Computational materials science
Which statement about the kinetic Monte Carlo (kMC) method is correct?
- AIt assigns rates of the form ν exp(−E_a/kT) to events such as atomic jumps, selects events with probability proportional to their rates and advances time, so it can follow long-time diffusion and precipitation
- BIt integrates the atomic equations of motion in femtosecond steps, so it tracks atomic thermal vibrations accurately while handling longer diffusion times than molecular dynamics at the same cost
- CIt has no concept of time; it accepts energy-raising trials with probability exp(−ΔE/kT) and can be used only to obtain average properties in equilibrium
Show answer and explanation
Answer: A. It assigns rates of the form ν exp(−E_a/kT) to events such as atomic jumps, selects events with probability proportional to their rates and advances time, so it can follow long-time diffusion and precipitation
In diffusion in solids, an atom vibrates a very large number of times before occasionally jumping into a neighboring vacancy. Molecular dynamics follows all these vibrations, so phenomena longer than microseconds are hard to handle. kMC skips the vibrations: it prepares a list of events such as vacancy jumps with their activation energies, selects the next event with probability proportional to the rate ν exp(−E_a/kT), and advances time according to the inverse of the sum of all event rates. Activation energies calculated by DFT are often used. This makes it possible to follow the growth of precipitates during aging and the evolution of irradiation defects in real time. Integrating equations of motion is a feature of molecular dynamics, and having no time while finding equilibrium averages is a feature of the Metropolis method.