Monte Carlo simulation of phonon transport in UO₂single crystals

Abstract

The Monte Carlo (MC) method is applied to solve the Boltzmann transport equation for phonons in uranium dioxide single crystals, with the objective of understanding thermal transport in this material at the mesoscale. The overall solution scheme tracks the phonon density as it evolves in space and time due to phonon drift and phonon–phonon scattering by normal and Umklapp processes. Unlike most previous works on solving the Boltzmann transport equation for phonons by the MC technique, our scheme for calculating phonon lifetime, based on normal and Umklapp scattering, eliminates the need for using many fitting parameters. Instead, the Grüneisen parameter, which is a well-characterized material property, is the only parameter of the problem. The results elucidate the simulation domain size over which the computed conductivity is size dependent; this helps to determine the minimum domain size required to simulate bulk thermal transport and hence calculate the thermal conductivity. The latter is computed over the temperature range 300–1000 K. The computed conductivity values are in good agreement with the previously published experimental and molecular dynamics simulation results.

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

“…The PMC method has been successfully applied to study thermal transport in various nanostructures such as membranes [71][72][73][74][75][76] and nanowires 72,[77][78][79][80] , and in Si [71][72][73][74][75][76][77][78][79]81 and a number of other materials. 78,80,[82][83][84][85][86] PMC has proven to be an effective tool to study nanoscale thermal transport in systems near equilibrium. 74,[86][87][88][89] It is also straightforward to include nontrivial geometries, such as rough boundaries or edges, in PMC.…”

“…From dispersion, we calculate properties such as the PDOS and group velocity. In previous PMC work, [71][72][73][74][77][78][79][80][81][82][83][84]86,87,90 isotropic approximations were often used to approximate the dispersion. However, the phonon dispersion relations of graphene are quite anisotropic.…”

Phonon transport mechanism of HfO2 ultrathin film with temperature-correction full-band Monte Carlo simulation

“…The kinetic-type Monte Carlo was developed by utilizing variance reduction, which considerably decreased the amount of computation and the error of results which promoted the MC method [18][19][20][21][22]. Then full-band Monte Carlo (FMC) was improved by performing first-principle method to obtain phonon information in the full Brillouin zone, which has been used to solve graphene, GaN, and other new materials and achieved good simulation results [23][24][25][26]. The MC method has also been used to study the phonon heat transport in films and interfaces with different materials [27][28][29].…”