Effect of Nanopores on the Phonon Conductivity of Crystalline CoSb3: A Molecular Dynamics Study

Molecular dynamics simulations have been performed to investigate the effect of nanometer-size pores on the phonon conductivity of single-crystal bulk CoSb₃. The cylindrical pores are uniformly distributed along two vertical principal crystallographic directions of a square lattice. Because pore diameter and porosity are two key factors that could affect the performance of the materials, they were varied individually in the ranges a ₀–6a ₀ and 0.1–5%, respectively, where a ₀ is the lattice constant of CoSb₃. The simulation results indicate that the phonon conductivity of nanoporous CoSb₃ is significantly lower than that of no-pore CoSb₃. The reduction of phonon conductivity in this simulation was consistent with the ballistic–diffusive microscopic effective medium model, demonstrating the ballistic character of phonon transport when the phonon mean-free-path is comparable with or larger than the pore size. Reducing pore diameter or increasing porosity are alternative means of effective reduction of the thermal conductivity of CoSb₃. These results are expected to provide a useful basis for the design of high-performance skutterudites.     

Monte Carlo Simulations of Thermal Conductivity in Nanoporous Si Membranes

We present a Monte Carlo study of heat transport in Si nanomeshes. Phonons are treated semiclassically as particles of specific energy and velocity that undergo phonon–phonon scattering and boundary scattering on the surfaces of the nanomesh pores. We investigate the influence of: (1) geometric parameters such as the pore arrangement/randomness and porosity, and (2) the roughness amplitude of the pore surfaces on the thermal conductivity of the nanomeshes. We show that the nanomesh porosity has a strong detrimental influence on the thermal conductivity. Boundary roughness still degrades the thermal conductivity, but its influence is smaller.     

Al2O3纳米复合陶瓷涂层激光熔覆试验研究

本文将等离子喷涂与激光熔覆工艺相结合 ,进行了纳米Al2 O3复合涂层的激光熔覆试验 ,分析了各工艺参数对熔覆工艺的影响 ,研究了熔覆过程中纳米陶瓷材料晶粒生长过程 ,得到了较为合理的纳米Al2 O3激光熔覆工艺。通过SEM、X射线衍射、摩擦磨损试验等手段对得到的复合涂层进行了微观组织、磨损性能等检测。结果表明 :采用优化的熔覆工艺 ,纳米Al2 O3熔覆材料的晶粒生长得到极大抑制 ,保持纳米结构 ,其在复合涂层常规材料表面与空洞间隙中紧密排列 ,极大提高了涂层质量与性能     

Phonon Scattering and Thermal Conductivity in p‐Type Nanostructured PbTe‐BaTe Bulk Thermoelectric Materials

Transmission electron microscopy studies show that a PbTe‐BaTe bulk thermoelectric system represents the coexistence of solid solution and nanoscale BaTe precipitates. The observed significant reduction in the thermal conductivity is attributed to the enhanced phonon scattering by the combination of substitutional point defects in the solid solution and the presence of high spatial density of nanoscale precipitates. In order to differentiate the role of nanoscale precipitates and point defects in reducing lattice thermal conductivity, a modified Callaway model is proposed, which highlights the contribution of point defect scattering due to solid solution in addition to that of other relevant microstructural constituents. Calculations indicate that in addition to a 60% reduction in lattice thermal conductivity by nanostructures, point defects are responsible for about 20% more reduction and the remaining reduction is contributed by the collective of dislocation and strain scattering. These results underscore the need for tailoring integrated length‐scales for enhanced heat‐carrying phonon scattering in high performance thermoelectrics.     

Heat conduction in microstructured materials

The phonon Boltzmann equation is solved numerically in order to study the phonon thermal conductivity of micro/nanostructured thin films with open holes in a host material. We focused on the size effect of embedded pores and film thickness on the decrease in thermal conductivity of the film. Simulations have revealed that the temperature profiles in the micro/nanostructured materials are very different from those in their bulk counterparts, due to the ballistic nature of the microscale phonon transport. These simulations clearly demonstrate that the conventional Fourier heat conduction equation cannot be applied to study heat conduction in solids at microscale. The effective thermal conductivity of thin films with micro/nanoholes is calculated from the applied temperature difference and the heat flux. In the present paper, the effective thermal conductivity is shown as a function of the size of the micro/nanoholes and the film thickness. For example, when the size of the hole becomes approximately 1/20th the phonon mean free path in a film, the thickness is 1/10th the mean free path of phonons and the effective thermal conductivity decreases to as low as 6% of the bulk value. The distribution of holes also affects the reduction in the effective thermal conductivity. Thin films embedded with staggered-hole arrays have slightly lower effective thermal conductivities than films with aligned-hole arrays. The cross-sectional area in the thermal transport direction is a significant parameter with respect to the reduction of thermal conductivity. The results of the present study may prove useful in the development of artificial micro/nanostructured materials, including thermoelectrics and low-k dielectrics.     

Full-wave computation of constitutive parameters for losslesscomposite chiral materials

Composite chiral materials are realized by embedding large numbers of handed inclusions within a host material. A computational methodology is presented whereby the effective constitutive parameters of artificial chiral materials are computed while accounting for all self and mutual interactions among the inclusions. This technique combines a full-wave, Monte-Carlo scattering solution for randomly oriented inclusions together with an analytical solution for the scattering by a canonically-shaped body having a properly chosen constitutive model. It is believed that the effective constitutive parameters shown in this paper are the first full-wave computation of these quantities to appear in the literature     

Calculation and measurement of the effective chirality parameter ofa composite chiral material over a wide frequency band

Materials that are effectively chiral at microwave frequencies can be fabricated by embedding identical, randomly oriented chiral inclusions, often metal helices, in a continuous matrix. We show that the chirality parameter can be calculated in the dilute limit using single scattering theory. The required tumble-averaged forward scattering by an individual inclusion is determined by the method of moments. Values of the effective chirality parameter are determined directly from the constitutive parameters of the matrix and the geometry and concentration of the inclusions. Comparisons are made with measurements previously reported in the literature. In addition, a chiral composite material was fabricated specifically to validate the calculations over frequencies including resonance. The measurements agree well with the calculations, providing quantitative values of the chirality parameter over a wide frequency band. It appears that the chirality parameter is appreciable only near the resonant frequencies of the inclusion. Finally, it is clear that an oscillator model can be used to describe the frequency dependence of the complex chirality parameter, and that therefore our results are consistent with the Kramers-Kronig relation     

Correlation between microstructure and drastically reduced lattice thermal conductivity in bismuth telluride/bismuth nanocomposites for high thermoelectric figure of merit

The concept of nanocomposite/nanostructuring in thermoelectric materials has been proven to be an effective paradigm for optimizing the high thermoelectric performance primarily by reducing the thermal conductivity. In this work, we have studied the microstructure details of nanocomposites derived by incorporating a semi-metallic Bi nanoparticle phase in Bi₂Te₃ matrix and its correlation mainly with the reduction in the lattice thermal conductivity. Incorporating Bi inclusion in Bi₂Te₃ bulk thermoelectric material results in a substantial increase in the power factor and simultaneous reduction in the thermal conductivity. The main focus of this work is the correlation of the microstructure of the composite with the reduction in thermal conductivity. Thermal conductivity of the matrix and nanocomposites was derived from the thermal diffusivity measurements performed from room temperature to 150 °C. Interestingly, significant reduction in total thermal conductivity of the nanocomposite was achieved as compared to that of the matrix. A detailed analysis of high-resolution transmission electron microscope images reveals that this reduction in the thermal conductivity can be ascribed to the enhanced phonon scattering by distinct microstructure features such as interfaces, grain boundaries, edge dislocations with dipoles, and strain field domains.     

Effect of Nonlinearity of the Phonon Spectrum on the Thermal Conductivity of Nanostructured Materials Based on Bi–Sb–Te

A theoretical investigation of the lattice thermal conductivity of nanostructured materials based on Bi–Sb–Te is presented. The calculations were based on relaxation time approximation and took into account both the real phonon spectra, obtained from first-principles by use of density functional theory, and the anisotropy of phonon relaxation time. Phonon relaxation time data were determined from experimental values of the lattice thermal conductivity. The decrease of the thermal conductivity caused by the nanostructure was compared with results from calculations based on the linear Debye approach. Estimation showed that phonon boundary scattering can lead to a 55% decrease of thermal conductivity for a grain size of ~20 nm in the Debye approximation. Taking the nonlinearity of the acoustic phonon spectrum into account leads to a 20% larger decrease of the thermal conductivity because of boundary scattering. The reason is that consideration of the real phonon spectrum increases the relative contribution to thermal conductivity of acoustic phonons with low frequencies that are scattered more strongly at nanograin boundaries. Similarly, estimation of lattice thermal conductivity reduction as a result of phonon scattering by nanoinclusions gave an 8% larger decrease when the real phonon spectrum was used rather than the linear Debye approximation. For such a substantial decrease of lattice thermal conductivity, the effect of the optical phonons was estimated; it was shown that optical phonons can reduce the change of thermal conductivity as a result of grain boundary scattering by no more than 10%. Finally, the minimum lattice thermal conductivity was estimated to be 0.07 W/m K because of acoustic modes (0.09 W/m K in the Debye approach) and 0.14 W/m K when the contribution of optical modes was also taken into consideration.     

Ultralow Thermal Conductivity of Single‐Crystalline Porous Silicon Nanowires

Porous materials provide a large surface‐to‐volume ratio, thereby providing a knob to alter fundamental properties in unprecedented ways. In thermal transport, porous nanomaterials can reduce thermal conductivity by not only enhancing phonon scattering from the boundaries of the pores and therefore decreasing the phonon mean free path, but also by reducing the phonon group velocity. Herein, a structure–property relationship is established by measuring the porosity and thermal conductivity of individual electrolessly etched single‐crystalline silicon nanowires using a novel electron‐beam heating technique. Such porous silicon nanowires exhibit extremely low diffusive thermal conductivity (as low as 0.33 W m^?1 K^?1 at 300 K for 43% porosity), even lower than that of amorphous silicon. The origin of such ultralow thermal conductivity is understood as a reduction in the phonon group velocity, experimentally verified by measuring the Young's modulus, as well as the smallest structural size ever reported in crystalline silicon (<5 nm). Molecular dynamics simulations support the observation of a drastic reduction in thermal conductivity of silicon nanowires as a function of porosity. Such porous materials provide an intriguing platform to tune phonon transport, which can be useful in the design of functional materials toward electronics and nanoelectromechanical systems.     

Use of Atomistic Phonon Dispersion and Boltzmann Transport Formalism to Study the Thermal Conductivity of Narrow Si Nanowires

We study the thermal properties of ultra-narrow silicon nanowires (NW) with diameters from 3 nm to 12 nm. We use the modified valence-force-field method for computation of phononic dispersion and the Boltzmann transport equation for calculation of phonon transport. Phonon dispersion in ultra-narrow 1D structures differs from dispersion in the bulk and dispersion in thicker NWs, which leads to different thermal properties. We show that as the diameter of the NW is reduced the density of long-wavelength phonons per cross section area increases, which increases their relative importance in carrying heat compared with the rest of the phonon spectrum. This effect, together with the fact that low-frequency, low-wavevector phonons are affected less by scattering and have longer mean-free-paths than phonons in the rest of the spectrum, leads to a counter-intuitive increase in thermal conductivity as the diameter is reduced to the sub-ten-nanometers range. This behavior is retained in the presence of moderate boundary scattering.     

Size-Dependent Lattice Thermal Conductivity of Nanostructured Bulk Semiconductors

Recently, nanostructuring of bulk semiconductors has emerged as an effective approach to develop high-efficiency thermoelectric materials for large-scale device applications, where the thermal conductivity reduction predominates in the enhanced figure of merit of these materials. In this work, a quantitative nanothermodynamic model was established to calculate the lattice thermal conductivity of semiconductor nanocomposites considering the interface scattering effects. It is found that the lattice thermal conductivity can be significantly reduced in nanostructured bulk semiconductors compared with their bulk counterparts. The findings in this work may provide new insights into the fundamental understanding of phonon transport in nanocomposites and also the development of high-performance thermoelectric materials.     

Modeling of multi-layered structure containing heterogeneous material layer with randomly distributed particles using infinite element method

In the electronics industry, filler particles are added to the epoxy to form a composite material in order to adjust the elastic modulus and the coefficient of thermal expansion (CTE). This paper enhances the infinite element method (IEM) for modeling and analyzing a multi-layered structure such as flip-chip assembly containing a heterogeneous material layer reinforced with randomly distributed multiple particles under thermal loading. The proposed method provides a straightforward and efficient means of modeling multiple particles since only one IE stiffness matrix of particle needs to be calculated for all of the other particles. Moreover, in analyzing the material interface problem, the proposed technique could put many number of element layers to measure the high stresses close to the edge of the multi-layered structure, and was easily applied to compare the maximum interfacial stresses near the corner.A series of problems relating to multi-layered structures containing heterogeneous materials are investigated. Initially, this study investigates the effect of varying the volume fraction of randomly arranged particles in the heterogeneous layer on the effective properties of the layer. The results obtained for the effective properties of the heterogeneous material and their influence on the interfacial stress are compared to those obtained from the Mori-Tanaka analytical method. Finally, in addition to equivalent models, three-dimensional finite element models containing multiple randomly distributed particles were built and studied. It is shown that at the free edge the interfacial stresses decrease when the number of particles close to the interface increases.     

Thermal Conductivity Reduction in a Nanophononic Metamaterial versus a Nanophononic Crystal: A Review and Comparative Analysis

The notion of a locally resonant metamaterial—widely applied to light and sound—has recently been introduced to heat, whereby the thermal conductivity is reduced primarily by intrinsic localized atomic vibrations rather than scattering mechanisms. This article reviews and analyzes this new emerging concept, termed nanophononic metamaterial (NPM), and contrasts it with the competing concept of a nanophononic crystal (NPC) in which thermal conductivity reduction is realized primarily via nanoscale Bragg scattering. Both the NPM and NPC core mechanisms require the presence of a sufficient level of wave behavior, which is possible when there is a relatively wide distribution of the phonon mean free path (MFP). Silicon serves as a perfect material to form NPMs and NPCs given its relatively large average phonon MFP. This offers a unique opportunity considering silicon's abundance and mature fabrication technology. It is shown in this comparative study that while both the NPM and NPC nanosystems may be rendered to serve as extreme insulators of heat, an NPM may do so without excessive reduction in the minimum feature size–which is key to keeping the electrical properties intact. This trait makes a silicon‐based NPM poised to serve as a low‐cost thermoelectric material with exceptional performance.     

Analyzing the Boundary Thermal Resistance of Epitaxially Grown Fe<Subscript>2</Subscript>VAl/W Layers by Picosecond Time-Domain Thermoreflectance

To gain deep insight into the mechanism of phonon scattering at grain boundaries, we investigated the boundary thermal resistance by using picosecond pulsed-laser time-domain thermoreflectance for epitaxially grown W/Fe₂VAl/W films. By using radio-frequency magnetron sputtering, we prepared a series of the three-layer films whose Fe₂VAl thickness ranged from 1 nm to 37 nm. The fine oscillation of reflectivity associated with the top W layer clearly appeared in synchrotron x-ray reflectivity measurements, indicating a less obvious mixture of elements at the boundary. The areal heat diffusion time, obtained from the time-domain thermoreflectance signal in the rear-heating front-detection configuration, reduced rapidly in samples whose Fe₂VAl layer was thinner than 15 nm. The ～ 10% mismatch in lattice constant between Fe₂VAl and W naturally produced the randomly distributed lattice stress near the boundary, causing an effective increase of boundary thermal resistance in the thick samples, but the stress became homogeneous in the thinner layers, which reduced the scattering probability of phonons.     

FF／FB媒质等效电磁参数的数值计算

FF/FB（feedforward/feedbackward)媒质是近年来提出的人工合成复杂媒质采用全波数值方法对FF/FB媒质中单个填充单元在平面电磁波照射下的极化和磁特性进行了分析,计算了平面电磁波垂直入射和斜入射时FF/FB媒质的等效电磁参数。建立了电偶极子-磁偶极子FF/FB物理模型,该数值方法可用于分析由任意结构（形状）前后端振子组成的FF/FB媒质的等效电磁参数。     

Thermal Conductivity and Phonon Scattering Processes of ALD Grown PbTe–PbSe Thermoelectric Thin Films

This work studies the thermal conductivity and phonon scattering processes in a series of n‐type lead telluride‐lead selenide (PbTe–PbSe) nanostructured thin films grown by atomic layer deposition (ALD). The ALD growth of the PbTe–PbSe samples in this work results in nonepitaxial films grown directly on native oxide/Si substrates, where the Volmer–Weber mode of growth promotes grains with a preferred columnar orientation. The ALD growth of these lead‐rich PbTe, PbSe, and PbTe–PbSe thin films results in secondary oxide phases, along with an increase microstructural quality with increased film thickness. The compositional variation and resulting point and planar defects in the PbTe–PbSe nanostructures give rise to additional phonon scattering events that reduce the thermal conductivity below that of the corresponding ALD‐grown control PbTe and PbSe films. Temperature‐dependent thermal conductivity measurements show that the phonon scattering in these ALD‐grown PbTe–PbSe nanostructured materials, along with ALD‐grown PbTe and PbSe thin films, are driven by extrinsic defect scattering processes as opposed to phonon–phonon scattering processes intrinsic to the PbTe or PbSe phonon spectra. The implication of this work is that polycrystalline, nanostructured ALD composites of thermoelectric PbTe–PbSe films are effective in reducing the phonon thermal conductivity, and represent a pathway for further improvement of the figure of merit (ZT), enhancing their thermoelectric application potential.     

A Thermal Conductivity Model for Micro-Nanoscale Diamond Thin Films Using Dispersion Curve Data

Thermal conductivity is investigated for a cubic C (diamond). Boundary scattering, Umklapp processes, normal processes, and the presence of impurities are the mechanisms considered for heat flow resistance. Three symmetry directions [001], [110], [111], and three polarizations for each direction in the first Brillouin zone are considered for the material. The main purpose of this study is to analyze the effect of the curvature of phonon dispersion curves on the thermal conductivity, and develop an accurate model. The model incorporates the effects of impurity and impurity concentration, film thickness, and crystal orientation on thermal conductivity. The model is validated by comparing results with experimental data for diamond in the [111] direction. The model is then used for the other symmetry directions using the appropriate dispersion curves. The results show that the curvature of the dispersion curves dramatically affects the thermal conductivity. A sensitivity analysis is conducted to study the effect of boundary scattering as the film decreases in thickness and the effect of impurities.     

Free carrier absorption and lattice vibrational modes in bulk ZnO

The electronic properties of semiconductors are highly dependent on carrier scattering mechanisms determined by crystalline structure, band structure, and defects in the material. Experimental characteristics of lattice vibrational modes and free carrier absorption in single-crystal ZnO samples obtained from different sources are presented in this work to provide a further understanding of carrier scattering processes pertaining to electronic properties. Infrared absorption measurements indicate strong absorption peaks due to a combination of optical and nonpolar phonon modes in the 9–13 μm spectral region. The Raman spectra obtained for these samples similarly reveal the presence of these phonon modes. Infrared absorption measurements also demonstrate free carrier absorption in the 3–9 μm spectral region for higher conductivity samples, where a λ^m dependence is observed with m=2.7–3, indicating both longitudinal optical phonon scattering and ionized impurity scattering. From these results, we show that infrared absorption can be used as a routine nondestructive technique to determine the material characteristics and quality of bulk ZnO.