Predicting Phonon Properties from Equilibrium Molecular Dynamics Simulations (original) (raw)
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A phonon heat bath approach for the atomistic and multiscale simulation of solids
International Journal for Numerical Methods in Engineering, 2007
We present a novel approach to numerical modelling of the crystalline solid as a heat bath. The approach allows bringing together a small and a large crystalline domain, and model accurately the resultant interface, using harmonic assumptions for the larger domain, which is excluded from the explicit model and viewed only as a hypothetic heat bath. Such an interface is non-reflective for the elastic waves, as well as providing thermostatting conditions for the small domain. The small domain can be modelled with a standard molecular dynamics approach, and its interior may accommodate arbitrary non-linearities. The formulation involves a normal decomposition for the random thermal motion term R(t) in the generalized Langevin equation for solid-solid interfaces. Heat bath temperature serves as a parameter for the distribution of the normal mode amplitudes found from the Gibbs canonical distribution for the phonon gas. Spectral properties of the normal modes (polarization vectors and normal frequencies) are derived from the interatomic potential. Approach results in a physically motivated random force term R(t) derived consistently to represent the correlated thermal motion of lattice atoms. We describe the method in detail, and demonstrate applications to one-and two-dimensional lattice structures.
Phonon thermal conductivity by non-local non-equilibrium molecular dynamics
arXiv: Materials Science, 2014
Non-equilibrium (NE) molecular dynamics (MD), or NEMD, gives a "direct" simulation of thermal conductivity kappa. Heat H(x) is added and subtracted in equal amounts at different places x. After steady state is achieved, the temperature T(x) is found by averaging over finite sections. Usually the aim is to extract a value of dT/dx from a place distant from sources and sinks of heat. This yields an effective kappa(L) for the thermal conductivity, L being the system size. The result is then studied as a function of L, to extract the bulk limit kappa. Here instead, our heat is H(x)~sin(qx), where q=2pi/L. This causes a steady-state temperature T_0 + Delta T sin(2pi x/L). A thermal conductivity kappa(q) is extracted, which is well converged at the chosen q (or L). Bulk conductivity kappa requires taking the q to 0 limit. The method is tested for liquid and crystalline argon. One advantage is reduced computational noise at a given total MD run time. Another advantage is that kap...
Relaxation of Phonons in Classical MD Simulation
Journal of Thermal Science and Technology, 2008
We propose a novel technique of molecular dynamics simulation to evaluate the relaxation time of phonons in solids for investigation of solid heat conductivity. The basic idea is to observe relaxation behavior of the power spectrum of atomic velocities after energetically stimulating modes in a specific frequency region. The transient entropy S (t) is defined with the power spectrum based on non-equilibrium statistical mechanics to quantitatively evaluate the relaxation speed. In this paper, two example systems are shown; Lennard-Jones model crystal and silicon crystal. For both systems, we found that the observed S (t) is well fitted to a single exponential function, from which we can obtain a frequency-dependent relaxation time.
Physical Review B, 2022
Approach-to-equilibrium molecular dynamics (AEMD) is a widely used molecular dynamics (MD) method to extract thermal transport properties in different material systems. Despite the success in many applications, the thermal transport mechanism in AEMD is not well understood. Although AEMD can simulate larger domain than other MD variants, it still suffers from simulation domain size effect. In addition, the size effect is quite different from that of the nonequilibrium molecular dynamics (NEMD) simulations. In this paper, we reveal the phonon transport mechanism in AEMD by comparing the size-dependent thermal conductivity values of AEMD and phonon Boltzmann transport equation. We show that the simulation size of AEMD should be defined as half of the size in the conventional AEMD simulations with periodic boundary conditions. Also, the size effect in AEMD originates from ballistic phonon transport. Different from NEMD, some phonons with long mean-free paths do not contribute to the thermal conductivity, resulting in a smaller thermal conductivity than NEMD with the same size. Based on the phonon transport mechanism in AEMD, we suggest an extrapolation method for AEMD to obtain bulk thermal conductivity.
STUDY OF PHONON HEAT TRANSFER IN METALLIC SOLIDS FROM MOLECULAR DYNAMICS SIMULATIONS
2000
To describe the thermal behaviour of nanostructured materials and nanoelectronic devices, new properties and models have to be determined at the atomic scale. Recent experimental techniques such as near field microscopy 1-2 allow to investigate heat transfer at small scales, but, the spatial resolution is still greater than 50 to 100 nm. This remains too large when the typical length of interest is a few nm. Moreover, at this scale, the sensor may have a significant influence on the temperature or the property to be measured. Numerical simulation is then the solution to study the matter at the atomic scale and to predict the thermophysical properties of solids.
Journal of Chemical Physics, 2019
Collective excitations of crystal vibrations or normal modes are customarily described using complex normal mode coordinates. While appropriate for calculating phonon dispersion, the mixed representation involving the complex conjugates does not allow the construction of equivalent phonon occupation number or modal dynamical quantities such as the energy or heat current specific to a wave-vector direction (q). Starting from a canonical solution that includes waves going to the left and right directions, we cast the Hamiltonian, normal mode population, and heat current in an exactly diagonalizable representation using real normal mode amplitudes. We show that the use of real amplitudes obviates the need for a complex modal heat current while making the passage to second quantization more apparent. Using nonequilibrium molecular dynamics simulations, we then compute the net modal energy, heat current, and equivalent phonon population in a linear lattice subjected to a thermal gradient. Our analysis paves a tractable path for probing and computing the direction-dependent thermal-phononic modal properties of dielectric lattices using atomistic simulations. Published under license by AIP Publishing. https://doi.org/10.1063/1.5099936 ., s
DSMC scheme to study phonon dynamics
Journal of Mechanical Science and Technology, 2011
In order to solve the Boltzmann transport equation (BTE) of phonons for investigating heat conduction in non-metallic solids, we propose employing a DSMC (direct simulation Monte Carlo) scheme to simulate the dynamics of phonons analogous to rarefied gas. In contrast to treating the BTE with conventional linear approximation, this scheme requires no relaxation times as input parameters. We can directly investigate couplings among phonons with different modes, although we have to assume an appropriate scattering model for phonon-phonon interactions. In this paper, we describe the DSMC scheme for phonon dynamics and present some results with our prototype codes for a simple solid model. In the first case of single-branch four-phonon processes, we carried out simulations of nonequilibrium thin films with a temperature gradient. We found that the temperature jump at the boundaries can be successfully achieved. For the second case of three phonon processes, we developed a simulation code that takes into consideration the different acoustic branches to evaluate the mode-dependent relaxation time and mean free path. This type of DSMC scheme for phonons enables us to include other relevant factors, such as optical branches and phonon-electron interactions.
Lattice Dynamics: Phonon Relaxation
Springer Series in Chemical Physics, 2014
• Frequency of lattice vibration fingerprints the stiffness (Yd) of a peculiarly representative bond in real space in the form of x µ z/d(E/l) 1/2 µ (Yd) 1/2 with involvement of the bond order (z), bond length (d), bond energy (E), and the reduced mass of a dimer. • The process of phonon scattering contributes less to the intrinsic vibration. • Atomic undercoordination softens the optical phonons of nanostructures. • Intergrain interaction results in emerging of the low-frequency phonons whose frequency undergoes blueshift with reduction in solid size. • The D and 2D modes in carbon arise from interaction of a certain atoms with all of its z neighbors; while the G mode in carbon and the E g mode (144 cm-1) in TiO 2 are dominated by dimer interaction only.
Physical Review B, 2010
We use classical molecular dynamics to evaluate the thermal conductivity ͑T͒ from the heat-flux correlation ͗j͑0͒j͑t͒͘ for a two-dimensional Lennard-Jones triangular lattice. Our work, which follows Ladd, Moran, and Hoover ͓Phys. Rev. B 34, 5058 ͑1986͔͒, finds large deviations from the Eucken-Debye result ͑T͒ = A / T predicted by the phonon-gas model, even though phonon quasiparticles are fairly well defined. The main source of deviations comes from higher order ͑anharmonic͒ terms in the heat-flux operator j. By separating different orders of terms j = j ͑2͒ + j ͑3͒ +¯, we examine various separate contributions to ͑T͒Ϸ 22 + 23 +¯, both from the harmonic and the anharmonic heat fluxes. We find that 22 ͑T͒ϷA / T follows quasiparticle theory fairly well but important terms from 23 and 24 are independent of T in the classical ͑high T͒ limit. We use diagrammatic perturbation theory applied to the quantum Kubo formula, to check and explain the T dependence found numerically from anharmonic heat fluxes. We also demonstrate the importance of vertex correction in obtaining the correct quasiparticle coefficient of 1 / T.