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ISSN 2053-2296

Structure determination of KScS2, RbScS2 and KLnS2 (Ln = Nd, Sm, Tb, Dy, Ho, Er, Tm and Yb) and crystal–chemical discussion Lubomı´r Havla´k,a Jan Fa´bry,a* Margarida Henriquesa and Michal Dusˇekb a

Received 13 March 2015 Accepted 20 June 2015 Edited by L. R. Falvello, Universidad de Zaragoza, Spain Keywords: alkali rare earth sulfides; X-ray singlecrystal structure determination; crystal chemistry. CCDC references: 1407927; 1407926; 1407925; 1407924; 1407923; 1407922; 1407921; 1407920; 1407919; 1407918 Supporting information: this article has supporting information at journals.iucr.org/c

Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic, and bInstitute of Physics of the Czech Academy of Sciences, Cukrovarnicka´ 10, 162 00 Praha 6, Czech Republic. *Correspondence e-mail: [email protected]

The title structures of KScS2 (potassium scandium sulfide), RbScS2 (rubidium scandium sulfide) and KLnS2 [Ln = Nd (potassium neodymium sufide), Sm (potassium samarium sulfide), Tb (potassium terbium sulfide), Dy (potassium dysprosium sulfide), Ho (potassium holmium sulfide), Er (potassium erbium sulfide), Tm (potassium thulium sulfide) and Yb (potassium ytterbium sulfide)] are either newly determined (KScS2, RbScS2 and KTbS2) or redetermined. All of them belong to the -NaFeO2 structure type in agreement with the ratio of the ionic radii r3+/r+. KScS2 , the member of this structural family with the smallest trivalent cation, is an extreme representative of these structures with rare earth trivalent cations. The title structures are compared with isostructural alkali rare earth sulfides in plots showing the dependence of several relevant parameters on the trivalent cation crystal radius; the parameters thus compared are c, a and c/a, the thicknesses of the S—S layers which contain the respective constituent cations, the sulfur fractional coordinates z(S2) and the bondvalence sums.

1. Introduction

# 2015 International Union of Crystallography

Acta Cryst. (2015). C71, 623–630

This study has been motivated by the potential applications of the rhombohedral alkali rare earth sulfides, which can be doped by other rare earth elements. Some of these doped rare earth sulfides are X-ray and white LED luminophors (Verheijen et al., 1975). Very recently, the optical properties of some alkali lanthanide ternary sulfides (M+Ln3+S2) have been reported, namely of RbLaS2 doped by Ce, Pr, Sm, Eu and Tb (Havla´k et al., 2011), of RbLuS2 doped by Ce, Pr, Sm and Tb (Jary´ et al., 2012), of RbGdS2 doped by Ce and Pr (Jary´ et al., 2013a), of KLuS2 doped by Eu (Jary´ et al., 2013b), of KLnS2 doped by Pr, Sm, Tb and Tm (Ln = La, Gd, Lu) (Jary´, Havla´k, Ba´rta, Miho´kova´ & Nikl, 2014), of KLuS2 doped by Ce (Jary´, Havla´k, Ba´rta, Miho´kova´, Pru˚sˇa & Nikl, 2014), and of KLuS2 doubly doped by Eu and one of the elements Pr, Sm or Ce (Havla´k et al., 2015). (The lanthanide elements are symbolized herein by Ln, and the rare earth elements – that is, Ln plus Sc and Y – by RE.) Electron paramagnetic resonance and luminescence spectroscopies were applied to study the incorporation and charge stability of Eu2+ cations in single crystals of KLuS2 doped by Eu (Laguta et al., 2014). The incorporation of Eu2+ into the structure of the -NaFeO2 type was unambiguously established and three different atomic sites were identified. Eu2+ occupied the positions of K+ and Lu3+, as well as being situated in defects in the structure (Laguta et al., 2014). http://dx.doi.org/10.1107/S2053229615011833

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research papers The structures of KLaS2, KPrS2, KEuS2, KGdS2, KLuS2, KYS2, RbYS2 and NaLaS2 have been determined recently (Fa´bry, Havla´k, Dusˇek et al., 2014). This study was followed by the determination of the structures of NaGdS2, NaLuS2 and NaYS2 (Fa´bry, Havla´k, Kucˇera´kova´ & Dusˇek, 2014). The article by Fa´bry, Havla´k, Dusˇek et al. (2014) also presents an extended crystal–chemical analysis of the alkali and thallium(1+) rare earth sulfides. All of these structures, except NaLaS2 , which is isostructural with a disordered NaCl structural type, belong to the -NaFeO2 structural family with the corresponding space group R3m. It turned out from these works (Fa´bry, Havla´k, Dusˇek et al., 2014; Fa´bry, Havla´k, Kucˇera´kova´ & Dusˇek, 2014) that some previously determined members of the -NaFeO2 structure type (Ballestracci, 1965; Ballestracci & Bertaut, 1965; Bronger et al., 1996; Ohtani et al., 1987; Plug & Verschoor, 1976; see also Table S1 in the Supporting information) suffered from less accurate structure determinations which do not fit the present state of the art, e.g. Fig. 6 in Fa´bry, Havla´k, Dusˇek et al. (2014). This was the motivation for the redetermination of the structures of KSmS2, KDyS2, KHoS2, KErS2, KTmS2 and KYbS2. In addition, for KTbS2, only the crystal data were known. Moreover, fractional coordinates of some KLnS2 compounds have only been estimated by analogy with other members of this structural family (see supplementary Table S1). As for the alkali scandium sulfides, up to now crystal data have been determined for LiScS2 [van Dijk & Plug, 1980; ICSD code 642305 (Inorganic Crystal Structure Database, 2014), PDF-4 card 00-041-0785 (International Centre for Diffraction Data, 2013)], NaScS2 (van Dijk & Plug, 1980; ICSD code 644971, PDF-4 cards 00-041-0786 and 04-0040009) and KScS2 [PDF-4 card 00-051-1228, with a = 3.8139 (2) ˚ , in good agreement with the present and c = 21.726 (2) A study]. The lattice parameters of the structures with Sc3+ (supplementary Table S1) indicate that they belong to the -NaFeO2 structural family, with the exception of TlScS2 (Teske et al., 2008), which belongs to a different structure type with the space group P63/mmc. Other members of the latter structural family are known to exist in CsLnS2, where Ln = Pr–Lu (Bronger et al., 1993). In the latter structure type, the lengths of the unit-cell c axes are equal to two-thirds of those of the corresponding members of the -NaFeO2 structural family (Bronger et al., 1993). The alkali scandium sulfides extend the stability region of the alkali rare earth sulfides, which so far has been accepted as lying in the ionic-ratio interval of 0.62 < r3+/r+ < 0.96 (Tromme, 1971). For both RbScS2 and LiScS2, the values of r3+/r+ are 0.593 and 1.094, respectively. [These values have been calculated using the crystal ionic radii given by Shannon (1976).] This is remarkable, especially for LiScS2, because the stability region for another frequent structural type (occupationally disordered NaCl), which is known to be present in the alkali lanthanide structural family, is 0.95 < r3+/r+ < 1.08 (Bronger et al., 1973; Verheijen et al., 1975). Thus, the other aim of this article is to provide structure analyses of the hitherto undescribed structures of KScS2 and

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RbScS2 (Fig. 1) and to compare these structures with other alkali rare earth sulfides. This is of interest because the crystal ionic radius of Sc3+ is the smallest among those of the trivalent rare earth cations: the crystal radii (Shannon, 1976) of Sc3+, Y3+, Lu3+, Ho3+ and La3+ are 0.885, 1.040, 1.001, 1.041 and ˚ , respectively, for a coordination number of 6 (CN = 6). 1.172 A For comparison, the crystal radii of the rare earth trivalent cations (RE3+) with CN = 6 decrease monotonically in the series La3+ > Ce3+ > Pr3+ > Nd3+ > Pm3+ > Sm3+ > Eu3+ > Gd3+ > Tb3+ > Dy3+ > Ho3+ > Y3+ > Er3+ > Tm3+ > Yb3+ > Lu3+ > Sc3+ (Shannon, 1976), and so also do the RE3+—S2 bond valences, with the following exceptions: Dy3+ < Ho3+ = Y3+; Yb3+ = Lu3+ (Brese & O’Keeffe, 1991).

2. Experimental 2.1. Synthesis and crystallization

The starting materials were K2CO3 (Alfa Aesar, >99.997%), Rb2CO3 (Alfa Aesar, >99.8%), Sc2O3 (Alfa Aesar, >99.99%), Nd2O3 (REacton, >99.99%), Sm2O3 (REacton, >99.99%), Tb2O3 (Koch–Light Laboratories, >99.9%), Dy2O3 (Koch– Light Laboratories, >99.9%), Ho2O3 (REacton, >99.99%), Er2O3 (Koch–Light Laboratories, >99.9%), Tm2O3 (Fluka, >99.9%), Yb2O3 (REacton, >99.9%) and Eu2O3 (Alfa Aesar, >99.99%). The gases used were Ar (Linde, >99.999%) and

Figure 1 A view of the unit cell of RbScS2, one of the isostructural title structures. The layer of atoms at z = 0 is composed of Rb+, which are depicted as white spheres. The following layer is composed of S2, depicted as yellow spheres, and the blue spheres in the layer above represent Sc3+. [Symmetry codes: (i) x  y + 23, y + 13, z + 13; (ii) x, y + 1, z; (iii) x  y + 13, y + 23, z + 23.] Acta Cryst. (2015). C71, 623–630

research papers Table 1 Experimental details.

Crystal data Chemical formula Mr Crystal system, space group Temperature (K) ˚) a, c (A ˚ 3) V (A Z Radiation type  (mm1) Crystal size (mm) Data collection Diffractometer

Absorption correction Tmin, Tmax No. of measured, independent and observed [I > 3(I)] reflections Rint ˚ 1) (sin /)max (A Refinement R[F 2 > 3(F 2)], wR(F 2), S No. of reflections No. of parameters ˚ 3) max, min (e A

Crystal data Chemical formula Mr Crystal system, space group Temperature (K) ˚) a, c (A ˚ 3) V (A Z Radiation type  (mm1) Crystal size (mm) Data collection Diffractometer

Absorption correction Tmin, Tmax No. of measured, independent and observed [I > 3(I)] reflections Rint ˚ 1) (sin /)max (A Refinement R[F 2 > 3(F 2)], wR(F 2), S No. of reflections No. of parameters ˚ 3) max, min (e A

(I)

(II)

(III)

(IV)

(V)

KScS2 148.2 Trigonal, R3m

RbScS2 194.5 Trigonal, R3m

KNdS2 247.5 Trigonal, R3m

KSmS2 253.6 Trigonal, R3m

KTbS2 262.1 Trigonal, R3m

292 3.8106 (3), 21.719 (2) 273.12 (4) 3 Mo K 4.04 0.46  0.27  0.05

293 3.8299 (6), 22.656 (3) 287.80 (7) 3 Mo K 15.35 0.17  0.14  0.04

301 4.1626 (3), 21.8996 (19) 328.62 (5) 3 Mo K 13.52 0.14  0.13  0.05

293 4.1174 (6), 21.888 (3) 321.35 (8) 3 Mo K 15.42 0.20  0.14  0.03

295 4.0523 (7), 21.885 (3) 311.23 (9) 3 Mo K 18.81 0.20  0.08  0.05

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.347, 0.832 1277, 119, 106

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.173, 0.609 611, 120, 118

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.258, 0.544 1538, 140, 140

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.227, 0.672 721, 135, 135

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.238, 0.447 674, 129, 129

0.052 0.686

0.069 0.680

0.036 0.692

0.086 0.683

0.061 0.687

0.025, 0.064, 1.92

0.033, 0.068, 1.86

0.010, 0.010, 0.60

0.031, 0.069, 1.86

0.017, 0.035, 0.97

119 8 0.48, 0.53

120 8 0.82, 0.97

140 9 0.17, 0.09

135 9 1.48, 1.79

129 9 0.45, 0.64

(VI)

(VII)

(VIII)

(IX)

(X)

KDyS2 265.7 Trigonal, R3m

KHoS2 268.1 Trigonal, R3m

KErS2 270.5 Trigonal, R3m

KTmS2 272.2 Trigonal, R3m

KYbS2 276.3 Trigonal, R3m

294 4.0315 (11), 21.890 (5) 308.11 (14) 3 Mo K 19.97 0.21  0.09  0.03

303 4.0098 (4), 21.878 (2) 304.64 (5) 3 Mo K 21.29 0.19  0.14  0.07

296 3.9935 (4), 21.866 (2) 302.00 (5) 3 Mo K 22.66 0.08  0.07  0.05

293 3.9761 (5), 21.841 (3) 299.03 (7) 3 Mo K 24.09 0.17  0.11  0.06

301 3.9615 (8), 21.810 (3) 296.42 (9) 3 Mo K 25.52 0.13  0.11  0.09

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.201, 0.703 658, 126, 124

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.090, 0.243 2289, 216, 139

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.255, 0.434 1405, 132, 132

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.111, 0.291 637, 124, 124

Xcalibur Gemini Ultra diffractometer with an Atlas detector Gaussian (JANA2006; Petrˇı´cˇek et al., 2014) 0.099, 0.193 444, 124, 124

0.100 0.688

0.058 0.687

0.070 0.684

0.048 0.687

0.069 0.682

0.052, 0.105, 2.32

0.020, 0.060, 1.56

0.027, 0.064, 1.81

0.016, 0.040, 1.12

0.029, 0.069, 1.65

126 9 4.44, 2.46

216 10 0.77, 1.00

132 9 1.54, 1.01

124 9 0.48, 1.00

124 9 1.42, 2.15

Computer programs: CrysAlis PRO (Agilent, 2014), SUPERFLIP (Palatinus & Chapuis, 2007), JANA2006 (Petrˇı´cˇek et al., 2014) and DIAMOND (Brandenburg & Putz, 2005).

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research papers H2S (Linde, >99.5%). The chemical reactions were carried out in a corundum tube (Dengfeng Jinyu Thermoelectric Material Co., >99.7% Al2O3). The tube was placed in an electric resistance furnace equipped with heating/cooling-rate regulation. The scheme of the set-up was outlined by Havla´k et al. (2011). Either Ar or H2S gas was allowed to flow into the reaction tube. The gases were taken directly from pressurized cylinders using a three-way stopcock to switch between them. A mixture of the pertinent carbonate (K2CO3 or Rb2CO3) with the rare earth oxide RE2O3 in the molar ratio 70:1 was used as the starting material. Only Sc2O3 was doped by 0.05 mol% of Eu2O3. (Eu was added because of the investigation of the title compounds as scintillation materials.) Eu doping was carried out by the simple mixing and grinding of Sc2O3 and Eu2O3. Prior to the reaction itself, the reagents (K2CO3 or Rb2CO3 and RE2O3 or Sc2O3:Eu2O3) were mixed and the mixture homogenized in an agate mortar. The mixture was placed in a corundum boat (Dengfeng Jinyu Thermoelectric Material Co., >99.7% Al2O3) and inserted into the corundum tube (inner volume = 0.9 l). The mixture was then heated to 1323 K using the electric resistance furnace (heating rate 10 K min1) under a flow of Ar (15 l h1). After the desired temperature had been reached, the reaction mixture was annealed for 90 min under a flow of H2S (15 l h1). Following annealing, the system was cooled under a flow of Ar (1 K min1, 0.3 l h1). Upon reaching room temperature, the corundum boat was removed from the tube furnace and the reaction products were purified by suspension and decantation, three times with distilled water and once with acetone. K2S or Rb2S was removed by water, while KRES2 or Eu-doped KScS2 or Eu-doped RbScS2 were left behind. The yield was nearly 100%, with any loss attributed to imperfect product separation. The products were stored in small glass flasks under an Ar atmosphere and used for further analysis. The ternary sulfide MRES2 (M = K, Rb) was formed at 1323 K according to reaction (1), while the excess of M2CO3 reacted following reaction (2):

Figure 2 The dependence of c/a on Z in the series of alkali and Tl+ rare earth sulfides. [TlK and TlD denote the structure determinations by Kabre´ et al. (1974) and Duczmal & Pawlak (1994), respectively; see Table S2 in the Supporting information.]

3. Results and discussion Fig. 2 shows the dependence of c/a on atomic number Z for the alkali rare earth sulfides. (The references for this figure are given in supplementary Table S2.) The smaller the trivalent cation, the larger the value of c/a. Compare also the crystal radii (Shannon, 1976) of Sc3+, Y3+, Lu3+ and La3+ for coordination number 6, which are given above. We note significant differences between the previous and recent determinations of ˚ the lattice parameters for NaGdS2 [a = 4.057, c = 19.990 A ˚ ´ (Sato et al., 1984); a = 4.0138 (4), c = 19.878 (2) A (Fabry, Havla´k, Kucˇera´kova´ & Dusˇek, 2014)], NaLuS2 [a = 3.8873 (2), ˚ (Schleid & Lissner, 1993); a = 3.8909 (13), c = c = 19.7058 (9) A ˚ (Fa´bry, Havla´k, Kucˇera´kova´ & Dusˇek, 2014)] and 19.850 (3) A ˚ (Ballestracci & Bertaut, 1964; NaYS2 [a = 3.968, c = 19.89 A ˚ Bru¨esch & Schu¨ler, 1971); a = 3.9604 (12), c = 19.867 (8) A

M2 CO3 ðlÞ þ RE2 O3 ðsÞ þ 4H2 S ðgÞ ! 2MRES2 ðsÞ þ 4H2 O ðgÞ þ CO2 ðgÞ;

ð1Þ

M2 CO3 ðlÞ þ H2 S ðgÞ ! M2 S ðlÞ þ H2 O ðgÞ þ CO2 ðgÞ:

ð2Þ

2.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. The structures were solved using SUPERFLIP (Palatinus & Chapuis, 2007) implemented in JANA2006 (Petrˇ´ıcˇek et al., 2014). The Eu content of KScS2 and RbScS2 (see Synthesis and crystallization, x2.1) was ignored during the refinement. In the title samples, no obverse–reverse twinning was detected, with the exception of KHoS2, where the twinning matrix (100/010/001) was applied. The domain fractions, i.e. 0.99986 (3) and 0.00014 (3), indicate a very small component for the second domain.

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Figure 3 The dependence of c/a on the ionic crystal radii of RE3+ (Shannon, 1976) in the series of alkali and Tl+ rare earth sulfides. The ionic radii decrease in the order La3+ > Ce3+ > Pr3+ > Nd3+ > Pm3+ > Sm3+ > Eu3+ > Gd3+ > Tb3+ > Dy3+ > Ho3+ > Y3+ > Er3+ > Tm3+ > Yb3+ > Lu3+ > Sc3+. See also Table S2 in the Supporting information. (For the meaning of TlK and TlD, see the caption of Fig. 2.) Acta Cryst. (2015). C71, 623–630

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Figure 4 The lattice parameter c as a function of the ionic crystal radii of RE3+ (Shannon, 1976) for the series of alkali and Tl+ rare earth sulfides. See also Table S2 in the Supporting information. (For the meaning of TlK and TlD, and the ordering of the cations, see the captions of Figs. 2 and 3, respectively.)

In alkali rare earth sulfides, the parameter c decreases slightly with the decreasing ionic radius of the trivalent cation (Fig. 4) in contrast with the dependence of a on the crystal radii (Fig. 5 and supplementary Fig. S2). The c-axis length is almost constant, while the a parameter decreases almost linearly with the radius of the trivalent cation. Thallium rare earth sulfides are the exception, as the c parameter increases slightly with the decreasing ionic radius of the trivalent cation (Fig. 4), while the a parameter keeps the same trend as for other alkali rare earth sulfides (Fig. 5 and supplementary Fig. S2). The previous dependences are related to the widths of the þ 3þ sulfur layers TM and TRE which contain the monovalent and trivalent cations, respectively (Fig. 1). It can be noticed in Fig. 1 that the layer of the trivalent rare earth cation is narrower than that of the monovalent alkali cation. The widths of the pertinent layers are given by the formulae    3þ ¼ 2  z S2  1=3  c ð3Þ TRE and

(Fa´bry, Havla´k, Kucˇera´kova´ & Dusˇek, 2014)]. However, the recent determinations have not been used in Figs. 2–4 because the older determinations form a series with similar systematic errors and therefore they are believed to show the trend better. Fig. 3 (and supplementary Table S2) presents a dependence analogous to the previous one, namely that of c/a on the crystal radii (Shannon, 1976) of the trivalent cations. Since the plots of other variables as a function of the crystal radii are nearly linearly dependent on the ionic radii of the constituent trivalent rare earth cations, these plots are going to be shown exclusively from this point on, while analogous dependences on Z of the trivalent rare earth cations have been included in the Supporting information. For example, supplementary Fig. S1 is analogous to Fig. 4.

  þ ¼ 2=3  2  z S2  c; TM

ð4Þ

where z(S2) is a z-fractional coordinate chosen in such a way that z(S2) < 0.25. [NB: in equations (2) and (3) of Fa´bry, Havla´k, Dusˇek et al. (2014), the identities of the cations in the 3þ þ and TM should be interchanged between left-hand terms TLn the two equations. The analogous equations given here are correct, with the additional difference that RE3+ is used here instead of the Ln3+ used in Fa´bry, Havla´k, Dusˇek et al. (2014).] Figs. 6 and 7 (and supplementary Figs. S3 and S4) present the dependence of the widths of the S—S layers on the monovalent and trivalent cations on the crystal radii. The corresponding data are given in supplementary Tables S3 and S4.

Figure 6 Figure 5 3+

The dependence of a on the ionic crystal radii of RE (Shannon, 1976) in the series of alkali and Tl+ rare earth sulfides. See also Table S2 in the Supporting information. (For the meaning of TlK and TlD, and the ordering of the cations, see the captions of Figs. 2 and 3, respectively.) Acta Cryst. (2015). C71, 623–630

The evolution of the widths of the S—S layers, which contain the monovalent M+ cations in the rare earth alkali sulfides, with the ionic crystal radii of RE3+ (Shannon, 1976). See also Table S3 in the Supporting information. (For the meaning of TlD and the ordering of the cations, see the captions of Figs. 2 and 3, respectively.) Havla´k et al.



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Figure 7 The dependence of the widths of the S—S layers, which contain the trivalent RE3+ cations in the rare earth alkali sulfides, on the ionic crystal radii of RE3+ (Shannon, 1976). See also Table S4 in the Supporting information. (For the meaning of TlD and the ordering of the cations, see the captions of Figs. 2 and 3, respectively.)

Verheijen et al. (1975) pointed out that the rather constant value of c within the alkali lanthanide sulfides (Fig. 4 and supplementary Fig. S1) is due to the compensation of the widths of the layers for the trivalent and monovalent cations. Figs. 6 and 7 confirm this view. The different tendency found across the Tl+ compounds (Fig. 4) suggests that their c axes increase in length with decreasing crystal radii of the constituent rare earth cations (Shannon, 1976). Thus, the question is: how do the dependences shown in Figs. 5–7 (and supplementary Figs. S2–S4) correlate with the interatomic distances observed in the structures of KRES2 and RbRES2 (Fig. 8; supplementary Tables S5 and S6, and Fig. S5)? ˚ for a coordiThe S2 anions with a crystal radius of 1.70 A

nation number of 6 are by far the largest among the constituent ions in the title structures, and therefore the S  S separation should be the most significant in the formation of their atomic frameworks. The S  Sii distances (Fig. 1) decrease as the ionic radius of the trivalent RE3+ rare earth cation decreases. Expressed alternatively, the S  S interatomic distances for the S atoms which are situated in the same sulfur layer decrease with the decreasing size of the trivalent rare earth cation. Thus, it is not surprising that the same dependence is observed for the a lattice parameters (Fig. 5 and supplementary Fig. S2). On the other hand, the shortest S  S distances (Fig. 8) between the S atoms in the S layers above and below the layer of the trivalent cations in KRES2 and RbRES2, e.g. S  Si in Fig. 1, decrease with the decreasing crystal radii of the triva3þ lent cations. This is in agreement with the dependence of TRE on the crystal radii, which is shown in Fig. 7 (and supplementary Fig. S4). However, the latter dependence is in contrast with the S  S distances (Fig. 8) between the S atoms which are situated in the S—S layers below and above the layer of the monovalent cations, e.g. S  Siii in Fig. 1. Fig. 8 (and supplementary Fig. S5) shows that the shortest RE3+—S2 distances are almost unaffected by the presence of the monovalent cation. The similarity between the distance dependences of KRES2 and RbRES2 suggests that these structure determinations are satisfactory. It may be considered as a paradox of the title structures that the respective distances K+—S2 or Rb+—S2 (Fig. 8 and supplementary Fig. S5) decrease with decreasing size of the trivalent cation, while the thicknesses of the S—S interatomic layers which contain these monovalent cations increase. The explanation follows from the fact that the S atoms in the same atomic layer (S  Sii in Fig. 1) become closer (Fig. 8 and supplementary Fig. S5) with the decreasing radii of the trivalent cations. This causes a concomitant increase in the

Figure 8 ˚ ) in K+RE3+S2 and The dependence of closest interatomic distances (A Rb+RE3+S2 on the ionic crystal radii of RE3+ (Shannon, 1976). See also the respective Tables S5 and S6 in the Supporting information, and Fig. 1. (SS1K, SS2K, SS3K, KS and RESK denote the S  Si, S  Sii, S  Siii, K  S and RE  S distances in the title potassium rare earth sulfides; the distances in the Rb compounds are indicated analogously.]

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Figure 9 The dependence of z(S2) in M+RE3+S2 on the ionic crystal radii of RE3+ (Shannon, 1976). See also Table S7 in the Supporting information. (For the meaning of TlD and the ordering of the cations, see the captions of Figs. 2 and 3, respectively.) Acta Cryst. (2015). C71, 623–630

research papers

Figure 10 The dependence of the bond-valence sums (Brese & O’Keeffe, 1991) on the ionic crystal radii of RE3+ (Shannon, 1976) in the actual rhombohedral and the hypothetical cubic K+RE3+S2 structures. See also Table S8 in the Supporting information. (For the ordering of the cations, see the caption of Fig. 3.)

thicknesses of the S—S layers which contain the monovalent cations, while these cations become closer to the S atoms. Fig. 9 (supplementary Fig. S6) shows the dependence of z(S2) for K+RE3+S2 and Rb+RE3+S2 on the crystal radii of RE3+ (Shannon, 1976). Again, a fairly linear trend is revealed. [The selected structure determinations with the corresponding values of z(S2) for these figures are listed in supplementary Table S7.] Fig. 10 (supplementary Fig. S7 and Table S8) shows the dependence of the bond-valence sums (Brese & O’Keeffe, 1991) on the crystal radii (Shannon, 1976) in K+RE3+S2, while Fig. 11 (supplementary Fig. S8) shows the analogous dependence for Rb+RE3+S2 (supplementary Table S9). In K+RE3+S2, the bond-valence sums of K+ tend to be higher than those of Rb+ in the Rb+RE3+S2 counterparts, in contrast with the trivalent cations. The bond-valence sums of K+ or Rb+

are fairly linearly dependent on the ionic radii, again in contrast with those of the trivalent cations. Figs. 10 and 11 also contain the bond-valence sums which have been calculated for the respective hypothetical structures in the NaCl structure type with the cations disordered, under the assumption of the same unit-cell volume as that of the real structures of the -NaFeO2 structure type. (The NaCl structure type is present in some lithium and sodium rare earth sulfides; Fa´bry, Havla´k, Dusˇek et al., 2014.) It turns out that the existence of these hypothetical KScS2 and RbScS2 compounds with the NaCl structure is certainly excluded under normal conditions. Figs. 10 and 11 also indicate that, in the hypothetical structures, the monovalent cations are substantially overbonded at the cost of the trivalent cations. From this point of view, the title Sc3+ structures are situated at the limit of the stability region of this structural type. The bond-valence sums of the constituent ions for KScS2 are 1.408 (K+), 2.763 (Sc3+) and 2.085 (S2), whereas they are 1.351 (Rb+), 2.719 (Sc3+) and 2.035 (S2) for RbScS2. The dependences of the bond-valence sums (Figs. 10 and 11, and supplementary Figs. S7 and S8) enhance the abovementioned paradox, since the bond-valence sums of the monovalent cations increase with the decreasing size of the trivalent cations, while the thicknesses of the S—S interatomic layers which contain the monovalent cations increase.

4. Conclusions The comparison of the title K+RE3+S2 and Rb+RE3+S2 structures shows that they seem to have been determined with state-of-the-art accuracy. Nevertheless, there are still incomplete or unsatisfactory structure determinations in this structural family, as is the case for LiLnS2 and NaLnS2. At present, we are directing our efforts towards the NaLnS2 compounds. The present analysis shows that the title structures with Sc3+, despite being the end-members of the series of the -NaFeO2 structural type due to the small size of Sc3+, have structural properties which are in agreement with those of the other members of this structural family. The stability region of the ionic ratios r3+/r+ for the alkali rare earth sulfides has been extended to 0.593–1.094 with the inclusion of MScS2.

Acknowledgements The projects TACˇR TA04010135 and GACˇR P204110809 are gratefully acknowledged. References

Figure 11 The dependence of the bond-valence sums (Brese & O’Keeffe, 1991) on the ionic crystal radii of RE3+ (Shannon, 1976) in the actual rhombohedral and the hypothetical cubic Rb+RE3+S2 structures. See also Table S9 in the Supporting information. (For the ordering of the cations, see the caption of Fig. 3.) Acta Cryst. (2015). C71, 623–630

Agilent (2014). CrysAlis PRO. Agilent Technologies Ltd, Yarnton, Oxfordshire, England. Ballestracci, R. (1965). Bull. Soc. Fr. Mineral. Cristallogr. 38, 207– 210. Ballestracci, R. & Bertaut, E.-F. (1964). Bull. Soc. Fr. Mineral. Cristallogr. 37, 512–517. Ballestracci, R. & Bertaut, E.-F. (1965). Colloques internationaux du CNRS, Orsay, France, 28 September to 1 October 1965, pp. 41– 49. Havla´k et al.



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Acta Cryst. (2015). C71, 623–630

supporting information

supporting information Acta Cryst. (2015). C71, 623-630

[doi:10.1107/S2053229615011833]

Structure determination of KScS2, RbScS2 and KLnS2 (Ln = Nd, Sm, Tb, Dy, Ho, Er, Tm and Yb) and crystal–chemical discussion Lubomír Havlák, Jan Fábry, Margarida Henriques and Michal Dušek Computing details For all compounds, data collection: CrysAlis PRO (Agilent, 2014); cell refinement: CrysAlis PRO (Agilent, 2014); data reduction: CrysAlis PRO (Agilent, 2014); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: JANA2006 (Petříček et al., 2014). Molecular graphics: Brandenburg & Putz (2005) for (II). For all compounds, software used to prepare material for publication: JANA2006 (Petříček et al., 2014). (I) Potassium scandium sulfide Crystal data KScS2 Mr = 148.2 Trigonal, R3m Hall symbol: -R 3 2" a = 3.8106 (3) Å c = 21.719 (2) Å V = 273.12 (4) Å3 Z=3 F(000) = 216

Dx = 2.703 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 936 reflections θ = 5.6–28.8° µ = 4.04 mm−1 T = 292 K Plate, yellow 0.46 × 0.27 × 0.05 mm

Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.347, Tmax = 0.832

1277 measured reflections 119 independent reflections 106 reflections with I > 3σ(I) Rint = 0.052 θmax = 29.2°, θmin = 5.6° h = −5→5 k = −5→5 l = −28→29

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.025 wR(F2) = 0.064 S = 1.92 119 reflections 8 parameters 0 restraints

Acta Cryst. (2015). C71, 623-630

0 constraints Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.002 Δρmax = 0.48 e Å−3 Δρmin = −0.53 e Å−3

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supporting information Special details Refinement. Refinement of a model with obverse–reverse twinning turned out to be insignificant. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Sc S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23113 (6)

0.0124 (5) 0.0062 (4) 0.0067 (4)

Atomic displacement parameters (Å2)

K Sc S

U11

U22

U33

U12

U13

U23

0.0139 (6) 0.0058 (5) 0.0066 (4)

0.0139 (6) 0.0058 (5) 0.0066 (4)

0.0094 (9) 0.0068 (7) 0.0068 (7)

0.0069 (3) 0.0029 (2) 0.0033 (2)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Ki K—Kii K—Kiii K—Kiv K—Kv K—Kvi K—Svii K—Sviii K—Six K—Sx K—Sxi K—Sxii Sc—Sci Sc—Scii Sc—Sciii Sc—Sciv Sc—Scv

3.8106 (9) 3.8106 (6) 3.8106 (6) 3.8106 (6) 3.8106 (6) 3.8106 (9) 3.1253 (11) 3.1253 (10) 3.1253 (11) 3.1253 (11) 3.1253 (10) 3.1253 (11) 3.8106 (9) 3.8106 (6) 3.8106 (6) 3.8106 (6) 3.8106 (6)

Sc—Scvi Sc—S Sc—Siv Sc—Svi Sc—Sxi Sc—Sxii Sc—Sxiii S—Si S—Sii S—Siii S—Siv S—Sv S—Svi S—Sx S—Sxi S—Sxii

3.8106 (9) 2.6078 (8) 2.6078 (8) 2.6078 (8) 2.6078 (8) 2.6078 (8) 2.6078 (8) 3.8106 (9) 3.8106 (6) 3.8106 (6) 3.8106 (6) 3.8106 (6) 3.8106 (9) 3.5611 (16) 3.5611 (16) 3.5611 (16)

S—Sc—Siv S—Sc—Svi S—Sc—Sxi S—Sc—Sxii S—Sc—Sxiii Siv—Sc—Svi Siv—Sc—Sxi Siv—Sc—Sxii Siv—Sc—Sxiii

93.88 (2) 93.88 (3) 86.12 (3) 86.12 (2) 180.0 (5) 93.88 (2) 86.12 (2) 180.0 (5) 86.12 (2)

Svi—Sc—Sxiii Sxi—Sc—Sxii Sxi—Sc—Sxiii Sxii—Sc—Sxiii Kxiv—S—Kxv Kxiv—S—Kxvi Kxv—S—Kxvi Sci—S—Sciii Sci—S—Sc

86.12 (3) 93.88 (2) 93.88 (3) 93.88 (2) 75.13 (3) 75.13 (3) 75.13 (3) 93.88 (3) 93.88 (3)

Acta Cryst. (2015). C71, 623-630

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supporting information Svi—Sc—Sxi Svi—Sc—Sxii

Sciii—S—Sc

180.0 (5) 86.12 (2)

93.88 (3)

Symmetry codes: (i) x−1, y−1, z; (ii) x−1, y, z; (iii) x, y−1, z; (iv) x, y+1, z; (v) x+1, y, z; (vi) x+1, y+1, z; (vii) x−2/3, y−1/3, z−1/3; (viii) x+1/3, y−1/3, z−1/3; (ix) x+1/3, y+2/3, z−1/3; (x) y−1/3, x−2/3, −z+1/3; (xi) y−1/3, x+1/3, −z+1/3; (xii) y+2/3, x+1/3, −z+1/3; (xiii) y+2/3, x+4/3, −z+1/3; (xiv) x−1/3, y−2/3, z+1/3; (xv) x−1/3, y+1/3, z+1/3; (xvi) x+2/3, y+1/3, z+1/3.

(II) Rubidium scandium sulfide Crystal data Dx = 3.367 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 539 reflections θ = 5.4–28.9° µ = 15.35 mm−1 T = 293 K Plate, yellow–green 0.17 × 0.14 × 0.04 mm

RbScS2 Mr = 194.5 Trigonal, R3m Hall symbol: -R 3 2" a = 3.8299 (6) Å c = 22.656 (3) Å V = 287.80 (7) Å3 Z=3 F(000) = 270 Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.173, Tmax = 0.609

611 measured reflections 120 independent reflections 118 reflections with I > 3σ(I) Rint = 0.069 θmax = 28.9°, θmin = 5.4° h = −5→3 k = −3→5 l = −25→30

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.033 wR(F2) = 0.068 S = 1.86 120 reflections 8 parameters 0 restraints

0 constraints Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.004 Δρmax = 0.82 e Å−3 Δρmin = −0.97 e Å−3

Special details Refinement. Refinement of a model with obverse–reverse twinning turned out to be insignificant. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

Rb Sc S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.22811 (10)

0.0145 (4) 0.0070 (6) 0.0073 (5)

Atomic displacement parameters (Å2)

Rb

U11

U22

U33

U12

U13

U23

0.0155 (5)

0.0155 (5)

0.0125 (7)

0.0078 (2)

0

0

Acta Cryst. (2015). C71, 623-630

sup-3

supporting information Sc S

0.0065 (6) 0.0072 (6)

0.0065 (6) 0.0072 (6)

0.0080 (11) 0.0075 (10)

0.0032 (3) 0.0036 (3)

0 0

0 0

Geometric parameters (Å, º) Rb—Si Rb—Sii Rb—Siii Rb—Siv Rb—Sv Rb—Svi Sc—S Sc—Svii Sc—Sviii Sc—Sv Sc—Svi

3.2515 (18) 3.2515 (17) 3.2515 (18) 3.2515 (18) 3.2515 (17) 3.2515 (18) 2.6129 (14) 2.6129 (12) 2.6129 (14) 2.6129 (14) 2.6129 (12)

Sc—Six S—Sx S—Sxi S—Sxii S—Svii S—Sxiii S—Sviii S—Siv S—Sv S—Svi

2.6129 (14) 3.8299 (18) 3.8299 (12) 3.8299 (12) 3.8299 (12) 3.8299 (12) 3.8299 (18) 3.555 (3) 3.555 (3) 3.555 (3)

Si—Rb—Sii Si—Rb—Siii Si—Rb—Siv Si—Rb—Sv Si—Rb—Svi Sii—Rb—Siii Sii—Rb—Siv Sii—Rb—Sv Sii—Rb—Svi Siii—Rb—Siv Siii—Rb—Sv Siii—Rb—Svi Siv—Rb—Sv Siv—Rb—Svi Sv—Rb—Svi S—Sc—Svii S—Sc—Sviii S—Sc—Sv

72.16 (3) 72.16 (3) 107.84 (3) 107.84 (3) 180.0 (5) 72.16 (3) 107.84 (3) 180.0 (5) 107.84 (3) 180.0 (5) 107.84 (3) 107.84 (3) 72.16 (3) 72.16 (3) 72.16 (3) 94.26 (4) 94.26 (4) 85.74 (4)

S—Sc—Svi S—Sc—Six Svii—Sc—Sviii Svii—Sc—Sv Svii—Sc—Svi Svii—Sc—Six Sviii—Sc—Sv Sviii—Sc—Svi Sviii—Sc—Six Sv—Sc—Svi Sv—Sc—Six Svi—Sc—Six Rbxiv—S—Rbxv Rbxiv—S—Rbxvi Rbxv—S—Rbxvi Scx—S—Scxii Scx—S—Sc

85.74 (4) 180.0 (5) 94.26 (4) 85.74 (4) 180.0 (5) 85.74 (4) 180.0 (5) 85.74 (4) 85.74 (4) 94.26 (4) 94.26 (4) 94.26 (4) 72.16 (4) 72.16 (4) 72.16 (4) 94.26 (6) 94.26 (6)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1, y−1, z; (xi) x−1, y, z; (xii) x, y−1, z; (xiii) x+1, y, z; (xiv) x−1/3, y−2/3, z+1/3; (xv) x−1/3, y+1/3, z+1/3; (xvi) x+2/3, y+1/3, z+1/3.

(III) Potassium neodymium sufide Crystal data KNdS2 Mr = 247.5 Trigonal, R3m Hall symbol: -R 3 2" a = 4.1626 (3) Å c = 21.8996 (19) Å V = 328.62 (5) Å3

Acta Cryst. (2015). C71, 623-630

Z=3 F(000) = 333 Dx = 3.75 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 1587 reflections θ = 5.6–29.4° µ = 13.52 mm−1

sup-4

supporting information T = 301 K Plate, blue

0.14 × 0.13 × 0.05 mm

Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 w/2q scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.258, Tmax = 0.544

1538 measured reflections 140 independent reflections 140 reflections with I > 3σ(I) Rint = 0.036 θmax = 29.5°, θmin = 5.6° h = −5→5 k = −5→5 l = −29→27

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.010 wR(F2) = 0.010 S = 0.60 140 reflections 9 parameters 0 restraints 0 constraints

Weighting scheme based on measured s.u.'s w = 1/[σ2(F) + 0.0001F2] (Δ/σ)max = 0.002 Δρmax = 0.17 e Å−3 Δρmin = −0.09 e Å−3 Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 160 (40)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Nd S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23595 (4)

0.0150 (3) 0.00774 (10) 0.0088 (2)

Atomic displacement parameters (Å2)

K Nd S

U11

U22

U33

U12

U13

U23

0.0160 (3) 0.00639 (13) 0.0082 (2)

0.0160 (3) 0.00639 (13) 0.0082 (2)

0.0131 (5) 0.01047 (16) 0.0101 (4)

0.00800 (17) 0.00320 (6) 0.00409 (13)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi Nd—S Nd—Svii

3.2132 (8) 3.2132 (7) 3.2132 (8) 3.2132 (8) 3.2132 (7) 3.2132 (8) 2.8421 (7) 2.8421 (5)

Nd—Sviii Nd—Sv Nd—Svi Nd—Six S—Siv S—Sv S—Svi

2.8421 (7) 2.8421 (7) 2.8421 (5) 2.8421 (7) 3.8708 (12) 3.8708 (11) 3.8708 (12)

Si—K—Sii Si—K—Siii

80.743 (14) 80.743 (16)

Svii—Nd—Sviii Svii—Nd—Sv

94.161 (16) 85.839 (16)

Acta Cryst. (2015). C71, 623-630

sup-5

supporting information Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Nd—Svii S—Nd—Sviii S—Nd—Sv S—Nd—Svi S—Nd—Six

99.257 (16) 99.257 (14) 180 80.743 (14) 99.257 (14) 180 99.257 (14) 180 99.257 (14) 99.257 (16) 80.743 (14) 80.743 (16) 80.743 (14) 94.161 (16) 94.161 (17) 85.839 (17) 85.839 (16) 180

Svii—Nd—Svi Svii—Nd—Six Sviii—Nd—Sv Sviii—Nd—Svi Sviii—Nd—Six Sv—Nd—Svi Sv—Nd—Six Svi—Nd—Six Kx—S—Kxi Kx—S—Kxii Kxi—S—Kxii Kxi—S—Ndxiii Kxi—S—Ndxiv Kxi—S—Nd Ndxiii—S—Ndxiv Ndxiii—S—Nd Ndxiv—S—Nd

180 85.839 (16) 180 85.839 (16) 85.839 (17) 94.161 (16) 94.161 (17) 94.161 (16) 80.743 (19) 80.74 (2) 80.743 (19) 92.183 (7) 170.68 (3) 92.183 (7) 94.16 (2) 94.16 (2) 94.16 (2)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(IV) Potassium samarium sulfide Crystal data KSmS2 Mr = 253.6 Trigonal, R3m Hall symbol: -R 3 2" a = 4.1174 (6) Å c = 21.888 (3) Å V = 321.35 (8) Å3 Z=3 F(000) = 339

Dx = 3.931 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 646 reflections θ = 5.6–28.9° µ = 15.42 mm−1 T = 293 K Plate, yellow 0.20 × 0.14 × 0.03 mm

Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.227, Tmax = 0.672

721 measured reflections 135 independent reflections 135 reflections with I > 3σ(I) Rint = 0.086 θmax = 29.0°, θmin = 5.6° h = −5→5 k = −4→5 l = −28→25

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.031 wR(F2) = 0.069 S = 1.86 135 reflections 9 parameters Acta Cryst. (2015). C71, 623-630

0 restraints 0 constraints Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.001 Δρmax = 1.48 e Å−3

sup-6

supporting information Δρmin = −1.79 e Å−3

Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 470 (150)

Special details Refinement. Refinement of a model with obverse-reverse twinning turned out to be insignificant. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Sm S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23520 (16)

0.0153 (11) 0.0073 (4) 0.0087 (8)

Atomic displacement parameters (Å2)

K Sm S

U11

U22

U33

U12

U13

U23

0.0174 (13) 0.0062 (5) 0.0092 (10)

0.0174 (13) 0.0062 (5) 0.0092 (10)

0.011 (2) 0.0096 (6) 0.0076 (15)

0.0087 (7) 0.0031 (2) 0.0046 (5)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi

3.204 (2) 3.204 (2) 3.204 (2) 3.204 (2) 3.204 (2) 3.204 (2)

Sm—S Sm—Svii Sm—Sviii Sm—Sv Sm—Svi Sm—Six

2.811 (2) 2.8109 (18) 2.811 (2) 2.811 (2) 2.8109 (18) 2.811 (2)

Si—K—Sii Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Sm—Svii

79.97 (5) 79.97 (5) 100.03 (5) 100.03 (5) 180.0 (5) 79.97 (5) 100.03 (5) 180.0 (5) 100.03 (5) 180.0 (5) 100.03 (5) 100.03 (5) 79.97 (5) 79.97 (5) 79.97 (5) 94.18 (6)

S—Sm—Svi S—Sm—Six Svii—Sm—Sviii Svii—Sm—Sv Svii—Sm—Svi Svii—Sm—Six Sviii—Sm—Sv Sviii—Sm—Svi Sviii—Sm—Six Sv—Sm—Svi Sv—Sm—Six Svi—Sm—Six Kx—S—Kxi Kx—S—Kxii Kxi—S—Kxii Smxiii—S—Smxiv

85.82 (6) 180.0 (5) 94.18 (6) 85.82 (6) 180.0 (5) 85.82 (6) 180.0 (5) 85.82 (6) 85.82 (6) 94.17 (6) 94.18 (6) 94.17 (6) 79.97 (7) 79.97 (7) 79.97 (7) 94.18 (8)

Acta Cryst. (2015). C71, 623-630

sup-7

supporting information S—Sm—Sviii S—Sm—Sv

94.18 (6) 85.82 (6)

Smxiii—S—Sm Smxiv—S—Sm

94.18 (8) 94.18 (8)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(V) Potassium terbium sulfide Crystal data Dx = 4.196 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 597 reflections θ = 5.6–28.7° µ = 18.81 mm−1 T = 295 K Prism, white 0.20 × 0.08 × 0.05 mm

KTbS2 Mr = 262.1 Trigonal, R3m Hall symbol: -R 3 2" a = 4.0523 (7) Å c = 21.885 (3) Å V = 311.23 (9) Å3 Z=3 F(000) = 348 Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.238, Tmax = 0.447

674 measured reflections 129 independent reflections 129 reflections with I > 3σ(I) Rint = 0.061 θmax = 29.3°, θmin = 5.6° h = −5→4 k = −5→5 l = −26→27

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.017 wR(F2) = 0.035 S = 0.97 129 reflections 9 parameters 0 restraints 0 constraints

Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.003 Δρmax = 0.45 e Å−3 Δρmin = −0.64 e Å−3 Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 1570 (120)

Special details Refinement. Refinement of a model with obverse–reverse twinning turned out to be insignificant. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Tb S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23463 (9)

0.0149 (6) 0.0076 (2) 0.0086 (5)

Acta Cryst. (2015). C71, 623-630

sup-8

supporting information Atomic displacement parameters (Å2)

K Tb S

U11

U22

U33

U12

U13

U23

0.0172 (7) 0.0067 (3) 0.0084 (5)

0.0172 (7) 0.0067 (3) 0.0084 (5)

0.0103 (11) 0.0094 (3) 0.0091 (8)

0.0086 (4) 0.00334 (14) 0.0042 (3)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi

3.1844 (16) 3.1844 (14) 3.1844 (16) 3.1844 (16) 3.1844 (14) 3.1844 (16)

Tb—S Tb—Svii Tb—Sviii Tb—Sv Tb—Svi Tb—Six

2.7723 (14) 2.7723 (11) 2.7723 (14) 2.7723 (14) 2.7723 (11) 2.7723 (14)

Si—K—Sii Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Tb—Svii S—Tb—Sviii S—Tb—Sv

79.03 (3) 79.03 (3) 100.97 (3) 100.97 (3) 180.0 (5) 79.03 (3) 100.97 (3) 180.0 (5) 100.97 (3) 180.0 (5) 100.97 (3) 100.97 (3) 79.03 (3) 79.03 (3) 79.03 (3) 93.92 (3) 93.92 (4) 86.08 (4)

S—Tb—Svi S—Tb—Six Svii—Tb—Sviii Svii—Tb—Sv Svii—Tb—Svi Svii—Tb—Six Sviii—Tb—Sv Sviii—Tb—Svi Sviii—Tb—Six Sv—Tb—Svi Sv—Tb—Six Svi—Tb—Six Kx—S—Kxi Kx—S—Kxii Kxi—S—Kxii Tbxiii—S—Tbxiv Tbxiii—S—Tb Tbxiv—S—Tb

86.08 (3) 180.0 (5) 93.92 (3) 86.08 (3) 180.0 (5) 86.08 (3) 180.0 (5) 86.08 (3) 86.08 (4) 93.92 (3) 93.92 (4) 93.92 (3) 79.03 (4) 79.03 (4) 79.03 (4) 93.92 (5) 93.92 (5) 93.92 (5)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(VI) Potassium dysprosium sulfide Crystal data KDyS2 Mr = 265.7 Trigonal, R3m Hall symbol: -R 3 2" a = 4.0315 (11) Å c = 21.890 (5) Å V = 308.11 (14) Å3 Z=3 F(000) = 351

Acta Cryst. (2015). C71, 623-630

Dx = 4.296 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 386 reflections θ = 5.9–28.6° µ = 19.97 mm−1 T = 294 K Block, white 0.21 × 0.09 × 0.03 mm

sup-9

supporting information Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.201, Tmax = 0.703

658 measured reflections 126 independent reflections 124 reflections with I > 3σ(I) Rint = 0.100 θmax = 29.3°, θmin = 5.6° h = −5→4 k = −3→5 l = −25→27

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.052 wR(F2) = 0.105 S = 2.32 126 reflections 9 parameters 0 restraints 0 constraints

Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.001 Δρmax = 4.44 e Å−3 Δρmin = −2.46 e Å−3 Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 1900 (400)

Special details Refinement. A model with inclusion of obverse–reverse twinning turned out to be insignificant. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Dy S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.2345 (3)

0.022 (3) 0.0137 (8) 0.0138 (19)

Atomic displacement parameters (Å2)

K Dy S

U11

U22

U33

U12

U13

U23

0.020 (3) 0.0106 (9) 0.011 (2)

0.020 (3) 0.0106 (9) 0.011 (2)

0.025 (5) 0.0199 (13) 0.019 (4)

0.0099 (14) 0.0053 (5) 0.0057 (10)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi Dy—S Dy—Svii

3.179 (5) 3.179 (5) 3.179 (5) 3.179 (5) 3.179 (5) 3.179 (5) 2.760 (4) 2.760 (4)

Dy—Sviii Dy—Sv Dy—Svi Dy—Six S—Siv S—Sv S—Svi

2.760 (4) 2.760 (4) 2.760 (4) 2.760 (4) 3.772 (8) 3.772 (8) 3.772 (8)

Si—K—Sii

78.72 (11)

S—Dy—Svi

86.18 (13)

Acta Cryst. (2015). C71, 623-630

sup-10

supporting information Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Dy—Svii S—Dy—Sviii S—Dy—Sv

78.72 (11) 101.28 (11) 101.28 (11) 180.0 (5) 78.72 (11) 101.28 (11) 180.0 (5) 101.28 (11) 180.0 (5) 101.28 (11) 101.28 (11) 78.72 (11) 78.72 (11) 78.72 (11) 93.82 (13) 93.82 (13) 86.18 (13)

S—Dy—Six Svii—Dy—Sviii Svii—Dy—Sv Svii—Dy—Svi Svii—Dy—Six Sviii—Dy—Sv Sviii—Dy—Svi Sviii—Dy—Six Sv—Dy—Svi Sv—Dy—Six Svi—Dy—Six Kx—S—Kxi Kx—S—Kxii Dyxiii—S—Dyxiv Dyxiii—S—Dy Dyxiv—S—Dy

180.0 (5) 93.82 (13) 86.18 (13) 180.0 (5) 86.18 (13) 180.0 (5) 86.18 (13) 86.18 (13) 93.82 (13) 93.82 (13) 93.82 (13) 78.72 (15) 78.72 (15) 93.82 (18) 93.82 (18) 93.82 (18)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(VII) Potassium holmium sulfide Crystal data KHoS2 Mr = 268.1 Trigonal, R3m Hall symbol: -R 3 2" a = 4.0098 (4) Å c = 21.878 (2) Å V = 304.64 (5) Å3 Z=3 F(000) = 354

Dx = 4.385 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 1327 reflections θ = 5.6–28.8° µ = 21.29 mm−1 T = 303 K Prism, yellow 0.19 × 0.14 × 0.07 mm

Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.090, Tmax = 0.243

2289 measured reflections 216 independent reflections 139 reflections with I > 3σ(I) Rint = 0.058 θmax = 29.2°, θmin = 5.6° h = −5→5 k = −5→5 l = −29→29

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.020 wR(F2) = 0.060 S = 1.56 216 reflections 10 parameters 0 restraints

Acta Cryst. (2015). C71, 623-630

0 constraints Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.002 Δρmax = 0.77 e Å−3 Δρmin = −1.00 e Å−3

sup-11

supporting information Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 1410 (130) Special details Refinement. Obverse–reverse twinning has been applied, with the twinning matrix (-1 0 0 / 0 - 1 0 / 0 0 1). The domainstate proportions are 0.99986 (3) and 0.00014 (3). Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Ho S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23430 (11)

0.0156 (8) 0.0077 (3) 0.0091 (6)

Atomic displacement parameters (Å2)

K Ho S

U11

U22

U33

U12

U13

U23

0.0180 (10) 0.0078 (4) 0.0105 (7)

0.0180 (10) 0.0078 (4) 0.0105 (7)

0.0108 (13) 0.0074 (4) 0.0063 (10)

0.0090 (5) 0.00390 (18) 0.0053 (4)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi

3.1708 (17) 3.1708 (17) 3.1708 (17) 3.1708 (17) 3.1708 (17) 3.1708 (17)

Ho—S Ho—Svii Ho—Sviii Ho—Sv Ho—Svi Ho—Six

2.7475 (14) 2.7475 (13) 2.7475 (14) 2.7475 (14) 2.7475 (13) 2.7475 (14)

Si—K—Sii Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Ho—Svii

78.44 (3) 78.44 (4) 101.56 (4) 101.56 (3) 180.0 (5) 78.44 (3) 101.56 (3) 180.0 (5) 101.56 (3) 180.0 (5) 101.56 (3) 101.56 (4) 78.44 (3) 78.44 (4) 78.44 (3) 93.73 (4)

S—Ho—Svi S—Ho—Six Svii—Ho—Sviii Svii—Ho—Sv Svii—Ho—Svi Svii—Ho—Six Sviii—Ho—Sv Sviii—Ho—Svi Sviii—Ho—Six Sv—Ho—Svi Sv—Ho—Six Svi—Ho—Six Kx—S—Kxi Kx—S—Kxii Kxi—S—Kxii Hoxiii—S—Hoxiv

86.28 (4) 180.0 (5) 93.73 (4) 86.28 (4) 180.0 (5) 86.28 (4) 180.0 (5) 86.28 (4) 86.28 (4) 93.72 (4) 93.72 (4) 93.72 (4) 78.44 (5) 78.44 (5) 78.44 (5) 93.73 (6)

Acta Cryst. (2015). C71, 623-630

sup-12

supporting information S—Ho—Sviii S—Ho—Sv

Hoxiii—S—Ho Hoxiv—S—Ho

93.73 (4) 86.28 (4)

93.73 (6) 93.73 (6)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(VIII) Potassium erbium sulfide Crystal data Dx = 4.462 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 1188 reflections θ = 5.6–28.9° µ = 22.66 mm−1 T = 296 K Block, pink 0.08 × 0.07 × 0.05 mm

KErS2 Mr = 270.5 Trigonal, R3m Hall symbol: -R 3 2" a = 3.9935 (4) Å c = 21.866 (2) Å V = 302.00 (5) Å3 Z=3 F(000) = 357 Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.255, Tmax = 0.434

1405 measured reflections 132 independent reflections 132 reflections with I > 3σ(I) Rint = 0.070 θmax = 29.1°, θmin = 2.8° h = −5→5 k = −5→5 l = −29→28

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.027 wR(F2) = 0.064 S = 1.81 132 reflections 9 parameters 0 restraints 0 constraints

Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.001 Δρmax = 1.54 e Å−3 Δρmin = −1.01 e Å−3 Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 770 (160)

Special details Refinement. The refinement of a model with obverse–reverse twinning turned out to be insignificant Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Er S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23407 (17)

0.0144 (13) 0.0074 (4) 0.0078 (9)

Acta Cryst. (2015). C71, 623-630

sup-13

supporting information Atomic displacement parameters (Å2)

K Er S

U11

U22

U33

U12

U13

U23

0.0138 (14) 0.0058 (5) 0.0075 (11)

0.0138 (14) 0.0058 (5) 0.0075 (11)

0.015 (2) 0.0105 (6) 0.0082 (17)

0.0069 (7) 0.0029 (2) 0.0038 (5)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi Er—S Er—Svii

3.166 (3) 3.166 (3) 3.166 (3) 3.166 (3) 3.166 (3) 3.166 (3) 2.737 (2) 2.737 (2)

Er—Sviii Er—Sv Er—Svi Er—Six S—Siv S—Sv S—Svi

2.737 (2) 2.737 (2) 2.737 (2) 2.737 (2) 3.742 (4) 3.742 (4) 3.742 (4)

Si—K—Sii Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Er—Svii S—Er—Sviii S—Er—Sv

78.19 (5) 78.19 (5) 101.81 (5) 101.81 (5) 180.0 (5) 78.19 (5) 101.81 (5) 180.0 (5) 101.81 (5) 180.0 (5) 101.81 (5) 101.81 (5) 78.19 (5) 78.19 (5) 78.19 (5) 93.72 (6) 93.72 (6) 86.28 (6)

S—Er—Svi S—Er—Six Svii—Er—Sviii Svii—Er—Sv Svii—Er—Svi Svii—Er—Six Sviii—Er—Sv Sviii—Er—Svi Sviii—Er—Six Sv—Er—Svi Sv—Er—Six Svi—Er—Six Kx—S—Kxi Kx—S—Kxii Kxi—S—Kxii Erxiii—S—Erxiv Erxiii—S—Er Erxiv—S—Er

86.28 (6) 180.0 (5) 93.72 (6) 86.28 (6) 180.0 (5) 86.28 (6) 180.0 (5) 86.28 (6) 86.28 (6) 93.72 (6) 93.72 (6) 93.72 (6) 78.19 (8) 78.19 (8) 78.19 (8) 93.72 (9) 93.72 (9) 93.72 (9)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(IX) Potassium thulium sulfide Crystal data KTmS2 Mr = 272.2 Trigonal, R3m Hall symbol: -R 3 2" a = 3.9761 (5) Å c = 21.841 (3) Å V = 299.03 (7) Å3 Acta Cryst. (2015). C71, 623-630

Z=3 F(000) = 360 Dx = 4.534 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 595 reflections θ = 5.6–29.1° µ = 24.09 mm−1

sup-14

supporting information T = 293 K Plate, yellow

0.17 × 0.11 × 0.06 mm

Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian JANA2006 (Petříček et al., 2014) Tmin = 0.111, Tmax = 0.291

637 measured reflections 124 independent reflections 124 reflections with I > 3σ(I) Rint = 0.048 θmax = 29.2°, θmin = 5.6° h = −5→3 k = −4→5 l = −28→20

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.016 wR(F2) = 0.040 S = 1.12 124 reflections 9 parameters 0 restraints 0 constraints

Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.001 Δρmax = 0.48 e Å−3 Δρmin = −1.00 e Å−3 Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 2710 (180)

Special details Refinement. The refinement of a model with obverse–reverse twinning turned out to be insignificant. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Tm S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23376 (11)

0.0143 (8) 0.0067 (3) 0.0083 (6)

Atomic displacement parameters (Å2)

K Tm S

U11

U22

U33

U12

U13

U23

0.0158 (10) 0.0061 (4) 0.0082 (7)

0.0158 (10) 0.0061 (4) 0.0082 (7)

0.0113 (15) 0.0079 (4) 0.0085 (11)

0.0079 (5) 0.00307 (19) 0.0041 (4)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi

3.1622 (19) 3.1622 (18) 3.1622 (19) 3.1622 (19) 3.1622 (18) 3.1622 (19)

Tm—S Tm—Svii Tm—Sviii Tm—Sv Tm—Svi Tm—Six

2.7235 (15) 2.7234 (14) 2.7235 (15) 2.7235 (15) 2.7235 (14) 2.7235 (15)

Si—K—Sii

77.91 (4)

S—Tm—Svi

86.23 (4)

Acta Cryst. (2015). C71, 623-630

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supporting information Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi Sv—K—Svi S—Tm—Svii S—Tm—Sviii S—Tm—Sv

77.91 (4) 102.09 (4) 102.09 (4) 180.0 (5) 77.91 (4) 102.09 (4) 180.0 (5) 102.09 (4) 180.0 (5) 102.09 (4) 102.09 (4) 77.91 (4) 77.91 (4) 77.91 (4) 93.77 (4) 93.77 (4) 86.23 (4)

S—Tm—Six Svii—Tm—Sviii Svii—Tm—Sv Svii—Tm—Svi Svii—Tm—Six Sviii—Tm—Sv Sviii—Tm—Svi Sviii—Tm—Six Sv—Tm—Svi Sv—Tm—Six Svi—Tm—Six Kx—S—Kxi Kx—S—Kxii Kxi—S—Kxii Tmxiii—S—Tmxiv Tmxiii—S—Tm Tmxiv—S—Tm

180.0 (5) 93.77 (4) 86.23 (4) 180.0 (5) 86.23 (4) 180.0 (5) 86.23 (4) 86.23 (4) 93.77 (4) 93.77 (4) 93.77 (4) 77.91 (5) 77.91 (5) 77.91 (5) 93.77 (6) 93.77 (6) 93.77 (6)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1/3, y−2/3, z+1/3; (xi) x−1/3, y+1/3, z+1/3; (xii) x+2/3, y+1/3, z+1/3; (xiii) x−1, y−1, z; (xiv) x, y−1, z.

(X) Potassium ytterbium sulfide Crystal data KYbS2 Mr = 276.3 Trigonal, R3m Hall symbol: -R 3 2" a = 3.9615 (8) Å c = 21.810 (3) Å V = 296.42 (9) Å3 Z=3 F(000) = 363

Dx = 4.643 Mg m−3 Mo Kα radiation, λ = 0.71073 Å Cell parameters from 582 reflections θ = 5.6–28.9° µ = 25.52 mm−1 T = 301 K Plate, yellow 0.13 × 0.11 × 0.09 mm

Data collection Xcalibur Gemini Ultra diffractometer with Atlas detector Radiation source: X-ray tube Graphite monochromator Detector resolution: 5.1873 pixels mm-1 ω scans Absorption correction: gaussian (JANA2006; Petříček et al., 2014) Tmin = 0.099, Tmax = 0.193

444 measured reflections 124 independent reflections 124 reflections with I > 3σ(I) Rint = 0.069 θmax = 29.0°, θmin = 5.6° h = −2→5 k = −5→4 l = −29→29

Refinement Refinement on F2 R[F2 > 2σ(F2)] = 0.029 wR(F2) = 0.069 S = 1.65 124 reflections 9 parameters 0 restraints

Acta Cryst. (2015). C71, 623-630

0 constraints Weighting scheme based on measured s.u.'s w = 1/[σ2(I) + 0.0004I2] (Δ/σ)max = 0.003 Δρmax = 1.42 e Å−3 Δρmin = −2.15 e Å−3

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supporting information Extinction correction: B-C type 1 Lorentzian isotropic [Becker, P. J. & Coppens, P. (1974). Acta Cryst. A30, 129–147] Extinction coefficient: 3900 (400)

Absolute structure: Refinement of a model with obverse–reverse twinning turned out to be insignificant

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

K Yb S

x

y

z

Uiso*/Ueq

0 0.333333 0

0 0.666667 0

0 0.166667 0.23346 (19)

0.0133 (13) 0.0063 (5) 0.0072 (10)

Atomic displacement parameters (Å2)

K Yb S

U11

U22

U33

U12

U13

U23

0.0146 (16) 0.0054 (6) 0.0077 (12)

0.0146 (16) 0.0054 (6) 0.0077 (12)

0.011 (2) 0.0081 (7) 0.0062 (16)

0.0073 (8) 0.0027 (3) 0.0039 (6)

0 0 0

0 0 0

Geometric parameters (Å, º) K—Si K—Sii K—Siii K—Siv K—Sv K—Svi Yb—S Yb—Svii Yb—Sviii Yb—Sv Yb—Svi

3.159 (3) 3.159 (3) 3.159 (3) 3.159 (3) 3.159 (3) 3.159 (3) 2.712 (2) 2.712 (2) 2.712 (2) 2.712 (2) 2.712 (2)

Yb—Six S—Sx S—Sxi S—Sxii S—Svii S—Sxiii S—Sviii S—Siv S—Sv S—Svi

2.712 (2) 3.961 (2) 3.9615 (16) 3.9615 (16) 3.9615 (16) 3.9615 (16) 3.961 (2) 3.704 (5) 3.704 (5) 3.704 (5)

Si—K—Sii Si—K—Siii Si—K—Siv Si—K—Sv Si—K—Svi Sii—K—Siii Sii—K—Siv Sii—K—Sv Sii—K—Svi Siii—K—Siv Siii—K—Sv Siii—K—Svi Siv—K—Sv Siv—K—Svi

77.67 (6) 77.67 (6) 102.33 (6) 102.33 (6) 180.0 (5) 77.67 (6) 102.33 (6) 180.0 (5) 102.33 (6) 180.0 (5) 102.33 (6) 102.33 (6) 77.67 (6) 77.67 (6)

S—Yb—Sviii S—Yb—Sv S—Yb—Svi S—Yb—Six Svii—Yb—Sviii Svii—Yb—Sv Svii—Yb—Svi Svii—Yb—Six Sviii—Yb—Sv Sviii—Yb—Svi Sviii—Yb—Six Sv—Yb—Svi Sv—Yb—Six Svi—Yb—Six

93.85 (7) 86.15 (7) 86.15 (7) 180.0 (5) 93.85 (7) 86.15 (7) 180.0 (5) 86.15 (7) 180.0 (5) 86.15 (7) 86.15 (7) 93.85 (7) 93.85 (7) 93.85 (7)

Acta Cryst. (2015). C71, 623-630

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supporting information Sv—K—Svi S—Yb—Svii

77.67 (6) 93.85 (7)

Kxiv—S—Kxv Kxiv—S—Kxvi

77.67 (8) 77.67 (9)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) x+1/3, y+2/3, z−1/3; (iv) y−1/3, x−2/3, −z+1/3; (v) y−1/3, x+1/3, −z+1/3; (vi) y+2/3, x+1/3, −z+1/3; (vii) x, y+1, z; (viii) x+1, y+1, z; (ix) y+2/3, x+4/3, −z+1/3; (x) x−1, y−1, z; (xi) x−1, y, z; (xii) x, y−1, z; (xiii) x+1, y, z; (xiv) x−1/3, y−2/3, z+1/3; (xv) x−1/3, y+1/3, z+1/3; (xvi) x+2/3, y+1/3, z+1/3.

Acta Cryst. (2015). C71, 623-630

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Structure determination of KScS₂, RbScS₂ and KLnS₂ (Ln = Nd, Sm, Tb, Dy, Ho, Er, Tm and Yb) and crystal-chemical discussion.

The title structures of KScS2 (potassium scandium sulfide), RbScS2 (rubidium scandium sulfide) and KLnS2 [Ln = Nd (potassium neodymium sufide), Sm (po...
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