Probing the mechanism of guest-framework bonding interactions through a first-principles study on the structural and electronic properties of type-II clathrate A x Si136 (A = Na, K, Rb; 0 ≤ x ≤ 24) under pressure.

The role of noncovalent bonding, including multiatomic interactions (van der Waals-like forces) and ionic characteristics, in the intermetallic clathrate A x Si136 (A = Na, K, Rb; 0 < x ≤ 24) is qualitatively discussed. Using the local density approximation (LDA) to density functional theory (DFT), we investigated the effect of different guest filling and pressure parameters on the structural and electronic properties of these materials. In the context of the rigid-band model, we first noted that the competition between van der Waals-like multiatomic interactions and ionicity due to the extent of charge transfer responsible for guest-framework complexes accounts for the nonmonotonic structural response upon guest filling in A x Si136 (0 ≤ x ≤ 8), which is in good agreement with previous experimental findings as well as theoretical predictions. In comparison with computational work initiated under zero temperature and pressure conditions, the DFT calculations at high pressure (P = 3 GPa) show no apparent variation with respect to the electronic structure. Regarding the A16Si136 compound, the encapsulated sodium atoms residing in the 20-atom cage cavity act as centers of somewhat localized electrons compared with the alkaline metal sites inside Si28 cage voids. Moreover, the substitution of heavier guest atoms (e.g., Rb) for all the Na atoms in Na8Si136 yields less significant charge transfer between the guest and framework constituents. The net effect of quickly increasing multiatomic interactions and slowly decreasing ionic bonding between the encapsulated atom and Si28 cage may prevent the entire lattice configuration from contracting in a more rapid way when guest species are tuned from Na to Rb in A x Si136 (A = Na, Rb; 0 < x ≤ 8) with increased composition x. In other words, the coulombic attraction due to ionic bonding slightly outweighs the repulsive interaction between the Rb atom and Si28 cage. In addition, the determined formation energy per conventional unit cell in K8Si136, Rb8Si136 and Na12Si136 attains a minimum value, demonstrating the stabilizing effect of guests incorporated into "oversized" cage cavities.

Electronic Property and Negative Thermal Expansion Behavior of Si136-xGex (x = 8, 32, 40, 104) Clathrate Solid Solution from First Principles.

We present the electronic and vibrational studies on Si136-xGex (x = 8, 32, 40, 104) alloys, using the local density approximation (LDA) scheme. We find that a "nearly-direct" band gap exists in the band structure of Si104Ge32 and Si96Ge40, when compared with the similarly reported results obtained using a different computational code. The calculated electronic density of state (EDOS) profiles for the valence band remain nearly identical and independent of the Ge concentration (x = 32, 40, 104) even though some variation is found in the lower conduction band (tail part) as composition x is tuned from 8 (or 40) to 104. The negative thermal expansion (NTE) phenomenon is explored using quasi-harmonic approximation (QHA), which takes the volume dependence of the vibrational mode frequencies into consideration, while neglecting the temperature effect on phonon anharmonicity. Determined macroscopic Grüneisen parameter trends show negative values in the low temperature regime (1 K < T < 115 K), indicating the NTE behavior found in Si128Ge8 is analogous to the experimental result for Si136. Meanwhile, calculations for the ratio of the vibrational entropy change to the volume change at several characteristic temperatures reconfirm the existence of NTE in Si128Ge8 and Si104Ge32.

First-Principles Analysis of Vibrational Properties of Type II SiGe Alloy Clathrates.

We have mostly performed vibrational studies of Type-II silicon-germanium clathrate alloys, namely, Si136-xGex (0 < x ≤ 128), using periodic density functional theory (DFT). Our computed lattice constant for various stoichiometric amount, namely, x, of Ge agrees to some extent with the observed X-ray diffraction (XRD) data, along with monotonically increasing dependence on x. According to our bandgap energy calculation via Vienna ab initio simulation package (VASP), Si128Ge8 has a "nearly-direct" bandgap of approximately 1.27 eV, which agrees well with the previously calculated result (~1.23 eV), which was obtained using the Cambridge sequential simulation total energy package (CASTEP). Most of our first-principles calculations focus on exploring the low-energy transverse acoustic (TA) phonons that contribute dominantly to the induction of negative thermal expansion (NTE) behavior. Moreover, our work has predicted that the Si104Ge32 framework exhibits NTE in the temperature range of 3-80 K, compared to the temperature regime (10-140 K) of NTE observed in such pure Si136. It is posited that the increased number of Ge-Ge bonds may weaken the NTE effect substantially, as the composition, which is denoted as x, in Si136-xGex is elevated from 32 (or 40) to 96 (or 104).

Effect of Guest Atom Composition on the Structural and Vibrational Properties of the Type II Clathrate-Based Materials AxSi136, AxGe136 and AxSn136 (A = Na, K, Rb, Cs; 0 ≤ x ≤ 24).

Type II clathrates are interesting due to their potential thermoelectric applications. Powdered X-ray diffraction (XRD) data and density functional calculations for NaxSi136 found a lattice contraction as x increases for 0 < x < 8 and an expansion as x increases for x > 8. This is explained by XRD data that shows that as x increases, the Si28 cages are filled first for x < 8 and the Si20 cages are then filled for x > 8. Motivated by this work, here we report the results of first-principles calculations of the structural and vibrational properties of the Type II clathrate compounds AxSi136, AxGe136, and AxSn136. We present results for the variation of the lattice constants, bulk moduli, and other structural parameters with x. These are contrasted for the Si, Ge, and Sn compounds and for guests A = Na, K, Rb, and Cs. We also present calculated results of phonon dispersion relations for Na4Si136, Na4Ge136, and Na4Sn136 and we compare these for the three materials. Finally, we present calculated results for the elastic constants in NaxSi136, NaxGe136, and NaxSn136 for x = 4 and 8. These are compared for the three hosts, as well as for the two compositions.

Type VIII Si based clathrates: prospects for a giant thermoelectric power factor.

Although clathrate materials are known for their small thermal conductivity, they have not shown a large thermoelectric power factor so far. We present the band structures of type VIII Si, Ge, and Sn clathrates as well as the alkali and alkaline-earth intercalated type VIII Si clathrates. Our calculations revealed that this group of materials has potentially large power factors due to the existence of a large number of carrier pockets near their band edges. In particular, we calculated the charge carrier transport properties of Si46-VIII both for n-type and p-type materials. The exceptionally high multi-valley band structure of Si46-VIII near the Fermi energy due to the high crystallographic symmetry resulted in a giant power factor in this material. It was shown that the intercalation of Si46-VIII with alkali and alkaline-earth guest atoms shifts the Fermi energy close to the conduction band edge and, except for Be8Si46 and Mg8Si46, they weakly influence the band structure of Si46. Among these clathrate systems, Ca8Si46, Sr8Si46, and Ba8Si46 showed negative formation energy, which should facilitate their synthesis. Our results imply that the intercalation affects the conduction band of Si46-VIII more than its valence band. Also, interestingly, the type VIII clathrates of Si46 and its derivatives (except Be8Si46 and Mg8Si46), Sn46, and Ge46 all have 26 carrier pockets near their valence band edge. Among the different derivatives of Si46-VIII, Rb8Si46 and Ba8Si46 have the highest number of electron pockets near their band edges. The thermoelectric power factor was predicted using a multiband Boltzmann transport equation linked with parameters extracted from density functional calculations. It was shown that both the increment of charge mobility and the existence of multiple band extrema contribute to the enhancement of the thermoelectric power factor considerably. Such a large power factor along with their inherently low thermal conductivity can make this group of clathrates promising thermoelectric materials.

Prediction of giant thermoelectric power factor in type-VIII clathrate Si46.

Clathrate materials have been the subject of intense interest and research for thermoelectric application. Nevertheless, from the very large number of conceivable clathrate structures, only a small fraction of them have been examined. Since the thermal conductivity of clathrates is inherently small due to their large unit cell size and open-framework structure, the current research on clathrates is focused on finding the ones with large thermoelectric power factor. Here we predict an extraordinarily large power factor for type-VIII clathrate Si(46). We show the existence of a large density of closely packed elongated ellipsoidal carrier pockets near the band edges of this so far hypothetical material structure, which is higher than that of the best thermoelectric materials known today. The high crystallographic symmetry near the energy band edges for Si(46)-VIII clathrates is responsible for the formation of such a large number of carrier pockets.

Prediction of a large number of electron pockets near the band edges in type-VIII clathrate Si46 and its physical properties from first principles.

The material design of type-VIII clathrate Si46 is presented based on first principles. The structural, electronic, elastic, vibrational, and thermodynamic properties of this hypothetical material are presented. Our results predict that type-VIII clathrate Si46 is an indirect semiconductor with a bandgap of 1.24 eV. The band structure revealed an interestingly large number of electron pockets near both conduction and valance band edges. Such a large density of states near the band edges, which is higher than that of the best thermoelectric materials discovered so far, can result in a large thermoelectric power factor (>0.004 W m(-1) K(-2)) making it a promising candidate for thermoelectric applications. The elastic properties as well as the vibrational modes and the phonon state densities of this material were also calculated. Our calculations predict that the heat capacity at constant volume (isochoric) of this clathrate increases smoothly with temperature and approaches the Dulong-Petit value near room temperature. The electronic band structure shows a large number of valleys closely packed around the valance band edge, which is rare among the known semiconducting materials. These valleys can contribute to transport at high temperature resulting in a possibly high performance (ZT > 1.5) p-type thermoelectric material.

Framework contraction in Na-stuffed Si(cF136).

Systematic crystal structure refinements from powder X-ray diffraction data as well as density functional theory calculations demonstrate that the silicon clathrate II Si(cF136) exhibits a lattice contraction as Na is introduced solely into the Si(28) cages. When the Si(20) cages, in addition, begin to be filled with Na, a contrasting lattice expansion results. The nonmonotonic structural response to filling is an indication of markedly dissimilar guest-framework interactions for Na@Si(20) and Na@Si(28).