The Tb–Ag–Ga system

Journal of Alloys and Compounds 352 (2003) 128–133

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The Tb–Ag–Ga system R.V. Gumeniuk, B.M. Stel’makhovych, Yu.B. Kuz’ma* Department of Analytical Chemistry, Ivan Franko National University of Lviv, Kyrylo and Mefodij Str. 6, Lviv 79005, Ukraine Received 23 September 2002; received in revised form 14 October 2002; accepted 14 October 2002

Abstract The isothermal section of the Tb–Ag–Ga system at 873 K has been constructed in the region up to 70 at.% Ga. The interaction between components in the region with higher gallium content has been studied at 573 K. The composition limits of the solid solution ranges of the binary compounds and the homogeneity ranges of the ternary ones have been determined. The existence of earlier known ternary gallides Tb 3 Ag 2.8 Ga 8.2 (La 3 Al 11 -type), TbAg 0.4 – 0.7 Ga 1.6 – 1.3 (CaIn 2 -type), TbAg 0.9 – 1.2 Ga 1.1 – 0.8 (KHg 2 -type) has been confirmed. The ] compounds TbAg 0.5 Ga 3.5 (unknown structure), Tb 4 Ag 0.9 Ga 12.1 (Y 4 PdGa 12 -type, space group Im3 m, a 50.86537(2) nm, R Brag 50.039), and TbAg 1.2 Ga 1.8 (b-YbAgGa 2 -type, space group Pnma, a50.69742(3), b50.43587(1), c51.02098(7) nm, R I 50.070) have been found for the first time.  2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth compounds; Crystal structure; Phase diagram; X-ray diffraction

1. Introduction Ternary Ln–Ag–Ga systems (Ln–rare earth metal) have been earlier studied only to synthesize the ternary compounds of definite compositions. In particular, three ternary compounds in the Tb–Ag–Ga system were reported (Table 1). A systematic investigation of the interaction between components in the Tb–Ag–Ga system is of great interest, because the results obtained allow us to predict the character of the interaction in other Ln–Ag–Ga systems. The phase diagrams of the binary Ag–Ga and Tb–Ga systems were studied in the whole concentration regions, and the Tb–Ag system was studied in the region up to 50 at.% Ag [4]. Two intermediate phases are known in the Ag–Ga system. The high-temperature z-phase (Mg-type) peritectically forms at 884 K and has a homogeneity range from 15 to 25 at.% Ga; the low-temperature z9-phase ] (space group P62 m, Ag 2 Ga-type) contains about 18–23 at.% Ga [5]; the temperature of polymorphous transition is about 698 K. Silver dissolves up to 19 at.% Ga at 884 K. Five binary compounds are found in the Tb–Ga phase diagram [4]. The compounds TbGa 6 (PuGa 6 -type), bTbGa 3 (AuCu 3 -type), TbGa (a-ITl-type), and Tb 5 Ga 3 (Cr 5 B 3 -type) form peritectically at 670, 1283, 1483, and *Corresponding author. E-mail address: [email protected] (Yu.B. Kuz’ma).

1403 K, respectively. The compound TbGa 2 (AlB 2 -type) melts congruently at 1653 K. The temperature of polymorphic transition of b-TbGa 3 (AuCu 3 -type)↔a-TbGa 3 (Mg 3 Cd-type) is higher than 673 K. Besides, the existence of two binary gallides Tb 3 Ga 5 (Tm 3 Ga 5 -type) [6] and Tb 3 Ga 2 (Gd 3 Ga 2 -type) [7] have been reported, but these compounds are not included in the Tb–Ga phase diagram. In the Tb–Ag system the compounds Tb 14 Ag 47 – 51 (Gd 14 Ag 51 -type), TbAg 2 (MoSi 2 -type), and TbAg (CsCltype) form congruently at 1235, 1185, and 1435 K, respectively [4].

2. Experimental details The samples for the investigation were prepared by arc-melting of the mixtures of the elemental components (Tb 99.5 wt.% pure, Ag 99.995 wt.%, and Ga 99.95 wt.%) in a purified argon atmosphere. All alloys were then sealed in evacuated quartz ampoules, and then homogenized at 873 K for 720 h (samples containing less than 70 at.% Ga), and at 573 K for 2880 h (samples containing more than 70 at.% Ga). The alloys were then quenched in cold water without breaking the ampoules. Phase analysis was carried out using powder diffraction patterns obtained in a Huber image plate Guinier camera in the 2u range of 6–1008 (exposition time 6315 min,

0925-8388 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01160-X

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Table 1 Crystallographic data for the earlier reported compounds in the Tb–Ag–Ga system Phase

Space group

Structure type

Tb 3 Ag 2.8 – 3.8 Ga 8.2 – 7.2

Immm

La 3 Al 11

TbAg 0.5 Ga 1.5 TbAgGa

P63 /mmc Imma

CaIn 2 KHg 2

Cu Ka 1 -radiation). The lattice parameters were refined by a least-squares method using germanium as internal standard (a50.565692 nm). For the crystal structure determination diffraction data were collected using the u 22u scan technique with 2u steps of 0.058 (2umax 51408) and exposition times of 25 s in every point (DRON-3M diffractometer, Cu Ka-radiation). An X-ray single-crystal investigation was carried out using photographic (Laue and rotation) methods. Diffraction data for the structure determination were collected on the DARTCH-1 diffractometer (Mo Ka radiation). All calculations were performed using CSD [8] and FULLPROF [9] softwares.

2.1. Phase diagrams Sixty-seven binary and ternary samples were synthesized for the investigation of the phase equilibria and the crystal structures of ternary compounds in the Tb–Ag–Ga system. The isothermal section of the phase diagram of the Tb–Ag–Ga system at 873 K is shown in Fig. 1. The existence of the binary compounds and the three earlier known ternary gallides presented in Fig. 1 was confirmed. Solid solution ranges of the binary compounds Tb 14 Ag 47 – 51 and TbAg were found. The approximate composition limit of the Tb 14 Ag 47 – 51 solid solution is

Lattice parameters (nm)

Refs.

a

b

c

0.43017– 0.42906 0.4466 0.4542

0.9484– 0.9524

1.2802– 1.2914 0.7206 0.7796

0.7119

[1] [2] [3]

described by the formula Tb 14 Ag 42.3 Ga 7.7 . The type of Ag and Ga distribution in this structure was refined for a single phase sample of the composition Tb 21 Ag 68 Ga 11 . The results of crystal structure determination are listed in Tables 2 and 3. The composition limit of the TbAg solid solution range was determined from Vegard’s rule. The corresponding values of the lattice parameters are listed in Table 2, and the plot of these parameters versus gallium content in the samples is shown in Fig. 2. The existence of the earlier known ternary compounds with the CaIn 2 and KHg 2 -type structures was confirmed, and their homogeneity ranges were established. The crystal structure of gallide of La 3 Al 11 -type was refined using single crystal diffraction data. A partial phase diagram of the Ga-rich region of the Tb–Ag–Ga system at 573 K is shown in Fig. 3. The existence of the binary compound TbGa 6 (PuGa 6 -type) and of three ternary gallides (Fig. 1), which also were obtained at 873 K, was confirmed. However the gallide TbAg 0.5 Ga 3.5 was not found at 573 K. Instead of it, the ternary compound Tb 4 Ag 0.9 Ga 12.1 (Y 4 AgGa 12 -type) forms at 573 K (Fig. 3).

2.2. Earlier known compounds and their crystal structure 2.2.1. Compound with La3 Al11 -type structure The examination of a single crystal extracted from the sample of the composition Tb 21 Ag 22 Ga 57 using Laue and rotation methods revealed an orthorhombic structure with the lattice parameters a51.275(9), b50.952(7), c5 0.432(3) nm. The crystal structure was solved by direct methods (MULTAN) using single crystal diffractometer data (Table 4). The obtained results confirmed the La 3 Al 11 -type structure for the investigated compound. Crystallographic data for the Tb 3 Ag 2.8 Ga 8.2 compound are listed in Table 2. The coordinates of the atoms, their type of distribution and their thermal parameters are given in Table 3. The anisotropic thermal parameters are given in Table 5. The refined composition of the investigated compound is within the limits of its homogeneity region, reported in Ref. [1].

Fig. 1. The isothermal section of the Tb–Ag–Ga system at 873 K.

2.2.2. Compound with CaIn2 -type structure The Tb–Ag–Ga ternary compound with the CaIn 2 structure was reported in Ref. [2] (Table 1). Our results

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Table 2 Crystallographic data for the composition limits of the solid solutions of the binary compounds and the homogeneity ranges of the ternary compounds in the Tb–Ag–Ga system No.

a

Phase

Tb 14 Ag 42.3 Ga 7.8 TbAg 12x Ga x

b c

Space group

Structure type

Lattice parameters (nm)

P6 /m ] Pm3 m

Gd 14 Ag 51 CsCl

1.25515(9)

x50.0 x50.2 x50.3 x50.4 x50.6

c c c c

1

TbAg 0.5 Ga 3.5

Unknown

–

Tb 3 Ag 2.8 Ga 8.2 Tb 4 Ag 0.9 Ga 12.1 TbAg 1.2 Ga 1.8 TbAg 0.4 – 0.7 Ga 1.6 – 1.3

Immm ] Im3m Pnma P63 /mmc

La 3 Al 11 Y 4 PdGa 12 b-YbAgGa 2 CaIn 2

3 4 c

TbAg 0.30 Ga 1.70 TbAg 0.36 Ga 1.64 TbAg 0.45 Ga 1.55 TbAg 0.60 Ga 1.40 TbAg 0.70 Ga 1.30 TbAg 0.78 Ga 1.22

c c c c c

5

TbAg 0.9 – 1.2 Ga 1.1 – 0.8

b

c 0.91728(2)

0.36203(5) 0.36151(6) 0.36135(5) 0.36102(5) 0.36070(8)

2 d

a

V (nm 3 310 3 )

1.2881(4) 0.86537(2) 0.69742(3)

47.450(9) 47.246(4) 47.183(4) 47.054(8) 46.930(3)

0.9517(3)

0.43155(9)

0.43587(1)

1.02098(7)

529.1(4) 648.06(2) 310.36(1)

0.7345(1) 0.7316(1) 0.7247(1) 0.72063(4) 0.71721(1) 0.71739(5)

124.00(4) 124.04(4) 124.17(3) 124.89(1) 125.41(4) 125.54(3)

0.77859(1)– 0.78231(2)

250.54(1)– 252.06(2)

0.44152(5) 0.44247(5) 0.44480(3) 0.44734(1) 0.44935(1) 0.44952(3) Imma

KHg 2

0.45246(3)– 0.45525(1)

1251.49(3)

0.71119(1)– 0.70774(2)

a

The limit composition of the solid solution on the base of Tb 14 Ag 48 – 51 compound. The limit composition of the solid solution on the base of TbAg compound described by the formula TbAg 0.48 Ga 0.52 . c Lattice parameters were refined by least square method using germanium as internal standard. d Compound is shown at Fig. 2 under the number 6.

b

have shown that this compound has a considerable homogeneity range described by the formula TbAg 0.4 – 0.7 Ga 1.6 – 1.3 . The lattice parameters are given in Table 2. The crystal structure was refined using powder diffraction data for the composition TbAg 0.7 Ga 1.3 , and the atomic parameters are listed in Table 3.

2.2.3. Compound with KHg2 -type Powder diffraction patterns of the samples with the compositions TbAg 0.9 Ga 1.1 and TbAg 1.2 Ga 0.8 were indexed assuming an orthorhombic cell (space group Imma), and the following refinement of the atomic coordinates confirmed the KHg 2 -structure for these compounds (Table 3). The homogeneity range of this compound was determined from the phase analysis data and can be described by the formula TbAg 0.9 – 1.2 Ga 1.1 – 0.8 . The composition of the earlier known gallide TbAgGa (KHg 2 -type) [3] is within the limits of proposed homogeneity range. 2.3. New ternary compounds and their crystal structure 2.3.1. The | TbAg0.5 Ga3.5 compound A new gallide with an unknown crystal structure was found in the sample with the composition TbAg 0.5 Ga 3.5 . The single crystals extracted from the samples annealed at 873 K were too small for a crystal structure investigation, and our attempts to synthesize larger crystals were unsuc-

cessful. The phase composition of the sample changed after the heat treatment (the sample was heated to 1173 K and then cooled to the room temperature during 48 h). The corresponding powder diffraction pattern contained the lines of the binary compound TbGa 2 (AlB 2 -type) and of the ternary compound Tb 3 Ag 2.8 Ga 8.2 (La 3 Al 11 -type). The investigation of the crystal structure of the new gallide will be a subject of our further work.

2.3.2. The Tb4 Ag0.9 Ga12.1 compound The powder diffraction pattern of a sample of the Tb 25 Ag 10 Ga 65 composition, annealed at 573 K, contained the reflections of two phases. One of them was the binary ] compound Ag 2 Ga (space group P62 m, a50.7766(1), c5 0.28760(5) nm). The strongest lines of the second phase were indexed assuming a cubic unit cell with lattice parameter a50.433 nm, which gave us reasons to suppose that the compound crystallizes with the AuCu 3 structure. However, the presence of additional non-indexed reflections indicated a more complex structure. Taking into account the 22 strongest reflections of the compound we have indexed the structure with a body-centred unit cell and lattice parameter a50.8653(1) nm using the TREOR90 program. The atomic parameters of the Y 4 PdGa 12 -type structure were taken as initial ones for crystal structure determination and refined for the new compound. Results of the Tb 4 Ag 0.9 Ga 12.1 crystal structure refinement for the

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Table 3 Atomic coordinates, isotropic thermal parameters of the atoms in the structures of the Tb–Ag–Ga phases Compounds: compositions, structure type and distribution of atoms

Space group and position

Tb 14 Ag 42.3 Ga 7.8 (Gd 14 Ag 51 -type)a 2Tb1 6Tb2 6Tb3 T1(1.72(2)Ag10.28(2)Ga) T2(2.20(8)Ag11.80(8)Ga) T3(3.66(6)Ag12.34(6)Ga) T4(8.6(1)Ag13.4(1)Ga) 12Ag1 12Ag2 2.08(6)Ag3

P6 /m 2(e) 6( j) 6(k) 2(c) 4(h) 6(k) 12(l) 12(l) 12(l) 6( j)

Tb 3 Ag 2.8 Ga 8.2 (La 3 Al 11 -type) 2Tb1 4Tb2 T1(1.46(2)Ag10.54(2)Ga) T2(3.56(4)Ag10.44(4)Ga) 8Ga T3(0.64(8)Ag17.36(8)Ga) Tb 4 Ag 0.9 Ga 12.1 (Y 4 PdGa 12 -type) 8Tb T1(1.72(2)Ag10.28(2)Ga) 12Ga1 12Ga2

Immm 2(a) 4( g) 2(c) 4( j) 8(l) 8(l) ] Im3 m 8(c) 2(a) 12(d) 12(e)

TbAg 1.2 Ga 1.8 (b-YbAgGa 2 -type) 4Tb 4Ag T1(0.73(4)Ag13.27(4)Ga) T2(0.18(4)Ag13.82(4)Ga)

Coordinates

Biso 310 2 (nm 2 )

x

y

z

0 0.3888(2) 0.1411(2) 1/3 1/3 0.2360(2) 0.1138(2) 0.2657(2) 0.4389(1) 0.1002(7)

0 0.1160(2) 0.4686(2) 2/3 2/3 0.0593(2) 0.4942(2) 0.1942(2) 0.1063(1) 0.1349(6)

0.3057(4) 0 1/2 0 0.2949(3) 1/2 0.1508(2) 0.2337(2) 0.3320(2) 0

0.56(9) 0.58(5) 0.59(5) 0.8(1) 0.82(8) 0.82(7) 0.83(4) 0.81(4) 0.73(3) 1.0(2)

0 0.2993(1) 1/2 0 0.3417(2) 0.1423(2)

0 0 0 0.6934(2) 0.3684(2) 0.2805(2)

0 0 1/2 1/2 0 0

0.93(4) 0.86(3) 1.02(6) 1.01(4) 1.02(4) 1.02(4)

1/4 0 0 0.3058(3)

1/4 0 1/4 0

1/4 0 1/2 0

0.94(1) 1.00(1) 1.04(1) 1.03(2)

Pnma 4(c) 4(c) 4(c) 4(c)

0.2798(2) 0.0429(2) 0.2042(3) 0.4286(4)

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

0.3290(1) 0.5986(1) 0.0371(2) 0.6527(2)

0.99(4) 1.12(4) 1.09(7) 1.07(7)

TbAg 0.7 Ga 1.3 (CaIn 2 -type) 2Tb T(1.32(4)Ag12.68(4)Ga)

P63 /mmc 2(b) 4( f )

0 1/3

0 2/3

1/4 0.4739(2)

0.20(4) 0.61(5)

TbAg 0.9 Ga 1.1 (KHg 2 -type) 4Tb T(3.68(8)Ag14.32(8)Ga)

Imma 4(l) 8(h)

1/4 1/4

1/2 0.2915(1)

0.7823(1) 0.4164(2)

1.07(3) 1.39(4)

TbAg 1.2 Ga 0.8 (KHg 2 -type) 4Tb T(4.72(8)Ag13.28(8)Ga)

Imma 4(l) 8(h)

1/4 1/4

1/2 0.2910(2)

0.7825(1) 0.4151(2)

1.17(2) 1.55(4)

a

R factors

R I 50.057 R P 50.092

R F 50.039 R W 50.046

R Brag 50.039 R P 50.125

R I 50.070 R P 50.114

R I 50.048 R P 50.108 R I 50.059 R P 50.094 R I 50.056 R P 50.110

The limit composition of the solid solution on the base of Tb 14 Ag 48 – 51 compound.

two-phase sample are given in Table 3. The residual factor for the Ag 2 Ga structure has a value of 0.061, which can be explained by the relatively small amount of this phase in the sample.

2.3.3. The TbAg1.2 Ga1.8 compound Powder diffraction patterns of the samples of the approximate composition Tb 25 Ag 30 Ga 45 annealed at 573 and 873 K were successfully indexed with an orthorhombic unit cell. Refinement of the crystal structure of the compound TbAg 1.2 Ga 1.8 revealed the b-YbAgGa 2 -type structure [10] with a statistical atomic distribution in two of the three crystallographic positions of the smaller atoms. The atomic coordinates and thermal parameters as well as the type of the atomic distribution in the TbAg 1.2 Ga 1.8

structure are listed in Table 3. The observed change of the TbAg 1.2 Ga 1.8 lattice parameters in the two- and threephase samples indicates the existence of a homogeneity range for this compound.

3. Discussion The Tb–Ag–Ga system is the first one among other related Ln–Ag–Ga systems which was studied systematically. Some peculiarities of the interaction in those systems should be noted. All known ternary compounds form in the region up to 33 at.% Tb and 40 at.% Ag. The Tb–Ag binary compounds dissolve gallium, while no significant solubility of silver in Tb–Ga binaries was

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Fig. 2. Unit cell dimensions of TbAg 12x Ga x alloys versus concentration; the homogeneous range is indicated by vertical bars. Table 5 Anisotropic thermal parameters for Tb 3 Ag 2.8 Ga 8.2 a Atom

B11

B22

B33

B12

Tb1 Tb2 T1 T2 Ga T3

0.76(7) 0.82(4) 1.1(1) 0.96(7) 1.08(7) 1.24(7)

0.95(7) 0.95(5) 0.83(9) 1.06(6) 0.89(6) 0.86(6)

1.07(6) 0.80(4) 1.2(1) 1.35(6) 1.08(6) 0.96(5)

0 0 0 0 0.17(6) 20.09(6)

a

B13 5 B23 5 0.

Fig. 3. the isothermal section of the Tb–Ag–Ga system at 573 K.

observed. The ternary gallides have considerable homogeneity ranges, which may reflect the great crystallochemical similarity of Ag and Ga. The isothermal sections at 573 and 873 K (see Figs. 1 and 3) demonstrate that there is an

Table 4 Parameters for the single-crystal X-ray data collection for the Tb 3 Ag 2.8 Ga 8.2 compound Structure type Space group Lattice parameters (nm)

Calculated density (g / cm 3 ) Number of atoms in cell Diffractometer Radiation Mode of refinement 2umax Restrictions Number of variables Number of measured reflections Number of unique reflections

La 3 Al 11 Immm a51.2881(4) b50.9517(3) c50.43155(9) 8.484(7) 28 DARTCH-1 Mo Ka F(hkl) 75 Fobs .4s (Fobs ) 13 617 440

essential influence of the annealing temperature on the phase equilibria in the Tb–Ag–Ga system. Taking into account the data available on the structure types of the ternary gallides in the Ln–Ag–Ga systems (Table 6) one can expect a formation of compounds with the b-YbAgGa 2 structure in the other Ln–Ag–Ga systems, where Ln represents a heavy rare earth metal. The Tb–Ag–Ga system differs considerably from related Ln–Cu–Ga systems as regards the character of the interaction between the components. In the later systems Table 6 Structure types of the ternary compounds in the Ln–Ag–Ga systems

The number in the squares refers to the reference.

R.V. Gumeniuk et al. / Journal of Alloys and Compounds 352 (2003) 128–133 Table 7 The shortest interatomic distances (d, nm) in Tb–Ag–Ga ternary compound Atoms

d

Tb 3 Ag 2.8 Ga 8.2 (La 3 Al 11 -type) Tb2–4Ga T1–4T3 Ga–1Ga T3–2Ga

0.3086(3) 0.2780(4) 0.2505(1) 0.2589(2)

Tb 4 Ag 0.9 Ga 12.1 (Y 4 PdGa 12 -type) Tb–6Ga1 T–6Ga2 Ga1–4Ga2

0.3060(1) 0.2682(2) 0.27198(1)

TbAg 1.2 Ga 1.8 (b-YbAgGa 2 -type) Tb–2T2 Ag–1T2 T1–2T2

0.2987(2) 0.2662(2) 0.2646(2)

TbAg 0.7 Ga 1.3 (CaIn 2 -type) Tb–12T T–2T

0.3051(2) 0.2621(3)

TbAg 1.2 Ga 0.8 (KHg 2 -type) Tb–12T T–2T

0.3116(1) 0.2610(1)

the ternary gallides contain a higher content of the dmetals. Probably, this is caused by the close values of the copper and gallium atomic radii (r Cu 50.1278, r Ga 50.135 nm) while rAg is 0.1445 nm [14]). The Tb–Cu–Ga system was studied only for obtaining ternary compounds of definite structures and compositions, and gallides of BaAl 4 [15] and CaIn 2 [16] types were synthesized. The Tb–Ag– Al system was studied in the region up to 50 at.% Tb [17]. Similarly to the Tb–Ag–Ga system, ternary compounds with the KHg 2 and La 3 Al 11 structures were found in the Tb–Ag–Al system. However, the formation of ternary aluminides with low Tb content is the main difference between the Tb–hCu,Agj–Al systems and Tb–Ag–Ga ones.

133

The shortest interatomic distances in the investigated structures of the Tb–Ag–Ga system are listed in Table 7. The maximum shortening of the distances (6%) is observed between the gallium atoms in the Tb 3 Ag 2.8 Ga 8.2 structure.

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