Origin of phonon glass-electron crystal behavior in thermoelectric layered cobaltate

Measurement of local disorder and lattice vibrations is of great importance for understanding the mechanisms whereby thermoelectric materials efficiently convert heat to electricity. Attaining high thermoelectric power requires minimizing thermal conductivity while keeping electric conductivity high. This situation is achievable by enhancing phonon scattering through specific structural disorder (phonon glass) that also retains sufficient electron mobility (electron crystal). It is demonstrated that the quantitative acquisition of multiple annular-dark-field images via scanning transmission electron microscopy at different scattering-angles simultaneously allows not only the separation but also the accurate determination of static and thermal atomic displacements in crystals. Applying the unique method to the layered thermoelectric material (Ca₂CoO₃)_0.62CoO ₂ discloses the presence of large incommensurate displacive modulation and enhanced local vibration of atoms, largely confined within its Ca₂CoO₃ sublayers. Relating the refined disorder to ab initio calculations of scattering rates is a tremendeous challenge. Based on an approximate calculation of scattering rates, it is suggested that this well-defined deterministic disorder engenders static displacement-induced scattering and vibrational-induced resonance scattering of phonons as the origin of the phonon glass. Concurrently, the crystalline CoO₂ sublayers provide pathways for highly conducting electrons and large thermal voltages. Accurate measurement of local disorder and lattice vibration is the key to the understanding of thermoelectric mechanisms. A new method is developed to advance such measurement in layered thermoelectric (Ca₂CoO₃) _0.62CoO₂, revealing significant local atomic vibration and long-range incommensurate disorder within its soft sublayers that effectively scatter phonons. Such atomic displacements are responsible to low thermal conductivity of the material.