Evaluation of Computational Techniques for Solving the Boltzmann Transport Equation for Lattice Thermal Conductivity Calculations

Three methods for computing thermal conductivity from lattice dynamics (the iterative method, the variational method, and the relaxation-time approximation) are compared for the prototypical case of solid argon. The iterative method is found to produce results in close agreement with Green-Kubo molecular-dynamics simulations, a formally correct method for computing thermal conductivity. The variational method and relaxation-time approximation are found to underestimate the thermal conductivity. The relationship among the methods is established; a combination of the iterative and variational methods is found to have a fastest convergence. Formal convergence of the iterative method is demonstrated and a simple mixing rule is shown to provide stability in practice. The ability to use these methods to provide detailed insight into the relationship between phonon properties and thermal conductivity is demonstrated

Anharmonic Properties in Mg₂X (X= C, Si, Ge, Sn, Pb) from First-Principles Calculations

Thermal conductivity reduction is one of the potential routes to improve the performance of thermoelectric materials. However, detailed understanding of the thermal transport of many promising materials is still missing. In this paper, we employ electronic-structure calculations at the level of density functional theory to elucidate thermal transport properties of the Mg2X (X=C, Si, Ge, Sn, and Pb) family of compounds, which includes Mg2Si, a material already identified as a potential thermoelectric. All these materials crystallize into the same antifluorite structure. Systematic trends in the anharmonic properties of these materials are presented and examined. Our calculations indicate that the reduction in the group velocity is the main driver of the thermal conductivity trend in these materials, as the phonon lifetimes in these compounds are very similar. We also examine the limits of the applicability of perturbation theory to study the effect of point defects on thermal transport and find that it is in good agreement with experiment in a wide range of scattering parameter values. The thermal conductivity of the recently synthesized Mg2C is computed and predicted to be 34 W/mK at 300°C

Interfacial phonon scattering in semiconductor nanowires by molecular-dynamics simulation

We use molecular-dynamics simulations of vibrational wave packets to study the scattering of longitudinal-acoustic modes from interfaces in semiconductor nanowires of varying diameters. The energy transmission coefficient at the interface is found to depend strongly on both the nanowire diameter and the frequency of the incident wave. By analyzing the scattering events, we determine the selection rules for nanowire scattering that can be understood in terms of the representations of the point-group symmetry of the nanowire. Using such symmetry arguments, we predict that the presence of gaps in the phonon spectrum of thin high-symmetry nanowires will result in a complete reflection of phonons at the interfaces. We discuss the implications of our results for interfacial scattering in real systems, including Si/Ge superlattice nanowires

Thermal conductance across grain boundaries in diamond from molecular dynamics simulation

We determine the dependence of the interfacial conductance on twist angle for (001) symmetric twist grain boundaries (GBs) in diamond. We find that the conductances are extremely large, ranging from 7.7 to 17.6 GW/m(2) K. Nevertheless, when normalized to the single-crystal conductivity, the resulting Kapitza lengths are actually longer in diamond than in Si, indicating that the diamond GBs are relatively worse conductors of heat. This result is consistent with the poorer bonding across the diamond grain boundaries. We find that the interfacial conductance and Kapitza length can be well fitted by an extended Read-Shockley model

Kapitza Resistance of Si/SiO₂ Interface

A phonon wave packet dynamics method is used to characterize the Kapitza resistance of a Si/SiO2 interface in a Si/SiO2/Si heterostructure. By varying the thickness of SiO2 layer sandwiched between two Si layers, we determine the Kapitza resistance for the Si/SiO 2 interface from both wave packet dynamics and a direct, non-equilibrium molecular dynamics approach. The good agreement between the two methods indicates that they have each captured the anharmonic phonon scatterings at the interface. Moreover, detailed analysis provides insights as to how individual phonon mode scatters at the interface and their contribution to the Kapitza resistance

Phonon Density of States and Anharmonicity of UO2

Phonon density of states (PDOS) measurements have been performed on polycrystalline UO2 at 295 and 1200 K using time-of-flight inelastic neutron scattering to investigate the impact of anharmonicity on the vibrational spectra and to benchmark ab initio PDOS simulations performed on this strongly correlated Mott-insulator. Time-of-flight PDOS measurements include anharmonic linewidth broadening inherently and the factor of ~ 7 enhancement of the oxygen spectrum relative to the uranium component by the neutron weighting increases sensitivity to the oxygen-dominated optical phonon modes. The first-principles simulations of quasi-harmonic PDOS spectra were neutron-weighted and anharmonicity was introduced in an approximate way by convolution with wavevector-weighted averages over our previously measured phonon linewidths for UO2 that are provided in numerical form. Comparisons between the PDOS measurements and the simulations show reasonable agreement overall, but they also reveal important areas of disagreement for both high and low temperatures. The discrepancies stem largely from an ~ 10 meV compression in the overall bandwidth (energy range) of the oxygen-dominated optical phonons in the simulations. A similar linewidth-convoluted comparison performed with the PDOS spectrum of Dolling et al. obtained by shell-model fitting to their historical phonon dispersion measurements shows excellent agreement with the time-of-flight PDOS measurements reported here. In contrast, we show by comparisons of spectra in linewidth-convoluted form that recent first-principles simulations for UO2 fail to account for the PDOS spectrum determined from the measurements of Dolling et al. These results demonstrate PDOS measurements to be stringent tests for ab initio simulations of phonon physics in UO2 and they indicate further the need for advances in theory to address lattice dynamics of UO2.Comment: Text slightly modified, results unchange

Impact of Homogeneous Strain On Uranium Vacancy Diffusion In Uranium Dioxide

We present a detailed mechanism of, and the effect of homogeneous strains on, the migration of uranium vacancies in UO2. Vacancy migration pathways and barriers are identified using density functional theory and the effect of uniform strain fields are accounted for using the dipole tensor approach. We report complex migration pathways and noncubic symmetry associated with the uranium vacancy in UO2 and show that these complexities need to be carefully accounted for to predict the correct diffusion behavior of uranium vacancies. We show that under homogeneous strain fields, only the dipole tensor of the saddle with respect to the minimum is required to correctly predict the change in the energy barrier between the strained and the unstrained case. Diffusivities are computed using kinetic Monte Carlo simulations for both neutral and fully charged state of uranium single and divacancies. We calculate the effect of strain on migration barriers in the temperature range 800–1800 K for both vacancy types. Homogeneous strains as small as 2% have a considerable effect on diffusivity of both single and divacancies of uranium, with the effect of strain being more pronounced for single vacancies than divacancies. In contrast, the response of a given defect to strain is less sensitive to changes in the charge state of the defect. Further, strain leads to anisotropies in the mobility of the vacancy and the degree of anisotropy is very sensitive to the nature of the applied strain field for strain of equal magnitude. Our results suggest that the influence of strain on vacancy diffusivity will be significantly greater when single vacancies dominate the defect structure, such as sintering, while the effects will be much less substantial under irradiation conditions where divacancies dominate

Lattice Thermal Conductivity of Quartz at High Pressure and Temperature from the Boltzmann Transport Equation

The thermal conductivities along the basal and hexagonal directions of α-quartz silica, the low-temperature form of crystalline SiO2, are predicted from the solution of the Boltzmann transport equation combined with the van Beest, Kramer, and van Santen potential for the temperature up to 900 K and the pressure as high as 4 GPa. The thermal conductivities at atmospheric pressure, which show a negative and nonlinear dependence on temperature, are in reasonable agreement with the experimental data. The influence of pressure on thermal conductivity is positive and linear. The pressure (P) and temperature (T) dependences of the thermal conductivity (λ) in basal and hexagonal directions are fitted to a function of the form λ = (b + cP) Ta. The thermal conductivity, influenced by temperature and pressure, is analyzed based on phonon properties, including spectral thermal conductivity, dispersion relation, phonon density of states, phonon lifetime, and phonon probability density distribution function