Local-Disorder-Induced Low Thermal Conductivity in Degenerate Semiconductor Cu22Sn10S32

Three-Fold Coordination of Copper in Sulfides: A Blockade for Hole Carrier Delocalization but a Driving Force for Ultralow Thermal Conductivity

Copper-rich sulfides are very promising for energy conversion applications due to their environmental compatibility, cost effectiveness, and earth abundance. Based on a comparative analysis of the structural and transport properties of Cu3BiS3 with those of tetrahedrite (Cu12Sb4S13) and other Cu-rich sulfides, we highlight the role of the cationic coordination types and networks on the electrical and thermal properties. By precession-assisted 3D electron diffraction analysis, we find very high anisotropic thermal vibration of copper attributed to its 3-fold coordination, with an anisotropic atomic displacement parameter up to 0.09 Å2. Density functional theory calculations reveal that these Cu atoms are weakly bonded and give rise to low-energy Einstein-like vibrational modes that strongly scatter heat-carrying acoustic phonons, leading to ultralow thermal conductivity. Importantly, we demonstrate that the 3-fold coordination of copper in Cu3BiS3 and in other copper-rich sulfides constituted of interconnected CuS3 networks causes a hole blockade. This phenomenon hinders the possibility of optimizing the carrier concentration and electronic properties through mixed valency Cu+/Cu2+, differently from tetrahedrite and most other copper-rich chalcogenides, where the main interconnected Cu-S network is built of CuS4 tetrahedra. The comparison with various copper-rich sulfides demonstrates that seeking for frameworks characterized by the coexistence of tetrahedral and 3-fold coordinated copper is very attractive for the discovery of efficient thermoelectric copper-rich sulfides. Considering that lattice vibrations and carrier concentration are key factors for engineering transport phenomena (electronic, phonon, ionic, etc.) in copper-rich chalcogenides for various types of applications, our findings improve the guidelines for the design of materials enabling sustainable energy solutions with wide-ranging applications.

Lone Pair Rotation and Bond Heterogeneity Leading to Ultralow Thermal Conductivity in Aikinite

Understanding the relationship between the crystal structure, chemical bonding, and lattice dynamics is crucial for the design of materials with low thermal conductivities, which are essential in fields as diverse as thermoelectrics, thermal barrier coatings, and optoelectronics. The bismuthinite-aikinite series, Cu_1-x□_xPb_1-xBi_1+xS₃ (0 ≤ x ≤ 1, where □ represents a vacancy), has recently emerged as a family of n-type semiconductors with exceptionally low lattice thermal conductivities. We present a detailed investigation of the structure, electronic properties, and the vibrational spectrum of aikinite, CuPbBiS₃ (x = 0), in order to elucidate the origin of its ultralow thermal conductivity (0.48 W m^-1 K^-1 at 573 K), which is close to the calculated minimum for amorphous and disordered materials, despite its polycrystalline nature. Inelastic neutron scattering data reveal an anharmonic optical phonon mode at ca. 30 cm^-1, attributed mainly to the motion of Pb²⁺ cations. Analysis of neutron diffraction data, together with ab-initio molecular dynamics simulations, shows that the Pb²⁺ lone pairs are rotating and that, with increasing temperature, Cu⁺ and Pb²⁺ cations, which are separated at distances of ca. 3.3 Å, exhibit significantly larger displacements from their equilibrium positions than Bi³⁺ cations. In addition to bond heterogeneity, a temperature-dependent interaction between Cu⁺ and the rotating Pb²⁺ lone pair is a key contributor to the scattering effects that lower the thermal conductivity in aikinite. This work demonstrates that coupling of rotating lone pairs and the vibrational motion is an effective mechanism to achieve ultralow thermal conductivity in crystalline materials.