System: Ba8Ga16–xSn30+x (1.1 ≤ x ≤ 2.8) Clathrates of Type-I and Type-VIII, and BaGa2–xSn4+x (x ≈ 0.2) with a Clathrate-like Structure

Systematic syntheses in the Ba–Ga–Sn system confirmed the existence of a new ternary phase BaGa1.79Sn4.21(2) (EuGa2Ge4 structure type; orthorhombic space group Cmcm, Pearson symbol oS28) with lattice parameters a = 4.5383(6) A, b = 12.2486(16) A, c = 14.3747(19) A. The structure is best viewed as an open-framework based on tetrahedrally coordinated Sn/Ga atoms with Ba atoms enclosed in the voids within it. The new phase co-precipitates with two other compounds with very similar compositions—Ba8Ga14.5Sn31.5(4) (K4Si23 structure type; cubic space group , Pearson symbol cP54; a = 11.6800(12) A), and Ba8Ga13.2Sn32.8(3), (Eu4Ga8Ge15 structure type; cubic space group , Pearson symbol cI54; a = 11.5843(7) A). Detailed discussion on how syntheses affect the crystal chemistry, and the temperature dependence of the atomic displacement parameters, obtained from single-crystal structure refinements, are also reported in this article.


Introduction
Clathrates based on Si, Ge, or Sn have been known for close to five decades already, but only recently, the interest in these compounds with rigid covalent networks has shifted towards their potential for optical, thermoelectric and other valuable applications [1][2][3].Although theoretical calculations suggest thermodynamic stability for a variety of such open-frameworks, only several structures (referred to as type-I, -II, etc.) have been found thus far.Clathrate type-I, which is the most common of all, crystallizes in primitive cubic unit cell with 46 framework-building atoms per unit cell, which are all tetrahedrally coordinated.They form 24-atom polyhedra with twelve pentagonal and two hexagonal faces and smaller 20-atom pentagonal dodecahedra.These "voids" can accommodate alkaliand/or alkaline-earth metal atoms, and thus, the formula of the fully stoichiometric clathrate type-I is A 8 Tt 46 , where A represents the corresponding metal atoms and Tt stands for Tetrel, i.e., group 14 elements, respectively.It has also been well established that the structure is amenable to modifications through substitution of Tt-atoms from the network with an electron-poorer element, from groups 13 or 12 for example, which allows for tunable properties [4].This approach can be applied to all known clathrate types as well.
While the crystal chemistry and the chemical bonding in most of the clathrate structures are satisfactorily understood today, one major difficulty persists, and it is in the selective synthesis of each type.The reasons for that are very simple: i) the ratios of framework atoms to cavity atoms in all of the clathrates are remarkably close; ii) the relative thermodynamic stability of the known clathrate types is nearly the same.A possible solution to this synthetic problem can be based on the fact that the polyhedra in the clathrates' structures are of quite different dimensions.Implementation of this idea allows for the rational synthesis of the clathrate type-II compounds (Cs or Rb) 8 Na 16 (Si or Ge) 136 [5,6] and (Cs or Rb) 8 Na 16 (Ga,Si) 136 [7]-ratio of 24:136 or 1:5.67-instead of the analogous clathrates type-I compounds Na 8 Si 46 [8] or Rb 8 Ga 8 Ge 38 [9]-ratio of 8:46 or 1:5.75-where the two cavities are closer in size.
With this paper, we report the results of our extensive work on type-I and type-VIII Ba 8 Ga 16 Sn 30 clathrates, which provide no evidence to support (ir)reversible α↔β phase transitions, suggesting they are better regarded as different, albeit closely related phases.We also further the knowledge on the phase-relationships in the Ba-Ga-Sn system, by reporting the novel ternary phase with a clathrate-like framework structure, BaGa 2 Sn 4 (rather BaGa 2-x Sn 4+x , where x ≈ 0.2), which is isotypic with EuGa 2 Ge 4 [16][17][18].BaGa 2-x Sn 4+x is only the second ternary compound with this structure, after the archetype, and our structure refinements from X-ray single-crystal data provide, for a first time, a reliable data on the distribution of Ga and Tt-atoms on the framework sites.

Synthesis and Thermal Analysis
In spite of the extensive prior experimental work in the system Ba-Ga-Sn [11][12][13][14][15][19][20][21][22][23][24], there remain some open questions, such as the existence of the only type-II clathrate with Sn, Ba 16 Ga 32 Sn 104 [25], and the proposed (but not proven) dimorphism of type-I and type-VIII Ba 8 Ga 16 Sn 30 clathrates [11][12][13][14][15].Our systematic investigations, using both conventional solid-state synthesis methods, as well as molten fluxes have produced evidence for only three phases in the Sn-rich part of the phase diagram-type-I Ba 8 Ga 16-x Sn 30+x (x ≤ ±1.5) clathrate, type-VIII Ba 8 Ga 16-x Sn 30+x (x ≤ ±2.8) clathrate, and the new ternary phase BaGa 2-x Sn 4+x (x ≈ 0.2).The results from our exploratory work can be summarized as follows: -type-I Ba 8 Ga 16-x Sn 30+x (previously known as β-form) clathrate is the major product of all stoichiometric or Sn flux reactions at high temperature, which are cooled quickly and annealed at temperatures below 450 °C before the removal of the flux; -BaGa 2-x Sn 4+x is the minor product of the above reactions and appears to always co-crystallize with the clathrate phase (note how close the nominal compositions are); -type-VIII Ba 8 Ga 16-x Sn 30+x (previously known as α-form) clathrate is the major product of Sn of Sn/Ga flux reactions at low temperature, e.g., 500 °C; -type-I Ba 8 Ga 16-x Sn 30+x clathrate readily forms via melting of stoichiometric mixtures of the elements at high-temperature, while type-VIII Ba 8 Ga 16-x Sn 30+x does not; -when the Sn flux method is employed, reactions with the same ratios of Ba, Ga and Sn produce different phases if the flux is removed at 700 °C (BaSn 3 [26]) vs 400 °C (type-I Ba 8 Ga 16-x Sn 30+x clathrate).
In addition, thermal analysis of pure type-I Ba 8 Ga 16-x Sn 30+x clathrate suggests that it decomposes above 500 °C, confirming the DSC results reported by Takabatake et al [14,27].However, temperature dependent in-situ powder X-ray diffraction reveals that the degradation of the sample begins at much lower temperature, ca.300-350 °C (Figure 1).As seen from the figure, the material is significantly changed even below 300 °C and completely molten above ca.500 °C; only Bragg peaks due to elemental Sn can be indexed upon cooling the melt to room temperature.Similar behavior is observed for the type-VIII Ba 8 Ga 16-x Sn 30+x clathrate with no signs of phase transitions neither in the calorimetry signals, nor in the in-situ powder X-ray diffraction pattern.The above indicates that the phase-relationships between type-I and type-VIII Ba 8 Ga 16 Sn 30 clathrates are different than those in the Eu-Ga-Ge counterparts.Apparently, both type-I and type-VIII Ba 8 Ga 16 Sn 30 clathrates decompose peritectically and cannot be transformed into each other (not at least under ambient pressure).Hence, we argue that the α-and β-designations are irreverent, and referring to the type-VIII and type-I clathrates as low-and high-temperature forms, respectively, is unjust.

Figure 1.
Temperature dependent in-situ powder X-ray diffraction patterns for type-I clathrate Ba 8 Ga 14.5 Sn 31.5 (4) .The peak at ca. 39° 2θ that does not change with T is from the Pt thermocouple.

Crystal Chemistry of Clathrate type-I
Ba 8 Ga 14.5 Sn 31.5(4) with type-I structure crystallizes in the cubic space group n Pm3 (no.223, Pearson symbol cP54; Table 1 and 2) with a periodicity constant a = 11.6800(12)Å at room temperature.This value is shorter than the reported unit cells for Ba 8 Ga 16.8 Sn 29.2 (a = 11.744(2)Å) [11] and Ba 8 Ga 15.2 Sn 30.8 (a = 11.708(1)Å) [12], which is somewhat unexpected given that our crystals are Sn-richer (vide supra) and that the Pauling's radius of Sn (1.42 Å) is larger than that of Ga (1.25 Å) [28].The open-framework (Figure 2, left) is made of statistically disordered Ga and Sn atoms, located at three different Wyckoff sites-6c, 16i and 24k.The 46 framework sites (per unit cell) can be viewed as forming six larger (Ga,Sn) 24 tetrakaidecahedra and two smaller (Ga,Sn) 20 dodecahedra (in analogy with the fullerenes, the former can be denoted as 5 12 6 2 , and the latter as 5 12 , respectively).The tetrakaidecahedra share their hexagonal faces and create a system of three perpendicular and nonintersecting "channels" running along the axes of the cube.Smaller 20-atom pentagonal dodecahedra are enclosed between them.We point out here that although the framework is made of approximately 1/3 Ga and 2/3 Sn, the distribution of two elements is not uniform on the three sites.For example, the 6c site (Ga:Sn = 67:33) is preferentially occupied by Ga (Table 3), while the Sn atoms are primarily found at the 16i (Ga:Sn = 31:69) and 24k (Ga:Sn = 23:77) sites.Very similar site occupancies are observed in Ba 8 Ga 16.8 Sn 29.2 (Sn amount: 27%, 64% and 73%, respectively) [11] and in Ba 8 Ga 16-x Sn 30+x (x ≤ ± 0.9); 29-33%, 64-66% and 74-75%, respectively) [12].Iversen et al. have analyzed these traits in other clathrates and have suggested that the reason for the preferential (sometimes even exclusive) occurrence of the Triel over the Tetrel element at the 6c site is so that the unfavorable Tr-Tr contacts are minimized [3].The (Ga,Sn) 24 tetrakaidecahedra host the Ba1 atoms, while the (Ga,Sn) 20 polyhedra encapsulate the Ba2 atoms (site 2a).The former reside not in the center of the cage (corresponding to site 6d), but are displaced by almost 0.4 Å to a 24k site (Figure 3).The 4-times greater multiplicity of the "off-center" position requires the Ba1 atom to be with a 25% occupation.Introducing positional disorder here is necessary because the anisotropic displacement parameter (ADP) of Ba1 is abnormally elongated if the electron density is not modeled as smeared around the center of the cage (Figure 3).Such anisotropy and large thermal ellipsoids of the alkaline-earth metal located in the tetrakaidecahedra is well documented in the literature, not only for Ba 8 Ga 16.8 Sn 29.2 [11], but also for other type-I clathrates like Ba 8 Ga 16-x Ge 30+x [14,29], Sr 8 Ga 16 Ge 30 [30], Ba 8 Cd x Ge 43-5x/8 □ 3-3x/8 (0 < x < 8) [31], and Ba 8 Zn x Ge 46-x-y □ y (2 < x < 8) [32].
From temperature dependent X-ray diffraction experiments carried out for a single-crystal of Ba 8 Ga 14.5 Sn 31.5(4)(Table 2), we see a nearly linear increase of the lattice parameter from a = 11.6588(8)Å at 100 K to a = 11.6800(12)Å at room temperature.This yields a coefficient of linear thermal expansion β = 9.6 × 10 -6 K -1 , which is comparable to many metals and alloys.Refinements of the anisotropic displacement parameters of all atoms and plotting the ADP values as a function of temperature is also instructive-the above described disorder at the Ba1 site can be clearly seen in Figure 4.The "jump" between 175 and 200 K is not understood as of yet, and might indicate the onset of an order-disorder transition, although the refinements at the six different temperatures agree well with the presented model.Such dynamic disorder has been previously dubbed "a rattling motion", which can be described by the Einstein oscillator model.Thereby, the temperature dependence of the Debye-Waller factors (assuming the rattling atoms to be harmonic oscillators exhibiting characteristic localized vibration frequency) can be given as where U iso is the slope of the isotropic mean-square displacement; k B is Boltzmann constant; T is temperature; K is the spring temperature of the oscillator, h is Planck's constant; m is the mass of the rattling atom; and Θ E is the Einstein temperature [2].The ADP data (Table 4) can be used to estimate the Einstein temperature of these atoms.This estimation results in Θ E = 47 K at 293 K for Ba 8 Ga 14.5 Sn 31.5 .Suekuni et al. reported an Einstein temperature of Θ E = 60 K at 300 K for Ba 8 Ga 15.8 Sn 30.2 [13].From this analysis it appears that the Ba atoms behave as normal "rattlers", even though we cannot ascertain from the ADP alone whether this corresponds to a static displacement or to some dynamic motion between the four off-center sites and the center of the cage.[12].The crystal structure (Figure 2, right) can be viewed as a framework of face-shared distorted (Ga,Sn) 20 polyhedra, centered by the single Ba site (8c).These are bridged by an additional vertex resulting in (Sn,Ga) 20+3 cages (6 3 6 3 5 3 5 3 ), shown in light blue in Figure 2. The packing of the polyhedra is not space-filling, and small, empty cages of eight framework atoms are left behind (shown in yellow).There are four crystallographically unique sites and the Ga/Sn distribution on them varies greatly.The Wyckoff site 2a is exclusively occupied by Sn atoms, while the other three sites, 8c, 12d and 24g, are occupied by statistical mixtures of Ga and Sn atoms in the following ratios-Ga:Sn = 62:38 at the 8c site; Ga:Sn = 13:87 at the 12d site; and Ga:Sn = 28:72 at the 24g site, respectively (Table 5).A similar distribution on the four sites is found in Ba 8 Ga 17.4 Sn 28.6 by Eisenmann et al. (Sn amount: 2a: 100%, 8c: 34%, 12d: 65% and 24g: 67%) [13].A largely different, yet unexplained, Ga/Sn distribution on all four sites can be found in the refinements of Ba 8 Ga 17.2 Sn 28.8 by Carrillo-Cabrera et al. [15] (Sn amount: 2a: 72%, 8c: 29%, 12d: 80% and 24g: 65%, respectively).Notice that the refined compositions are virtually identical in both cases, suggesting the preparative methods-convection heating vs induction heating and annealing-to be the reason for the observed differences.3) a U eq is defined as one third of the trace of the orthogonalized U ij tensor, investigations of the thermoelectric properties, the electronic structure and carrier tuning of both type-I and type-VIII Ba 8 Ga 16-x Sn 30+x clathrates by virtue of optimizing the and n-type carriers can be found elsewhere [12,14,19,20].We might just add here that utmost care should be exercised when synthesizing such compounds in large batches, as sample homogeneity and phase-purity could complicate the transport measurements.A testament to this conjecture is the resistivity measurements of three different batches of type-I Ba 8 Ga 16-x Sn 30+x clathrates, displayed in Figure 5.The three single-crystals are poor metals with room temperature resistivity between 4 and 10 mOhm•cm.These values are several orders of magnitude higher than the resistivities of normal metals.As seen from the temperature dependence of ρ(T), the resistivity decreases almost linearly with temperature, but the slopes are different, even though the samples have been prepared following the same synthetic procedure and are expected to be identical.Most likely, differences in the concentration of defects and impurities in the samples are the cause of such behaviour.At low temperature (below ca.20 K), ρ(T) in the three data sets rich plateaus, with residual resistivities occurring in the range from 1 and 3 mOhm•cm-obviously shows another sign of variations in the samples.Below ca. 5 K the resistivity of all samples drops to zero, which is indicative of superconducting transitions.Likely, the drops in the resistivities are not due to bulk superconductivity of the type-I Ba 8 Ga 16-x Sn 30+x clathrate, but to small amounts of Sn/Ga flux present in the samples, as confirmed by the heat capacity, illustrated for one of these samples in Figure 5 as well.The main panel in Figure 5 shows the heat capacity over the whole temperature range approaching the value predicted by the law of Dulong-Petit at high temperatures, as expected.In the inset C/T vs T is plotted in the temperature range around the superconducting plateaus found in the resistivity data.There are no indications of a transition, confirming that no bulk superconductivity is present in the samples.

Experimental Section
All synthetic manipulations were carried out in an argon-filled glove box or under vacuum.In the syntheses we employed pure metallic elements, purchased from Alfa or Aldrich with purities greater than 99.9% (metal basis).Two methods were generally used-direct fusion of elements in sealed niobium containers and flux reactions with Ga or Sn as molten fluxes.The basic synthetic procedure for the former method was as follows: the elements were loaded in the desired stoichiometric ratios in niobium tubes, which were subsequently sealed using an arc-welder (under high purity Argon gas).The niobium tubes were then put in fused silica jackets, and flame-sealed under high vacuum.Melting the reaction mixtures was accomplished using suitable heating scheme in high temperature tube furnaces.The niobium tubes were then brought back in the glove box and opened.The basic synthetic procedure for the flux reactions was as follows: the elements were loaded in the desired molar ratios in 2 cm 3 alumina crucibles that were subsequently flame-sealed in evacuated fused silica tubes.The reaction mixtures were subjected to different heat treatments in high temperature muffle furnaces.Upon cooling to desired temperatures (above the melting point of the specific flux), the excess molten metal was removed by decantation.The silica tubes were then brought back in the glove box, crack-opened, and the crystals were isolated.
The new BaGa 1.79 Sn 4.21(2) compound was never obtained as a single phase product and always co-crystallized with type-I Ba 8 Ga 14.5 Sn 31.5(4)clathrate, when Sn flux reaction were used.The optimized experiment involved a mixture Ba:Ga:Sn = 2:4:15, which was heated to 1000 °C (rate 10 °C/h), homogenized for 5 h, cooled to 450 °C (rate -300 °C/h), annealed for 28 h and cooled to 400 °C (rate -10 °C/h), where the excess Sn was removed.Clathrate type-I Ba 8 Ga 16-x Sn 30+x (x ≤ ±1.5), in addition to the method above, could also be obtained by stoichiometric reactions Ba:Ga:Sn = 2:4:7.5.After sealing the mixtures in Nb tubes (jacketed in fused silica tubes), they were heated to 1000 °C (rate 10 °C/h), equilibrated for 5 h, cooled to 450 °C (rate -300 °C/h), annealed for 12 h and cooled to room temperature (rate -20 °C/h).The products from such reactions were identified by powder and single-crystal X-ray diffraction.
Clathrate type-VIII Ba 8 Ga 13.2 Sn 32.8(3) is hard to obtain from stoichiometric reactions, but large (up to 4-5 mm) crystals can be readily grown from Ga/Sn flux reactions.The optimized experiment required the elements to be loaded in the Ba:Ga:Sn = 2.5:14:67 molar ratio.The samples were heated to 500 °C (rate 20 °C/h) and homogenized for 500 h.The flux was removed, after cooling to 400 °C (rate -5 °C/h).
The compositions of all synthesized materials were confirmed by EDX measurements (JEOL 7400F electron microscope equipped with an INCA-OXFORD energy-dispersive spectrometer).

Figure 2 .
Figure 2. Crystal structures of Ba 8 Ga 14.5 Sn 31.5(4)(type-I, left) and Ba 8 Ga 13.2 Sn 32.8(3) (type-VIII, right).Ba atoms residing in the (Ga,Sn) 20 cages (clathrate type-I) and the augmented (Ga,Sn) 20+3 cages (clathrate type-VIII) are drawn as light blue spheres, while the Ba atoms residing in the (Ga,Sn) 24 tetrakaidecahedra (clathrate type-I only) are drawn as red spheres.The empty cubic voids in the clathrate type-VIII are shown in yellow.

Figure 3 .
Figure 3. Representations with anisotropic displacement parameters of: (a) the Ba1 atom at the 24k site (off-set from center of the (Ga,Sn) 24 tetrakaidecahedra); and (b) the Ba2 atom at the 2a site (center of the (Ga,Sn) 20 pentagonal dodecahedra).Thermal ellipsoids are drawn at the 95% probability level.

Figure 5 .
Figure 5. Resistivity and specific heat as a function of temperature of single-crystalline type-I Ba 8 Ga 16-x Sn 30+x clathrate.

Figure 6 .
Figure 6.Polyhedral view of the orthorhombic crystal structure of BaGa 2-x Sn 4+x .Ba atoms residing in the (Ga,Sn) 18 polyhedra are drawn as red spheres.The empty 9-atom voids are shown in yellow.Sn1 atoms (8f site, 100% occupancy by Sn) are shown as black spheres, while the remaining two framework sites with statistical mixtures of Sn/Ga atoms are represented as blue spheres, respectively.

Table 2 .
Selected structure refinement parameters for Ba 8 Ga 14.