The microscopic origin of ultra-low thermal conductivity in Indium Tellurium

Rattling describes a situation that occurs in materials formed by loosely bound atoms within large open spaces such as oversized ‘cage structures’. When these systems are heated, the cage expands, which translates at the atomic level to an increase in the distance between the atoms. This weakens the forces between the atoms, causing the frequencies at which the atoms vibrate (phonons) to decrease. “This classical picture where increasing temperature causes the frequency to decrease is referred to as anharmonicity,” explains Michael Koza, scientist and co-responsible for the thermal neutron time-of-flight spectrometer (PANTHER) at the Institut Laue Langevin (ILL). “Something different happens, though, to the loosely bound atom within the cage. As the temperature increases, this atom vibrates with increasing amplitude until it is basically banging against the wall of the cage causing the specific frequency of the rattler to rise with increasing temperature.”

In order to reveal the effect of lone pair electrons (a pair of electrons not involved in chemical bonding and thus not shared with another atom) on thermal conductivity, the study required a system where, within the same structure type, the rattlers could be either with or without lone pair electrons. InTe proved ideal: a cage-like system with extremely low thermal conductivity at high temperatures, the rattlers can be either ions such as potassium (K) or rubidium (Rb) without lone pair electrons, or indium (In) with s² lone pair electrons.

Jiawei Zhang, working as a postdoctoral researcher at Aarhus University and now at Shanghai Institute of Ceramics, applied complex computational methods (including chemical bonding analysis, thermal conductivity calculations and harmonic and anharmonic phonon calculations) to probe the atomic dynamics of InTe. Though thermal conductivity measurements were carried out at Aarhus University, further experimentation was required in order to form a strong and convincing explanation. “With the strong support of my supervisor, Bo Iversen, to explore additional experimental techniques, I contacted Michael Koza at the ILL and Alfred Baron at the RIKEN SPring-8 Center, experts in inelastic neutron and X-ray scattering, and together an international multidisciplinary collaboration was formed,” explains Zhang.

Each theoretical and experimental technique employed within the study enabled a different question to be answered. Combined together, the techniques revealed the microscopic origin of ultra-low thermal conductivity in InTe. “Thermal conductivity measurements can quantify the very low thermal conductivity of InTe but they can’t explain why it’s so low,” explains Koza. “Inelastic neutron scattering provides the frequency distribution, basically how the atoms in the sample vibrate. Neutrons can also very quickly measure how the system behaves in response to perturbations, such as temperature, and thus indicate whether the system is harmonic, anharmonic or rattling. However, if the system is anisotropic, as is the case with InTe, you need to examine how it behaves in different directions. Though neutrons can be used for directional studies, for this study it wasn’t feasible due to the large size of the samples needed and the brittle nature of InTe. Inelastic X-ray scattering enabled the full phonon dispersion to be acquired using very small samples and providing the foundation for comparison with complex calculations which are capable of elucidating how exactly the atoms are bound to each other.” 

The inelastic neutron scattering experiments were performed using PANTHER, a state-of-the-art thermal neutron time-of-flight spectrometer at the ILL, unique in its ability to optimise not only the range of energies to measure but also the flux within that range. The higher flux achieved, compared to other equivalent instruments, was particularly valuable for this study due to the strong neutron absorbing nature of indium. “The inelastic scattering data is beautiful,” explains Zhang. “It very clearly shows that as temperature increases, the higher frequencies decrease, demonstrating the standard anharmonic nature of the overall structure. But if you look at the very low frequencies, which are particularly important for low thermal conductivity, you see they’re increasing with temperature, which is characteristic of rattling. Moreover, the magnitude of the increase is anomalously high. When a system is heated, the frequency change is typically of the order of 5-10%. In our case, the frequency of the low-lying phonons, which correspond to rattling atom motions, nearly doubled as the temperature increased, referred to as giant anharmonicity.”

The results of the comprehensive study, recently published in Angewandte Chemie International Edition, reveal for the first time the microscopic origin of giant phonon anharmonicity driven by rattling atoms with lone pair activity and its impact on thermal conductivity in InTe. “We now understand the mechanism responsible for very low thermal conductivity at high temperatures in InTe. Our next objective is to investigate whether the performance of the material can be further enhanced by slight modifications, for example, by doping,” explains Koza. “The ultimate objective of these microscopic origin studies is to achieve the design of efficient materials with ultra-low thermal conductivity that are required by a number of different technologies,” explains Zhang.