Type-I clathrates of K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4)

Abstract

Type-I clathrates of K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) are synthesized directly from the corresponding elements. The structures are resolved by powder XRD data by means of a least-squares technique using WinCSD program. The refined lattice parameters are a = 10.70783(3) Å and a = 10.84493(3) Å for K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4), respectively. The electronic band structure and density of states indicate K₈Cu₃Ge₄₃ and Rb₈Ag₃Ge₄₃ are p-type semiconductors with narrow indirect band gaps of 0.33 and 0.24 eV. In addition, K_7.69(2)Cu_2.94(6)Ge_43.06(6) displays a diamagnetism with χ = −1.102(1) × 10⁻³ emu mol⁻¹ in the field of 7 T at 400 K and has a strong Einstein model with θ_E = 56.3(1) K and θ_D = 297(3) K.

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Introduction

Clathrate compounds comprise host frameworks that embrace guest species in polyhedral cages.¹ Inorganic clathrates form some structure types according to respective polyhedral types and their arrangements, such as type-I clathrates,^1–3 type-II clathrates,^4,5 type-III clathrate,⁶ type-VIII clathrates,^7,8 type-IX clathrate,⁹ type-X clathrates,¹⁰ etc. Clathrates can be classified into cationic,^1–4,7–9 neutral⁵ and anionic^6,10 according to the charge distribution between framework and guest atoms, as well as clathrate hydrates of natural gases.¹¹ The recent growing interest in clathrates of tetrels (elements of group 14) in which the host framework is based on Si, Ge, or Sn atoms is motivated in particular by the search for a new generation of efficient thermoelectric materials.¹²

The Zintl–Klemm rule offers an explanation for the formation of electronically-balanced clathrates with partial substitutions on the framework and guest atom sites.^3,6 The recent growing interest in clathrates of tetrels (elements of group 14) in which the host framework is based on Si, Ge, or Sn atoms is motivated in particular by the search for a new generation of efficient thermoelectric materials.¹² The most anionic 14 group element M (M = Si/Ge/Sn) based type-I clathrates with alkaline metal A (A = Na, K, Rb, Cs) in the cages are built with 13 group elements T (T = B, Al, Ga, In): such as Ge based clathrates K₇B₇Ge₃₉,³ K₈Al₈Ge₃₈,¹³ K₈Al_23.3Ge_22.7,¹⁴ K₈Ga₂₃Ge₂₃,^14,15 K₈In₆Ge₄₀,¹⁶ K₈In_8.14Ge_37.86,¹⁷ K₈In₁₆Ge₃₀,¹⁵ Rb₈Al_7.84Ge_38.16,¹⁸ Rb₈Ga₈Ge₃₈,¹⁹ Rb₈In_7.81Ge_38.19,¹⁷ etc. There are only a few transition metal clathrates: e.g. K₈Hg_3.19Ge_42.81,²⁰ Rb₈Hg_3.03Ge_42.97,²⁰ and (Rb, K)_8−xAu_yGe_46−y.²¹ We found alkaline earth metal and transition metal clathrate of Ba₈Au_5.3Ge_43.7 has good thermoelectric properties with ZT = 0.3–0.9.²² It is worth to explore alkali metal and transition metal clathrates for potential thermoelectric applications.

Herein the synthesis and structure of K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) are investigated. The magnetic properties and heat capacity of K_7.69(2)Cu_2.94(6)Ge_43.06(6) are also presented.

Results and discussion

The synthesized K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) products are grey blocks. The element compositions of K_8.6(1)Cu_2.8(1)Ge_43.2(1) and Rb₉₍₂₎Ag_2.2(5)Ge_43.8(5) are confirmed by EDX analysis. Composition and occupancy of K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) are further refined by powder XRD data using WinCSD program.²³

The systematic absences are same (hhl: 2h + l = 2n and h00: h = 2n) for Pm3̄n (223) and P4̄3n (218) space groups. Transition metal with a low amount of substitution in type-I clathrates^20–22 usually locate at 6c site like most anionic type-I clathrates with group 13 elements (B/Al/Ga/In) in Pm3̄n space group.^{1–3,13–19} Only a few cationic type-I clathrates Ge₃₈P₈I₈,²⁴ Ge₃₈As₈I₈,²⁴ Ge₃₈Te₁₆,²⁵ etc. crystallize in P4̄3n (218) space group in which double 8e sites replace 16i site in Pm3̄n. For K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) with low amount of Cu and Ag substitution for Ge we choose cubic Pm3̄n (223) space group.

During the initial steps of the refinement, all framework atoms are treated as Ge, and the guest atoms at 2a sites (K1/Rb1) and 6d sites (K2/Rb2) in cubic Pm3̄n (223) space group. Subsequent refinement sets Cu1/Ag1 at 6c position with Ge1 atoms. The isotropic atomic displacement parameters for K2 are large. Further refinement allowed the site position of K2 shift from 6d sites (1/4, 0, 1/2) to 24k sites (x, 0, y) and the refined occupancy is 0.237(1). The K vacancy is common in K content clathrates K_6.71Au_2.21Ge_43.79.²¹ For Rb2 neither split model nor partial occupancy reduces the displacement parameters. The refined XRD patterns for K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.83(2)Ge_43.17(2) with R = 5.78% and R = 5.36% are given in Fig. 1. The final atomic coordinates, site occupancies, isotropic atomic displacement parameters and R factors for K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) are listed in Table 1. The important interatomic distances of K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) are given in Table 2. For the large Rb and Ag atoms in Rb₈Ag_2.79(4)Ge_43.21(4) the Ag/Ge–Ge and Rb–Ge distances are longer than Cu/Ge–Ge and K–Ge distances in K_7.69(2)Cu_2.94(6)Ge_43.06(6).

Fig. 1 Refined XRD patterns of K_7.69(2)Cu_2.94(6)Ge_43.06(6) (top) and Rb₈Ag_2.79(4)Ge_43.21(4) (bottom).

Table 1 Fractional atomic coordinates, isotropic or equivalent isotropic displacement parameters (Ų) and occupancy for K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) in cubic Pm3̄n (223) space group

Label	Sites	x	y	z	Biso/Bequ	Occ.
K7.69(2)Cu2.94(6)Ge43.06(6), a = 10.70783(3) Å, R = 5.78%
K1	2a	0	0	0	0.277(2)	1
K2	24k	0.2598(6)	0.4723(4)	0	0.341(2)	0.237(1)
Ge1/Cu1	6c	1/4	0	1/2	1.330(2)	0.51(1)/0.49
Ge2	16i	0.18308(4)	x	x	0.933(2)	1
Ge3	24k	0	0.31124(5)	0.11862(5)	0.956(2)	1
Rb8Ag2.79(4)Ge43.21(4), a = 10.84493(3) Å, R = 5.36%
Rb1	2a	0	0	0	1.105(2)	1
Rb2	6d	1/4	1/2	0	2.142(2)	1
Ge1/Ag1	6c	1/4	0	1/2	1.495(2)	0.535(6)/0.465
Ge2	16i	0.18323(5)	x	x	0.984(2)	1
Ge3	24k	0	0.30716(6)	0.11855(6)	0.876(2)	1

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Table 2 Selected geometric parameters (Å, °) for K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21 in cubic Pm3̄n (223) space group

K7.69(2)Cu2.94(6)Ge43.06(6)
K1–8Ge2	3.3955(5)	K2–2Ge1	3.872(5)	Ge3–2Ge2	2.4906(6)
K1–12Ge3	3.5667(6)	K2–1Ge1	3.931(5)	Ge3–1Ge3	2.5404(8)
K2–2Ge3	3.413(5)	K2–2Ge2	4.121(2)	Ge3–Ge1–Ge3	109.05(2)
K2–1Ge1	3.504(5)	K2–2Ge3	4.165(1)	Ge3–Ge1–Ge3	110.32(2)
K2–2Ge3	3.511(5)	K2–2Ge2	4.258(4)	Ge3–Ge2–Ge2	107.24(3)
K2–2Ge3	3.627(5)	K2–1Ge3	4.414(4)	Ge3–Ge2–Ge3	111.61(3)
K2–2Ge2	3.757(4)	Ge1–4Ge3	2.4625(6)	Ge2–Ge3–Ge2	103.83(3)
K2–1Ge3	3.827(4)	Ge2–1Ge2	2.4822(7)	Ge1–Ge3–Ge2	107.10(2)
K2–2Ge2	3.829(2)	Ge2–3Ge3	2.4906(6)	Ge2–Ge3–Ge3	106.09(3)
K2–2Ge3	3.837(5)	Ge3–1Ge1	2.4625(6)	Ge1–Ge3–Ge3	124.84(3)
Rb8Ag2.79(4)Ge43.21
Rb1–8Ge2	3.4417(6)	Ge2–1Ge2	2.5086(8)	Ge3–Ge2–Ge2	108.09(3)
Rb1–12Ge3	3.5705(7)	Ge2–3Ge3	2.4993(7)	Ge3–Ge2–Ge3	110.81(3)
Rb2–8Ge3	3.6576(5)	Ge3–1Ge1	2.5311(7)	Ge2–Ge3–Ge2	105.32(3)
Rb2–4Ge1	3.8343(1)	Ge3–2Ge2	2.4993(7)	Ge1–Ge3–Ge2	106.63(3)
Rb2–8Ge2	4.0342(1)	Ge3–1Ge3	2.571(1)	Ge2–Ge3–Ge3	106.30(3)
Rb2–4Ge3	4.1830(7)	Ge3–Ge1–Ge3	108.50(2)	Ge1–Ge3–Ge3	124.28(3)
Ge1–4Ge3	2.5311(7)	Ge3–Ge1–Ge3	111.44(2)

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The crystal structure of Rb₈Ag_2.79(4)Ge_43.21(4) is shown in Fig. 2. Pink Rb1 lies in 2a, and violet Rb2 at 6d sites. Brown Ag1/Ge1 at 6c sites, cyan Ge2 at 16i and blue Ge3 at 24k sites form the fused the violet perpendicular tetrakaidecahedra double chains in the middle of a couple of opposite edges of three directions in the cubic lattice. The yellow pentagonal dodecahedra formed by Ge2 and Ge3 fill the rest vacancies of the corners and body center of the cubic lattice. For K_7.69(2)Cu_2.94(6)Ge_43.06(6) the only difference lies in the K2 split from the center of 6d sites to 24k sites with 23.7(1)% occupancy. For simple we give only Rb₈Ag_2.79(4)Ge_43.21(4) structure.

In order to prove if K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4) are semiconductors, theoretical calculations are performed using VASP on ordered K₈Cu₃Ge₄₃ and Rb₈Ag₃Ge₄₃ models. Calculated band structure and high-symmetry axes of the Brillouin zone for K₈Cu₃Ge₄₃ and Rb₈Ag₃Ge₄₃ are shown in Fig. 3. The abscissa of Fig. 3 means the high symmetry directions in Brillouin zone paths (Γ(0, 0, 0) → X(1/2, 0, 0) → M(1/2, 1/2, 0) → Γ(0, 0, 0) → R(1/2, 1/2, 1/2)) of the reciprocal lattice. The dashed line corresponds to Fermi energy level. The other multi coloured lines of the figure are electronic energy levels of different bands. The coloured lines are electronic energy bands, which are occupied by electrons below Fermi energy level and are empty above Fermi level. The highest occupied orbit locates at M(1/2, 1/2, 1) direction and the lowest empty orbit lies at X(1/2, 0, 0). The band structure displays a characterized by semiconductor feature with an in indirect band gap of 0.33 and 0.24 eV, respectively. The calculated total and partial density of states are presented in Fig. 4. The major features can be summarized as follows. The upper VB is mainly derived from Ge 4p at the high energy side with partially hybridized Cu d/Ag d states, while the lower CB is mainly derived from Ge 4p at low energy side.

Fig. 2 Crystal structures of Rb₈Ag_2.79(4)Ge_43.21(4): brown Ge1 at 6c sites, cyan Ge2 at 16i and blue Ge3 at 24k sites form the tetrakaidecahedra caged with violet Rb2, Ge2 and Ge3 construct pentagonal dodecahedra caged with pink Rb1.

Fig. 3 The energy band structure of (top) K₈Cu₃Ge₄₃ and (bottom) Rb₈Ag₃Ge₄₃ displaying an indirect p-type semiconductor with energy band gap of 0.33 and 0.24 eV, respectively.

Fig. 4 Total and partial density of states of Cu d, Ag d, Ge p states for (a) K₈Cu₃Ge₄₃ and (b) Rb₈Ag₃Ge₄₃.

The magnetic susceptibility χ versus temperature of K_7.69(2)Cu_2.94(6)Ge_43.06(6) reveals diamagnetic behavior. The susceptibility is −1.102(1) × 10⁻³ emu mol⁻¹ in the field of 7 T at 400 K (Fig. 5). Heat capacity can be described by the sum of three contributions: the electronic contribution C_e = γT, and the lattice contributions C_l from both the rigid cage forming network and the guest atoms within the cages. The latter two contributions may be described by a Debye term and an Einstein term, respectively. The existence of a low energy Einstein contribution is often motivated by the presence of a maximum in the representation C_l/T³ = (C_p − γT)/T³ which basically illustrates the deviations from the Debye T³ law valid in the low T limit. Resorting to the standard description of specific heat, the data can be expressed as C_p = γT + βT³. Heat capacity of K_7.69(2)Cu_2.94(6)Ge_43.06(6) plotted as C_p/T³ versus temperature is shown in Fig. 6 and inset of it is plotted as C_p/T versus T² with the fitted line. Fig. 6 demonstrates that also for K_7.69(2)Cu_2.94(6)Ge_43.06(6) such a maximum at about T = 20 K. The resulting parameters for K_7.69(2)Cu_2.94(6)Ge_43.06(6) from a fit of the data with 1.8 K < T < 3.1 K are γ = 26.6(3) mJ mol⁻¹ K⁻² and β = 4.00(4) mJ mol⁻¹ K⁻⁴. The fitted Debye temperature Θ_D ≈ 297(3) K and Einstein temperature Θ_E ≈ 56.3(1) K are obtained.

Fig. 5 Temperature dependence of susceptibility χ for K_7.69(2)Cu_2.94(6)Ge_43.06(6).

Fig. 6 Heat capacity of K_7.69(2)Cu_2.94(6)Ge_43.06(6), plotted as C_p/T³ versus temperature, inset of it is plotted as C_p/T versus T² with the fitted curve.

Experimental

Synthetic procedures

The target compositions A₈T_2.7Ge_43.3 (A = K, Rb; T = Cu, Ag) are chosen according the Zintl–Klemm rule in order to obtain charge-balanced systems according to A₈⁺T_2.7³⁻Ge_43.3⁰. The starting materials are loaded in Ta tubes in molar ratio K/Rb : Cu/Ag : Ge = 8 : 2.7 : 43.3. The containers are welded in an argon-filled glovebox [c(O₂) and c(H₂O) ≤ 1 ppm] and sealed in a quartz ampoule in vacuum. After 1 week of heating at 700 °C, the grey products are obtained and washed with distilled water and acetone, then dried at 80 °C for 12 h.

Composition

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

Powder X-ray diffraction

The powder XRD patterns are collected by Guinier technique (Huber Image Plate Camera G670, Cu Kα1 radiation, λ = 1.54056 Å, 3.0° < 2θ < 100.3°, step width 0.005°). The structures are resolved by powder XRD data by means of least-squares technique using WinCSD program.²³ For the structure presentation the program Diamond 3.0 is used.²⁶

Theoretical calculation

The observed composition is very close to the Zintl count, which may cause the semiconductor-like behaviour. In order to prove this assumption, the first-principles calculations is carried out by means of the density functional theory using the pseudopotential as implemented in the VASP code.²⁷ The exchange-correlation potential is calculated using the generalized gradient approximation (GGA) as proposed by Perdew–Burke–Ernzerhof.²⁸ Throughout the calculations, a 500 eV cutoff in the plane wave expansion and a 6 × 6 × 6 Monkhorst-Pack k grid are chosen to ensure the calculation with an accuracy of 10⁻⁵ eV. Furthermore, those calculations are performed using the experimental crystal structure. Because of partial occupancy of K and Cu/Ag and Ge disorders in K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.79(4)Ge_43.21(4), we use the integral number ordered K₈Cu₃Ge₄₃ and Rb₈Ag₃Ge₄₃ lattices with half Cu/Ag and half Ge at 6c sites in order to simplify the calculation.

Physical properties

Magnetization is measured from 1.8 to 400 K at 7 T field on a SQUID magnetometer (MPMS, Quantum Design). The heat capacity is determined applying PPMS (Quantum Design, HC option) from 1.8 to 400 K.

Conclusions

K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.83(3)Ge_43.17(3) clathrates are synthesized. The lattice parameters and crystal structures are refined by powder XRD data using WinCSD package. Theoretical calculation of K₈Cu₃Ge₄₃ and Rb₈Ag₃Ge₄₃ indicates p-type indirect semiconductors with about 0.33 and 0.24 eV band gaps. K_7.69(2)Cu_2.94(6)Ge_43.06(6) is a diamagnetism and has a strong Einstein model in heat capacity. K_7.69(2)Cu_2.94(6)Ge_43.06(6) and Rb₈Ag_2.83(3)Ge_43.17(3) may be potential p-type thermoelectric materials.

Acknowledgements

This work was financially supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grants XDB04040200 and XDB04040300), the Natural Science Foundation of China (Grants 91122034, 51125006, 51202279, 61376056, 11204338, 11227902, and 11404359), Science and Technology Commission of Shanghai (Grant 13JC1405700), and Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant 2015187).

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Footnote

† CCDC 1401202 and 1401203. For crystallographic data in CIF or other electronic format see DOI: 10.1039/c5ra09382a

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