Anharmonic rattling leading to ultra-low lattice thermal conductivity in Cu12Sb4S13 tetrahedrites

Abstract

Disorder, instability and anharmonicity driven phonon propagations are highly favourable for achieving essential ultra-low lattice thermal conductivity (κ_l). Further, the propagation directions of heat-carrying phonons can be engineered if one can construct complex atomic arrangements through cage-like structures, large unit cell dimensions, and anharmonic interaction among heat carriers. In this regard, we discuss the detailed phonon and associated vibrational properties of sulfosalt tetrahedrite (Cu₁₂Sb₄S₁₃) minerals through in-depth Raman spectroscopy. Anharmonic phonon behavior evolves particularly from a cage-like “Sb–[S(2a)Cu(12e)S(24g)₂]–Sb” sub-unit cell through hierarchy in chemical bonding. The inhomogeneous bond strength of trigonal planar S(2a)–Cu(12e)–S(24g)₂ and the interaction of Cu(12e) with Sb lone pair electrons result in large atomic displacement parameters and rattling-like vibrations. The double-well potential energy surfaces of Cu(12e) have strong influence on phonon properties. Owing to the large anharmonic behavior, anomalous phonon hardening is observed for low-frequency regions, whereas large phonon softening (∼14 cm⁻¹ for A₁ (∼360 cm⁻¹)) is observed for higher frequency modes. The large number of unit cell atoms (58) bring different energy scaled acoustic and optical branches closer to each other, and the interaction among them enhances phonon scattering. Further, poor mean sound velocity (∼1840 m s⁻¹), large Grüneisen parameter (∼2.3), boson-like peak and rattling-like localized Einstein vibrations lead to an ultra-low κ_l value. Besides the poor thermal properties, a high power-factor of ∼950 μW m⁻¹ K⁻² results in a thermoelectric figure of merit of ∼0.7 (at ∼710 K), making the undoped Cu₁₂Sb₄S₁₃ crystalline material a potential material for energy harvesting applications.