Na–Ga–Si type-I clathrate single crystals grown via Na evaporation using Na–Ga and Na–Ga–Sn fluxes

Single crystals of a Na–Ga–Si clathrate, Na8Ga5.70Si40.30, of size 2.9 mm were grown via the evaporation of Na from a Na–Ga–Si melt with the molar ratio of Na : Ga : Si = 4 : 1 : 2 at 773 K for 21 h under an Ar atmosphere. The crystal structure was analyzed using X-ray diffraction with the model of the type-I clathrate (cubic, a = 10.3266(2) Å, space group Pm3̄n, no. 223). By adding Sn to a Na–Ga–Si melt (Na : Ga : Si : Sn = 6 : 1 : 2 : 1), single crystals of Na8GaxSi46−x (x = 4.94–5.52, a = 10.3020(2)–10.3210(3) Å), with the maximum size of 3.7 mm, were obtained via Na evaporation at 723–873 K. The electrical resistivities of Na8Ga5.70Si40.30 and Na8Ga4.94Si41.06 were 1.40 and 0.72 mΩ cm, respectively, at 300 K, and metallic temperature dependences of the resistivities were observed. In the Si L2,3 soft X-ray emission spectrum of Na8Ga5.70Si40.30, a weak peak originating from the lowest conduction band in the undoped Si46 was observed at an emission energy of 98 eV.


Introduction
cages with ve-membered rings of Si [5 12 ] and tetrakaidecahedral [Si] 24 cages with vemembered rings and six-membered rings of Si [5 12 6 2 ]. 1 Each cage encapsulates a Na as a guest atom. Since this compound was rst synthesized by Kasper et al. in 1965, 1 it has attracted signicant attention from researchers owing to its unique structure as well as being a member of group 14 intermetallic chathrates, the variants of which are of interest for photovoltaic, 2 thermoelectric, 3 and superconducting materials. 4 Na 8 Si 46 has conventionally been synthesized along with another type of Na-Si clathrate (type-II, Na 24 Si 36 ) via the solidthermal decomposition of Na 4 Si 4 (melting point 1071 K (ref. 5)) in the temperature range 593-823 K under high vacuum (<10 À2 Pa). 1,6,7 The samples obtained by this method are powdery solids with a grain size of micrometers. The Na-Si clathrates have been regarded as metastable or intermediate phases. The single crystals of Na 8 Si 46 could not be directly grown from the Na-Si melt. In 2009, Beekman et al. succeeded in growing type-II Na 24 Si 136 single crystal growth using a spark plasma sintering (SPS) system. 8 Single crystals of type-I and type-II clathrates were selectively synthesized by the reaction of Na 4 Si 4 and graphite akes with a spatial separation layer of NaCl. 9,10 This process was named the kinetically controlled thermal decomposition (KCTD) method. Type-I Na 8 Si 46 single crystal with sizes of about 200 mm was obtained by heating at 858 K. 9 Recently, our research group found that the single crystal of the Na-Si binary clathrates can be grown in Na-Sn rich Na-Sn-Si ternary melt by Na evaporation. 11,12 Single crystals of type-I and type-II clathrates were selectively prepared by setting the growth temperatures at 773 and 873 K, respectively. The maximum size of the type-I Na 8 Si 46 single crystal was 5 Â 3 Â 3 mm 3 , having {110} habit planes. 12 The electric properties of ternary type-I clathrates A 8 M 8 Si 38 (A ¼ Na, K, Rb, Cs; M ¼ Al, Ga, In) have been predicted using rst-principles calculation. 13,14 Indirect transition semiconductor characters of A 8 M 8 Si 38 with band gaps of 0.45-0.89 eV 13 and their thermoelectric properties 14 were presented by the calculation. A 8 Al 8 Si 38 (A ¼ K, Rb, Cs) have been synthesized using ux materials of Al and alkali-metal halide salts. 15 The samples for the transport measurements were prepared by compacting at 4 GPa in a high-pressure multianvil apparatus. Dong et al. synthesized microcrystalline Na 8 Al 8 Si 38 by the KCTD method using a Na 4 Si 4 + NaAlSi mixture as the precursor and prepared bulk polycrystalline samples by SPS to characterize the transport properties. 16 Sui et al. synthesized A 8 Ga 8 Si 38 (A ¼ K, Rb, Cs) via a direct reaction of constituent elements. 17 They sintered the powders of A 8 Ga 8 Si 38 using SPS to obtain polycrystalline bulk samples for characterization of thermoelectric properties, and measured the band gaps of 1.14-1.18 eV by the surface electromotive force of the powder samples. 17 A cubic lattice parameter of 10.36Å was only reported for Na 8 Ga 23 Si 23 , 18 but details of synthesis and crystal structures of the clathrates have not been claried. The present paper reports crystal growth of the type-I clathrate Na 8 Ga 5.70 Si 40.30 using a Na-Ga-Si melt and Na 8 Ga x Si 46Àx (x ¼ 4.94-5.52) using Na-Ga-Si-Sn melts. The crystal structures were analyzed by single crystal Xray diffraction (XRD) and some single crystals were characterized by electrical resistivity measurement and so X-ray emission spectroscopy (SXES).
The crucible containing the starting sample was taken out from the stainless-steel container in the glove box under Ar atmosphere, and transferred to the upper part of another long stainless-steel container (outer diameter 12.7 mm, inner diameter 10.7 mm, height 300 mm). A schematic view of the container is shown in Fig. S1 of ESI. † The crucible at the upper part of the container was heated at 723-873 K for 3-24 h in atmospheric-pressure Ar using a tubular electric furnace, and the lower part of the container was cooled with a fan to maintain a temperature gradient in the container. Na evaporated from the melt of the starting sample was condensed at the lower inside part of the container. Aer heating, the sample was cooled to room temperature by turning off the electric power to the furnace and taken out the sample from the container in the glove box. The amount of evaporated Na was evaluated using the weight loss of the sample aer heating. Unvaporized Na and Na-Ga, Na-Si, and/or Na-Sn compounds formed in the sample were reacted with 2-propanol and ethanol in air, and subsequently, the water-soluble reactants were removed by washing with water. Single crystals were obtained aer the removal of residual Ga and Sn via a reaction with hydrochloric acid water solution (35.0-37.0 mass% HCl) (alcohol and acid treatments).
Caution: conrm the complete decomposition of the reactive compounds containing Na through reaction with alcohol before washing with water.
The compositions of the single crystals were analyzed using an electron probe microanalyzer (EPMA, JEOL, JXA-8200) attached to wavelength dispersive X-ray spectrometers. The densities of the single crystals were measured using the Archimedes method. The X-ray diffraction (XRD) data of the single crystals were collected using a single-crystal XRD diffractometer (Bruker, D8QUEST, Mo-Ka radiation) and analyzed using the APEX3 program. 19 X-ray absorption correction and structure renement were performed by using the SADABS 19 and SHELEXL-97 programs, 20 respectively. The structures of Si/Ga cages containing Na were depicted using VESTA. 21 So X-ray emission (SXE) spectra were measured using   an SXE spectrometer attached to a port of a wavelengthdispersive spectrometer of a scanning electron microscope (SEM, JEOL, JSM-6480LV 22,23 ). The electric resistivities of the single crystals were measured from 10 to 300 K using the fourterminal method with Ag paste electrodes.

Results and discussion
The conditions of crystal growth and mole fractions of the evaporated Na against the initial amounts of Na in the starting samples are listed in Table 1. It can be observed that 84% of Na was evaporated during the heating of Na-Ga-Si starting sample at 773 K for 21 h. Single crystals of size up to 2.9 mm were obtained. When the Na-Ga-Si-Sn starting samples were heated at 723 K for 24 h, 773 K for 12 h, 823 K for 9 h, and 873 K for 3 h, 48-55% of Na was evaporated. Fig. 1 shows an optical micrograph of the single crystals grown by heating the Na-Ga-Si-Sn starting sample at 873 K for 3 h. The maximum sizes of the single crystals grown at 723, 773, 823, and 873 K were 2.3, 2.5, 2.6, and 3.7 mm, respectively. Table 2 shows the compositions of the single crystals grown by heating the Na-Ga-Si starting sample at 773 K (crystal 1) and the Na-Ga-Si-Sn starting samples at 723 (crystal 2), 773 (crystal 3), 823 (crystal 4), and 873 K (crystal 5). Elements other than Na, Ga, and Si were not detected from these crystals using EPMA. When the total number of the Ga and Si cage atoms was set to 46, based on the ideal formula of type-I clathrates Na 8 Ga x Si 46Àx , the contents of Na analyzed using EPMA were converted from 7.99(6) to 8.23 (6), which is close to the ideal Na number of 8.   The Ga number of crystal 1 grown at 773 K from the Na-Ga-Si starting sample was 5.67 (8). The Ga numbers x of Na 8 Ga x Si 46Àx for crystals 2, 3, 4, and 5 grown from the Na-Ga-Si-Sn starting mixture were 5.41(3), 5.35(3), 5.19 (6), and 4.78(3) respectively, which decreased with the increase in the heating temperature from 723 to 873 K as shown in Fig. 2.
The results of crystal structure analysis and rened atomic positional and equivalent isotropic displacement parameters of the single crystals are shown in Tables 3 and S1. † All the single crystals were analyzed with the type-I structure (cubic system, space group Pm 3n). In the structure renements, Na1(6d) and Na2(2a) sites were fully occupied and the occupancies of Ga in Si/Ga1(24k), Si2(16i), and Si/Ga3(6c) sites were rened. As the occupancy of the Si2(16i) site equaled 1 within the standard deviation, it was xed to 1 in the nal renements. The reliability factors R 1 (all data) for samples 1-5 were 1.02-1.90%. The formulae of the clathrates based on the rened occupancies were in accordance with those determined using EPMA. The aaxis length of Na 8 Ga x Si 46Àx increased from 10.3020(2) to 10.3226(2)Å with the increase in the Ga content x from 4.94(6) to 5.70(7) as shown in Fig. 3(a). The densities in the range 2.554-2.584 Mg m À3 , which were calculated using the lattice parameters and the formulas, were consistent with those measured using the Archimedes method ( Table 3).
The Na2-centered [Si/Ga] 20 and Na1-centered [Si/Ga] 24 cages of Na 8 Ga 5.70 Si 40.30 are shown in Fig. 4(a). The occupancies of Ga in the Si/Ga1(24k) and Si/Ga3(6c) sites are plotted against the Ga content x in Fig. 3(b). The Si/Ga3 site, constituting sixmembered rings of the [Si/Ga] 24 cage, was preferentially occupied by Ga atoms with occupancies in the range 64.8(3)-73.0(4)%. The volume increasing rate of the [Si/Ga] 24 cage is larger than that of the [Si/Ga] 20 cage (Fig. 3(c)). Similar Ga preferential occupation of the Si/Ga3 site in the [Si/Ga] 24 cages, which prevents Ga-Ga atom contact, was previously reported for A 8 Ga 8 Si 38 (A ¼ K, Rb, Cs) type-I clathrate. 17 In Fig. 4(b), the atomic arrangement of Na 8 Ga 5.70 Si 40.30 is shown with 99% probability ellipsoids using the anisotropic atomic displacement parameters (Table S2 † 16 In the present study, the highest Ga content x of Na 8 Ga x Si 46Àx was 5.70(7), whereas A 8 Ga 8 Si 38 (x ¼ 8) was  reported for other alkali elements A ¼ K, Rb, and Cs. 17 However, the a-axis lengths of Na 8 Ga 5.70 Si 40.30 and these type-I gallium silicon clathrates are plotted on the same line against the ionic radii of the alkali metals as shown in Fig. 5 (10.3266(2)Å) are similar. As there is a linear relation between the a-axis length of Na 8 Ga x -Si 46Àx and x, the a-axis length of hypothetical Na 8 Ga 8 Si 36 could be estimated to be 10.375Å via extrapolation (Fig. 3(a)). The length is plotted out of the line in the graph shown in Fig. 5. Although it is not apparent whether Na 8 Ga 8 Si 36 was formed at this moment, there might be an upper size limit of cages containing Na atoms in the type-I clathrate structure. Thus, a highpressure condition may be required to crystalize Na 8 Ga 8 Si 38 . Fig. 6 shows the SXE spectra of crystal 1 (Na 8 Ga 5.70 Si 40.30 ), Na-Si binary type-I clathrate (Na 8 Si 46 ) synthesized in the previous study, 11 and diamond-type cubic Si (d-Si), which was the same as the starting material. The peaks observed around 99 and 98 eV in the spectra of Na 8 Si 46 and Na 8 Ga 5.70 Si 40.30 are consistent with the peak observed at 99 eV for Na 8 Si 46 by Moewes et al. 24 It was considered that the peak edges corresponded to the lower end of the conduction band where the Fermi level exists. Although the peak of 99 eV with a sharp edge at 101 eV was observed for Na 8 Si 46 , the corresponding peak of Na 8 Ga 5.70 Si 40.30 was small, which indicates the difference between the electronic states of these clathrates.
The peak observed around 93-94 eV in the Na 8 Si 46 spectrum shied higher by approximately 0.5 eV from that of the d-Si. The peak of Na 8 Ga 5.70 Si 40.30 was further shied by approximately +0.3 eV from that of Na 8 Si 46 . The Si-Si distances of d-Si and Na 8 Si 46 , and the Si/Ga-Si/Ga distance of Na 8 Ga 5.70 Si 40.30 were 2.35166Å, 25 2.3286(11)-2.3941(9)Å, 11 and 2.3610(10)-2.4370(4)Å (Table S3 †), respectively. As the Si-Si or Si/Ga-Si/Ga distance increases, the band gap decreases. Consequently, the energy gaps between the inner shell levels and valence band increase and the spectra shi to the higher energy side.
The electrical resistivities measured for crystal 1 (Na 8 Ga 5.70 -Si 40.30 ) and crystal 5 (Na 8 Ga 4.94 Si 41.06 ) together with the resistivity of Na 8 Si 46 (ref. 11) are shown against the temperature in Fig. 7. These crystals showed metallic behavior. The electrical resistivity decreased as the Ga content decreased, and those of Na 8 Ga 5.70 Si 40.30 and Na 8 Ga 4.94 Si 41.06 at 300 K were 1.40 and 0.72 mU cm, respectively. These values were greater than the resistivity of Na 8 Si 46 (0.24 mU cm at 300 K (ref. 11)). In the case of Na 8 Si 46 , most electrons supplied from Na to the Si cage remain Fig. 5 Plot of a-axis length versus ionic radius (coordination number 12) of the guest atoms for Na 8 Si 46 , 11 Na 8 Ga 5.7 Si 40.3 and A 8 (Al/Ga) 8 Si 38 (A ¼ Na, K, Rb, and Cs). [15][16][17] The hypothetical a-axis length of Na 8 -Ga 8 Si 38 estimated in Fig. 3(a) is also plotted with Â.