type-I Clathrate Research Articles

A DFT Computational Study of Type-I Clathrates A8Sn46-x (A = Cs or NH4, x = 0 or 2).

Semiconducting clathrates have attracted considerable interest in the field of thermoelectric materials. We report here a computational study on the crystal structure, the enthalpy of formation, and the physical properties of the following type-I clathrates: (a) experimentally studied Cs8Sn44 and hypothetical Cs8Sn46 and (b) hypothetical (NH4)8Sn46-x (x = 0 or 2). The ab initio VASP calculations for the nominal stoichiometries include the geometry optimization of the initial structural models, enthalpies of formation, and the electronic and phonon density of states. Comparison of the chemical bonding of the structural models is performed via the electron localization function. The results show that the presence and distribution of defects in the Sn framework for both Cs8Sn46-x and (NH4)8Sn46-x systems significantly alters the formation energy and its electrical properties, ranging from metallic to semiconducting behavior. In particular, one defect per six-membered Sn ring in a 3D spiro-network is the thermodynamically preferred configuration that results in the Cs8Sn44 and (NH4)8Sn44 stoichiometries with narrow-band gap semiconducting behavior. Moreover, the rotation of the ammonium cation in the polyhedral cavities is an interesting feature that may promote the use of ammonium or other small molecular cations as guests in clathrates for thermoelectric applications; this is due to the decrease in the lattice thermal conductivity.

Type-I clathrate calcium hydride and its hydrogen-vacancy structures at high pressure

Type-I clathrate calcium hydride and its hydrogen-vacancy structures at high pressure

Deformation and Failure Mechanisms of Element-Substituted Thermoelectric Type-I and Type-VIII Clathrates.

Clathrates are potential "phonon-glass, electron-crystal" thermoelectric semiconductors, whose structure of polyhedron stacks is very attractive. However, their mechanical properties have not yet met the requirements of industrial applications. Here, we report the ideal strength of element-substituted type-I and type-VIII clathrates and the shear deformation mechanism by using density functional theory. The results show that the framework element is the determinant of the intrinsic mechanical properties of the clathrates and is affected by sequential weakening of Si-Ge-Sn. The highest ideal shear strength is 8.71 GPa for I-Ba8Au6Si40 along the (110)/[001] slip system, which is attributed to the formation of higher-energy Si-Si covalent bonds. Meanwhile, the ideal shear strength of Ba-filled I/VIII clathrates (4.51/2.65 GPa) is higher than that of Sr-filled clathrates (3.64 GPa/1.91 GPa). In addition, the strength and ultimate strain of VIII-Ba8Ga16Sn30 can be significantly increased by the structural coordination accommodating with the stiffness of the Ga-Ge bond to achieve simultaneous bond breaking. Our findings demonstrate that the element substitution strategy is an effective approach for designing highly robust clathrates.

High-temperature superconductivity in La4H23 below 100 GPa

High-temperature superconductivity has been observed in binary hydrides such as LaH10 at pressures close to 180GPa, whereby hydrogen cagelike structures have been identified as a common motif beneficial for high critical temperatures Tc. Efforts are now focused on finding hydride high-temperature superconductors at lower pressures. We present evidence for high-temperature superconductivity in binary La4H23 at a pressure of P=95GPa, with A15-type arrangement of the lanthanum atoms in the type-I clathrate structure. We synthesize La4H23 from a lanthanum film capped with a palladium catalyst promoting the dissociation of hydrogen. In resistance measurements, we observe superconductivity with a transition temperature Tc∼90K. The A15-type lanthanum sublattice is identified in x-ray diffraction on the same sample, in agreement with previous x-ray diffraction and structure prediction studies. Our study reinforces the favorability of cagelike networks of the hydrogen lattice for high-temperature superconductivity. Published by the American Physical Society 2024

Computational Screening and Stabilization of Boron-Substituted Type-I and Type-II Carbon Clathrates.

Boron substitution represents a promising approach to stabilize carbon clathrate structures, but no thermodynamically stable substitution schemes have been identified for frameworks other than the type-VII (sodalite) structure type. To investigate the possibility for additional tetrahedral carbon-based clathrate networks, more than 5000 unique boron decoration schemes were investigated computationally for type-I and type-II carbon clathrates with a range of guest elements including Li, Na, K, Rb, Cs, Mg, Ca, Sr, and Ba. Density functional theory calculations were performed at 10 and 50 GPa, and the stability and impact of boron substitution were evaluated. The results indicate that the boron-substituted carbon clathrates are stabilized under high-pressure conditions. Full cage occupancies of intermediate-sized guest atoms (e.g., Na, Ca, and Sr) are the most favorable energetically. Clathrate stability is maximized when the boron atoms are substituted within the hexagonal rings of the large [51262]/[51264] cages. Several structures with favorable formation enthalpies <-200 meV/atom were predicted, and type-I Ca8B16C30 is on the convex hull at 50 GPa. This structure represents the first thermodynamically stable type-I clathrate identified and suggests that boron-substituted carbon clathrates may represent a large family of diamond-like framework materials with a range of structure types and guest/framework substitutions.

Effects of Si substitution on ferromagnetic order and off-center rattling of Eu ions in the type-I clathrate Eu8Ga16Ge30

In the ferromagnetic type-I clathrate Eu8Ga16Ge30, the divalent Eu ions are known to rattle among off-center positions in the tetrakaidecahedral cage. We have studied effects of Si substitution on the ferromagnetic state and the rattling motion of the Eu ions in Eu8Ga16Ge30 by measuring the magnetization M, electrical resistivity ρ, thermopower, specific heat C, and Eu partial phonon density of states (Eu pDOS) of Eu8Ga16−xGe30+x−y−zSiy□z (□ = vacancy, 0 ≤y≤ 7.3). Upon increasing y from 0 to 7.3, the lattice parameter decreases by 0.7%, which has no effect on the divalent state of Eu. The Curie temperature TC decreases from 36.2 K to 32.6 K, whereas the specific heat jump at TC, ΔC, increases twofold. For y= 0, both ρ (T) and dM(T)/dT exhibit anomalies below TC at T∗∼ 24 K, which are suppressed by applying magnetic field of 1 T. The anomalies at T∗ disappear by Si substitution at a low level, y = 3.7. The measured Eu pDOS indicates that the low-lying phonon energy of the Eu ions decreases with Si substitution. This softening means that the off-center rattling is changed to on-center one with large amplitude in an anharmonic potential. Based on these findings, we discuss relationship between the off-center Eu rattling and their collective magnetic behavior.

Magnetocaloric and hydrogen storage multi-functional properties of Eu4Ga8Ge16 compounds

We investigated the anisotropic magnetic, electrical transport, and heat capacity of Eu4Ga8Ge16 single crystals. Magnetization measurements with temperature and magnetic field revealed a complex behavior. Specifically, we observed anisotropic metamagnetic transitions at low magnetic field, and inverse hysteresis at high magnetic fields. These phenomena can be attributed to a Heisenberg ferromagnetic spin chain aligned along the a-axis. Additionally, this ferromagnetic behavior is interspersed with antiferromagnetic interactions between adjacent Heisenberg spin chains. We also noticed an anomalous increase in electrical resistivity at low temperature under magnetic fields, as well as different temperature-exponents of ρ(T) depending on crystal directions, which are attributed to the anisotropic scattering of carriers due to anisotropic magnetic interactions. We also evaluated the magnetocaloric effect and found a substantial magnetic entropy change than those of type-I Eu-based clathrates. The high entropy change (-ΔSM = 13.5 J kg−1 K−1) and adiabatic temperature difference (ΔTad = 7.8 K) near Néel temperature TN = 7.9 K reveal that the Heisenberg spin chain system might be advantageous for inducing a larger magnetic entropy change. Furthermore, we measured the hydrogen storage capacity of Eu4Ga8Ge16 as a multifunctional property because the zeolite-like cage structure can be a good candidate for hydrogen storage applications. Although the hydrogen storage capacity is considerably lower than that of the leading-edge materials, the hydrogen storage capacity can be improved further when we control the Eu-deficiency to place the hydrogen molecule at the cage site, because the hydrogen molecules reside at the (Ga,Ge) framework not in the cage site for fully occupied Eu atomic chain compounds. Hence, Eu4Ga8Ge16 emerges as a versatile substrate for engineering multifunctional energy materials, excelling in both low-temperature magnetocaloric effects and hydrogen storage potential.

Strong Scattering from Low-Frequency Rattling Modes Results in Low Thermal Conductivity in Antimonide Clathrate Compounds

Recent discoveries of materials with ultralow thermal conductivity open a pathway to significant developments in the field of thermoelectricity. Here, we conduct a comparative study of three chemically similar antimonides to establish the root causes of their extraordinarily low thermal conductivity (0.4–0.6 W m–1 K–1 at 525 K). The materials of interest are the unconventional type-XI clathrate K58Zn122Sb207, the tunnel compound K6.9Zn21Sb16, and the type-I clathrate K8Zn15.5Cu2.5Sb28 discovered herein. Calculations of the phonon dispersions show that the type-XI compound exhibits localized (i.e., rattling) phonon modes with unusually low frequencies that span the entire acoustic regime. In contrast, rattling in type I clathrate is observed only at higher frequencies, and no rattling modes are present in the tunnel structure. Modeling reveals that low-frequency rattling modes profoundly limit the acoustic scattering time; the scattering time of the type-XI clathrate is half that of the type-I clathrate and a quarter of that of the tunnel compound. For all three materials, the thermal conductivities are additionally suppressed by soft framework bonding that lowers the acoustic group velocities and structural complexity that leads to diffusonic character of the optical modes. Understanding the details of thermal transport in structurally complex materials will be crucial for developing the next generation of thermoelectrics.

Size Effect on the Thermal Conductivity of a Type-I Clathrate

Clathrates are a materials class with an extremely low phonon thermal conductivity, which is a key ingredient for a high thermoelectric conversion efficiency. Here, we present a study on the type-I clathrate La1.2Ba6.8Au5.8Si38.8□1.4 directed at lowering the phonon thermal conductivity even further by forming mesoscopic wires out of it. Our hypothesis is that the interaction of the low-energy rattling modes of the guest atoms (La and Ba) with the acoustic modes, which originate mainly from the type-I clathrate framework (formed by Au and Si atoms, with some vacancies □), cuts off their dispersion and thereby tilts the balance of phonons relevant for thermal transport to long-wavelength ones. Thus, size effects are expected to set in at relatively long length scales. The structuring was carried out using a top-down approach, where the wires, ranging from 1260 nm to 630 nm in diameter, were cut from a piece of single crystal using a focused ion beam technique. Measurements of the thermal conductivity were performed with a self-heating 3ω technique down to 80 K. Indeed, they reveal a reduction of the room-temperature phonon thermal conductivity by a sizable fraction of ∼40 % for our thinnest wire, thereby confirming our hypothesis.

New Trick for an Old Dog: From Prediction to Properties of “Hidden Clathrates” Ba2Zn5As6 and Ba2Zn5Sb6

The zinc-antimony phase space has been heavily investigated due to the structural complexity and abundance of high-performing thermoelectric materials. Consequentially, the desire to use zinc and antimony as framework elements to encage rattling cations and achieve phonon-glass-electron-crystal-type properties has remained an enticing goal with only two alkali metal clathrates to date, Cs8Zn18Sb28 and K58Zn122Sb207. Guided by Zintl electron-counting predictions, we explored the Ba-Zn-Pn (Pn = As, Sb) phase space proximal to the expected composition of the type-I clathrate. In situ powder X-ray diffraction studies revealed two "hidden" compounds which can only be synthesized in a narrow temperature range. The ex situ synthesis and crystal growth unveiled that instead of type-I clathrates, compositionally close but structurally different new clathrate-like compounds formed, Ba2Zn5As6 and Ba2Zn5Sb6. These materials crystallize in a unique structure, in the orthorhombic space group Pmna with the Wyckoff sequence i2h6gfe. Single-phase synthesis enabled the exploration of their transport properties. Rattling of the Ba cations in oversized cages manifested low thermal conductivity, which, coupled with the high Seebeck coefficients observed, are prerequisites for a promising thermoelectric material. Potential for further optimization of the thermoelectric performance by aliovalent doping was computationally analyzed.

Phonon dispersion curves in the type-I crystalline and molten clathrate compound Eu8Ga16Ge30

The dynamic structure factor , where Q and E are momentum and energy transfer, respectively, has been measured for liquid Eu8Ga16Ge30 (EGG), using inelastic x-ray scattering. The excitation energy of the longitudinal acoustic mode in the liquid was scaled to that in liquid Ba8Ga16Sn30 (BGS) with the effective mass. This result means that the local structure in both liquids are similar. The longitudinal acoustic excitation energy of type-I clathrate compound EGG disperses faster than that in the liquid, suggesting that the interatomic force is weakened on melting. The lower energy excitation was observed in both liquid EGG and liquid BGS. In comparison with the longitudinal phonon dispersion in crystalline clathrate compound EGG obtained by density functional theory-based calculations, the lower energy in the liquid was found to be near the optical mode energy. The result indicates that the lower energy mode arises from the relative motion between Eu and (Ga, Ge) atoms.

Lithium metal atoms fill vacancies in the germanium network of a type-I clathrate: synthesis and structural characterization of Ba8Li5Ge41.

Clathrate phases with crystal structures exhibiting complex disorder have been the subject of many prior studies. Here we report syntheses, crystal and electronic structure, and chemical bonding analysis of a Li-substituted Ge-based clathrate phase with the refined chemical formula Ba8Li5.0(1)Ge41.0, which is a rare example of ternary clathrate-I where alkali metal atoms substitute framework Ge atoms. Two different synthesis methods to grow single crystals of the new clathrate phase are presented, in addition to the classical approach towards polycrystalline materials by combining pure elements in desired stoichiometric ratios. Structure elucidations for samples from different batches were carried out by single-crystal and powder X-ray diffraction methods. The ternary Ba8Li5.0(1)Ge41.0 phase crystallizes in the cubic type-I clathrate structure (space group Pm3̄n no. 223, a ≈ 10.80 Å), with the unit cell being substantially larger compared to the binary phase Ba8Ge43 (Ba8□3Ge43, a ≈ 10.63 Å). The expansion of the unit cell is the result of the Li atoms filling vacancies and substituting atoms in the Ge framework, with Li and Ge co-occupying one crystallographic (6c) site. As such, the Li atoms are situated in four-fold coordination environment surrounded by equidistant Ge atoms. Analysis of chemical bonding applying the electron density/electron localizability approach reveals ionic interaction of barium with the Li-Ge framework, while the lithium-germanium bonds are strongly polar covalent.

Electrochemical Flux Synthesis of Type-I Na8Si46 Clathrates: Particle Size Control Using a Solid or Molten Na–Sn Mass Transport Mediator

Sodium-filled silicon clathrates have a host of interesting properties for thermoelectric, photovoltaic, and battery applications. However, the metastability of the clathrates has made it difficult to synthesize them with the desired morphology and crystallite size. Herein, we demonstrate an electrochemical method whereby Na4Si4 dissolved in a Sn-based flux is converted to the Na8Si46 type-I clathrate using galvanostatic (constant current) oxidation. The temperature has a large influence on the products, with the reactions at 485 °C resulting in clathrates with small particle sizes (1-2 μm), while larger single crystals are obtained at 538 °C. The difference in microstructure is attributed to the solid vs liquid state of the Na-Sn phase at the reaction temperature, which is supported by the observed voltage profiles. The demonstrated method is promising for the tunable growth of Si clathrates and could be applicable to a broad range of intermetallic compounds.

Anharmonic phonon renormalization and thermal transport in the type-I Ba8Ga16Sn30 clathrate from first principles

Effects of strong phonon anharmonicity of a type-I clathrate ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Sn}}_{30}$ induced by the quadruple-well potential of guest atoms were investigated. Phonon transport including a coherent interbranch component was analyzed using a first-principles-based self-consistent phonon (SCP) theory that gives temperature-dependent harmonic interatomic force constants and by solving off-diagonal components of group velocity operator. Experimentally observed thermal conductivities have been reasonably reproduced by considering both lattice and electron contributions. Through the analysis with the SCP theory, we found that hardening of guest modes leads to an increase in lattice thermal conductivity at frequencies below those of framework-dominant flat modes ($&lt;40\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$), which finally results in the slow decay of the total lattice thermal conductivity with increasing temperature. Detailed analyses revealed that the increase in lattice thermal conductivity at low frequency is attributed to (a) the increase in both group velocities and lifetimes of phonon modes located at frequencies below that of the flat guest modes and (b) abnormal increase in lifetimes of phonon modes located between frequencies of the flat guest and framework modes with increasing temperature.

Evolution of structure and transport properties of the Ba8Cu16P30 clathrate-I framework with the introduction of Ga

Two type-I clathrates were synthesized by introducing Ga into the framework of the Ba8Cu16P30 type-I clathrate. The introduction of minute amounts of Ga, 1.9% Ga/Mtotal (where Mtotal = Cu + Ga), resulted in the disturbance of the completely ordered Pbcn superstructure of Ba8Cu16P30. Ba8Cu15.43(2)Ga0.3P30.26(3) crystallizes in a partially ordered orthorhombic Pmna clathrate-I superstructure with five out of 15 framework sites being jointly occupied by metal+phosphorus. Increasing the Ga content resulted in all framework sites being occupied by metal + phosphorus in the archetype cubic Pm3¯n clathrate-I crystal structure of Ba8Cu14.5(3)Ga1.3P30.2(4) with 8.2% Ga/Mtotal. A combination of energy dispersive x-ray spectroscopy, inductively coupled plasma mass spectroscopy, and single crystal x-ray diffraction was used to determine the structures alongside the compositions. The positional disorder was verified by 31P solid state NMR spectroscopy. Characterization of the transport properties indicated that the Ga-substituted samples exhibit higher Seebeck coefficients and electrical resistivities compared to its pristine counterpart, in line with the expected reduction of the hole concentration due to Ga/Cu substitution. Moderate improvements in the thermoelectric power factor and overall figure-of-merit were observed for samples with 6.9% and 3.8% Ga/Mtotal as compared to those for the pristine Ba8Cu16P30 clathrate. Band structure calculations shed light on how Ga substitution affects the electronic structure and thermoelectric properties of studied clathrates.

Temperature-dependent crystal structure investigation of 4f hybridized thermoelectric clathrate Ba8-xCexAuySi46-y.

Thermoelectric materials allow for conversion of waste heat into electrical energy, and they represent a green solution for improving our energy efficiency. Inclusion of 4f electrons near the Fermi level may boost the Seebeck coefficient, which is essential for high thermoelectric performance. In this study, Ce was successfully substituted for Ba on the guest atom sites in the type-I clathrate Ba8-xCexAuySi46-y and the material was characterized using high-resolution synchrotron powder X-ray diffraction data measured from 100 K to 1000 K to investigate potential structural implications of the inclusion of a 4f element. The thermal expansion and bonding of the host structure are not affected by the presence of Ce, as seen from the linear coefficient of unit-cell thermal expansion of 7.30 (8) × 10-6 K-1 and the average host Debye temperature of 404 (7) K determined from the multi-temperature atomic displacement parameters, both of which are similar to values obtained for pure Ba8AuySi46-y. The anisotropic atomic displacement parameters on the guest atom site in the large clathrate cage populated by Ba surprisingly reveals isotropic behavior, which is different from all other clathrates reported in literature, and thus represents a unique host-guest bonding situation.

Deformation and Failure Mechanisms of Thermoelectric Type-I Clathrate Ba8Au6Ge40.

Type-I clathrate Ba8Au6Ge40, possessing an interesting structure stacked by polyhedrons, is a potential "phonon-glass, electron-crystal" thermoelectric material. However, the mechanical properties of Ba8Au6Ge40 vital for industrial applications have not been clarified. Here, we report the first density functional theory calculations of the intrinsic mechanical properties of thermoelectric clathrate Ba8Au6Ge40. Among the different loading directions, the {110}/⟨001⟩ shearing and ⟨110⟩ tension are the weakest, with strengths of 4.51 and 6.64 GPa, respectively. Under {110}/⟨001⟩ shearing, the Ge-Ge bonds undergo significant stretching and twisting, leading to a severe distortion of the tetrakaidecahedral cage, giving rise to the fast softening of the flank Au-Ge bonds. At a strain of 0.2655, the Au-Ge bonds suddenly break, resulting in the collapse of the cage and the failure of the material. Under a ⟨110⟩ tension, the stretching of the Ge-Ge bonds keeps accelerating the softening of the Au-Ge bonds in the top/bottom hexagons, which releases the stress and disables the structure. The Au-Ge bonds are more rigid, contributing two-thirds of the structural deformation resistance. This work provides a new insight to understand the failure mechanisms of type-I clathrates with varied framework constitutions, which should help inform the design of robust thermoelectric clathrate materials.

From Phonons to the Thermal Properties of Complex Thermoelectric Crystals: The Case of Type-I Clathrates

From Phonons to the Thermal Properties of Complex Thermoelectric Crystals: The Case of Type-I Clathrates

Investigating the Chemical Ordering in Quaternary Clathrate Ba8AlxGa16-xGe30.

Recently, there has been an increased interest in quaternary clathrate systems as promising thermoelectric materials. Because of their increased complexity, however, the chemical ordering in the host framework of quaternary clathrates has not yet been comprehensively analyzed. Here, we have synthesized a prototypical quaternary type-I clathrate Ba8AlxGa16–xGe30 by Czochralski and flux methods, and we employed a combination of X-ray and neutron diffraction along with atomic scale simulations to investigate chemical ordering in this material. We show that the site occupancy factors of trivalent elements at the 6c site differ, depending on the synthesis method, which can be attributed to the level of equilibration. The flux-grown samples are consistent with the simulated high-temperature disordered configuration, while the degree of ordering for the Czochralski sample lies between the ground state and the high-temperature state. Moreover, we demonstrate that the atomic displacement parameters of the Ba atoms in the larger tetrakaidecahedral cages are related to chemical ordering. Specifically, Ba atoms are either displaced toward the periphery or localized at the cage centers. Consequently, this study reveals key relationships between the chemical ordering in the quaternary clathrates Ba8AlxGa16–xGe30 and the structural properties, thereby offering new perspectives on designing these materials and optimizing their thermoelectric properties.

Thermoelectric characterization of the clathrate-I solid solution Ba8− δ AuxGe46−x

Clathrate-I-based materials are promising for waste-heat recovering applications via thermoelectric (TE) effects. However, the lack of highly efficient p-type materials hampers the development of clathrate-based TE devices. In this work, the synthesis of the p-type semiconductor Ba7.8Au5.33Ge40.67 with clathrate-I structure is up-scaled by steel-quenching and spark plasma sintering treatment at 1073 K. A thermoelectric figure of merit ZT ≈ 0.9 at 670 K is reproducibly obtained, and 40 chemically homogeneous module legs of 5 × 5 × 7 mm3 are fabricated. By using a carbon layer as a diffusion barrier, electrical contacts are sustainable at elevated application temperatures. Eight couples with the clathrate-I compounds Ba7.8Au5.33Ge40.67 as p-type and Ba8Ga16Ge30 as n-type materials are integrated into a TE module with an output power of 0.2 W achieved under a temperature difference ΔT = 380 K (T1 = 673 K and T2 = 293 K). The thermoelectric performance of Ba7.8Au5.33Ge40.67 demonstrates the potential of type-I clathrates for waste heat recycling.