Single crystal growth and structure analysis of type-I (Na/Sr)–(Ga/Si) quaternary clathrates

Single crystals of (Na/Sr)–(Ga/Si) quaternary type-I clathrates, Na8−ySryGaxSi46−x, were synthesized by evaporating Na from a mixture of Na–Sr–Ga–Si–Sn in a 6 : 0.5 : 1 : 2 : 1 molar ratio at 773 K for 12 h in an Ar atmosphere. Electron-probe microanalysis and single-crystal X-ray diffraction revealed that three crystals from the same product were Na8−ySryGaxSi46−x with x and y values of 7.6, 2.96; 8.4, 3.80; and 9.1, 4.08. It was also shown that increasing the Sr and Ga contents increased the electrical resistivity of the crystal from 0.34 to 1.05 mΩ cm at 300 K.


Introduction
Silicon (Si) clathrate compounds are composed of host Si atoms organized in three-dimensional frameworks and guest atoms enclosed in the Si cages of the frameworks. Kasper et al. rst synthesized binary Si clathrate, Na 8 Si 46 , in 1965. 1 Since then, many researchers have studied Si clathrate compounds, 2 altering their physical properties by partial or full substitution of different elements for the host and guest atoms. Kawaji et al. synthesized a type-I clathrate, (Na,Ba) 8 Si 46 ; 3 this compound was the rst Si clathrate superconductor with a T C value of 4 K derived from the partial substitution of Ba for Na in the Na 8 Si 46 cages. Another Si clathrate, Ba 8 Si 46 , which was synthesized at high pressure (3 GPa) and 1073 K, exhibited the highest T C value 8 K among the various Si clathrate compounds. 4 The framework Si atoms can also be partially replaced by Ga atoms in some type-I clathrate compounds, such as A 8 Ga 8 Si 38 (A ¼ K, Rb, Cs), as described by Sui et al. 5 A 8 Ga 8 Si 38 powder was sintered by spark plasma sintering to obtain bulk polycrystalline samples, which exhibited band gaps in the range of 1.14-1.18 eV. 5 Another clathrate composed of Ga/Si cages and Ba atoms, Ba 7.94 Ga 15.33 Si 30.67 , was shown to have a relatively high thermoelectric dimensionless gure of merit, ZT, of 0.87 at 870 K. 6,7 Sr 8 Ga 11 Si 35 8 and Sr 8 Ga 13.6 Si 32.4 , 9 which contain Sr guest atoms in Ga/Si cages, exhibit electrical resistivities of approximately 0.2 and 0.26 mU cm, respectively, at 280 K.
Some ternary silicon clathrates could be synthesized via solidstate reactions between each elements at high temperature 5 or melting method. 6,8,9 However, the silicon clathrates containing a Na atom could not be synthesized by simple reaction because these clathrates have been regarded as metastable or intermediate phases. These clathrates were generally prepared by thermal decomposition of the precursor compounds. For example, the binary silicon clathrates containing Na, Na 8 Si 46 and Na 24 Si 136 , were synthesized by thermal decomposition of Na 4 Si 4 Zintl compound. 1,2 The clathrate samples obtained by this method were powdery due to the solid state of the precursor compounds. Therefore, it is difficult to prepare the bulk crystal of the silicon clathrates containing Na. In our previous study, the single crystals of the Na-Si binary clathrate were successfully grown by using Sn ux. 10,11 Single crystals of type-I Na 8 Si 46 and type-II Na 24 Si 136 clathrates were selectively grown in Na-Sn rich Na-Sn-Si ternary melt by Na evaporation. 11 Single crystals of a ternary type-I clathrate, Na 8 Ga 5.70 Si 40.30 , could also be prepared by a self-ux method using Ga as a ux. 12 Furthermore, the crystal growth of Na 8 Ga x Si 46Àx (x ¼ 4.94-5.52) clathrates was achieved by adding a Sn ux to the starting melt. We could measure the electrical resistivity of the single crystals for these clathrates containing Na. The clathrates exhibited metallic conduction, and their electrical resistivity decreased as the Ga content decreased (e.g., the resistivities of Na 8 Ga 5.70 Si 40.30 and Na 8 Ga 4.94 Si 41.06 were 1.40 and 0.72 mU cm, respectively, at 300 K).
To extend the variation of clathrate compounds and their eld of properties and applications, doping or partial substitution of other atoms at the Na atom site is also designed. Recently, quaternary Ga/Si and Zn/Si clathrates having Na and Rb or Cs guest atoms, such as Cs 6 Na 2 Ga 8.25 Si 37.75 , Rb 6.34 -Na 1.66 Ga 8.02 Si 37.98 , and Rb 8 Na 16 Zn 8.4 Si 127.6 , have been synthesized using a Ga or Zn ux. 13 However, the typical size of the single crystals was below 0.1 mm, and the properties of the crystals could not be characterized. So, synthesis of quaternary Na and Si based clathrate single crystals with a size enough for characterization is still challenging. In the present study, we succeeded in growing the single crystals of quaternary Ga-Si cage clathrate compounds encapsulating Na and Sr guest atoms by the Sn ux method. The compounds are the rst examples of the Ga/Si clathrates containing Na (1+) and other guest cations with a different formal ionic charge (2+). The crystal structures and electrical properties were investigated for the single crystals of the new clathrates.

Experimental methods
The experiments were conducted as described in the previous studies. [10][11][12] Metal Na pieces (Nippon Soda Co. Ltd., 99.95%), Si powder (Kojundo Chemical Laboratory Co. Ltd., 4N), Ga grains (Dowa Electronics Co. Ltd., 6N), and Sn granules (Mitsuwa Chemicals Co. Ltd., 5N) were combined by weight at a Na : Ga : Si : Sn molar ratio of 6 : 1 : 2 : 1 (total 8.70 mmol) in a glove box with an Ar atmosphere. The raw material mixture was then put in a boron nitride (BN) crucible (Showa Denko KK; inner diameter of 6.5 mm and depth of 18 mm) and sealed in a stainless steel (SUS) container (SUS316, outer diameter of 12.7 mm, inner diameter of 10.7 mm, and height of 80 mm) with Ar gas. The SUS container was heated in an electric furnace at 1173 K for 12 h then the furnace was cooled to room temperature. The BN crucible was then taken from the SUS container in the glove box and Sr grains (Alfa Aeser, 4N) were added to the Na-Ga-Si-Sn mixture in the BN crucible to make the Na : Sr : Ga : Si : Sn molar ratio 6 : 0.5 : 1 : 2 : 1. Next, the BN crucible was sealed in the upper part of another long SUS container (outer diameter of 12.7 mm, inner diameter of 10.7 mm, and height of 300 mm) with Ar gas. The upper part of the container was heated at 773 K for 12 h, and the lower part was cooled using a fan to keep the temperature almost the same with the room temperature. By generating a temperature gradient in the container, the Na was evaporated from the mixture in the crucible, and condensed on the inner wall in the lower cooler part of the container.
Aer heating, the crucible was taken out in the glove box, and the weight loss from the sample was measured to calculate the amount of evaporated Na against the amount of Na in the starting mixture. The sample in the crucible was subjected to an alcohol treatment by which any excess Na and Na-Sn and Na-Ga compounds in the sample were completely reacted with 2propanol followed by ethanol, and the reaction products of Na were removed from the samples by washing with water. A mixture of Ga and Sn remained aer the decomposition of Na-Sn and Na-Ga compounds by the alcohol treatment and a Sr-Ga-Si ternary compound in the sample were then subjected to a hydrochloric acid treatment by dissolving in an aqueous hydrochloric acid (35.0-37.0 mass% HCl) and rinsing the residue with water.
The morphologies of the obtained single crystals were observed with an optical microscope (Olympus, SZX16) and a scanning electron microscope (SEM; JEOL, JXA-8200) at an accelerating voltage of 15 kV. The single crystals were cut to about 100-150 mm in size and subjected to X-ray diffraction (XRD) measurements (Bruker, D8 QUEST). APEX3 14 was used to collect the diffraction data and rene the unit cells. X-ray absorption correction was performed by SADABS installed in APEX3. 14 SHELEXL-97 soware 15 was used to rene the occupancies, coordinates, and displacement parameters of the atoms. The crystal structure was drawn by VESTA. 16 The compositions of the obtained single crystals were analyzed with an electron-probe microanalyzer (EPMA, JEOL, JXA-8200). The electrical characteristics of the single crystals were measured in the range of 8-300 K by the four-terminal method using Ag paste as electrodes.

Results and discussion
When Sr was heated with other starting materials, at 1173 K for 12 h, a SrGaSi ternary compound was crystallized. 17 Once this compound was formed, it did not melt or dissolve into a liquid phase at 773 K and Sr was not provided to the crystal growth of clathrate. Thus, Sr was added to the Na-Ga-Si-Sn mixture prepared in advance. By heating the Na-Ga-Si-Sn mixture and Sr at 773 K for 12 h, 46% of Na was evaporated. The residual excess Na and Na of Na-Sn and Na-Ga compounds in the sample were removed by the alcohol treatment. Aer hydrochloric acid treatment for removal of Sn and Ga by decomposition of the Na-Sn and Na-Ga compounds and a SrGaSi compound contained in the product, the black single crystals of clathrate were clearly separated. Fig. 1 shows optical and SEM micrographs of the crystals picked up from the obtained sample. Quantitative EPMA analyses were performed on the at surfaces of the three black single crystals with sizes of 0.96 mm (crystal 1), 0.93 mm (crystal 2), and 0.83 mm (crystal 3) which were taken from the same sample. The Na, Sr, Ga, and Si contents of crystals 1, 2, and 3 are summarized in Table 1. The chemical formulas of crystals 1, 2, and 3 were calculated by setting the total number of Si and Ga atoms to 46 (based on the general formula of the type-I clathrate, Na 8Ày Sr y Ga x Si 46Àx ) as Na 4.9(2) Sr 3.3(2) Ga 7.6(2) Si 38.4(2) , Na 3.8(5) Sr 4.0(3) Ga 8.4(2) Si 37.3 (2) , and Na 3.2(1) Sr 4.8(1) Ga 9.1(1) Si 36.9(2) , respectively. The sum of the Na and Sr numbers was close to 8. As shown in Fig. 2, the Sr content, y, linearly increased as the Ga content, x, increased. The largest crystal, crystal 1, had the smallest Sr and Ga contents among the three crystals.
In addition, cross sections of the crystals were also analyzed by EPMA; the results are shown in Fig. S1. † In crystals 2 and 3, Na, Sr, Ga, and Si were homogeneously distributed. In contrast, in crystal 1, the surface was Na 4.9(2) Sr 3.3(2) Ga 7.6(2) Si 38.4 (2) , but its composition changed sharply at one region that did not contain Sr and had a composition of Na 8.3(2) Ga 4.3(2) Si 41.7 (2) . The crystal 1 containing the Na-Ga-Si ternary clathrate part which were surrounded with the low Sr content Na 4.9(2) Sr 3.3(2) Ga 7.6(2) Si 38.4 (2) was probably grown at the early stage of the crystal formation. This may indicate that Sr which was added to the Na-Ga-Si-Sn mixture was gradually provided to the melt during heating at 773 K. Homogeneous and high Sr concentrations in the crystals 2 and 3 suggest the crystal growth from Sr-rich melts at later stages. Further studies are needed to clarify the process by which crystals with different Sr and Ga contents are grown from the same starting mixture.
The results of the X-ray crystal structure analyses of pieces from the surface of crystals 1-3 are listed in Tables 2-4. The crystal structures were analyzed based on the model of a type-I clathrate (space group, Pm 3n). The occupancies of Si/Ga1(24k), Si/Ga2(16i), and Si/Ga3(6c) were rened under the constraint that the total Ga content was equal to that measured by EPMA. The reliability factor, R1(all), was in the range of 1.13-1.34% for all analyses. The chemical formulas of crystals 1, 2, and 3 were calculated from the rened occupancies as Na 5 Fig. 3. In crystals 1, 2, and 3, the Ga occupancies for the Si/Ga1(24k), Si/Ga2(16i), and Si/Ga3(6c) sites ranged from 0.1005(7) to 0.1387(8), 0.0344(10) to 0.0613 (11), and 0.773(2) to 0.798(2), respectively, and Ga atoms preferentially occupied the Si/Ga3(6c) sites in the [Si/Ga] 24 cages. Similar preferential occupation of Ga atoms in the Si/Ga3(6c) sites has been previously reported for other type-I clathrates, Rb 6  more electronegative Ga atoms (c Ga P ¼ 1.81). In the case of Na 8Ày Sr y Ga x Si 46Àx , the electronegativities of Sr (c Sr P ¼ 0.95) and Na (c Na P ¼ 0.93) were similar, but the rst ionization energy of Na (5.139 eV) was smaller than that of Sr (5.695 eV). 19 Thus, Na atoms may preferentially occupy the Ga-rich [Si/Ga] 24 cages of Na 8Ày Sr y Ga x Si 46Àx clathrates.
The crystal structure of Na 3.92 Sr 4.08(2) Ga 9.1 Si 36.9 (crystal 3) is drawn with displacement ellipsoids representing the 99% probability region in Fig. S2. † The U 22 ¼ U 33 parameters of the Na/Sr1(6d) sites in crystals 1, 2, and 3 were 0.0508(4), 0.0524(5), and 0.0512(5)Å 2 , respectively, which were larger than the atomic displacement parameters of U 11 (0.0272(5), 0.0244(5), Table 2 Crystal data, data collection, and refinement for the XRD analysis of Na-Sr-Ga-Si quaternary single crystals a where F o is the observed structure factor, F c is the calculated structure factor, s is the standard deviation of F c 2 , and P ¼ ( where n is the number of reections and p is the total number of parameters rened.  Fig. 4 shows the temperature dependence of electrical resistivity, r, measured for the three crystals and the type-I clathrate single crystal, Na 8 Ga 5.7 Si 40.3 , synthesized by our group in a previous study. 12 The r values for crystals 1, 2, and 3 increased with increasing temperature, reaching 0.34, 0.55, and 1.05 mU cm, respectively, at room temperature (300 K). The previously reported electrical resistivities at 280-300 K for other type-I clathrates, Na 8 Si 46 , 20 Na 8 Ga x Si 46Àx , 12 and Sr 8 Ga x Si 46Àx , 8,9 are compared to those in the Na 8Ày Sr y Ga x Si 46Àx sample (crystal 1: Na 5.0 Sr 3.0 Ga 7.6 Si 38.4 , crystal 2: Na 4.2 Sr 3.8 Ga 8.4 Si 37.6 , and crystal 3: Na 3.9 Sr 4.1 Ga 9.1 Si 36.9 ) with respect to their respective Ga contents, x, in Fig. 5. The electrical resistivity of crystal 1 was plotted at x ¼ 7.6 in Fig. 5 even though one region in the Na 4.9(2) Sr 3.3(2) Ga 7.6(2) Si 38.4 (2) crystal had a composition of Na 8.3(2) Ga 4.3(2) Si 41.7(2) (as shown in Fig. S1 †).
The resistivity of Na 8 Ga x Si 46Àx was greater than that of Na 8 Si 46 (0.098 mU cm) as measured previously by Stefanoski at 300 K 20 and increased with increasing x. 12 Eight electrons are formally transferred from Na to the Si framework to form Na 8 Si 46 ; these electrons enter into the conduction band. Since the valences of Si and Ga are 4 and 3, respectively, the number