Accelerating the molecular time steps for nanomechanical simulations: Hybrid Monte Carlo method

Abstract

A majority of computational mechanical analyses of nanocrystalline materials or nanowires have been carried out using classical molecular dynamics (MD). Due to the fundamental reason that the MD simulations must resolve atomic level vibrations, they cannot be carried out at a time scale of the order of microseconds in a reasonable computing time. Additionally, MD simulations have to be carried out at very high loading rates (∼108 s−1) rarely observed during experiments. In this investigation, a modified hybrid Monte Carlo (HMC) method that can be used to analyze time-dependent (strain-rate-dependent) atomistic mechanical deformation of nanostructures at higher time scales than currently possible using MD is established for a Cu nanowire and for a nanocrystalline Ni sample. In this method, there is no restriction on the size of MD time step except that it must ensure a reasonable acceptance rate between consecutive Monte Carlo (MC) steps. In order to establish the method, HMC analyses of a Cu nanowire deformation at two different strain rates, viz., 108 and 109 s−1, and of a nanocrystalline Ni sample deformation at a strain rate of 109 s−1 with three different time steps, viz., 2, 4, and 8 fs, are compared with the analyses based on MD simulations at the same strain rates and with a MD time step of 2 fs. MD simulations of the Cu nanowire as well as nanocrystalline Ni deformations reproduce the defect nucleation and propagation results as well as strength values reported in the literature. Defect formation and stress-strain responses of the Cu nanowire, as well as of the nanocrystalline Ni sample during HMC simulations with a time step of 8 fs, are similar to that observed in the case of MD simulations with the maximum permissible time step of 2 fs (for the interatomic potential used, 2 fs is the highest MD time step). Simulation time analyses show that by using HMC approximately 4 times saving in computational time can be achieved bringing the atomistic analyses closer to the continuum time scales.