Intrinsically ultralow thermal conductivity in all-inorganic superatomic bulk crystals

This study reports the successful growth of high-quality all-inorganic superatomic single crystals (Re6Se8Te7 and Re6Te15) that exhibit intrinsically ultralow thermal conductivity at room temperature, a property attributed to their unique structural composition of rigid clusters embedded in soft networks which induces strong anharmonicity and glass-like phonon transport.

The Gist

The Big Idea: Building a "Thermal Insulator" from Atomic Lego

Imagine you are trying to stop a crowd of people (heat) from running through a hallway. Usually, you can't stop them completely, but you can make the hallway so bumpy, confusing, and full of obstacles that they move incredibly slowly.

Scientists have discovered a new family of materials made of "atomic Lego blocks" that are so good at stopping heat flow that they are among the best insulators ever found in the world of pure inorganic crystals. These materials are called Superatomic Compounds.

What are "Superatoms"?

Think of a normal crystal like a wall made of individual bricks. Now, imagine a wall made of giant, pre-assembled Lego structures. In these new materials, groups of atoms stick together tightly to form a single, rigid "super-atom" (like a tiny, heavy cube).

• The Rigid Blocks: In this study, the scientists used clusters of Rhenium and Selenium (or Tellurium) that act like heavy, stiff, solid cubes.
• The Soft Connectors: These heavy cubes are not glued together with strong cement. Instead, they are connected by a "net" made of Tellurium atoms that acts like a floppy, stretchy spring or a hinge.

The Problem: Why is Heat Hard to Stop?

Heat travels through solids via vibrations. Imagine shaking one end of a rope; the wave travels to the other end. In normal materials, the "rope" is tight, so the vibration (heat) zips through very fast.

To stop heat, you need to:

1. Make the rope heavy (so it's hard to shake).
2. Make the connections loose (so the shake doesn't transfer well).
3. Make the structure wobbly (so the energy gets lost in chaos).

The Solution: The "Scissor-Hinge" Effect

The scientists grew high-quality crystals of two specific materials: Re₆Se₈Te₇ and Re₆Te₁₅. Here is why they work so well:

1. Heavy Blocks: The "super-atom" cubes are very heavy. Heavy things are hard to get moving, which slows down the heat vibrations.
2. The Wobbly Net: The most important part is the Te₇ net. Imagine the heavy cubes are connected by a net made of rubber bands or a scissor-hinge. When the cubes try to vibrate, the rubber bands stretch and wobble instead of passing the energy along.
   • This creates a "mismatch." The cubes want to be stiff, but the connection is soft and floppy.
   • This floppiness causes the vibrations to get confused and scatter, turning the organized heat wave into chaotic, useless noise.

The Results: A "Glass-Like" Crystal

Usually, crystals are good conductors of heat, and glass is a bad conductor. These materials are special because they are crystals (ordered structure) that behave like glass (disordered, bad at conducting heat).

• The Numbers: At room temperature, these materials have a thermal conductivity of just 0.32 and 0.53. To put that in perspective, that is almost as low as glass and significantly lower than most metals or standard crystals.
• The "Boson Peak": The researchers found a specific "hump" in the data (called a Boson peak). You can think of this as hearing a "thud" instead of a "ring." It proves that the vibrations are getting stuck in the wobbly net, behaving like they are in a messy, disordered pile of junk rather than a neat crystal.

Why Does This Matter?

Why do we care about stopping heat?

1. Energy Efficiency: If we can stop heat from escaping, we can build better insulation for buildings or electronics.
2. Thermoelectrics: These materials are semiconductors. If you can keep one side hot and the other side cold (because the heat can't flow through), you can generate electricity from waste heat (like from a car engine or a computer).
3. New Design Rules: This paper proves that you don't need to mix organic and inorganic materials to get great insulation. You can do it just by arranging inorganic atoms into "super-atoms" connected by "soft springs."

Summary Analogy

Imagine a line of heavy bowling balls (the super-atoms) trying to pass a message to each other by tapping.

• In a normal crystal: The balls are touching. One taps, the next moves instantly. The message (heat) travels fast.
• In this new material: The bowling balls are separated by a long, floppy slinky. When the first ball taps the slinky, the slinky just wiggles and flops around. The energy gets lost in the wiggling, and the next ball barely feels a tap.

The scientists successfully built this "bowling ball and slinky" structure in a perfect crystal, creating a material that is incredibly good at keeping heat in (or out). This opens the door to designing better materials for managing energy in our future technology.

Technical Summary

1. Problem Statement

• Challenge: Superatomic compounds, which consist of atomic clusters linked by weak chemical bonds, are theoretically excellent candidates for materials with ultralow thermal conductivity ($\kappa$) due to their large anharmonicity and structural complexity. However, synthesizing high-quality bulk single crystals of these materials is extremely difficult due to complex chemical compositions and bonding requirements.
• Gap: Consequently, studies on the intrinsic thermal transport properties of superatomic materials are scarce. Previous measurements were often limited to polycrystalline pellets (which introduce grain boundary scattering) or organic-inorganic hybrids, leaving the intrinsic limits of all-inorganic superatomic crystals unknown.
• Specific Target: The authors aimed to grow bulk single crystals of Re$_6$Se$_8$Te$_7$ and Re$_6$Te$_{15}$ to accurately measure their intrinsic thermal properties and understand the mechanisms behind their low $\kappa$.

2. Methodology

• Crystal Growth: High-quality bulk single crystals (approx. 2×2×2 mm$^3$) were synthesized using a high-temperature K$_2$Te flux method. This involved solid-state reaction precursors followed by a controlled cooling process (1000°C to 600°C) to facilitate crystal growth.
• Structural Characterization:
  • Single-crystal X-ray diffraction (SC-XRD) at 300 K and 50 K to determine crystal structures (space group Pbca).
  • High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) to validate atomic arrangements.
  • X-ray photoelectron spectroscopy (XPS) to determine valence states.
• Physical Property Measurements:
  • Electrical Transport: Resistivity and Seebeck coefficient measurements under ambient and high-pressure conditions to determine band gaps and carrier types.
  • Thermal Conductivity: Measured via Frequency-Domain Thermoreflectance (FDTR) to ensure high accuracy for single crystals.
  • Heat Capacity: Measured from 2–400 K to analyze anharmonic vibrations and boson peaks.
  • Sound Velocity: Measured using the pulse-echo method to determine longitudinal ($v_l$) and transverse ($v_t$) velocities.
  • High-Pressure Studies: In-situ XRD and electrical transport under pressure to study structural stability and phase transitions.
• Theoretical Calculations:
  • Density Functional Theory (DFT): Used to calculate phonon density of states (PDOS), interatomic force constants (IFCs), and Crystal Orbital Hamilton Population (COHP) to analyze bonding strength.
  • Modeling: Data was fitted using the Debye-Callaway model (for phonon scattering) and compared against the Cahill-Pohl diffusion model (glass-like limit). The Grüneisen parameter ($\gamma$) was calculated to quantify anharmonicity.

3. Key Contributions

• First Bulk Single Crystals: Successfully grew the first bulk single crystals of Re$_6$Se$_8$Te$_7$ and Re$_6$Te$_{15}$, enabling the first accurate measurement of their intrinsic thermal properties.
• Structural Insight: Identified a unique "soft-hard" mismatch architecture where rigid quasi-cubic Re$_6$Se$_8$ (or Re$_6$Te$_8$) clusters are interconnected by flexible, scissor-hinge-like Te$_7$ nets.
• Mechanism Elucidation: Demonstrated that the ultralow thermal conductivity arises from a combination of:
  1. Large Grüneisen parameter ($\gamma \approx 1.93$): Indicating strong anharmonicity.
  2. Low sound speed ($< 1482$ m/s): Caused by the weak bonding of the Te$_7$ nets.
  3. Disordered Phonon Transport: Evidenced by the appearance of a boson peak (hump in $C_p/T^3$) and low-frequency Einstein modes, suggesting diffusive-like phonon damping.
• Glass-Like Limit: Showed that above 350 K, the thermal conductivity of these crystals approaches the theoretical minimum (Cahill-Pohl limit) typically associated with amorphous glasses, despite being crystalline.

4. Key Results

• Thermal Conductivity ($\kappa$):
  • At room temperature (300 K), Re$_6$Se$_8$Te$_7$ exhibits $\kappa = \mathbf{0.32 \pm 0.02}$ W m$^{-1}$ K$^{-1}$, and Re$_6$Te$_{15}$ exhibits $\kappa = \mathbf{0.53 \pm 0.02}$ W m$^{-1}$ K$^{-1}$.
  • These values are among the lowest reported for all-inorganic 3D bulk crystals.
  • At 390 K, values drop further to 0.26 and 0.31 W m$^{-1}$ K$^{-1}$, respectively.
• Electronic Properties: Both materials are narrow-bandgap semiconductors (band gaps ~0.12–0.18 eV) that transition to metallic behavior under external pressure.
• Anharmonicity & Vibration:
  • The Te$_7$ nets exhibit large atomic displacement parameters (ADP), comparable to "rattling" atoms in clathrates.
  • Boson Peak: Observed at ~7 K, confirming the presence of disordered, low-energy vibrational modes associated with the weak Te$_7$ connections.
  • Grüneisen Parameter: The average $\gamma$ is 1.93 for Re$_6$Se$_8$Te$_7$, significantly higher than many standard thermoelectric materials, indicating strong phonon-phonon scattering.
• Sound Velocity: The average sound velocity is remarkably low (~1420–1480 m/s), particularly the longitudinal component, due to the "spring-like" nature of the Te$_7$ nets connecting the rigid clusters.
• Modeling: The temperature dependence of $\kappa$ fits the Debye-Callaway model well at lower temperatures but converges to the Cahill-Pohl glass limit at $T > 350$ K, indicating a transition to diffusive heat transport.

5. Significance

• Material Design Strategy: This work establishes a new design paradigm for ultralow thermal conductivity materials: creating a mismatch between rigid superatomic clusters and soft, weakly bonded connecting networks.
• Inorganic vs. Organic: Unlike previous low-$\kappa$ superatomic materials that relied on organic ligands (which can be unstable or difficult to process), these are all-inorganic systems, offering better thermal stability and potential for high-temperature applications.
• Energy Management: The ability to achieve glass-like thermal conductivity in a crystalline semiconductor makes these materials highly promising for thermoelectric energy conversion and thermal management applications where minimizing heat loss is critical.
• Fundamental Physics: The study provides a rare experimental verification of how structural complexity and specific bonding motifs (soft nets between hard clusters) can induce glass-like phonon transport in a single crystal, bridging the gap between crystalline and amorphous thermal transport theories.