Effective Mean Free Path Research Articles

Thermal Conductivity of Graphene-hBN Superlattice Ribbons

Superlattices are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport. Single layer heterostructures of graphene and hexagonal boron nitride have been produced recently with sharp edges and controlled domain sizes. In this study we employ nonequilibrium molecular dynamics simulations to investigate the thermal conductivity of superlattice nanoribbons with equal-sized domains of graphene and hexagonal boron nitride. We analyze the dependence of the conductivity with the domain sizes, and with the total length of the ribbons. We determine that the thermal conductivity reaches a minimum value of 89 W m−1K−1 for ribbons with a superlattice period of 3.43 nm. The effective phonon mean free path is also determined and shows a minimum value of 32 nm for the same superlattice period. Our results also reveal that a crossover from coherent to incoherent phonon transport is present at room temperature for BNC nanoribbons, as the superlattice period becomes comparable to the phonon coherence length. Analyzing phonon populations relative to the smallest superlattice period, we attribute the minimum thermal conductivity to a reduction in the population of flexural phonons when the superlattice period equals 3.43 nm. The ability to manipulate thermal conductivity using superlattice-based two-dimensional materials, such as graphene-hBN nanoribbons, opens up opportunities for application in future nanostructured thermoelectric devices.

Gas dynamic trap: experimental results and future prospects

The gas dynamic trap (GDT) is a version of a magnetic mirror with a long mirror-to-mirror distance far exceeding the effective mean free path of ion scattering into the loss cone, with a large mirror ratio (R ∼ 100; R = Bmax/Bmin is the ratio of magnetic field inductions at the mirror and at the trap center) and with axial symmetry. Under these conditions, in contrast to a conventional magnetic mirror, the plasma confined in a GDT is isotropic and Maxwellian. The plasma loss rate through the ends is governed by a set of simple gas dynamic equations; hence, the name of the device. The plasma lifetime in a GDT is on the order of LR/VTi, where L is the mirror-to-mirror distance, and VTi is the ion thermal velocity. Thus, increasing both the length of the device and the mirror ratio can, in principle, make the plasma lifetime sufficient for fusion applications. This paper discusses plasma confinement and heating results from the Novosibirsk GDT facility and examines prospects for using GDTs to develop a high-flux volumetric neutron source for fusion material testing and for driving subcritical fission reactors.

Ultra-low thermal conductivities along c-axis of naturally misfit layered Bi2[AE]2Co2Oy (AE = Ca, Ca0.5Sr0.5, Sr, Ba) single crystals

The intrinsically low thermal conductivity is fundamentally important for the development of high-performance thermoelectric and thermal insulating materials. Here, we observed ultra-low cross-plane thermal conductivities of naturally misfit layered single crystals Bi2[AE]2Co2Oy (AE = Ca, Ca0.5Sr0.5, Sr, and Ba) using the time-domain thermoreflectance method. These low values are comparable to the lowest conductivity in crystalline oxides and approaching the theoretical conductivity minimum of disordered crystals. Besides, these samples show the amorphous-like temperature dependence at cryogenic temperatures and the effective mean free paths are in the same magnitudes as the lattice constants.

Dielectric tensor of low-dimensional metal systems

The dielectric tensor of a low-dimensional metal system has been introduced on the basis of the density matrix in the relaxation time approximation. The properties of this tensor have been analyzed. It has been proved that anisotropy and nonlocality are decisive features of the response of low-dimensional systems to an electromagnetic field. In particular, the expression has been derived for the dielectric tensor of nanometer- thick metal films. It has been shown that the dielectric tensor components can be reduced to the Drude dielectric function for a homogeneous metal in the case when the film thickness considerably exceeds the effective electron mean free path. The application of the classical distribution function for describing electrons in the film is justified under these conditions.

Diffusion modeling in cemented carbides: Solubility assessment for Co, Fe and Ni binder systems

The increasing interest in alternative binder solutions for WC based cemented carbide systems leads to more integration of ICME (Integrated Computational Materials Engineering) based concepts in the materials development. This work investigates the non-equilibrium W and C solubilities upon furnace-cooling in a wide range of Co and Fe-Ni based binder systems by computational means. It is shown that the solubilities strongly depend on the C-activity and binder matrix elements, revealing that Ni dissolves most W and Fe most C out of the investigated systems. Furthermore, the effect of the binder mean free path and the cooling rates on the solubilities was investigated. The presented method and results provide insights to control the binder chemistry and will help to design the properties for future binder systems in a fast and efficient way.

Anomalous strain effect on the thermal conductivity of borophene: a reactive molecular dynamics study

Borophene, an atomically thin, corrugated, crystalline two-dimensional boron sheet, has been recently synthesized. Here we investigate mechanical properties and lattice thermal conductivity of borophene using reactive molecular dynamics simulations. We performed uniaxial tensile strain simulations at room temperature along in-plane directions, and found 2D elastic moduli of 188Nm−1 and 403Nm−1 along zigzag and armchair directions, respectively. This anisotropy is attributed to the buckling of the borophene structure along the zigzag direction. We also performed non-equilibrium molecular dynamics to calculate the lattice thermal conductivity. Considering its size-dependence, we predict room-temperature lattice thermal conductivities of 75.9 ± 5.0Wm−1K−1 and 147 ± 7.3Wm−1K−1, respectively, and estimate effective phonon mean free paths of 16.7 ± 1.7nm and 21.4 ± 1.0nm for the zigzag and armchair directions. In this case, the anisotropy is attributed to differences in the density of states of low-frequency phonons, with lower group velocities and possibly shorten phonon lifetimes along the zigzag direction. We also observe that when borophene is strained along the armchair direction there is a significant increase in thermal conductivity along that direction. Meanwhile, when the sample is strained along the zigzag direction there is a much smaller increase in thermal conductivity along that direction. For a strain of 8% along the armchair direction the thermal conductivity increases by a factor of 3.5 (250%), whereas for the same amount of strain along the zigzag direction the increase is only by a factor of 1.2 (20%). Our predictions are in agreement with recent first principles results, at a fraction of the computational cost. The simulations shall serve as a guide for experiments concerning mechanical and thermal properties of borophene and related 2D materials.

Large electronic sputtering yield of nanodimensional Au thin films: Dominant role of thermal conductivity and electron phonon coupling factor

Detailed experiments and theoretical calculations on electronic sputtering of Au thin films (5-200 nm) on a quartz substrate are performed, revealing unusually large electronic sputtering, dependent on the thickness of the films. The dependence of electronic thermal conductivity (κe), electron-phonon coupling factor (g), and lattice thermal conductivity (κa) on the effective electron mean free path is taken into account in the thermal spike calculation for nanodimensional systems to elucidate the combined effect of the thickness and grain size on the electronic sputtering yield. The thermal spike simulation with refined parameters for nanodimensional systems gives a better explanation of the electronic sputtering process with a very good correlation between the experimental and theoretical yields than that of the thermal spike model with bulk parameters.

Ultrafast inhomogeneous magnetization dynamics analyzed by interface-sensitive nonlinear magneto-optics

We analyze laser-induced ultrafast, spatially inhomogeneous magnetization dynamics of epitaxial Co/Cu(001) films in a 0.4–10 nm thickness range with time-resolved magnetization-induced second harmonic generation, which probes femtosecond spin dynamics at the vacuum/Co and Co/Cu interfaces. The interference of these two contributions makes the overall signal particularly sensitive to differences in the transient magnetization redistribution between the two interfaces, i.e., ultrafast magnetization profiles in the ferromagnetic film. We conclude that the magnetization dynamics within the first several hundred femtoseconds is characteristically dependent on the Co film thickness. In films up to 3 nm thickness, we find a stronger demagnetization at the film surface compared to the Cu/Co interface, which we explain by a spin current from Co into the Cu substrate with an effective mean free path of about 3 nm. For film thicknesses larger than 3 nm, the transient magnetization profile over the Co film reverses its sign since spins can be transferred into the substrate only from the interface near region. Our work emphasizes that spatial inhomogeneities in the dynamic magnetic response to femtosecond laser excitation allow conclusions on the underlying microscopic processes.

Effect of microstructure on mechanical behavior for eutectoid steel with ultrafine- or fine-grained ferrite+cementite structure

A eutectoid steel with various ultrafine- or fine-grained ferrite matrix (α)+cementite particle (θ) structures was fabricated to explore the effects of the microstructural features on the mechanical behavior of hard particle-strengthened two-phase alloys. The effect of microstructure on the parameters of an analytical model and the mechanical behavior for the eutectoid steel with ultrafine- or fine-grained α+θ structure were analyzed basing on statistical data and physical metallurgy. The results showed that the rate of dislocation-storage caused by ferrite grain boundaries and cementite particles is approximately a microstructural constant and is proportional to the dislocation mean free path. The larger ferrite grains and the larger volume fraction of intragranular cementite particles are beneficial to obtaining a lower rate of dynamic recovery when ultrafine- or fine-grained α+θ structures with an equal dislocation mean free path, and the uniform elongation increases with the decrease in the rate of dynamic recovery. Moreover, the ultimate strength is closely related to the effective dislocation mean free path including both roles of the storage and the recovery of dislocations. It is feasible to design a microstructure consisting of ultrafine- or fine-grained ferrite matrix and tiny cementite particles mainly within grain interior to possess an enhanced strength-plasticity synergy for the eutectoid steel.

Reconstruction of an effective magnon mean free path distribution from spin Seebeck measurements in thin films

A thorough understanding of the mean-free-path (MFP) distribution of the energy carriers is crucial to engineer and tune the transport properties of materials. In this context, a significant body of work has investigated the phonon and electron MFP distribution, however, similar studies of the magnon MFP distribution have not been carried out so far. In this work, we used thickness-dependence measurements of the longitudinal spin Seebeck (LSSE) effect of yttrium iron garnet films to reconstruct the cumulative distribution of a SSE related effective magnon MFP. By using the experimental data reported by (Guo et al 2016 Phys. Rev. X 6 031012), we adapted the phonon MFP reconstruction algorithm proposed by (Minnich 2012 Phys. Rev. Lett. 109 205901) and apply it to magnons. The reconstruction showed that magnons with different MFP contribute in different manner to the total LSSE and the effective magnon MFP distribution spreads far beyond their typical averaged values.

A Comprehensive Study on Gamma Rays and Fast Neutron Sensing Properties of GAGOC and CMO Scintillators for Shielding Radiation Applications

The WinXCom program has been used to calculate the mass attenuation coefficients (μm), effective atomic numbers (Zeff), effective electron densities (Nel), half-value layer (HVL), and mean free path (MFP) in the energy range 1 keV–100 GeV for Gd3Al2Ga3O12Ce (GAGOC) and CaMoO4 (CMO) scintillator materials. The geometrical progression (G-P) method has been used to compute the exposure buildup factors (EBF) and gamma ray energy absorption (EABF) in the photon energy range 0.015–15 MeV and up to a 40 penetration depth (mfp). In addition, the values of the removal cross section for a fast neutron ∑R have been calculated. The computed data observes that GAGOC showed excellent γ-rays and neutrons sensing a response in the broad energy range. This work could be useful for nuclear radiation sensors, detectors, nuclear medicine applications (medical imaging and mammography), nuclear engineering, and space technology.

Thin-Film Phase Plates for Transmission Electron Microscopy Fabricated from Metallic Glasses.

Thin-film phase plates (PPs) have become an interesting tool to enhance the contrast of weak-phase objects in transmission electron microscopy (TEM). The thin film usually consists of amorphous carbon, which suffers from quick degeneration under the intense electron-beam illumination. Recent investigations have focused on the search for alternative materials with an improved material stability. This work presents thin-film PPs fabricated from metallic glass alloys, which are characterized by a high electrical conductivity and an amorphous structure. Thin films of the zirconium-based alloy Zr65.0Al7.5Cu27.5 (ZAC) were fabricated and their phase-shifting properties were evaluated. The ZAC film was investigated by different TEM techniques, which reveal beneficial properties compared with amorphous carbon PPs. Particularly favorable is the small probability for inelastic plasmon scattering, which results from the combined effect of a moderate inelastic mean free path and a reduced film thickness due to a high mean inner potential. Small probability plasmon scattering improves contrast transfer at high spatial frequencies, which makes the ZAC alloy a promising material for PP fabrication.

Record Low Thermal Conductivity of Polycrystalline Si Nanowire: Breaking the Casimir Limit by Severe Suppression of Propagons

Thermoelectrics offer an attractive pathway for addressing an important niche in the globally growing landscape of energy demand. Nanoengineering existing low-dimensional thermoelectric materials pertaining to realizing fundamentally low thermal conductivity has emerged as an efficient route to achieve high energy conversion performance for advanced thermoelectrics. In this paper, by performing nonequilibrium and Green-Kubo equilibrium molecular dynamics simulations we report that the thermal conductivity of Si nanowires (NWs) in polycrystalline form can reach a record low value substantially below the Casimir limit, a theory of diffusive boundary limit that regards the direction-averaged mean free path is limited by the characteristic size of the nanostructures. The astonishingly low thermal conductivity of polycrystalline Si NW is 269 and 77 times lower with respect to that of bulk Si and pristine Si NW, respectively, and is even only about one-third of the value of the purely amorphous Si NW at room temperature. By examining the mode level phonon behaviors including phonon group velocities, lifetime, and so forth, we identify the mechanism of breaking the Casimir limit as the strong localization of the middle and high frequency phonon modes, which leads to a prominent decrease of effective mean free path of the heat carriers including both propagons and diffusons. The contribution of the propagons to the overall thermal transport is further quantitatively characterized and is found to be dramatically suppressed in polycrystalline Si NW form as compared with bulk Si, perfect Si NW, and pure amorphous Si NW. Consequently, the diffusons, which transport the heat through overlap with other vibrations, carry the majority of the heat in polycrystalline Si NWs. We also proposed approach of introducing "disorder" in the polycrystalline Si NWs that could eradicate the contribution of propagons to achieve an even lower thermal conductivity than that ever thought possible. Our investigation provides a deep insight into the thermal transport in polycrystalline NWs and offers a promising strategy to construct a new kind of semiconducting thermoelectric NW with high figure of merit.

Quantitative Dopant Profiling by Energy Filtering in the Scanning Electron Microscope

Two-dimensional dopant mapping using secondary electrons (SEs) in the scanning electron microscope (SEM) is a technique under intense research and development due to improvements in instrumental resolution and its potential to enable rapid low-cost diagnostics in process optimization for microelectronic and optoelectronic fabrication. However, an initial drawback of the technique is the lack of a complete quantitative model to obtain accurate information on dopant profiles. This paper focuses on detailed studies of dopant profiling quantification on a wide range of doped silicon homojunctions in an SEM under various operating conditions for the first time. Doping type and geometry-dependent effects from the specimen are taken into account, and improved sensitivity, resolution, and quantification accuracy due to energy filtering of the SEs are demonstrated. The resulting SE intensities under varying operating conditions are surveyed with an indication of aspects of the mechanism responsible for doping contrast, including the patch fields, surface band bending, and inelastic mean free path effects in the specimen, as well as the angular velocities of the SEs. Although all samples satisfied the classical logarithmic doping dependence of contrast approximation, some of them required specialized energy-filtering techniques. The theoretical model based on energy filtering to determine the built-in voltage across the $p\!-\!n$ junction that is in the literature does not accurately apply to $n^{+}\!-i-n$ homojunctions. The surface band bending and inelastic mean free path dependence of the SE kinetic energy models have been derived in this paper, which accurately describe the quantitative contrast characteristics from donor distributions, thereby producing more accurate quantification of this technique in semiconductor research and industry.

Thermal conductivity and mechanical properties of nitrogenated holey graphene

Nitrogenated holey graphene (NHG), a two-dimensional graphene-derived material with a C2N stoichiometry and evenly distributed holes and nitrogen atoms in its basal plane, has recently been synthesized. We performed first principles calculations and molecular dynamics simulations to investigate mechanical and heat transport properties of this novel two-dimensional material at various temperatures. First principles calculations based on density functional theory yield an elastic modulus of 400 ± 5 GPa at 0 K, 10% larger than predicted by molecular dynamics simulations at low temperatures. We observed an overall decreasing trend in elastic modulus and tensile strength as temperature increases. At room temperature, we found that NHG can present a remarkable elastic modulus of 335 ± 5 GPa and tensile strength of 60 GPa. We also investigated the thermal conductivity of NHG via non-equilibrium molecular dynamics simulations. At 300 K an intrinsic thermal conductivity of 64.8 W/m-K was found, with an effective phonon mean free path of 34.0 nm, both of which are smaller than respective values for graphene, and decrease with temperature. Our modeling-based predictions should serve as guide to experiments concerning physical properties of this novel material.

Phonon Scattering Effects in Drain-Current Model of Carbon Nanotube and Silicon Nanowire Field-Effect Transistors

Carbon nanotubes (CNTs) and silicon nanowires (Si NWs) are the potential candidate for the channel material in the next generation of transistors. Although previous works have shown that both CNT- and Si NW-based field-effect-transistors (FET) are able to deliver better performance than conventional devices, phonon scattering occurs. In this paper, we examine the phonon scattering effects on the electrical transport characteristic of CNTFETs and Si NWFETs. The impact of phonon scattering is incorporated into the devices through the transmission probability into the ballistic current equation. There are two types of phonons, acoustic phonons and optical phonons, with different mean free paths (MFP). The results show that the effective MFP follows the acoustic phonon MFP at a low gate bias and switches to the optical phonon MFP at a high gate bias. The acoustic phonon is the primary cause of current reduction at a low gate bias, while the optical phonon is dominant in reducing the current at a high gate bias. The ballisticity, which is the ratio of the scattering current to the ballistic current at different channel lengths is examined. It is revealed that transistors with a shorter length operate close to the ballistic region, which is expected, as they approach the phonon MFP. Performances metrics such as drain-induced barrier lowering (DIBL), subthreshold swing (SS) and on-off ratio at different channel length are calculated. The potential of CNTFETs and Si NWFETs work as logic gates are determined through the voltage transfer characteristic (VTC). Finally, the accuracy of the simulation results is verified by comparing with published models and experimental data, exhibiting good agreement with both data.

Simulation of micro flow in the transition regime using effective-viscosity-based multi-relaxation-time lattice Boltzmann model

With the rapid development of micro-electro-mechanical systems (MEMS), microscale rarefied gas flows have received considerable attention in the past decades. Recently, the lattice Boltzmann method (LBM) emerges as a promising way to study the flow in MEMS for its kinetic nature and distinctive computational features. Various LBM models have been used to simulate the microscale and nanoscale flow, among which the two-dimensional and nine-velocities (D2Q9)-based LBM is most widely accepted due to its extremely simplicity and high efficiency. However, the D2Q9-based LBM encounters great difficulties in the transition regime due to the rarefaction effects on mean free path and gas viscosity. An effective way to improve the capability of the existing LBM model is to incorporate an effective viscosity into the relaxation time, which can improve the accuracy of LBM model while keeping the simplicity and efficiency of LBM. However, the existing D2Q9-based LBM models with effective viscosity cannot give satisfactory predictions of the none-equilibrium phenomenon at moderate or high Knudsen (Kn) number both in accuracy and efficiency. To solve the above problem, in this study, an effective mean free path function proposed by Dongari et al. (Dongari N, Zhang Y H, Reese J M 2011 J. Fluids Eng. 133 071101) via modular dynamics mean is introduced into the D2Q9 multi-relaxation-time lattice Boltzmann model (MRT-LBM) to account for the effect of Knudsen layer in transition flow regime, and the viscosity in the MRT-LBM model is modified correspondingly. The combination of the bounce-back and specular reflection boundary condition is used to deal with the velocity slip, and the relaxation time and the reflection coefficient are properly set to eliminate the numerical artifact on the boundaries as the kinetic boundary condition is used. Micro Couette flow at Kn=0.1-6.77, and periodic Poiseuille flow at Kn=0.1128-2.2568, respectively, are numerically investigated by using the proposed MRT-LBM model, and the numerical results, including the non-dimensional velocity profile and the mass flow rate, are verified by the direct simulation Monte~Carlo (DSMC) data, the linearized Boltzmann solutions and the existing LBM model. The calculation results demonstrate that in transition regime, with the increase of Knudsen number, the dimensionless slip velocity at the wall significantly increases. It is shown that the velocity profiles predicted by the present MRT-LBM model agree well with the DSMC data and linearized Boltzmann solutions up to Kn=4.5 in Couette flow, which is much more accurate than that obtained from the existing LBM model. And the present LBM model gives at least the same order of accuracy in the prediction of velocity profile and mass flow rate as the existing LBM model in periodic Poiseuille flow. What is more, the Knudsen minimum phenomenon of flow in the microchannel is successfully captured at around Kn=1. The results demonstrate that the proposed model can enhance the ability of LBM in capturing the non-equilibrium phenomenon in micro flow in the transition regime both in accuracy and efficiency.

TURBULENT COSMIC-RAY REACCELERATION AT RADIO RELICS AND HALOS IN CLUSTERS OF GALAXIES

Radio relics are synchrotron emission found on the periphery of galaxy clusters. From the position and the morphology, it is often believed that the relics are generated by cosmic-ray (CR) electrons accelerated at shocks through a diffusive shock acceleration (DSA) mechanism. However, some radio relics have harder spectra than the prediction of the standard DSA model. One example is observed in the cluster 1RXS J0603.3+4214, which is often called the ``Toothbrush Cluster''. Interestingly, the position of the relic is shifted from that of a possible shock. In this study, we show that these discrepancies in the spectrum and the position can be solved if turbulent (re)acceleration is very effective behind the shock. This means that for some relics turbulent reacceleration may be the main mechanism to produce high-energy electrons, contrary to the common belief that it is the DSA. Moreover, we show that for efficient reacceleration, the effective mean free path of the electrons has to be much smaller than their Coulomb mean free path. We also study the merging cluster 1E 0657-56 or the ``Bullet Cluster'', in which a radio relic has not been found at the position of the prominent shock ahead of the bullet. We indicate that a possible relic at the shock is obscured by the observed large radio halo that is generated by strong turbulence behind the shock. We propose a simple explanation if the morphological differences of radio emission among the Toothbrush, the Bullet, and the Sausage (CIZA J2242.8+5301) Clusters.

Plasmon-resonant Raman spectroscopy in metallic nanoparticles: Surface-enhanced scattering by electronic excitations

Since the discovery of surface-enhanced Raman scattering (SERS) 40 years ago, the origin of the ``background'' that is systematically observed in SERS spectra has remained questionable. To deeply analyze this phenomenon, plasmon-resonant Raman scattering was recorded under specific experimental conditions on a panel of composite multilayer samples containing noble metal (Ag and Au) nanoparticles. Stokes, anti-Stokes, and wide, including very low, frequency ranges have been explored. The effects of temperature, size (in the nm range), embedding medium (${\text{SiO}}_{\text{2}}, {\text{Si}}_{\text{3}}{\text{N}}_{\text{4}}$, or ${\text{TiO}}_{\text{2}}$) or ligands have been successively analyzed. Both lattice (Lamb modes and bulk phonons) and electron (plasmon mode and electron-hole excitations) dynamics have been investigated. This work confirms that in Ag-based nanoplasmonics composite layers, only Raman scattering by single-particle electronic excitations accounts for the background. This latter appears as an intrinsic phenomenon independently of the presence of molecules on the metallic surface. Its spectral shape is well described by revisiting a model developed in the 1990s for analyzing electron scattering in dirty metals, and used later in superconductors. The ${g}_{s}$ factor, that determines the effective mean-free path of free carriers, is evaluated, ${g}_{s}^{\mathrm{expt}}=0.33\ifmmode\pm\else\textpm\fi{}0.04$, in good agreement with a recent evaluation based on time-dependent local density approximation ${g}_{s}^{\mathrm{theor}}=0.32$. Confinement and interface roughness effects at the nanometer range thus appear crucial to understand and control SERS enhancement and more generally plasmon-enhanced processes on metallic surfaces.

Nanoshells with a gain layer: the effects of surface scattering

The optical properties of layered nanoparticles containing at least one metallic layer and one gain medium layer are calculated. The mean free path effect, resulting from the surface scattering of the conduction electrons, is taken into account in the usual way, by modifying the dielectric function of the metallic shell. There exist in the literature a number of effective mean free path model choices for the shell geometry. We investigate the dependence of the optical spectra, as well as the critical gain values, on the choice of the surface scattering model.