We present an ab initio theoretical approach to accurately describe phonon thermal transport in semiconductors and insulators free of adjustable parameters. This technique combines a Boltzmann formalism with density functional calculations of harmonic and anharmonic interatomic force constants. Without any fitting parameters, we obtain excellent agreement (<5% difference at room temperature) between the calculated and measured intrinsic lattice thermal conductivities of silicon and germanium. As such, this method may provide predictive theoretical guidance to experimental thermal transport studies of bulk and nanomaterials as well as facilitating the design of new materials.

The lattice thermal conductivity ($\kappa$) of the thermoelectric materials, Mg${}_2$Si, Mg${}_2$Sn, and their alloys, are calculated for bulk and nanowires, without adjustable parameters. We find good agreement with bulk experimental results. For large nanowire diameters, size effects are stronger for the alloy than for the pure compounds. For example, in 200 nm diameter nanowires $\kappa$ is lower than its bulk value by 30$\%$, 20$\%$, and 20$\%$ for Mg${}_2$Si${}_{0.6}$Sn${}_{0.4}$, Mg${}_2$Si, and Mg${}_2$Sn, respectively. For nanowires less than 20 nm thick, the relative decrease surpasses 50$\%$, and it becomes larger in the pure compounds than in the alloy. At room temperature, $\kappa$ of Mg${}_2$Si${}_x$Sn${}_{1-x}$ is less sensitive to nanostructuring size effects than Si${}_x$Ge${}_{1-x}$, but more sensitive than PbTe${}_x$Se${}_{1-x}$. This suggests that further improvement of Mg${}_2$Si${}_x$Sn${}_{1-x}$ as a nontoxic thermoelectric may be possible.

We present a first-principles theoretical approach to calculate the lattice thermal conductivity of diamond based on an exact solution of the Boltzmann transport equation. Density-functional perturbation theory is employed to generate the harmonic and third-order anharmonic interatomic force constants that are required as input. A central feature of this approach is that it provides accurate representations of the interatomic forces and at the same time introduced no adjustable parameters. The calculated lattice thermal conductivities for isotopically enriched and naturally occurring diamond are both in very good agreement with experimental data. The role of the scattering of heat-carrying acoustic phonons by optic branch phonons is also investigated. We show that inclusion of this scattering channel is indispensable in properly describing the thermal conductivity of semiconductors and insulators. The accurate adjustable-parameter-free results obtained herein highlight the promise of this approach in providing predictive descriptions of the lattice thermal conductivity of materials.

Using ab initio calculations we have investigated the thermal conductivity ($\kappa$) of diamond nanowires, unveiling unusual features unique to this system. In sharp contrast with Si, $\kappa \left(T\right)$ of diamond nanowires as thick as 400 nm still increase monotonically with temperature up to 300 K, and room-temperature size effects are stronger than for Si. A marked dependence of $\kappa$ on the crystallographic orientation is predicted, which is apparent even at room temperature. [001] growth direction always possesses the largest $\kappa$ in diamond nanowires. The predicted features point to a potential use of diamond nanowires for the precise control of thermal flow in nanoscale devices.