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Kinetic Monte Carlo

Kinetic Monte Carlo (KMC), or dynamic Monte Carlo (DMC), uses known rates of reaction to predict the time evolution of a system. From known reaction rates, given events can be ranked by their likelihood of occurring. The algorithm proceeds by generating a random number u, and selecting an event based upon its probability and the random number. The reaction thus selected is carried out in the simulation, and the simulation time is incremented by Δt = -log u/R, where R is the sum of the rates of all reactions slower than the selected reaction.

KMC is used in the RPL to calculate the diffusivity of vacancies in solid oxide lattices. By quantum simulations, we determine the energy barriers to vacancy migration, and hence the rate for vacancy diffusion across one lattice site. KMC is then used to predict oxygen motion over larger distances from the rates of diffusion between adjacent sites.

First principles quantum simulations complemented with kinetic Monte Carlo (KMC) calculations were performed to gain insight into the oxygen vacancy diffusion mechanism and to explain the effect of dopant composition on ionic conductivity in yttria stabilized zirconia (YSZ). Density functional theory (DFT) within the local density approximation with gradient correction, was used to calculate a set of energy barriers that oxygen ions encounter during migration in YSZ by a vacancy mechanism. Kinetic Monte Carlo simulations were then performed using Boltzmann probabilities based on the calculated DFT barriers to determine the dopant concentration dependence of the oxygen self-diffusion coefficient in (Y₂O₃)_x(ZrO₂)_(1-2x) with x increasing from 6% to 15%. The results from the simulations suggest that the maximum conductivity occurs at 7-9 mol % Y₂O₃ at 600-1500 K and that the effective activation energy increases at higher Y doping concentrations in good agreement with previously reported literature data.

Figure 1: KMC Model