arXiv subjects

Patrick K. Schelling

Publications and source records attributed to Patrick K. Schelling.

10 recordsLinked to original sources

arXiv2026

Thermal-response Functions and the Peierls-Boltzmann Equation for Second Sound and Phonon Hydrodynamics in Graphene

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.

cond-mat.other↗

arXiv2025

Thermal response functions and second sound in graphene

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=300K for length scales equal to L=68.1nm 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 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 (LBTE) 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.

cond-mat.mes-hall↗

arXiv2025

Thermal response functions and second sound in single-layer hexagonal boron nitride

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.

cond-mat.stat-mech↗

arXiv2024

Connection between partial pressure, volatility, and the Soret effect elucidated using simulations of non-ideal supercritical fluid mixtures

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 $γ_{s}^{S}$, 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 $γ_{2}^{S}-γ_{1}^{S}$ 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 $γ_{s}^{S}$ 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.

cond-mat.soft↗

arXiv2022

Physical mechanisms of the Soret effect in binary Lennard-Jones liquids elucidated with thermal-response calculations

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 a different response to pressure gradients. First, the so-called isotope effect occurs because light atoms tend to respond more rapidly to the 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 accumulates 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 the dependence on temperature gradients.

cond-mat.soft↗

arXiv2022

Analysis of ballistic transport and resonance in the $α$-Fermi-Pasta-Ulam-Tsingou model

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 towards 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.

cond-mat.stat-mech↗

arXiv2022

Dissipation and adhesion hysteresis between (010) forsterite surfaces using molecular-dynamics simulation and the Jarzynski equality

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.

cond-mat.mtrl-sci↗

arXiv2021

Non-local linear-response functions for thermal transport computed with equilibrium molecular-dynamics simulation

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.

cond-mat.mes-hall↗

arXiv2020

Epitaxial metals for interconnects beyond Cu

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.

cond-mat.mes-hall↗

arXiv2019

Dissipation and plastic deformation in collisions between metallic nanoparticles

Collisions between amorphous Fe nanoparticles were studied using molecular-dynamics simulation. For head-on collisions of nanoparticles with radii $R =$ 1.4 nm, $R =$ 5.2 nm, and $R =$ 11 nm, 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 $R \leq$ 11 nm, 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 $R$ $\sim$ 1 $μ$m. This work provides a new perspective on collisional dissipation and adhesion with an important connection to the modern understanding of tribology and friction.

physics.comp-ph↗