Cumulative Thermal Conductivity Research Articles

Comparison on two ways of phonon spectral property reconstruction from thermal spectroscopy experiment

We examine the reliability of the cumulative thermal conductivity as a function of the free path, F(Λ), in the context of reconstruction of phonon transport properties from thermal spectroscopy experiments. We specifically show that a given F(Λ)does not correspond to a unique relaxation-times function, in the sense that more than one distribution of relaxation-times can result in the same F(Λ). Since different relaxation-time distributions will, in general, lead to different thermal responses, F(Λ) does not uniquely predict the material thermal response in all transport regimes. This implies that in the context of thermal transport at the nanoscale within the Boltzmann relaxation-time approximation framework, the “fundamental” property that should be reconstructed from the thermal spectroscopy experiments is the frequency-dependent relaxation-times function (provided group velocities are known), since it explicitly appears in the governing equation as the input material property. Extensive global optimization studies show that a previously proposed formulation for reconstruction based on the frequency-dependent relaxation-times function [Physical Review B 94, 155439 (2016)] provides numerically unique solutions.

MCBTE: A variance-reduced Monte Carlo solution of the linearized Boltzmann transport equation for phonons

MCBTE solves the linearized Boltzmann transport equation for phonons in three-dimensions using a variance-reduced Monte Carlo solution approach. The algorithm is suited for both transient and steady-state analysis of thermal transport in structured materials with size features in the nanometer to hundreds of microns range. The code is portable and integrated with both first-principles density functional theory calculations and empirical relations for the input of phonon frequency, group velocity, and mean free path required for calculating the thermal properties. The program outputs space- and time-resolved temperature and heat flux for the transient study. For the steady-state simulations, the frequency-resolved contribution of phonons to temperature and heat flux is written to the output files, thus allowing the study of cumulative thermal conductivity as a function of phonon frequency or mean free path. We provide several illustrative examples, including ballistic and quasi-ballistic thermal transport, the thermal conductivity of thin films and periodic nanostructures, to demonstrate the functionality and to benchmark our code against available theoretical/analytical/computational results from the literature. Moreover, we parallelize the code using the Matlab Distributed Computing Server, providing near-linear scaling with the number of processors. Program summaryProgram Title:MCBTECPC Library link to program files:https://doi.org/10.17632/rzn86w7t3p.1Developer's repository link:https://github.com/abhipath90/MCBTECode Ocean capsule:https://codeocean.com/capsule/7196257Licensing provisions: GPLv3Programming language: MATLABNature of problem: Calculation of time- and space-dependent temperature and heat flux profiles, and frequency-resolved effective thermal conductivity in structured systems where heat is carried by phonons.Solution method: Solution of linearized Boltzmann transport equation for phonons, variance-reduced Monte Carlo approach.Additional comments including restrictions and unusual features: Runtime about 1 to 10 hours on a personal computer.

First-Principles Study on Lattice Dynamics and Thermal Conductivity of Thermoelectric Intermetallics Fe3Al2Si3

Thermoelectric materials have been expected as a critical underlying technology for developing an autonomous power generation system driven at near room temperature. For this sake, Fe3Al2Si3 intermetallic compound is a promising candidate, though its high lattice thermal conductivity is a bottleneck toward practical applications. Herein, we have performed the first-principles calculations to clarify the microscopic mechanism of thermal transport and establish effective ways to reduce the lattice thermal conductivity of Fe3Al2Si3. Our calculations show that the lowest-lying optical mode has a significant contribution from Al atom vibration. It should correspond to large thermal displacements Al atoms. However, these behaviors do not directly cause an increase of the 3-phonon scattering rate. The calculated lattice thermal conductivity shows a typical temperature dependence and moderate magnitude. From the calculated thermal conductivity spectrum and cumulative thermal conductivity, we can see that there is much room to reduce the lattice thermal conductivity. We can expect that heavy-element doping on Al site and controlling fine microstructure are effective strategies to decrease the lattice thermal conductivity. This work suggests useful information to manipulate the thermal transport of Fe3Al2Si3, which will make this material closer to practical use.

Hydrostatic Pressure Tuning of Thermal Conductivity for PbTe and PbSe Considering Pressure-Induced Phase Transitions.

Flexibly modulating thermal conductivity is of great significance to improve the application potential of materials. PbTe and PbSe are promising thermoelectric materials with pressure-induced phase transitions. Herein, the lattice thermal conductivities of PbTe and PbSe are investigated as a function of hydrostatic pressure by first-principles calculations. The thermal conductivities of both PbTe and PbSe in NaCl phase and Pnma phase exhibit complex pressure-dependence, which is mainly ascribed to the nonmonotonic variation of a phonon lifetime. In addition, the thermal transport properties of the Pnma phase behave anisotropically. The thermal conductivity of Pnma-PbTe is reduced below 1.1 W/m·K along the c-axis direction at 7–12 GPa. The mean free path for 50% cumulative thermal conductivity increases from 7 nm for NaCl-PbSe at 0 GPa to 47 nm for the Pnma-PbSe in the a-axis direction at 7 GPa, making it convenient for further thermal conductivity reduction by nanostructuring. The thermal conductivities of Pnma-PbTe in the c-axis direction and Pnma-PbSe in the a-axis direction are extremely low and hypersensitive to the nanostructure, showing important potential in thermoelectric applications. This work provides a comprehensive understanding of phonon behaviors to tune the thermal conductivity of PbTe and PbSe by hydrostatic pressure.

Investigation of phonon properties and thermal behavior of UO2 crystal using density-functional theory

Understanding thermal behavior and processes underlying the heat transport of UO2 nuclear fuel in nuclear reactor plays a key role in predicting the efficiency of the fuel. If the heat transport, which is an important parameter in temperature distribution of the fuel, does not occur properly, the continuous increase of temperature would lead to the melting of the fuel and therefore, environmental hazards. In this work, by using a non-spin-polarized calculation for the simple description of the paramagnetic state and ignoring the Hubbard correction, the thermal properties and phonon properties of bulk UO2 are calculated. These calculations are based on the density-functional theory (DFT) and density-functional perturbation theory (DFPT). To determine the lattice-vibration properties by the finite-displacement method, we have calculated the second-order and third-order force constants based on which such quantities as constant-volume specific heat, Gruneisen parameter, three-phonon scattering rate, scattering rate due to different levels of isotopic enrichment, and cumulative thermal conductivity are calculated. The results of the calculated specific heat based on the harmonic approximation show a good agreement with the experimental values, specifically for temperatures lower than 400 Kelvin. The results obtained for three-phonon scattering rate reveal that the scattering rate increases with temperature, thereby leading to the decrease of thermal conductivity. The results related to different levels of isotopic enrichments do not show any sensible changes in the scattering rates.

Intrinsic Thermal conductivities of monolayer transition metal dichalcogenides MX2 (M\u2009=\u2009Mo, W; X\u2009=\u2009S, Se, Te)

The successful synthesis of the single to few layer transition metal dichalcogenides has opened a new era in the nanoelectronics. For their efficient implementations in the electronic devices while taking care of their overheating issues, the characterization of their thermal transport properties is extremely vital. So, we have systematically investigated the thermal transport properties of monolayer transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te) by combining the first-principles calculations with Boltzmann transport equation. We find that monolayer WTe2 possesses the lowest lattice thermal conductivity κL (33:66 Wm−1K−1 at 300 K) among these six semiconducting materials, in contrast to the highest κL (113:97 Wm−1K−1 at 300 K) of WS2 among them. Further analyses reveal that the higher (lower) anharmonic and isotopic scatterings together with the lower (higher) phonon group velocities lead to the lowest (highest) value of κL in WTe2 (WS2) monolayer. In addition, we have also calculated the cumulative thermal conductivity κC as a function of mean free path, which indicates that the nanostructures with the length of about 400 nm would reduce κL drastically. These results offer important understanding from thermal conductivity point of view to design the 2D transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te) electronics.

Thermal conductivity of hetero-epitaxial ZnO thin films on c- and r-plane sapphire substrates: Thickness and grain size effect

The thermal conductivities of c- and a-axis-oriented zinc oxide (ZnO) thin films with nominal thicknesses of 100, 200, and 300 nm are investigated. The c- and a-axis-oriented ZnO thin films were synthesized by radio frequency magnetron sputtering on the c- and r-plane sapphire substrates, respectively. The epitaxial relationship between the ZnO thin film and the c-plane sapphire substrate is (0001)[11¯00] || (0001)[112¯0], and that between the ZnO thin film and the r-plane sapphire substrate is (112¯0)[11¯00] || (011¯2)[112¯0]. The c-axis-oriented ZnO thin film has a columnar structure, whereas the a-axis-oriented ZnO thin film has a single domain-like structure and a significantly flat surface. The thermal conductivity of the c-axis-oriented ZnO thin film is in the range of 18–24 W m−1 K−1, whereas for the a-axis-oriented ZnO thin film, it is in the range of 24–29 W m−1 K−1. For the c-axis-oriented ZnO thin films, the phonon scattering on both the out-of-plane and in-plane grain boundaries affects the thermal conductivity. In contrast, the thermal conductivity of the a-axis-oriented ZnO thin films decreases with the decrease of the film thickness. The distribution of the normalized cumulative thermal conductivity of the a-axis-oriented ZnO thin films suggests that the heat transport carrier mostly consists of phonons with the mean free paths between 100 nm and 1 μm.

Phonon transport in Na2He at high pressure from a first-principles study

Phonon transport of recently fabricated Na2He at high pressure is investigated from a combination of first-principles calculations and the linearized phonon Boltzmann equation within the single-mode relaxation time approximation. The calculated room-temperature lattice thermal conductivity is 149.19 W m−1 K−1, which is very close to that of Si. It is found that low-frequency optical modes comprise 16% of the lattice thermal conductivity, while high-frequency optical modes have negligible contribution. The high lattice thermal conductivity is due to large group velocities, small Grüneisen parameters, and long phonon lifetimes. The size effects on lattice thermal conductivity are considered by cumulative thermal conductivity with respect to the phonon mean free path. To significantly reduce the lattice thermal conductivity, the characteristic length smaller than 100 nm is required and can reach a decrease of 36%. These results may be useful to understand thermal transport processes that occur inside giant planets.

The contribution of propagons and diffusons in heat transport through calcium-silicate-hydrates

Whether it is glass, ceramics, cement, or concrete, minimizing thermal conduction through disordered materials is a determining factor when it comes to reducing the energy consumption of cities. In this work, we explore underlying physical processes involved in thermal conduction through the disordered glue of cement, calcium-silicate-hydrates (CSH). We find that at 300 K, phonon-like propagating modes in accordance with the Boltzmann transport theory, propagons, account for more than 30% of the total thermal conductivity, while diffusons, described via the Allen-Feldman theory, contribute to the remainder. The cumulative thermal conductivity proves to be close to both equilibrium molecular dynamics calculations and experimental values. These findings help us establish different strategies, such as localization schemes (to weaken diffusons) and scattering mechanisms (to constrain propagons), for reduction of thermal conductivity of CSH without sacrificing its mechanical properties.

Coherent heat transport in 2D phononic crystals with acoustic impedance mismatch

In this work we have calculated the cumulative thermal conductivities of micro-phononic crystals formed by different combinations of inclusions and matrices at a sub-Kelvin temperature regime. The low-frequency phonon spectra (up to tens of GHz) were obtained by solving the generalized wave equation for inhomogeneous media with the plane wave expansion method. The thermal conductivity was calculated from Boltzmann transport theory highlighting the role of the low-frequency thermal phonons and neglecting phonon–phonon scattering. A purely coherent thermal transport regime was assumed throughout the structures. Our findings show that the cumulative thermal conductivity drops dramatically when compared with their bulk counterpart. Depending on the structural composition this reduction may be attributed to the phonon group velocity due to a flattening of the phonon dispersion relation, the extinction of phonon modes in the density of states or due to the presence of complete band gaps. According to the contrast between the inclusions and the matrices, three types of two dimensional phononic crystals were considered: carbon/epoxy, carbon/polyethylene and tungsten/silicon, which correspond respectively to a moderate, strong and very strong mismatch in the mechanical properties of these materials.

Heat Conduction in Nanostructured Materials Predicted by Phonon Bulk Mean Free Path Distribution

We develop a computational framework, based on the Boltzmann transport equation (BTE), with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path (MFP) distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with the frequency-dependent (FD) approach. Second, when the MFP distribution is available from theoretical models, our approach allows one to include easily the material dispersion in the calculations without discretizing the phonon frequencies for all polarizations thereby reducing considerably computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multiscale method that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon MFP distributions length. After validating our model against the FD approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has the potential to advance high-efficiency thermoelectric devices.

Scaling laws of cumulative thermal conductivity for short and long phonon mean free paths

Cumulative thermal conductivity (CTC), an accumulation function of lattice thermal conductivity with respect to the phonon mean free path (PMFP), is a useful single-crystal property to gain insight into how much nanostructuring can potentially reduce thermal conductivity. While the details of the CTC profile depend on each material, we have identified that the profile has universal features in the short and long PMFP regimes with each characteristic length scale. In each PMFP regime, by scaling the PMFP with the characteristic length derived using phenomenological models, CTC calculated based on first principles for various materials collapse on a master curve. We also find an empirical relation between the short and long PMFP characteristic length scales, which allows us to roughly estimate the onset/offset PMFP of CTC (i.e., PMFP when CTC are 10%/90% of the total thermal conductivity) only with the knowledge of bulk thermal conductivity and averaged group velocity. The finding provides a facile way to estimate the range of PMFP with noticeable contribution to lattice thermal conductivity, which is useful for designing nanostructured materials with low thermal conductivity, particularly in developing thermoelectric materials.

Assessment of the Holland model for silicon phonon-phonon relaxation times using lattice dynamics calculations

We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dynamics data. Instead, we introduce a simple method based on using cumulative thermal conductivity functions to obtain better predictions of the frequency-dependence of relaxation times.

Thermal transport in SiGe superlattice thin films and nanowires: Effects of specimen and periodic lengths

We compute the thermal conductivity of superlattice (SL) thin films and nanowires for various SL periods and total specimen lengths using nonequilibrium molecular dynamics. Both types of materials exhibit similar behaviors with respect to SL period but the thermal conductivity of the thin films exhibits a significantly higher sensitivity to the specimen length. Notably, the thermal conductivity of SL thin films is smaller than those of the corresponding nanowires for specimen lengths below approximately 35 nm. These results arise from the complex dependence of the conductivities of the interfaces and the SL components on the specimen size and period. These trends and observations are explained using a simple phonon model that builds on the relationship between the cumulative thermal conductivity and the phonon wavelength.

Mode-Dependent Phonon Transport Analysis of Silicon Crystal by Molecular Dynamics Method

In this work, we have investigated phonon transport in silicon crystal using molecular dynamics and lattice dynamics methods. The phonon relaxation time is derived from molecular phase space trajectories through two different analysis methods using normal mode projection and spectral energy density. By performing the calculations for wavevectors spanning the entire first Brillouin zone, we find that these two relaxation-time calculation methods give almost the same results despite the fundamental difference in the underlying theories. With the obtained phonon relaxation time and group velocity calculated by lattice dynamics method, we have quantified the contribution from each phonon mode to the overall thermal conductivity. In addition, by calculating the cumulative thermal conductivity, we have quantified contributions to thermal conductivity from phonons with different mean free paths to gain insight into the scale effect of heat conduction in nanoscale.