New clathrates of Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3)

Abstract

New Tl type-I clathrates of K_7.62(1)Tl_0.38(1)Ge_45.34(3) and Rb_7.50(1)Tl_0.50(1)Ge₄₆ were synthesized via solid-state reaction. Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3) were found to crystallize in space groups Pm3̄n and Ia3̄d with lattice parameters of a = 10.81559(7) Å and a = 21.4290(2) Å, respectively. Theoretical calculations indicated metallic features based on the calculation models of Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆ in the space group of Pm3̄. The densities of states at the Fermi level were predominantly determined by the Ge s and Ge p orbitals of Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆.

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Introduction

Clathrate compounds are composed of host frameworks that embrace guest species in polyhedral cages. The first representatives were hydrates of various gases and liquids.¹ The discovery of sodium silicide Na₈Si₄₆ and Na_xSi₁₃₆ started the era of intermetallic and semiconducting clathrates.^2–13 Interest in clathrates had grown rapidly due to development of the “phonon glass-electron crystal” concept,¹⁴ according to which clathrates are promising thermoelectric materials. Furthermore, some clathrates demonstrated a high thermoelectric figure of merit ZT, e.g. Ba₈Ge₃₀Ga₁₆ (ref. 15) with ZT = 1.3 at 800 K and Ba₈Au_5.3Ge_40.7 (ref. 16) with ZT = 0.92 at 600 K. Besides thermoelectric properties, superconductivity and ferromagnetism were revealed for clathrates in Ba_8−xSi₄₆,¹⁷ Eu₈Ga₁₆Ge₃₀ (ref. 18) and Ba₈Mn₂Ge₄₄.¹⁹ Binary, ternary and quaternary clathrates with various structure types have been synthesized.^1–37 To date type-I clathrates,^{1,2,4–11,14–17,19–27} type-II clathrates,^{3,12,13,28–32} type-III clathrates,^33,34 type-VIII clathrates,^35,36 type-IX clathrates¹⁸ and type-X clathrates³⁷ have been discovered.

The majority of clathrates belong to the type-I structure type, and most type-I clathrates crystallize in the cubic space group Pm3̄n.^20–22 The crystal structure feature a three-dimensional host framework, based on the group 14 elements Si, Ge and Sn, encapsulating guest atoms in large cavities. Strong covalent bonds exist within the framework, whereas the guest atoms are held within the framework cavities by weaker interactions. In polar clathrates electron balance between host and guest substructures obey the Zintl rules.³⁸ It implies that electronegative atoms accepted electrons from more electropositive atoms to complete the 8-electron shell.

The clathrates based on alkaline metal Si/Ge^2–8,12,13 were synthesized previously by thermal decomposition the binary AM (A = alkali metal, M = Si/Ge) compounds. Later binary tin based clathrates^9–11 and ternary clathrates^25–49 were prepared via solid-state reactions from the constituent elements. We have successfully prepared alkaline metal and thallium clathrate-II Cs₈Na_16−xTl_xGe₁₃₆ via solid-state reaction.³⁰ Herein the synthesis and structure of thallium clathrate-I Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3) are reported.

Experimental

Synthetic procedure

The starting materials were high-purity elemental Rb, K, Tl and Ge. The assumed compositions of Rb₆Tl₂Ge₄₄ and K₆Tl₂Ge₄₄ were determined according to a clathrate-I containing 184 electrons per unit cell. Circa 1 gram of determined stoichiometric ratios of the mixed raw materials were loaded into Ta tubes. The containers were sealed by welding in an argon-filled glovebox [c(O₂) and c(H₂O) ≤ 1 ppm]. The Ta tubes were then taken out of the glovebox and put into quartz ampoules. The quartz tubes were sealed in a vacuum atmosphere, then heated at 650 °C for 2 weeks. The containers were then opened in air. The products were washed with distilled water and acetone then dried at 80 °C for 12 h in air.

Morphology and composition

The appropriately prepared metallographic specimens were investigated on a Philips XL 30 scanning electron microscope equipped with a LaB₆ cathode. The chemical composition was determined by energy dispersive X-ray spectroscopy (EDXS; EDXS Genesis Software V4.61) using a Si (Li) detector attached to the scanning electron microscope. Compositions were calculated from the background-corrected intensities of the X-ray lines Rb L, K K, Tl L and Ge K, which were excited by the electron beam at a 25 kV acceleration voltage. A standardless method with ZAF-matrix corrections was used.

Powder X-ray diffraction

The powder XRD patterns were collected using Guinier technique (Huber Image Plate Camera G670, Cu K_α1 radiation, λ = 1.54056 Å, 3.0° < 2θ < 100.3°, step width 0.005°). The structures were resolved from powder XRD data by means of least-squares technique using the WinCSD program.⁵⁰ For structure presentation the program Diamond 3.0 was used.⁵¹

Theoretical calculation

First-principle calculations were carried out by means of density functional theory using the pseudo-potential as implemented in the VASP code.⁵² The exchange-correlation potential was calculated using the generalized gradient approximation (GGA) as proposed by Perdew Burke Ernzerhof.⁵³ The calculation accuracy was 10⁻⁵ eV using a 280 eV cut-off in the plane wave expansion and a 2 × 2 × 2 Monkhorst–Pack k grid on the simplified structure models of Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₅. Rb₇Tl₁Ge₄₆ structure model was obtained by first revision the crystallographic information file to get ordered file through changing the occupancy Tl1 to 1 to obtain Rb₆Tl₂Ge₄₆. Next the ordered model Rb₆Tl₂Ge₄₆ was input. Its symmetry was set to P1 then one Tl1 atom was changed to Rb1. A new symmetry of Pm3̄ was found and the calculation model Rb₇Tl₁Ge₄₆ in Pm3̄ was obtained. K_7.62(1)Tl_0.38(1)Ge_45.34(3) in space group of Ia3̄d was a 2 × 2 × 2 times superstructure of Rb_7.50(1)Tl_0.50(1)Ge₄₆. For simplicity we used crystallographic information file of Rb_7.50(1)Tl_0.50(1)Ge₄₆ as the original model of K_7.62(1)Tl_0.38(1)Ge_45.34(3) by changing the lattice parameter to 10.7145(1) Å in space group Pm3̄n, setting Rb1 and Rb2 to Tl1 and K2 with complete occupancy to obtain ordered K₆Tl₂Ge₄₆. K₆Tl₂Ge₄₆ was imported. Its symmetry was set to P1, then one Tl1 was changed to K1. A new symmetry of Pm3̄ was found and the calculation model of K₇Tl₁Ge₄₆ was obtained. The ordered input files of Rb₆Tl₂Ge₄₆ and K₆Tl₂Ge₄₆ together with the calculation models of Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆ as well as their structure figures were given as ESI.†

Results and discussion

Morphology and composition

The synthesized samples of Rb_7.50(1)Tl_0.50(1)Ge₄₆ (inset of Fig. 1 top) and K_7.62(1)Tl_0.38(1)Ge_45.34(3) (inset of Fig. 1 bottom) samples were grey particles of 100–200 μm and had distinct facets. The elemental compositions were confirmed by EDX analysis as K_7.6(5)Tl_1.5(1)Ge_45.0(4) and Rb_7.0(2)Tl_1.7(5)Ge_45.03(8) with large standard errors. The final compositions of K_7.62(1)Tl_0.38(1)Ge_45.34(3) and Rb_7.50(1)Tl_0.50(1)Ge₄₆ were determined by structural refinement based on powder XRD data.

Fig. 1 Full profile simulated XRD patterns of Rb_7.50(1)Tl_0.50(1)Ge₄₆ (refined with Ge impurity) (top) and K_7.62(1)Tl_0.38(1)Ge_45.34(3) (bottom), inset of which are their corresponding SEM images.

X-ray powder diffraction

The peak searching, indexing and structural refinement were performed on powder XRD data using WinCSD software.⁵⁰ The indexed X-ray powder diffraction data indicated Rb_7.50(1)Tl_0.50(1)Ge₄₆ was a type-I clathrate in space group Pm3̄n with unit cell parameter of a = 10.81559(7) Å and Ge impurity was observed. K_7.62(1)Tl_0.38(1)Ge_45.34(3) was indexed using a 2 × 2 × 2 times superstructure in space group Ia3̄d with lattice parameters of a = 21.4290(2) Å.

Structure refinement

The full profile simulated X-ray powder diffraction patterns of Rb_7.50(1)Tl_0.50(1)Ge₄₆ (top) and K_7.62(1)Tl_0.38(1)Ge_45.34(3) (bottom) were given in Fig. 1 with experimental data in red circles, simulated curves in black lines, brag sites in black bars and difference curves in black lines. Weak impurity peaks appeared in Rb_7.50(1)Tl_0.50(1)Ge₄₆ (top) and K_7.62(1)Tl_0.38(1)Ge_45.34(3) (bottom), which belonged to Tl rich mixtures in Tl–Ge–Rb/K system according to SEM images and EDX analysis.

The structures of Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3) were resolved by direct method using the WinCSD program. During the refinement procedures for Rb_7.50(1)Tl_0.50(1)Ge₄₆ the three framework atom sites of 6c, 16i, and 24k were set as Ge1, Ge2 and Ge3, the guest atom sites at the 2a and 6d sites were set as Rb1 and Rb2 in a typical clathrate-I structure. The displace parameter for Rb1 (at 2a) was found too low. The subsequent refined occupancy indicated possible heavier atom in this site. Finally Rb1 was refined with Tl1 together. The structure refinement yielded complete occupancies for Ge1, Ge2, Ge3 and Rb2 in Rb_7.50(1)Tl_0.50(1)Ge₄₆.

K_7.62(1)Tl_0.38(1)Ge_45.34(3) crystallized in a 2 × 2 × 2 times superstructure in Ia3̄d space group. During the refinement procedures for K_7.62(1)Tl_0.38(1)Ge_45.34(3) the six framework atom sites of 24c, 24d, 32e and three 96h were set as Ge1, Ge2, Ge3, Ge4, Ge5 and Ge6, the guest atom sites at the 16a and 48g sites were set as K1 and K2. The displacement parameter for K1 was found too low. The refined occupancy indicated possible heavier atom in this position. Subsequently K1 site was refined with Tl1. The displacement parameters for Ge1 (at 24c) and Ge2 (at 24d) were higher than that of other Ge sites. The subsequent refinement indicated partial vacancies at Ge1 and Ge2 sites. The refinement yielded complete occupancies for Ge3, Ge4, Ge5, Ge6 and K2.

The final atomic coordinates, site occupancies, isotropic atomic displacement parameters and R factors for Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3) were listed in Table 1. The selected bond distances and angles of Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3) were given in Table 2 as ESI materials.†

Table 1 Atomic coordinates and equivalent isotropic displacement parameters (Ų) for Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3)

Atom	Site	x	y	z	Uiso	Occ.
Rb7.50(1)Tl0.50(1)Ge46		a = 10.81559(7) Å	R = 9.33	Pm3̄n
Rb1/Tl1	2a	0	0	0	0.00319(3)	0.750(4)/0.250(4)
Rb2	6d	1/4	0	1/2	0.02164(3)	1
Ge1	6c	1/4	1/2	0	0.00354(3)	1
Ge2	16i	0.18341(8)	x	x	0.01537(3)	1
Ge3	24k	0	0.1194(1)	0.3070(1)	0.01988(3)	1
K7.62(1)Tl0.38(1)Ge45.34(3)		a = 21.4290(2) Å	R = 11.4	Ia3̄d
K1/Tl1	16a	0	0	0	0.02774(8)	0.810(6)/0.190(6)
K2	48g	1/8	0.2380(2)	0.0119(2)	0.00859(8)	1
Ge1	24c	1/8	0	1/4	0.01592(8)	0.90(1)
Ge2	24d	3/8	0	1/4	0.02788(8)	0.88(1)
Ge3	32e	0.0948(2)	0.0948(2)	0.0948(2)	0.01742(8)	1
Ge4	96h	0.1569(2)	0.3445(2)	0.1667(1)	0.01051(8)	1
Ge5	96h	0.0914(1)	0.2512(2)	0.1899(2)	0.00938(8)	1
Ge6	96h	0.0948(1)	0.2432(2)	0.3103(2)	0.00740(8)	1

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Table 2 Selected bond distances and angles (Å, °) of Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3)

Rb7.50(1)Tl0.50(1)Ge46
Rb1–8Ge2	3.4360 (9)	Rb2–Ge3	4.162 (1)	Ge3–Ge1–Ge3	111.82 (4)	Ge2–Ge3–Ge2	105.59 (5)
Rb1–12Ge3	3.563 (1)	Ge1–Ge3	2.520 (1)	Ge3–Ge1–Ge3	108.31 (4)	Ge2–Ge3–Ge1	106.80 (4)
Rb2–12Ge3	3.6514 (8)	Ge2–Ge3	2.4902 (7)	Ge3–Ge2–Ge3	110.84 (5)	Ge2–Ge3–Ge3	106.13 (5)
Rb2–4Ge1	3.8239 (1)	Ge2–Ge2	2.495 (1)	Ge3–Ge2–Ge2	108.07 (5)	Ge1–Ge3–Ge3	124.09 (5)
Rb2–8Ge2	4.0222 (2)	Ge3–Ge3	2.584 (2)
K7.62(1)Tl0.38(1)Ge45.34(3)
K1–6Ge4	3.357 (3)	K2–Ge4	3.983 (5)	Ge5–Ge6	2.589 (4)	Ge5–Ge4–Ge4	105.01 (14)
K1–2Ge3	3.521 (3)	K2–3Ge4	4.083 (5)	Ge5–Ge1–Ge5	108.48 (10)	Ge1–Ge5–Ge4	110.69 (13)
K1–6Ge6	3.571 (3)	K2–3Ge4	4.326 (5)	Ge5–Ge1–Ge5	109.31 (10)	Ge1–Ge5–Ge3	104.88 (13)
K1–6Ge5	3.636 (3)	K2–2Ge6	4.387 (5)	Ge5–Ge1–Ge5	110.64 (10)	Ge1–Ge5–Ge6	126.83 (14)
K2–2Ge5	3.359 (4)	Ge1–4Ge5	2.400 (3)	Ge6–Ge2–Ge6	108.46 (10)	Ge4–Ge5–Ge3	106.51 (14)
K2–2Ge6	3.460 (4)	Ge2–4Ge6	2.463 (3)	Ge6–Ge2–Ge6	111.52 (10)	Ge4–Ge5–Ge6	103.60 (14)
K2–2Ge3	3.604 (5)	Ge3–Ge3	2.237 (4)	Ge3–Ge3–Ge5	108.72 (2)	Ge3–Ge5–Ge6	102.67 (14)
K2–2Ge5	3.606 (4)	Ge3–3Ge5	2.580 (4)	Ge5–Ge3–Ge5	110.21 (15)	Ge4–Ge6–Ge2	103.40 (13)
K2–2Ge1	3.621 (3)	Ge4–Ge6	2.430 (4)	Ge6–Ge4–Ge5	115.68 (15)	Ge4–Ge6–Ge5	104.51 (14)
K2–2Ge5	3.889 (5)	Ge4–Ge5	2.495 (4)	Ge6–Ge4–Ge6	115.48 (15)	Ge2–Ge6–Ge4	112.57 (13)
K2–2Ge6	3.950 (4)	Ge4–Ge6	2.516 (4)	Ge6–Ge4–Ge4	114.77 (15)	Ge2–Ge6–Ge5	122.27 (14)
K2–2Ge2	3.981 (3)	Ge4–Ge4	2.600 (4)	Ge5–Ge4–Ge6	107.56 (14)	Ge4–Ge6–Ge5	110.91 (14)

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Structure description

The crystal structures of Rb_7.50(1)Tl_0.50(1)Ge₄₆ (left) and K_7.62(1)Tl_0.38(1)Ge_45.34(3) (right) were shown in Fig. 2. Rb_7.50(1)Tl_0.50(1)Ge₄₆ crystallized in a type-I clathrate structure in space group Pm3̄n. The clathrate-I contains 46 framework Ge atoms which form two kinds of polyhedral cages. One kind of yellow pentagonal dodecahedron was composed of 12 pentagonal faces ([5¹²]) formed by 8 Ge2 (cyan, at 16i site) and 12 Ge3 (blue, at 24k site). Another kind of violet tetrakaidecahedron was built of 2 hexagonal and 12 pentagonal faces ([5¹²6²]) formed by 4 Ge1 (brown, at 6c site), 8 Ge2 and 12 Ge3. The violet tetrakaidecahedra formed the fused the perpendicular double chains in the middle of a couple of opposite edges of three directions in the unit cell by sharing the hexagonal faces. The yellow pentagonal dodecahedra shared 12 pentagonal faces with 12 tetrakaidecahedra, filled the rest vacancies of the corners and body center of the cubic lattice. Red Rb1 (at 2a site) lied in the center of the cage of yellow pentagonal dodecahedron. Violet Rb2 (at 6d site) located in the violet tetrakaidecahedron center.

Fig. 2 Clathrate-I structure of Rb_7.50(1)Tl_0.50(1)Ge₄₆ (left): brown Ge1 at 6c sites, cyan Ge2 at 16i and blue Ge3 at 24k sites form the violet tetrakaidecahedron caged with violet Rb2 (at 6d); Ge2 and Ge3 construct yellow pentagonal dodecahedron caged with red Rb1/Tl1 (at 2a). The 2 × 2 × 2 times superstructure of clathrate-I of K_7.62(1)Tl_0.38(1)Ge_45.34(3) (right) with partial ordering of vacancies brown Ge1 (at 24c) and yellow Ge2 (at 24d), green Ge3 (at 32e), cyan Ge4 (at 96h), blue Ge5 (at 96h), deep blue Ge6 (at 96h) form the violet tetrakaidecahedron caged with violet Rb2 (at 48g) which deviates from the center of tetrakaidecahedron; Ge3, Ge4, Ge5 and Ge6 construct yellow pentagonal dodecahedron caged with red K1 (at 16a).

K_7.62(1)Tl_0.38(1)Ge_45.34(3) crystallized Ia3̄d space group with 2 × 2 × 2 times superstructure of clathrate-I. Wyckoff site transformation from Pm3̄n space group to Ia3̄d space group was shown in Scheme 1. In K_7.62(1)Tl_0.38(1)Ge_45.34(3) superstructure K1/Tl1 (red at 16a) and K2 (violet at 48g) were deduced from 2a and 6d; Ge1 (brown at 24c)/Ge2 (yellow at 24d), Ge3 (green at 32e)/Ge4 (cyan at 96h) and Ge5 (blue at 96h)/Ge6 (deep blue at 96h) were split from 6c, 16i and 24k sites in Pm3̄n. The structure of K_7.62(1)Tl_0.38(1)Ge_45.34(3) was isotypic with Ba₈Ge₄₃ (Ia3̄d).²⁴ In Ba₈Ge₄₃ Ge preferred at 24d sites and vacancies preferred at 24c sites. Ba2 deviated less from the center of tetrakaidecahedron compared with K2. In Rb_7.50(1)Tl_0.50(1)Ge₄₆, Rb1/Tl1–Ge2/Ge3 distances in dodecahedron varied in a small range of 3.4360(9) to 3.563(1) Å and Rb2–Ge distances in tetrakaidecahedron changed in a large range of 3.6514 (8) to 4.162(1) Å. Ge–Ge bond distances altered in the range of 2.4902(7) to 2.584 (2) Å. Ge1–Ge3–Ge3 bond angle 124.09(5)° in the six member ring deviated furthest from ideal tetrahedral angle of 109°08′ compared with others.

Scheme 1 Wyckoff sites occupied in the transformation from space group Pm3̄n to space group Ia3̄d.

In K_7.62(1)Tl_0.38(1)Ge_45.34(3), K1/Tl1–Ge2/Ge3 distances in dodecahedron varied in a small range of 3.357(3) to 3.636(3) Å. K2–Ge1/Ge2/Ge3 distances in tetrakaidecahedron changed in a large range of 3.359(4) to 4.387(5) Å. The shortest Ge3–Ge3 bond length was 2.237(4) Å and the longest Ge4–Ge4 bond length was 2.600(4) Å. Ge1–Ge5–Ge6 bond angle 126.83(14)° and Ge2–Ge6–Ge5 bond angle 122.27(5)° in six-member ring deviated far away from an ideal tetrahedral angle of 109°08′ compared with others.

Theoretical calculation

Theoretical calculations were performed based on simplified models of Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆ in Pm3̄ space group as described in theoretical calculations section. Calculated band structures and high-symmetry axes of the Brillouin Zone for Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆ models are shown in Fig. 3. The abscissa in Fig. 3 indicate the high symmetry directions in Brillouin zone paths of X(0.5, 0, 0), R(0.5, 0.5, 0.5), M(0.5, 0.5, 0) and G(0, 0, 0) in the reciprocal lattices of Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆. The dashed lines correspond to Fermi energy level. The other coloured lines of the figures are electronic energy levels of different bands, which are occupied by electrons below Fermi energy level and are empty above Fermi level. The band structures indicate metallic features for Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆. The atom deduced densities of States (DOS) for Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆ are given in Fig. 4. DOS at Fermi level are mainly determined by Ge s, Ge p orbitals, partial Tl p orbitals and Rb s and Rb p or K s, K p in Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆.

Fig. 3 The band structures of Rb₇Tl₁Ge₄₆ (left) and K₇Tl₁Ge₄₆ (right).

Fig. 4 Total and atom deduced densities of states of Rb₇Tl₁Ge₄₆ (left) and K₇Tl₁Ge₄₆ (right).

Conclusions

Type-I clathrates of Rb_7.50(1)Tl_0.50(1)Ge₄₆ and K_7.62(1)Tl_0.38(1)Ge_45.34(3) were synthesized from constituent elements. Rb_7.50(1)Tl_0.50(1)Ge₄₆ crystallized in a clathrate-I structure in Pm3̄n space group with the unit cell parameter of a = 10.81559(7) Å. K_7.62(1)Tl_0.38(1)Ge_45.34(3) was a 2 × 2 × 2 times superstructure of clathrate-I, which crystallized in Ia3̄d space group with lattice parameter of a = 21.4290(2) Å. The structural transformation from Rb_7.50(1)Tl_0.50(1)Ge₄₆ in Pm3̄n to K_7.62(1)Tl_0.38(1)Ge_45.34(3) in Ia3̄d was indicated. The band structures indicated metallic features for both Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆. The densities of states at Fermi level were mainly determined by Ge s and Ge p orbitals in Rb₇Tl₁Ge₄₆ and K₇Tl₁Ge₄₆.

Acknowledgements

This work was financially supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grants XDB04040200 andXDB04040300).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. CCDC 1430735 and 1430736. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c6ra14614g

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