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Abstract This article attempts to summarize our understanding of heat flow in different solid materials and its relationship to atomistic structure of materials. This knowledge can be used to understand and design materials for electricity generation or cooling through the thermoelectric effect. We start with the fundamentals of heat transport in solids: mechanisms of phonon scattering in crystals, the role of interfaces and coherence, and the relationship between chemical bonding and heat transport will be elucidated. Theories used to model thermal conductivity of solids will be exposed next. They include the Green–Kubo formulation, Boltzmann transport equation and its recent quantum extensions, and Allen–Feldman theory of heat diffusion in noncrystalline solids and its recent extensions. In terms of phenomenology, we will distinguish between the kinetic regime based on independent single carriers and the collective or hydrodynamic one which occurs when normal or momentum-conserving processes dominate. Next, we will focus on advanced measurement and characterization techniques, and the knowledge extracted from them. Nanoscale thermal conductivity methods, such as the pump-probe thermoreflectance methods (TDTR/FDTR), have become fairly common allowing researchers to measure thermal conductivity of thin-film thermoelectrics. We will review recent advances of the method: the Gibbs excess approach, which measures thermal resistance across a grain boundary of polycrystals through mapping TDTR/FDTR measurements, and the transient Raman method, where pump-probe Raman spectroscopy realizes in-plane thermal conductivity measurements of two-dimensional materials even on a substrate. We will also review the progress in mode-resolved phonon property measurements, such as inelastic x-ray scattering for thin-film samples, which allows direct observation of the modulation of phonon band and lifetime by nanostructures, and thermal diffuse scattering for quick characterization of phonon dispersion relations. Finally, because the main focus of this issue is thermoelectrics, we will review different classes of materials and strategies to lower their thermal conductivities. Graphical abstract 

We introduce a lattice dynamics package which calculates elastic, thermodynamic and thermal transport properties of crystalline materials from data on their force and potential energy as a function of atomic positions. The data can come from density functional theory (DFT) calculations or classical molecular dynamics runs performed in a supercell. First, the model potential parameters, which are anharmonic force constants are extracted from the latter runs. Then, once the anharmonic model is defined, thermal conductivity and equilibrium properties at finite temperatures can be computed using lattice dynamics, Boltzmann transport theories, and a variational principle respectively. In addition, the software calculates the mechanical properties such as elastic tensor, Gruneisen parameters and the thermal expansion coefficient within the quasi-harmonic approximation (QHA). Phonons, elastic constants and thermodynamic properties results applied to the germanium crystal will be illustrated. Using the force constants as a force field, one may also perform molecular dynamics (MD) simulations in order to investigate the combined effects of anharmonicity and defect scattering beyond perturbation theory. 

Entropy stabilized oxide of MgNiCoCuZnO5, also known as J14, is a material of active research interest due to a high degree of lattice distortion and tunability. Lattice distortion in J14 plays a crucial role in understanding the elastic constants and lattice thermal conductivity within the single-phase crystal. In this work, a neuroevolution machine learning potential (NEP) is developed for J14, and its accuracy has been compared to density functional theory calculations. The training errors for energy, force, and virial are 5.60 meV/atom, 97.90 meV/Å, and 45.67 meV/atom, respectively. Employing NEP potential, lattice distortion, and elastic constants is studied up to 900 K. In agreement with experimental findings, this study shows that the average lattice distortion of oxygen atoms is relatively higher than that of all transition metals in entropy-stabilized oxide. The observed distortion saturation in the J14 arises from the competing effects of minimum site distortion, which increases with increasing temperature due to enhanced thermal vibrations, and maximum site distortion, which decreases with increasing temperature. Furthermore, a series of molecular dynamics simulations up to 900 K are performed to study the stress–strain behavior. The elastic constants, bulk modulus, and ultimate tensile strength obtained from these simulations indicate a linear decrease in these properties with temperature, as J14 becomes softer owing to thermal effects. Finally, to gain some insight into thermal transport in these materials, with the so-developed NEP potential, and using non-equilibrium molecular dynamics simulations, we study the lattice thermal conductivity (κ) of the ternary compound MgNiO2 as a function of temperature. It is found that κ decreases from 4.25 W m−1 K−1 at room temperature to 3.5 W m−1 K−1 at 900 K. This suppression is attributed to the stronger scattering of low-frequency modes at higher temperatures. 

Metavalent descriptors of LaP exhibit a stronger pressure dependence than those of LaBi. Strong anharmonicity in LaP bonds come from its antibonding π* valence bands. These features in LaP make its thermal conductivity lower than LaBi. 

This dataset includes THERMACOD, a part of the Anharmonic Lattice Dynamics (ALADYN) suite of codes. THERMACOD is an open-source software tool for ab initio calculations of phonon thermal transport in crystalline bulk materials. It solves the phonon Boltzmann transport equation either approximately, using the relaxation time approximation (RTA), or exactly, via iterative or direct methods. Additionally, this dataset contains results for phonon linewidths and thermal transport properties of Ge and GeSe. 

The compressed file ge-060-tar.gz contains the inputs to and the outputs from the code focus version 8.8 to generate force constants of 2nd and 3rd rank for Germanium 

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation–dissipation theorem and the Donsker–Furutsu–Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures.