Calculation of the thermal conductivity coefficient of nanocrystals

Mathematical modeling methods are powerful tools in the design of various types of nanosystems and the analysis of processes taking place in them. Note that the main tasks of mathematical modeling in nanoscale systems are: the formation of nanoelements, the interaction of individual elements of the nanosystem, the determination of the structure of the isolated nanosystem in dynamic states, the calculation of the parameters of the nanosystem during its interaction with the environment, the calculation of the macro parameters of the nanosystem. With this work, we continue the consistent presentation of theoretical foundations, methods of modeling, and results of calculations of macro characteristics of nanosystems, based on the work on modeling of processes of formation and structure of different nanosystems. This paper provides the physical basis as well as numerical methods for calculating the thermal conductivity of homogeneous nanosystems. Computer simulation of the calculation of the thermal conductivity coefficient of silicon-based nanocrystals by molecular dynamics was carried out in the LAMMPS software complex. Equations describing multi-particle MEAM potentials are considered. The problem of determining the thermal conductivity coefficient has been solved in several steps. In molecular dynamic calculations, the value of the thermal conductivity coefficient can be calculated in various ways. This work uses the Green - Kubo formalism, which associates the autocorrelation function of heat flow with the coefficient of thermal conductivity. Temperature dependencies of thermal conductivity coefficient for silicon-based materials are determined. Calculations of thermophysical characteristics of homogeneous silicon-based nanosystems were made. The curves of the temperature dependence of thermal conductivity coefficient for systems of different dimensions are presented. Data obtained using MEAM potentials were compared with experimental data. It was found that the nature of the curves and the values obtained during the simulation are well consistent with the experimental data.