Lattice Instability and Ultralow Lattice Thermal Conductivity of Layered PbIF

Abstract: Understanding the interplay between various design strategies (for instance, bonding heterogeneity and lone pair induced anharmonicity) to achieve ultralow lattice thermal conductivity ($\kappa_l$) is indispensable for discovering novel functional materials for thermal energy applications. In the present study, we investigate layered PbXF (X = Cl, Br, I), which offers bonding heterogeneity through the layered crystal structure, anharmonicity through the Pb$^{2+}$ $6s^2$ lone pair, and phonon softening through the mass difference between F and Pb/X. The weak inter-layer van der Waals bonding and the strong intra-layer ionic bonding with partial covalent bonding result in a significant bonding heterogeneity and a poor phonon transport in the out-of-plane direction. Large average Gr\"uneisen parameters ($\geq$ 2.5) demonstrate strong anharmonicity. The computed phonon dispersions show flat bands, which suggest short phonon lifetimes, especially for PbIF. Enhanced Born effective charges are due to cross-band-gap hybridization. PbIF shows lattice instability at a small volume expansion of 0.1$\%$. The $\kappa_l$ values obtained by the two channel transport model are 20-50$\%$ higher than those obtained by solving the Boltzmann transport equation. Overall, ultralow $\kappa_l$ values are found at 300 K, especially for PbIF. We propose that the interplay of bonding heterogeneity, lone pair induced anharmonicity, and constituent elements with high mass difference aids the design of low $\kappa_l$ materials for thermal energy applications.