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Prediction and Synthesis of a Non-Zintl Silicon Clathrate Tiago F. T. Cerqueira,† Stéphane Pailhès,*,‡ Régis Debord,‡ Valentina M. Giordano,‡ Romain Viennois,§ Jingming Shi,‡ Silvana Botti,*,†,∥ and Miguel A. L. Marques∥,⊥ †

Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany Institut Lumière Matière (UMR5306), Université Lyon 1-CNRS, Université de Lyon, F-69622 Villeurbanne Cedex, France § Institut Charles Gerhardt Montpellier, Université de Montpellier and CNRS, place Eugène Bataillon, F-34095 Montpellier, France ∥ European Theoretical Spectroscopy Facility ⊥ Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany ‡

S Supporting Information *

ABSTRACT: We use computational high-throughput techniques to study the thermodynamic stability of ternary type I Si clathrates. Two strategies to stabilize the structures are investigated: through endohedral doping of the 2a and 6d Wyckoff positions (located at the center of the small and large cages, respectively) and by substituting the Si 6c positions. Our results agree with the overwhelming majority of experimental results and predict a series of unknown clathrate phases. Many of the stable phases can be explained by the simple Zintl− Klemm rule, but some are unexpected. We then successfully synthesize one of the latter compounds, a new type I silicon clathrate containing Ba (inside the cages) and Be (in the 6c position). These results prove the predictive power and reliability of our strategy and motivate the use of high-throughput screening of materials properties for the accelerated discovery of new clathrate phases.

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INTRODUCTION

alkaline earth metal, and lanthanoids as precursors, under highpressure and high-temperature conditions. The superconductivity found in silicon clathrates is based on a strong covalent sp3 network and has attracted much attention for the past decades.13−16 More recently, inorganic clathrates have been widely investigated in the field of thermoelectricity: the electronic conduction is ensured by the cage framework, and the band gap can be easily tuned because of the many possible substitutions of framework elements, giving rise to metallic or semiconducting behavior.17 On the other hand, the unit cell complexity and the host−guest interaction are responsible for the depression of the heat-carrying acoustic phonons, resulting in a very low lattice thermal conductivity,18−20 without affecting the electronic conductivity. Thus, although they are crystals, clathrates are very poor heat conductors, while offering a wide range of electronic properties. They are therefore a perfect example of Slack’s concept of a phonon glass and electron crystal.21−23 It is not surprising that important experimental and theoretical research effort has been devoted to finding and optimizing the functional properties of clathrates. In this quest, the ZK rule serves as an important guide to experimentalists, to select among all the possible combinations of substitutions in

Clathrates form a class of fairly special materials based on a host−guest structure that consists of regular lattices of cages in which guest atoms or molecules are encapsulated. In strict terms, clathrates are the duals of the intermetallic phases known as Frank−Kasper structures that contain only tetrahedral interstices and are closely related to a family of quasicrystals.1,2 Since the seminal work of Cros et al.,3,4 who synthesized the first Si clathrates in 1965, many inorganic, group IV, clathrate phases have become known. These are commonly described in a first approach as cubic solids with a unit cell composed of large cages of silicon, germanium, or tin. Their stability5,6 and their electrical properties (metal or semiconductor character) are, in a first approximation, fully understood in terms of the socalled Zintl−Klemm (ZK) rule (or charge balance rule):7−11 assuming that every guest atom in the cages completely donates its electrons, the structure maximizes its stability when each framework atom realizes an electron octet. Zintl clathrates are compounds of the form AaXxSim = (An+)a(Xan/x−)xSim, where A is a strongly electropositive metal such as alkali metal, alkaline earth metal, or lanthanoid, X is an (electronegative) noble or post-transition metal or semimetal, and n is the number of electrons transferred from the active metal to x acceptor atoms, which build together with m Si atoms the covalent bonds of the cagelike framework.12 Indeed, silicon clathrates are usually synthesized starting from Zintl binary silicides with alkali metal, © XXXX American Chemical Society

Received: January 28, 2016 Revised: April 27, 2016

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DOI: 10.1021/acs.chemmater.6b00392 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials the different crystallographic sites of guest and host atoms. However, although most clathrates are Zintl phases from the point of view of their formal electronic structures, some of their properties cannot be explained in terms of the Zintl concept and violations of this rule were observed, notably in clathrates containing transition metal elements.22,24 In this article, we go beyond the ZK rule and use densityfunctional theory to screen the stability of a very large number of silicon clathrate phases. Our theoretical methodology is based on high-throughput calculations 25 and involves trying out a large set of combinations of guest and framework atoms. We consider the case of the very popular and heavily documented ternary type I Si clathrates, whose general chemical formula is A8XxSi46−x. To study this ternary composition, we do not make any a priori assumption about which guest atom and/or dopant atom could lead to stable clathrate phases. Instead, we use all elements of the periodic table up to Bi, excluding the lanthanides. We first demonstrate the reliability of the computational approach by confirming the stability of all experimentally known clathrates. Then, and more convincingly, we predict and synthesize for the first time a new stable phase of the well-studied family of Ba−Si clathrates, namely Ba8BexSi46−x. We selected this example as it does not satisfy the ZK rule, and therefore, it could not have been suggested by simple intuition.

Figure 1. Type I clathrate structure with different atoms indicating the relevant Wickoff positions of cubic space group #223: 16i and 24k (dark blue), 6c (cyan), 2a (purple), and 6d (green).

positions, the 6d positions, or both. Further (co)doping can be achieved by substitution of the 16i, 24k, and 6c positions. This latter substitution is experimentally known to be the most favorable, and we performed calculations to verify this fact by comparing formation energies of atomic substitutions at different Wickoff positions. We observe that an exhaustive study would require that doping of individual lattice sites be tested, including the contribution to the free energy of the configurational entropy. As we want to explore a large variety of chemical compositions, we had to make the choice to restrict our model of codoping to the substitution of all 6c Si atoms. We started studying the stability of the empty cages by replacing the 6c Si atoms. All elements (with the unsurprising exception of Ge) occupying the 6c position destabilize considerably the Si clathrate framework. Then, we filled the 2a, 6d, and 6d+2a positions individually, while preserving the Si cages. Several guest elements in the 2a position lead to a slight stabilization, but the largest effect was obtained occupying the 6d or 6d+2a positions, as shown in Figure 2. The color scale

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HIGH-THROUGHPUT CALCULATIONS To estimate the stability of a given composition, we use as a criterion the distance to the convex hull of thermodynamic stability.25,50−52 If this distance is zero, the structure is defined as being thermodynamically stable. Otherwise, its positive distance corresponds to the energy gained in decomposing the clathrate structure into the most stable combination of its constituents. It is worth underlining here that for ternary and multinary systems this criterion is much more relevant than the formation energies, which measure only the decomposition in elementary phases. In the literature on clathrates, we noticed that the sign of the formation energy is usually used to define stability instead of the distance to the convex hull.42,53−55 However, we found several cases in which, despite the negative formation energy, the distance to the convex hull is large because of the possible decomposition into other binary or ternary phases, thus destabilizing the structure. For each system, we perform a full geometry optimization, including both the ion positions and the lattice, with the code Vasp.56,57 The pseudopotentials are taken from version 5.2 of Vasp to guarantee compatibility with the Materials Project database,58 and we use the Perdew−Burke−Ernzerhof approximation59 to the exchange-correlation potential. For the final calculation of the energy, we use a cutoff of 520 eV and a 5 × 5 × 5 k-point grid. This ensures convergence of the total energy to better than 2 meV/atom. The distance to the convex hull is calculated by comparing the energy of the system under investigation to all possible decomposition channels to materials present in the Materials Project database.58 The type I clathrate structure is depicted in Figure 1. In the pure Si46 clathrate, all the Wyckoff positions 16i, 24k, and 6c are occupied by Si atoms, and the 2a (center of small cages) and 6d positions (center of large cages) are empty. This is our reference structure that turns out to be 63 meV/atom above the convex hull, on which lies the standard diamond structure of Si. Endohedral doping can be achieved by filling either the 2a

Figure 2. Distance to the convex hull (in millielectronvolts per atom) for the clathrate X2a+6dSi46, where X occupies the 2a+6d Wyckoff positions (all cages occupied). The circles denote phases with similar stoichiometries that were synthesized experimentally (for a review, see ref 26): X2a+6dSi46 (X = Na, K, Rb, Cs, or Ba).27−30

denotes the distance to the convex hull, where green means less than around 50 meV/atom from the hull. Furthermore, circles mean that a similar stoichiometry was synthesized experimentally. Results are in good agreement with published experiments, as the elements Na [7 meV/atom above the convex hull if all cages (2a+6d) are filled, 20 meV above the convex hull if only 6d sites are filled], K (4 meV/atom in 2a+6d and 3 meV in 6d), Rb (26 meV/atom in 2a+6d and 11 meV in 6d), and Cs (65 meV/atom in 2a+6d and 31 meV in 6d) yield already nearly thermodynamically stable phases. Indeed, these clathrates have been reported experimentally.27−29 The only B


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Chemistry of Materials exception is the iodine compound that has been reported experimentally60 but that in our calculations is more than 130 meV above the hull. We note, however, that this iodine structure was synthesized at high pressures and high temperatures, and that the experimental stoichiometry, Si44.5I9.5, suggests that this cationic clathrate is likely to have a structure more complicated than the one investigated in this paper. Indeed, experimental data60 indicate that in Si44.5I9.5 clathrates iodine not only occupies the center of the cages but also replaces Si atoms of the framework. The specific case of iodine clathrates would therefore require a detailed study that goes beyond the purpose of this work. From our results, we then selected the guest elements that were within 110 meV/atom of the convex hull for further studies. This included Li, Na, K, Rb, Cs, Ca, Sr, Ba, Hg, In, Tl, He, and Ne. For all these systems, we performed calculations of simultaneous codoping of the 6c and the 6d+2a Wyckoff positions. In total, more than 1300 different compositions were investigated. In Figures 3 and 4, we present a summary of our results, including all relevant phases that are close to stability. Before calculations and experimental data can be compared, it is important to clarify the approximations involved in our theoretical predictions. (i) There is the Perdew−Burke− Ernzerhof approximation59 to the exchange-correlation potential, which can give errors in formation energies as large as 0.1−

Figure 4. Distance to the convex hull (in millielectronvolts per atom) for the clathrate Z6d+2aX6cSi40, where Z is (d) Cs, (e) Sr, or (f) Ba. The circles denote phases with similar stoichiometries that were synthesized experimentally: Cs8Al6cSi40,35 Cs8Ga6cSi40,36 Sr8X6cSi40 (X = Al or Ga),37,38 and Ba8X6cSi40 (X = Al, Ga, Ni, Cu, Zn, Rh, Pd, Ag, Cd, Ir, Pt, or Au).39−49

0.2 eV/atom.61,62 We believe that our error is considerably smaller than this range, as our ternary clathrates usually decompose to binary silicides that have a chemical arrangement similar to that of the clathrates. This should lead to systematic errors in the calculation of total energies, which mostly cancel out when evaluating the distance to the convex hull. (ii) Pseudopotentials are another source of unavoidable systematic errors in our methodology, but again most of this error should cancel when calculating energy differences. (iii) All calculations were performed at zero temperature, and they did not include the correction coming from the zero-point energy and vibrational entropy. This leads to variations in total energy differences on the order of tens of millielectronvolts per atom in the case of light compounds, such as hydrogen alanates.63,64 We calculated the vibrational entropy of Ba8Si46 and found a stabilization (i.e., decrease in the distance to the convex hull of stability) of 5 meV per atom at 0 K and of 15 meV per atom at 900 K. We expect therefore a very limited effect on the clathrates studied in this work. (iv) More importantly, we did not consider stabilization due to formation of vacancies or other defects, leading possibly to off stoichiometry. (v) Moreover, we did not take into account disorder, and therefore configurational entropy, as we always substituted all equivalent atoms of the original clathrate structure (i.e., for example, we substituted all 6c atoms of Si with another element, and we did not try all other possibilities with one, two, three, four, five, etc.,

Figure 3. Distance to the convex hull (in millielectronvolts per atom) for the clathrate Z6d+2aX6cSi40, where Z is (a) Na, (b) K, or (c) Rb. The circles denote phases with similar stoichiometries that were synthesized experimentally:26 Na8X6cSi40 (X = Al),31 K8X6cSi40 (X = Ga or B),32,33 Rb8X6cSi40 (X = Ga),34 A8X6cSi40 (A = K or Rb, and X = Al),35 and A8X6cSi40 (A = K or Rb, and X = Ga).36 C


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Chemistry of Materials

orthorhombic BaSi2 and silicon are 9% and 3%, respectively. Increasing the Be content in the starting mixture leads to an increase of the proportion of orthorhombic BaSi2, which starts to include Be atoms. The X-ray diffraction pattern of the new phase is shown in the left panel of Figure 5. The Rietveld-refined (GSAS

dopant atoms). Of course, this allows us to reduce dramatically the number of possible systems to study, making feasible an extensive study of all possible dopants. The price to pay is that we will necessarily get an upper bound for the distance to the convex hull of stability. In fact, we can observe that the reported experimental stoichiometries deviate slightly from the ideal ones that we are simulating. A defectuous stoichiometry can indeed stabilize further a structure, explaining why we obtain a (small) positive distance to the convex hull for clathrates that are produced experimentally. As a result of the considerations mentioned above, taking into account the accuracy of our calculations and the structure stabilization due to differences in doping, effects of temperature, and disorder, we can reasonably set the threshold of stability of our calculations at 50 meV per atom (to be compared with the room-temperature thermal energy of ∼25 meV). We can now compare experimental data and simulations in Figures 3 and 4. Our results are in convincing agreement with experiments, as all experimentally realized phases are light green colored in the figures. A complete summary of the results is available as Supporting Information, including the calculated values for energies of formation, distances to the convex hull of stability, and decomposition channels. We can see that, to some extent, the simple ZK rule emerges from the figure: when an alkali element is at the center of the cages, we find the maximal stability for codoping with elements close to the IIIA group of the periodic table, while for Sr and Ba, the maximal stability is around the IIB group. What the ZK rule cannot explain, however, is the large number of stable compounds with codopants from groups IB and VIIIB. Moreover, compounds with Be, Li, and Mg (such as Sr8Be6Si40 and Ba8Be6Si40) are completely unexpected, as these atoms would give further electrons to the clathrate framework in the Zintl picture.

Figure 5. (a) Experimental XRD pattern of Ba8Be3.7Si42.3 (symbols) at room temperature. The red solid line is the Rietveld fitting using a structural model in which Be and Si atoms share the 6c sites and considering the presence of 9% in mass of orthorhombic BaSi2 and 3% of Si. The lower solid blue line is the difference (observed minus calculated). (b) Temperature dependence of the zero-field cooled dc magnetic susceptibility measured at 50 Oe in a pellet of Ba8Be3.7Si42.3.

software) composition is Ba8Be3.7Si42.3 with a unit cell parameter of 10.216 Å, which is considerably lower than the value for the parent material, recently measured in a single crystal of Ba8Si46 and found to be a = 10.328 Å.18 The reduced cell parameter is perfectly in agreement with our simulation that predicts a value of a = 10.297 Å for the high-symmetry configuration Ba8Be6Si40 instead of 10.392 Å for Ba8Si46. The Rietveld analysis confirms the Ba8BexSi46−x phase with the Be atoms located in the 6c sites and not in the Ba sites. This is at variance with the usual behavior of alkali and alkali earth metals that are found inside the cages and not in the host framework. A comparative analysis of the partial densities of states of Ba8Al6Si40, Ba8Zn6Si40, and Ba8Be6Si40 is shown in Figure 6, and Bader charges are reported in Table 1. All three materials turn out to be remarkably similar, which is compatible with the interpretation that Be, Al, and Zn play the same role by compensating for the charge of the endohedral atom. Note that the Fermi energy of the Al clathrate is further displaced into the valence band due to the extra valence electron of Al with respect to Be and Zn. Striking similarities are also found in the Bader charges. These results prove that Be assumes in this specific compound the acceptor role that the noble metal or semimetal has according to the ZK rule. The effect of Be doping on the superconducting properties of Ba8Si46 was then studied in the annealed Ba8Be3.7Si42.3 clathrate by measurements of the zero-field-cooled magnetic susceptibility in a SQUID (QD MPMS 5XL). The pellet was first cooled at 2 K without a magnetic field (using the magnet reset option). A magnetic field of 50 Oe was applied, and we recorded the diamagnetic signal by increasing the temperature in increments of 0.1 K. Despite a long annealing of the raw material, we did not observe bulk superconductivity. We measured the onset of the superconducting transition at a temperature of 4 K (see the right panel of Figure 5), which is however lower than the transition temperature of the undoped material (Tc ∼ 8 K for Ba8Si46). It is interesting to compare the

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SYNTHESIS AND EXPERIMENTAL CHARACTERIZATION In view of the approximations involved in our model of doping, to assess the quality of our predictions, we decided to attempt the synthesis of the new clathrate in the Ba−Be−Si ternary system, as this is the most surprising stable composition stemming from our search. The immediate success of this attempt gives us confidence in the reliability of our predictions. Because of the high toxicity of the Be oxide, we restricted our investigation of Ba8BexSi46−x to a set of three compositions x = 4, 9, and 12. We did not try to optimize the phase purity, our goal being to confirm only the Be doping predicted by the simulation. The synthesis process was performed entirely in a glovebox. Pellets that were 6 mm in diameter were first made by pressing at 700 MPa a stoichiometric mixture of a high-purity powder of Si (Aldrich, 99.999%), high-purity cut pieces of Ba (STREM, 99.7%), and Be (Alfa Aesar, 99.5%). The pellets were then arc melted, loaded, and sealed in Ar-filled quartz tubes. The sealed tubes were taken out from the glovebox and placed in a quartz tube for annealing under Ar at 500 °C for 1 week. The samples were then quenched at room temperature. The structural characterization of the annealed samples was performed by Xray diffraction (XRD) θ−2θ measurements taken on a Bruker D8 Advance powder diffractometer (Kα1,2 Cu wavelengths). All the peaks in the diffraction pattern were indexed with three phases (clathrate, BaSi2, and Si). The best purity obtained in Ba8Be3.7Si42.3 is 88%. In this sample, the proportions of D


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Figure 6. Density of states in states per electronvolt of Ba8Al6Si40, Ba8Zn6Si40, and Ba8Be6Si40 separated by atomic species (top row), separated by angular momentum channel (middle row), and total (bottom row). The Fermi energy is at zero.

Table 1. Bader Charges in Units of |e| for Ba8Al6Si40, Ba8Zn6Si40, and Ba8Be6Si40 Ba (2a) Ba (6d) X (6c) Si (16i) Si (16i) Si (24k) Si (24k)

Al

Zn

Be

1.216 1.263 1.545 −0.167 −0.229 −0.610 −0.733

1.190 1.326 0.019 −0.171 −0.227 −0.240 −0.365

1.199 1.304 1.256 −0.134 −0.193 −0.689 −0.573

convex hull to be lower than 30 meV per atom, 20 new phases in the clathrate of type I could likely be produced experimentally: Na8X6cSi40 (X = Ga or Pt), K8X6cSi40 (X = Al, Zn, In, Pt, or Au), Rb8X6cSi40 (X = Zn, In, or Au), Cs8X6cSi40 (X = Al, Ga, In, or Zn), and Sr8X6cSi40 (X = Pt, Au, Zn, Cu, or Pd). Moreover, all the phases with a distance to the convex hull ranging from 30 to 60 meV might be synthesized by means of a nonequilibrium synthesis process (high pressure, high temperature, and thin films). Our theoretical results therefore provide a starting point for further experimental studies, establishing a novel methodology of a theoretically assisted, accelerated materials discovery, as proven here in the case of the Ba−Be−Si clathrate. In conclusion, we used high-throughput computational techniques to investigate the stability of ternary clathrate phases based on a Si framework. Our results explain the vast majority of experimental results and predict the existence of a wealth of new clathrate phases. On the basis of this prediction, we succeeded in experimentally synthesizing the clathrate Ba8Be3.7Si42.3, which cannot be expected on the basis of the simple Zintl−Klemm rule but comes out naturally from our calculations. This shows the efficiency of our approach and indicates that experiment coupled to high-throughput computational approaches is the most cost-effective approach at our disposal for accelerated material discovery.

superconducting properties of the Be-doped sample with those of Ag-, Au-, Cu-, and Al-doped Ba−Si clathrates. Herrmann et al.65 measured a superconducting transition at approximately 5−6 K for the replacement of three or four Si atoms with Au, Ag, or Cu. They also found a reduced superconducting fraction in their sample, which is similar to what we observe here for Be doping. Al doping was studied by Li et al.66 and Liu et al.,67 who found Tc values similar to those for Be doping.

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CONCLUSION Going back to the other green cases of the periodic tables in Figures 3 and 4 that have not been reported experimentally, our results indicate that there are a large number of Si clathrate phases still to be synthesized. If one limits the distance to the E


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(13) Connétable, D.; Timoshevskii, V.; Masenelli, B.; Beille, J.; Marcus, J.; Barbara, B.; Saitta, A. M.; Rignanese, G.-M.; Mélinon, P.; Yamanaka, S.; Blase, X. Superconductivity in Doped sp3 Semiconductors: The Case of the Clathrates. Phys. Rev. Lett. 2003, 91, 247001. (14) Toulemonde, P.; Adessi, C.; Blase, X.; San Miguel, A.; Tholence, J. L. Superconductivity in the (Ba1−xSrx)8Si46 clathrates (x⩽0.75): Experimental and ab initio investigation. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 094504. (15) Toulemonde, P.; Miguel, A. S.; Merlen, A.; Viennois, R.; Floch, S. L.; Adessi, C.; Blase, X.; Tholence, J. High pressure synthesis and properties of intercalated silicon clathrates. J. Phys. Chem. Solids 2006, 67, 1117−1121. Proceedings of the 13th International Symposium on Intercalation Compounds, Clermont-Frerrand, France, June 6−9, 2005. (16) Yamanaka, S. Silicon clathrates and carbon analogs: high pressure synthesis, structure, and superconductivity. Dalton Trans. 2010, 39, 1901−1915. (17) Shi, X.; Yang, J.; Bai, S.; Yang, J.; Wang, H.; Chi, M.; Salvador, J. R.; Zhang, W.; Chen, L.; Wong-Ng, W. On the design of highefficiency thermoelectric clathrates through a systematic crosssubstitution of framework elements. Adv. Funct. Mater. 2010, 20, 755−763. (18) Pailhès, S.; Euchner, H.; Giordano, V. M.; Debord, R.; Assy, A.; Gomès, S.; Bosak, A.; Machon, D.; Paschen, S.; de Boissieu, M. Localization of propagative phonons in a perfectly crystalline solid. Phys. Rev. Lett. 2014, 113, 025506. (19) Euchner, H.; Pailhès, S.; Nguyen, L. T. K.; Assmus, W.; Ritter, F.; Haghighirad, A.; Grin, Y.; Paschen, S.; de Boissieu, M. Phononic filter effect of rattling phonons in the thermoelectric clathrate Ba8Ge40+xNi6−x. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 224303. (20) Tadano, T.; Gohda, Y.; Tsuneyuki, S. Impact of rattlers on thermal conductivity of a thermoelectric clathrate: A first-principles study. Phys. Rev. Lett. 2015, 114, 95501. (21) Takabatake, T.; Suekuni, K.; Nakayama, T.; Kaneshita, E. Phonon-glass electron-crystal thermoelectric clathrates: Experiments and theory. Rev. Mod. Phys. 2014, 86, 669−716. (22) Christensen, M.; Johnsen, S.; Iversen, B. B. Thermoelectric clathrates of type I. Dalton Trans. 2010, 39, 978−992. (23) Slack, G. CRC handbook of thermoelectrics; CRC Press: Boca Raton, FL, 1995; Vol. 407. (24) Kovnir, K. A.; Shevelkov, A. V. Semiconducting clathrates: synthesis, structure and properties. Russ. Chem. Rev. 2004, 73, 923− 938. (25) Curtarolo, S.; Hart, G. L. W.; Nardelli, M. B.; Mingo, N.; Sanvito, S.; Levy, O. The high-throughput highway to computational materials design. Nat. Mater. 2013, 12, 191−201. (26) Kirsanova, M. A.; Shevelkov, A. V. Clathrates and semiclathrates of Type-I: crystal structure and superstructures. Z. Kristallogr. - Cryst. Mater. 2013, 228, 215−227. (27) Reny, E.; Gravereau, P.; Cros, C.; Pouchard, M. Structural characterisations of the NaSi136 and Na8Si46 silicon clathrates using the Rietveld method. J. Mater. Chem. 1998, 8, 2839−2844. (28) Ramachandran, G. K.; McMillan, P. F.; Dong, J.; Sankey, O. F. K7.62(1)Si46 and Rb6.15(2)Si46: Two structure I clathrates with fully occupied framework sites. J. Solid State Chem. 2000, 154, 626−634. (29) Wosylus, A.; Veremchuk, I.; Schnelle, W.; Baitinger, M.; Schwarz, U.; Grin, Y. Cs8−xSi46: A type-I clathrate with expanded silicon framework. Chem. - Eur. J. 2009, 15, 5901−5903. (30) Yamanaka, S.; Enishi, E.; Fukuoka, H.; Yasukawa, M. HighPressure Synthesis of a New Silicon Clathrate Superconductor Ba8Si46. Inorg. Chem. 2000, 39, 56−58. (31) Dong, Y.; Chai, P.; Beekman, M.; Zeng, X.; Tritt, T. M.; Nolas, G. S. Precursor routes to complex ternary intermetallics: Single-crystal and microcrystalline preparation of clathrate-I Na8Al8Si38 from NaSi + NaAlSi. Inorg. Chem. 2015, 54, 5316−5321.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b00392. Tables of formation energies, distances to the convex hull, and decomposition channels for all considered clathrates and details about the Rietveld refinements of X-ray data (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.A.L.M., S.B., and S.P. acknowledge financial support from French ANR Projects ANR-12-BS04-0001-02 and ANR-13PRGE-0004. Computational resources were provided by GENCI (Project x2014096017).

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REFERENCES

(1) O’Keeffe, M.; Adams, G. B.; Sankey, O. F. Duals of Frank-Kasper structures as C, Si and Ge clathrates: Energetics and structure. Philos. Mag. Lett. 1998, 78, 21−28. (2) Kuo, K. H. From Frank-Kasper phases to the icosahedral quasicrystal. J. Phys. Colloques 1986, 47, 425−436. (3) Cros, C.; Pouchard, M.; Hagenmuller, P. Sur deux nouvelles phases du système silicium sodium. C. R. Acad. Sci. Paris 1965, 260, 4764−4767. (4) Kasper, J. S.; Hagenmuller, P.; Pouchard, M.; Cros, C. Clathrate structure of silicon Na8Si46 and NaxSi136 (x < 11). Science 1965, 150, 1713−1714. (5) San-Miguel, A.; Kéghélian, P.; Blase, X.; Mélinon, P.; Perez, A.; Itié, J. P.; Polian, A.; Reny, E.; Cros, C.; Pouchard, M. High Pressure Behavior of Silicon Clathrates: A New Class of Low Compressibility Materials. Phys. Rev. Lett. 1999, 83, 5290−5293. (6) San-Miguel, A.; Mélinon, P.; Connétable, D.; Blase, X.; Tournus, F.; Reny, E.; Yamanaka, S.; Itié, J. P. Pressure stability and low compressibility of intercalated cagelike materials: The case of silicon clathrates. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 054109. (7) Fässler, T. F., Ed. Quantitative advances in the Zintl-Klemm formalism. In Zintl phases; Structure and bonding; Springer: Berlin, 2011; Vol. 139, pp 1−55. (8) Schafer, H. On the problem of polar intermetallic compounds: The stimulation of E. Zintl’s work for the modern chemistry of intermetallics. Annu. Rev. Mater. Sci. 1985, 15, 1−41. (9) Shevelkov, A. V.; Kovnir, K. Zintl clathrates. In Zintl Phases; Fässler, T. F., Ed.; Structure and bonding; Springer: Berlin, 2011; Vol. 139, pp 97−142. (10) Karttunen, A. J.; Fässler, T. F.; Linnolahti, M.; Pakkanen, T. A. Structural principles of semiconducting group 14 clathrate frameworks. Inorg. Chem. 2011, 50, 1733−1742. (11) Toberer, E. S.; May, A. F.; Snyder, G. J. Zintl chemistry for designing high efficiency thermoelectric materials. Chem. Mater. 2010, 22, 624−634. (12) As an example, in Na8Al6Si40 Na donates 8 valence electrons to the cage. Adding these 8 electrons to the 160 valence electrons or 40 Si atoms and 18 valence electrons of 6 Al atoms, we obtain 186 electrons, i.e., 2 electrons more than the number that gives compete electron octets (184). Note that a cage with 46 atoms of Si has 192 electrons. F


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Chemistry of Materials (32) Kraner, R.; Peters, K.; Von Schnering, H. G.; Nesper, R. Crystal structure of the clathrates K8Ga8Si38 and K8Ga8Sn38. Z. Kristallogr.-New Cryst. Struct. 1998, 213, 667. (33) Jung, W.; Lörincz, J.; Ramlau, R.; Borrmann, H.; Prots, Y.; Haarmann, F.; Schnelle, W.; Burkhardt, U.; Baitinger, M.; Grin, Y. K7B7Si39 a borosilicide with the clathrate I structure. Angew. Chem., Int. Ed. 2007, 46, 6725−6728. (34) von Schnering, H. G.; Kröner, R.; Menke, H.; Peters, K.; Nesper, R. Crystal structure of the clathrates Rb8Ga8Sn38, Rb8Ga8Ge38 and Rb8Ga8Si38. Z. Kristallogr.-New Cryst. Struct. 1998, 213, 677. (35) Baran, V.; Senyshyn, A.; Karttunen, A.; Fischer, A.; Scherer, W.; Raudaschl-Sieber, G.; Fässler, T. F. Raudaschl-Sieber, G.; Fässler, T. A combined metal-halide/metal flux synthetic route towards type-I clathrates: Crystal structures and thermoelectric properties of A8Al8Si38 (A = K, Rb, and Cs). Chem. - Eur. J. 2014, 20, 15077−15088. (36) Sui, F.; He, H.; Bobev, S.; Zhao, J.; Osterloh, F.; Kauzlarich, S. Synthesis, structure, thermoelectric properties, and band gaps of alkali metal containing type I clathrates: A8Ga8Si38 (A = K, Rb, Cs) and K8Al8Si38. Chem. Mater. 2015, 27, 2812−2820. (37) Roudebush, J. H.; Tsujii, N.; Hurtando, A.; Hope, H.; Grin, Y.; Kauzlarich, S. M. Phase range of the type-I clathrate Sr8AlxSi46−x and crystal structure of Sr8Al10Si36. Inorg. Chem. 2012, 51, 4161−4169. (38) Carrillo-Cabrera, W.; Cardoso Gil, R.; Grin, Y. Crystal structure of the clathrate Sr8Ga16−xSi30+x, x = 2.18, 4.05. Z. Kristallogr. - New Cryst. Struct. 2002, 217, 179−180. (39) Cordier, G.; Woll, P. Neue ternär e intermetallische Verbindungen mit Clathratstruktur: Ba 8 (T,Si) 6 Si 4 0 und Ba6(T,Ge)6Ge40 mit T = Ni, Pd, Pt, Cu, Ag, Au. J. Less-Common Met. 1991, 169, 291−302. (40) Aydemir, U.; Candolfi, C.; Ormeci, A.; Borrmann, H.; Burkhardt, U.; Oztan, Y.; Oeschler, N.; Baitinger, M.; Steglich, F.; Grin, Y. Synthesis, crystal structure, and physical properties of the type-I clathrate Ba8−δNix□ySi46−x−y. Inorg. Chem. 2012, 51, 4730− 4741. (41) Anno, H.; Yamada, H.; Nakabayashi, T.; Hokazono, M.; Shirataki, R. Influence of preparation conditions on thermoelectric properties of Ba8Ga16Si30 clathrate by combining arc melting and spark plasma sintering methods. J. Phys.: Conf. Ser. 2012, 379, 012007. (42) Yan, X.; Chen, M. X.; Laumann, S.; Bauer, E.; Rogl, P.; Podloucky, R.; Paschen, S. Thermoelectric properties of Ba-Cu-Si clathrates. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 165127. (43) Zeiringer, I.; Bauer, E.; Grytsiv, A.; Rogl, P.; Effenberger, H. Phase equilibria, crystal chemistry, and physical properties of Ag-Ba-Si clathrates. Jpn. J. Appl. Phys. 2011, 50, 05FA01. (44) Anno, H.; Hokazono, M.; Shirataki, R.; Nagami, Y. Crystallographic, thermoelectric, and mechanical properties of polycrystalline type-I Ba8Al16Si30-based clathrates. J. Mater. Sci. 2013, 48, 2846−2854. (45) Nasir, N.; Grytsiv, A.; Melnychenko-Koblyuk, N.; Rogl, P.; Bauer, E.; Lackner, R.; Royanian, E.; Giester, G.; Saccone, A. Clathrates Ba8Zn, CdxSi46−x, x ∼ 7: synthesis, crystal structure and thermoelectric properties. J. Phys.: Condens. Matter 2009, 21, 385404. (46) Melnychenko-Koblyuk, N.; Grytsiv, A.; Rogl, P.; Bauer, E.; Lackner, R.; Royanian, E.; Rotter, M.; Giester, G. Structure and physical properties of clathrate I systems Ba 8 Pd x Si46−x and Ba8PtxSi46−x. J. Phys. Soc. Jpn. 2008, 77, 54−60. (47) Candolfi, C.; Aydemir, U.; Baitinger, M.; Oeschler, N.; Steglich, F.; Grin, Y. High temperature thermoelectric properties of the type-I clathrate Ba8AuxSi46−x. J. Appl. Phys. 2012, 111, 043706. (48) Jung, W.; Kessens, H.; Ormeci, A.; Schnelle, W.; Burkhardt, U.; Borrmann, H.; Nguyen, H.; Baitinger, M.; Grin, Y. Synthesis, crystal structure and physical properties of the clathrate-I phase Ba8RhxSi46−x−y. Dalton Trans. 2012, 41, 13960. (49) Falmbigl, M.; Grytsiv, A.; Rogl, P.; Giester, G. Clathrate formation in the systems Ba-Ir-Ge and Ba-Rh, Ir-Si: Crystal chemistry and phase relations. Intermetallics 2013, 36, 61−72. (50) Curtarolo, S.; Morgan, D.; Persson, K.; Rodgers, J.; Ceder, G. Predicting crystal structures with data mining of quantum calculations. Phys. Rev. Lett. 2003, 91, 135503.

(51) Ravi, C.; Wolverton, C. First-principles study of crystal structure and stability of Al-Mg-Si-(Cu) precipitates. Acta Mater. 2004, 52, 4213−4227. (52) Curtarolo, S.; Morgan, D.; Ceder, G. Accuracy of ab initio methods in predicting the crystal structures of metals: A review of 80 binary alloys. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2005, 29, 163−211. (53) Blake, N. P.; Bryan, D.; Latturner, S.; Møllnitz, L.; Stucky, G. D.; Metiu, H. Structure and stability of the clathrates Ba8Ga16Ge30, Sr8Ga16Ge30, Ba8Ga16Si30, and Ba8In16Sn30. J. Chem. Phys. 2001, 114, 10063−10074. (54) Chan, K. S.; Miller, M. A.; Liang, W.; Ellis-Terrell, C. Computational design and synthesis of nitrogen-substituted carbon and silicon clathrates. Mater. Res. Lett. 2014, 2, 70−75. (55) Chan, K. S.; Miller, M. A.; Liang, W.; Ellis-Terrell, C.; Peng, X. First-principles computational design and synthesis of hybrid carbonsilicon clathrates. J. Mater. Sci. 2014, 49, 2723−2733. (56) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15−50. (57) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (58) Jain, A.; Ong, S. P.; Hautier, G.; Chen, W.; Richards, W. D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; Persson, K. A. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Mater. 2013, 1, 011002. (59) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (60) Reny, E.; Yamanaka, S.; Cros, C.; Pouchard, M. High pressure synthesis of an iodine doped silicon clathrate compound. Chem. Commun. 2000, 24, 2505−2506. (61) Stevanović, V.; Lany, S.; Zhang, X.; Zunger, A. Correcting density functional theory for accurate predictions of compound enthalpies of formation: Fitted elemental-phase reference energies. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 115104. (62) Sarmiento-Pérez, R.; Botti, S.; Marques, M. A. L. Optimized exchange and correlation semilocal functional for the calculation of energies of formation. J. Chem. Theory Comput. 2015, 11, 3844−3850. (63) Amsler, M.; Flores-Livas, J. A.; Huan, T. D.; Botti, S.; Marques, M. A. L.; Goedecker, S. Novel Structural Motifs in Low Energy Phases of LiAlH4. Phys. Rev. Lett. 2012, 108, 205505. (64) Huan, T. D.; Amsler, M.; Marques, M. A. L.; Botti, S.; Willand, A.; Goedecker, S. Low-Energy Polymeric Phases of Alanates. Phys. Rev. Lett. 2013, 110, 135502. (65) Herrmann, R. F.; Tanigaki, K.; Kuroshima, S.; Suematsu, H. Superconductivity in silicon based barium-inclusion clathrates. Chem. Phys. Lett. 1998, 283, 29−32. (66) Li, Y.; Garcia, J.; Chen, N.; Liu, L.; Li, F.; Wei, Y.; Bi, S.; Cao, G.; Feng, Z. S. Superconductivity in Al-substituted Ba8Si46 clathrates. J. Appl. Phys. 2013, 113, 203908. (67) Liu, L.; Bi, S.; Peng, B.; Li, Y. Effect of Eu substitution on superconductivity in Ba8−xEuxAl6Si40 clathrates. J. Appl. Phys. 2015, 117, 17E117.

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