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Register a new userMachine Learning for Predicting Thermal Transport Properties of Solids
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Quantitative descriptions of the structure-thermal property correlation have been a bottleneck in designing materials with superb thermal properties. In the past decade, the first-principles phonon calculations using density functional theory and the Boltzmann transport equation have become a common practice for predicting the thermal conductivity of new materials. However, first-principles calculations are too costly for high-throughput material screening and multi-scale structural design. First-principles calculations also face several fundamental challenges in modeling thermal transport properties, e.g., of crystalline materials with defects, of amorphous materials, and for materials at high temperatures. In the past five years, machine learning started to play a role in solving these challenges. This review provides a comprehensive summary and discussion on the state-of-the-art, future opportunities, and the remaining challenges in implementing machine learning for studying thermal conductivity. After an introduction to the working principles of machine learning and descriptors of material structures, recent research using machine learning to study thermal transport is discussed. Three major applications of machine learning for predicting thermal properties are discussed. First, machine learning is applied to solve the challenges in modeling phonon transport of crystals with defects, in amorphous materials, and at high temperatures. Machine learning is used to build high-fidelity interatomic potentials to bridge the gap between first-principles calculations and molecular dynamics simulations. Second, machine learning can be used to study the correlation between thermal conductivity and other properties for high-throughput materials screening. Finally, machine learning is a powerful tool for structural design to achieve target thermal conductance or thermal conductivity.
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Thermal expansion in materials can be accurately modeled with careful anharmonic phonon calculations within density functional theory. However, because of interest in controlling thermal expansion and the time consumed evaluating thermal expansion properties of candidate materials, either theoretically or experimentally, an approach to rapidly identifying materials with desirable thermal expansion properties would be of great utility. When the ionic bonding is important in a material, we show that the fraction of crystal volume occupied by ions, (based upon ionic radii), the mean bond coordination, and the deviation of bond coordination are descriptors that correlate with the room-temperature coefficient of thermal expansion for these materials found in widely accessible databases. Correlation is greatly improved by combining these descriptors in a multi-dimensional fit. This fit reinforces the physical interpretation that open space combined with low mean coordination and a variety of local bond coordinations leads to materials with lower coefficients of thermal expansion, materials with single-valued local coordination and less open space have the highest coefficients of thermal expansion.
In this work, we discuss use of machine learning techniques for rapid prediction of detonation properties including explosive energy, detonation velocity, and detonation pressure. Further, analysis is applied to individual molecules in order to explore the contribution of bonding motifs to these properties. Feature descriptors evaluated include Morgan fingerprints, E-state vectors, a custom sum over bonds descriptor, and coulomb matrices. Algorithms discussed include kernel ridge regression, least absolute shrinkage and selection operator (LASSO) regression, Gaussian process regression, and the multi-layer perceptron (a neural network). Effects of regularization, kernel selection, network parameters, and dimensionality reduction are discussed. We determine that even when using a small training set, non-linear regression methods may create models within a useful error tolerance for screening of materials.
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that can be used to perform machine-learning of tensorial properties of arbitrary rank for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions (SOAP) kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous electrical response of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.
We herein present a first-principles formulation of the Green-Kubo method that allows the accurate assessment of the non-radiative thermal conductivity of solid semiconductors and insulators in equilibrium ab initio molecular dynamics calculations. Using the virial for the nuclei, we propose a unique ab initio definition of the heat flux. Accurate size- and time convergence are achieved within moderate computational effort by a robust, asymptotically exact extrapolation scheme. We demonstrate the capabilities of the technique by investigating the thermal conductivity of extreme high and low heat conducting materials, namely diamond Si and tetragonal ZrO$_2$.
We report the electrical resistivity, thermoelectric power, and thermal conductivity of single-crystalline and sintered samples of the 5d pyrochlore oxide CsW2O6. The electrical resistivity of the single crystal is 3 mohm cm at 295 K and gradually increases with decreasing temperature above 215 K (Phase I). The thermoelectric power of the single-crystalline and sintered samples shows a constant value of approximately -60 uV K-1 in Phase I. These results reflect that the electron conduction by W 5d electrons in Phase I is incoherent and in the hopping regime, although a band gap does not open at the Fermi level. The thermal conductivity in Phase I of both samples is considerably low, which might be due to the rattling of Cs+ ions. In Phase II below 215 K, the electrical resistivity and the absolute value of thermoelectric power of both samples strongly increase with decreasing temperature, corresponding to a transition to a semiconducting state with a band gap open at the Fermi level, while the thermal conductivity in Phase II is smaller than that in Phase I.
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