Abstract
Crystalline-liquid duality in specific heat is observed in lead-free bismuth halide perovskite A3Bi2×9 [A= FA, MA, Cs, and X = I, Br, Cl] semiconductor. All crystals exhibit unusual liquid-like behavior and show substantial deviation from the classical Dulong-Petit law at room temperature. This unusual liquid-like behavior of specific heat is attributed to the dynamic disorder and strong anharmonicity in the soft crystal lattice. The low-temperature specific heat was modeled using the combined Debye-Einstein model and obtained Einstein modes demonstrate strong anharmonic coupling of the low-energy optical modes with acoustic modes resulting in ultrasoft frequency dampening of acoustic phonons. The combination of strong acoustic−optical phonon coupling, soft elastic layered structure, and abundance of low-energy optical phonons results in anomalous thermodynamic specific heat duality in these bismuth-based phonon glass electron crystals. Our study is of fundamental interest in thermodynamics and will help to design novel thermoelectric materials.
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