Ultralow Thermal Conductivity in Earth-Abundant Cu_1.6Bi_4.8S₈: Anharmonic Rattling of Interstitial Cu

Abstract

Earth-abundant, nontoxic crystalline compounds with intrinsically low lattice thermal conductivity (κlat) are centric to the development of thermoelectrics and thermal barrier coatings. Investigation of the fundamental origins of such low κlat and understanding its relationship with the chemical bonding and structure in solids thus stands paramount in order to furnish such low thermally conductive compounds. Herein, we synthesized earth-abundant, cost-effective, and nontoxic n-type ternary sulfide Cu1.6Bi4.8S8, which exhibits an intrinsically ultralow κlat of ∼0.71–0.44 W/m·K in the temperature range of 296–736 K. Structural analysis via atomic refinement unveiled large atomic displacement parameters (ADPs) for interstitial Cu clusters, demonstrating intrinsic rattling-like behavior. Electron localization function (ELF) analysis further shows that these rattling Cu atoms are weakly bonded and thus can generate low-energy Einstein vibrational modes. Low-temperature heat capacity (C p ) and temperature-dependent Raman spectra concord the presence of such low-energy optical modes. Density functional theory (DFT)-based phonon dispersions reveal that these low-lying optical phonons arise primarily due to the presence of chemical bonding hierarchy and simultaneous rattling of weakly bonded interstitial Cu atoms. These low-energy optical modes strongly scatter the heat-carrying acoustic phonons, thereby reducing the phonon lifetime to an ultrashort value (2–4.5 ps) and κlat to a very low value, which is lower than that of the many state-of-the-art metal sulfides.

Quasi-layered Crystal Structure Coupled with Point Defects Leading to Ultralow Lattice Thermal Conductivity in n-Type Cu2.83Bi10Se16

“…The fully occupied Bi atoms show comparable ADP values along different directions (Figures S6 and S7). The abnormal vibration of splitting Bi atoms along a specific direction increases the bonding strength hierarchy of the structure framework. , In addition to the abnormal atomic vibration, the elongated bonds between Bi and Se from two different slabs result in the quasi-layered crystal structure of Cu 2.83 Bi 10 Se 16 , which is also confirmed by the speed of sound measurement and anisotropic electrical conductivity results ( vide infra ).…”

“…More comprehensive studies such as employing the pair distribution function (PDF) to study local ordering of Cu and Bi defects are ongoing. The study of Cu 1.6 Bi 4.8 S 8 , which has similar Cu disorder to Cu 2.83 Bi 10 Se 16 , demonstrates that the interstitial rattling of Cu atoms plays the key role in reducing lattice thermal conductivity . The measured lattice thermal conductivity of Cu 1.6 Bi 4.8 S 8 is 0.44–0.71 W m –1 K –1 in a temperature range of 296–736 K, which is higher than Cu 2.83 Bi 10 Se 16 with 0.36–0.58 W m –1 K –1 in a temperature range of 300–775 K.…”

“…In the structure of Cu 2.83 Bi 10 Se 16 , there are three distinct Cu atoms with occupancy of 0.15(1)–0.34(1). The Cu atoms exhibit abnormally high anisotropic ADP as summarized in Figure S13, which may result in a bonding strength hierarchy. , Cu disorder efficiently suppressing lattice thermal conductivity was proven very recently within a related family of sulfides, Cu 1.6 Bi 4.8 S 8 . To study how the Cu and Bi defects impact the lattice dynamic and thermal transport properties, the heat capacity of Cu 2.83 Bi 10 Se 16 was measured in a temperature range of 2–50 K, which is shown in Figure S13.…”

“…The fitting of the C p / T vs T curve via Debye + two Einstein modes was not successful. To accurately fit the C p / T vs T curve, four Einstein oscillator models with characteristic temperatures of Θ E1 = 17.81 K, Θ E2 = 38.04 K, Θ E3 = 66.31 K, and Θ E4 = 137.46 K, were necessary (Figure S13b), which indicates comprehensive low-lying optical models that may originate from Cu and Bi defects . These low-lying optical models would couple with the acoustic phonons to suppress lattice thermal conductivity.…”

“…45,46 Cu disorder efficiently suppressing lattice thermal conductivity was proven very recently within a related family of sulfides, Cu 1.6 Bi 4.8 S 8 . 46 To study how the Cu and Bi defects impact the lattice dynamic and thermal transport properties, the heat capacity of Cu 2.83 Bi 10 Se 16 was measured in a temperature range of 2−50 K, which is shown in Figure S13. The heat capacity measurements exhibit smooth, phase transition-free signals over the measured temperature range of 2−50 K (Figure S13a).…”