Crystal structure and magnetic properties of R3Co0.5GeS7 (R = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R = Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm)

Journal of Alloys and Compounds 647 (2015) 445e455

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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Crystal structure and magnetic properties of R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) M. Daszkiewicz a, Yu.O. Pashynska b, O.V. Marchuk c, L.D. Gulay d, D. Kaczorowski a, * a

Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland Department of Material Science, Lutsk National Technical University, L'vivska str. 75, 43018 Lutsk, Ukraine Department of Inorganic and Physical Chemistry, Eastern European National University, Voli Ave 13, 43009 Lutsk, Ukraine d Department of Ecology and Protection of Environment, Eastern European National University, Voli Ave 13, 43009 Lutsk, Ukraine b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 May 2015 Received in revised form 5 June 2015 Accepted 6 June 2015 Available online 19 June 2015

The crystal structure of quaternary compounds R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) (La3Mn0.5SiS7 structure type, space group P63, Pearson symbol hP23) was determined by means of X-ray single crystal diffraction. The R atoms are located in trigonal prisms with two additional atoms, the Co (Ni) atoms occupy octahedra, the Ge atoms are located in tetrahedra. Magnetic properties of the compounds R3Co0.5GeS7 (R ¼ Sm and Gd) and R3Ni0.5GeS7 (R ¼ Gd, Dy, Er and Tm) were studied down to 1.72 K. Their magnetic behaviour is governed by trivalent rare-earth and divalent transition-metal constituents. In each material, the magnetic exchange interactions are dominated by antiferromagnetic correlations, which promote long-range magnetic orderings at low temperatures. © 2015 Elsevier B.V. All rights reserved.

Keywords: Rare earth compounds Chalcogenides Crystal structures X-ray single crystal diffraction Magnetic properties

1. Introduction Designing new functional materials with increasingly complex compositions (ternary and quaternary) has become a primary direction in modern science and technology. Complex rare-earthbased chalcogenides are interesting due to their specific thermal, electrical, magnetic and optical properties. In recent years, various chalcogenide materials find numerous applications in the field of infrared and nonlinear optics. Systematic investigation of complex rare earth chalcogenide systems is an important way for discovering new materials with useful properties [1,2]. Recently, we reported on the crystal structures and the magnetic properties of the compounds R3Mn0.5GeS7 (R ¼ Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho and Er) and R3Fe0.5GeS7 (R ¼ Y, La, Ce, Pr, Sm, Gd, Tb, Dy, Ho, Er and Tm), crystallizing with the La3Mn0.5SiS7-type structure (space group P63) [3,4]. Here, we present our results obtained for the compounds R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho,

* Corresponding author. E-mail address: [email protected] (D. Kaczorowski). http://dx.doi.org/10.1016/j.jallcom.2015.06.059 0925-8388/© 2015 Elsevier B.V. All rights reserved.

Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm). 2. Experimental details Samples with the nominal compositions R3Co0.5GeS7 and R3Ni0.5GeS7 (R ¼ rare earth metal, except for Eu, Yb and Lu) were prepared by solid state syntheses carried out in resistance furnaces. The calculated amounts of the elemental constituents (the purity was better than 99.9 wt. %) with the atomic ratio R:M:Ge:S ¼ 3:0.5:1:7 (M ¼ Co, Ni) were sealed in evacuated quartz tubes. The ampoules were first heated with a rate of 30  C per hour up to 1150  C, and then kept at this temperature for 3 h. Afterwards, the samples were cooled slowly (10  C per hour) down to 500  C, and annealed at this temperature for 720 h. Subsequently, the ampoules were quenched in cold water. The obtained materials were checked by X-ray powder diffraction (XRD) using a DRON-4-13 powder diffractometer (CuKa radiation, 10  2Q  100 , step scan mode with a step size of 0.05 and counting time of 5 s per data point). Phase analysis was carried out. Small single crystals suitable for crystal structure investigations were selected from all the prepared R3Co0.5GeS7 samples and most

446

Table 1 Crystal data and structure refinement details of the R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd and Sm) compounds.

Reflections collected Independent reflections Refinement method Absolute structure parameter Data/restraints/ parameters Goodness-of-fit on F2 Final R indices [I > 2s(I)] R indices (all data) Extinction coefficient Largest diff. peak and hole

Y3Co0.5GeS7 593.21 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.729(1) Å c ¼ 5.7744(9) Å 473.3(1) Å3 2

La3Co0.5GeS7 743.21 P63 (No. 173) La3Mn0.5SiS7 a ¼ 10.3181(7) Å c ¼ 5.8091(6) Å 535.60(8) Å3 2

Ce3Co0.5GeS7 746.83 P63 (No. 173) La3Mn0.5SiS7 a ¼ 10.2168(7) Å c ¼ 5.7843(6) Å 522.89(7) Å3 2

Pr3Co0.5GeS7 749.21 P63 (No. 173) La3Mn0.5SiS7 a ¼ 10.1474(7) Å c ¼ 5.7735(5) Å 514.85(7) Å3 2

Nd3Co0.5GeS7 759.20 P63 (No. 173) La3Mn0.5SiS7 a ¼ 10.0868(7) Å c ¼ 5.7606(5) Å 507.58(7) Å3 2

Sm3Co0.5GeS7 777.53 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.9766(7) Å c ¼ 5.7469(5) Å 495.37(7) Å3 2

4.162 g/cm3 23.665 mm1

4.608 g/cm3 16.546 mm1

4.743 g/cm3 17.751 mm1

4.833 g/cm3 18.961 mm1

4.967 g/cm3 20.178 mm1

5.213 g/cm3 22.734 mm1

549 Red 0.11  0.04  0.04 mm 2.42e27.47

657 Black 0.07  0.05  0.04 mm 3.95e27.43

663 Black 0.08  0.04  0.04 mm 4.21e27.42

669 Black 0.06  0.05  0.05 mm 4.02e27.46

675 Black 0.07  0.05  0.04 mm 4.67e27.48

687 Black 0.07  0.06  0.04 mm 4.09e27.30

12  h  12 12  k  12 7  l  7 6286

13  h  13 13  k  13 7  l  7 4650

13  h  12 13  k  13 7  l  7 4536

10  h  13 13  k  12 7  l  7 4525

13  h  12 12  k  13 7  l  7 4420

12  h  12 12  k  12 6  l  7 4342

734 [R(int.) ¼ 0.0880]

815 [R(int.) ¼ 0.0312]

794 [R(int.) ¼ 0.0318]

787 [R(int.) ¼ 0.0333]

760 [R(int.) ¼ 0.0298]

735 [R(int.) ¼ 0.0333]

Full-matrix leastsquare on F2 0.03(1)

Full-matrix leastsquare on F2 0.01(2)

Full-matrix leastsquare on F2 0.02(1)

Full-matrix leastsquare on F2 0.02(2)

Full-matrix leastsquare on F2 0.00(2)

Full-matrix leastsquare on F2 0.02(1)

734/1/37

815/1/37

794/1/38

787/1/37

760/1/37

735/1/38

1.086

1.218

1.235

1.042

1.118

1.069

R1 ¼ 0.0388, wR2 ¼ 0.0642 R1 ¼ 0.0448, wR2 ¼ 0.0659

R1 ¼ 0.0182, wR2 ¼ 0.0414 R1 ¼ 0.0187, wR2 ¼ 0.0416

R1 ¼ 0.0138, wR2 ¼ 0.0305 R1 ¼ 0.0144, wR2 ¼ 0.0306 0.0453(8)

R1 ¼ 0.0187, wR2 ¼ 0.0317 R1 ¼ 0.0223, wR2 ¼ 0.0323

R1 ¼ 0.0165, wR2 ¼ 0.0353 R1 ¼ 0.0172, wR2 ¼ 0.0354

R1 ¼ 0.0146, wR2 ¼ 0.0295 R1 ¼ 0.0163, wR2 ¼ 0.0298 0.0151(4)

0.841 and 0.980 e/Å3

0.591 and 1.303 e/Å3

0.609 and 1.260 e/Å3

0.508 and 0.714 e/Å3

0.868 and 1.019 e/Å3

0.605 and 0.802 e/Å3

M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

Empirical formula Formula weight Space group Structure type Unit cell dimensions Volume Number of formula units per unit cell Calculated density Absorption coefficient F(000) Crystal color Crystal size Q range for data collection Index ranges

Table 2 Crystal data and structure refinement details of the R3Co0.5GeS7 (R ¼ Gd, Tb, Dy, Ho, Er and Tm) compounds.

Volume Number of formula units per unit cell Calculated density Absorption coefficient F(000) Crystal color Crystal size Q range for data collection Index ranges

Reflections collected Independent reflections Refinement method Absolute structure parameter Data/restraints/parameters Goodness-of-fit on F2 Final R indices [I > 2s(I)] R indices (all data) Extinction coefficient Largest diff. peak and hole

Gd3Co0.5GeS7 798.22 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.8909(8) Å c ¼ 5.7406(6) Å 486.36(8) Å3 2

Tb3Co0.5GeS7 803.23 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.8147(9) Å c ¼ 5.7376(7) Å 478.65(9) Å3 2

Dy3Co0.5GeS7 813.97 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.7509(8) Å c ¼ 5.7618(6) Å 474.44(7) Å3 2

Ho3Co0.5GeS7 821.27 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.6793(9) Å c ¼ 5.8006(6) Å 470.64(8) Å3 2

Er3Co0.5GeS7 828.26 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.6084(9) Å c ¼ 5.8432(8) Å 467.18(9) Å3 2

Tm3Co0.5GeS7 833.27 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.5621(6) Å c ¼ 5.8838(5) Å 465.90(6) Å3 2

5.451 g/cm3 25.499 mm1 699 Black 0.07  0.05  0.04 mm 4.27e27.42 12  h  12 12  k  12 7  l  7 4287 739 [R(int.) ¼ 0.0336]

5.573 g/cm3 27.289 mm1 705 Black 0.07  0.06  0.04 mm 4.15e27.75 12  h  12 12  k  12 7  l  7 6352 754 [R(int.) ¼ 0.0568]

5.698 g/cm3 28.796 mm1 711 Black 0.05  0.04  0.04 mm 4.28e27.40 12  h  12 12  k  12 7  l  7 6285 730 [R(int.) ¼ 0.0537]

5.795 g/cm3 30.430 mm1 717 Black 0.05  0.04  0.03 mm 3.51e27.46 12  h  12 12  k  12 7  l  7 6252 725 [R(int.) ¼ 0.0771]

5.888 g/cm3 32.197 mm1 723 Black 0.07  0.06  0.05 mm 3.49e27.44 12  h  12 12  k  12 7  l  7 6175 717 [R(int.) ¼ 0.0899]

Full-matrix least-square on F2 0.02(2) 739/1/37 1.165 R1 ¼ 0.0179, wR2 ¼ 0.0404

Full-matrix least-square on F2 0.03(2) 754/1/38 1.077 R1 ¼ 0.0217, wR2 ¼ 0.0418

Full-matrix least-square on F2 0.03(3) 730/1/38 1.075 R1 ¼ 0.0235, wR2 ¼ 0.0428

Full-matrix least-square on F2 0.00(5) 725/1/38 1.111 R1 ¼ 0.0371, wR2 ¼ 0.0856

Full-matrix least-square on F2 0.08(6) 717/1/39 1.353 R1 ¼ 0.0406, wR2 ¼ 0.0962

5.940 g/cm3 33.831 mm1 729 Black 0.09  0.05  0.04 mm 4.25e27.38 12  h  12 12  k  12 7  l  7 4072 711 [R(int.) ¼ 0.0524] Full-matrix least-square on F2 0.04(3) 711/1/39 1.065 R1 ¼ 0.0216, wR2 ¼ 0.0505

R1 ¼ 0.0193, wR2 ¼ 0.0407

R1 ¼ 0.0233, wR2 ¼ 0.0422 0.0068(3) 1.277 and 0.905 e/Å3

R1 ¼ 0.0252, wR2 ¼ 0.0432 0.0041(2) 1.151 and 0.871 e/Å3

R1 ¼ 0.0379, wR2 ¼ 0.0859

R1 ¼ 0.0424, wR2 ¼ 0.0968 0.0029(6) 1.777 and 1.719 e/Å3

0.682 and 1.104 e/Å

3

3

1.136 and 2.200 e/Å

R1 ¼ 0.0220, wR2 ¼ 0.0507 0.0141(7) 1.030 and 1.089 e/Å3

M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

Empirical formula Formula weight Space group Structure type Unit cell dimensions

447

448

Table 3 Crystal data and structure refinement details of the R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb and Dy) compounds.

Volume Number of formula units per unit cell Calculated density Absorption coefficient F(000) Crystal color Crystal size Q range for data collection Index ranges

Y3Ni0.5GeS7 593.09 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.7185(9) Å c ¼ 5.7832(7) Å 473.04(8) Å3 2

4.164 g/cm3 23.799 mm1 550 Black 0.08  0.06  0.05 mm 2.42e27.48 12  h  12 12  k  12 7  l  7 Reflections collected 6293 Independent reflections 735 [R(int.) ¼ 0.0862] Refinement method Full-matrix least-square on F2 Absolute structure parameter 0.02(1) Data/restraints/parameters 735/1/37 Goodness-of-fit on F2 1.110 Final R indices [I > 2s(I)] R1 ¼ 0.0376, wR2 ¼ 0.0609 R indices (all data) R1 ¼ 0.0412, wR2 ¼ 0.0619 Extinction coefficient Largest diff. peak and hole 0.790 and 0.865 e/Å3

Ce3Ni0.5GeS7 746.72 P63 (No. 173) La3Mn0.5SiS7 a ¼ 10.1920(8) Å c ¼ 5.7817(6)Å 520.12(8) Å3 2

Sm3Ni0.5GeS7 777.42 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.9597(6) Å c ¼ 5.7430(5) Å 493.36(6) Å3 2

Gd3Ni0.5GeS7 798.11 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.869(1) Å c ¼ 5.7321(7) Å 483.52(9) Å3 2

Tb3Ni0.5GeS7 803.13 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.8038(8) Å c ¼ 5.7373(6) Å 477.56(7) Å3 2

Dy3Ni0.5GeS7 813.86 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.7430(7) Å c ¼ 5.7727(5) Å 474.56(6) Å3 2

4.768 g/cm3 17.953 mm1 664 Black 0.05  0.04  0.03 mm 4.21e27.48 13  h  13 13  k  13 7  l  7 6843 796 [R(int.) ¼ 0.0453] Full-matrix least-square on F2 0.02(2) 796/1/38 1.136 R1 ¼ 0.0181, wR2 ¼ 0.0368 R1 ¼ 0.0197, wR2 ¼ 0.0372

5.233 g/cm3 22.940 mm1 688 Black 0.07  0.06  0.05 mm 4.26e27.33 12  h  12 12  k  12 7  l  7 4263 745 [R(int.) ¼ 0.0340] Full-matrix least-square on F2 0.00(2) 745/1/37 1.202 R1 ¼ 0.0168, wR2 ¼ 0.0415 R1 ¼ 0.0170, wR2 ¼ 0.0415

5.482 g/cm3 25.765 mm1 700 Black 0.06  0.05  0.03 mm 4.13e27.46 12  h  12 12  k  12 7  l  7 6411 748 [R(int.) ¼ 0.0651] Full-matrix least-square on F2 0.02(3) 748/1/37 1.199 R1 ¼ 0.0286, wR2 ¼ 0.0541 R1 ¼ 0.0306, wR2 ¼ 0.0547

5.585 g/cm3 27.468 mm-1 706 Black 0.08  0.05  0.04 mm 4.29e27.41 12  h  12 12  k  12 7  l  7 6297 734 [R(int.) ¼ 0.0591] Full-matrix least-square on F2 0.01(3) 734/1/37 1.205 R1 ¼ 0.0231, wR2 ¼ 0.0465 R1 ¼ 0.0243, wR2 ¼ 0.0469

0.836 and 0.550 e/Å3

0.596 and 1.137 e/Å3

0.855 and 1.330 e/Å3

0.721 and 1.063 e/Å3

5.696 g/cm3 28.906 mm1 712 Black 0.09  0.08  0.06 mm 4.28e27.46 12  h  12 12  k  12 7  l  7 4110 714 [R(int.) ¼ 0.0444] Full-matrix least-square on F2 0.01(5) 714/1/38 1.379 R1 ¼ 0.0413, wR2 ¼ 0.0819 R1 ¼ 0.0421, wR2 ¼ 0.0821 0.0020(4) 2.860 and 3.875 e/Å3

M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

Empirical formula Formula weight Space group Structure type Unit cell dimensions

M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

449

Table 4 Crystal data and structure refinement details of the R3Ni0.5GeS7 (R ¼ Ho, Er and Tm) compounds. Empirical formula Formula weight Space group Structure type Unit cell dimensions Volume Number of formula units per unit cell Calculated density Absorption coefficient F(000) Crystal color Crystal size Q range for data collection Index ranges

Reflections collected Independent reflections Refinement method Absolute structure parameter Data/restraints/parameters Goodness-of-fit on F2 Final R indices [I > 2s(I)] R indices (all data) Extinction coefficient Largest diff. peak and hole

Ho3Ni0.5GeS7 821.15 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.6826(7) Å c ¼ 5.8182(6) Å 472.39(7) Å3 2 5.773 g/cm3 30.436 mm1 718 Black 0.07  0.07  0.05 mm 3.50e27.38 11  h  12 12  k  12 7  l  7 4123 717 [R(int.) ¼ 0.0585] Full-matrix least-square on F2 0.01(2) 717/1/38 1.134 R1 ¼ 0.0185, wR2 ¼ 0.0382 R1 ¼ 0.0197, wR2 ¼ 0.0384 0.846 and 0.881 e/Å3

of the R3Ni0.5GeS7 materials (in the latter series no useful crystals were found for R ¼ La, Pr and Nd). The X-ray intensities data were collected on a KUMA Diffraction KM-4 four-circle diffractometer equipped with a CCD detector, using graphite-monochromatized MoKa radiation (l ¼ 0.71073 Å). The raw data were treated with the CrysAlis Data Reduction program [5] taking into account an absorption correction. The intensities of the reflections were corrected for Lorentz and polarization factors. The crystal structure was solved by Patterson methods and refined by the full-matrix least-squares method using SHELXL-97 [6]. Acentric space group P63 was checked with the PLATON program, and no additional symmetry elements were found [7]. The chemical compositions of all the examined single crystals were confirmed by EDX analysis (EDAX PV9800 microanalyzer). Magnetic studies were performed in the temperature range 1.72e400 K and in external magnetic fields up to 5 T employing a Quantum Design MPMS-5 SQUID magnetometer. For this purpose loose powders were placed in gelatin capsules, the contribution of which was taken into account in the experimental data evaluation. The magnetic measurements were carried out only for the samples proved by the powder XRD to be free of any foreign phases. 3. Results and discussion 3.1. Crystal structures The crystal structure of the R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) compounds was found to be hexagonal of the space group P63. The details on the crystal structure refinements are summarized in Tables 1e4, and the refined atomic coordinates and the thermal displacement factors are listed in Tables 5 and 6. In the unit cell of each compound, there are one position of R, one position of Co (Ni), one position of Ge and three positions of S. The sites of the R, Ge and S atoms are fully occupied. In contrast, the site occupancy factors for the Co (Ni) atoms observed in the refinements were always close to 0.5, and hence in the final

Er3Ni0.5GeS7 828.14 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.5896(7) Å c ¼ 5.8569(6) Å 466.44(7) Å3 2 5.896 g/cm3 32.368 mm1 724 Black 0.08  0.06  0.05 mm 3.48e27.46 12  h  12 12  k  12 7  l  7 6148 719 [R(int.) ¼ 0.0773] Full-matrix least-square on F2 0.01(3) 719/1/39 1.084 R1 ¼ 0.0221, wR2 ¼ 0.0492 R1 ¼ 0.0228, wR2 ¼ 0.0496 0.0080(4) 0.908 and 1.484 e/Å3

Tm3Ni0.5GeS7 883.15 P63 (No. 173) La3Mn0.5SiS7 a ¼ 9.532(1) Å c ¼ 5.886(1) Å 463.1(1) Å3 2 5.974 g/cm3 34.151 mm1 730 Black 0.07  0.06  0.04 mm 3.46e27.45 12  h  12 12  k  12 7  l  7 6117 714 [R(int.) ¼ 0.0784] Full-matrix least-square on F2 0.00(3) 714/1/39 1.084 R1 ¼ 0.0253, wR2 ¼ 0.0532 R1 ¼ 0.0258, wR2 ¼ 0.0534 0.0148(7) 1.062 and 1.391 e/Å3

calculations they were fixed at this value. It should be noted that the derived occupancy factors satisfy charge balance requirements for each of the compound considered. It is also worth stressing that for the two series no indication of superstructure formation was observed, and the experimental data were in good accordance with the La3Mn0.5SiS7 structure type. The unit cell and coordination polyhedra of La, Co and Ge atoms in the structure of La3Co0.5GeS7 are shown in Fig. 1. The La atoms form [LaS14S23S31] bi-capped trigonal prisms. The Co atoms ale located practically in the centres of [CoS16] octahedra, while the Ge atoms form [GeS23S31] tetrahedra. All the polyhedra in the crystal structure of La3Co0.5GeS7 are mutually connected by corners or faces. The relevant interatomic distances and the coordination numbers of the R, Co (Ni) and Ge atoms for the R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) compounds are listed in Tables 7 and 8, respectively. All the interatomic distances are close to the sums of the respective ionic radii [8]. The shortest ReS distances systematically decrease on going from La to Tm, reflecting the lanthanide contraction. The observed shortening of the CoeS and NieS distances follow the changes in the unit cell volumes. Figs. 2 and 3 show the hexagonal lattice parameters (a and c) and the unit cell volume (V) for the R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) compounds, respectively, as a function of the ionic radii of the rare earth elements. The observed variation of the unit cell volumes for both series follows the lanthanide contraction. The lattice parameters a systematically decrease with decreasing the R ionic radii, whereas the change of the lattice parameters c with decreasing the R ionic radii is not regular. 3.2. Magnetic properties Fig. 4 presents the results of magnetic measurements performed on powder samples of Sm3Co0.5GeS7 and Gd3Co0.5GeS7. The inverse magnetic susceptibility of the former compound is strongly curvilinear over the entire temperature range studied, which reflects

Table 5 Atomic coordinates and thermal displacement factors for R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm). Atom

Posi-tion

Y3Co0.5GeS7 Y 6c Co 2a Ge 2b S1 6c S2 6c S3 2b La3Co0.5GeS7 La 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Ce3Co0.5GeS7 Ce 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Pr3Co0.5GeS7 Pr 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Nd3Co0.5GeS7 Nd 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Sm3Co0.5GeS7 Sm 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Gd3Co0.5GeS7 Gd 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Tb3Co0.5GeS7 Tb 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Dy3Co0.5GeS7 Dy 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Ho3Co0.5GeS7 Ho 6c Co 2a Ge 2b S1 6c S2 6c S3 2b Er3Co0.5GeS7 Er 6c Co 2a Ge 2b S1 6c S2 6c S3 2b

x/a

y/b

z/c

Occupancy

Ueq., Å2

U11

U22

U33

U23

U13

U12

0.35800(8) 0 2/3 0.1505(2) 0.5750(2) 2/3

0.13771(8) 0 1/3 0.2486(2) 0.0962(2) 1/3

0.4580(1) 0.7517(7) 0.8793(2) 0.5032(3) 0.7208(3) 0.2560(6)

1 0.50 1 1 1 1

0.0114(1) 0.0111(8) 0.0096(3) 0.0137(4) 0.0098(4) 0.0111(7)

0.0092(3) 0.008(1) 0.0101(5) 0.0108(9) 0.0106(9) 0.011(1)

0.0101(4) 0.008(1) 0.0101(5) 0.0117(9) 0.0079(9) 0.011(1)

0.0146(4) 0.017(2) 0.0085(7) 0.020(1) 0.0103(9) 0.010(1)

0.0010(4) 0 0 0.0026(8) 0.0000(8) 0

0.0013(4) 0 0 0.0022(8) 0.0013(9) 0

0.0047(3) 0.0041(5) 0.0050(2) 0.0073(8) 0.0041(8) 0.0056(5)

0.22972(2) 0 1/3 0.2426(1) 0.4786(1) 1/3

0.35603(2) 0 2/3 0.0858(1) 0.5852(1) 2/3

0.5375(1) 0.2754(7) 0.1192(1) 0.5234(3) 0.2664(2) 0.7449(4)

1 0.50 1 1 1 1

0.00801(9) 0.0123(4) 0.0074(1) 0.0120(2) 0.0088(2) 0.0102(4)

0.0079(1) 0.0098(6) 0.0083(3) 0.0132(5) 0.0082(5) 0.0120(6)

0.0072(1) 0.0098(6) 0.0083(3) 0.0080(5) 0.0098(5) 0.0120(6)

0.0080(1) 0.017(1) 0.0057(4) 0.0155(5) 0.0094(5) 0.006(1)

0.0009(1) 0 0 0.0013(6) 0.0010(5) 0

0.0001(1) 0 0 0.0001(7) 0.0005(5) 0

0.00320(9) 0.0049(3) 0.0041(1) 0.0057(4) 0.0052(5) 0.0060(3)

0.35597(2) 0 2/3 0.1567(1) 0.5841(1) 2/3

0.12696(2) 0 1/3 0.2433(1) 0.1047(1) 1/3

0.46257(9) 0.7265(5) 0.8809(1) 0.4776(2) 0.7312(1) 0.2562(3)

1 0.50 1 1 1 1

0.00770(8) 0.0116(3) 0.0074(1) 0.0115(1) 0.0087(1) 0.0096(3)

0.0063(1) 0.0097(5) 0.0083(2) 0.0087(4) 0.0085(4) 0.0116(5)

0.0081(1) 0.0097(5) 0.0083(2) 0.0113(4) 0.0080(4) 0.0116(5)

0.0086(1) 0.0155(8) 0.0058(3) 0.0160(4) 0.0104(4) 0.0057(8)

0.0007(1) 0 0 0.0012(5) 0.0006(4) 0

0.0007(1) 0 0 0.0021(5) 0.0015(4) 0

0.00361(8) 0.0049(2) 0.0041(1) 0.0061(3) 0.0046(4) 0.0058(3)

0.35599(3) 0 2/3 0.1564(1) 0.5832(1) 2/3

0.12781(3) 0 1/3 0.2444(1) 0.1035(1) 1/3

0.4624(1) 0.7279(8) 0.8803(1) 0.4795(3) 0.7299(2) 0.2560(4)

1 0.50 1 1 1 1

0.00854(8) 0.0127(5) 0.0079(2) 0.0120(3) 0.0092(3) 0.0099(5)

0.0073(1) 0.0108(7) 0.0087(3) 0.0089(6) 0.0096(8) 0.0120(8)

0.0090(1) 0.0108(7) 0.0087(3) 0.0113(6) 0.0088(7) 0.0120(8)

0.0091(1) 0.016(1) 0.0062(4) 0.0169(7) 0.0104(6) 0.005(1)

0.0008(2) 0 0 0.0000(9) 0.0013(6) 0

0.0009(2) 0 0 0.0017(9) 0.0019(7) 0

0.0040(1) 0.0054(4) 0.0043(1) 0.0058(5) 0.0054(6) 0.0060(4)

0.22766(3) 0 1/3 0.2448(1) 0.4800(1) 1/3

0.35617(2) 0 2/3 0.0887(1) 0.5824(1) 2/3

0.5374(1) 0.2694(7) 0.1195(1) 0.5192(3) 0.2712(2) 0.7428(4)

1 0.50 1 1 1 1

0.00876(8) 0.0114(4) 0.0085(2) 0.0122(2) 0.0093(2) 0.0103(5)

0.0093(1) 0.0111(6) 0.0103(3) 0.0131(5) 0.0098(6) 0.0139(7)

0.0085(1) 0.0111(6) 0.0103(3) 0.0095(5) 0.0105(6) 0.0139(7)

0.0076(1) 0.012(1) 0.0049(4) 0.0145(6) 0.0079(5) 0.003(1)

0.0006(1) 0 0 0.0017(6) 0.0014(5) 0

0.0001(1) 0 0 0.0004(7) 0.0009(5) 0

0.0039(1) 0.0055(3) 0.0051(1) 0.0059(4) 0.0052(5) 0.0070(4)

0.22638(3) 0 1/3 0.2463(1) 0.4805(1) 1/3

0.35635(2) 0 2/3 0.0907(1) 0.5807(1) 2/3

0.5380(1) 0.2671(7) 0.1196(1) 0.5147(3) 0.2738(2) 0.7417(4)

1 0.50 1 1 1 1

0.00822(9) 0.0108(5) 0.0075(2) 0.0110(3) 0.0083(3) 0.0087(5)

0.0081(1) 0.0088(6) 0.0089(3) 0.0104(6) 0.0078(6) 0.0108(7)

0.0071(1) 0.0088(6) 0.0089(3) 0.0085(5) 0.0094(7) 0.0108(7)

0.0085(1) 0.014(1) 0.0047(4) 0.0140(7) 0.0085(6) 0.004(1)

0.0007(1) 0 0 0.0008(6) 0.0005(6) 0

0.0000(1) 0 0 0.0009(7) 0.0005(6) 0

0.0032(1) 0.0044(3) 0.0044(1) 0.0047(5) 0.0048(5) 0.0054(4)

0.35668(3) 0 2/3 0.1546(1) 0.5790(1) 2/3

0.13203(3) 0 1/3 0.2476(1) 0.0984(1) 1/3

0.4612(1) 0.7395(7) 0.8801(1) 0.4899(3) 0.7244(3) 0.2580(5)

1 0.50 1 1 1 1

0.00783(9) 0.0113(7) 0.0067(3) 0.0104(3) 0.0082(3) 0.0081(5)

0.0063(1) 0.0090(7) 0.0076(3) 0.0079(6) 0.0097(8) 0.0090(8)

0.0079(1) 0.0090(7) 0.0076(3) 0.0097(6) 0.0064(7) 0.0090(8)

0.0089(1) 0.0160(19) 0.0049(5) 0.0149(8) 0.0086(7) 0.006(1)

0.0008(1) 0 0 0.0016(7) 0.0003(6) 0

0.0011(1) 0 0 0.0028(7) 0.0007(7) 0

0.0034(1) 0.0045(4) 0.0038(1) 0.0055(5) 0.0042(6) 0.0045(4)

0.22311(4) 0 1/3 0.2480(2) 0.4802(2) 1/3

0.35713(3) 0 2/3 0.0948(2) 0.5775(2) 2/3

0.5396(1) 0.2556(8) 0.1197(2) 0.5054(4) 0.2772(3) 0.7417(5)

1 0.50 1 1 1 1

0.0084(1) 0.0094(8) 0.0072(3) 0.0115(4) 0.0082(4) 0.0086(7)

0.0078(1) 0.0078(9) 0.0082(4) 0.0093(8) 0.0079(9) 0.010(1)

0.0066(1) 0.0078(9) 0.0082(4) 0.0073(8) 0.0095(9) 0.010(1)

0.0100(1) 0.013(2) 0.0050(6) 0.018(1) 0.0083(8) 0.004(1)

0.0010(2) 0 0 0.0013(7) 0.0007(8) 0

0.0003(2) 0 0 0.0023(8) 0.0006(7) 0

0.0030(1) 0.0039(4) 0.0041(2) 0.0043(7) 0.0051(8) 0.0053(5)

0.35766(4) 0 2/3 0.1513(2) 0.5758(2) 2/3

0.13665(4) 0 1/3 0.2482(2) 0.0961(3) 1/3

0.4594(1) 0.7497(8) 0.8803(2) 0.5012(4) 0.7216(4) 0.2571(6)

1 0.50 1 1 1 1

0.0092(1) 0.010(1) 0.0079(3) 0.0117(5) 0.0083(4) 0.0092(7)

0.0074(1) 0.009(1) 0.0092(5) 0.0100(9) 0.010(1) 0.011(1)

0.0090(1) 0.009(1) 0.0092(5) 0.0095(9) 0.007(1) 0.011(1)

0.0106(1) 0.010(3) 0.0052(7) 0.016(1) 0.008(1) 0.003(1)

0.0009(3) 0 0 0.0028(8) 0.0003(9) 0

0.0010(2) 0 0 0.0030(8) 0.0007(9) 0

0.0037(1) 0.0049(5) 0.0046(2) 0.0055(7) 0.0050(9) 0.0060(6)

0.21800(8) 0 1/3 0.2486(6) 0.4783(5) 1/3

0.35855(8) 0 2/3 0.1000(5) 0.5733(5) 2/3

0.5420(2) 0.242(1) 0.1196(5) 0.4905(7) 0.2773(7) 0.743(1)

1 0.50 1 1 1 1

0.0090(2) 0.012(2) 0.0073(7) 0.0110(9) 0.0076(8) 0.009(1)

0.0083(3) 0.008(2) 0.008(1) 0.012(2) 0.007(2) 0.012(2)

0.0068(4) 0.008(2) 0.008(1) 0.007(2) 0.009(2) 0.012(2)

0.0110(3) 0.020(5) 0.005(1) 0.016(2) 0.009(1) 0.005(3)

0.0022(4) 0 0 0.001(1) 0.001(1) 0

0.0008(4) 0 0 0.004(1) 0.000(1) 0

0.0032(3) 0.004(1) 0.0041(5) 0.006(1) 0.004(1) 0.006(1)

0.21486(9) 0 1/3 0.2496(7) 0.4772(7) 1/3

0.35905(9) 0 2/3 0.1028(6) 0.5701(7) 2/3

0.5431(3) 0.235(1) 0.1189(6) 0.4836(9) 0.2768(9) 0.744(1)

1 0.50 1 1 1 1

0.0117(3) 0.012(2) 0.0099(9) 0.012(1) 0.011(1) 0.010(1)

0.0108(4) 0.013(3) 0.009(1) 0.012(3) 0.010(3) 0.012(3)

0.0094(5) 0.013(3) 0.009(1) 0.012(3) 0.014(3) 0.012(3)

0.0146(4) 0.010(6) 0.009(1) 0.016(3) 0.012(2) 0.006(4)

0.0008(6) 0 0 0.000(1) 0.001(2) 0

0.0006(6) 0 0 0.001(1) 0.001(2) 0

0.0049(4) 0.006(1) 0.0050(6) 0.009(2) 0.009(2) 0.006(1)

Table 5 (continued ) Atom

Posi-tion

Tm3Co0.5GeS7 Tm 6c Co 2a Ge 2b S1 6c S2 6c S3 2b

x/a

y/b

z/c

Occupancy

Ueq., Å2

U11

U22

U33

U23

U13

U12

0.35976(5) 0 2/3 0.1436(4) 0.5677(3) 2/3

0.14732(5) 0 1/3 0.2498(4) 0.0919(3) 1/3

0.4548(1) 0.7699(8) 0.8809(3) 0.5233(5) 0.7211(4) 0.2544(7)

1 0.50 1 1 1 1

0.0101(1) 0.008(1) 0.0076(5) 0.0110(5) 0.0085(5) 0.0071(9)

0.0078(2) 0.007(1) 0.0091(7) 0.009(1) 0.010(1) 0.007(1)

0.0102(2) 0.007(1) 0.0091(7) 0.009(1) 0.008(1) 0.007(1)

0.0114(2) 0.010(2) 0.0048(7) 0.014(1) 0.007(1) 0.005(1)

0.0006(3) 0 0 0.0016(9) 0.000(1) 0

0.0008(3) 0 0 0.002(1) 0.001(1) 0

0.0037(1) 0.0038(7) 0.0045(3) 0.004(1) 0.005(1) 0.0039(7)

Ueq. is defined as one third of the trace of the orthogonalized Uij tensor. The anisotropic temperature factor exponent takes the form: 2p2[h2a*2U11 þ … þ 2hka*b*U12]. Table 6 Atomic coordinates and thermal displacement factors for R3Ni0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm). Atom

Posi-tion

Y3Ni0.5GeS7 Y 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Ce3Ni0.5GeS7 Ce 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Sm3Ni0.5GeS7 Sm 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Gd3Ni0.5GeS7 Gd 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Tb3Ni0.5GeS7 Tb 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Dy3Ni0.5GeS7 Dy 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Ho3Ni0.5GeS7 Ho 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Er3Ni0.5GeS7 Er 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b Tm3Ni0.5GeS7 Tm 6c Ni 2a Ge 2b S1 6c S2 6c S3 2b

x/a

y/b

z/c

Occupancy

Ueq., Å2

U11

U22

U33

U23

U13

U12

0.35748(7) 0 2/3 0.1495(2) 0.5751(2) 2/3

0.13742(7) 0 1/3 0.2468(2) 0.0955(2) 1/3

0.4579(1) 0.7546(7) 0.8791(2) 0.5020(4) 0.7215(4) 0.2566(6)

1 0.50 1 1 1 1

0.0101(1) 0.0105(8) 0.0082(3) 0.0138(4) 0.0094(4) 0.0103(7)

0.0080(3) 0.0080(8) 0.0089(4) 0.0088(8) 0.0104(8) 0.0105(9)

0.0096(3) 0.0080(8) 0.0089(4) 0.0114(8) 0.0075(8) 0.0105(9)

0.0119(4) 0.016(2) 0.0067(7) 0.021(1) 0.011(1) 0.009(1)

0.0013(4) 0 0 0.0016(9) 0.0008(8) 0

0.0013(4) 0 0 0.0020(8) 0.0004(9) 0

0.0038(3) 0.0040(4) 0.0044(2) 0.0054(7) 0.0052(7) 0.0052(5)

0.22843(3) 0 1/3 0.2413(1) 0.4788(1) 1/3

0.35564(3) 0 2/3 0.0861(1) 0.5834(1) 2/3

0.5377(1) 0.2728(7) 0.1191(1) 0.5231(3) 0.2682(2) 0.7443(4)

1 0.50 1 1 1 1

0.0087(1) 0.0128(4) 0.0084(2) 0.0134(3) 0.0103(3) 0.0110(5)

0.0084(1) 0.0123(6) 0.0094(3) 0.0127(6) 0.0092(6) 0.0131(8)

0.0076(1) 0.0123(6) 0.0094(3) 0.0084(5) 0.0117(7) 0.0131(8)

0.0090(1) 0.013(1) 0.0064(4) 0.0194(6) 0.0103(6) 0.006(1)

0.0008(1) 0 0 0.0032(8) 0.0013(6) 0

0.0002(1) 0 0 0.0005(9) 0.0003(6) 0

0.0032(1) 0.0062(3) 0.0046(1) 0.0056(5) 0.0054(5) 0.0065(4)

0.22593(3) 0 1/3 0.2441(1) 0.4805(1) 1/3

0.35586(3) 0 2/3 0.0898(1) 0.5807(1) 2/3

0.5380(1) 0.2643(6) 0.1193(1) 0.5155(3) 0.2730(2) 0.7423(4)

1 0.50 1 1 1 1

0.00668(9) 0.0079(5) 0.0055(2) 0.0100(3) 0.0069(3) 0.0072(5)

0.0066(1) 0.0066(6) 0.0066(3) 0.0083(5) 0.0058(6) 0.0080(7)

0.0054(1) 0.0066(6) 0.0066(3) 0.0061(5) 0.0079(6) 0.0080(7)

0.0070(1) 0.010(1) 0.0034(4) 0.0151(6) 0.0069(6) 0.005(1)

0.0007(1) 0 0 0.0014(6) 0.0012(5) 0

0.0000(1) 0 0 0.0020(7) 0.0004(5) 0

0.00237(9) 0.0033(3) 0.0032(1) 0.0033(4) 0.0033(5) 0.0040(3)

0.35627(4) 0 2/3 0.1535(3) 0.5788(3) 2/3

0.13202(4) 0 1/3 0.2457(3) 0.0984(3) 1/3

0.4613(1) 0.740(1) 0.8798(3) 0.4884(5) 0.7253(4) 0.2580(7)

1 0.50 1 1 1 1

0.0088(1) 0.010(1) 0.0079(4) 0.0131(5) 0.0091(5) 0.0089(9)

0.0072(2) 0.009(1) 0.0089(5) 0.011(1) 0.010(1) 0.008(1)

0.0091(2) 0.009(1) 0.0089(5) 0.009(1) 0.006(1) 0.008(1)

0.0099(2) 0.010(3) 0.0058(7) 0.019(1) 0.009(1) 0.009(2)

0.0006(3) 0 0 0.000(1) 0.000(1) 0

0.0002(3) 0 0 0.002(1) 0.002(1) 0

0.0039(1) 0.0050(5) 0.0045(3) 0.0061(9) 0.004(1) 0.0044(6)

0.22279(4) 0 1/3 0.2456(2) 0.4800(2) 1/3

0.35672(4) 0 2/3 0.0938(2) 0.5776(3) 2/3

0.5398(1) 0.2527(7) 0.1197(2) 0.5053(4) 0.2764(3) 0.7420(6)

1 0.50 1 1 1 1

0.0079(1) 0.0085(9) 0.0063(3) 0.0113(5) 0.0075(4) 0.0071(7)

0.0075(1) 0.007(1) 0.0074(5) 0.0088(9) 0.006(1) 0.007(1)

0.0060(1) 0.007(1) 0.0074(5) 0.0069(9) 0.008(1) 0.007(1)

0.0093(1) 0.010(3) 0.0042(6) 0.017(1) 0.0084(9) 0.005(1)

0.0008(2) 0 0 0.0004(8) 0.0011(9) 0

0.0004(2) 0 0 0.0040(9) 0.0011(8) 0

0.0028(1) 0.0038(5) 0.0037(2) 0.0034(8) 0.0045(9) 0.0039(5)

0.35719(7) 0 2/3 0.1501(5) 0.5753(5) 2/3

0.13668(7) 0 1/3 0.2460(5) 0.0951(5) 1/3

0.4588(3) 0.752(1) 0.8813(5) 0.5004(8) 0.7230(7) 0.255(1)

1 0.50 1 1 1 1

0.0090(2) 0.006(1) 0.0059(6) 0.0120(9) 0.0074(7) 0.007(1)

0.0078(4) 0.005(1) 0.0064(8) 0.007(1) 0.008(1) 0.009(2)

0.0083(3) 0.005(1) 0.0064(8) 0.009(1) 0.006(1) 0.009(2)

0.0107(3) 0.009(5) 0.004(1) 0.020(3) 0.007(1) 0.006(3)

0.0000(5) 0 0 0.002(1) 0.000(1) 0

0.0005(4) 0 0 0.002(1) 0.001(1) 0

0.0040(3) 0.0025(9) 0.0032(4) 0.005(1) 0.004(1) 0.004(1)

0.21735(4) 0 1/3 0.2488(3) 0.4782(3) 1/3

0.35811(4) 0 2/3 0.1002(2) 0.5726(3) 2/3

0.5427(1) 0.2372(7) 0.1195(2) 0.4913(4) 0.2779(3) 0.7438(5)

1 0.50 1 1 1 1

0.0120(1) 0.016(1) 0.0075(3) 0.0146(5) 0.0094(4) 0.0092(7)

0.0101(1) 0.010(1) 0.0090(5) 0.011(1) 0.009(1) 0.011(1)

0.0094(1) 0.010(1) 0.0090(5) 0.0090(9) 0.012(1) 0.011(1)

0.0165(1) 0.028(3) 0.0045(5) 0.023(1) 0.0086(8) 0.004(1)

0.0007(3) 0 0 0.0008(8) 0.000(1) 0

0.0009(2) 0 0 0.0054(8) 0.0001(9) 0

0.0047(1) 0.0054(5) 0.0045(2) 0.0055(8) 0.0064(9) 0.0057(6)

0.21404(5) 0 1/3 0.2470(4) 0.4764(3) 1/3

0.35889(5) 0 2/3 0.1022(3) 0.5692(3) 2/3

0.5443(1) 0.2304(9) 0.1200(3) 0.4820(5) 0.2784(5) 0.7467(8)

1 0.50 1 1 1 1

0.0094(1) 0.008(1) 0.0067(4) 0.0113(6) 0.0084(6) 0.0063(9)

0.0098(2) 0.006(1) 0.0073(6) 0.009(1) 0.008(1) 0.007(1)

0.0076(3) 0.006(1) 0.0073(6) 0.006(1) 0.008(1) 0.007(1)

0.0100(2) 0.011(3) 0.0054(8) 0.017(1) 0.008(1) 0.004(2)

0.0007(3) 0 0 0.000(1) 0.001(1) 0

0.0006(3) 0 0 0.005(1) 0.000(1) 0

0.0038(1) 0.0034(7) 0.0037(3) 0.003(1) 0.004(1) 0.0037(7)

0.35949(6) 0 2/3 0.1424(4) 0.5681(4) 2/3

0.14789(6) 0 1/3 0.2471(4) 0.0923(4) 1/3

0.4568(1) 0.775(1) 0.8823(4) 0.5261(6) 0.7232(5) 0.2551(9)

1 0.50 1 1 1 1

0.0090(1) 0.009(1) 0.0057(6) 0.0103(6) 0.0074(7) 0.005(1)

0.0070(3) 0.008(1) 0.0063(8) 0.006(1) 0.009(1) 0.006(1)

0.0090(3) 0.008(1) 0.0063(8) 0.008(1) 0.006(1) 0.006(1)

0.0103(2) 0.011(3) 0.004(1) 0.016(1) 0.007(1) 0.003(2)

0.0005(4) 0 0 0.002(1) 0.000(1) 0

0.0008(4) 0 0 0.002(1) 0.000(1) 0

0.0034(2) 0.0042(9) 0.0031(4) 0.003(1) 0.005(1) 0.0032(9)

Ueq. is defined as one third of the trace of the orthogonalized Uij tensor. The anisotropic temperature factor exponent takes the form: 2p2[h2a*2U11 þ … þ 2hka*b*U12].

4

6

8

2.652(3) 2.701(3) 2.724(3) 2.782(3) 2.840(3) 2.819(1) 3.032(3) 3.468(3) 2.533(4) 2.556(4) 2.197(4) 2.219(3) 2.667(5) 2.715(5) 2.733(5) 2.788(6) 2.837(4) 2.848(6) 3.012(6) 3.396(5) 2.541(7) 2.555(7) 2.191(8) 2.215(6) 2.680(4) 2.727(4) 2.764(4) 2.791(4) 2.855(5) 2.859(3) 3.000(5) 3.332(4) 2.543(6) 2.556(6) 2.182(7) 2.212(5) 2.696(2) 2.735(2) 2.801(2) 2.793(2) 2.866(2) 2.887(1) 2.987(2) 3.259(2) 2.552(3) 2.562(3) 2.171(4) 2.218(2) 2.712(1) 2.744(1) 2.833(2) 2.802(1) 2.883(2) 2.908(1) 2.980(1) 3.206(2) 2.565(3) 2.566(3) 2.169(3) 2.218(2) 2.734(1) 2.758(1) 2.866(1) 2.821(1) 2.905(1) 2.936(1) 2.983(1) 3.178(1) 2.578(3) 2.580(3) 2.169(3) 2.221(1) 2.758(1) 2.775(1) 2.904(1) 2.841(1) 2.929(1) 2.964(1) 2.990(1) 3.158(1) 2.581(3) 2.596(3) 2.172(2) 2.221(1) 2.790(1) 2.797(1) 2.944(1) 2.869(1) 2.961(1) 3.0009(9) 3.010(1) 3.144(1) 2.600(2) 2.602(2) 2.171(2) 2.221(1) 2.807(1) 2.812(1) 2.960(2) 2.886(1) 2.978(1) 3.022(1) 3.023(1) 3.147(2) 2.606(3) 2.616(3) 2.169(2) 2.221(1) 2.8260(9) 2.8294(9) 2.981(1) 2.903(1) 2.998(1) 3.0421(8) 3.036(1) 3.145(1) 2.615(1) 2.621(1) 2.170(1) 2.223(1) 2.853(1) 2.857(1) 3.003(1) 2.931(1) 3.028(1) 3.0727(9) 3.060(1) 3.158(1) 2.629(2) 2.642(2) 2.175(2) 2.224(1) Ge

Co

Tm3Co0.5GeS7 Er3Co0.5GeS7 Ho3Co0.5GeS7 Dy3Co0.5GeS7 Tb3Co0.5GeS7 Gd3Co0.5GeS7 Sm3Co0.5GeS7 Nd3Co0.5GeS7 Pr3Co0.5GeS7 Ce3Co0.5GeS7 La3Co0.5GeS7 Y3Co0.5GeS7

d, Å

2.689(1) 2.736(1) 2.787(2) 2.788(2) 2.863(2) 2.878(1) 2.994(2) 3.283(2) 2.552(3) 2.562(3) 2.175(4) 2.213(2) -1S1 -1S1 -1S1 -1S2 -1S2 -1S3 -1S2 -1S1 -3S1 -3S1 -1S3 -3S2 R

Fig. 1. Unit cell and coordination polyhedra of the La, Co and Ge atoms in the structure of La3Co0.5GeS7.

Atoms

small energy separation of the terms 6H5/2 and 6H7/2 originating from the ground multiplet of trivalent samarium ions [9]. No indication of any long-range magnetic ordering was found neither in the low-temperature c(T) data nor in the field variation of the magnetization s(H) taken at 1.72 K (see the insets to Fig. 4). Above about 100 K, the magnetic susceptibility of this compound can be described by the modified CurieeWeiss law c(Τ) ¼ C/(T  qp) þ c0. In contrast, the inverse magnetic susceptibility of Gd3Co0.5GeS7 follows the regular CurieeWeiss (CW) function, where c0 ¼ 0. The CW parameters derived for both compounds are listed in Table 9. Presuming that besides the R atoms also cobalt possibly contributes to the overall magnetic properties of Sm3Co0.5GeS7 and Gd3Co0.5GeS7, the experimentally derived Curie constants C should be compared with the theoretical values Cteo calculated as Cteo ¼ ð1=8Þð3m2R þ ð1=2Þm2Co Þ, where mR and mCo stand for the effective magnetic moments of R and Co ions, respectively, and the number of particular magnetic species in the formula unit is taken into account. The Cteo values obtained assuming that Sm and Gd are in their stable trivalent states, while Co ions are divalent (assigned by direct analogy to the divalent Fe ions in the isostructural R3Fe0.5GeS7 compounds; see Ref. [4]) are listed in Table 9. In the calculations, the free-ion mR moments given by the Russell-Saunders LS-coupling scenario (see the Table) and the spin-only moment of Co2þ (mCo ¼ 3.87 mB) were used. As can be inferred from the results, for each compound, the so-calculated Cteo value is fairly close to the experimental C value, hence corroborating the presumed oxidation states of the R and Co ions. For Sm3Co0.5GeS7, the paramagnetic Curie temperature qp is strongly negative, and this feature may be caused by the closeness of the 6H5/2 and 6H7/2 terms, typical for Sm-based compounds. For Gd3Co0.5GeS7, qp is also negative, yet its magnitude is much smaller and seems to reflect antiferromagnetic correlations between the magnetic ions. Though no obvious indication of any magnetic phase transition is observed in the c(T) data (see the upper inset to Fig. 4), some tendency of flattening of this variation below ca. 4 K hints at possible formation in this compound of magnetically ordered state. In line with such a hypothesis, the magnetization isotherm s(H) measured at 1.72 K (cf. the lower inset to Fig. 4) shows a tiny metamagnetic-like inflection near 2 T. The low-temperature magnetic properties of the ternaries R3Ni0.5GeS7 (R ¼ Gd, Dy, Er and Tm) are displayed in Fig. 5. For each

C.N.

M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

Table 7 Interatomic distances (d, Å) and coordination numbers (C.N.) of the R, Co and Ge atoms in R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm).

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M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

453

Table 8 Interatomic distances (d, Å) and coordination numbers (C.N.) of the R, Ni and Ge atoms in R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm).

d, Å

Atoms

R

Ni Ge

-1S1 -1S1 -1S1 -1S2 -1S2 -1S3 -1S2 -1S1 -3S1 -3S1 -1S3 -3S2

C.N.

Y3Ni0.5GeS7

Ce3Ni0.5GeS7

Sm3Ni0.5GeS7

Gd3Ni0.5GeS7

Tb3Ni0.5GeS7

Dy3Ni0.5GeS7

Ho3Ni0.5GeS7

Er3Ni0.5GeS7

Tm3Ni0.5GeS7

2.8260(9) 2.8294(9) 2.981(1) 2.903(1) 2.998(1) 3.0421(8) 3.036(1) 3.145(1) 2.615(1) 2.621(1) 2.170(1) 2.223(1)

2.734(1) 2.758(1) 2.866(1) 2.821(1) 2.905(1) 2.936(1) 2.983(1) 3.178(1) 2.578(3) 2.580(3) 2.169(3) 2.221(1)

2.747(1) 2.760(1) 2.910(1) 2.843(1) 2.929(1) 2.965(1) 2.986(1) 3.156(1) 2.565(2) 2.572(2) 2.165(2) 2.217(1)

2.723(2) 2.745(2) 2.875(3) 2.820(2) 2.904(3) 2.933(1) 2.978(3) 3.170(3) 2.553(4) 2.568(4) 2.168(4) 2.214(3)

2.704(2) 2.733(2) 2.836(2) 2.806(2) 2.884(2) 2.908(1) 2.978(2) 3.212(2) 2.538(3) 2.555(3) 2.167(3) 2.212(2)

2.689(4) 2.723(4) 2.812(5) 2.805(4) 2.875(4) 2.892(3) 2.978(4) 3.267(5) 2.534(6) 2.550(6) 2.161(7) 2.225(4)

2.680(2) 2.724(2) 2.770(2) 2.797(2) 2.862(2) 2.863(1) 3.006(2) 3.339(2) 2.540(3) 2.567(3) 2.186(3) 2.219(2)

2.659(3) 2.705(3) 2.730(3) 2.784(3) 2.847(3) 2.837(2) 3.020(3) 3.424(3) 2.523(4) 2.534(4) 2.186(5) 2.213(3)

2.646(4) 2.702(3) 2.703(4) 2.783(3) 2.829(3) 2.816(2) 3.032(4) 3.479(3) 2.521(5) 2.523(5) 2.195(5) 2.209(4)

8

6 4

compound, the reciprocal magnetic susceptibility exhibits a straight-line behaviour at least above 100 K. Applying the CW law to these data yielded the CW parameters gathered in Table 9. Remarkably, the qp values do not show any systematic variation with changing the rare-earth element R, and for Er3Ni0.5GeS7 it is positive, despite the observed antiferromagnetic ordering (see below). Alike for the Co-bearing counterparts, the Cure constants are close to the theoretical values Cteo ¼ ð1=8Þð3m2R þ ð1=2Þm2Ni Þ with mNi ¼ 2.83 mB representing the spin-only effective magnetic moment of the divalent Ni ion and mR being the Russell-Saunders effective magnetic moment of the trivalent rare-earth ions (see Table 9). At low temperatures, the c(T) curves of Dy3Ni0.5GeS7, Er3Ni0.5GeS7 and Tm3Ni0.5GeS7 slightly deviate from the CW behaviour, likely due to crystalline electric field (CEF) interactions. In turn, pronounced maxima in these variations occurring near 6e7 K mark the onsets of magnetically ordered states. In the case of the Er- and Tm-based materials, the maxima are fairly broad, yet no other anomaly is seen down to 1.72 K. The magnetization isotherms s(H) measured at this terminal temperature have a shape characteristic of metamagnets with the critical field of about 0.5 and 1 T, respectively (see the insets to Fig. 5). In strong magnetic fields, the magnetization of Er3Ni0.5GeS7 nearly saturates at a value of 125 emu/g that corresponds to the magnetic moment of 18.5 mB per formula unit. In Tm3Ni0.5GeS7, s(H) exhibits some tendency for saturation, and the moment achieved in 5 T amounts to 9.8 mB per formula unit. These values are distinctly smaller than those expected for magnetic lattices built of free Er3þ (9 mB per ion) and Tm3þ (9 mB per ion), respectively. Additionally, based on the

paramagnetic susceptibility data, some sizable contribution to the magnitude of s(H) of the two compounds is expected from their Ni sublattices. Hence, the observed reduction of the magnetization in strong magnetic fields should be attributed primarily to the CEF effect acting on the R ions. The magnetic behaviour in Dy3Ni0.5GeS7 is distinctly different from that established for Er3Ni0.5GeS7 and Tm3Ni0.5GeS7. Namely, the maximum in c(T) is much narrower, and the susceptibility sharply changes its low-temperature variation, showing a rapid rise below 3.8 K (see the relevant inset to Fig. 5). The latter feature seems to signal a reconstruction of the antiferromagnetic structure that form below 5.8 K. It should be recalled that very similar shape of the susceptibility maximum near 6 K was found before for the isostructural compound Dy3Mn0.5GeS7 [3]. However, in the latter case, no upturn in c(T) was observed in the ordered state. Remarkably, the s(H) dependence measured for Dy3Ni0.5GeS7 at 1.72 K does not bear any typical antiferromagnetic character, and hence notably differs from those of Er3Ni0.5GeS7 and Tm3Ni0.5GeS7. In conjunction with the c(T) data it implies more complex magnetic properties than in the latter two compounds. As can be inferred from the comparison of Figs. 4 and 5, the magnetic behaviour in Gd3Ni0.5GeS7 is similar to that in Gd3Co0.5GeS7. Below 5 K, c(T) forms a plateau that may arise due to a kind of magnetic ordering. The s(H) isotherm measured at 1.72 K shows a smeared sigmoid-like character that hints at antiferromagnetic character of the ordered state. Interestingly, nearly identical magnetic data were previously reported for Gd3Fe0.5GeS7 [4].

Fig. 2. Dependencies of the unit cell volume and the lattice parameters of the R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) compounds on the ionic radii of the rare earth elements.

Fig. 3. Dependencies of the unit cell volume and the lattice parameters of the R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) compounds on the ionic radii of the rare earth elements.

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M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

Fig. 4. Temperature dependencies of the reciprocal molar magnetic susceptibility of the R3Co0.5GeS7 (R ¼ Sm and Gd) compounds measured in a field of 0.1 T. The solid lines represent the fits discussed in the text. Upper insets: magnetic susceptibility at low temperatures. Lower insets: magnetic field variations of the magnetization measured at 1.72 K with increasing (full circles) and decreasing (open circles) magnetic field strength.

Table 9 Magnetic susceptibility characteristics of the R3Co0.5GeS7 and R3Ni0.5GeS7 phases in the paramagnetic state (see the text). The values of mCo and mNi used for calculations of Cteo were 3.87 and 2.83 mB, respectively. Compound

qp (K)

C (emu/mol)

mR (mB)

Cteo (emu/mol)

Sm3Co0.5GeS7a Gd3Co0.5GeS7 Gd3Ni0.5GeS7 Dy3Ni0.5GeS7 Er3Ni0.5GeS7 Tm3Ni0.5GeS7

49.4(8) 4.0(3) 11.6(2) 0.7(2) þ9.8(3) 13.6(5)

1.307(7) 25.087(6) 24.875(4) 45.475(3) 32.385(4) 21.729(3)

0.85 7.94 7.94 10.65 9.58 7.56

1.207 24.577 24.142 43.034 34.917 21.933

a

modified CurieeWeiss behavior c(Τ) ¼ c0 þ C/(T  qp) with c0 ¼ 1.49(7)  103 emu/mol.

Fig. 5. Temperature dependencies of the reciprocal molar magnetic susceptibility of the R3Ni0.5GeS7 (R ¼ Gd, Tb, Er and Tm) compounds measured in a field of 0.1 T. The solid lines represent the fits discussed in the text. Upper insets: magnetic susceptibility at low temperatures. Lower insets: magnetic field variations of the magnetization measured at 1.72 K with increasing (full circles) and decreasing (open circles) magnetic field strength.

M. Daszkiewicz et al. / Journal of Alloys and Compounds 647 (2015) 445e455

4. Summary The sulphides R3Co0.5GeS7 (R ¼ Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm) and R3Ni0.5GeS7 (R ¼ Y, Ce, Sm, Gd, Tb, Dy, Ho, Er and Tm) are members of the large family of the compounds with the general formula R3MZX7, where R e lanthanide element; M1 mono-valent element (for example, Cu or Ag), 1/2 of di-valent element (for example, Mg, Mn or Fe) or 1/4 of four-valent element (Si, Ge, Sn); Z e Si, Ge, Sn and XeS, Se. All these materials crystallize with the hexagonal structures of the space group P63, and have similar structural fragments. In particular, they exhibit analogous packing of the [RX8] trigonal prisms and of the [ZX4] tetrahedra. The differences are observed only in the filling of the octahedra located along the hexagonal c axes. In terms of three possible filling schemes of these fragments by M atoms (for discussion see Ref. [1]), the compounds investigated in the present work belong to the group characterized by the M atoms being located nearly in the centres of the octahedra. The R3Co0.5GeS7 (R ¼ Sm and Gd) and R3Ni0.5GeS7 (R ¼ Gd, Dy, Er and Tm) compounds are CurieeWeiss paramagnets due to the magnetic sublattices formed by trivalent rare-earth ions and divalent transition-metal ions. For Dy3Ni0.5GeS7, Er3Ni0.5GeS7 and Tm3Ni0.5GeS7 the formation of antiferromagnetically ordered states below TN ¼ 6e7 K was inferred from the magnetic susceptibility and magnetization data. In the former sulphide, an additional magnetic phase transition seems to take place near 3.8 K. In each compound, the long-range magnetism seems to arise as a

455

combined effect of exchange interactions that involve both the R3þ and Ni2þ magnetic sublattices. Possibly, also the two Gd-based compounds studied, i.e. Gd3Co0.5GeS7 and Gd3Ni0.5GeS7, order magnetically below about 5 K, yet for these two materials the hypothetical ordering is less obvious. In contrast, down to 1.72 K, no hint at any long-range magnetic ordering was found for Sm3Co0.5GeS7. In order to verify the actual character of the ordered states in the R3Co0.5GeS7 and R3Ni0.5GeS7 compounds and determine their magnetic structures neutron diffraction experiments are required. References [1] L.D. Gulay, M. Daszkiewicz, Ternary and quaternary chalcogenides of Si, Ge, Sn, Pb, Ch. 250, in: K.A. Gschneidner Jr., J.-C.G. Bünzli, V.K. Pecharsky (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 41, 2011. [2] K. Mitchell, J.A. Ibers, Chem. Rev. 102 (2002) 1929. [3] M. Daszkiewicz, O.V. Marchuk, L.D. Gulay, D. Kaczorowski, J. Alloys Compd. 610 (2014) 258. [4] M. Daszkiewicz, Yu.O. Pashynska, O.V. Marchuk, L.D. Gulay, D. Kaczorowski, J. Alloys Compd. 616 (2014) 243. [5] Oxford Diffraction, CrysAlis CCD and CrysAlis RED. Version 1.171.30.3, Oxford Diffraction Ltd, Abingdon, Oxfordshire, England, 2006. [6] G.M. Sheldrick, SHELXS97 and SHELXL97, Programs for the Solution and the € ttingen, Germany, 1997. Refinement of Crystal Structures, University of Go [7] A.L. Spek, A. PLATON, Multipurpose Crystallographic Tool, Utrecht University, Utrecht, The Netherlands, 2007. [8] N. Wiberg, Lehrbuch der Anorganischen Chemie, Walter de Gruyter, Berlin, 1995, pp. 1838e1841. [9] K.N.R. Taylor, M.I. Darby, Physics of Rare Earth Solids, Chapman and Hall, London, 1972.