discrepancies may be noticed between calculation and experiments in the liquidus curve close to the Nd-rich eutectic. Figs. 10 and 11 show integral thermodynamic functions of formation of the solid and liquid phases, respectively. General considerations reported for Al-La and Al-Ce hold for Al-Nd also. The optimization results show a good agreement also with the C, data reported by [71Dee] and the partial Gibbs energy of Nd in the liquid at 1033 K measured by [77Kerl. The vapor pressure measurements by [79She2] and the e.m.f. measurements by [79Kob] and [84Kob], however, seems to be inconsistent with the other experimental data and have been rejected during the optimization. The present re-optimization of the Al-Nd system has to be considered an update of the optimization previously carried out by [98Cac]. Present results are also in quite good agreement with the optimizations by [93Cac, 96Cla, 96Wan] which, however, do not take into account the more recent literature data by [96Sac].
0.6-I
_
\
"/
0
0
0.2
0.4
0.6
0.6
1.0
Molefraction Ce Fig. 7: Al-Ce system: activity of Al and Ce in
the liquid phase at K.
0
I 50
I I I I I I 100 150 200 250 300 350 400 Temperature(K)
Fig. 8: Al-Ce system: low temperature molar heat capacity of the CeAlz phase.
G. CACCIAMANI
592
I
1800 f
(Al)
6oo
AND R. FERRO
I
I
I •.I [65Bus2] III [89Gsc] A [SOKon] 0 [96Sac] x [97Kal]
0:s
0:s
$
” /
% i
300 + 0
I
0.4
0,
1 I
Mole fraction Nd Fig. 9: Optimized
AI-Nd phase diagram compared to a selection of experimental points.
-45 -
-60 ! 0
I 0.2
I 0.4
I 0.6
I 0.6
I 1.0
Mole fraction Nd
Fig. 10: AI-Nd system: enthalpy and entropy of formation of the solid phases at 300 K.
-50
0
I 0.2
A [76Zvi] 1250 R [76Zvi] 1550 I I 0.4 0.6
K K I 0.6
1.0
Mole fraction Nd
Fig. 11: AI-Nd system: enthalpy, entropy and Gibbs energy of mixing of the liquid phase at 1500 K.
THERMODYNAMIC
MODELING
Table 4: Calculated
OF ALUMINIUM-RARE invariant
EARTH BINARY SYSTEMS
593
equilibria in the Al-Nd system. Composition
Invariant
Temperature 00
equilibrium
First Phase (At % Nd)
Second Phase (At % Nd)
Third Phase (At % Nd)
901 1214
Liquid H aNdsA1tt + (Al) fiNdsAlIt t) aNd,Alr,
2.79 21.43
21.43 21.43
0.00 __-
1496 1479 1736
Liquid + NdAlz f~ PNd3Alti BNdsAlrt + NdAlz TV NdA13 Liquid tj NdAlz
17.33 21.43 34.33
32.89 32.91 34.33
21.43 25.00 -_-
1219 1072 1046 1000 925
Liquid Liquid Liquid Liquid @Nd)
65.59 73.30 76.02 82.86 90.32
41.39 50.00 66.67 75.00 75.00
50.00 66.67 75.00 88.71 93.33
+ + + f3 ti
NdAl2 t) NdAl NdAl C) NdzAl NdsAl tj NdsAl NdsAl + ((3Nd) Nd3Al + (&Nd)
,
Final remarks
In all the calculated phase diagram the RAl2 phase show appreciable solubility ranges at high temperature, not determined in literature. These, however, have been considered realistic, and no excess parameters have been introduced to reduce them. This also in agreement with some indication coming from the analysis of ternary systems such as Al-Mg-Er [02Sac]. In some cases thermodynamic functions of the binary Al-R liquid phases have been described by means of an associate model (see, for inst. [87Soml). In the present assessment a Redlich-Kister expansion was preferred for easier extrapolation to higher order systems and because no confirmation of the existence of associate species in the liquid was found in literature. Finally we may notice smooth variations of the phase diagram shapes on passing from La to Ce to Nd (especially for La and Gel and clear similarities between the parameter values reported in the Appendix. We may also notice the large values of the entropies of formation of the solid and liquid phases. They are in agreement with the optimization results obtained for other Al-R binary systems and with first principles calculations recently performed by Asta and Ozoling 101Ast] on the Al-SC system. It will be interesting to study the trend of these parameters along the complete series of lanthanides. This will be done as soon as more R-Al systems are assessed. In the particular case of the Pr-Al system the thermodynamic optimisation will be performed when the results of some experiments in progress are available.
Acknowledgements
The authors wish to dedicate this paper to the memory of Dr. I. Ansara: his friendship and his scientific advice will be greatly missed. Italian “Consiglio Nazionale delle Ricerche” is acknowledged with thanks for the financial support given in the framework of the “Progetto Finalizzato Matriali Speciali per Tecnologie Avanzate II”.
References 12vog
24Bil 32Can 57vuc
R. Vogel, Z. Anorg. Chem., 75 (1912) 41. W. Biltz and H. Pieper, Z. Anorg. Chem., 134 (1924) 13. G. Canneri and A. Rossi, Gazz. Chim. Ital., 62 (1932) 202-211. J.H.N. van Vucht, Z. Metallkunde, 48 (1957) 253.
594 65Bus1 65Bus2 66Bus 71Dee 72Leb 76Zvi 77Ker 77Kob 77Yam 79Esi 79Kob 79Shel 79She2 80Yam 81Esi 82Kob 83Yam 84Kob 85Col 85Sun 87Som 88Gscl 88Gsc2 88Som 89Cah 89Gsc 89Jed 90Cat 90Kon 91Bor 91Jun 93Bar 93Bor 93Cac 93Mes 94Wan 95Cac 96C1a 96Sac 96SGT
G. CACCIAMANI AND R. FERRO K.H.J. Buschow, J.H.N. van Vucht, Philips Res. Rep., 20 (1965) 337-348. K.H.J. Buschow, J. Less-Common Metals, 9 (1965) 452-456. K.H.J. Buschow and J.H.N. van Vucht, Z. Metallkunde, 57 (1966) 162. C. Deenadas, A.V. Thompson, R.S. Craig, W.E. Wallace, J. Phys, Chem. Solids, 32 (1971) 18531866. V.A. Lebedev, V.I. Kober, I.F. Nichkov, S.P. Raspopin, A.A. Kalinowskii, Izv. Akad. Nauk SSSR, Metal. (1972) issue 2, 91-95. G.N. Zviadadze, L.A. Chkhikvadze, M.V. Kereselidze, Soobshch. Akad. Nauk Gruz. SSR, 81 (1976) 149. M.V. Kereselidze, G.N. Zviadadze, M.Sh. Pkhachiashvilil I.S. Omiadze, L.A. Chkhikvadze,, Soobshch. Akad. Nauk Gruz. SSR, 85 (1977) 129. V.I. Kober, I.F. Nichkov, S.P. Raspopin and V.A. Nauman, Izv. Vyssh. Uchebn. Zaved., Tsvetn. MetaU., 5 (1977) 83-86. L.F. Yamshchikov, V.A. Lebedev, V.I. Kober, I.F. Nichkov and S.P. Raspopin, Izv, Akad. Nauk. SSSR, Met., (1977) issue 5, 90-96. Yu.O. Esin, G.M. Ryss and P.V. Gel'd, Zh. Fiz. Khim., 53 (1979) 2380-2381. V.L Kober, I.F. Nichkov, S.P. Raspopin, V.M. Kuz'minykh, Termodin. Svoistva Met. Rasplavov, Mater. Vses. Soveshch. Termodin. Met. Splavov (Rasplavy), (1979) issue 4, 72-77. V.G. Shevchenko, V.I. Kononenko, A.L. Sukhman, Zh. Fiz. Khim., 53 (1979) 1351. V.G. Shevchenko, V.I. Kononenko, A.L. Sukhman, I.I. Feodoritov, Zh. Fiz. Khim., 53 (1979) 314317. L.F. Yamshchikov, V.A. Lebedev, I.F. Nichkov, S.P. Raspopin and O.K, Kokoulin, Izv. Vyssh. Uchebn. Zaved., Tsvetn. MetaU., (1980) issue 5, 50-54. Yu.O. Esin, S.P. Kolesnikov, V.M. Baev, M.S. Petrushevskii, P.V. Gerd, Russian J. Phys. Chem., 55 (1981) 893-894. V.I. Kober, I.F. Nichkov, S.P. Raspopin, A.S. Kondratov, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metali. (1982) issue 5,101-102. L.F. Yamshchikov, V.A. Lebedev, I.F. Nichkov, S.P. Raspopin, V.G. Shein, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall. (1983) issue 2, 64-66. V.I. Kober, I.F. Nichkov, S.P. Raspopin and A.G. Osval'd, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall., (1984) issue 5, 125-127. C. Colinet, A. Pasturel, K.H.J. Buschow, J. Chem. Thermodyn., 17 (1985) 1133-1139. B. Sundman, B. Jansson, J.-O. Andersson, Calphad, 9 (1985) 153-190. F. Sommer and M. Keita, J. Less-Common Met., 136 (1987) 95-99. K.A.Gschneidner Jr. and F.W.Calderwood, Bull. Alloy Phase Diagrams, 9 (1988) 686-689. K.A.Gschneidner Jr. and F.W.Calderwood, Bull. Alloy Phase Diagrams, 9 (1988) 669-672. F. Sommer, M. Keita, H.G. Krull and B. Predel, J. Less-Common Met., 137 (1988) 267-275. R.W.Cahn, Science, 341 (1989) 183. K.A. Gschneidner, Jr. and F.W. Calderwood, Bull. Alloy Phase Diagrams, 10 (1989) 28-30. J. Jedlinski, K. Godlewski, S. Mrowec, Mater. Sci. Eng., AI20 (1989) 539. G. Cacciamani, G. Borzone and R. Ferro, Anales de Fisica, B86 (1990) 160-162. V.I. Kononenko and S.V. Golubev, Izv. Akad Nauk SSSR, Met., 2 (1990) 197-199. G. Borzone, G..Cacciamani and R. Ferro, Met. Trans., A22 (1991) 2119-2123. W.-G. Jung, O.J. Kleppa and L. Topor, J. Alloys and Compounds, 176 (1991) 309-318. M. Barieco, L. Battezzati, G. Borzone, G. Cacciamani, J. Chim. Phys., 90 (1993) 261-268. G. Borzone, A.M. Cardinale, G. Cacciamani, R. Ferro, Z. Metallkunde, 84 (1993) 635-640. G. Cacciamani, G. Borzone, R. Ferro, Calphad XXII, Barcelona, 15-21/5/1993. S.V. Meschel, O.J. Kleppa, J. Alloys and Compounds, 197 (1993) 75-81. J. Wang, Calphad, 18 (1994) 269-272. G. Caeciamani, G. Borzone, R. Ferro, J. Alloys and Compounds, 220 (1995) 106-110. N. Clavaguera, Y. Du, J. Phase Equilibria, 17 (1996) 107-111. A. Saccone, A.M. Cardinale, S. Delfino, R. Ferro, Z. MetaUkunde, 87 (1996) 82-87. SGTE pure element database ver. 3.00 updated from: A.T. Dinsdale, Calphad, 15 (1991) 317425.
THERMODYNAMIC 96Wan 97Bor 97Kal 97Sta 98Bar 98Bis 98Cac
981no 98Sac 99Cac 0OLt.m OOPin OlAst OlFer OlHil 02Cac 02Sac
MODELING
OF ALUMINIUM-RARE
EARTH BINARY SYSTEMS
595
J. Wang, Calphad, 20 (1996) 135138. G. Borzone, A.M. Cardinale, N. Parodi, G. Cacciamani, J. Alloys and Compounds, 247 (1997) 141. G.B. Kale, A. Biswas, I.G. Sharma, Scripta Mater., 37 (1997) 999-1003. J.T. Staley, J. Liu and W.T.Hunt, Jr., Adv. Materials and Processes, 152 (1997) 17 M. Baricco, F. Gaertner, G. Cacciamani, P. Rizzi, L. Battezzati, A.L. Greer, Mat. Sci. Forum, 269. 272 (1998) 553-558. A. Biswas, I.G. Sharma, G.B. Kale, D.K. Bose, Met. Mat. Trans., B29 (1998) 309. G. Cacciamani, G. Borzone, R. Ferro in I. Ansara, A.T. Dinsdale, M.H. Rand Eds. ‘COST 507 Thermochemical database for light metal alloys’ vol. 2, Office for Official Publications of the European Communities, Luxembourg (1998) p.20 and p.75. A. Inoue in K.A. Gscneidner Jr. and L. Eyring Eds. ‘Handbook on the Physics and Chemistry of the Rare Earths’, 25 (1998) 83. A. Saccone, G. Cacciamani, D. Macci6, G. Borzone, R. Ferro, Intermetallics, 6 (1998) 201. G. Cacciamani, P. Riani, G. Borzone, N. Parodi, A. Saccone, R. Ferro, A. Pisch, R. SchmidFetzer, Intermetallics, 7 (1999) 101-108. R. Lundin, J.R. Wilson, Advanced Materials and Processes, July (2000) 52. D.H. Ping, K. Hono, A. moue, Met. Mat. Trans., A31 (2000) 607. M. Asta, y. OzolinS, Phys. Rev. B, 64 (2001) 094104. R. Ferro, G. Cacciamani, A. Saccone, G. Borzone, J. Alloys and Compounds, 320 (2001) 326-340. M. Hillert, J. of Alloys and Compounds, 320 (2001) 161-176. G. Cacciamani, A. Saccone, S. De Negri, R. Ferro, J. Phase Equilibria (to be published in Feb. 2002). A. Saccone, S. De Negri, G. Cacciamani, R. Ferro, J. Phase Equilibria (to be published in Feb. 2002).
596
G. CACCIAMANI AND R. FERRO
~J
• ~-~
o
,
,
° i
~
m i..,
~° +
~o
s
~~
I
4-
E~
+ °~
~.~= ct~
"~o~
ee~e. [.-.
~
°.
~t
+181500-42.5 T +2 GHSERLA +GHSERAL -574000+173 T ill GHSERAL+3 GHSERLA -570533+144.1 T +ll GHSERAL+3 GHSERLA -176000+50 9 T -& +3 GHSERAL+GHSERLA -46360+12 71 2’ -& +0.707 GHSERAL
G(RAlz,R:Al;O) -2 H298(SER,R;O)-H2p8(SER.Al;O)
G(aR~Alll,Al:R;O) -11 H298(SER,Al;O)-3 Hzp8(SER,R;O)
G(~IR~AI,I,AI:R;O) -11 H298(SER,Al;O)-3 HB8(SER,R;O)
G(RA&,Al:R;O) -3 H298(SER,A1;0)-H2p8(SER,R;O)
G(RzAla,Al:R;O) -0.707 HB8(SER,Al;O) -0.293 f18(sER,~;0) G(RA1 CeAl,Al:R;O) -HT8(SER 1Al.O)-HB8(SER , 7R.0) I
(Al) (Rh
(AU W3 R&_AuCu3
(AIN& R&_ Ni3Sn
(Al)(R) R3U
itAc_ErAl
(Al)(R)
RAl_CeAl
(Ahm(Rh.m
&z&3
(AIMR)
R43
(Ah(R),
P&Ah
(Ah(R)3
T +GHSERAL+3 GHSERLA
___
G(R3AI AuCu3,AI:R;O) -Hm(SER,Al;O)-3 Hzg8(SER,R;O)
-91100+28.09
---
G(R2Al,Al:R;O) -H298(SER,Al;O)-2 Hn8(SER,R;O)
G(R3AI Ni&h,Al:R;O) -e(SER,Al;O)-3 Hzp8(SER,R;O)
---
G(RAI ErAI,AI:R;O) -fP8(~~R,Ai;0bHzg8(~~~,~~0~
+GHSERAL+GHSERU
-92000+29 66 T -A
+0.293 GHSERLA
-1515OO+42 59 T -A +2 GHSERAL+GHSERLA
G(RAl,,Al:R;O) -2 HZ9S(SER,Al;O)-H2p%ER,~O)
a&Ah
+ MWOi3GHSERL4
G(RA12,R:R;O)-3 H=(SER,R;O)
@!J&(ALB
H‘=(SER,AI;O)
AI-La --__+ 15000+3GHSERAL
G(RAl,,AI:AI;Ob3
Parameters
R&
Phase Name and Model
T
T
T +GHSERAL+3 GHSERCE
-97000+21.01
+GHSERAL+3 GHSERCE
-101000+28.66
___
-_-
T +GHSERAL+GHSERCE
-86000+19.07
___
+3 GHSERAL+GHSERCE
-180000+41 28 T -&
6T +I1 GHSERAL+3 GHSERCE
-541000+104 -A
+2 GHSERCE+GHSERAL -581000+135 6T -d +I 1 GHSERAL+3 GHSERCE
+180000-30
+2 GHSERAL+GHSERCE
-150000+30 T
+15000+3GHSERCE
Parameter values Al-Ce +15000+3GHSERAL
T T
--_
T +GHSERAL+3 GHSERND
-110000+33.75
T +GHSERAL+2 GHSERND
-109500+36.86
+GHSERAL+GHSERND
-100000+32 63 T -A
_-_
___
-180000+46.76 T +3 GHSERAL+GHSERND
-527000+114 1T -A iI1 GHSERAL+3 GHSERND
+2 GHSERND+GHSERAL -548000+1314 T -A +I 1 GHSERAL+3 GHSERND
+189000-41.37
+2 GHSERALiGHSERhfD
-159000+41.37
+15000+3GHSERND
Al-Nd +15000+3GHSERAL
5
iz ;;I
cn
m z
2
I..
s
5
ki
i’