The propagation of second sound, and more broadly the ballistic transport of heat, is of central importance in heat dissipation from electronic devices at very short length and time scales. Recently, we have developed thermal response functions appropriate for elucidating physics beyond the diffusive regime, including time-dependent sources and wave-like heat propagation. The methods are applied to graphene simulated using molecular-dynamics (MD) with empirical potentials. The simulations predict a strong oscillatory transport at T = 300 K for length scales equal to L = 68.1 nm and below. It is shown that at these temperatures and scales, the lifetime of the oscillatory transport is determined largely by wave coherence connected to the phonon band structure. While most Boltzmann transport equation (BTE) theories for second sound neglect this effect, and may not be suitable at very short length scales, they nevertheless are accurate for describing perturbations at longer length scales. Calculations using the linearized BTE are also presented, along with analysis of second sound. This approach results in significantly longer lifetimes for second sound in comparison to our MD simulation results. Predictions for the response due to time-dependent sources are also presented, including insight into how time-dependent experiments might probe the spectra associated with second sound. Results are discussed in relation to recent experiments on graphite.

We connect expressions for phonon phase-space distribution functions to microscopic physics of the evolution of heat waves. The role of interference effects that arise as a result of a periodic heating source typically encountered in transient thermal grating (TTG) experiments is then explored. The distribution functions are evaluated as solutions to the Peierls-Boltzmann equation (PBE) in the relaxation-time approximation (RTA). Starting from the PBE, we next develop thermal response functions. The response functions are computed using data from density-functional theory (DFT) calculations. Using this approach, it is shown how solutions to the PBE can be related to the propagation of second phonons as elementary excitations, and within this perspective the necessary conditions for the propagation and observation of second sound is elucidated. The approach developed therefore shows how PBE theory for phonon hydrodynamics and second sound can be modified to properly describe interference and phonon decoherence effects that are likely important at shorter length scales. Finally, we then discuss how many-body theory can be extended to include coupled scattering channels and hence provide a quantitative theory beyond the RTA.

Ballistic heat transport and second sound propagation in solids is of direct relevance in electronic and energy applications at short length scales and low temperatures. Measurement or calculation of thermal conductivity, which is typically a primary objective, may be of limited usefulness for predicting heat transport which does not follow the heat-diffusion equation. In this paper, molecular-dynamics simulations of hexagonal BN (h-BN) are used to compute thermal response functions from equilibrium correlation functions defined in Fourier space. The response functions are useful for describing the time-dependent transport beyond the usual assumptions of Fourier's law. The results demonstrate that for length scales 110nm at T=100K second sound should be experimentally observable. At higher temperatures and longer length scales, while second sound may not be directly observable, thermal transport can nevertheless strongly deviate from predictions based on the heat-diffusion equation. Along with classical simulations, we outline a first-principles, many-body theoretical approach for calculation of the response function based on solutions of the Bethe-Salpeter equation. The relevant expressions for heat current clarify the importance of phase coherence within a phonon branch to the observation of second sound. Previous work on one-dimensional chains is also discussed to show that materials characterized by linear dispersion and simple phonon band structure should more readily display second sound.

Building on recent simulation work, it is demonstrated using molecular-dynamics (MD) simulations of two-component fluid mixtures that the chemical contribution to the Soret effect in two-component non-ideal fluid mixtures arises due to differences in how the partial pressures of the components respond to temperature and density gradients. Further insight is obtained by reviewing the connection between activity and deviations from Raoult's law in the measurement of the vapor pressure of a liquid mixture. A new parameter $\gamma_{s}^{S}$, defined in a manner similar to the activity coefficient, is used to characterize differences deviations from ``ideal'' behavior. It is then shown that the difference $\gamma_{2}^{S}-\gamma_{1}^{S}$ is predictive of the sign of the Soret coefficient and is correlated to its magnitude. We hence connect the Soret effect to the relative volatility of the components of a fluid mixture, with the more volatile component enriched in the low-density, high-temperature region, and the less volatile component enriched in the high-density, low-temperature region. Because $\gamma_{s}^{S}$ is closely connected to the activity coefficient, this suggests the possibility that measurement of partial vapor pressures might be used to indirectly determine the Soret coefficient. It is proposed that the insight obtained here is quite general and should be applicable to a wide range of materials systems. An attempt is made to understand how these results might apply to other materials systems including interstitials in solids and multicomponent solids with interdiffusion occurring via a vacancy mechanism.

The Soret effect is the tendency of fluid mixtures to exhibit concentration gradients in the presence of a temperature gradient. Using molecular-dynamics simulation of two-component Lennard-Jones liquids, it is demonstrated that spatially sinusoidal heat pulses generate both temperature and pressure gradients. Over short timescales, the dominant effect is the generation of compressional waves, which dissipate over time as the system approaches mechanical equilibrium. The approach to mechanical equilibrium is also characterized by a decrease in particle density in the high-temperature region and an increase in particle density in the low-temperature region. It is demonstrated that concentration gradients develop rapidly during the propagation of compressional waves through the liquid. Over longer timescales, heat conduction occurs to return the system to thermal equilibrium, with the particle current acting to restore a more uniform particle density. It is shown that the Soret effect arises due to the fact that the two components of the fluid exhibit different responses to pressure gradients. First, the so-called isotope effect occurs because light atoms tend to respond more rapidly to evolving conditions. In this case, there appears to be a connection to previous observations of “fast sound” in binary fluids. Second, it is shown that the partial pressures of the two components in equilibrium, and more directly, the relative magnitudes of their derivatives with respect to temperature and density, determine which species accumulate in the high- and low-temperature regions. In the conditions simulated here, the dependence of the partial pressure on density gradients is larger than the dependence on temperature gradients. This is directly connected to the accumulation of the species with the largest partial pressure in the high-temperature region and the accumulation of the species with the smallest partial pressure in the low-temperature region. The results suggest that further development of theoretical descriptions of the Soret effect might begin with hydrodynamical equations in two-component liquids. Finally, it is suggested that the recently proposed concept of “thermophobicity” may be related to the sensitivity of partial pressures in a multicomponent fluid to changes in temperature and density.

Ballistic transport and resonance phenomena are elucidated in the one-dimensional α-Fermi-Pasta-Ulam-Tsingou (FPUT) model using an approach of computing thermal response functions. The existence of periodic oscillations in spatially sinusoidal temperature profiles seen in previous studies is confirmed. However, the results obtained using response functions enable a more complete understanding. In particular, it is shown that resonance involves beats between normal modes which tend to reinforce in a one-dimensional chain. Anharmonic scattering acts to destroy phase coherence across the statistical ensemble, and with increasing anharmonicity, transport is driven toward the diffusive regime. These results provide additional insight into anomalous heat transport in low-dimensional systems. Normal-mode scattering is also explored using time correlation functions. Interestingly, these calculations, in addition to demonstrating loss of phase coherence across an ensemble of simulations, appear to show evidence of so-called q-breathers in conditions of strong anharmonicity. Finally, we describe how the approach outlined here could be developed to include quantum statistics and also also first-principles estimates of phonon scattering rates to elucidate second sound and ballistic transport in realistic materials at low temperatures.

Dissipation and adhesion are important in many areas of materials science, including friction and lubrication, cold spray deposition, and micro-electromechanical systems (MEMS). Another interesting problem is the adhesion of mineral grains during the early stages of planetesimal formation in the early solar system. Molecular-dynamics (MD) simulation has often been used to elucidate dissipative properties, most often in the simulation of sliding friction. In this paper, we demonstrate how the reversible and irreversible work associated with interactions between planar surfaces can be calculated using the dynamical contact simulation approach based on MD and empirical potentials. Moreover, it is demonstrated how the approach can obtain the free-energy ΔA(z) as a function of separation between two slabs using the Jarzynksi equality applied to an ensemble of trajectories which deviate significantly from equilibrium. Furthermore, the dissipative work can also be obtained using this method without the need to compute an entire cycle from approach to retraction. It is expected that this technique might be used to efficiently compute dissipative properties which might enable the use of more accurate approaches including density-functional theory. In this paper, we present results obtained for forsterite surfaces both with and without MgO-vacancy surface defects. It is shown that strong dissipation is possible when MgO-vacancy defects are present. The mechanism for strong dissipation is connected to the tendency of less strongly-bound surface units to undergo large displacements including mass transfer between the two surfaces. Systems with strong dissipation tend to exhibit a long-tailed distribution rather than the Gaussian distribution often anticipated in near-equilibrium applications of the JE.

A realistic tight-binding model is developed and employed to elucidate the resistivity size effect due to steps on Ru thin films. The resistivity of two different film orientations, (0001) and (11̄00), is computed for transport along a [112̄0] direction both for smooth surfaces and for surfaces with monolayer-high steps. In the case of smooth films, the systems are also studied using solutions to the Boltzmann transport equation (BTE). Interestingly, the resistivity of (11̄00) surfaces exhibits a significant size effect even in the absence of surface steps. When monolayer-high steps are spaced ∼ 10 nm apart, the resistivity is shown to increase due to scattering from the steps. However, only a small increase was found which cannot explain the large effect seen in recent experiments with Ru thin films. This highlights the need for further elucidation of the resistivity size effect. Theoretical analysis suggest that films made from materials with a relatively large ballistic conductance per area like Ru should exhibit a reduced resistivity size effect. This result points to Ru as a promising interconnect material. Finally, because a very efficient algorithm for computing resistivity based on the kernel polynomial method (KPM) is used, the approach fulfills a need for realistic models that can span length scales directly relevant to experimental results. The calculations described here include films approaching 5 nm in thickness, with in-plane distances up to ∼ 160 nm and 3.8× 10 atomic sites.

How dust grains aggregate into planetesimals is still an open question. It is experimentally observed that binary collisions between micron-sized dust grains result in adhesion for collisions up to ∼1 ms−1. However, aggregates at scales ∼1 mm and above have been shown to exhibit fragmentation or bouncing at relevant collision velocities, resulting in a barrier preventing the formation of larger aggregates. One key factor is the weak adhesion observed between dust particles in aggregates leading to ruptures even in low-velocity collisions. To better understand the structure and strength of the adhered interface resulting from collisions, we performed molecular-dynamics simulations of head-on collisions between amorphous FeO nanoparticles. The results demonstrate several important phenomena which indicate how bonding between aggregates might become stronger than is often observed in experiments. For nanograins, it is shown that strong attractive interactions result in a minimum relative collision speed vc determined just before impact. The values of vc for particle radii 7 nm and below are computed to be in the range 40–100 ms−1. This high collision speed is shown to result in strong bond reordering at the interface. Moreover, increasing the incident collision speed vrel is shown to increase the work of adhesion Wadh, which is correlated to substantial bond rearrangement. Specifically, for values of vrel in the range between 10–90 ms−1, the interface between adhered grains is structured very closely to perfectly coordinated FeO amorphous solid. The reported results suggest stronger bonding results from collisions between particles with unpassivated surfaces, especially when particles are small, have amorphous surface structures, or when collisions occur at higher relative speeds. These factors should generate aggregates with stronger bonds that are less easily broken in subsequent collisions, and hence might be responsible for aggregates less likely to fragment at larger length scales.

In this article we develop the theory of nonlocal thermal transport within the context of the fluctuation-dissipation theorem. The theory goes beyond the usual Green-Kubo integrals used to obtain the thermal conductivity by including the response of a system to external heat sources that are nonuniform in space and time. Through the integration of current-current correlation functions, the relevant response functions are determined from equilibrium molecular-dynamics simulations of an Ar crystal modeled using the standard Lennard-Jones potential. It is shown that for low temperatures and short length scales, the approach can be used to elucidate partially-ballistic transport. Transport can be understood to be heat waves in the sense that transport is primarily limited by the sound velocity. By contrast, at longer length scales and higher temperatures, the response functions become more comparable to what is expected from Fourier's law where diffusive heat transport is the dominant mechanism. It is also shown how the effective thermal conductivity can be determined in a partially-ballistic regime. The results demonstrate the known reduction in the effective thermal conductivity seen in the partially-ballistic regime. Finally, we show how determination of the relevant response functions can be used to model heating of a crystal without requiring additional atomic-scale simulations. This approach is used to show how temperature profiles differ from those expected from the diffusive Fourier's law due to nonlocal transport effects.

We establish an approach to compute linear-response functions to elucidate heat waves and non-local thermal transport. The theory is able to describe the response of a system to external heat sources that are nonuniform in space and time. The response functions are computed using equilibrium molecular-dynamics simulations of an Ar crystal modeled using the standard Lennard-Jones potential. It is shown that for low temperatures and short length scales, transport can be partially or even completely ballistic, with the response primarily limited by the group velocity of lattice waves. By contrast, at longer length scales and higher temperatures, the response functions correspond more closely to diffusive transport characteristic of Fourier’s law. It is also shown how the effective thermal conductivity can be determined in a partially-ballistic regime. The results demonstrate the known reduction in the effective thermal conductivity observed when system dimensions are smaller than the mean-free path for lattice waves. Finally, we show how determination of the relevant response functions can be used to model heating of a crystal without requiring additional atomic-scale simulations. Differences between computed results and predictions from Fourier’s law represent wave-like, partially-ballistic transport.

The experimentally measured resistivity of Co(0001) and Ru(0001) single crystal thin films, grown on c-plane sapphire substrates, as a function of thickness is modeled using the semiclassical model of Fuchs-Sondheimer. The model fits show that the resistivity of Ru would cross below that for Co at a thickness of approximately 20 nm. For Ru films with thicknesses above 20 nm, transmission electron microscopy evidences threading and misfit dislocations, stacking faults and deformation twins. Exposure of Co films to ambient air, and the deposition of oxide layers of SiO2, MgO, Al2O3 and Cr2O3 on Ru degrade the surface specularity of the metallic layer. However, for the Ru films, annealing in a reducing ambient restores the surface specularity. Epitaxial electrochemical deposition of Co on epitaxially-deposited Ru layers is used as an example to demonstrate the feasibility of generating epitaxial interconnects for back-end of line structures. An electron transport model based on a tight-binding approach is described, with Ru interconnects used an example. The model allows conductivity to be computed for structures comprising large ensembles of atoms (10^5-10^6), scales linearly with system size and can also incorporate defects.

Collisions between amorphous Fe nanoparticles were studied using molecular-dynamics simulation. For head-on collisions of nanoparticles with radii R=1.4nm, R=5.2nm, and R=11nm, sticking was observed at all simulated velocities. The results were compared to the description provided by the JKR model. It was found that strong disagreement exists between the predictions of JKR and the results of the molecular-dynamics simulation due to the presence of additional dissipative processes which strengthen sticking behavior. First, it is demonstrated that very strong dissipation into atomic vibrations occurs during the collision. The dissipation is strong enough to prevent significant rebound of the nanoparticles. Additionally, the morphology of the adhered nanoparticles includes a “neck” that increases in radius with increasing collision velocity which results in amplified irreversibility and adhesion. Approximate calculation of the stress during the collision indicates that stress levels are well above typical yield stress values even for low velocity collisions, consistent with the observation of plastic deformation. Furthermore, it is shown that for nanoparticles with R⩽11nm, the dominance of surface attraction results in large effective collision velocities and plastic deformation. By obtaining scaling relations for computed quantities, predictions are made for larger nanoparticles up to R∼1μm. This work provides a new perspective on collisional dissipation and adhesion with an important connection to the modern understanding of tribology and friction.

It is demonstrated that olivine powders heated to subsolidus temperatures in reducing conditions can develop significant concentrations of 10-50 nm diameter Fe nanoparticles on grain surfaces and that these display strong catalytic activity not observed in powders without Fe nanoparticles. Reduced surfaces were exposed to NH3, CO, and H-2, volatiles that may be present on the surfaces of comet and volatile-rich asteroids. In the case of NH3 exposure, rapid decomposition was observed. When exposed to a mixture of CO and H-2, significant coking of the mineral surfaces occurred. Analysis of the mineral grains after reaction indicated primarily the presence of graphene or graphitic carbon. The results demonstrate that strong chemical activity can be expected at powders that contain nanophase Fe particles. This suggests space-weathered mineral surfaces may play an important role in the synthesis and processing of organic species. This processing may be part of the weathering processes of volatile-rich but atmosphereless solar-system bodies. (C) 2017 Elsevier Inc. All rights reserved.

The accretion of dust grains to form larger objects, including planetesimals, is a central problem in planetary science. It is generally thought that weak van der Waals interactions play a role in accretion at small scales where gravitational attraction is negligible. However, it is likely that in many instances, chemical reactions also play an important role, and the particular chemical environment on the surface could determine the outcomes of dust grain collisions. Using atomic-scale simulations of collisional aggregation of nanometer-sized silica (SiO2) grains, we demonstrate that surface hydroxylation can act to weaken adhesive forces and reduce the ability of mineral grains to dissipate kinetic energy during collisions. The results suggest that surface passivation of dangling bonds, which generally is quite complete in an Earth environment, should tend to render mineral grains less likely to adhere during collisions. It is shown that during collisions, interactions scale with interparticle distance in a manner consistent with the formation of strong chemical bonds. Finally, it is demonstrated that in the case of collisions of nanometer-scale grains with no angular momentum, adhesion can occur even for relative velocities of several kilometers per second. These results have significant implications for early planet formation processes, potentially expanding the range of collision velocities over which larger dust grains can form.

In the presence of a temperature gradient, the components of a binary liquid tend to segregate. This phenomenon, generally referred to as thermodiffusion or the Soret effect, is usually quantified by the heat of transport. We report heat of transport values Qc∗ for NiAl and NiCu melts computed using molecular-dynamics simulation and the Green-Kubo formalism. Thermal conductivities are also reported. To develop a clear picture of the phenomena, we determined contributions to Qc∗ due to the convective and virial components of the heat current, which were then compared to the related terms in the partial enthalpy. It is shown that the contribution to Qc∗ from the convective component of the heat current is comparable to the average energy of the diffusing atoms, differing by an amount comparable to the activation energy for diffusion. The contribution to Qc∗ from the virial heat current is closely related to the pressure-volume term pcΩ in the partial enthalpy. It is established that the virial heat current plays a dominant role in determining the sign of the reduced heat of transport Qc∗′=Qc∗-hc. By comparing results obtained with different empirical potentials, a trend emerges. Specifically, it is found that the sign of the reduced heat of transport is correlated with the sign of the partial pressure associated with the low-mass component. It is also shown that two different empirical potentials for the NiAl system give vastly different results for Qc∗′. The results indicate that in developing a potential that might accurately predict Qc∗′, the distribution of the partial energy and partial pressure between the two components is critical. Based on these observations, it would appear that existing empirical potentials may not be able to generate reliable predictions for Qc∗′ without additional validation.