Phonon-mediated Thermal Transport Research Articles

Thermal conductivity suppression in uranium-doped thorium dioxide due to phonon-spin interactions

In this work, impact of low level of uranium (U) atom substitution on thermal conductivity of thorium dioxide (ThO2) is investigated. ThO2 is an electronic insulator with a wide optical band-gap and no unpaired electrons whose thermal transport is governed by phonons. U-substitution introduces unpaired f-electrons resulting in paramagnetic behavior of UThO2 at room temperature, which significantly suppresses its thermal conductivity. A single crystal of UThO2 with graded composition of U is grown using a hydrothermal synthesis method, and thermal conductivity measurements are performed in regions with uniform composition of U at levels of 0%, 6%, 9% and 16%. Measured thermal conductivity profiles over 77–300 K temperature range are analyzed using an analytical expression for phonon-mediated thermal transport based on Klemens-Callaway model. Temperature dependent thermal conductivity is found to deviate significantly from the Rayleigh scattering trend expected for a simple substitutional point defect with a small perturbation to mass and interatomic forces. With the resonant scattering term, observed large suppression of thermal conductivity at low temperatures can be closely reproduced. Additionally, the extracted phonon-spin coupling constants imply a nonlinear relation of phonon-spin interaction intensity with respect to U doping percentage. Our study reveals how phonon-spin scattering contributed by unpaired f-electrons in U atoms influences thermal transport in the UThO2 system.

A combined theoretical-experimental investigation of thermal transport in low-dose irradiated thorium dioxide

During reactor operation, nuclear fuels are subject to extreme temperature and irradiation conditions which can significantly degrade the fuel's thermal transport properties. The reduction in thermal conductivity of the fuel as a result of irradiation-induced lattice defects is arguably the most important fuel performance metric in regard to reactor efficiency and safety. Because thorium dioxide (ThO2) is suitable as a model system for more complex materials such as UO2 and its mixed oxides, we present a theoretical investigation of thermal conductivity reduction seen in defect-bearing thorium dioxide and compare directly to experimental measurements. Phonon-mediated thermal transport of the fuel is modeled by a solution to the Boltzmann transport equation (BTE) for phonons. A cluster dynamics (CD) model for lattice defect evolution during irradiation predicts defect densities which are used as input to the BTE for modeling phonon-defect scatterings. Phonon scatterings by lattice defects include those from point defects and vacancy clusters and interstitial clusters of various sizes. The CD model is benchmarked against structural defect characterization of irradiated thorium dioxide using electron microscopy. Thermal conductivity predicted by the BTE model is compared to measured values for irradiated thorium dioxide specimens below room temperature to isolate effects of phonon-defect scattering from intrinsic 3-phonon processes, which dominate at higher temperatures. The computed conductivity values are in partial agreement at temperatures close to room temperature while slight deviations are observed at the lowest measured temperatures, suggesting that implemented phonon-defect scattering cross-section expressions may not be adequate for low temperatures. The presented work provides a necessary investigation of the influence of irradiation induced defects on fuel performance and represents a first step toward a full characterization of phonon mediated thermal transport in irradiated materials with complex defect microstructure.

Perspective on multi-scale simulation of thermal transport in solids and interfaces.

Phonon-mediated thermal transport is inherently multi-scale. The wave-length of phonons (considering phonons as waves) is typically at the nanometer scale; the typical size of a phonon wave energy packet is tens of nanometers, while the phonon mean free path (MFP) can be as long as microns. At different length scales, the phonons will interact with structures of different feature sizes, which can be as small as 0D defects (point defects), short to medium range linear defects (dislocations), medium to large range 2D planar defects (stacking faults and twin boundaries), and large scale 3D defects (voids, inclusions, and various microstructures). The nature of multi-scale thermal transport is that there are different heat transfer physics across different length scales and in the meantime the physics crossing the different scales is interdependent and coupled. Since phonon behavior is usually mode dependent, thermal transport in materials with a combined micro-/nano-structure complexity becomes complicated, making modeling this kind of transport process very challenging. In this perspective, we first summarize the advantages and disadvantages of computational methods for mono-scale heat transfer and the state-of-the-art multi-scale thermal transport modeling. We then discuss a few important aspects of the future development of multi-scale modeling, in particular with the aid of modern machine learning and uncertainty quantification techniques. As more sophisticated theoretical and computational methods continue to advance thermal transport predictions, novel heat transfer physics and thermally functional materials will be discovered for the pertaining energy systems and technologies.

Thermal transport in nanoporous holey silicon membranes investigated with optically induced transient thermal gratings

In this study, we use transient thermal gratings—a non-contact, laser-based thermal metrology technique with intrinsically high accuracy—to investigate room-temperature phonon-mediated thermal transport in two nanoporous holey silicon membranes with limiting dimensions of 120 nm and 250 nm, respectively. We compare the experimental results with ab initio calculations of phonon-mediated thermal transport according to the phonon Boltzmann transport equation (BTE) using two different computational techniques. We find that the calculations conducted within the Casimir framework, i.e., based on the BTE with the bulk phonon dispersion and diffuse scattering from surfaces, are in quantitative agreement with the experimental data and thus conclude that this framework is adequate for describing phonon-mediated thermal transport in silicon nanostructures with feature sizes of the order of 100 nm.

A Study on Phonon-Mediated Thermal Transport and Lattice Thermal Conductivity Prediction Using First-Principles Calculations

The systematic theoretical approaches and atomistic simulation programs to predict thermal properties of crystalline nanostructured materials within first-principles framework are studied here. Recent progress in computational power has enabled an accurate and reliable way to investigate nanoscale thermal transport in crystalline materials using first-principles based calculations. Extracting a large set of anharmonic force constants with low computational effort remains a big challenge in lattice dynamics and condensed-matter physics. This paper focuses on recent progress in first-principles phonon calculations for semiconductor materials and summarizes advantages and limitations of each approach and simulation programs by comparing accuracy of numerical solutions, computational load and calculating feasibility to a wide range of crystalline materials. This work also reviews and presents the coupling model of first-principles molecular dynamic (FPMD) approach that can extract anharmonic force constants directly and solution of linearized Boltzmann transport equation to predict phonon-mediated lattice thermal conductivity of crystalline materials.

Thermal transport across nanoscale damage profile in sapphire irradiated by swift heavy ions

We studied the degradation of thermal conductivity in single crystal sapphire (α-Al2O3) irradiated by 167 MeV Xe swift heavy ions (SHIs) over the multiple fluences in the range of 1012–1014 ions/cm2. Thermal conductivity was measured primarily in the cross-plane direction using a noncontact ultrafast optical pump-probe technique called picosecond time domain thermoreflectance (TDTR). Multiple samples with variable ion fluences allowed us to probe distinct regions resulting from different regimes of microstructure evolution caused by electronic energy loss. By tuning the penetration depth of the thermal waves using different modulation frequencies, two regions with distinct conductivities were identified and the values of which were found to be consistent with phonon-mediated thermal transport models while the microstructure was confirmed by electron microscopy characterization. These damaged regions were determined to be a several micrometer thick ion track region and several tens of nanometer-thick amorphous layer present only above 5.0 × 1013 ions/cm2. These results demonstrate the applicability of TDTR to resolve thermal transport behavior in SHI irradiated oxides having nonhomogeneous damage profile on a nanometer scale. The presented approach facilitates future studies aiming at resolving the impact of distinct damage resulting from electronic and nuclear stopping regimes under irradiation.

Transient grating spectroscopy: An ultrarapid, nondestructive materials evaluation technique

Abstract

Passing waves from atomistic to continuum

Progress in the development of coupled atomistic–continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic–continuum interface. This problem is mainly caused by the difference in material descriptions between the atomistic and continuum models, which results in a mismatch in phonon dispersion relations. In this work, we introduce a new method based on atomistic dynamics of lattice coupled with a concurrent atomistic–continuum method to enable a full phonon representation in the continuum description. This permits the passage of short-wavelength, high-frequency phonon waves from the atomistic to continuum regions. The benchmark examples presented in this work demonstrate that the new scheme enables the passage of all allowable phonons through the atomistic–continuum interface; it also preserves the wave coherency and energy conservation after phonons transport across multiple atomistic–continuum interfaces. This work is the first step towards developing a concurrent atomistic–continuum simulation tool for non-equilibrium phonon-mediated thermal transport in materials with microstructural complexity.

Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes

Knowledge of the mean-free-path distribution of heat-carrying phonons is key to understanding phonon-mediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A noncontact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15--1500 nm in thickness. A decrease in the thermal conductivity from 74--13% of the bulk value is observed over this thickness range, which is attributed to diffuse phonon boundary scattering. Due to the well-defined relation between the membrane thickness and phonon mean-free-path suppression, combined with the range and accuracy of the measurements, we can reconstruct the bulk thermal conductivity accumulation vs. phonon mean free path, and compare with theoretical models.

Molecular dynamics study of phonon-mediated thermal transport in a Ni50Al50 melt: case analysis of the influence of the process on the kinetics of solidification

The phonon-mediated contribution to the thermal transport properties of liquid NiAl alloy is investigated in detail over a wide temperature range. The calculations are performed in the framework of equilibrium molecular dynamics making use of the Green–Kubo formalism and one of the most reliable embedded-atom method potentials for the intermetallic alloy. The phonon-mediated contribution to the thermal conductivity of the liquid alloy is calculated at equilibrium as well as for the steady state. The relative magnitude of the thermal conductivity decrease induced by the transition to the steady state is estimated to be less than 2% below 2000 K and less than 1% at 3000 and 4000 K. It is also found that the phonon-mediated contribution to the thermal conductivity of the liquid alloy can be accurately estimated (well within 1%) on the basis of an approximation which invokes the straightforwardly accessible microscopic expression for the total heat flux without demanding calculations of the partial enthalpies needed for the precise evolution of the reduced heat flux (pure heat conduction). On the basis of these calculations, the correspondence between the experimentally observed and modelled kinetics of solidification due to a difference in thermal conductivity is discussed.

Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation

The relaxation of an one-dimensional transient thermal grating (TTG) in a medium with phonon-mediated thermal transport is analyzed within the framework of the Boltzmann transport equation (BTE), with the goal of extracting phonon mean free path (MFP) information from TTG measurements of non-diffusive phonon transport. Both gray-medium (constant MFP) and spectrally dependent MFP models are considered. In the gray-medium approximation, an analytical solution is derived. For large TTG periods compared to the MFP, the model yields an exponential decay of grating amplitude with time in agreement with Fourier's heat diffusion equation, and at shorter periods, phonon transport transitions to the ballistic regime, with the decay becoming strongly non-exponential. Spectral solutions are obtained for Si and PbSe at 300 K using phonon dispersion and lifetime data from density functional theory calculations. The spectral decay behaviors are compared to several approximate models: a single MFP solution, a frequency-integrated gray-medium model, and a “two-fluid” BTE solution. We investigate the utility of using the approximate models for the reconstruction of phonon MFP distributions from non-diffusive TTG measurements.

Resonant Oscillations in Multiple-Filled Skutterudites

Partially filled skutterudites were investigated by ultrafast spectroscopy using a femtosecond laser system, which excites resonant oscillations due to the host–guest interactions. To investigate the effect of individual guest elements on phonon-mediated thermal transport, four skutterudite samples were studied: three samples partially filled with Ba, Yb, and La, respectively, and a fourth with a combination of these three elements. The spectrum of the oscillations in the transient thermoreflectance signal was analyzed by Fourier transformation. Comparison with the Raman spectra shows that different guest elements cause resonant oscillations with different frequencies, which can scatter phonons in different spectrum spans. This further demonstrates that multiple guest elements can scatter a wider spectrum of phonons than a single guest element at similar filling fractions, which results in lower lattice thermal conductivity (jL) in skutterudites. These findings are consistent with thermal conductivity measurements reported previously.

Onset of size effects in lattice thermal conductivity and lifetime of low-frequency thermal phonons

ABSTRACTThe onset of size effects in phonon-mediated thermal transport along a thin film at temperatures comparable or greater than the Debye temperature is analyzed theoretically. Assuming a quadratic frequency dependence of phonon relaxation rates in the low-frequency limit, a simple closed-form formula for the reduction of the in-plane thermal conductivity of thin films is derived. The effect scales as the square root of the film thickness, which leads to the prediction of measurable size-effects even at “macroscopic” distances ~100 μm. However, this prediction needs to be corrected to account for the deviation from the ω−2 dependence of phonon lifetimes at sub-THz frequencies due to the transition from Landau-Rumer to Akhiezer mechanism of phonon dissipation.