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## Tsuneyuki Research Group |

In solids, thermal energy is mainly carried by electrons and phonons, latter of which becomes dominant in insulators and semiconductors. The magnitude of the lattice thermal conductivity \(\kappa_{L}\) varies significantly for different materials and is closely related to the lattice anharmonicity. For example, the diamond shows very high lattice thermal conductivity (\(\kappa_{L} > 1000\) W/mK) because its lattice vibration is quite harmonic. Conversely, the \(\kappa_{L}\) value of an ionic compound PbTe is very small (\(\kappa_{L} \sim 1\) W/mK), which can be attributed to the strong phonon scattering resulting from the large lattice anharmonicity. Developing a non-empirical method to calculate lattice thermal conductivity is desired not only for gaining a robust understanding of thermal transport phenomena in solids but also for optimizing the figure-of-merit of thermoelectric materials.

Our research group has been developing a versatile method to compute lattice thermal conductivity of solids.
In our approach, we first express the potential energy surface of the interacting atomic system as a Taylor expansion with respect to the atomic displacements from equilibrium positions \( \{u_{i}\}\).
The coupling coefficients are harmonic and anharmonic interatomic force constants (IFCs), which are determined by first-principles calculations based on density-functional theory (DFT).
The estimated IFCs are then employed to calculate the lattice thermal conductivity either by conducting a (non-equilibrium) molecular dynamics simulation or by solving the Boltzmann transport equation.
We applied the method to Si and a thermoelectric material Mg_{2}Si and obtained reasonable \(\kappa_{L}\) values that were comparable with experimental results [1].
The computational code developed by our group is now distributed as an open-source software [2], which can be used with any DFT packages, such as VASP and Quantum-ESPRESSO, to predict the lattice thermal conductivity.

[1] T. Tadano, Y. Gohda, and S. Tsuneyuki, J. Phys.: Condens. Matter 26, 225402 (2014).

[2] T. Tadano, ALAMODE package.

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