Deciphering Pauling's Third Rule: Uncovering Strong Anharmonicity and Exceptionally Low Thermal Conductivity in TlAgSe for Thermoelectrics.

ABSTRACT

Pauling's third empirical rule deals with the cationic repulsion due to proximity in the face or edge shared polyhedra in a crystal structure, can bring about the lattice instability required to suppress the lattice thermal conductivity (κL). Here, we demonstrate the presence of such instability in TlAgSe, leading to a ultra-low κL of 0.17 W/m.K at 573 K. Our study reveals the instability arising from Ag-Ag repulsion within edge-shared AgSe4 tetrahedra through investigation of the local structure using synchrotron X-ray pair distribution function (PDF)  and supported by density functional theory. We observe correlation between weakening in the Ag  and the Tl-sublattice, providing direct experimental evidence of Pauling's third rule. The correlated rattling of Ag and Tl induces a highly anharmonic lattice and low energy optical phonons, resulting in suppressed sound velocity and ultralow κL. The electronic origin of soft and anharmonic lattice is the presence of filled antibonding states in the valence band near the Fermi level constructed by Ag(4d)-Se(4p) and Tl(6s)-Se(4p) interactions. This work demonstrates that the evidence of dynamic distortion in a crystal lattice is governed by the third empirical rule given by Pauling, which can act as a potential new strategy for diminishing κL in crystalline solids.