Predictions of the bulk scale thermal conductivity of solids using non-equilibrium molecular dynamics (MD) simulations have relied on the linear extrapolation of the thermal resistivity versus the reciprocal of the system length in the simulations. Several studies have reported deviation of the extrapolation from linearity near the micro-scale, raising a concern of its applicability to large systems. To investigate this issue, present work conducted extensive MD simulations of silicon with two different potentials (EDIP and Tersoff-II) for unprecedented length scales up to 10.3 μm and simulation times up to 530 ns. For large systems ≥0.35 μm in size the non-linearity of the extrapolation of the reciprocal of the thermal conductivity is mostly due to ignoring the dependence of the thermal conductivity on temperature. To account for such dependence, the present analysis fixes the temperature range for determining the gradient for calculating the thermal conductivity values. However, short systems ≤0.23 μm in size show significant non-linearity in the calculated thermal conductivity values using a temperature window of 500 ± 10 K from the simulations results with the EDIP potential. Since these system sizes are shorter than the mean phonon free path in EDIP (~0.22 μm), the nonlinearity may be attributed to phonon transport. For the MD simulations with the Tersoff-II potential there is no significant non-linearity in the calculated thermal conductivity values for systems ranging in size from 0.05 to 5.4 μm.
The lack of a reliable method to evaluate the convergence of molecular dynamics simulations has contributed to discrepancies in different areas of molecular dynamics. In the present work, the method of information entropy is introduced to molecular dynamics for stationarity assessment. The Shannon information entropy formalism is used to monitor the convergence of the atom motion to a steady state in a continuous spatial domain and is also used to assess the stationarity of calculated multidimensional fields such as the temperature field in a discrete spatial domain. It is demonstrated in this work that monitoring the information entropy of the atom position matrix provides a clear indicator of reaching steady state in radiation damage simulations, non-equilibrium molecular dynamics thermal conductivity computations, and simulations of Poiseuille and Couette flow in nanochannels. A main advantage of the present technique is that it is non-local and relies on fundamental quantities available in all molecular dynamics simulations. Unlike monitoring average temperature, the technique is applicable to simulations that conserve total energy such as reverse non-equilibrium molecular dynamics thermal conductivity computations and to simulations where energy dissipates through a boundary as in radiation damage simulations. The method is applied to simulations of iron using the Tersoff/ZBL splined potential, silicon using the Stillinger-Weber potential, and to Lennard-Jones fluid. Its applicability to both solids and fluids shows that the technique has potential for generalization to other areas in molecular dynamics.
The Corrected Rigid Spheres (CRIS) equation of state (EOS) model [Kerley, J. Chem. Phys. 73, 469 (1980); 73, 478 (1980); 73, 487 (1980)], developed from fluid perturbation theory using a hard sphere reference system, has been successfully used to calculate the EOS of many materials, including gases and metals. The radial distribution function (RDF) plays a pivotal role in choosing the sphere diameter, through a variational principle, as well as the thermodynamic response. Despite its success, the CRIS model has some shortcomings in that it predicts too large a temperature for liquid-vapor critical points, can break down at large compression, and is computationally expensive. We first demonstrate that an improved analytic representation of the hard sphere RDF does not alleviate these issues. Relaxing the strict adherence of the RDF to hard spheres allows an accurate fit to the isotherms and vapor dome of the Lennard-Jones fluid using an arbitrary reference system. The second order correction is eliminated, limiting the breakdown at large compression and significantly reducing the computation cost. The transferability of the new model to real systems is demonstrated on argon, with an improved vapor dome compared to the original CRIS model.
Understanding the propagation of radiation damage in a material is paramount to predicting the material damage effects. To date, no current literature has investigated the Threshold Displacement Energy (TDE) of Ca and F atoms in CaF2 through molecular dynamics and simulated statistical analysis. A set of interatomic potentials between Ca-Ca, F-F, and F-Ca were splined, fully characterizing a pure CaF2 simulation cell, by using published Born-Mayer-Huggins, standard ZBL, and Coulomb potentials, with a resulting structure within 1% of standard density and published lattice constants. Using this simulation cell, molecular dynamics simulations were performed with LAMMPS using a simulation that randomly generated 500 Ca and F PKA directions for each incremental set of energies, and a simulation in each of the [1 0 0], [1 1 0], and [1 1 1] directions with 500 trials for each incremental energy. MD simulations of radiation damage in CaF2 are carried out using F and Ca PKAs, with energies ranging from 2 to 200 eV. Probabilistic determinations of the TDE and Threshold Vacancy Energy (TVE) of Ca and F atoms in CaF2 were performed, as well as examining vacancy, interstitial, and antisite production rates over the range of PKA energies. Many more F atoms were displaced from both PKA species, and though F recombination appears more probable than Ca recombination, F vacancy numbers are higher. The higher number of F vacancies than Ca vacancies suggests F Frenkel pairs dominate CaF2 damage.
The effects of irradiation on 3C-silicon carbide (SiC) and amorphous SiC (a-SiC) are investigated using both in situ transmission electron microscopy (TEM) and complementary molecular dynamics (MD) simulations. The single ion strikes identified in the in situ TEM irradiation experiments, utilizing a 1.7 MeV Au3+ ion beam with nanosecond resolution, are contrasted to MD simulation results of the defect cascades produced by 10-100 keV Si primary knock-on atoms (PKAs). The MD simulations also investigated defect structures that could possibly be responsible for the observed strain fields produced by single ion strikes in the TEM ion beam irradiation experiments. Both MD simulations and in situ TEM experiments show evidence of radiation damage in 3C-SiC but none in a-SiC. Selected area electron diffraction patterns, based on the results of MD simulations and in situ TEM irradiation experiments, show no evidence of structural changes in either 3C-SiC or a-SiC.
Molecular dynamics simulations are carried out to characterize irradiation effects in TiO2 rutile, for wide ranges of temperatures (300-900 K) and primary knock-on atom (PKA) energies (1-10 keV). The number of residual defects decreases with increased temperature and decreased PKA energy, but is independent of PKA type. In the ballistic phase, more oxygen than titanium defects are produced, however, the primary residual defects are titanium vacancies and interstitials. Defect clustering depends on the PKA energy, temperature, and defect production. For some 10 keV PKAs, the largest cluster of vacancies at the peak of the ballistic phase and after annealing has up to ≈1200 and 100 vacancies, respectively. For the 10 keV PKAs at 300 K, the energy storage, primarily in residual Ti vacancies and interstitials, is estimated at 140-310 eV. It decreases with increased temperature to as little as 5-180 eV at 900 K. Selected area electron diffraction patterns and radial distribution functions confirm that although localized amorphous regions form during the ballistic phase, TiO2 regains full crystallinity after annealing.