Copper ion liquid-like thermoelectrics

Journal name:
Nature Materials
Year published:
Published online

Advanced thermoelectric technology offers a potential for converting waste industrial heat into useful electricity, and an emission-free method for solid state cooling1, 2. Worldwide efforts to find materials with thermoelectric figure of merit, zT values significantly above unity, are frequently focused on crystalline semiconductors with low thermal conductivity2. Here we report on Cu2−xSe, which reaches a zT of 1.5 at 1,000 K, among the highest values for any bulk materials. Whereas the Se atoms in Cu2−xSe form a rigid face-centred cubic lattice, providing a crystalline pathway for semiconducting electrons (or more precisely holes), the copper ions are highly disordered around the Se sublattice and are superionic with liquid-like mobility. This extraordinary ‘liquid-like’ behaviour of copper ions around a crystalline sublattice of Se in Cu2−xSe results in an intrinsically very low lattice thermal conductivity which enables high zT in this otherwise simple semiconductor. This unusual combination of properties leads to an ideal thermoelectric material. The results indicate a new strategy and direction for high-efficiency thermoelectric materials by exploring systems where there exists a crystalline sublattice for electronic conduction surrounded by liquid-like ions.

At a glance


  1. Crystal structure of Cu2Se at high temperatures (β-phase) with a cubic anti-fluorite structure.
    Figure 1: Crystal structure of Cu2Se at high temperatures (β-phase) with a cubic anti-fluorite structure.

    a, Unit cell where only the 8c and 32f interstitial positions are shown with Cu atoms. b, Projected plane representation of the crystal structure along the cubic direction. The arrows indicate that the Cu ions can freely travel among the interstitial sites. There are two Cu layers between the neighbouring Se (111) planes. The structure changes to a monoclinic α-phase by stacking the ordered Cu ions along the cubic [111] direction when cooled to room temperature.

  2. Thermoelectric properties of the low-temperature (α) and high-temperature (β) phases in Cu2−xSe.
    Figure 2: Thermoelectric properties of the low-temperature (α) and high-temperature (β) phases in Cu2−xSe.

    ad, Temperature dependences of electrical resistivity ρ (a), thermopower S(b), thermal conductivity κ (c) and dimensionless figure-of-merit zT (d).

  3. In situ HRTEM observation of the phase transformation in Cu2Se.
    Figure 3: In situ HRTEM observation of the phase transformation in Cu2Se.

    a, HRTEM at 423 K. b, HRTEM at room temperature. At high temperatures the structure is of anti-fluorite cubic type, which is characterized by the formation of multiple nano-sized twins. On cooling, the cubic structure is transformed to a monoclinic structure, which shows a doubled interplanar distance on a {111}c plane due to the ordering of Cu ions.

  4. The high-temperature specific heat capacity of Cu2Se.
    Figure 4: The high-temperature specific heat capacity of Cu2Se.

    The theoretical value (Dulong–Petit) for the high-temperature specific heat at constant volume Cv (Cph) is 3NkB in a solid crystal. The lowest Cv theoretical value in a liquid is 2NkB. Cu2Se shows a reduced Cv, approaching 2NkB at high temperatures. The dashed blue line shows the expected value of the specific heat at constant pressure Cp in a solid crystal Cu2Se without liquid-like properties, which is usually beyond the Dulong–Petit limit at high temperatures owing to the extra contributions by carriers (Ce) and lattice thermal expansion (see the details in Supplementary Information). B is the bulk modulus, V is the volume per atom and α is the thermal expansion coefficient.


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Author information


  1. CAS Key Laboratory of Energy-conversion Materials, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China

    • Huili Liu,
    • Xun Shi &
    • Lidong Chen
  2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China

    • Huili Liu
  3. State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China

    • Xun Shi,
    • Fangfang Xu,
    • Linlin Zhang &
    • Wenqing Zhang
  4. Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

    • Qiang Li
  5. Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

    • Ctirad Uher
  6. Department of Materials Science, California Institute of Technology, Pasadena, California 91125, USA

    • Tristan Day &
    • G. Jeffrey Snyder


H.L. and X.S. prepared the samples and measured the thermoelectric properties. F.X., W.Z., L.C., Q.L., G.J.S. and C.U. provided discussion on the experimental data. F.X. and L.Z. performed TEM measurements and analysis. T.D. and G.J.S. performed room-temperature speed of sound measurements. H.L., X.S., L.C., Q.L., C.U. and G.J.S. wrote and edited the manuscript.

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