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Phase relations in the Nd–Ga–Si system at 870 K
Journal of Alloys and Compounds 367 (2004) 64–69
Phase relations in the Nd–Ga–Si system at 870 K Ya.O. Tokaychuk a,b,∗ , A.O. Fedorchuk a , O.I. Bodak a , I.R. Mokra a a
Department of Inorganic Chemistry, Ivan Franko National University of L’viv, Kyryla i Mefodiya Str. 6, L’viv UA-79005, Ukraine b Laboratoire de Cristallographie, Université de Genève, Quai Ernest-Ansermet 24, Genève CH-1211, Switzerland
Abstract The isothermal section of the Nd–Ga–Si phase diagram at 870 K was constructed using X-ray phase analysis. Two ternary phases with a wide homogeneity ranges were found in the NdGa2−x Six section: ∼NdGa1.32−0.92 Si0.68−1.08 (structure type ␣-ThSi2 , space group I41 /amd, Pearson code tI12) and ∼NdGa0.86−0.68 Si1.14−1.32 (structure type ␣-GdSi2 , space group Imma, Pearson code oI12). The binary gallides NdGa2+x (structure type AlB2 ), NdGa (structure type CrB) and Nd9 Ga4 (structure type Sm9 Ga4 ) dissolve 15, 30 and 12 at.% Si, respectively, whereas the binary silicides NdSi1.8 (structure type ␣-GdSi2 ) and NdSi (structure type FeB) dissolve 6 and 7 at.% Ga, respectively. The solubility of the third component in other binary compounds does not exceed 5 at.%. © 2003 Elsevier B.V. All rights reserved. Keywords: Nd–Ga–Si; Phase diagram; Isothermal section; Intermetallic compounds; Crystal structure
1. Introduction An investigation of the Nd–Ga–Si ternary system is a part of a systematical study of the interaction of rare earth metals with gallium and silicon. Recently, we reported the isothermal sections of the La–Ga–Si [1], Ce–Ga–Si [2] and Pr–Ga–Si [3] systems at 870 K. The binary systems at the boundaries of the Nd–Ga–Si ternary system have been widely studied, including the phase diagrams over the whole concentration regions. The phase diagram of the Nd–Ga system was investigated by Kimmel et al. [4] (0–33.3 at.% Nd) and by Manory et al. [5] (33.3–100 at.% Nd). Including the Nd3 Ga2 [6] and Nd9 Ga4 [7] binary phases, which were found later, seven compounds exist in this system. Recently, Gur and Kimmel [8] investigated the pairwise substitution of Nd atoms by gallium in the Nd1−x Ga2+2x solid solution. They established the positional ordering of Ga2 pairs located in the basal planes of this AlB2 derivative type compound at the composition Nd1−x Ga2+2x (x = 0.18). Data on the Nd–Si system were evaluated by Gokhale et al. [9] and the existence of six binary phases was reported. Recently, some new binary compounds were found. Crystallographic data of the binary compounds re∗ Corresponding author. Tel.: +41-22-37-96372; fax: +41-22-37-96108. E-mail address: [email protected] (Ya.O. Tokaychuk).
0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.08.013
ported in the Nd–Ga and Nd–Si systems are summarized in Table 1. No binary compounds exist in the Ga–Si system. This system is characterized by an eutectic reaction at a temperature very close to the melting point of gallium [23]. This study was carried out to construct the isothermal section of the Nd–Ga–Si phase diagram at 870 K, to establish the formation of the solid solutions, to obtain ternary intermediate phases and determine their crystal structures.
2. Experimental One hundred and ten binary and ternary alloys were prepared by direct arc melting of the constituent metals (>99.9 wt.% pure) in a water-cooled copper hearth under a purified argon atmosphere with Ti as a getter. To ensure homogeneity, the samples were remelted twice. The ingots were wrapped in tantalum foil, annealed at 870 K in quartz ampoules under vacuum for 720 h and subsequently quenched in cold water. During the sample preparation the weight losses were <1% of the total mass, which was about 1 g for each sample. The phase analysis was carried out using X-ray powder diffraction—Debye–Scherrer technique (cameras RKD-57.3, non-filtered Cr K␣ radiation) and powder diffractometer (DRON-2, Fe K␣ radiation, germanium as an internal standard). The crystal structures of the ternary compounds were refined using the X-ray powder diffraction data obtained on DRON-4 and PHILIPS PW 1050/80
Ya.O. Tokaychuk et al. / Journal of Alloys and Compounds 367 (2004) 64–69
65
Table 1 Crystallographic data of the binary compounds in the Nd–Ga and Nd–Si systems Compound
a
NdGa6 NdGa2 NdGa Nd3 Ga2 Nd5 Ga3 Nd9 Ga4 Nd3 Gaa ␣-NdSi1.8 (LT) -NdSi1.8 (HT)a NdSi1.5 Nd3 Si4 a NdSi Nd5 Si4 Nd5 Si4 a Nd5 Si3 Nd5 Si3 a a
Structure type
PuGa6 AlB2 CrB Gd3 Ga2 Cr5 B3 Sm9 Ga4 AuCu3 ␣-GdSi2 ␣-ThSi2 AlB2 Cr3 NiB6 FeB Zr5 Si4 Sm5 Ge4 Cr5 B3 Mn5 Si3
Space group
P4/nbm P6/mmm Cmcm I4/mcm I4/mcm I4/m ¯ Pm3m Imma I41 /amd P6/mmm Cmcm Pnma P41 21 2 Pnma I4/mcm P63/mcm
Pearson code
tP14 hP3 oS8 tI80 tI32 tI26 cP4 oI12 tI12 hP3 oS20 oP8 tP36 oP36 tI32 hP16
Cell parameter (Å)
Ref.
a
b
c
5.996 4.271 4.4164 11.915 7.881 12.001 5.43 4.133 4.142 3.940 4.362 8.12 7.869 7.779 7.694 8.66
– – 11.2758 – – – – 4.100 – – 24.584 3.91 – 14.67 – –
7.620 4.270 4.1835 15.34 14.395 5.121 – 13.790 13.65 4.258 3.916 5.88 14.8077 7.779 13.70 6.53
[4] [4] [10] [6] [11] [7] [12] [13–15] [13,16] [13,17] [18] [19] [20] [21] [21] [22]
Compound not observed at 870 K.
diffractometers (Cu K␣ radiation). Data were collected with a scan step of 0.02◦ and collecting times of 10–20 s in a 2θ range of 10–120◦ . All the procedures, including indexing, refinements of lattice and atomic parameters and calculations of interatomic distances, were performed with the FullProf [24] and CSD [25] program packages.
3. Results and discussion We have studied the boundary binary systems at 870 K with respect to the formation of compounds. The formation of five binary compounds was confirmed in the Nd–Ga system: NdGa2+x (AlB2 type), NdGa (CrB type), Nd3 Ga2 (Gd3 Ga2 type), Nd5 Ga3 (Cr5 B3 type) and Nd9 Ga4 (Sm9 Ga4 type). The Nd–Si binary system is also characterized by the formation of five binary silicides at 870 K: NdSi1.8 (␣-GdSi2 type) with a certain homogeneity range, NdSi1.5 (AlB2 type), NdSi (FeB type), Nd5 Si4 (Zr5 Si4 type) and Nd5 Si3 (Cr5 B3 type). The isothermal section of the phase diagram of the Nd–Ga–Si ternary system at 870 K is shown in Fig. 1. This system is characterized by the formation of a continuous solid solution between the isostructural binary compounds Nd5 Ga3 and Nd5 Si3 (structure type Cr5 B3 ) and limited solid solutions of the third component in the other binary compounds. Thus, the binary gallides NdGa2+x (structure type AlB2 ), NdGa (structure type CrB) and Nd9 Ga4 (structure type Sm9 Ga4 ) dissolve 15, 30 and 12 at.% Si, respectively, whereas the binary silicides NdSi1.8 (structure type ␣-GdSi2 ) and NdSi (structure type FeB) dissolve 6 and 7 at.% Ga, respectively. The extensions of the solid solutions based on NdGa2+x (along the line at 33.3 at.% Nd) and NdGa (along the line at 50 at.% Nd) were determined from the plots of the unit cell volume versus
silicon concentration (Fig. 2). The solubility of the third component in the other binary compounds does not exceed 5 at.%. During the investigation of the phase equilibria in the Nd–Ga–Si ternary system at 870 K, we did not observe the binary compound NdSi1.5 in the ternary alloys, although it is present in the binary system. Two ternary phases were found to exist in the 33.3 at.% Nd section of the Nd–Ga–Si system at 870 K. The first one ∼NdGa1.32−0.92 Si0.68−1.08 crystallizes in the tetragonal ␣-ThSi2 structure type (space group I41 /amd, Pearson code tI12) and is in equilibrium with the solid solution of Si in the hexagonal AlB2 -type NdGa2+x binary phase. At increasing Si concentration another phase forms, ∼NdGa0.86−0.68 Si1.14−1.32 with an orthorhombic
Fig. 1. Isothermal section of the phase equilibria diagram of the Nd–Ga–Si system at 870 K.
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Ya.O. Tokaychuk et al. / Journal of Alloys and Compounds 367 (2004) 64–69
Fig. 2. Unit cell volumes for the (a) NdGa2−x Six (x = 0–0.45) and (b) NdGa1−x Six (x = 0–0.6) solid solutions vs. silicon content.
␣-GdSi2 -type structure (space group Imma, Pearson code oI12), which is in equilibrium with the isostructural binary compound NdSi1.8 . Unfortunately, no two-phase region between ternary phases was found. Fig. 3 shows the experimental and calculated powder diffraction patterns of
three samples from the NdGa2−x Six section: a two-phase sample Nd33.3 Ga44.7 Si22 (a), which contains ␣-ThSi2 and AlB2 -type phases, and two single-phase samples Nd33.3 Ga30.7 Si36 (b) and Nd33.3 Ga26.7 Si40 (c), which crystallize in the ␣-ThSi2 - and ␣-GdSi2 -type, respectively.
Table 2 Crystallographic data of the NdGa2−x Six phase, crystallizing in a tetragonal ␣-ThSi2 -type structure (space group I41 /amd, Pearson code tI12) at various compositions (x) x 0.66a
0.81
0.90
0.96
1.08
Sample composition
Nd33.3 Ga44.7 Si22
Nd33.3 Ga39.7 Si27
Nd33.3 Ga36.7 Si30
Nd33.3 Ga34.7 Si32
Nd33.3 Ga30.7 Si36
Lattice parameters a (Å) c (Å) V (Å3 )
4.20329(7) 14.4146(3) 254.673(7)
4.19399(4) 14.3256(2) 251.982(9)
4.19308(4) 14.3105(2) 251.606(7)
4.19220(4) 14.2967(2) 251.259(9)
4.19292(5) 14.3102(2) 251.582(1)
0.4562(1)
0.4580(2)
0.4593(2)
0.4582(2)
0.4589(2)
0.0031(3) 0.0104(7) – –
0.0078(4) 0.0164(14) 0.0062(5) 0.0109(9)
0.0055(3) 0.0115(5) – –
0.0088(4) 0.0188(6) 0.0077(5) 0.0109(8)
0.0073(3) 0.0095(8) 0.0073(5) 0.0073(7)
0.019(2) 0.020(2) 0.017(2)
0.014(2) 0.010(2) 0.004(2)
Positional parametersb z(X)c parametersd
Displacement Uiso/eq (Nd) Uiso/eq (X) U11 (Nd) = U22 (Nd) U33 (Nd) U11 (X) U22 (X) U33 (X)
Interatomic distancese (Å) Nd–4X Nd–8X Nd–4Nd Nd–4Nd
(Å2 )
– – –
0.029(3) 0.013(3) 0.007(2)
– – –
3.1956(1) 3.2027(1) 4.1709(2) 4.2021(2)
3.181(2) 3.1952(5) 4.1502(2) 4.1941(3)
3.165(2) 3.2011(6) 4.1467(2) 4.1931(3)
3.175(2) 3.1939(7) 4.1435(2) 4.1921(2)
3.170(2) 3.1986(8) 4.1466(2) 4.1929(1)
X–1X X–2X X–2Nd X–4Nd
2.3904(1) 2.4259(1) 3.1956(1) 3.2027(1)
2.378(4) 2.418(2) 3.181(2) 3.1952(5)
2.398(2) 2.413(3) 3.165(2) 3.2011(6)
2.378(3) 2.413(2) 3.175(2) 3.1939(7)
2.401(3) 2.404(2) 3.170(2) 3.1986(8)
RI Rp
0.073 0.135
0.0654 0.1264
0.0572 0.1137
0.0659 0.1200
0.0483 0.1169
a b c d e
Two-phase sample, containing a hexagonal AlB2 -type phase. Nd (4a): 0 3/4 1/8, X (8e): 0 1/4 z. X: statistical mixture of Ga and Si atoms. U12 = U13 = U23 = 0 for all atoms. Distances between the atoms within the limits of the coordination polyhedrons.
Ya.O. Tokaychuk et al. / Journal of Alloys and Compounds 367 (2004) 64–69
67
Fig. 3. Parts of the experimental (circles) and calculated (continuous lines) powder diffraction profiles for three alloys from the NdGa1−x Six section: (a) Nd33.3 Ga44.7 Si22 , two-phase sample, which contains tetragonal ␣-ThSi2 - and hexagonal AlB2 -type phases (reflections from the hexagonal phase are indicated by ∗); (b) Nd33.3 Ga30.7 Si36 , ␣-ThSi2 -type phase; (c) Nd33.3 Ga28.7 Si38 , orthorhombic ␣-GdSi2 -type phase. The reflection positions are indicated by vertical bars.
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Ya.O. Tokaychuk et al. / Journal of Alloys and Compounds 367 (2004) 64–69
The crystallographic data, values of the interatomic distances and the results of the Rietveld refinements of the ␣-ThSi2 - and ␣-GdSi2 -type ternary phases are listed in Tables 2 and 3, respectively. Table 3 Crystallographic data of the NdGa2−x Six phase, crystallizing in an orthorhombic ␣-GdSi2 -type structure (space group Imma, Pearson code oI12) at various compositions (x) x
Sample composition
1.14
1.21
1.29
Nd33.3 Ga28.7 Si38
Nd33.3 Ga26.4 Si40.3
Nd33.3 Ga23 Si43
4.2138(3) 4.2001(5) 14.100(1) 249.55(1)
4.20870(1) 4.20268(1) 14.0780(3) 249.01(2)
Lattice parameters a (Å) 4.21572(1) b (Å) 4.19796(1) c (Å) 14.1025(3) V (Å3 ) 249.58(2) Positional parametersa z(Nd) 0.3788(2) z(X1)b z(X2)b
0.9611(5) 0.7912(3)
Displacement parametersc (Å2 ) 0.0076(8) Uiso/eq (Nd) 0.015(4) Uiso/eq (X1) Uiso/eq (X1) 0.016(2) U11 (Nd) U22 (Nd) U33 (Nd) U11 (X1) U22 (X1) U33 (X1) U11 (X2) U22 (X2) U33 (X2)
0.0082(15) 0.0094(15) 0.0053(10) 0.009(7) 0.027(8) 0.010(6) 0.020(4) 0.019(5) 0.008(3)
Interatomic distancesd (Å) Nd–2X1 3.090(6) Nd–2X2 3.186(4) Nd–4X1 3.193(3) Nd–4X2 3.221(2)
0.38016(1)
0.3801(3)
0.9592(3) 0.7925(2)
0.9587(5) 0.7890(4)
0.0116(5) 0.019(2) 0.0110(6)
0.0078(7) 0.016(4) 0.015(3)
0.0153(9) 0.0102(8) 0.0093(6) 0.011(4) 0.032(4) 0.013(3) 0.018(3) 0.012(3) 0.003(2)
0.005(2) 0.011(2) 0.0076(7) 0.007(6) 0.023(7) 0.017(5) 0.019(5) 0.012(5) 0.014(4)
3.093(3) 3.176(2) 3.214(3) 3.221(1)
3.095(6) 3.173(3) 3.175(5) 3.238(3)
Nd–2Nd Nd–2Nd Nd–2Nd Nd–2Nd
4.012(4) 4.1980(1) 4.199(4) 4.2157(1)
3.978(2) 4.1996(1) 4.2139(1) 4.232(2)
3.977(5) 4.2027(1) 4.2087(1) 4.224(5)
X1–2X1 X1–1X2 X1–2Nd X1–4Nd
2.369(5) 2.396(9) 3.090(6) 3.193(3)
2.350(5) 2.394(3) 3.093(3) 3.176(2)
2.388(8) 2.402(5) 3.095(6) 3.173(3)
X2–1X1 X2–2X2 X2–2Nd X2–4Nd
2.396(9) 2.407(3) 3.186(4) 3.221(2)
2.350(5) 2.423(2) 3.214(3) 3.221(1)
2.374(3) 2.388(8) 3.175(5) 3.238(3)
RI Rp
0.0791 0.1284
0.0453 0.1131
0.0589 0.1357
a
Nd (4e): 0 1/4 z, X1 (4e): 0 1/4 z, X2 (4e): 0 1/4 z. X1 and X2: statistical mixtures of Ga and Si atoms. c U = U = U = 0 for all atoms. 12 13 23 d Distances between the atoms within the limits of the coordination polyhedrons. b
The isothermal section of the phase diagram of the Nd–Ga–Si ternary system at 870 K is very similar to the previously investigated isothermal sections of the phase diagrams of the La–Ga–Si [1], Ce–Ga–Si [2] and Pr–Ga–Si [3] systems at the same temperature. The characteristic feature of the interaction of the components in these systems is the formation of substitutional solid solutions of different lengths based on the binary compounds, and of intermediate ternary phases with wide homogeneity ranges in the sections RGa2−x Six (R = La, Ce, Pr, Nd). The formation of ternary compounds with ␣-ThSi2 -type structure was established and structural transitions from hexagonal (RGa2 with AlB2 -type) to tetragonal (␣-ThSi2 -type) were observed in these systems. Recently, we determined the crystal structure of the ternary compound SmGa1.1 Si0.9 , which also crystallizes in the ␣-ThSi2 structure type and is in equilibrium with the solid solution of Si in the hexagonal AlB2 -type SmGa2+x binary phase [26]. The interaction of the components in the NdGa2−x Six system is more complicated: on increasing the Si content, the structural transitions AlB2 → α-ThSi2 → α-GdSi2 (hexagonal → tetragonal → orthorhombic) were observed. Similar transitions had previously been observed in the Nd–Al–Si [27–30] and Nd–Ga–Ge systems [31]. According to the classification of the structure types proposed by Kripyakevich [32], AlB2 , ␣-ThSi2 and ␣-GdSi2 -types are members of the same structure class (with a trigonal-prismatic coordination of the smallest atoms). The AlB2 structure is formed by trigonal prisms [Al6 ], which are oriented along [0 0 1] with B atoms inside. The ␣-ThSi2 structure type can also be constructed from trigonal prisms [Th6 ] with Si atoms inside. Contrary to the AlB2 type, the layers of these prisms are oriented perpendicularly to the [0 0 1] direction and each neighboring layer is turned by 90◦ with respect to the previous one. The structure type ␣-GdSi2 can be obtained from the ␣-ThSi2 type by orthorhombic deformation.
Acknowledgements The ICDD’s financial support during the preparation of this article is appreciated.
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[21] A. Raman, Trans. Ind. Inst. Met. 21 (1968) 5. [22] E.I. Gladyshevskii, P.I. Kripyakevich, Izv. Akad. Nauk SSSR Neorg. Mater. 1 (1965) 644. [23] R.W. Olesinski, N. Kanani, G.J. Abbaschian, Bull. Alloy Phase Diagrams 6 (1984) 362. [24] J. Rodriguez-Carvajal, in: Cong. Int. Union of Crystallography, Toulouse, Satellite Meeting on Powder Diffraction, 1990, p. 127. [25] L.G. Akselrud, P.Yu. Zavalii, Yu.N. Grin, V.K. Pecharsky, B. Baumgartner, E. Wolfel, Mater. Sci. Forum 133–136 (1993) 335. [26] Ya.O. Tokaychuk, A.O. Fedorchuk, I.R. Mokra, Visn. Lviv. Univ. Ser. Khim. 38 (1999) 31. [27] A. Raman, H. Steinfink, Inorg. Chem. 6 (1967) 1789. [28] T.I. Yanson, Ph.D. Thesis, Lviv University, Lviv, 1975. [29] Z. Long, Y. Zhou, Y. Zhuang, R. Chen, J. Liu, X. Wang, J. Alloys Compd. 325 (2001) 190. [30] N.Z. Semus’o, Ph.D. Thesis, Lviv Univ., Lviv, 2002. [31] I.M. Opainych, Yu.N. Grin, I.A. Gryniv, O.M. Sichevich, O.R. Myakush, A.A. Fedorchuk, A.V. Zelinsky, Red Book. Constitutional Data and Phase Diagrams of Metallic Systems, MSI GmbH, Stuttgart, 41, 1999, p. 1522. [32] P.I. Kripyakevich, Structure Types of Intermetallic Compounds, Nauka, Moscow, 1977 (in Russian).
Phase relations in the Nd–Ga–Si system at 870 K Ya.O. Tokaychuk a,b,∗ , A.O. Fedorchuk a , O.I. Bodak a , I.R. Mokra a a
Department of Inorganic Chemistry, Ivan Franko National University of L’viv, Kyryla i Mefodiya Str. 6, L’viv UA-79005, Ukraine b Laboratoire de Cristallographie, Université de Genève, Quai Ernest-Ansermet 24, Genève CH-1211, Switzerland
Abstract The isothermal section of the Nd–Ga–Si phase diagram at 870 K was constructed using X-ray phase analysis. Two ternary phases with a wide homogeneity ranges were found in the NdGa2−x Six section: ∼NdGa1.32−0.92 Si0.68−1.08 (structure type ␣-ThSi2 , space group I41 /amd, Pearson code tI12) and ∼NdGa0.86−0.68 Si1.14−1.32 (structure type ␣-GdSi2 , space group Imma, Pearson code oI12). The binary gallides NdGa2+x (structure type AlB2 ), NdGa (structure type CrB) and Nd9 Ga4 (structure type Sm9 Ga4 ) dissolve 15, 30 and 12 at.% Si, respectively, whereas the binary silicides NdSi1.8 (structure type ␣-GdSi2 ) and NdSi (structure type FeB) dissolve 6 and 7 at.% Ga, respectively. The solubility of the third component in other binary compounds does not exceed 5 at.%. © 2003 Elsevier B.V. All rights reserved. Keywords: Nd–Ga–Si; Phase diagram; Isothermal section; Intermetallic compounds; Crystal structure
1. Introduction An investigation of the Nd–Ga–Si ternary system is a part of a systematical study of the interaction of rare earth metals with gallium and silicon. Recently, we reported the isothermal sections of the La–Ga–Si [1], Ce–Ga–Si [2] and Pr–Ga–Si [3] systems at 870 K. The binary systems at the boundaries of the Nd–Ga–Si ternary system have been widely studied, including the phase diagrams over the whole concentration regions. The phase diagram of the Nd–Ga system was investigated by Kimmel et al. [4] (0–33.3 at.% Nd) and by Manory et al. [5] (33.3–100 at.% Nd). Including the Nd3 Ga2 [6] and Nd9 Ga4 [7] binary phases, which were found later, seven compounds exist in this system. Recently, Gur and Kimmel [8] investigated the pairwise substitution of Nd atoms by gallium in the Nd1−x Ga2+2x solid solution. They established the positional ordering of Ga2 pairs located in the basal planes of this AlB2 derivative type compound at the composition Nd1−x Ga2+2x (x = 0.18). Data on the Nd–Si system were evaluated by Gokhale et al. [9] and the existence of six binary phases was reported. Recently, some new binary compounds were found. Crystallographic data of the binary compounds re∗ Corresponding author. Tel.: +41-22-37-96372; fax: +41-22-37-96108. E-mail address: [email protected] (Ya.O. Tokaychuk).
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ported in the Nd–Ga and Nd–Si systems are summarized in Table 1. No binary compounds exist in the Ga–Si system. This system is characterized by an eutectic reaction at a temperature very close to the melting point of gallium [23]. This study was carried out to construct the isothermal section of the Nd–Ga–Si phase diagram at 870 K, to establish the formation of the solid solutions, to obtain ternary intermediate phases and determine their crystal structures.
2. Experimental One hundred and ten binary and ternary alloys were prepared by direct arc melting of the constituent metals (>99.9 wt.% pure) in a water-cooled copper hearth under a purified argon atmosphere with Ti as a getter. To ensure homogeneity, the samples were remelted twice. The ingots were wrapped in tantalum foil, annealed at 870 K in quartz ampoules under vacuum for 720 h and subsequently quenched in cold water. During the sample preparation the weight losses were <1% of the total mass, which was about 1 g for each sample. The phase analysis was carried out using X-ray powder diffraction—Debye–Scherrer technique (cameras RKD-57.3, non-filtered Cr K␣ radiation) and powder diffractometer (DRON-2, Fe K␣ radiation, germanium as an internal standard). The crystal structures of the ternary compounds were refined using the X-ray powder diffraction data obtained on DRON-4 and PHILIPS PW 1050/80
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65
Table 1 Crystallographic data of the binary compounds in the Nd–Ga and Nd–Si systems Compound
a
NdGa6 NdGa2 NdGa Nd3 Ga2 Nd5 Ga3 Nd9 Ga4 Nd3 Gaa ␣-NdSi1.8 (LT) -NdSi1.8 (HT)a NdSi1.5 Nd3 Si4 a NdSi Nd5 Si4 Nd5 Si4 a Nd5 Si3 Nd5 Si3 a a
Structure type
PuGa6 AlB2 CrB Gd3 Ga2 Cr5 B3 Sm9 Ga4 AuCu3 ␣-GdSi2 ␣-ThSi2 AlB2 Cr3 NiB6 FeB Zr5 Si4 Sm5 Ge4 Cr5 B3 Mn5 Si3
Space group
P4/nbm P6/mmm Cmcm I4/mcm I4/mcm I4/m ¯ Pm3m Imma I41 /amd P6/mmm Cmcm Pnma P41 21 2 Pnma I4/mcm P63/mcm
Pearson code
tP14 hP3 oS8 tI80 tI32 tI26 cP4 oI12 tI12 hP3 oS20 oP8 tP36 oP36 tI32 hP16
Cell parameter (Å)
Ref.
a
b
c
5.996 4.271 4.4164 11.915 7.881 12.001 5.43 4.133 4.142 3.940 4.362 8.12 7.869 7.779 7.694 8.66
– – 11.2758 – – – – 4.100 – – 24.584 3.91 – 14.67 – –
7.620 4.270 4.1835 15.34 14.395 5.121 – 13.790 13.65 4.258 3.916 5.88 14.8077 7.779 13.70 6.53
[4] [4] [10] [6] [11] [7] [12] [13–15] [13,16] [13,17] [18] [19] [20] [21] [21] [22]
Compound not observed at 870 K.
diffractometers (Cu K␣ radiation). Data were collected with a scan step of 0.02◦ and collecting times of 10–20 s in a 2θ range of 10–120◦ . All the procedures, including indexing, refinements of lattice and atomic parameters and calculations of interatomic distances, were performed with the FullProf [24] and CSD [25] program packages.
3. Results and discussion We have studied the boundary binary systems at 870 K with respect to the formation of compounds. The formation of five binary compounds was confirmed in the Nd–Ga system: NdGa2+x (AlB2 type), NdGa (CrB type), Nd3 Ga2 (Gd3 Ga2 type), Nd5 Ga3 (Cr5 B3 type) and Nd9 Ga4 (Sm9 Ga4 type). The Nd–Si binary system is also characterized by the formation of five binary silicides at 870 K: NdSi1.8 (␣-GdSi2 type) with a certain homogeneity range, NdSi1.5 (AlB2 type), NdSi (FeB type), Nd5 Si4 (Zr5 Si4 type) and Nd5 Si3 (Cr5 B3 type). The isothermal section of the phase diagram of the Nd–Ga–Si ternary system at 870 K is shown in Fig. 1. This system is characterized by the formation of a continuous solid solution between the isostructural binary compounds Nd5 Ga3 and Nd5 Si3 (structure type Cr5 B3 ) and limited solid solutions of the third component in the other binary compounds. Thus, the binary gallides NdGa2+x (structure type AlB2 ), NdGa (structure type CrB) and Nd9 Ga4 (structure type Sm9 Ga4 ) dissolve 15, 30 and 12 at.% Si, respectively, whereas the binary silicides NdSi1.8 (structure type ␣-GdSi2 ) and NdSi (structure type FeB) dissolve 6 and 7 at.% Ga, respectively. The extensions of the solid solutions based on NdGa2+x (along the line at 33.3 at.% Nd) and NdGa (along the line at 50 at.% Nd) were determined from the plots of the unit cell volume versus
silicon concentration (Fig. 2). The solubility of the third component in the other binary compounds does not exceed 5 at.%. During the investigation of the phase equilibria in the Nd–Ga–Si ternary system at 870 K, we did not observe the binary compound NdSi1.5 in the ternary alloys, although it is present in the binary system. Two ternary phases were found to exist in the 33.3 at.% Nd section of the Nd–Ga–Si system at 870 K. The first one ∼NdGa1.32−0.92 Si0.68−1.08 crystallizes in the tetragonal ␣-ThSi2 structure type (space group I41 /amd, Pearson code tI12) and is in equilibrium with the solid solution of Si in the hexagonal AlB2 -type NdGa2+x binary phase. At increasing Si concentration another phase forms, ∼NdGa0.86−0.68 Si1.14−1.32 with an orthorhombic
Fig. 1. Isothermal section of the phase equilibria diagram of the Nd–Ga–Si system at 870 K.
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Fig. 2. Unit cell volumes for the (a) NdGa2−x Six (x = 0–0.45) and (b) NdGa1−x Six (x = 0–0.6) solid solutions vs. silicon content.
␣-GdSi2 -type structure (space group Imma, Pearson code oI12), which is in equilibrium with the isostructural binary compound NdSi1.8 . Unfortunately, no two-phase region between ternary phases was found. Fig. 3 shows the experimental and calculated powder diffraction patterns of
three samples from the NdGa2−x Six section: a two-phase sample Nd33.3 Ga44.7 Si22 (a), which contains ␣-ThSi2 and AlB2 -type phases, and two single-phase samples Nd33.3 Ga30.7 Si36 (b) and Nd33.3 Ga26.7 Si40 (c), which crystallize in the ␣-ThSi2 - and ␣-GdSi2 -type, respectively.
Table 2 Crystallographic data of the NdGa2−x Six phase, crystallizing in a tetragonal ␣-ThSi2 -type structure (space group I41 /amd, Pearson code tI12) at various compositions (x) x 0.66a
0.81
0.90
0.96
1.08
Sample composition
Nd33.3 Ga44.7 Si22
Nd33.3 Ga39.7 Si27
Nd33.3 Ga36.7 Si30
Nd33.3 Ga34.7 Si32
Nd33.3 Ga30.7 Si36
Lattice parameters a (Å) c (Å) V (Å3 )
4.20329(7) 14.4146(3) 254.673(7)
4.19399(4) 14.3256(2) 251.982(9)
4.19308(4) 14.3105(2) 251.606(7)
4.19220(4) 14.2967(2) 251.259(9)
4.19292(5) 14.3102(2) 251.582(1)
0.4562(1)
0.4580(2)
0.4593(2)
0.4582(2)
0.4589(2)
0.0031(3) 0.0104(7) – –
0.0078(4) 0.0164(14) 0.0062(5) 0.0109(9)
0.0055(3) 0.0115(5) – –
0.0088(4) 0.0188(6) 0.0077(5) 0.0109(8)
0.0073(3) 0.0095(8) 0.0073(5) 0.0073(7)
0.019(2) 0.020(2) 0.017(2)
0.014(2) 0.010(2) 0.004(2)
Positional parametersb z(X)c parametersd
Displacement Uiso/eq (Nd) Uiso/eq (X) U11 (Nd) = U22 (Nd) U33 (Nd) U11 (X) U22 (X) U33 (X)
Interatomic distancese (Å) Nd–4X Nd–8X Nd–4Nd Nd–4Nd
(Å2 )
– – –
0.029(3) 0.013(3) 0.007(2)
– – –
3.1956(1) 3.2027(1) 4.1709(2) 4.2021(2)
3.181(2) 3.1952(5) 4.1502(2) 4.1941(3)
3.165(2) 3.2011(6) 4.1467(2) 4.1931(3)
3.175(2) 3.1939(7) 4.1435(2) 4.1921(2)
3.170(2) 3.1986(8) 4.1466(2) 4.1929(1)
X–1X X–2X X–2Nd X–4Nd
2.3904(1) 2.4259(1) 3.1956(1) 3.2027(1)
2.378(4) 2.418(2) 3.181(2) 3.1952(5)
2.398(2) 2.413(3) 3.165(2) 3.2011(6)
2.378(3) 2.413(2) 3.175(2) 3.1939(7)
2.401(3) 2.404(2) 3.170(2) 3.1986(8)
RI Rp
0.073 0.135
0.0654 0.1264
0.0572 0.1137
0.0659 0.1200
0.0483 0.1169
a b c d e
Two-phase sample, containing a hexagonal AlB2 -type phase. Nd (4a): 0 3/4 1/8, X (8e): 0 1/4 z. X: statistical mixture of Ga and Si atoms. U12 = U13 = U23 = 0 for all atoms. Distances between the atoms within the limits of the coordination polyhedrons.
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Fig. 3. Parts of the experimental (circles) and calculated (continuous lines) powder diffraction profiles for three alloys from the NdGa1−x Six section: (a) Nd33.3 Ga44.7 Si22 , two-phase sample, which contains tetragonal ␣-ThSi2 - and hexagonal AlB2 -type phases (reflections from the hexagonal phase are indicated by ∗); (b) Nd33.3 Ga30.7 Si36 , ␣-ThSi2 -type phase; (c) Nd33.3 Ga28.7 Si38 , orthorhombic ␣-GdSi2 -type phase. The reflection positions are indicated by vertical bars.
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The crystallographic data, values of the interatomic distances and the results of the Rietveld refinements of the ␣-ThSi2 - and ␣-GdSi2 -type ternary phases are listed in Tables 2 and 3, respectively. Table 3 Crystallographic data of the NdGa2−x Six phase, crystallizing in an orthorhombic ␣-GdSi2 -type structure (space group Imma, Pearson code oI12) at various compositions (x) x
Sample composition
1.14
1.21
1.29
Nd33.3 Ga28.7 Si38
Nd33.3 Ga26.4 Si40.3
Nd33.3 Ga23 Si43
4.2138(3) 4.2001(5) 14.100(1) 249.55(1)
4.20870(1) 4.20268(1) 14.0780(3) 249.01(2)
Lattice parameters a (Å) 4.21572(1) b (Å) 4.19796(1) c (Å) 14.1025(3) V (Å3 ) 249.58(2) Positional parametersa z(Nd) 0.3788(2) z(X1)b z(X2)b
0.9611(5) 0.7912(3)
Displacement parametersc (Å2 ) 0.0076(8) Uiso/eq (Nd) 0.015(4) Uiso/eq (X1) Uiso/eq (X1) 0.016(2) U11 (Nd) U22 (Nd) U33 (Nd) U11 (X1) U22 (X1) U33 (X1) U11 (X2) U22 (X2) U33 (X2)
0.0082(15) 0.0094(15) 0.0053(10) 0.009(7) 0.027(8) 0.010(6) 0.020(4) 0.019(5) 0.008(3)
Interatomic distancesd (Å) Nd–2X1 3.090(6) Nd–2X2 3.186(4) Nd–4X1 3.193(3) Nd–4X2 3.221(2)
0.38016(1)
0.3801(3)
0.9592(3) 0.7925(2)
0.9587(5) 0.7890(4)
0.0116(5) 0.019(2) 0.0110(6)
0.0078(7) 0.016(4) 0.015(3)
0.0153(9) 0.0102(8) 0.0093(6) 0.011(4) 0.032(4) 0.013(3) 0.018(3) 0.012(3) 0.003(2)
0.005(2) 0.011(2) 0.0076(7) 0.007(6) 0.023(7) 0.017(5) 0.019(5) 0.012(5) 0.014(4)
3.093(3) 3.176(2) 3.214(3) 3.221(1)
3.095(6) 3.173(3) 3.175(5) 3.238(3)
Nd–2Nd Nd–2Nd Nd–2Nd Nd–2Nd
4.012(4) 4.1980(1) 4.199(4) 4.2157(1)
3.978(2) 4.1996(1) 4.2139(1) 4.232(2)
3.977(5) 4.2027(1) 4.2087(1) 4.224(5)
X1–2X1 X1–1X2 X1–2Nd X1–4Nd
2.369(5) 2.396(9) 3.090(6) 3.193(3)
2.350(5) 2.394(3) 3.093(3) 3.176(2)
2.388(8) 2.402(5) 3.095(6) 3.173(3)
X2–1X1 X2–2X2 X2–2Nd X2–4Nd
2.396(9) 2.407(3) 3.186(4) 3.221(2)
2.350(5) 2.423(2) 3.214(3) 3.221(1)
2.374(3) 2.388(8) 3.175(5) 3.238(3)
RI Rp
0.0791 0.1284
0.0453 0.1131
0.0589 0.1357
a
Nd (4e): 0 1/4 z, X1 (4e): 0 1/4 z, X2 (4e): 0 1/4 z. X1 and X2: statistical mixtures of Ga and Si atoms. c U = U = U = 0 for all atoms. 12 13 23 d Distances between the atoms within the limits of the coordination polyhedrons. b
The isothermal section of the phase diagram of the Nd–Ga–Si ternary system at 870 K is very similar to the previously investigated isothermal sections of the phase diagrams of the La–Ga–Si [1], Ce–Ga–Si [2] and Pr–Ga–Si [3] systems at the same temperature. The characteristic feature of the interaction of the components in these systems is the formation of substitutional solid solutions of different lengths based on the binary compounds, and of intermediate ternary phases with wide homogeneity ranges in the sections RGa2−x Six (R = La, Ce, Pr, Nd). The formation of ternary compounds with ␣-ThSi2 -type structure was established and structural transitions from hexagonal (RGa2 with AlB2 -type) to tetragonal (␣-ThSi2 -type) were observed in these systems. Recently, we determined the crystal structure of the ternary compound SmGa1.1 Si0.9 , which also crystallizes in the ␣-ThSi2 structure type and is in equilibrium with the solid solution of Si in the hexagonal AlB2 -type SmGa2+x binary phase [26]. The interaction of the components in the NdGa2−x Six system is more complicated: on increasing the Si content, the structural transitions AlB2 → α-ThSi2 → α-GdSi2 (hexagonal → tetragonal → orthorhombic) were observed. Similar transitions had previously been observed in the Nd–Al–Si [27–30] and Nd–Ga–Ge systems [31]. According to the classification of the structure types proposed by Kripyakevich [32], AlB2 , ␣-ThSi2 and ␣-GdSi2 -types are members of the same structure class (with a trigonal-prismatic coordination of the smallest atoms). The AlB2 structure is formed by trigonal prisms [Al6 ], which are oriented along [0 0 1] with B atoms inside. The ␣-ThSi2 structure type can also be constructed from trigonal prisms [Th6 ] with Si atoms inside. Contrary to the AlB2 type, the layers of these prisms are oriented perpendicularly to the [0 0 1] direction and each neighboring layer is turned by 90◦ with respect to the previous one. The structure type ␣-GdSi2 can be obtained from the ␣-ThSi2 type by orthorhombic deformation.
Acknowledgements The ICDD’s financial support during the preparation of this article is appreciated.
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