Intrinsically ultralow thermal conductivity in all-inorganic superatomic bulk crystals

Abstract: Superatomic compounds, composed of atomic clusters interwoven by weak chemical bonds exhibit large anharmonicity vibrations, are excellent candidates for ultralow thermal conductivity (\k{appa}) materials. However, growing bulk superatomic single crystals is challenging due to complex chemical composition and chemical bonds, and studies on their intrinsic thermal property are scarce. Here, we grew high-quality superatomic single crystals of Re6Se8Te7 and Re6Te15, both of which are narrow band gap semiconductors that change into metals under external physical pressure. At room-temperature, the \k{appa} are 0.32 W m-1 K-1 and 0.53 W m-1 K-1 in Re6Se8Te7 and Re6Te15, respectively, ranking among the lowest value reported in all-inorganic bulk crystals. It is mainly attributed to the large Grüneisen parameter (1.93) and low average sound speed (< 1482 m/s), which are due to soft Te7 nets weakly embedded among the rigid Re6Se8 (Re6Te8) quasi-cubic clusters. The appearance of boson peak, i. e., hump of C(T)/T3, verifies the existence of disordered phonon transports. Besides, the temperature dependence of \k{appa} can be described by classic Debye-Callaway model. Notably, above 350 K, the \k{appa} values of Re6Se8Te7 and Re6Te15 are remarkably close to the upper limit derived from glassy-like diffusion model. This finding sets the superatomic compounds as a promising family for searching ultralow-\k{appa} and energy management materials.

• The paper demonstrates that all-inorganic superatomic crystals intrinsically exhibit ultralow thermal conductivity due to their unique cluster-net architecture.
• The authors synthesized high-quality Re₆Se₈Te₇ and Re₆Te₁₅ crystals, achieving room-temperature lattice conductivities as low as 0.32 and 0.53 W·m⁻¹·K⁻¹.
• The study reveals that strong anharmonicity, weak Te–Te bonding, and dominant Umklapp scattering yield glass-like heat transport in these ordered crystals.

Intrinsically Ultralow Thermal Conductivity in All-Inorganic Superatomic Bulk Crystals

Introduction

The paper "Intrinsically ultralow thermal conductivity in all-inorganic superatomic bulk crystals" (2603.28267) presents a comprehensive investigation of the lattice thermal transport in bulk single crystals of two superatomic materials, Re₆Se₈Te₇ and Re₆Te₁₅. These compounds feature quasi-cubic rhenium chalcogenide clusters interconnected by hinge-like tellurium nets and represent a structurally complex, all-inorganic family characterized by low-frequency vibrations. The study addresses the longstanding experimental challenge of growing high-quality bulk superatomic crystals and provides previously unavailable direct measurements of intrinsic thermal conductivity in these systems.

Experimental Realization of Bulk Superatomic Crystals

The authors successfully synthesized millimeter-scale single crystals of Re₆Se₈Te₇ and Re₆Te₁₅ using a high-temperature K₂Te flux method. Crystallographic analysis revealed a three-dimensional Pbca structure consisting of rigid, pseudo-cubic Re₆Q₈ (Q = Se, Te) clusters and soft, flexible Te₇ nets. The clusters are characterized by strong Re-Q bonding, while the Te₇ nets connect the clusters via weaker Te-Te bonds, resulting in a pronounced rigidity contrast. STEM and XPS confirmed structural motifs and valence assignments ([Re₆Se₈]²⁺/ [Re₆Te₈]²⁺, [Te₇]²⁻).

Both compounds behave as narrow-gap p-type semiconductors at ambient conditions, with optical and electrical band gaps of 0.17–0.18 eV (Re₆Se₈Te₇) and 0.10–0.12 eV (Re₆Te₁₅). Under increased pressure, a semiconductor-to-metal transition is observed.

Ultralow Intrinsic Lattice Thermal Conductivity

Thermal conductivity measurements demonstrated that at 300 K, Re₆Se₈Te₇ has a lattice thermal conductivity ($\kappa$) of 0.32 W·m⁻¹·K⁻¹ and Re₆Te₁₅ achieves 0.53 W·m⁻¹·K⁻¹. These values are among the lowest ever reported in three-dimensional all-inorganic crystals, and importantly, they reflect the bulk single-crystalline intrinsic $\kappa$. Prior values for polycrystalline Re₆Te₁₅ were significantly higher (~1.3 W·m⁻¹·K⁻¹), underscoring the necessity of high crystalline quality for exposing intrinsic phonon physics in such complex materials.

The temperature dependence of $\kappa$ follows an inverse trend characteristic of Umklapp-dominated phonon scattering. Crucially, above 350 K, $\kappa$ in both materials saturates near the Cahill-Pohl minimum limit for glassy lattice diffusion—a regime rarely approached by inorganic crystalline solids.

Origins of Strong Phonon Scattering

A detailed analysis of vibrational properties showed that all atomic vibrations are confined below 245 cm⁻¹, primarily due to the large atomic mass and weak inter-cluster coupling. Isotropic atomic displacement parameters are highest for Te atoms in the nets, consistent with large-amplitude, "rattling" motion.

Phonon density of states calculations, Raman measurements, and heat capacity data were interpreted using the Debye-Einstein model, requiring multiple Einstein oscillators for accurate description. A boson peak captured in $C_p/T^3$ vs. $T$ curves around 7 K evidences excess low-frequency modes and phonon disorder, a hallmark of structural inhomogeneity typical of glassy or amorphous materials but rarely observed in ordered crystals.

The rigid cluster/soft net structure yields exceptionally low average sound velocities—1420 m/s in Re₆Se₈Te₇ (substantially below other ultralow-$\kappa$ systems, e.g., BiCuSeO, K₂Bi₈Se₁₃)—and large Grüneisen parameters (1.93 from bulk modulus/thermal expansion; >2 for low-frequency Einstein modes), confirming strong lattice anharmonicity.

DFT-based force constant and COHP analyses established that the Te-Te bonds in the nets are much softer and electronically less coupled than Re-Q or intra-cluster Re-Te bonds, leading to reduced acoustic phonon velocities and enhanced scattering.

Theoretical Modeling of Anharmonic Lattice Dynamics

Thermal conductivity was modeled using a modified Debye-Callaway formalism incorporating phonon-phonon Umklapp scattering. Best-fit values for sound velocity and Grüneisen parameter aligned with experiment. At the single-superatom scale, mean free paths for relevant phonons approach or even fall below the Ioffe-Regel limit, highlighting the breakdown of propagative phonon modes and the onset of diffuson-dominated transport typical of glasses.

The coupling of optical modes (Einstein frequencies 15–31 cm⁻¹) with acoustic branches, observed in the phonon dispersions, further enhances scattering via resonance and four-phonon processes, also captured in the temperature dependence of vibrational mode linewidths.

Implications and Prospects

These results place Re₆Se₈Te₇ and Re₆Te₁₅ at the forefront of all-inorganic ultralow thermal conductivity materials, with room-temperature $\kappa$ values comparable to or below most established complex chalcogenides and even approaching some organic-inorganic hybrid superatoms.

The demonstration that mismatched vibrational and bonding strength between rigid superatomic clusters and flexible nets produces glass-like phonon transport, even in well-ordered crystals, opens a new paradigm for thermoelectric and thermal management material design. The findings strongly suggest that further exploration of superatomic and cluster-based solids incorporating heavy atoms and flexible linkers could systematically lower lattice thermal conductivity toward the glassy minimum, without chemical disorder or extrinsic point defect engineering.

Applications may extend to thermoelectrics, thermal barrier coatings, and other technologies requiring minimal phonon-mediated thermal transport. On a theoretical level, these results highlight the importance of coupling between structural motif, chemical bonding hierarchy, and multiscale lattice dynamics in dictating emergent thermal transport regimes.

Conclusion

This study establishes that all-inorganic superatomic crystals, exemplified by Re₆Se₈Te₇ and Re₆Te₁₅, intrinsically manifest ultralow lattice thermal conductivity as a direct consequence of their cluster-net architecture, phonon disorder, and extreme anharmonicity. By focusing on the structural chemistry of superatomic solids, rather than compositional complexity or extrinsic disorder, it provides a robust design principle for accessing glass-like thermal transport in crystalline phases and points toward future advances in high-efficiency thermoelectric and heat management systems.