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Experimental investigation of the Al–Ce–Nd system
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Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226
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Experimental investigation of the Al–Ce–Nd system A.M. Cardinale, G. Cacciamani, G. Borzone∗, R. Ferro Universit`a di Genova, Dipartimento di Chimica e Chimica Industriale, via Dodecaneso 31 - 16146 Genoa, Italy Received 21 July 2003; accepted 27 July 2003
Abstract In the framework of a systematic investigation of intermetallic systems including rare earths and aluminum, Ce–Nd–Al alloys have recently been investigated by x-ray diffraction, optical microscopy, scanning electron microscopy and electron probe microanalysis. In particular, the Ce–Nd–Al isothermal section at 500 ◦ C has been experimentally determined. This section is characterized by several line compounds extending from the binary R–Al subsystems into the ternary field. Complete solid solutions are found in the ternary system when the Ce–Al and the corresponding Nd–Al compounds are isostructural (CeAl3 and NdAl3 , CeAl2 and NdAl2 ). The remaining binary phases show lower ternary solubilities. These results have been used together with the thermodynamic data available in literature on the binary subsystems for a thermodynamic modeling and optimization of the Ce–Nd–Al system, by means of the CALPHAD method (Calphad (this issue)). © 2003 Elsevier Ltd. All rights reserved.
1. Introduction
2. Literature data
In the past year several thermodynamic properties of binary R–Al alloys have been investigated by our research group. Particular attention was devoted to the determination of the enthalpy of formation of alloys formed in the binary R–Al systems (R = La [21], Ce [14], Pr [16], Nd [15], Sm [18], Sc [22]) by using direct reaction calorimetry [7, 19]. In several cases, such as for the Y–Al system, the calorimetric investigation was combined with emf measurements, in order to get a more complete thermodynamic description of the system [23]. Recently, the heat capacity and phase equilibria in the R-rich R–Al alloys (R = La, Pr and Nd) have been investigated [20, 24]. Selected R1−x Rx Aly sections have also been studied by means of optical and electron microscopy and x-ray powder diffraction [17]. In the present paper, the results obtained in the experimental study of the Ce–Nd–Al alloys are reported.
2.1. Compound formation in the light rare earth–aluminum systems The crystallochemistry of the R–Al phases (R = La, Ce, Pr, Nd) is summarized in Table 1 and several remarks may be noteworthy. The R3 Al compound in the La system exists only in the ∼400 to ∼520 ◦C temperature range and belongs to the hP8-Ni3 Sn type. For cerium and praseodymium it shows two different structures (hP8-Ni3 Sn, low temperature form and cP4-AuCu3 type, high temperature form) while it presents only the hP8-Ni3 Sn type structure for neodymium. Considering the R2 Al stoichiometry, no compound has been described for Ce, while praseodymium and neodymium form the orthorhombic oP12-Co2 Si structure. For the RAl compounds, La and Ce form the orthorhombic oC16-CeAl type structure, Pr gives two forms: oC16-CeAl type (at high temperature) and oP16-ErAl (at low temperature). For NdAl only the oP16-ErAl form has been observed. RAl2 as well as RAl3 and R3 Al11 compounds exist in the same structural types for all the light rare earths. 2.2. Ce–Al system
∗ Corresponding author. Tel.: +39-10-3536153; fax: +39-10-3625051.
E-mail address: [email protected] (G. Borzone). 0364-5916/$ - see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2003.07.002
The Ce–Al diagram is based mainly on the work by van Vucht [1] and Buschow [4] and the more recent revision
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Table 1 R–Al systems (R = La, Ce, Pr and Nd) crystal structures of the phases and indication of their temperature range of stability (T/◦ C) Stoichiometry
La
Ce
Pr
Nd
Structural types
R3 Al
520–400
685–250 <250
685–330 <330
<780
cP4-AuCu3 hP8-Ni3 Sn
<735
<795
oP12-Co2 Si
R2 Al RAl
<873
<845
905–700 <700
<940
oC16–CeAl oP16-ErAl
RAl2
<1405
<1480
<1480
<1460
cF24-MgCu2
RAl3
<1170
<1135
<1075
<1205
hP8-Ni3 Sn
R3 Al11
1240–915 <915
1235–1020 <1020
1240–965 <965
1235–950 <950
tI10-BaAl4 (Al def.) oI28-αLa3 Al11
by [20]. Five intermetallic line compounds are present: Ce3 Al melting point at 685 ◦ C, showing a structural transformation at about 250 ◦C from the hexagonal structure (α-Ce3 Al, low temperature form) to the cubic structure (β-Ce3 Al, high temperature form), CeAl orthorhombic, peritectic formation at 845 ◦C, CeAl2 melting point 1480 ◦C, CeAl3 peritectoidal decomposition at 1135 ◦C, Ce3 Al11 peritectic formation at 1235 ◦C. The low temperature α-Ce3 Al11 (below 1020 ◦C) has an orthorhombic oI28-α-La3 Al11 structure and the β-Ce3 Al11 has a tetragonal tI10-BaAl4 , Al-deficient structure. Three eutectic reactions are reported at ∼14.0 at.% Al at 600 ◦C, at 27.5 at.% Al at 660 ◦C and at ∼97.4 at.% Al at 633 ◦C [13]. The maximum solid solubility of aluminum in δ-Ce is about 2.5 at.% at the 700 ◦C, catatectic reaction temperature. At the same temperature very little solid solubility of Al in γ -Ce, less than 1 at.% Al, was proposed. Recently an assessed version has been reported by [25]. 2.3. Nd–Al system The Nd–Al diagram was determined by Buschow [3] and assessed by Gschneidner and Calderwood [11]. Recent investigations were performed in the Nd-rich [20, 24] and Al-rich regions [13]. This system shows six intermetallic compounds: Nd3 Al, peritectic formation at 780 ◦C, Nd2 Al, peritectic formation at 795 ◦C, NdAl, orthorhombic oP16ErAl, peritectic formation at 940 ◦ C, NdAl2 melting point 1460 ◦C, NdAl3 peritectoidal decomposition at 1205 ◦C, Nd3 Al11 peritectic formation at 1235 ◦C. Low temperature α-Nd3 Al11 (below 950 ◦C) has an orthorhombic oI28-α-La3 Al11 structure and β-Nd3 Al11 has a tetragonal tI10-BaAl4 , Al-deficient structure. Two eutectic reactions are reported at ∼19.0 at.% Al and 685 ◦C and ∼97.5 at.% Al at 632 ◦C. The maximum solid solubility of Al in β-Nd is about 12 at.% Al at the eutectic temperature and 10 at.% Al and 10 at.% Al at the eutectoid temperature of 650 ◦C. At this temperature the maximum solid solubility of Al in α-Nd is about 2 at.% Al. An optimization of the Nd–Al system is reported in [25].
2.4. Ce–Nd system No phase diagram is available in literature, but Speight et al. [5] have measured the room temperature lattice parameters for the Ce–Nd alloy system. In addition to this work, Gschneidner et al. [2] reported the lattice parameter of a Ce-rich alloy containing 2 at.% Nd. A likely form of the Ce–Nd phase diagram based on the information given in these papers was drawn by Moffat [8] and reported by Massalski [12]. It shows complete mutual solid solubility at high temperature in the bcc modifications (δ-Ce and β-Nd). The continuous solid solution decomposes on cooling into the two phases based on γ -Ce and α-Nd. 2.5. Ce–Nd–Al system An investigation of the CeAl2 –NdAl2 section at 800 ◦C was previously done [6, 10]. A continuous solid solution with a linear variation of the unit cell, according to Vegard’s law was determined. 3. Experimental 3.1. Alloys preparation The metals used were cerium, neodymium and aluminum 99.9, 99.9 and 99.999 mass% nominal purity respectively. The samples were prepared by melting in an induction furnace, under argon atmosphere, pieces of the constituent metals sealed in small tantalum crucibles for compositions between 0 and 40 at.% of aluminum. Alumina crucibles were used for compositions over 40 at.% of aluminum; the sample mass was about 0.8–1.0 g. The alloys were generally annealed at 500 ◦ C for one week and then quenched in cold water. Several samples were annealed at 600 ◦C for 4 days, then at 500 ◦C for 1 week, and quenched in cold water. For the annealing, either tantalum or alumina crucibles were placed in steel tubes sealed by arcwelding under argon. On the basis of results obtained from
A.M. Cardinale et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226 1.0 0.9 0.8
fra ctio nA l
(Ce1–y Nd y )Al
(Ce x Nd 1–x )Al 3
0.7
(Ce x Nd 1–x )Al 2
0.6 (Ce x Nd 1–x )Al
Mo le
0.5
0.4 (Ce x Nd 1–x ) 2 Al
0.3
(Ce1–y Nd y ) 3 Al 0.2
(Ce x Nd 1–x ) 3 Al
0.1 0 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Nd Fig. 1. Al–Ce–Nd system. Two- and three-phase equilibria at 500 ◦ C are reported. Experimental tie lines and tie triangles obtained from selected alloys in the ∼25 to 75 at.% Al composition range (see Table 2) are also shown.
2.19
Average atomic volume (nm 3 10 2 )
the modeling, in order to determine information on selected liquidus temperatures, a few samples were subjected to thermal analysis (DTA) with heating and cooling rates of 10 K min−1 . The following results were obtained for the studied compositions (±5 ◦C): Ce30 Nd35 Al35 Tliq = 845 ◦C, Ce35 Nd25 Al40 Tliq = 900 ◦C, Ce25 Nd45Al30 Tliq = 850 ◦C. Metallographic, electron probe and x-ray diffraction analyses were used to characterize all the samples. For metallographic analysis, the specimens were prepared using SiC and diamond-paste polishing; according to their composition, they were etched in dilute HNO3 (R-rich samples) or in dilute KOH (Al-rich samples). The average composition of the different phases was determined by performing at different points of the buttons electron probe microanalysis (EPMA) using an energydispersive x-ray analyzer. Cobalt standard was used for calibration and the x-ray intensities were considered for ZAF effects using pure elements as standards; the compositional values derived were usually accurate to ±1 at.% for Ce and Nd. As for Al-rich alloys, the microprobe analysis generally indicated an Al concentration of the phases higher than the stoichiometric value. As for the global composition which generally was nearly coincident with the nominal composition, a higher uncertainty was estimated because the analyzed surface in some cases could not represent the overall sample composition. XRD examination was performed on powder samples using the Debye method (Cu-Kα filtered radiation); the observed diffraction intensities were compared with those calculated by means of the program Pulverix [9]. The values of the lattice parameters were refined using a least-squares routine.
223
2.17 2.15 2.13 2.11 RAl 3 , hP8–Ni 3 Sn
2.09
RAl 2 , cF24–MgCu 2 2.07 0.00
0.20
0.40
0.60
0.80
1.00
x
4. Results and discussion The data obtained in the preparation and examination of different alloys are reported in Table 2 where data for the phases observed in the different samples are also given. The results obtained are also summarized in the isothermal section at 500 ◦C proposed in Fig. 1. In the same figure the experimental tie lines and tie triangles have been reported. These were drawn on the basis of the coexisting phases observed by EPMA and XRD in some samples prepared in these fields. The CeAl2 –NdAl2 , CeAl–NdAl and Ce3 Al–Nd3 Al sections have been studied. Particular attention was devoted to alloys having compositions along the CeAl–NdAl and Ce3 Al–Nd3 Al sections. The phase relations observed are described and discussed in the following. As we can expect on the basis of the binary phase diagrams and the crystal structures reported in literature, no ternary phases, but only ternary extensions of the binary phases were observed. On the basis of our data we propose the sequence of equilibria in Fig. 1: we notice the existence of some solid solutions, more or less extending from the
Fig. 2. Average atomic volume of the (Cex Nd1−x )Al2 and (Cex Nd1−x )Al3 phases plotted as a function of the Ce content.
binary edges into the ternary field. Figs. 2 and 3 show the trend of the average atomic volume, plotted as a function of the Ce content, for the various phases formed along the investigated sections. 4.1. CeAl2 –NdAl2 This section was previously investigated by Swift [6] and by Iandelli and Olcese [10]. The formation of a solid solution between the isostructural RAl2 phases cF24-Cu2 Mg type was confirmed and a linear variation of the lattice parameters according to V´egard’s law was observed. In these samples the presence of a certain quantity of Cex Nd(1−x) Al3 phase (a continuous solid solution based on the hP8-Ni3 Sn type) coexisting in equilibrium with the Cex Nd(1−x) Al2 phase was often observed. In the figures here reported, instead of the lattice parameters the average atomic volume was represented: this in order to have an easier comparison between
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Table 2 Crystallographic and microanalysis data of Ce–Nd–Al ternary alloys annealed for 1 week at 500 ◦ C and quenched N
Lattice parameters (nm) a b c
Microprobe analysis at.% Ce at.% Nd
at.% Al
cF24-MgCu2 hP8-Ni3 Sn
0.8020 0.6482
0.4608
11.0 9.5
22.0 14.0
67.0 76.5
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
cF24-MgCu2 hP8-Ni3 Sn
0.8034 0.6496
0.4630
16.0 13.0
16.0 13.5
68.0 76.5
20.0 Ce 10.0 Nd 70.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
cF24-MgCu2 hP8-Ni3 Sn
0.8040 0.6516
0.4608
21 17.5
10.5 5.0
68.5 77.5
32.0 Ce 1.0 Nd 67.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
cF24-MgCu2 hP8-Ni3 Sn
0.8058 0.6575
0.4659
32.0 25.0
2.0 1.0
66.0 74.0
5
5.0 Ce 45.0 Nd 50.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5954 0.8007
1.1750
0.5736
4.5 2.5
44.5 29.0
51.0 68.5
6
10.0 Ce 39.0 Nd 51.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5959 0.8013
1.1760
0.5740
9.5 6.0
42.5 27.0
48.0 67.0
7
13.0 Ce 37.0 Nd 50.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5960 0.8013
1.1764
0.5745
12.0 7.0
36.5 23.5
51.5 69.5
8
17.5 Ce 30.5 Nd 52.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al
cF24-MgCu2 oP16-ErAl
0.8021 0.5968
1.1784
0.5760
11.0 17.0
23.0 33.0
66.0 50.0
17.0 Ce 29.0 Nd 54.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
cF24-MgCu2
18.5 11.0
33.0 23.0
49.5 66.0
10
17.0 Ce 31.5 Nd 51.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5967 0.8025
1.1783
0.5743
16.0 9.5
32.0 20.0
52.0 70.5
11
19.0 Ce 29.5 Nd 51.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5967 0.8024
1.1786
0.5750
18.0 10.5
31.0 22.0
51.0 67.5
12
20.0 Ce 28.0 Nd 52.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
cF24-MgCu2
22.0 13.0
30.0 20.5
48.0 66.5
13
21.0 Ce 29.5 Nd 49.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
21.5 12.5
29.5 20.5
50.0 67.0
14
21.5 Ce 26.0 Nd 52.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
23.0 14.0
27.5 18.0
49.5 68.0
15
22.5 Ce 26.0 Nd 51.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9244 0.8035
0.7652
0.5717
22.0 14.0
28.0 19.0
50.0 67.0
16
25.5 Ce 22.5 Nd 52.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9245 0.8033
0.7656
0.5737
26.0 16.5
25.5 17.0
49.5 66.5
17
32.0 Ce 17.0 Nd 51.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9258 0.8041
0.7673
0.5747
33.0 22.0
17.0 11.0
50.0 67.0
1
2
3
4
9
Global analysis (at.%)
Phases observed, reported in the order of their amount
Structure type
10.0 Ce 20.0 Nd 70.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
16.0 Ce 14.0 Nd 70.0 Al
0.9240 0.8028
0.7648
0.5735
A.M. Cardinale et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226
225
Table 2 (continued) N
Global analysis (at.%)
Phases observed, reported in the order of their amount
Structure type
Lattice parameters (nm) a b c
Microprobe analysis at.% Ce at.% Nd
at.% Al
18
32.0 Ce 12.0 Nd 56.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9261 0.8044
0.7665
0.5751
34.5 21.0
13.0 9.0
52.5 70.0
19
40.0 Ce 7.5 Nd 52.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9268 0.805
0.7671
0.5752
40.5 27.5
7.5 4.0
52.0 68.5
20
44.5 Ce 2.0 Nd 53.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9276 0.8057
0.7685
0.5757
44.0 30.0
3.5 1.0
52.5 69.0
21
40.5 Ce 18.5 Nd 41 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )3 Al
oC16-CeAl
0.9246
0.7655
0.5742
33.0 57.0
18.0 17.0
49.0 26.0
22
29.0 Ce 22.0 Nd 49.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )3 Al
28.0 49.0
22.0 24.0
50.0 27.0
23
31.0 Ce 32.5 Nd 36.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )3 Al
22.0 39.5
27.0 33.5
51.0 27.0
24
6.5 Ce 63.5 Nd 30.0 Al
(Cex Nd(1−x) )2 Al (Cex Nd(1−x) )3 Al
5.5 8.5
62.0 66.0
32.5 25.5
25
26.5 Ce 45.0 Nd 28.5 Al
(Cex Nd(1−x) )2 Al (Cex Nd(1−x) )3 Al
23.0 32.0
45.0 43.5
32.0 24.5
26
75.0 Ce 5.0 Nd 20.0 Al
(Cex Nd(1−x) )3 Al
cP4-AuCu3
0.4965
69.0 93.0
5.0 5.0
26.0 2.0
27
66.5 Ce 7.0 Nd 27.0 Al
(Cex Nd(1−x) )3 Al (Cex Nd(1−x) )Al
hP8-Ni3 Sn
0.7037
0.5433
67.0 45.0
6.5 6.0
26.5 49.0
28
60.0 Ce 12.0 Nd 28.0 Al
(Cex Nd(1−x) )3 Al
hP8-Ni3 Sn
0.7044
0.5441
61.0
11.0
28.0
29
47.5 Ce 26.0 Nd 26.5 Al
(Cex Nd(1−x) )3 Al
hP8-Ni3 Sn
0.7026
0.5437
49.0
25.5
25.5
30
31.0 Ce 43.0 Nd 26.0 Al
(Cex Nd(1−x) )3 Al (Cex Nd(1−x) )2 Al
hP8-Ni3 Sn
0.7000
0.5424
32.0 24.0
43.0 44.5
25.0 31.5
31
16.0 Ce 59.5 Nd 24.5 Al
(Cex Nd(1−x) )3 Al (Cex Nd(1−x) )2 Al
hP8-Ni3 Sn
0.6990
0.5420
17.0 13.0
60.0 55.0
23.0 32.0
phases having different structures. The few values obtained along the Cex Nd(1−x) Al3 section are also shown in Fig. 2. 4.2. CeAl–NdAl This section is characterized by two wide homogeneity regions based on the structure of the CeAl and NdAl binary phases. One solid solution, Cex Nd(1−x) Al, based on the NdAl structure (oP16-ErAl type), extends deeply into the ternary field up to a composition of about x = 0.38. The second one, Ce(1−y) Ndy Al, having the CeAl structure (oC16-CeAl type), extends up to about y = 0.59.
The variation of the average atomic volume of the ErAltype and of the CeAl-type solid solutions as a function of the Ce content is reported in Table 2 and Fig. 3. It was not possible to determine the lattice parameters of the coexisting phases in this section. 4.3. Ce3 Al–N3 dAl As for this section, the (Cex Nd(1−x) )3 Al phase (hP8Ni3 Sn type) extends into the ternary field up to x = 0.91. The same structure type is stable, for Ce3 Al, at lower temperatures (T < 250 ◦C) where a continuous solid solution
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Average atomic volume (nm 3 10 2 )
References 2.95
2.85 (Ce x Nd 1– x )Al oP16–ErAl 2.75
(Ce 1– y Nd y)Al oC16–CeAl (Ce x Nd 1– x )3Al hP8– Ni 3 Sn
2.65
2.55
2.45 0.00
0.20
0.40
0.60
0.80
1.00
x, (1– y) Fig. 3. Average atomic volume of the (Cex Nd1−x )Al, (Ce1−y Ndy )Al and (Cex Nd1−x )3 Al phases plotted as a function of the Ce content.
is probably formed. At the investigated temperature the cP4-AuCu3 type Ce3 Al phase is stable and it dissolves a small amount of Nd. 4.4. Thermodynamic calculation of phase equilibria The results obtained have been used together with the thermodynamic data available in literature on the binary subsystems for a thermodynamic modeling and optimization of the Ce–Nd–Al system, by means of the CALPHAD method. A complete description of the ternary system and, in particular, a prediction of the solid–liquid phase equilibria has been obtained, and the thermodynamic calculation of the 500 ◦C isothermal section is in agreement with the experimental data. This will be discussed in detail in another paper in this issue [26]. Acknowledgement The Italian Ministero dell’ Istruzione dell’ Universit`a e della Ricerca is acknowledged with thanks for the financial support given in the framework of a National research project entitled “Leghe e composti intermetallici: stabilit`a termodinamica, propriet`a fisiche e reattivit`a”.
[1] J.H.N. vanVucht, Z. Metallkd. 48 (1957) 253. [2] K.A. Gschneidner Jr., R.O. Elliot, M.Y. Prince, in: J.R. Nachman, C.E. Lundin (Eds.), Rare Earth Research, Gordon and Breach, New York, 1962. [3] K.H.J. Buschow, J. Less-Comm. Metals 9 (1965) 452–456. [4] K.H.J. Buschow, J.H.N. vanVucht, Z. MetallKd. 57 (1966) 162–166. [5] J.D. Speight, I.R. Harris, G.V. Raynor, J. Less-Common Met. 15 (1968) 317–330. [6] W.M. Swift, W.E. Wallace, J. Phys. Chem. Solids 29 (1968) 2053–2061. [7] R. Cappelli, R. Ferro, A. Borsese, Termochim. Acta 10 (1974) 13–21. [8] W.G. Moffat (Ed.), Handbook of Binary Phase Diagrams, Business Growth Services, General Electric Co., Schenectady, NY, 1976. [9] K. Yvon, W. Jeitschko, E. Parth´e, J. Appl. Crystallogr. 10 (1977) 73–74. [10] A. Iandelli, G.L. Olcese, J. Less-Comm. Metals 111 (1985) 145–156. [11] K.H. Gschneidner, Jr., F.W. Calderwood, Bull. Alloy Phase Diag. 10 (1989) 28–49. [12] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak (Eds.), Binary Alloy Phase Diagrams, ASM International Materials Park, Ohio, 1990. [13] V.I. Kononenko, S.V. Golubev, Izv. Akad. Nauk. SSSR, Met. 2 (1990) 197–199. [14] G. Borzone, G. Cacciamani, R. Ferro, Metall. Trans. A22 (1991) 2119–2123. [15] G. Borzone, A.M. Cardinale, G. Cacciamani, R. Ferro, Z. Metallkd. 84 (1993) 635–640. [16] R. Ferro, G. Borzone, N. Parodi, G. Cacciamani, J. Phase Equilibra 15 (1994) 317–329. [17] G. Zanicchi, P. Riani, D. Mazzone, R. Marazza, D. Rossi, R. Ferro, J. Alloys Compd. 215 (1994) 181–186. [18] G. Borzone, A.M. Cardinale, A. Saccone, R. Ferro, J. Alloys Compd. 220 (1995) 122–125. [19] G. Cacciamani, G. Borzone, R. Ferro, J. Alloys Compd. 220 (1995) 106–110. [20] A. Saccone, A.M. Cardinale, S. De1fino, R. Ferro, Z. Metallkd. 87 (1996) 82–87. [21] G. Borzone, A.M. Cardinale, N. Parodi, G. Cacciamani, J. Alloys Compd. 247 (1997) 141–147. [22] G. Cacciamani, P. Riani, G. Borzone, N. Parodi, A. Saccone, R. Ferro, A. Pisch, R. Schmidt-Fetzer, Intermetallics 7 (1999) 101–108. [23] G. Borzone, A. Ciccioli, P.L. Cignini, M. Ferrini, D. Gozzi, Intermetallics 8 (2000) 203–212. [24] G. Borzone, N. Parodi, R. Ferro, J.P. Bros, J.P. Dub`es, M. Gambino, J. Alloys Compd. 320 (2001) 242–250. [25] G. Cacciamani, R. Ferro, Calphad 25 (2002) 583–594. [26] G. Cacciamani, A.M. Cardinale, G. Borzone, R. Ferro, Calphad 27 (2003) 227–233.
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Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226
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Experimental investigation of the Al–Ce–Nd system A.M. Cardinale, G. Cacciamani, G. Borzone∗, R. Ferro Universit`a di Genova, Dipartimento di Chimica e Chimica Industriale, via Dodecaneso 31 - 16146 Genoa, Italy Received 21 July 2003; accepted 27 July 2003
Abstract In the framework of a systematic investigation of intermetallic systems including rare earths and aluminum, Ce–Nd–Al alloys have recently been investigated by x-ray diffraction, optical microscopy, scanning electron microscopy and electron probe microanalysis. In particular, the Ce–Nd–Al isothermal section at 500 ◦ C has been experimentally determined. This section is characterized by several line compounds extending from the binary R–Al subsystems into the ternary field. Complete solid solutions are found in the ternary system when the Ce–Al and the corresponding Nd–Al compounds are isostructural (CeAl3 and NdAl3 , CeAl2 and NdAl2 ). The remaining binary phases show lower ternary solubilities. These results have been used together with the thermodynamic data available in literature on the binary subsystems for a thermodynamic modeling and optimization of the Ce–Nd–Al system, by means of the CALPHAD method (Calphad (this issue)). © 2003 Elsevier Ltd. All rights reserved.
1. Introduction
2. Literature data
In the past year several thermodynamic properties of binary R–Al alloys have been investigated by our research group. Particular attention was devoted to the determination of the enthalpy of formation of alloys formed in the binary R–Al systems (R = La [21], Ce [14], Pr [16], Nd [15], Sm [18], Sc [22]) by using direct reaction calorimetry [7, 19]. In several cases, such as for the Y–Al system, the calorimetric investigation was combined with emf measurements, in order to get a more complete thermodynamic description of the system [23]. Recently, the heat capacity and phase equilibria in the R-rich R–Al alloys (R = La, Pr and Nd) have been investigated [20, 24]. Selected R1−x Rx Aly sections have also been studied by means of optical and electron microscopy and x-ray powder diffraction [17]. In the present paper, the results obtained in the experimental study of the Ce–Nd–Al alloys are reported.
2.1. Compound formation in the light rare earth–aluminum systems The crystallochemistry of the R–Al phases (R = La, Ce, Pr, Nd) is summarized in Table 1 and several remarks may be noteworthy. The R3 Al compound in the La system exists only in the ∼400 to ∼520 ◦C temperature range and belongs to the hP8-Ni3 Sn type. For cerium and praseodymium it shows two different structures (hP8-Ni3 Sn, low temperature form and cP4-AuCu3 type, high temperature form) while it presents only the hP8-Ni3 Sn type structure for neodymium. Considering the R2 Al stoichiometry, no compound has been described for Ce, while praseodymium and neodymium form the orthorhombic oP12-Co2 Si structure. For the RAl compounds, La and Ce form the orthorhombic oC16-CeAl type structure, Pr gives two forms: oC16-CeAl type (at high temperature) and oP16-ErAl (at low temperature). For NdAl only the oP16-ErAl form has been observed. RAl2 as well as RAl3 and R3 Al11 compounds exist in the same structural types for all the light rare earths. 2.2. Ce–Al system
∗ Corresponding author. Tel.: +39-10-3536153; fax: +39-10-3625051.
E-mail address: [email protected] (G. Borzone). 0364-5916/$ - see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2003.07.002
The Ce–Al diagram is based mainly on the work by van Vucht [1] and Buschow [4] and the more recent revision
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Table 1 R–Al systems (R = La, Ce, Pr and Nd) crystal structures of the phases and indication of their temperature range of stability (T/◦ C) Stoichiometry
La
Ce
Pr
Nd
Structural types
R3 Al
520–400
685–250 <250
685–330 <330
<780
cP4-AuCu3 hP8-Ni3 Sn
<735
<795
oP12-Co2 Si
R2 Al RAl
<873
<845
905–700 <700
<940
oC16–CeAl oP16-ErAl
RAl2
<1405
<1480
<1480
<1460
cF24-MgCu2
RAl3
<1170
<1135
<1075
<1205
hP8-Ni3 Sn
R3 Al11
1240–915 <915
1235–1020 <1020
1240–965 <965
1235–950 <950
tI10-BaAl4 (Al def.) oI28-αLa3 Al11
by [20]. Five intermetallic line compounds are present: Ce3 Al melting point at 685 ◦ C, showing a structural transformation at about 250 ◦C from the hexagonal structure (α-Ce3 Al, low temperature form) to the cubic structure (β-Ce3 Al, high temperature form), CeAl orthorhombic, peritectic formation at 845 ◦C, CeAl2 melting point 1480 ◦C, CeAl3 peritectoidal decomposition at 1135 ◦C, Ce3 Al11 peritectic formation at 1235 ◦C. The low temperature α-Ce3 Al11 (below 1020 ◦C) has an orthorhombic oI28-α-La3 Al11 structure and the β-Ce3 Al11 has a tetragonal tI10-BaAl4 , Al-deficient structure. Three eutectic reactions are reported at ∼14.0 at.% Al at 600 ◦C, at 27.5 at.% Al at 660 ◦C and at ∼97.4 at.% Al at 633 ◦C [13]. The maximum solid solubility of aluminum in δ-Ce is about 2.5 at.% at the 700 ◦C, catatectic reaction temperature. At the same temperature very little solid solubility of Al in γ -Ce, less than 1 at.% Al, was proposed. Recently an assessed version has been reported by [25]. 2.3. Nd–Al system The Nd–Al diagram was determined by Buschow [3] and assessed by Gschneidner and Calderwood [11]. Recent investigations were performed in the Nd-rich [20, 24] and Al-rich regions [13]. This system shows six intermetallic compounds: Nd3 Al, peritectic formation at 780 ◦C, Nd2 Al, peritectic formation at 795 ◦C, NdAl, orthorhombic oP16ErAl, peritectic formation at 940 ◦ C, NdAl2 melting point 1460 ◦C, NdAl3 peritectoidal decomposition at 1205 ◦C, Nd3 Al11 peritectic formation at 1235 ◦C. Low temperature α-Nd3 Al11 (below 950 ◦C) has an orthorhombic oI28-α-La3 Al11 structure and β-Nd3 Al11 has a tetragonal tI10-BaAl4 , Al-deficient structure. Two eutectic reactions are reported at ∼19.0 at.% Al and 685 ◦C and ∼97.5 at.% Al at 632 ◦C. The maximum solid solubility of Al in β-Nd is about 12 at.% Al at the eutectic temperature and 10 at.% Al and 10 at.% Al at the eutectoid temperature of 650 ◦C. At this temperature the maximum solid solubility of Al in α-Nd is about 2 at.% Al. An optimization of the Nd–Al system is reported in [25].
2.4. Ce–Nd system No phase diagram is available in literature, but Speight et al. [5] have measured the room temperature lattice parameters for the Ce–Nd alloy system. In addition to this work, Gschneidner et al. [2] reported the lattice parameter of a Ce-rich alloy containing 2 at.% Nd. A likely form of the Ce–Nd phase diagram based on the information given in these papers was drawn by Moffat [8] and reported by Massalski [12]. It shows complete mutual solid solubility at high temperature in the bcc modifications (δ-Ce and β-Nd). The continuous solid solution decomposes on cooling into the two phases based on γ -Ce and α-Nd. 2.5. Ce–Nd–Al system An investigation of the CeAl2 –NdAl2 section at 800 ◦C was previously done [6, 10]. A continuous solid solution with a linear variation of the unit cell, according to Vegard’s law was determined. 3. Experimental 3.1. Alloys preparation The metals used were cerium, neodymium and aluminum 99.9, 99.9 and 99.999 mass% nominal purity respectively. The samples were prepared by melting in an induction furnace, under argon atmosphere, pieces of the constituent metals sealed in small tantalum crucibles for compositions between 0 and 40 at.% of aluminum. Alumina crucibles were used for compositions over 40 at.% of aluminum; the sample mass was about 0.8–1.0 g. The alloys were generally annealed at 500 ◦ C for one week and then quenched in cold water. Several samples were annealed at 600 ◦C for 4 days, then at 500 ◦C for 1 week, and quenched in cold water. For the annealing, either tantalum or alumina crucibles were placed in steel tubes sealed by arcwelding under argon. On the basis of results obtained from
A.M. Cardinale et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226 1.0 0.9 0.8
fra ctio nA l
(Ce1–y Nd y )Al
(Ce x Nd 1–x )Al 3
0.7
(Ce x Nd 1–x )Al 2
0.6 (Ce x Nd 1–x )Al
Mo le
0.5
0.4 (Ce x Nd 1–x ) 2 Al
0.3
(Ce1–y Nd y ) 3 Al 0.2
(Ce x Nd 1–x ) 3 Al
0.1 0 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Nd Fig. 1. Al–Ce–Nd system. Two- and three-phase equilibria at 500 ◦ C are reported. Experimental tie lines and tie triangles obtained from selected alloys in the ∼25 to 75 at.% Al composition range (see Table 2) are also shown.
2.19
Average atomic volume (nm 3 10 2 )
the modeling, in order to determine information on selected liquidus temperatures, a few samples were subjected to thermal analysis (DTA) with heating and cooling rates of 10 K min−1 . The following results were obtained for the studied compositions (±5 ◦C): Ce30 Nd35 Al35 Tliq = 845 ◦C, Ce35 Nd25 Al40 Tliq = 900 ◦C, Ce25 Nd45Al30 Tliq = 850 ◦C. Metallographic, electron probe and x-ray diffraction analyses were used to characterize all the samples. For metallographic analysis, the specimens were prepared using SiC and diamond-paste polishing; according to their composition, they were etched in dilute HNO3 (R-rich samples) or in dilute KOH (Al-rich samples). The average composition of the different phases was determined by performing at different points of the buttons electron probe microanalysis (EPMA) using an energydispersive x-ray analyzer. Cobalt standard was used for calibration and the x-ray intensities were considered for ZAF effects using pure elements as standards; the compositional values derived were usually accurate to ±1 at.% for Ce and Nd. As for Al-rich alloys, the microprobe analysis generally indicated an Al concentration of the phases higher than the stoichiometric value. As for the global composition which generally was nearly coincident with the nominal composition, a higher uncertainty was estimated because the analyzed surface in some cases could not represent the overall sample composition. XRD examination was performed on powder samples using the Debye method (Cu-Kα filtered radiation); the observed diffraction intensities were compared with those calculated by means of the program Pulverix [9]. The values of the lattice parameters were refined using a least-squares routine.
223
2.17 2.15 2.13 2.11 RAl 3 , hP8–Ni 3 Sn
2.09
RAl 2 , cF24–MgCu 2 2.07 0.00
0.20
0.40
0.60
0.80
1.00
x
4. Results and discussion The data obtained in the preparation and examination of different alloys are reported in Table 2 where data for the phases observed in the different samples are also given. The results obtained are also summarized in the isothermal section at 500 ◦C proposed in Fig. 1. In the same figure the experimental tie lines and tie triangles have been reported. These were drawn on the basis of the coexisting phases observed by EPMA and XRD in some samples prepared in these fields. The CeAl2 –NdAl2 , CeAl–NdAl and Ce3 Al–Nd3 Al sections have been studied. Particular attention was devoted to alloys having compositions along the CeAl–NdAl and Ce3 Al–Nd3 Al sections. The phase relations observed are described and discussed in the following. As we can expect on the basis of the binary phase diagrams and the crystal structures reported in literature, no ternary phases, but only ternary extensions of the binary phases were observed. On the basis of our data we propose the sequence of equilibria in Fig. 1: we notice the existence of some solid solutions, more or less extending from the
Fig. 2. Average atomic volume of the (Cex Nd1−x )Al2 and (Cex Nd1−x )Al3 phases plotted as a function of the Ce content.
binary edges into the ternary field. Figs. 2 and 3 show the trend of the average atomic volume, plotted as a function of the Ce content, for the various phases formed along the investigated sections. 4.1. CeAl2 –NdAl2 This section was previously investigated by Swift [6] and by Iandelli and Olcese [10]. The formation of a solid solution between the isostructural RAl2 phases cF24-Cu2 Mg type was confirmed and a linear variation of the lattice parameters according to V´egard’s law was observed. In these samples the presence of a certain quantity of Cex Nd(1−x) Al3 phase (a continuous solid solution based on the hP8-Ni3 Sn type) coexisting in equilibrium with the Cex Nd(1−x) Al2 phase was often observed. In the figures here reported, instead of the lattice parameters the average atomic volume was represented: this in order to have an easier comparison between
224
A.M. Cardinale et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226
Table 2 Crystallographic and microanalysis data of Ce–Nd–Al ternary alloys annealed for 1 week at 500 ◦ C and quenched N
Lattice parameters (nm) a b c
Microprobe analysis at.% Ce at.% Nd
at.% Al
cF24-MgCu2 hP8-Ni3 Sn
0.8020 0.6482
0.4608
11.0 9.5
22.0 14.0
67.0 76.5
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
cF24-MgCu2 hP8-Ni3 Sn
0.8034 0.6496
0.4630
16.0 13.0
16.0 13.5
68.0 76.5
20.0 Ce 10.0 Nd 70.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
cF24-MgCu2 hP8-Ni3 Sn
0.8040 0.6516
0.4608
21 17.5
10.5 5.0
68.5 77.5
32.0 Ce 1.0 Nd 67.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
cF24-MgCu2 hP8-Ni3 Sn
0.8058 0.6575
0.4659
32.0 25.0
2.0 1.0
66.0 74.0
5
5.0 Ce 45.0 Nd 50.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5954 0.8007
1.1750
0.5736
4.5 2.5
44.5 29.0
51.0 68.5
6
10.0 Ce 39.0 Nd 51.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5959 0.8013
1.1760
0.5740
9.5 6.0
42.5 27.0
48.0 67.0
7
13.0 Ce 37.0 Nd 50.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5960 0.8013
1.1764
0.5745
12.0 7.0
36.5 23.5
51.5 69.5
8
17.5 Ce 30.5 Nd 52.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al
cF24-MgCu2 oP16-ErAl
0.8021 0.5968
1.1784
0.5760
11.0 17.0
23.0 33.0
66.0 50.0
17.0 Ce 29.0 Nd 54.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
cF24-MgCu2
18.5 11.0
33.0 23.0
49.5 66.0
10
17.0 Ce 31.5 Nd 51.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5967 0.8025
1.1783
0.5743
16.0 9.5
32.0 20.0
52.0 70.5
11
19.0 Ce 29.5 Nd 51.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oP16-ErAl cF24-MgCu2
0.5967 0.8024
1.1786
0.5750
18.0 10.5
31.0 22.0
51.0 67.5
12
20.0 Ce 28.0 Nd 52.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
cF24-MgCu2
22.0 13.0
30.0 20.5
48.0 66.5
13
21.0 Ce 29.5 Nd 49.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
21.5 12.5
29.5 20.5
50.0 67.0
14
21.5 Ce 26.0 Nd 52.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
23.0 14.0
27.5 18.0
49.5 68.0
15
22.5 Ce 26.0 Nd 51.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9244 0.8035
0.7652
0.5717
22.0 14.0
28.0 19.0
50.0 67.0
16
25.5 Ce 22.5 Nd 52.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9245 0.8033
0.7656
0.5737
26.0 16.5
25.5 17.0
49.5 66.5
17
32.0 Ce 17.0 Nd 51.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9258 0.8041
0.7673
0.5747
33.0 22.0
17.0 11.0
50.0 67.0
1
2
3
4
9
Global analysis (at.%)
Phases observed, reported in the order of their amount
Structure type
10.0 Ce 20.0 Nd 70.0 Al
(Cex Nd(1−x) )Al2 (Cex Nd(1−x) )Al3
16.0 Ce 14.0 Nd 70.0 Al
0.9240 0.8028
0.7648
0.5735
A.M. Cardinale et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 221–226
225
Table 2 (continued) N
Global analysis (at.%)
Phases observed, reported in the order of their amount
Structure type
Lattice parameters (nm) a b c
Microprobe analysis at.% Ce at.% Nd
at.% Al
18
32.0 Ce 12.0 Nd 56.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9261 0.8044
0.7665
0.5751
34.5 21.0
13.0 9.0
52.5 70.0
19
40.0 Ce 7.5 Nd 52.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9268 0.805
0.7671
0.5752
40.5 27.5
7.5 4.0
52.0 68.5
20
44.5 Ce 2.0 Nd 53.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )Al2
oC16-CeAl cF24-MgCu2
0.9276 0.8057
0.7685
0.5757
44.0 30.0
3.5 1.0
52.5 69.0
21
40.5 Ce 18.5 Nd 41 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )3 Al
oC16-CeAl
0.9246
0.7655
0.5742
33.0 57.0
18.0 17.0
49.0 26.0
22
29.0 Ce 22.0 Nd 49.0 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )3 Al
28.0 49.0
22.0 24.0
50.0 27.0
23
31.0 Ce 32.5 Nd 36.5 Al
(Cex Nd(1−x) )Al (Cex Nd(1−x) )3 Al
22.0 39.5
27.0 33.5
51.0 27.0
24
6.5 Ce 63.5 Nd 30.0 Al
(Cex Nd(1−x) )2 Al (Cex Nd(1−x) )3 Al
5.5 8.5
62.0 66.0
32.5 25.5
25
26.5 Ce 45.0 Nd 28.5 Al
(Cex Nd(1−x) )2 Al (Cex Nd(1−x) )3 Al
23.0 32.0
45.0 43.5
32.0 24.5
26
75.0 Ce 5.0 Nd 20.0 Al
(Cex Nd(1−x) )3 Al
cP4-AuCu3
0.4965
69.0 93.0
5.0 5.0
26.0 2.0
27
66.5 Ce 7.0 Nd 27.0 Al
(Cex Nd(1−x) )3 Al (Cex Nd(1−x) )Al
hP8-Ni3 Sn
0.7037
0.5433
67.0 45.0
6.5 6.0
26.5 49.0
28
60.0 Ce 12.0 Nd 28.0 Al
(Cex Nd(1−x) )3 Al
hP8-Ni3 Sn
0.7044
0.5441
61.0
11.0
28.0
29
47.5 Ce 26.0 Nd 26.5 Al
(Cex Nd(1−x) )3 Al
hP8-Ni3 Sn
0.7026
0.5437
49.0
25.5
25.5
30
31.0 Ce 43.0 Nd 26.0 Al
(Cex Nd(1−x) )3 Al (Cex Nd(1−x) )2 Al
hP8-Ni3 Sn
0.7000
0.5424
32.0 24.0
43.0 44.5
25.0 31.5
31
16.0 Ce 59.5 Nd 24.5 Al
(Cex Nd(1−x) )3 Al (Cex Nd(1−x) )2 Al
hP8-Ni3 Sn
0.6990
0.5420
17.0 13.0
60.0 55.0
23.0 32.0
phases having different structures. The few values obtained along the Cex Nd(1−x) Al3 section are also shown in Fig. 2. 4.2. CeAl–NdAl This section is characterized by two wide homogeneity regions based on the structure of the CeAl and NdAl binary phases. One solid solution, Cex Nd(1−x) Al, based on the NdAl structure (oP16-ErAl type), extends deeply into the ternary field up to a composition of about x = 0.38. The second one, Ce(1−y) Ndy Al, having the CeAl structure (oC16-CeAl type), extends up to about y = 0.59.
The variation of the average atomic volume of the ErAltype and of the CeAl-type solid solutions as a function of the Ce content is reported in Table 2 and Fig. 3. It was not possible to determine the lattice parameters of the coexisting phases in this section. 4.3. Ce3 Al–N3 dAl As for this section, the (Cex Nd(1−x) )3 Al phase (hP8Ni3 Sn type) extends into the ternary field up to x = 0.91. The same structure type is stable, for Ce3 Al, at lower temperatures (T < 250 ◦C) where a continuous solid solution
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Average atomic volume (nm 3 10 2 )
References 2.95
2.85 (Ce x Nd 1– x )Al oP16–ErAl 2.75
(Ce 1– y Nd y)Al oC16–CeAl (Ce x Nd 1– x )3Al hP8– Ni 3 Sn
2.65
2.55
2.45 0.00
0.20
0.40
0.60
0.80
1.00
x, (1– y) Fig. 3. Average atomic volume of the (Cex Nd1−x )Al, (Ce1−y Ndy )Al and (Cex Nd1−x )3 Al phases plotted as a function of the Ce content.
is probably formed. At the investigated temperature the cP4-AuCu3 type Ce3 Al phase is stable and it dissolves a small amount of Nd. 4.4. Thermodynamic calculation of phase equilibria The results obtained have been used together with the thermodynamic data available in literature on the binary subsystems for a thermodynamic modeling and optimization of the Ce–Nd–Al system, by means of the CALPHAD method. A complete description of the ternary system and, in particular, a prediction of the solid–liquid phase equilibria has been obtained, and the thermodynamic calculation of the 500 ◦C isothermal section is in agreement with the experimental data. This will be discussed in detail in another paper in this issue [26]. Acknowledgement The Italian Ministero dell’ Istruzione dell’ Universit`a e della Ricerca is acknowledged with thanks for the financial support given in the framework of a National research project entitled “Leghe e composti intermetallici: stabilit`a termodinamica, propriet`a fisiche e reattivit`a”.
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