The isothermal section at 600 ∘C of the ternary Pr–Au–Sn phase diagram

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

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The isothermal section at 600 ◦ C of the ternary Pr–Au–Sn phase diagram D. Mazzone a,b,∗ , R. Marazza a,b , P. Riani a,b , G. Zanicchi a,b , G. Cacciamani a,b , M.L. Fornasini c , P. Manfrinetti c,d a

Sezione di Chimica Inorganica, Dipartimento di Chimica e Chim. Industriale, Università di Genova, Via Dodecaneso 31, 16146 Genova, Italy

b

INSTM, Italy

c

Sezione di Chimica Fisica, Dipartimento di Chimica e Chim. Industriale, Università di Genova, Via Dodecaneso 31, 16146 Genova, Italy

d

LAMIA-CNR-INFM, Italy

article

info

Article history: Received 12 June 2008 Received in revised form 12 September 2008 Accepted 13 September 2008 Available online 18 October 2008 Dedicated to the memory of Professor Riccardo Ferro. We would like to sincerely thank and remember Prof. Riccardo Ferro who made this work possible. His irreplaceable expertise and sound advice will be greatly missed

a b s t r a c t The ternary Pr–Au–Sn isothermal section at 600 ◦ C has been investigated by X-ray diffraction, optical and scanning electron microscopy and electron probe microanalysis. The ten new ternary phases τ 1 PrAu2−x Snx , τ 2 Pr61 Au25 Sn14 , τ 3 PrAu6−x Snx , τ 4 Pr4 Au11 Sn5 , τ 5 PrAu2 Sn, τ 6 Pr30 Au40+x Sn30−x , τ 8 Pr5 AuSn3 , τ 9 Pr3 Au6 Sn5 , τ 10 Pr2 Au3 Sn4 , τ 11 Pr2 Au3 Sn6 have been identified and the ternary equiatomic τ7 PrAuSn compound confirmed. The structures of some of these phases have been investigated by powder diffraction methods, and the results have been reported. The τ 3 PrAu6−x Snx solid solution at x = 1.77 and the τ 9 Pr3 Au6 Sn5 ternary compound have been examined by single crystal method, resulting to be cubic ¯ and orthorhombic oP28, space group Pmmn, respectively. The tie-triangles cI208-38.2, space group Im3, of the ternary section have been determined and their trend has been discussed. The results obtained have been compared to the Ce–Au–Sn ternary section at 750 ◦ C. © 2008 Elsevier Ltd. All rights reserved.

Keywords: Rare-earth intermetallics Ternary alloy systems Phase identification Site occupancy X-ray diffraction

1. Introduction The Rx Ty Xz ternary compounds made by the rare earth metals R with the transition elements T and those X belonging to the 13 (B, Al, Ga, In, Tl) and 14 (C, Si, Ge, Sn, Pb) groups of the periodic system, show a large number of different stoichiometries and form a class of materials which are promising for their magnetic, electric and transport properties [1–8]. The influence of a third component, like a rare earth metal, on the properties of the compounds formed by copper, silver and gold with tin in a ternary system is of substantial interest and relevant to our investigations. In particular, the low melting point of the Au–Sn alloys in the Snrich side of the binary diagram makes some of them useful as leadfree soldering systems and makes the ternary systems involving

Au–Sn worthy of investigation. The systems already investigated by our research group were the R–Cu–Sn phase diagrams using Ce, Pr and Nd [9–11] as light, and Yb [12] as heavy rare earths. Similarly, the R–Ag–Sn systems formed with Ce, Pr and Yb [13– 15] have been determined. As regards the R–Au–Sn systems, the coexistence and relationships among the different compounds existing in the Ce–Au–Sn isothermal section at 750 ◦ C have already been studied [16]. The compounds existing in the Pr–Au–Sn ternary system, together with the isothermal section at 600 ◦ C, are here presented and discussed. 2. Literature data 2.1. Binary systems

∗

Corresponding address: Dipartimento di Chimica e Chim. Industriale, Università di Genova, Via Dodecaneso 31, 16146 Genova, Italy. Tel.: +39 010 3536151; fax: +39 010 3625051. E-mail address: [email protected] (D. Mazzone). 0364-5916/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2008.09.017

The crystal data of the unary and binary phases pertaining to the three binary boundary systems are reported in Table 1.

32

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

Table 1 Crystallographic data for the unary and binary boundary phases in the system Pr–Au–Sn. Element or phase

Structure type

Pearson symbol

Space group

Unit cell dimension (in pm) a

Au β Pr α Pr β Sn α Sn (Au, Sn) 0–6.6 at.% Sn β or Au10 Sn (8.2–9.1 at.% Sn)

ζ

(12.7–16.3 at.% Sn) ζ ’ or Au5 Sn (16.7 at.% Sn) δ or AuSn (50–50.5 at.% Sn) ε or AuSn2 (66.7 at.% Sn) η or AuSn4 (80.0 at.% Sn) PrSn3 Pr2 Sn5 Pr3 Sn7 PrSn2 β Pr3 Sn5 (H.T. form) α Pr3 Sn5 Pr2 Sn3 PrSn PrSn0.98 Pr11 Sn10 Pr5 Sn4 β Pr5 Sn3 (H.T. form) α Pr5 Sn3 Pr3 Sn PrAu6 Pr14 Au51 (21.5–∼25 at.% Pr) Pr17 Au36 Pr17 Au36 β PrAu2 (H.T. form) α PrAu2 Pr3 Au4 γ PrAu β PrAu α PrAu Pr2 Au

b

References c

Cu W α La β Sn Cdia Cu

cF 4 cI2 hP4 tI4 cF 8 cF 4

¯ Fm3m ¯ Im3m P63 /mmc I41 /amd ¯ Fd3m ¯ Fm3m

407.84 413 367.2 583.1 648.9 407.8–410.5

1183.3 318.1

[20] [20] [20] [19] [19] [19]

Ni3 Ti

hP16

P63 /mmc

290.4

953.6

[19]

Mg

hP2

P63 /mmc

290.8–293.68

478.6–476.9

[19]

Au5 Sn

hR6

R3

292.0

477

[19]

NiAs

hP4

P63 /mmc

432.18

552.30

[19]

AuSn2

oP24

Pbca

691.0

703.7

1178.9

[19]

PtSn4

oC 20

Aba2

650.2

654.3

1170.5

[19]

AuCu3 Ce2 Sn5 Ce3 Sn7 NdSn2

cP4 oC 28 oC 20 oC 12 Unknown oC 32 aP20

¯ Pm3m Cmmm Cmmm Cmmm

471.59 458.48 451.08 448.20

3517.84 2582.35 1589.73

463.38 460.37 459.01

Cmcm P 1¯

1018 604.5 α = 107.33◦

821 845.2 β = 96.76◦

1054 1114.0 γ = 99.99◦

Cmmm

1733.5

1739.0

1174.0

1594

842.9 677.9 614.6

774.5

907.6 β = 100.3◦ 930.5–924.9

Pu3 Pd5 Nd2 Sn3

Unknown

Sm5 Ge4 Mn5 Si3 W5 Si3 AuCu3 PrAu6

Unknown oP36 hP16 tI32 cP4 mC 28

Pnma P63 /mcm I4/mcm ¯ Pm3m C 2/c

827.0 928.1 1251.2 498 776.5

Gd14 Ag51

hP65

P6/m

1277–1270

Nd17 Au36 Nd17 Au36 NdAu2 CeCu2 Pu3 Pd4 CsCl CrB FeB CoSi2

tP106 tP106 tP108 oI12 hR14 cP2 oC 8 oP8 oP12

P4/nmm P4/nmm P4/nmm Imma R3 ¯ Pm3m Cmcm Pnma Pnma

1567.6 1595.5 1600 467.2 1383.7 368.0 387.0 738.0 724.1

704.0

1110 463.0 504.6

914.1 934.8 936.0 817.8 621.3 472.0 590.0 928.7

[1] [29] [29] [29] [27] [27] [30] [27] [31] [28] [1] [1] [1] [27] [24] [22] [24] This work [22] [22] [24] [22] [22] [22] [22]

2.1.1. Au–Sn The Au–Sn binary system has been adopted from Okamoto [17]. This evaluation updates the diagram reported by Okamoto and Massalski [18], mainly based on the assessment previously made by the same authors [19].

and Pr17 Au36 phases were identified and their crystal structure determined. Lastly, the thermodynamic critical assessment of the system, made by means of the CALPHAD method, has been reported by Du et al. in [25].

2.1.2. Pr–Au The Pr–Au binary system was evaluated by Gschneidner et al. [20] mainly on the basis of the experimental diagram investigated by Griffin and Gschneidner [21] in the Pr-rich region and McMasters et al. [22] who determined the structure of many compounds. The five compounds PrAu6 , Pr14 Au51 , PrAu2 , PrAu and Pr2 Au were reported with the crystal structure and lattice parameter data. The standard enthalpies of formation of the Pr14 Au51 , PrAu2 and PrAu intermetallic compounds have been experimentally determined by Fitzner and Kleppa [23]. The Pr–Au diagram was re-examined in the whole composition range by Saccone et al. [24] on the basis of differential thermal analysis (DTA), X-ray diffraction and electron probe microanalysis (EPMA) studies. All the previous compounds and the new Pr3 Au4

2.1.3. Pr–Sn The R–Sn binary systems generally present a high number of intermetallic compounds, often generated by peritectic reactions, and their definition has always been very complex owing to the high oxidizability of the alloys in large ranges of their composition. For this reason some of these diagrams have not been completely defined yet. The Pr–Sn phase diagram was reported by Massalski [26], mainly based on the preliminary version of Eremenko et al. [27]. In this version only the eight Pr3 Sn, α -Pr5 Sn3 , β -Pr5 Sn3 , Pr5 Sn4 , PrSn, α -Pr3 Sn5 , β -Pr3 Sn5 and PrSn3 phases were reported. Subsequently the PrSn2 , Pr3 Sn7 and Pr2 Sn5 compounds have been reported by several authors [1,28, 29], and the existence of the Pr11 Sn10 compound, initially reported by Komarovskaya et al. [28], still has to be fully confirmed. These data have been compared and reported in [10]. The new

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

33

Table 2 Ternary phases and crystal structure data. Phase

Composition (at.%) Pr

Sn

33.3

12–15

61 14

14 18–28

PrAu4.30 Sn1.77

14.1

25.1

τ 4 Pr4 Au11 Sn5

20

25

τ 5 PrAu2 Sn τ 6 Pr30 Au40+x Sn30−x 0
25 29

25 26–29

33.3

33.3

τ 8 Pr5 AuSn3

55.5

33.3

τ 9 Pr3 Au6 Sn5

21

36

τ 10 Pr2 Au3 Sn4 τ 11 Pr2 Au3 Sn6

22.2 18.2

44.4 54.5

τ 1 PrAu2−x Snx 0.36 < x < 0.45 τ 2 Pr61 Au25 Sn14 τ 3 PrAu6−x Snx 1.26 < x < 1.96

Pearson symbol, Space group, Structure type

Lattice parameters (pm)

hP3, P6/mmm AlB2 type Unknown cI208-38.2, Im 3¯ YCd6 type

a = 472.6(1)–472.57(3) c = 356.8(1)–359.95(5)

Powder diffraction data

a = 1515.8(8)–1515.1(4)

Powder diffraction data

a = 1515.5(5)

Single crystal and powder diffraction data Powder diffraction data

This work

Hexagonal Unknown type Unknown Unknown

a = 951.1(2) c = 957.7(2)

hP6, P63 mc, LiGaGe type hP18, P63 /mcm, Hf5 CuSn3 type oP28, Pmmn, Ce3 Pd6 Sb5 type

a = 471.07(6) c = 764.26(9) a = 945.8(1) c = 677.9(2) a = 455.6(1) b = 1354.8(5) c = 1020.8

Unknown tI22, I4mm, Nd2 Cu3 Sn6 type

compounds with the formula Pr2 Sn3 and PrSn0.98 have been identified by Fornasini et al. in [30] and [31]. Therefore, owing to the presence of these new compounds, the study of the phase equilibria among the compounds existing in the region of the phase diagram around the equiatomic composition is not completely defined. 2.2. Ternary R–Au–Sn systems and compounds As regards the ternary systems of the rare earth metals with Au and Sn, the Ce–Au–Sn isothermal section at 750 ◦ C is the only one completely investigated by means of X-ray diffraction, light optical microscopy (LOM), scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) [16]. Despite the high temperature, for which the gold-tin side is mainly in the liquid state as well as the Ce-rich corner of the Ce–Au system, seven ternary compounds have been identified, some of them with appreciable solubility ranges, and magnetic measurements have been performed. Recently the formation of a new stable quasicrystal approximant has been reported for the Ce15 Au65 Sn20 composition [32]. The R–Au–Sn ternary compounds presenting equiatomic composition are the most widely studied. The originally attributed CaIn2 structure type [33] has been substituted by ordered variants as LiGaGe or NdPtSb type, accepted by several authors for La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, [34–38]. Moreover the MgAgAs structural type was reported for dimorphic Ho [33,35], and the same structural type was determined for Er [39], Tm [37] and Lu [40] on the basis of structural refinements. YbAuSn, previously reported as oP12, Pnma, TiNiSi type [41], has been more recently reported as a superstructure of the KHg2 (CeCu2 ) type [42]. Another superstructure of the same basic type, now with quintupled b-axis, had already been found for EuAuSn [43]. Several compounds have also been studied for their interesting magnetic and transport properties [41,44–47], while electronic structures have been investigated for Pr and Nd [48,49], and for Ce,Gd, Er and Lu [38]. A new stannide having the Eu2 Au2 Sn5 stoichiometry has been obtained by Kussmann et al. [50] and its structure has been reported as an ordered defect variant of the BaAl4 type. No other R–Au–Sn ternary diagrams or compounds have so far been investigated.

Notes

Ref.

Literature

a = 471 c = 764

a = 456.9(2) c = 2589(1)

Powder diffraction data

[33]

Powder diffraction data Single crystal and powder diffraction data

Powder diffraction data

3. Experimental details The samples were prepared by different techniques. The Pr-rich compounds were prepared by melting the weighed metals, sealed under argon atmosphere in Ta crucibles, in an induction furnace. The reactive samples, protected by tantalum, could be easily and rapidly quenched in cold water. Then they were annealed for three weeks at 600 ◦ C in quartz ampoules under argon atmosphere and then quenched in water again. The alloys obtained with this method could reach equilibrium in optimum conditions. Due to the reactivity of gold with the Ta crucibles, the richest gold alloys (more than 50 at.% Au) have been prepared by arc melting stoichiometric amounts of the constituent metals under pure argon atmosphere, at the presence of a Zr getter. The samples were remelted a few times to ensure a complete homogeneity and, after solidification, the weight loss of the ingots was less than 0.5 wt%. Since the cooling rate was lower, the thermal treatment of these samples needed to be prolonged to reach the equilibrium state. The used metals were obtained by ingots supplied by Newmet Koch Ltd, having a purity of a 99.999 mass% for gold and tin and 99.9 mass% for praseodymium. All the samples have been examined by X-ray diffraction analysis, light optical microscopy (LOM), scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). X-ray analysis was carried out on most of the samples with a vertical powder diffractometer (Kα Cu radiation), or with a Guinier–Stoe powder camera, adding silicon as internal standard. In both cases the powder patterns were indexed using the LAZY PULVERIX program [51], and a least squares refinement method was adopted to optimize the values of the lattice parameters. The structures of Pr3 Au6 Sn5 and PrAu4.30 Sn1.77 were determined from single crystals picked out in homogeneous samples with Pr21 Au44 Sn35 and Pr14 Au60 Sn26 composition, respectively, and checked by Laue method. Intensities were collected at 294 K on a Bruker–Nonius MACH3 diffractometer with graphite monochromatized Mo Kα radiation. Lattice parameters obtained from Guinier patterns are reported in Table 2. The structure of Pr3 Au6 Sn5 was solved by SIR97 [52], while a starting model was used for PrAu4.30 Sn1.77 . Both refinements were done with SHELXL-97 [53], applying anisotropic displacement parameters, and all atomic coordinates were standardized by STRUCTURETIDY [54]. Crystal data for both compounds are given in Table 3.

34

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

Table 3 Crystal structure data for Pr3 Au6 Sn5 and PrAu4.30 Sn1.77 .

Space group, Z Crystal size (mm3 ) Scan mode hkl range µ(Mo Kα) (mm−1 ) Absorption correction Refl. measured Refl. unique Rint Refl. with Fo > 4σ (Fo ) Refined parameters wR(F 2 ) (all reflexions) R(F ) [Fo > 4σ (Fo )] GoF (F 2 ) Extinction coefficient x 1ρmin , 1ρmax (e × 10−6 pm−3 ) Formula after refinement

Pr3 Au6 Sn5

PrAu4.30 Sn1.77

Pmmn (No. 59), 2 0.03 × 0.06 × 0.12 ω − 2θ +6, ±19, ±14 90.5 ψ -scan over 5 refl. 4058 1056 0.114 655 48 0.115 0.047 0.859 0.00129(12) −4.2, 5.1

¯ Im3(No. 204), 24 0.03 × 0.11 × 0.13

ω−θ +19, +19, +19

123.9 Analytical 2317 739 0.125 359 54 0.106 0.049 0.767 0.00006(1) −4.9, 4.1 PrAu4.30(6) Sn1.77(6)

Further details of the crystal structure investigation may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein–Leopoldshafen, Germany, fax: +49 7247 808 666; e-mail: [email protected], on quoting the deposition numbers CSD-419491 (Pr3 Au6 Sn5 ), CSD-419492 (PrAu4.30 Sn1.77 ). Optical and electronic investigations were carried out on all the samples to check their appearance and phase composition. The scanning electron microscope (Zeiss EVO 40) was equipped with an energy dispersive Si(Li) detector and a microanalysis ‘‘INCA energy’’ ZAF system (Oxford Instruments) to process the X-ray data. For obtaining the quantitative analyses the spectra were collected at a beam energy of 20 keV and a counting time of 50 s, after a calibration made with pure Co in the same operative conditions. Only the homogeneous unetched phases identified by a solid state back scattered electrons (BSE) detector have been considered.

Fig. 1. Pr–Au–Sn system: isothermal section at 600 ◦ C.

4. Results and discussion 4.1. Pr–Au–Sn isothermal section at 600 ◦ C Selected data obtained from the examination of about a hundred samples are summarized in Table 4, which reports the composition of the identified phases and, when possible, their crystal structure and lattice parameters. The isothermal section obtained on the basis of these data is shown in Fig. 1, and the following comments can be made. The isothermal section lying near the Au–Sn side is not defined, because a sizeable portion of the binary system is molten at the selected temperature. It is therefore impossible to obtain an unambiguous definition of the equilibria among the binary and ternary compounds in this side. Only the solid solution (Au, Sn) is at the solid state up to 6 at.% Sn. The liquid domain boundary is marked by a dotted and dashed line. The remaining part of the ternary section is fully solid, and that allowed us to determine the equilibria among the ternary Pr–Au–Sn and binary Pr–Au and Pr–Sn compounds. 4.2. Binary boundary Pr–Au and Pr–Sn compounds All the phases reported for the binary boundary Pr–Au system have been detected and confirmed. The compounds formed in the Au-rich side show extended solubility fields in the ternary system, owing to the capability of Sn to replace Au in many structures. In particular the composition of PrAu6 (mC28, C2/c, PrAu6 -type) is extended in the range PrAu6−x Snx with 0 < x < 0.7, that of Pr14 Au51 (hP65, P6/m, Gd14 Ag51 type) in the range Pr14 Au51−x Snx ¯ Pu3 Pd4 type) in with 0 < x < 8.45 and that of Pr3 Au4 (hR14, R3,

Fig. 2. Alloy N. 43, BSE image at 1280 X: grey crystals of Pr17 Au36−x Snx (x = 2.12) + binary eutectic with white Pr14 Au51−x Snx (x = 4.55).

the range Pr3 Au4−x Snx with 0 < x < 0.56. The PrAu2 dissolves only five at.% Sn and for PrAu no solubility ranges have been detected. The Pr17 Au36 compound, which was reported as a high temperature phase, has been found at the temperature of the ternary section with a lower Pr content and a capability to dissolve up to 4–5 at.% Sn, like PrAu2 . The appearance of one of the samples in which the compound was observed is reported in Fig. 2 and the cell dimensions in Tables 1 and 4. The Pr2 Au compound does not show any appreciable solid solution. In a similar way, Au can replace Sn in some Pr–Sn binary compounds, thereby forming significant solid solutions. Up to 8 at.% of Sn are replaced by Au in PrSn3−x Aux (0 < x < 0.32), and up to 5 at.% in Pr3 Sn5−x Aux (0 < x < 0.4). Furthermore a wide solubility range has been observed for the compound having the formula PrSn0.98 [31]. The existence of this compound has been confirmed and up to 10 at.% of Au were measured by EPMA, giving a general formula PrSn0.98−x Aux (0 < x < 0.2). The PrSn compound, which lies at a very near composition, only dissolves 5 at.% Sn. Among the compounds present in the Pr-rich side of the Pr–Sn diagram, the Pr5 Sn3 binary compound can change its composition by adding gold atoms. Two alloys, examined by EPMA, showed the gold content increasing up to 5 at.% Au in the binary phase. The other binary Pr–Sn compounds (Pr2 Sn5 , Pr3 Sn7 , PrSn2 , Pr2 Sn3 , Pr5 Sn4 , Pr3 Sn) showed a very small capability to dissolve Au atoms. Moreover the compound Pr11 Sn10 was not observed in

7.0

8.0 10.0

11.0 13.0

13.0

14.0

14.0

14.0

14.0 14.0

14.5

17.0

17.5

19.0

19.0

19.5

20.0

20.0

20.0

20.0

20.0

20.0

20.0

2 3

4 5

6

7

8

9

10 11

12

13

14

15

16

17

18

19

20

21

22

23

24

37.0

31.0

31.0

26.0

24.0

19.0

10.0

15.0

56.0

15.0

8.0

13.5

21.5

58.0 68.0

26.0

15.0

6.0

29.0

45.0 26.0

73.0 9.0

5.0

21.0

21.0

21.0

20.0

20.0

20.0

21.0

21.0

18.0

21.0

14.0

14.0

14.0

18.0 18.0

14.0

14.0

14.0

14.0

21.0 14.5

18.0 14.0

0.0

36.0

35.5

36.0

25.0

24.5

24.0

8.0

13.0

55.0

13.0

10.0

18.0

21.5

54.5 56.0

25.5

18.0

5.0

28.0

36.0 26.0

55.0 10.0

3.0

14.0

τ 4 Pr4 Au11 Sn5

a = 455.6(1) b = 1354.8(5) c = 1020.8(3)

20.0

τ 9 Pr3 Au6 Sn5 τ 9 Pr3 Au6 Sn5

20.0

τ 9 Pr3 Au6 Sn5

a = 951.1(2) c = 957.7(2)

14.0

14.0

14.0

22.0

14.0

τ 4 Pr4 Au11 Sn5

= 1287.5(4) = 936.8(3) = 456.9(2) = 2589(1)

21.0

21.0

25.0

14.0

21.0

a c a c

a = 1515.4(4)

a = 1515.5(5)

a = 1515.8(8)

a = 1515.1(4)

a = 1515.2(1)

0.0

13.5

Pr14 Au51−x Snx x = 8.45 Pr14 Au51−x Snx x = 5.20 τ 4 Pr4 Au11 Sn5

PrAu6−x Snx x = 0.7 Pr14 Au51−x Snx x = 8.45 τ 11 Pr2 Au3 Sn6

τ 3 PrAu6−x Snx x = 1.50 τ 3 PrAu6−x Snx x = 1.26

Au1−x Snx x = 0.03 τ 11 Pr2 Au3 Sn6 PrAu6−x Snx x = 0.70 τ 9 Pr3 Au6 Sn5 τ 3 PrAu6−x Snx x = 1.82 τ 3 PrAu6−x Snx x = 1.96 PrAu6−x Snx x = 0.35 τ 3 PrAu6−x Snx x = 1.26 τ 3 PrAu6−x Snx x = 1.78 τ 11 Pr2 Au3 Sn6 τ 11 Pr2 Au3 Sn6

24.5

25.0

28.0

26.0

13.5

20.0

23.0

46.0

22.0

5.0

6.0

66.0

10.0

7.0

6.5

Sn

Pr

Unit cell

IInd phase

Sn

Ist phase

Pr

Pr

Sn

Phases observed in the alloys, reported in the order of their amount Composition from EPMA (at.%) and lattice parameters (pm)

Nominal alloy composition (at.%)

1

Code N◦

Table 4 Pr–Au–Sn system — Results obtained from selected alloys annealed at 600 ◦ C.

τ 4 Pr4 Au11 Sn5

Pr14 Au51−x Snx x = 8.78 τ 3 PrAu6−x Snx x = 1.82 τ 3 PrAu6−x Snx x = 1.96 τ 4 Pr4 Au11 Sn5

τ 3 PrAu6−x Snx x = 1.61 τ 3 PrAu6−x Snx x = 1.40

Pr14 Au51−x Snx x = 3.90 Pr14 Au51−x Snx x = 3.25 τ 3 PrAu6−x Snx x = 1.54 τ 10 Pr2 Au3 Sn4

Liquid phase PrSn3−x Aux x = 0.36

PrAu6−x Snx x = 0.70

Liquid phase

PrAu6−x Snx x = 0.45 Liquid phase Au1−x Snx x = 0.07 Liquid phase Liquid phase

1514.5(5)

a = 1515.0(3)

Unit cell

14.0

14.0

14.0

25.0

28.0

28.0

23.0

67.0

Sn

IIIrd phase Pr

τ 3 PrAu6−x Snx x = 1.96 τ 3 PrAu6−x Snx x = 1.96

τ 3 PrAu6−x Snx x = 1.61

PrSn3−x Aux x = 0.32

Liquid phase

Liquid phase

See Fig. 4

Note

(continued on next page)

Unit cell

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43 35

20.0 20.0

21.0 22.0 22.0 23.0

24.0

24.0

24.0

24.0

24.5

25.0

25.0

25.0

25.0 26.0

26.0

28.0

28.0

28.0

29.0

29.0

29.0

29.0 31.0

27 28 29 30

31

32

33

34

35

36

37

38

39 40

41

42

43

44

45

46

47

48 49

66.0 22.0

53.0

28.0

8.0

12.0

6.0

0.0

31.0

41.0 8.0

35.0

27.0

20.0

23.0

72.0

53.0

31.0

11.0

47.0 27.0 44.0 35.0

40.0 71.0

28.5 29.0

32.5

29.0

33.0

33.5

31.0

31.5

28.0

22.0 22.0

21.0

25.0

21.0

25.0

25.0

22.0

21.0

22.0

22.0 21.0 22.0 21.0

21.0 25.0

71.5 26.0

34.0

28.0

13.0

14.0

4.0

0.0

28.0

45.0 7.0

36.0

25.0

12.5

25.0

71.0

44.0

36.0

11.0

44.0 24.0 44.5 35.5

38.0 67.0

Pr2 Sn5 τ 6 Pr30 Au40+x Sn30−x x=4

Pr17 Au36−x Snx x = 2.12 τ 1 PrAu2−x Snx x = 0.42 τ 1 PrAu2−x Snx x = 0.39 τ 6 Pr30 Au40+x Sn30−x x=2 τ 7 PrAuSn

= 1595.5(3) = 934.8(3) = 1596.7(3) = 936.6(2)

a = 476.76(4) c = 3596.5(6)

a c a c

33.0 33.0

25.0

25.5

22.0

23.0

22.0

22.0

21.0

33.0 33.0

33.0

τ 9 Pr3 Au6 Sn5 τ 10 Pr2 Au3 Sn4 Pr14 Au51−x Snx x = 4.55 τ 6 Pr30 Au40+x Sn30−x x=2 Pr17 Au36

21.0

30

21.0

Pr14 Au51−x Snx x = 8.12 τ 5 PrAu2 Sn

PrSn3−x Aux x = 0.16 τ 5 PrAu2 Sn

24.5

τ 10 Pr2 Au3 Sn4

34.0 16.0

67.0

25.0

6.0

10.0

7.0

0.0

36.0

34.0 12.0

33.5

36.0

27

13.0

67.0

25.0

27.0

33.5

33.0 30.0

55.0 25.0

54.0 55.0

18.0 25.0

18.0 18.0

25.0

a = 1286.4(2) c = 936.6(2)

a = 468.6(2)

Pr14 Au51−x Snx x = 7.15 τ 9 Pr3 Au6 Sn5

τ 9 Pr3 Au6 Sn5 PrSn3−x Aux x = 0.32 τ 10 Pr2 Au3 Sn4 τ 4 Pr4 Au11 Sn5 τ 10 Pr2 Au3 Sn4 τ 9 Pr3 Au6 Sn5

Sn

Pr

Unit cell

IInd phase

Sn

Ist phase

Pr

Pr

Sn

Phases observed in the alloys, reported in the order of their amount Composition from EPMA (at.%) and lattice parameters (pm)

Nominal alloy composition (at.%)

25 26

Code N◦

Table 4 (continued)

PrSn3−x Aux x = 0.32 τ 7 PrAuSn τ 1 PrAu2−x Snx x = 0.48

Pr14 Au51−x Snx x = 4.55 Pr14 Au51−x Snx x = 6.50 Pr14 Au51−x Snx x = 3.9 τ 5 PrAu2 Sn

Pr14 Au51

τ 7 PrAuSn τ 1 PrAu2−x Snx x = 0.36 τ 9 Pr3 Au6 Sn5

τ 7 PrAuSn

Pr14 Au51−x Snx x = 8.45 τ 6 Pr30 Au40+x Sn30−x x=3 τ 9 Pr3 Au6 Sn5

PrSn3−x Aux x = 0.34 Liquid phase

a c a c

= 1276.5(2) = 929.3(1) = 1283.4(2) = 931.5(2)

a = 471.2(1) c = 764.3(2)

33.0

28.0

31.0

21.0

28.0

33.0

28.0

τ 6 Pr30 Au40+x Sn30−x x=3 τ 5 PrAu2 Sn

32.5

71.0

4.0

36.0

28.0

34.0

28.0

τ 7 PrAuSn

Pr2 Sn5

Pr17 Au36−x Snx x = 2.12

τ 9 Pr3 Au6 Sn5

τ 6 Pr30 Au40+x Sn30−x x=2

τ 6 Pr30 Au40+x Sn30−x x=2 τ 7 PrAuSn

τ 6 Pr30 Au40+x Sn30−x x=0

30.0

τ 7 PrAuSn 30.0

τ 9 Pr3 Au6 Sn5 τ 9 Pr3 Au6 Sn5

21.5 21.0

τ 11 Pr2 Au3 Sn6 τ 5 PrAu2 Sn 37.0 36.0

Liquid phase

Sn

IIIrd phase Pr

τ 11 Pr2 Au3 Sn6 τ 11 Pr2 Au3 Sn6

Unit cell

Unit cell

DTA

See Fig. 2

Note

36 D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

31.0

32.0

32.0

32.5

33.0

33.5

34.0

34.0

34.0

34.0

35.0

35.0

35.0

35.0 38.0

39.0

40.0

42.0

43.0

44.0

45.0

46.0

48.0

49.0

51

52

53

54

55

56

57

58

59

60

61

62

63 64

65

66

67

68

69

70

71

72

73

46.0

38.0

15.0

5.0

51.0

32.0

43.0

55.0

51.0

63.0 17.0

21.0

10.0

4.0

61.0

26.0

16.0

15.0

53.0

34.0

8.0

30.0

24.0

31.0

50.0

51.0

43.0

43.0

37.0

51.0

33.0

37.0

38.0

33.0 43.0

33.5

33.0

33.0

37.0

33.0

33.0

33.0

37.0

33.0

33.0

33.0

29.0

30.0

47.0

41.0

8.0

4.0

58.0

40.0

34.0

58.0

57.0

67.0 4.0

22.5

12.0

5.0

59.0

33.0

15.0

14.0

58.0

34.0

12.0

33.0

26.0

30.0

a = 471.20(6) c = 763.8(2)

τ 7 PrAuSn

PrSn0.98−x Aux x = 0.18 Pr3 Sn5−x Aux x = 0.4 Pr3 Au4−x Snx x = 0.28 Pr3 Au4−x Snx x = 0.56 PrSn0.98−x Aux x = 0.16 PrSn

a = 472.6(1) c = 356.8(1)

c = 359.95(5)

x = 0.45

Pr3 Sn5−x Aux x = 0.32 PrAu2−x Snx x = 0.15 τ 1 PrAu2−x Snx x = 0.36 τ 1 PrAu2−x Snx x = 0.67 PrSn2 Pr3 Au4−x Snx x = 0.28 Pr3 Sn5−x Aux x = 0.4 Pr3 Sn5−x Aux x = 0.4 τ 7 PrAuSn

a = 472.57(3)

a = 471.07(6) c = 764.26(9)

Pr3 Sn5−x Aux x = 0.4 τ 1 PrAu2−x Snx x = 0.42 τ 1 PrAu2−x Snx

τ 1 PrAu2−x Snx x = 0.36 τ 7 PrAuSn

τ 6 Pr30 Au40+x Sn30−x x=2 τ 6 Pr30 Au40+x Sn30−x x=4 τ 7 PrAuSn

51.0

33.0

50.0

49.5

50.0

33.0

48.0

48.0

48.0

37.0 33.5

43.0

42.0

42.0

30.0

33.0

33.0

42.5

33.0

22.0

30.0

29.0

33.0

32.5

46.0

34.0

38.0

1.5

47.0

33.0

48.0

50.0

48.0

61.0 32.0

5.0

0.0

0.0

70.0

14.0

32.5

3.0

35.0

44.0

3.0

26.0

15.0

33.0

Sn

Pr

Unit cell

IInd phase

Sn

Ist phase

Pr

Pr

Sn

Phases observed in the alloys, reported in the order of their amount Composition from EPMA (at.%) and lattice parameters (pm)

Nominal alloy composition (at.%)

50

Code N◦

Table 4 (continued)

PrSn0.98−x Aux x = 0.02

PrSn0.98−x Aux x = 0.22 τ 7 PrAuSn

PrAu

PrSn

34.5

33.0

43.0

τ 7 PrAuSn

33.5

33.0

33.0

33.0

42.0

43.0

38.0

a = 362.9(3)

a = 1381(1) c = 613.1(4)

a = 473.6(3) c = 357.6(8)

c = 764.4(2)

a = 471.0(1)

33.0

30.0

33.0

34.5

35.0

8.0

57.0

35.0

34.0

32.0

35.0

4.0

4.0

32.0

70.0

32.5

Sn

IIIrd phase Pr

PrSn

PrSn

PrSn

Pr3 Au4−x Snx x = 0.35 Pr3 Sn5 τ 7 PrAuSn

Pr3 Au4

Pr3 Au4

Pr3 Sn7

τ 1 PrAu2−x Snx x = 0.42

Pr3 Au4−x Snx x = 0.21 τ 7 PrAuSn

τ 7 PrAuSn

Pr17 Au36−x Snx x = 1.60 τ 10 Pr2 Au3 Sn4

τ 1 PrAu2−x Snx x = 0.45 τ 6 Pr30 Au40+x Sn30−x x=4

τ 7 PrAuSn

Unit cell

τ 7 PrAuSn

Pr3 Sn5−x Aux x = 0.4 Pr3 Au4−x Snx x = 0.56 τ 7 PrAuSn

τ 7 PrAuSn

τ 7 PrAuSn

τ 7 PrAuSn

Pr3 Au4−x Snx x = 0.28 τ 7 PrAuSn

x = 0.28

Pr3 Au4−x Snx

τ 7 PrAuSn

Pr3 Sn7

τ 7 PrAuSn

See Fig. 9

Oxidizable

as cast

See Fig. 3

See Fig. 5

Note

(continued on next page)

a= 1379.1(2) c= 614.9(1)

Unit cell

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43 37

52.0

52.0

54.0

55.0

56.0

57.0 58.0

59.0

60.0 60.0 60.5 61.0

62.0 65.0 69.5 73.0

75

76

77

78

79 80

81

82 83 84 85

86 87 88 89

11.0 15.0 30.5 10.0

14.0 26.0 5.5 36.5

36.0

17.0 38.0

32.0

35.0

41.0

40.0

25.0

62.0 61.0 74.0 33.5

61.0 62.0 61.0 61.0

59.0

62.0 58.0

55.5

51.0

51.0

51.0

55.5

13.0 14.0 26.0 0.0

14.0 37.0 14.0 37.0

37.0

37.0 37.0

34.5

38.0

41.0

40.0

34.5

Pr5 Sn3 Pr5 Aux Sn3 x = 0.42 Pr5 Aux Sn3 x = 0.33 τ 2 Pr61 Au25 Sn14 Pr5 Sn3 τ 2 Pr61 Au25 Sn14 Pr5 Aux Sn3 x = 0.16 τ 2 Pr61 Au25 Sn14 τ 2 Pr61 Au25 Sn14 Pr3 Sn Pr2 Au

PrSn0.98−x Aux x = 0.18 PrSn0.98−x Aux x = 0.16 PrSn0.98−x Aux x = 0.21 τ 8 Pr5 AuSn3

τ 8 Pr5 AuSn3

a = 945.8(1) c = 677.9(2)

66.5 74.0 62.0 75.0

50.0 50.0 66.5 51.0

50.0

61.0 55.5

50.0

60.0

55.5

55.0

51.0

0.0 26.0 38.0 25.0

49.0 1.0 1.0 2.0

0.0

14.0 44.5

0.0

38.0

44.5

44.5

37.0

Sn

Pr

Unit cell

IInd phase

Sn

Ist phase

Pr

Pr

Sn

Phases observed in the alloys, reported in the order of their amount Composition from EPMA (at.%) and lattice parameters (pm)

Nominal alloy composition (at.%)

74

Code N◦

Table 4 (continued)

Pr2 Au Pr3 Sn Pr5 Sn3 Pr3 Sn

PrAu PrAu Pr2 Au PrAu

β PrAu

τ 2 Pr61 Au25 Sn14 Pr5 Sn4

Pr5 Aux Sn3 x = 0.16 PrAu

Pr5 Sn4

PrSn0.98−x Aux x = 0.24 Pr5 Sn4

Unit cell

0.0 0.0 0.0

100

36.0 14.0 0.5

0.0

37.0

34.0

2.0

50.0 66.5

63.0 61.0 49.5

49.5

59.0

55.0

50.0

Sn

IIIrd phase Pr

Pr

PrAu Pr2 Au

PrAu

Pr5 Sn3

τ 2 Pr61 Au25 Sn14

Pr5 Aux Sn3 x = 0.33 PrAu

τ 8 Pr5 AuSn3

PrAu

Unit cell

See Fig. 6

Note

38 D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

Fig. 3.

Alloy N. 61, BSE image at 7790 X: grey crystals of the ternary

τ 1 PrAu2−x Snx (x = 0.36) solid solution with small quantities of binary Pr3 Au4 .

the examined samples. All the Pr–Sn samples were found to be very oxidizable, mainly around the equiatomic composition, and needed to be handled under argon atmosphere, although a better stability to oxidation has been observed for those compounds which can dissolve some quantities of gold.

39

Fig. 4. Alloy N. 8, BSE image at 874 X: white crystals of the binary PrAu6−x Snx (x = 0.70) solid solution + grey crystals of the τ 3 PrAu6−x Snx (x = 1.26) ternary solid solution based on PrAu6 stoichiometry.

4.3. Ternary Pr–Au–Sn phases Among the ternary phases identified in the present investigation only the equiatomic PrAuSn compound (hP6, P63 mc, LiGaGe type) has been reported in literature. Ten other ternary compounds, most of which showed compositions near the gold rich side of the ternary diagram, have been identified and examined. All these compounds together with their crystallographic data are reported in Table 2 and will be described below.

τ 1 PrAu2−x Snx — The phase PrAu2−x Snx (0.36 < x < 0.45) forms a solid solution extended from 12 to 15 at.% Sn. In Fig. 3 is reported the sample N. 61, which at high magnification shows the grey crystals of the lower side of the solution. This almost singlephase sample and the other corresponding to the upper side, at 15 at.% Sn, have been indexed from Guinier powder patterns on the basis of the AlB2 structure type. The crystal structure of this phase is still under examination. The corresponding phase CeAu2−x Snx was also found by Boulet et al. [16] in a range up to 22 at.% Sn. Accordingly with this diagram, a Pr35 Au43 Sn22 (N. 62) quenched sample revealed that the solid solution at high temperature can be extended up to 22 at.% Sn.

Fig. 5. Alloy N. 51, BSE image at 5970 X: grey crystals of the ternary τ 6 Pr30 Au40+x Sn30−x (x = 4) solid solution + white τ 1 PrAu2−x Snx (x = 0.45) + dark grey τ7 PrAuSn.

τ 5 PrAu2 Sn — The nearly stoichiometric τ 5 PrAu2 Sn compound has been identified and its structure is under investigation. The CeAu2 Sn compound, found by Boulet et al. [16] with a small solubility range and indexed on the basis of a hexagonal cell, seems to have a different structure.

τ 6 Pr30 Au40+x Sn30−x (0 < x < 4) — Several alloys prepared around

content, has been identified by EPMA and presents the same stoichiometric composition in all the samples prepared. Its crystal structure is still unknown and needs further investigations.

this composition and examined by EPMA revealed the existence of a solid solution range. Crystals having a composition of 30 at.% of Pr and a variable gold content have been found. Fig. 5 shows this phase together with PrAuSn and PrAu2−x Snx (see alloy N. 51 in Table 4). The crystal structure of this phase is under investigation.

τ 3 PrAu6−x Snx — In the gold-rich side of the diagram has

τ 7 PrAuSn — The existence of this phase and its crystal structure

τ 2 Pr61 Au25 Sn14 — This compound, having a rich rare earth

been found an extended solid solution based on the PrAu6−x Snx composition, 1.26 < x < 1.96, separated from the pseudobinary PrAu6−x Snx , 0 < x < 0.7. The coexistence of the two separate phases is shown in Fig. 4. The lattice parameters obtained by the X-ray examination of the samples prepared on all the composition range are reported in Tables 2 and 4. A single crystal from a sample having composition Pr14 Au60 Sn26 has been studied and the structure will be later discussed (see Section 4.4).

τ 4 Pr4 Au11 Sn5 — This new phase has been identified by EPMA in many samples with a nearly stoichiometric composition. The Guinier powder pattern has been indexed on the basis of a hexagonal cell, and the lattice parameters are reported in Table 2. The crystal structure has not been determined.

were already known [33] and well studied. Baran et al. [34] examined this compound by neutron diffraction and described its magnetic structure. Łatka ¸ et al. [46] presented the results of magnetic susceptibility and Sn-119 Mössbauer spectroscopy measurements. The composition and crystal data of this compound resulted to be in good agreement with the literature data and are reported in Tables 2 and 4.

τ 8 Pr5 AuSn3 — This phase is the filled variant of the Mn5 Si3 structure type formed by the β Pr5 Sn3 binary compound above

352 ◦ C, and crystallizes with the hexagonal Hf5 CuSn3 structure type. As discussed before, compositions ranging from binary β Pr5 Sn3 with a gold content increasing up to 5 at.% were observed in some samples examined by EPMA. The Pr5 AuSn3 compound

40

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

Fig. 6. Alloy N. 78, BSE image at 1743 X: grey dendrites of the τ 8 Pr5 AuSn3 ternary compound + white PrAu + dark spots of Pr5 Aux Sn3 (x = 0.33).

is formed with a ternary ordered structure and its appearance is reported in Fig. 6.

τ 9 Pr3 Au6 Sn5 — This new compound has been found in many samples in the gold-rich region, always showing a well defined stoichiometry. It is connected with all the neighboring phases by tie-lines which showed an unambiguous definition of the equilibria. The lattice parameters are reported in Table 2 and the results obtained from single crystal structural investigation will be discussed later (see Section 4.4).

τ 10 Pr2 Au3 Sn4 — The composition of this phase was identified on the basis of the EPMA data. A phase having analogous composition had been reported for the Ce–Au–Sn system and was indexed on the basis of a tetragonal cell, superstructure of the ThCr2 Si2 type. A tentative indexing on this base did not allowed to obtain satisfactory results. The crystal structure of this phase is still under examination.

τ 11 Pr2 Au3 Sn6 — This phase, not revealed during the study of the Ce–Au–Sn system, had been already identified and studied for the Nd–Cu–Sn system [11] as a structural prototype. Powder diffraction data obtained by a Guinier–Stoe camera allowed us to assign the same tI22, I4mm, Nd2 Cu3 Sn6 type to the structure of this compound, and the lattice parameters obtained are reported in Table 2. 4.4. Crystallographic properties of the PrAu4.30 Sn1.77 and Pr3 Au6 Sn5 ternary phases

τ 3 PrAu4.30 Sn1.77 — For the phase a model was derived from the original YCd6 type [55] and refined, considering the distinctive features related to this structure and highlighted in several papers [56–59,32]. Interest in these phases has recently arisen since they represent icosahedral quasicrystal approximants. Atomic parameters and interatomic distances of PrAu4.30 Sn1.77 are reported in Tables 5 and 6, respectively. These structures have the same basic atomic arrangement, but show different details going from the cell origin along the main diagonal. One point concerns the group of 12 atoms filling the void around the origin, here called Sn1 (24 g). They form an icosahedron inside a pentagonal dodecahedron of 12 Au2/Sn and 8 Au4 atoms, as shown in Fig. 7. However, twelve Sn1 atoms cannot coexist, because too short Sn–Sn distances would occur, and on the whole only six atoms forming two triangles around (0, 0, 0) and (1/2,1/2,1/2) are allowed per unit cell. Another point is the presence of Sn4 atoms, partially filling nearly perfect cubic voids. Similar features were already found, for instance, in the Yb(Zn, Al)∼6 and YbZn∼6 structures where, however, a partial occupation of the origin position by ytterbium was

Fig. 7. View along [111] of part of the PrAu4.30 Sn1.77 structure. A pentagonal dodecahedron formed by Au4 (full circles) and Au2/Sn atoms (open circles) surrounds a Sn1 icosahedron (small grey circles), but only three out of twelve Sn1 atoms can coexist (see text). Cubes partially filled by Sn4 (grey circles) and formed by Au4 (full circles) and Au1/Sn atoms (open circles) are also shown. Two cubes in the central part are removed for clarity.

also observed [59]. Three other atoms show Au/Sn substitutional disorder, while a split position is observed for Sn2 coupled with Au4. Besides the Pr site, ordered positions are found for the Au3 and Sn3 atoms, both surrounded icosahedrally. The formula obtained after refinement is in very good agreement with the microprobe analysis of the sample. The structure of PrAu4.30 Sn1.77 is substantially similar to that of Ca3 Au12.2 In6.3 [58]. The main difference regards the void around the origin, filled by a triangle of tin instead of a tetrahedron of indium atoms. PrAu4.30 Sn1.77 can be also compared with Ce3 Au13.8 Sn3.4 , recently re-investigated in the space group Im3¯ by full profile Rietveld refinement [32]. Although the general framework remains the same, in the two structures several sites are occupied differently. This is not surprising, since the composition of the two phases is different and both show a rather large solid solubility range. Moreover, no filling of the void around the origin in the Ce structure is given.

τ 9 Pr3 Au6 Sn5 — Atomic parameters and interatomic distances of Pr3 Au6 Sn5 are reported in Tables 7 and 8, respectively. The structure of the Pr3 Au6 Sn5 compound can be considered as isopointal with the Ce3 Pd6 Sb5 type [60]. The space group is the same, but several atomic coordinates show a significant variation, leading to changes in distances and coordination of the involved atoms. For instance, d(Au2 − Au3) = 299.3 pm, though greater than the sum of the elemental radii [61], can be included in the coordination of both atoms, while the analogous Pd–Pd distance of 311.3 pm in the prototype is 13% greater than the sum of the respective radii. Another clear difference is found between the coordinates of Sn3 (z = 0.2699) and Sb3 (z = 0.3310), so that the Sn3 and Pr1 atoms in Pr3 Au6 Sn5 practically lie in the same plane perpendicular to c. All these differences cause the atomic arrangement in Pr3 Au6 Sn5 to be more similar to the body-centred structure of Yb3 Cu6 Sn5 [62] (Dy3 Co6 Sn5 -type [63]), except for the different ordering of the Au and Sn atoms. These structures are compared in Fig. 8.

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

41

Table 5

¯ Atomic coordinates and equivalent isotropic displacement parameters for PrAu4.30(6) Sn1.77(6) with space group Im3. Atom

Position

occ.

x

y

z

Ueq (pm2 )

Pr Au1/Sn Sn1 Au2/Sn Au3 Au4 Sn2 Sn3 Au5/Sn Sn4

24g 48h 24g 24g 24g 16f 16f 12e 12d 8c

1 0.83(3)/0.17 0.25 0.68(3)/0.32 1 0.866(9) 0.134(9) 1 0.77(4)/0.23 0.48(3)

0 0.11339(12) 0 0 0 0.15288(13) 0.1117(16) 0.1886(4) 0.4085(2) 1/4

0.18716(18) 0.34014(11) 0.0607(10) 0.24450(18) 0.40296(14) 0.15288(13) 0.1117(16) 0 0 1/4

0.3040(2) 0.20048(11) 0.0882(9) 0.09166(18) 0.34659(14) 0.15288(13) 0.1117(16) 1/2 0 1/4

116(7) 229(7) 110(30) 175(9) 153(6) 223(9) 223(9) 245(14) 172(13) 360(70)

Table 6 Interatomic distances (pm) in PrAu4.30 Sn1.77 . Pr-

2 Au1/Sn Au5/Sn 2 Au1/Sn 2 Au1/Sn 2 Au2/Sn 2 Au4 Au2/Sn Au3 2 Au3 Sn3 2 Sn2

321.5(3) 324.9(3) 328.4(2) 328.4(3) 328.4(3) 329.8(2)a 333.3(4) 333.4(4) 335.4(3) 351.7(5) 356(2)a

Sn1-

Sn1 4 Sn1 Au2/Sn 2 Au4 2 Au2/Sn 2 Sn2

267(3)b 278(3)b 279(1) 288(1) 290(1) 313(4)

Au3-

Sn3 Sn3 Au3 2 Au1/Sn 2 Au1/Sn 2 Au5/Sn Pr 2 Pr

270.8(4) 280.9(6) 294.1(4) 294.9(2) 296.0(3) 308.0(3) 333.4(4) 335.4(3)

Sn2-

3 Au2/Sn 3 Sn1 3 Pr

264.7(2) 313(4)b 356(2)

Au5/Sn-

Au5/Sn 2 Au2/Sn 4 Au3 2 Sn3 2 Pr

277.2(7) 284.8(4) 308.0(3) 317.7(6) 324.9(3)

a b

Au1/Sn-

Sn4 Au2/Sn Au3 Au3 2 Au1/Sn Sn3 Au4 Pr Pr Pr

259.1(2) 278.8(3) 294.9(2) 296.0(3) 297.2(3) 297.6(2) 298.9(3) 321.5(3) 328.4(2) 328.4(3)

Au2/Sn-

2 Sn2 Au2/Sn Sn1 2 Au1/Sn Au5/Sn 2 Au4 2 Sn1 2 Pr Pr

264.7(2)a 277.8(5) 279(1)b 278.8(3) 284.8(4) 285.6(2)a 290(1)b 328.4(3) 333.3(4)

Au4-

Sn4 3 Au2/Sn 3 Sn1 3 Au1/Sn 3 Pr

254.9(4) 285.6(2) 288(1)b 298.9(3) 329.8(2)

Sn3-

2 Au3 2 Au3 4 Au1/Sn 2 Au5/Sn 2 Pr

270.8(4) 280.9(6) 297.6(2) 317.7(6) 351.7(5)

Sn4-

2 Au4 6 Au1/Sn

254.9(4) 259.1(2)

Alternative distances. The number of coordinated atoms depends on the site occupancy.

Fig. 8. Comparison of the Pr3 Au6 Sn5 (Pmmn) and Yb3 Cu6 Sn5 (Immm) structures. Large circles: Pr or Yb; medium circles: Sn; full circles: Au or Cu.

Table 7 Atomic coordinates and equivalent isotropic displacement parameters for Pr3 Au6 Sn5 with space group Pmmn, origin at 1. Atom

Position

x

y

z

Ueq (pm2 )

Pr1 Pr2 Au1 Au2 Au3 Au4 Sn1 Sn2 Sn3

4e 2b 4e 4e 2a 2a 4e 4e 2b

1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4

0.06299(10) 3/4 0.08991(10) 0.60707(10) 1/4 1/4 0.08663(15) 0.60775(16) 3/4

0.74544(17) 0.7452(3) 0.12011(12) 0.47519(11) 0.5391(2) 0.9412(2) 0.37991(19) 0.02486(18) 0.2699(3)

146(3) 160(4) 207(3) 200(3) 220(4) 264(4) 145(4) 152(4) 195(6)

4.5. Phase equilibria The isothermal section presented in Fig. 1 has been drawn up on the basis of the results reported in Table 4. As already mentioned,

the equilibria existing on the side lying along the Au–Sn axis could not be defined due to the presence of the liquid state, whereas the equilibria connecting all the solid binary and ternary phases could be. Extended solid solutions of some binary and ternary compounds have been detected in the region close to the Au-rich corner. By adding a certain amount of Sn, the binary PrAu6−x Snx and PrAu2−x Snx solid solutions show a change in their crystal structure and turn into ternary compounds which are equally able to substitute gold with tin. These phases are connected by large two-phase fields to the binary solid solution Pr14 Au51−x Snx which shows the region having a lower tin content linked to the binary PrAu6−x Snx solid solution on the left side and to the binary Pr17 Au36−x Snx solid solution on the right side. The same phase with a higher tin content is connected to the cubic τ 3 -PrAu6−x Snx and to the hexagonal τ 1 -PrAu2−x Snx ternary solid solutions.

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D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

Table 8 Interatomic distances (pm) in Pr3 Au6 Sn5 . Pr1-

Au4 2 Au2 Au3 2 Sn1 2 Sn2 2 Au1 2 Sn3 Au2 Sn2 Sn1

322.7(2) 325.9(2) 329.5(2) 330.7(2) 332.5(2) 337.1(2) 341.1(1) 359.4(2) 367.2(3) 374.5(2)

Sn1 2 Sn2 Au4 Sn2 2 Pr1 2 Pr2

265.2(2) 272.7(1) 283.5(2) 284.9(3) 337.1(2) 343.2(2)

Au4-

2 Au1 4 Sn2 2 Sn3 2 Pr1

283.5(2) 300.4(2) 313.6(3) 322.7(2)

Sn2-

2 Au1 Au1 2 Au4 Sn3 2 Pr1 Pr2 Pr1

272.7(1) 284.9(3) 300.4(2) 315.8(3) 332.5(2) 344.4(3) 367.2(3)

Au1-

Pr2-

2 Au2 4 Sn1 4 Au1 2 Sn2

336.9(3) 342.3(2) 343.2(2) 344.4(3)

Au2-

2 Sn1 Sn1 Sn3 2 Au3 2 Pr1 Pr2 Pr1

273.0(1) 279.9(3) 285.3(3) 299.3(1) 325.9(2) 336.9(3) 359.4(2)

Au3-

2 Sn1 4 Au2 2 Sn3 2 Pr1

274.6(2) 299.3(1) 299.8(3) 329.5(2)

Sn1-

Au1 2 Au2 Au3 Au2 2 Pr1 2 Pr2 Pr1

265.2(2) 273.0(1) 274.6(2) 279.9(3) 330.7(2) 342.3(2) 374.5(2)

2 Au2 2 Au3 2 Au4 2 Sn2 4 Pr1

285.3(3) 299.8(3) 313.6(3) 315.8(3) 341.1(1)

Sn3-

All the compounds having a tin content equal or greater than 25 at.% Sn and a praseodymium content lower than 33.3 at.% Pr are nearly stoichiometric. The chemical compositions of these phases differ in only a few atoms %, and they lie very close in this region of the isothermal section (see τ4 –τ7 and τ9 –τ11 in Table 2 and Fig. 1). As regards the Pr-rich corner, the two compounds Pr4 Au11 Sn5 and Pr5 AuSn3 , have been identified. Both are connected to PrAu and to binary compounds pertaining to the Pr–Sn system, with Pr not directly involved in the tie-lines of this region. Owing to the high oxidability of the samples, poor X-ray data have been obtained in the region close to the Pr–Sn binary diagram, and most of the equilibria have been defined on the basis of the EPMA data. An example can be observed in Fig. 9, in which the coexistence of the two binary PrSn and PrSn0.98−x Aux and the ternary PrAuSn compounds has been confirmed (see alloy N. 73 in Table 4).

Fig. 9. Alloy N. 73, BSE image at 1160 X: grey matrix of PrSn + dark grey PrSn0.98−x Aux (x = 0.02) + white τ 7 PrAuSn (very oxidizable alloy).

5. Conclusions The Pr–Au–Sn isothermal section at 600 ◦ C has been determined, ten new ternary phases identified and the ternary equiatomic PrAuSn compound confirmed. The structures of some of these phases have been determined by single crystal or powder diffraction methods. A comparison can be made with the ternary section at 750 ◦ C of the Ce–Au–Sn system and, despite the different temperatures, some similarities can be observed for the two systems reported in Fig. 10. Cubic ternary solid solutions at about 14 at.% of rare earth and a slightly different tin content have been observed in both systems, just like the ternary RAu2−x Snx solid solutions, based on similar substitutional formation mechanism. Almost all the remaining ternary compounds identified in the Ce–Au–Sn system, such as τ 5 CeAu2 Sn, τ 7 CeAuSn, τ 8 Ce5 AuSn3 and τ 10 Ce2 Au3 Sn4 , have also been found in the Pr–Au–Sn system, excepting the τ 12 CeAu2 Sn2 phase. The solubility of the binary compounds in the two ternary diagrams is fairly extended and, even though the Pr–Sn diagram presents a few more compounds than Ce-Sn and the Ce–Au system is partially liquid, the tie-lines connecting the binary to the ternary phases in the two systems show very similar trends. The most significant differences between the two systems are due to the

Fig. 10. Isothermal sections of the two R–Au–Sn systems: Ce–Au–Sn at 750 ◦ C [16] and Pr–Au–Sn at 600 ◦ C [this work].

D. Mazzone et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 31–43

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