Key Role of Positional Disorder and Soft Structural Framework for Lowering the Thermal Conductivity of Quaternary Ag_1–xCu_3+xTiSe₄ (0 ≤ x ≤ 0.8) System to an Ultralow Limit

Abstract

Low thermal conductive semiconductors have attracted huge attention for heat management and heat harvesting applications. Although the weak chemical bonding in the Cu/Agbased chalcogenides is promising in suppressing heat transport, their quaternary analogs remain less explored. Here, we report on a comparative study of the crystal structure and thermal conductivity of various Ag-containing variants of Cu 4 TiSe 4 , i.e., Ag 1−x Cu 3+x TiSe 4 (x = 0−0.8) samples. Analysis of the crystal structure, phase transition, and temperature-dependent lattice thermal conductivity (κ L ) of pristine AgCu 3 TiSe 4 and Ag 1−x Cu 3+x TiSe 4 have been carried out both experimentally and theoretically. The cubic crystal structure (space group P4̅ 3m) of these Ag variants is identical to that of Cu 4 TiSe 4 or Cu 4 TiTe 4 , where a positionally disordered Cu sublattice is either replaced by Ag (for AgCu 3 TiSe 4 ) or by Ag/Cu substructure (for Ag 1−x Cu 3+x TiSe 4 ). Upon cooling, the symmetry reduction to a rhombohedral (space group R3m) structure is attributed to the partial ordering of the positionally disordered Ag. The proposed structural models at different temperatures have been further analyzed using the Maximum Entropy Method (MEM). X-ray photoelectron spectroscopy measurement suggests that the parent compound forms a charge-precise (Ag + )(Cu + ) 3 (Ti 4+ )(Se 2− ) 4 chemical formula. Interestingly, the lattice thermal conductivity of the Ag 1−x Cu 3+x TiSe 4 samples remains very low, with values varying in the range of ∼0.65−0.24 W m −1 K −1 between 293 and 623 K. Density Functional Theory (DFT) calculation shows the presence of antibonding states of Cu(3d)/Ag(4d)−Se(4p) below the Fermi level (E F ), providing softness to the lattice of AgCu 3 TiSe 4 . In addition, the positional disordered site plays a crucial role in further softening the framework and provides large lattice anharmonicity. The calculated phonon dispersions evidence the presence of several soft optical phonon modes at ca. 25 cm −1 , originating from the atomic vibrations of Ag, Cu, and Se. Further confirmation of these phonon modes is obtained from the low-temperature heat capacity study. The low-lying optical phonon modes in AgCu 3 TiSe 4 are mainly caused by the presence of a soft lattice framework, positional disorder and associated rattling-like vibrations of Ag + /Cu + ions. Their strong interaction with the heat-carrying acoustic phonon modes is key ingredient that explains the very low κ L .