Thermal conductivity in intermetallic clathrates: A first-principles perspective

Abstract

Inorganic clathrates such as Ba8GaxGe46−x and Ba8GaxSi46−x commonly exhibit very low thermal conductivities. A quantitative computational description of this important property has proven difficult, in part due to the large unit cell, the role of disorder, and the fact that both electronic carriers and phonons contribute to transport. Here, we conduct a systematic analysis of the temperature and composition dependence of low-frequency modes associated with guest species in Ba8GaxGe46−x and Ba8AlxSi46−x ("rattler modes"), as well as of thermal transport in stoichiometric Ba8Ga16Ge30. To this end, we account for phonon-phonon interactions by means of temperature dependent effective interatomic force constants (TDIFCs), which we find to be crucial in order to achieve an accurate description of the lattice part of the thermal conductivity. While the analysis of the thermal conductivity is often largely focused on the rattler modes, here, it is shown that at room temperatures modes with ω 10 meV account for 50% of lattice heat transport. Finally, the electronic contribution to the thermal conductivity is computed, which shows the Wiedemann-Franz law to be only approximately fulfilled. As a result, it is crucial to employ the correct prefactor when separating electronic and lattice contributions for experimental data. arXiv:1807.01502v2 [cond-mat.mtrl-sci]

Efficient construction of linear models in materials modeling and applications to force constant expansions

“…In this section, we are concerned with the inorganic clathrate Ba 8 Ga 16 Ge 30 , in which the motion of Ba atoms is strongly anharmonic 29 . This manifests itself in a strong temperature dependence of vibrational modes associated with Ba 49 and moreover has implications for the thermal conductivity 30,33,49 . While perturbation theory formally provides an expression for the temperature induced phonon frequency shifts caused by the third-order FC terms 14 , one commonly carries the expansion at least to the next higher even order, when analyzing frequency shifts 30,33,50 .…”

“…Instead, one can consider general displacement patterns, involving many (or all) atoms in the supercell, and then employ regression techniques to reconstruct the underlying FCs. This approach has been shown to produce accurate higher order FCs 1,7,9,10,[30][31][32][33] but can also be used to construct effective FC models 20,21,30,34 . The force acting on atom i along α can be written as…”

“…In the present case, in which we focus on the third-order FCs we effectively obtain only one such hyperparameter, namely the third-order cutoff. The number of cutoff parameters increases with the expansion order and in more complex materials can require fine tuning e.g., between different atomic species or crystallographic sites 30 . In such situations it can be advantageous to employ generic feature selection algorithms.…”

“…The low thermal conductivity of inorganic clathrates is often attributed to the rattling motion of the guest species 29,49 . These modes exhibit a notable temperature dependence 49 that needs to be accounted for in order to predict the thermal conductivity accurately 30,33 . The common approach to Boltzmann transport theory, however, only considers terms up to third-order and neglects the temperature dependence of the phonon frequencies.…”

“…The common approach to Boltzmann transport theory, however, only considers terms up to third-order and neglects the temperature dependence of the phonon frequencies. The fourth-order model allows us to investigate the temperature dependence of the frequency spectrum and include this effect when calculating the thermal conductivity via the temperature-dependent FCs approach 30,34,53 . Yet instead of training effective third-order models from ab-initio MD simulations, we train them against snapshots and forces generated from MD simulations using the full fourth-order model.…”