Crystal structure and electrical resistance property of Rb0.21(H2O) y WS2.

Rb0.21(H2O) y WS2, rubidium hydrate di-thio-tungstate, is a new quasi two-dimensional sulfide. Its crystal structure consists of ordered WS2 layers, separated by disordered Rb+ ions and water mol-ecules. All atomic sites are located on mirror planes. The WS2 layers are composed of edge-sharing [WS6] octa-hedra and extend parallel to (001). The presence of structural water was revealed by thermogravimetry, but the position and exact amount could not be determined in the present study. The temperature dependence of the electrical resistance indicates that Rb0.21(H2O) y WS2 is semiconducting between 80-300 K.

Chemical context

Typical two-dimensional structures of MS2 compounds (M = transition metals of group IVB–VIB) facilitate the inter­calation of various atoms, ions or organic mol­ecules (Whittingham et al., 1978 ▸). For example, A x MS2 (A = alkali metal; M = Nb, Ta, Ti, V) compounds can be prepared in high-temperature solid-state reactions (800–1000 K). These com­pounds can react with water mol­ecules to form ionic hydrates A + (H2O)[MS2] (Omloo & Jellinek, 1970 ▸; Lerf & Schöllhorn, 1977 ▸; Lobert et al., 1992 ▸) that exhibit ion-exchange and solvent-exchange capacities. Some of the A + (H2O)[MS2] compounds show unusual superconducting properties (Schöllhorn & Weiss, 1974 ▸; Sernetz et al., 1974 ▸). Recently, by removing alkali ions from inter­calated A + (H2O)[MS2] (A = alkali metal) compounds, several metastable MS2 (M = Mo, W) phases with new crystal structures and novel physical properties were reported (Fang et al., 2018 ▸, 2019 ▸). In order to identify the formation mechanism of metastable MS2 from A + (H2O)[MS2], it is necessary to uncover the role of alkali ions inter­calated into the inter­layers of MS2.

In this communication, we report the preparation of Rb0.21(H2O)WS2, its crystal structure determination by single crystal X-ray diffraction, its thermal behaviour and its electrical resistance property.

Structural commentary

Rb0.21(H2O)WS2 crystallizes in the monoclinic P21/m (No. 11) space group. The structure consists of one independent W site, two independent S sites and two independent Rb sites, all of them located on a mirror plane (Wyckoff position 2e). The crystal structure features ordered WS2 layers separated by disordered Rb+ ions, and of water mol­ecules. The latter could not be localized in the current study, hence y in Rb0.21(H2O)WS2 remains undetermined (see Experimental, and discussion below). Compared with [WS6]8– trigonal prisms in 2H-WS2 (Schutte et al., 1987 ▸), the WS2 layer in Rb0.21(H2O)WS2 is composed of edge-sharing [WS6]8.21– octa­hedra. The W—S bond lengths range from 2.403 (4) Å to 2.550 (5) Å, and thus the average W—S distance is larger than that in 2H-WS2 [2.405 (5) Å; Schutte et al., 1987 ▸]. The WS2 layers extend parallel to (001) (Fig. 1 ▸). The shortest W—W bond length of 2.7678 (15) Å is between pairs of W atoms aligned in the [10] direction, much shorter than the W⋯W distance of 3.2524 (18) Å along [010]. Similar metal–metal separations also exist in some metastable MS2 phases prepared by de-inter­calating alkali ions from A x(H2O)y MS2 compounds (Yu et al., 2018 ▸; Shang et al., 2018 ▸). The Rb+ cations show a one-sided coordination to the S atoms of the adjacent layer. The Rb—S bonds range from 3.47 (7) Å to 3.64 (5) Å, comparable to the Rb—S bonds [3.344 (7)–3.561 (1) Å] in RbCr5S8 (Huster, 1978 ▸).

Figure 1

Crystal structure of Rb0.21(H2O)WS2 with displacement ellipsoids drawn at the 30% probability level.

Similar to K(H2O)TaS2 and K(H2O)NbS2 (Graf et al., 1977 ▸), it was impossible to determine the light O atoms of water mol­ecules in the title compound from X-ray diffraction data at room temperature, as a result of diffuse electron density in the inter­layer space. However, we could localize the positions of disordered Rb+ ions with large displacement parameters. Stacking disorder of the layers is common for layered dichalcogenides, which may contribute to the diffuse electron density. Large displacement parameters of exchangeable cations and water mol­ecules were also reported for A x(H2O)yTaS2 and A x(H2O)yNbS2 (A = alkali metal) compounds (Röder et al., 1979 ▸; Wein et al. 1986 ▸; Lobert et al., 1992 ▸).

Electrical resistance property

The electrical resistance of Rb0.21(H2O)WS2 increases with the decrease of temperature (80–300 K) (Fig. 2 ▸), which is characteristic of a semiconductor.

Figure 2

Temperature-dependence of the log(Resistance) for Rb0.21(H2O)WS2.

Synthesis and crystallization

A rubidium di­thio­tungstate RbWS2 was synthesized in a solid-state reaction. The starting Rb2S2 powder was prepared in a reaction of stoichiometric amounts of Rb pieces and S powder in liquid NH3. The obtained Rb2S2 powder, W powder and S powder were mixed in the molar ratio of 1:1:1 in a glove box filled with Ar. The mixture was ground carefully and loaded in a carbon-coated fused-silica tube. The tube was sealed under a 10−4 Torr atmosphere and slowly heated to 1123 K at 5 K min−1. After three days, the furnace was cooled down naturally to room temperature. Subsequent removal of the extra flux by washing with distilled water led to the isolation of crystals of Rb0.21(H2O)WS2. The morphology and element composition were investigated by using an EDXS-equipped Hitachi S-4800 scanning electronic microscope. In addition, the Rb/W ratio in the Rbx(H2O)yWS2 crystals was determined by ICP-OES. The SEM image and EDX spectrum of Rb0.21(H2O)yWS2 crystals are shown in Fig. 3 ▸. The ratio of Rb/W from the EDXS analysis is close to 0.21, which is consistent with the the diffraction data and results from ICP–OES measurements (Table 1 ▸). The experimental powder X-ray diffraction (PXRD) pattern matches well with the simulated one (Fig. 4 ▸) by using the Rietveld refinement method (Rodríguez-Carvajal, 1993 ▸; R p = 9.9%, R wp = 12.6% and χ 2 = 1.3). In the TG–DTA analyses (Fig. 5 ▸), one obvious endothermic effect and concomitant mass loss were observed at 343 K, which is associated with water evaporation. In order to judge whether water mol­ecules are surface-adsorbed water or structural water, the Rb0.21(H2O)WS2 crystals were heated up to 373 K for further PXRD measurement. The sample was prepared in an Ar-protected glove box and sealed with vacuum tape. The (002) reflection clearly moved to higher diffraction angles, indicating the shrinkage of the unit cell due to loss of inter­calated water (Fig. 6 ▸). However, it was impossible to accurately determine the water content by mass loss alone because of the inter­ference of possible surface-adsorbed water.

Figure 3

SEM image and EDXS spectrum of Rb0.21(H2O)WS2.

Table 1

Results of ICP–OES measurement of Rb0.21(H2O)WS2

Element	Weight (%)	atom (%)
W	67.6	36.77
Rb	6.6	7.72

Figure 4

Rietveld plot of Rb0.21(H2O)WS2.

Figure 5

TG–DTA analysis of Rb0.21(H2O)WS2.

Figure 6

Power X-ray diffraction pattern of Rb0.21(H2O)WS2 and Rb0.21WS2.

Refinement details

Crystal data, data collection and structure refinement details are summarized in Table 2 ▸. The localization of ordered W and S sites of the WS2 layers was unproblematic. The highest inter­layer difference electron density peak was then treated as a single but partially occupied Rb site. No evidence of superstructure reflections in reciprocal space was found for the ordering of the Rb site. Then, the W, S sites and the underoccupied Rb site were refined with anisotropic displacement parameters. Because of very large anisotropic displacement parameters (U 11 = 0.59 Å2) of the Rb site, splitting of this site was considered, resulting in a residual R 1 = 0.051. Modelling the O sites as being part of this disorder, or of remaining electron density peaks in the vicinity of the Rb sites was not successful, and therefore we did not include the apparently disordered water mol­ecules in the final structure model. The remaining maximum and minimum electron densities are located 0.87 and 1.14 Å, respectively, from the W1 site.

Table 2

Experimental details

Crystal data
Chemical formula	Rb0.21(H2O)yWS2
M r	277.23
Crystal system, space group	Monoclinic, P21/m
Temperature (K)	298
a, b, c (Å)	5.703 (3), 3.2524 (18), 9.423 (5)
β (°)	99.724 (16)
V (Å3)	172.27 (16)
Z	2
Radiation type	Mo Kα
μ (mm−1)	39.25
Crystal size (mm)	0.05 × 0.03 × 0.01
Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2015 ▸)
T min, T max	0.251, 0.674
No. of measured, independent and observed [I > 2σ(I)] reflections	1167, 352, 327
R int	0.030
(sin θ/λ)max (Å−1)	0.593
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.050, 0.124, 1.10
No. of reflections	352
No. of parameters	33
H-atom treatment	H-atom parameters not defined
Δρmax, Δρmin (e Å−3)	2.45, −1.66

Computer programs: APEX3 and SAINT (Bruker, 2015 ▸), SHELXS (Sheldrick, 2008 ▸), SHELXL2014/7 (Sheldrick, 2015 ▸), DIAMOND (Brandenburg, 2004 ▸) and publCIF (Westrip, 2010 ▸).

Crystal structure: contains datablock(s) I. DOI: 10.1107/S2056989019007941/wm5498sup1.cif

Structure factors: contains datablock(s) I. DOI: 10.1107/S2056989019007941/wm5498Isup2.hkl

CCDC reference: 1920386

Additional supporting information: crystallographic information; 3D view; checkCIF report

Rb0.21(H2O)yWS2	F(000) = 237
Mr = 277.23	Dx = 5.345 Mg m−3
Monoclinic, P21/m	Mo Kα radiation, λ = 0.71073 Å
a = 5.703 (3) Å	Cell parameters from 68 reflections
b = 3.2524 (18) Å	θ = 3.9–23.0°
c = 9.423 (5) Å	µ = 39.25 mm−1
β = 99.724 (16)°	T = 298 K
V = 172.27 (16) Å3	Plate, black
Z = 2	0.05 × 0.03 × 0.01 mm

Bruker APEXII CCD diffractometer	327 reflections with I > 2σ(I)
phi and ω scans	Rint = 0.030
Absorption correction: multi-scan (SADABS; Bruker, 2015)	θmax = 24.9°, θmin = 2.2°
Tmin = 0.251, Tmax = 0.674	h = −6→6
1167 measured reflections	k = −3→3
352 independent reflections	l = −11→10

Refinement on F2	0 restraints
Least-squares matrix: full	H-atom parameters not defined
R[F2 > 2σ(F2)] = 0.050	w = 1/[σ2(Fo2) + (0.1024P)2] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.124	(Δ/σ)max < 0.001
S = 1.10	Δρmax = 2.45 e Å−3
352 reflections	Δρmin = −1.66 e Å−3
33 parameters

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

	x	y	z	Uiso*/Ueq	Occ. (<1)
W1	0.19782 (11)	0.7500	1.00615 (8)	0.0371 (5)
S2	0.3744 (9)	0.2500	0.8600 (6)	0.0376 (12)
S3	0.1409 (10)	0.2500	1.1850 (6)	0.0401 (12)
Rb4	0.21 (4)	−0.2500	0.534 (6)	0.14 (6)	0.14 (7)
Rb5	0.38 (2)	−0.2500	0.525 (8)	0.17 (2)	0.20 (6)

	U11	U22	U33	U12	U13	U23
W1	0.0319 (7)	0.0374 (7)	0.0423 (7)	0.000	0.0073 (4)	0.000
S2	0.034 (2)	0.038 (3)	0.041 (3)	0.000	0.007 (2)	0.000
S3	0.041 (3)	0.039 (3)	0.041 (3)	0.000	0.008 (2)	0.000
Rb4	0.28 (14)	0.12 (4)	0.04 (2)	0.000	0.06 (4)	0.000
Rb5	0.18 (6)	0.24 (6)	0.08 (3)	0.000	0.01 (3)	0.000

W1—S3i	2.403 (4)	Rb4—Rb5	0.99 (10)
W1—S3	2.403 (4)	Rb4—Rb4x	2.9 (3)
W1—S3ii	2.408 (5)	Rb4—Rb4xi	2.9 (3)
W1—S2	2.454 (4)	Rb4—Rb5xii	3.0 (3)
W1—S2i	2.454 (4)	Rb4—Rb5xiii	3.0 (3)
W1—S2iii	2.550 (5)	Rb4—Rb4i	3.252 (2)
W1—W1ii	2.7678 (15)	Rb4—Rb4v	3.2524 (19)
W1—W1iv	2.7678 (15)	Rb4—Rb5i	3.40 (3)
S2—W1v	2.454 (4)	Rb4—Rb5v	3.40 (3)
S2—W1iii	2.550 (5)	Rb4—S2v	3.47 (7)
S2—Rb4	3.47 (7)	Rb4—S3vii	3.58 (11)
S2—Rb4i	3.47 (7)	Rb5—Rb5xii	2.23 (19)
S2—Rb5i	3.56 (8)	Rb5—Rb5xiii	2.23 (19)
S2—Rb5	3.56 (8)	Rb5—Rb4xii	3.0 (3)
S3—W1v	2.403 (4)	Rb5—Rb4xiii	3.0 (3)
S3—W1ii	2.408 (5)	Rb5—Rb5i	3.2524 (18)
S3—Rb5vi	3.53 (6)	Rb5—Rb5v	3.2524 (18)
S3—Rb4vii	3.58 (11)	Rb5—Rb4v	3.40 (3)
S3—Rb4viii	3.63 (4)	Rb5—Rb4i	3.40 (3)
S3—Rb4ix	3.63 (4)	Rb5—S3vi	3.53 (6)
S3—Rb5viii	3.64 (5)	Rb5—S2v	3.56 (8)
S3—Rb5ix	3.64 (5)
S3i—W1—S3	85.18 (18)	Rb5xii—Rb4—Rb5i	40 (3)
S3i—W1—S3ii	109.76 (14)	Rb5xiii—Rb4—Rb5i	106 (4)
S3—W1—S3ii	109.76 (14)	Rb4i—Rb4—Rb5i	16.9 (16)
S3i—W1—S2	163.5 (2)	Rb4v—Rb4—Rb5i	163.1 (16)
S3—W1—S2	93.55 (13)	Rb5—Rb4—Rb5v	73.1 (16)
S3ii—W1—S2	86.20 (17)	Rb4x—Rb4—Rb5v	71 (3)
S3i—W1—S2i	93.55 (13)	Rb4xi—Rb4—Rb5v	140 (7)
S3—W1—S2i	163.5 (2)	Rb5xii—Rb4—Rb5v	106 (4)
S3ii—W1—S2i	86.20 (17)	Rb5xiii—Rb4—Rb5v	40 (3)
S2—W1—S2i	82.99 (18)	Rb4i—Rb4—Rb5v	163.1 (16)
S3i—W1—S2iii	83.36 (18)	Rb4v—Rb4—Rb5v	16.9 (16)
S3—W1—S2iii	83.36 (18)	Rb5i—Rb4—Rb5v	146 (3)
S3ii—W1—S2iii	161.7 (2)	Rb5—Rb4—S2v	87 (10)
S2—W1—S2iii	80.13 (16)	Rb4x—Rb4—S2v	91.3 (12)
S2i—W1—S2iii	80.13 (16)	Rb4xi—Rb4—S2v	124 (4)
S3i—W1—W1ii	102.78 (13)	Rb5xii—Rb4—S2v	108 (5)
S3—W1—W1ii	54.97 (13)	Rb5xiii—Rb4—S2v	79 (2)
S3ii—W1—W1ii	54.79 (10)	Rb4i—Rb4—S2v	118.0 (6)
S2—W1—W1ii	89.78 (11)	Rb4v—Rb4—S2v	62.0 (6)
S2i—W1—W1ii	140.78 (13)	Rb5i—Rb4—S2v	116 (4)
S2iii—W1—W1ii	136.53 (8)	Rb5v—Rb4—S2v	62 (2)
S3i—W1—W1iv	54.97 (13)	Rb5—Rb4—S2	87 (10)
S3—W1—W1iv	102.78 (13)	Rb4x—Rb4—S2	124 (4)
S3ii—W1—W1iv	54.79 (10)	Rb4xi—Rb4—S2	91.3 (12)
S2—W1—W1iv	140.78 (13)	Rb5xii—Rb4—S2	79 (2)
S2i—W1—W1iv	89.78 (11)	Rb5xiii—Rb4—S2	108 (5)
S2iii—W1—W1iv	136.53 (8)	Rb4i—Rb4—S2	62.0 (6)
W1ii—W1—W1iv	71.96 (5)	Rb4v—Rb4—S2	118.0 (6)
W1v—S2—W1	82.99 (18)	Rb5i—Rb4—S2	62 (2)
W1v—S2—W1iii	99.87 (16)	Rb5v—Rb4—S2	116 (4)
W1—S2—W1iii	99.87 (16)	S2v—Rb4—S2	56.0 (12)
W1v—S2—Rb4	96.3 (15)	Rb5—Rb4—S3vii	138 (10)
W1—S2—Rb4	137 (3)	Rb4x—Rb4—S3vii	68 (4)
W1iii—S2—Rb4	122 (3)	Rb4xi—Rb4—S3vii	68 (4)
W1v—S2—Rb4i	137 (3)	Rb5xii—Rb4—S3vii	133.8 (12)
W1—S2—Rb4i	96.3 (15)	Rb5xiii—Rb4—S3vii	133.8 (12)
W1iii—S2—Rb4i	122 (3)	Rb4i—Rb4—S3vii	90.000 (2)
Rb4—S2—Rb4i	56.0 (12)	Rb4v—Rb4—S3vii	90.000 (1)
W1v—S2—Rb5i	150.1 (12)	Rb5i—Rb4—S3vii	102.5 (13)
W1—S2—Rb5i	105.1 (13)	Rb5v—Rb4—S3vii	102.5 (12)
W1iii—S2—Rb5i	106.8 (18)	S2v—Rb4—S3vii	56.3 (7)
Rb4—S2—Rb5i	57.9 (7)	S2—Rb4—S3vii	56.3 (7)
Rb4i—S2—Rb5i	16.1 (18)	Rb4—Rb5—Rb5xii	132 (4)
W1v—S2—Rb5	105.1 (13)	Rb4—Rb5—Rb5xiii	132 (4)
W1—S2—Rb5	150.1 (12)	Rb5xii—Rb5—Rb5xiii	94 (10)
W1iii—S2—Rb5	106.8 (18)	Rb4—Rb5—Rb4xii	146 (2)
Rb4—S2—Rb5	16.1 (18)	Rb5xii—Rb5—Rb4xii	14.3 (18)
Rb4i—S2—Rb5	57.9 (7)	Rb5xiii—Rb5—Rb4xii	80 (8)
Rb5i—S2—Rb5	54.4 (14)	Rb4—Rb5—Rb4xiii	146 (2)
W1v—S3—W1	85.18 (18)	Rb5xii—Rb5—Rb4xiii	80 (8)
W1v—S3—W1ii	70.24 (14)	Rb5xiii—Rb5—Rb4xiii	14.3 (18)
W1—S3—W1ii	70.24 (14)	Rb4xii—Rb5—Rb4xiii	66 (7)
W1v—S3—Rb5vi	111.4 (15)	Rb4—Rb5—Rb5i	90.00 (5)
W1—S3—Rb5vi	111.4 (16)	Rb5xii—Rb5—Rb5i	43 (5)
W1ii—S3—Rb5vi	178 (2)	Rb5xiii—Rb5—Rb5i	137 (5)
W1v—S3—Rb4vii	132.7 (12)	Rb4xii—Rb5—Rb5i	57 (3)
W1—S3—Rb4vii	132.7 (11)	Rb4xiii—Rb5—Rb5i	123 (3)
W1ii—S3—Rb4vii	94 (3)	Rb4—Rb5—Rb5v	90.00 (10)
Rb5vi—S3—Rb4vii	83.2 (13)	Rb5xii—Rb5—Rb5v	137 (5)
W1v—S3—Rb4viii	159 (2)	Rb5xiii—Rb5—Rb5v	43 (5)
W1—S3—Rb4viii	109.0 (6)	Rb4xii—Rb5—Rb5v	123 (3)
W1ii—S3—Rb4viii	129 (3)	Rb4xiii—Rb5—Rb5v	57 (3)
Rb5vi—S3—Rb4viii	49 (5)	Rb5i—Rb5—Rb5v	180.00 (7)
Rb4vii—S3—Rb4viii	47 (5)	Rb4—Rb5—Rb4v	73.1 (17)
W1v—S3—Rb4ix	109.0 (6)	Rb5xii—Rb5—Rb4v	153 (5)
W1—S3—Rb4ix	159 (2)	Rb5xiii—Rb5—Rb4v	60 (6)
W1ii—S3—Rb4ix	129 (3)	Rb4xii—Rb5—Rb4v	140 (3)
Rb5vi—S3—Rb4ix	49 (5)	Rb4xiii—Rb5—Rb4v	74 (4)
Rb4vii—S3—Rb4ix	47 (5)	Rb5i—Rb5—Rb4v	163.1 (16)
Rb4viii—S3—Rb4ix	53.3 (7)	Rb5v—Rb5—Rb4v	16.9 (16)
W1v—S3—Rb5viii	147.5 (16)	Rb4—Rb5—Rb4i	73.1 (16)
W1—S3—Rb5viii	103.9 (12)	Rb5xii—Rb5—Rb4i	60 (6)
W1ii—S3—Rb5viii	142.2 (16)	Rb5xiii—Rb5—Rb4i	153 (5)
Rb5vi—S3—Rb5viii	36 (3)	Rb4xii—Rb5—Rb4i	74 (4)
Rb4vii—S3—Rb5viii	61 (4)	Rb4xiii—Rb5—Rb4i	140 (3)
Rb4viii—S3—Rb5viii	15.7 (16)	Rb5i—Rb5—Rb4i	16.9 (16)
Rb4ix—S3—Rb5viii	55.8 (6)	Rb5v—Rb5—Rb4i	163.1 (16)
W1v—S3—Rb5ix	103.9 (12)	Rb4v—Rb5—Rb4i	146 (3)
W1—S3—Rb5ix	147.5 (16)	Rb4—Rb5—S3vi	125 (9)
W1ii—S3—Rb5ix	142.2 (16)	Rb5xii—Rb5—S3vi	75 (3)
Rb5vi—S3—Rb5ix	36 (3)	Rb5xiii—Rb5—S3vi	75 (3)
Rb4vii—S3—Rb5ix	61 (4)	Rb4xii—Rb5—S3vi	67 (4)
Rb4viii—S3—Rb5ix	55.8 (6)	Rb4xiii—Rb5—S3vi	67 (4)
Rb4ix—S3—Rb5ix	15.7 (16)	Rb5i—Rb5—S3vi	90.000 (5)
Rb5viii—S3—Rb5ix	53.0 (8)	Rb5v—Rb5—S3vi	90.000 (2)
Rb5—Rb4—Rb4x	141 (2)	Rb4v—Rb5—S3vi	100 (3)
Rb5—Rb4—Rb4xi	141 (2)	Rb4i—Rb5—S3vi	100 (3)
Rb4x—Rb4—Rb4xi	69 (9)	Rb4—Rb5—S2v	77 (8)
Rb5—Rb4—Rb5xii	34 (2)	Rb5xii—Rb5—S2v	128 (3)
Rb4x—Rb4—Rb5xii	157 (2)	Rb5xiii—Rb5—S2v	87 (3)
Rb4xi—Rb4—Rb5xii	107.5 (14)	Rb4xii—Rb5—S2v	123 (3)
Rb5—Rb4—Rb5xiii	34 (2)	Rb4xiii—Rb5—S2v	92.3 (10)
Rb4x—Rb4—Rb5xiii	107.5 (13)	Rb5i—Rb5—S2v	117.2 (7)
Rb4xi—Rb4—Rb5xiii	157 (2)	Rb5v—Rb5—S2v	62.8 (7)
Rb5xii—Rb4—Rb5xiii	66 (7)	Rb4v—Rb5—S2v	59.7 (19)
Rb5—Rb4—Rb4i	90.00 (5)	Rb4i—Rb5—S2v	112 (3)
Rb4x—Rb4—Rb4i	125 (5)	S3vi—Rb5—S2v	55.4 (8)
Rb4xi—Rb4—Rb4i	55 (5)	Rb4—Rb5—S2	77 (8)
Rb5xii—Rb4—Rb4i	57 (3)	Rb5xii—Rb5—S2	87 (3)
Rb5xiii—Rb4—Rb4i	123 (3)	Rb5xiii—Rb5—S2	128 (3)
Rb5—Rb4—Rb4v	90.000 (19)	Rb4xii—Rb5—S2	92.3 (10)
Rb4x—Rb4—Rb4v	55 (5)	Rb4xiii—Rb5—S2	123 (3)
Rb4xi—Rb4—Rb4v	125 (5)	Rb5i—Rb5—S2	62.8 (7)
Rb5xii—Rb4—Rb4v	123 (3)	Rb5v—Rb5—S2	117.2 (7)
Rb5xiii—Rb4—Rb4v	57 (3)	Rb4v—Rb5—S2	112 (3)
Rb4i—Rb4—Rb4v	180.00 (10)	Rb4i—Rb5—S2	59.7 (19)
Rb5—Rb4—Rb5i	73.1 (16)	S3vi—Rb5—S2	55.4 (8)
Rb4x—Rb4—Rb5i	140 (7)	S2v—Rb5—S2	54.4 (14)
Rb4xi—Rb4—Rb5i	71 (3)