Heat Current Autocorrelation Function Research Articles

Super-suppression of long phonon mean-free-paths in nano-engineered Si due to heat current anticorrelations

The ability to minimize the thermal conductivity of dielectrics with minimal structural intervention that could affect electrical properties is an important capability for engineering thermoelectric efficiency in low-cost materials such as Si. We recently reported the discovery of special arrangements for nanoscale pores in Si that produce a particularly large reduction in thermal conductivity accompanied by strongly anticorrelated heat current fluctuations [1] – a phenomenon that is missed by the diffuse adiabatic boundary conditions conventionally used in Boltzmann transport models. This manuscript presents the results of molecular dynamics simulations and a Monte Carlo ray tracing model that teases apart this phenomenon to reveal that special pore layouts elastically backscatter long-wavelength heat-carrying phonons. This means that heat carriage by a phonon before scattering is undone by the scattered phonon, resulting in an effective mean-free-path that is significantly shorter than the geometric line-of-sight due to the pores. This effect is particularly noticeable for the long-wavelength, long mean-free-path phonons whose transport is impeded drastically more than is expected purely from the usual considerations of scattering defined by the distance between defects. This “super-suppression” of the mean-free-path below the characteristic length scale of the nanostructuring offers a route for minimizing thermal conductivity with minimal structural impact, while the stronger impact on long wavelengths offers possibilities for the design of band-pass phonon filtering. Moreover, the ray tracing model developed in this paper shows that different forms of correlated scattering imprint a unique signature in the heat current autocorrelation function that could be used as a diagnostic in other nanostructured systems.

Computational Study on the Thermal Conductivity of a Protein.

Protein molecules are thermally fluctuating and tightly packed amino acid residues strongly interact with each other. Such interactions are characterized in terms of heat current at the atomic level. We calculated the thermal conductivity of a small globular protein, villin headpiece subdomain, based on the linear response theory using equilibrium molecular dynamics simulation. The value of its thermal conductivity was 0.3 ± 0.01 [W m-1 K-1], which is in good agreement with experimental and computational studies on the other proteins in the literature. Heat current along the main chain was dominated by local vibrations in the polypeptide bonds, with amide I, II, III, and A bands on the Fourier transform of the heat current autocorrelation function.

Analysis of thermotransport and thermal and ionic conductivity in doped lanthanum gallate (LSGM) using molecular dynamics

The lattice thermal conductivity, ionic conductivity and thermotransport of doped lanthanum gallate (LSGM) were investigated using molecular dynamics (MD) using the Green-Kubo formalism across a wide temperature range. The lattice thermal conductivity was estimated by the heat current autocorrelation function directly from the simulation. Data from the autocorrelation function and the tracer diffusion coefficient of the mean squared displacement were used to calculate the ionic conductivity. The Green-Kubo formalism was employed to calculate the Onsager cross-coefficients (LAq and LqA). The results showed that the concentration of the dopant had a significant effect on both the thermotransport and the ionic conductivity. The results of this study demonstrated good agreement with the available experimental and theoretical data.

Theoretical study on enhancement of thermal conductivity and viscosity with volume fraction for ethylene glycol-based iron nanofluid

Gaining more higher heat transferability in nanofluids is one of the most serious relevant problems for improving efficiency in a variety of technology areas. In this study, the thermophysical properties of ethylene glycol-based (EG) iron nanofluid in comparison to its base fluid are investigated by using Equilibrium Molecular Dynamics (EMD) simulations combined with the hybrid pair potential in a LAMMPS (Large Scale Atomic-Molecular Massively Parallel Simulator) software that incorporates the 12–6 Lennard-Jones (L-J) potential with an Embedded Atom Method (EAM). The simulation findings showed that suspending spherical shaped iron nanoparticles in EG base fluid improves their viscosity, and conductivity (thermal) compare to the base fluid. Heat Current Autocorrelation function (HCACF) shows oscillatory behaviour initially. The amplitude of oscillation decays asymptotically around zero up to 0.75 ps. Thermal conductivity (TC) increases with volume fraction and temperature. Stress Autocorrelation function (SACF) decreases monotonically and viscosity increases with volume fraction but decreases with temperature.

Interpretation of apparent thermal conductivity in finite systems from equilibrium molecular dynamics simulations

We propose a way to properly interpret the apparent thermal conductivity obtained for finite systems using equilibrium molecular dynamics simulations (EMD) with fixed or open boundary conditions in the transport direction. In such systems the heat current autocorrelation function develops negative values after a correlation time which is proportional to the length of the simulation cell in the transport direction. Accordingly, the running thermal conductivity develops a maximum value at the same correlation time and eventually decays to zero. By comparing EMD with nonequilibrium molecular dynamics (NEMD) simulations, we conclude that the maximum thermal conductivity from EMD in a system with domain length $2L$ is equal to the thermal conductivity from NEMD in a system with domain length $L$. This facilitates the use of nonperiodic-boundary EMD for thermal transport in finite samples in close correspondence to NEMD.

Molecular Dynamics Determination of the Lattice Thermal Conductivity of the Cubic Phase of Hafnium Dioxide

The wide range of industrial applications is the main reason for an increased interest in dioxides such as HfO2. In this study, classical molecular dynamic simulations were performed to calculate the lattice thermal conductivity of the cubic phase of HfO2, over a temperature range of 100-3000 K, based on the Green-Kubo fluctuation method. In this research, the heat current autocorrelation function and lattice thermal conductivity were calculated in the a-direction. The lattice thermal conductivity of the cubic phase of HfO2 was found to be a result of three contributions. These were the optical and acoustic short-range and long-range phonon modes. Comparisons between the results of the research and experimental data when available indicate good agreement. Keywords: lattice thermal conductivity, molecular dynamics, Green-Kubo formalism, heat current autocorrelation function, hafnium dioxid

Phonon Thermal Conductivity of the Cubic and Monoclinic Phases of Zirconia by Molecular Dynamics Simulation

Zirconia has a number of remarkable properties, including a very low thermal conductivity. In this research, the phonon thermal conductivity of two phases (cubic and monoclinic) of zirconia (ZrO2) are calculated. For this purpose, an equilibrium molecular dynamics simulation employing the Green-Kubo formalism is used. The results are presented in detail over a wide temperature range, from 100 K to 2400 K and 100 K to 1400 K for the above-mentioned structures, respectively, with a 100K temperature step. The temperature dependence of the equilibrium atomic volume demonstrated a reasonable agreement with the experimental data. Moreover, the lattice thermal conductivity was calculated by analysing the heat current autocorrelation function. The results showed that zirconia has a low thermal conductivity that is dependent on the temperature. It was also shown that the lattice thermal conductivity of the two phases of zirconia can be decomposed into three contributions due to the acoustic shortrange and long-range phonon and optical phonon modes. Finally, the results from this research are compared with the available experimental data.

Prediction of the lattice thermal conductivity of zircon and the cubic and monoclinic phases of zirconia by molecular dynamics simulation

Zirconia (ZrO2) and zircon (ZrSiO4) have high strengths and stabilities at high temperatures and also have remarkable thermal properties, such as rather low thermal conductivities. In the present research, the phonon thermal conductivity of zircon and two polymorphs (cubic and monoclinic phases) of zirconia are investigated. For this purpose, equilibrium molecular dynamics simulations using classical interatomic potentials and the Green-Kubo formalism are presented. The results are given in detail over a wide temperature range, with a 100 K temperature step, from 200 K to 2400 K and 200 K to 1400 K for the cubic and monoclinic phases of zirconia, respectively, and 200 K to 1400 K for zircon. The temperature dependence of the lattice parameters and the equilibrium atomic volumes show good agreement with available experimental data. Next, the phonon thermal conductivity is calculated by analysing the raw data of the heat current autocorrelation function. The results illustrate that the above-mentioned materials have quite low thermal conductivities that are dependent on temperature. It is also shown that the lattice thermal conductivity of the different phases of zirconia and zircon can be decomposed into three contributions due to the acoustic short-range, long-range phonon and optical phonons modes. Finally, the thermal conductivity results from this study are compared with previous experimental studies and very good agreement is found.

The Thermal Conductivity of Magnesite, Dolomite and Calcite as Determined by Molecular Dynamics Simulation

In this study, the phonon-based thermal conductivity of magnesite (MgCO3) and dolomite (CaMg(CO3)2) is calculated and compared with an earlier recent calculation on calcite (CaCO3). Equilibrium molecular dynamics simulation by way of the elegant Green-Kubo formalism is used for calculating the thermal conductivity. The thermal conductivity is investigated over a wide temperature range (from 200 K to 800 K) for all of the above mentioned materials. The most reliable potential parameters are used for characterising the interatomic interactions. In all of the models, two independent mechanisms are considered. The first is temperature independent, which is relevant to the acoustic short-range and optical phonons, and the other is temperature dependent, which is linked to the acoustic long-range phonons. In the study, the heat current autocorrelation function (HCACF) is calculated over the averages of the NPT, NVT and NVE ensembles in the x- and z- directions. In addition, it is shown that the optical, acoustic short- and long-range phonon modes are the main contributors to the decomposition model of the thermal conductivity. In a further investigation, the effects of the computational cell sizes on the thermal conductivity are investigated with five different simulation blocks containing 30, 240, 810, 1920 and 6480 atoms. Finally, this research provides a comparison of the thermal conductivity from this study and experimental studies: they are in good agreement.

Determination of the lattice thermal conductivity of the TiO2 polymorphs rutile and anatase by molecular dynamics simulation

In this study, the structure of the lattice thermal conductivity of two TiO2 polymorphs, namely rutile and anatase, is determined by using equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism. The most reliable potential parameters are used to describe the interatomic potentials. The results are investigated over a wide temperature range, from 200 to 800 K, with a 100 K temperature step. As titanium dioxide is an anisotropic material, all of the parameters are investigated in both the a- and c-directions. The raw data for the heat current autocorrelation function is analysed to determine the structure of the lattice thermal conductivity. It is revealed that the lattice thermal conductivity of the TiO2 polymorphs can be decomposed into three contributions due to the acoustic short-range and long-range phonon and optical phonon modes. These three contributions can be presented in the form of simple kinetic formulae consisting of the products of the heat capacity, the square of the average phonon velocity and the average relaxation time of the acoustic short- and long-range phonon and optical phonon modes. In particular, it is shown that the average phonon velocities of the acoustic short- and long-range phonon and optical phonon modes are approximately equal to each other and can be expressed through the second-order fluctuations of the heat current vector. The effects of different simulation cell sizes at different temperatures on the lattice thermal conductivity are also investigated. Finally, the results from this work are compared with the experimental data and good agreement is found.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases.

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

A molecular dynamics study of liquid layering and thermal conductivity enhancement in nanoparticle suspensions

Liquid layering is considered to be one of the factors contributing to the often anomalous enhancement in thermal conductivity of nanoparticle suspensions. The extent of this layering was found to be significant at lower particle sizes, as reported in an earlier work by the authors. In continuation to that work, an investigation was conducted to better understand the fundamental parameters impacting the reported anomalous enhancement in thermal conductivity of nanoparticle suspensions (nanofluids), utilizing equilibrium molecular dynamics simulations in a copper-argon system. Nanofluids containing nanoparticles of size less than 6 nm were investigated and studied analytically. The heat current auto-correlation function in the Green-Kubo formulation for thermal conductivity was decomposed into self-correlations and cross-correlations of different species and the kinetic, potential, collision and enthalpy terms of the dominant portion of the heat current vector. The presence of liquid layering around the nanoparticle was firmly established through simulations that show the dominant contribution of Ar-Ar self-correlation and the trend displayed by the kinetic-potential cross-correlation within the argon species.

The thermal conductivity decomposition of calcite calculated by molecular dynamics simulation

Calcite based materials are being used in a range of new energy technologies for power generation and energy storage; in addition to their traditional use in manufacturing, agri-food industry and medicine. The optimum design of these new energy technology platforms requires an in-depth knowledge of the thermo-physical properties of calcite. In this study, the lattice thermal conductivity of calcite (CaCO3) is investigated in detail over a wide temperature range. Calculations are performed within the framework of equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism. To describe the interatomic interactions, the potential parameters of the shell model potentials for calcite developed by Pavese et al. are used. Within the framework of this model we calculate the heat current autocorrelation function over the temperature range of 200–800K for averages over the NPT, NVT and NVE ensembles in the a- and c- directions. It is revealed that the lattice thermal conductivity can be decomposed into three contributions due to the optical, acoustic short- and long-range phonon modes. Finally, results from this study can be compared with previous related dielectric materials and experimental studies, with good agreement.

Thermal conductivity calculation of nano-suspensions using Green–Kubo relations with reduced artificial correlations

The presence of artificial correlations associated with Green–Kubo (GK) thermal conductivity calculations is investigated. The thermal conductivity of nano-suspensions is calculated by equilibrium molecular dynamics (EMD) simulations using GK relations. Calculations are first performed for a single alumina (Al2O3) nanoparticle dispersed in a water medium. For a particle size of 1 nm and volume fraction of 9%, results show enhancements as high as 235%, which is much higher than the Maxwell model predictions. When calculations are done with multiple suspended particles, no such anomalous enhancement is observed. This is because the vibrations in alumina crystal can act as low frequency perturbations, which can travel long distances through the surrounding water medium, characterized by higher vibration frequencies. As a result of the periodic boundaries, they re-enter the system resulting in a circular resonance of thermal fluctuations between the alumina particle and its own image, eventually leading to artificial correlations in the heat current autocorrelation function (HCACF), which when integrated yields abnormally high thermal conductivities. Adding more particles presents ‘obstacles’ with which the fluctuations interact and get dissipated, before they get fed back to the periodic image. A systematic study of the temporal evolution of HCACF indicates that the magnitude and oscillations of artificial correlations decrease substantially with increase in the number of suspended nanoparticles.

Lattice thermal conductivity of boron nitride nanoribbon from molecular dynamics simulation

The lattice thermal conductivity of boron nitride nanoribbon(BNNR) is calculated by using equilibrium molecular dynamics (EMD) simulation method. The Green–Kubo relation derived from linear response theory is used to acquire the thermal conductivity from heat current auto-correlation function (HCACF). HCACF of the selected BNNR system shows a tendency of a very fast decay and then be followed by a very slow decay process, finally, approaching zero approximately within 3 ps. The convergence of lattice thermal conductivity demonstrates that the thermal conductivity of BNNR can be simulated by EMD simulation using several thousands of atoms with periodic boundary conditions. The results show that BNNR exhibit lower thermal conductivity than that of boron nitride(BN) monolayer, which indicates that phonons boundary scatting significantly suppresses the phonons transport in BNNR. Vacancies in BNNR greatly affect the lattice thermal conductivity, in detail, only 1% concentration of vacancies in BNNR induce a 60% reduction of the lattice thermal conductivity at room temperature.

Modulating thermal conduction by the axial strain

Recent studies have revealed that the symmetry of interparticle potential plays an important role in the one-dimensional thermal conduction problem. Here we demonstrate that, by introducing strain into the Fermi–Pasta–Ulam-β lattice, the interparticle potential can be converted from symmetric to asymmetric, which leads to a change of the asymptotic decaying behavior of the heat current autocorrelation function. More specifically, such a change in the symmetry of the potential induces a fast decaying stage, in which the heat current autocorrelation function decays faster than power-law manners or in a power-law manner but faster than ~t−1, in the transient stage. The duration of the fast decaying stage increases with increasing strain ratio and decreasing of the temperature. As a result, the thermal conductivity calculated following the Green–Kubo formula may show a truncation-time independent behavior, suggesting a system-size independent thermal conductivity.

Key role of asymmetric interactions in low-dimensional heat transport

We study the heat current autocorrelation function (HCAF) in one-dimensional, momentum-conserving lattices. In particular, we explore if there is any link between the decaying characteristics of the HCAF and asymmetric interparticle interactions. The Lennard-Jones model is investigated intensively in view of its significance to applications. It is found that, in the time range accessible to numerical simulations, the HCAF decays faster than power-law manners, and in some cases it decays even exponentially. Following the Green–Kubo formula, fast decay of the HCAF implies convergence of the heat conductivity, which is also corroborated by simulations. In addition, with a comparison to the Fermi–Pasta–Ulam-β model of symmetric interactions, the HCAF of the Fermi–Pasta–Ulam-α–β model of asymmetric interactions is also investigated. The results of all these studies lead to that, in certain ranges of parameters, fast decaying of the HCAF can be observed and correlated to the asymmetry degree of interactions.

Insight into lattice thermal impedance via equilibrium molecular dynamics: case study on Al

Using results of equilibrium molecular dynamics simulation in conjunction with the Green–Kubo formalism, we present a general treatment of thermal impedance of a crystal lattice with a monatomic unit cell. The treatment is based on an analytical expression for the heat current autocorrelation function which reveals, in a monatomic lattice, an energy gap between the origin of the phonon states and the beginning of the energy spectrum of the so-called acoustic short-range phonon modes. Although, we consider here the f.c.c. Al model as a case example, the analytical expression is shown to be consistent for different models of elemental f.c.c. crystals over a wide temperature range. Furthermore, we predict a frequency ‘window’ where the thermal waves can be generated in a monatomic lattice by an external periodic temperature perturbation.

Phonon-mediated heat dissipation in a monatomic lattice: case study on Ni

The recently introduced analytical model for the heat current autocorrelation function of a crystal with a monatomic lattice [Evteev et al., Phil. Mag. 94 (2014) p. 731 and 94 (2014) p. 3992] is employed in conjunction with the Green–Kubo formalism to investigate in detail the results of an equilibrium molecular dynamics calculations of the temperature dependence of the lattice thermal conductivity and phonon dynamics in f.c.c. Ni. Only the contribution to the lattice thermal conductivity determined by the phonon–phonon scattering processes is considered, while the contribution due to phonon–electron scattering processes is intentionally ignored. Nonetheless, during comparison of our data with experiment an estimation of the second contribution is made. Furthermore, by comparing the results obtained for f.c.c. Ni model to those for other models of elemental crystals with the f.c.c. lattice, we give an estimation of the scaling relations of the lattice thermal conductivity with other lattice properties such as the coefficient of thermal expansion and the bulk modulus. Moreover, within the framework of linear response theory and the fluctuation-dissipation theorem, we extend our analysis in this paper into the frequency domain to predict the power spectra of equilibrium fluctuations associated with the phonon-mediated heat dissipation in a monatomic lattice. The practical importance of the analytical treatment lies in the fact that it has the potential to be used in the future to efficiently decode the generic information on the lattice thermal conductivity and phonon dynamics from a power spectrum of the acoustic excitations in a monatomic crystal measured by a spectroscopic technique in the frequency range of about 1–20 THz.

Two-fluid nature of phonon heat conduction in a monatomic lattice

The thermal resistance of a crystal lattice with a monatomic unit cell due to three-phonon scattering processes is investigated in detail theoretically. A general expression for the lattice thermal conductivity is derived from a combined analysis based on: (i) the Boltzmann equation and (ii) data on the heat current autocorrelation function obtained via molecular dynamics simulations in conjunction with the Green–Kubo formalism. It is argued that the phonon gas in a monatomic lattice conducts heat as if it consisted of two distinct parts (two ‘thermal fluids’), so that the lattice thermal conductivity can be decomposed into contributions from these two parts. The origin of the behaviour of the phonon gas, which is explored in the present work, is due to an intrinsic interplay between Umklapp and normal three-phonon scattering processes. New insight into the nature of the lattice thermal conductivity is demonstrated and the results of the present work are in agreement with previous studies in this area.