High-Throughput Prediction of the Thermal and Electronic Transport Properties of Large Physical and Chemical Spaces Accelerated by Machine Learning: Charting the ZT of Binary Skutterudites

Thermal and electronic transport properties are the keys to many technological applications of materials. Thermoelectric, TE, materials can be considered a singular case in which not only one but three different transport properties are combined to describe their performance through their TE figure of merit, ZT. Despite the availability of high-throughput experimental techniques, synthesizing, characterizing, and measuring the properties of samples with numerous variables affecting ZT are not a cost- or time-efficient approach to lead this strategy. The significance of computational materials science in discovering new TE materials has been running in parallel to the development of new frameworks and methodologies to compute the electron and thermal transport properties linked to ZT. Nevertheless, the trade-off between computational cost and accuracy has hindered the reliable prediction of TE performance for large chemical spaces. In this work, we present for the first time the combination of new ab initio methodologies to predict transport properties with machine learning and a high-throughput framework to establish a solid foundation for the accurate prediction of thermal and electron transport properties. This strategy is applied to a whole family of materials, binary skutterudites, which are well-known as good TE candidates. Following this methodology, it is possible not only to connect ZT with the experimental synthetic (carrier concentration and grain size) and operando (temperature) variables but also to understand the physical and chemical phenomena that act as driving forces in the maximization of ZT for p-type and n-type binary skutterudites.

applications of materials.Thermoelectric, TE, materials can be considered a singular case in which not only one but three different transport properties are combined to describe their performance through their TE figure of merit, ZT .Despite the availability of high-throughput experimental techniques, synthesizing, characterizing, and measuring properties of samples with numerous variables affecting ZT is not a cost-or timeefficient approach to lead this strategy.The significance of Computational Materials Science in discovering new TE materials has run in parallel to the development of new frameworks and methodologies to compute the electron and thermal transport properties linked to ZT .Nevertheless, the trade-off between computational cost and accuracy has hindered the reliable prediction of TE performance for large chemical spaces.In this work, we present for first the time the combination of new ab-initio methodologies to predict transport properties with machine learning and a high-throughput framework to establish a solid foundation for the accurate prediction of thermal and electron transport properties.This strategy is applied to a whole family of materials, binary skutterudites, which are well-known as good TE candidates.Following this methodology, it is not only possible to connect ZT with the experimental synthetic (carrier concentration and grain size) and operando (temperature) variables but also to understand the physical and chemical phenomena that act as driving forces in the maximization of ZT for p-type and n-type binary skutterudites.

Electronic transport properties -AMSET
AMSET code solves the BTE for electrons without the RTA.Scattering rates are calculated using the Matthiesen's rule: where τ ADP , τ IMP , τ ADP and τ MFP represent the scattering times due to the acoustic deformation potential, ionized impurities, polar optical phonons and grain boundaries, respectively.
Piezoelectric scattering has not been included due to the centrosymmetric nature of skutterudites.The mode-dependent scattering rates, from state |nk⟩ to state |mk + q⟩, are calculated using the Fermi's golden rule: with ε being the electron energy, δ the Dirac delta function, and g the coupling matrix element.
Electron transport properties were computed by the generalized transport coefficients, where α and β represent cartesian coordinates, αβ (ε) is the spectral conductivity, ε F is the Fermi level at a doping concentration and temperature and f 0 is the Fermi-Dirac distribution.
Finally, electronic transport properties are calculated as, Required material parameters for the calculation of scattering times are obtained through DFT calculations.Dense uniform band structure and wave function coefficients are obtained through single point calculations of the fully relaxed primitive cells.Wavefunction was considered converged when the energy difference between two consecutive electronic steps was smaller than 10 −8 eV, using a dense mesh of 10 × 10 × 10 k-points and the HSE06 functional proposed by Heyd et al. 1 Deformation potential, D nk , is calculated as, where S is the uniform stress tensor and ε nk is the energy of a band in a specific k-point.
The deformation potential is averaged over contraction (-0.5 %) and expansion (+0.5 %) of the lattice and calculated separately for each component of the strain tensor.Eigenvalues are aligned to the average energy level of the core states which are calculated using the initial-state approximation. 2,3Calculated dielectric constants and effective polar phonon frequency are obtained using density functional perturbation theory (DFPT) 4,5 using the PBE functional. 6Due to the strong dependence between the band gap and the high-frequency dielectric constant, our values have been corrected considering the linear correlation found between the computed and experimental values (Fig. 3).Effective phonon frequency is determined from the phonon frequencies and phonon eigenvectors.To capture scattering from the full phonon band structure in a single phonon frequency, each phonon mode is weighted by the dipole moment.
Transport properties calculations were conducted under p-and n-type doping conditions within a range from 10 17 to 10 20 cm −3 , and the temperature range from 300 to 1000 K.
Ionized impurity scattering was calculated using a charge of ±1 for the impurity.In order to ensure converged properties, interpolation factor was set to 50 for all calculations and the energy cutoff used to determine which bands to include in the interpolation and scattering rate calculation was set to 1.5 eV.