Implementation of this scheme was achieved by incorporating the kinetic Monte Carlo (KMC) algoritm into i-Pi, which is a universal force engine interface code written in Python, designed to be used together with an ab-initio, force-field, or Neural Network potential evaluation of the interactions between the atoms.
kinetic MC simulation algorithm carries out elementary swaps on a virtual 3D grid with Periodic Boundery Condiction applied. This grid is on-lattice and follows the fcc-sites (example for Al). It can represent an idealized picture of vacancy migrations and precipitation sequence for fcc-alloy with many trace elements (example for two trace elements, i.e. Silicon and Magnesium). The defects as solute atoms and vacancies, are artificially and randomly introduced into the system to represent an initial state that corresponds to a Supersaturated Solid Solution.
Next, the energy of local minima is calculated for all these tracked-down process. The energy minimization cycle is performed by a fixed number of steps of the Limited memory BFGS.
The rates are, in turn, estimated based on activation barriers, which are a correction to those calculated with the Nudged Elastic Band method for the vacancy-assisted jump of an isolated solute atom. The new activation barrier for a swap involving a solute X is given by
where is the local minimized Neural Network energy at KMC
step n and
is the minimized Neural Network energies for the i-th candidate at step n+1.
is the DFT energy barrier for a swap of an isolate atom (e.g Vacancy/Al-atom,
Vacancy/Mg-atom, or Vacancy/Si-atom).
Rates computed based on these barriers are consistent with detailed balance.
A Python interface for ab initio path integral molecular dynamics simulations. i-PI is composed of a Python server (i-pi itself, that does not need to be compiled but only requires a relatively recent version of Python and Numpy) that propagates the (path integral) dynamics of the nuclei, and of an external code that acts as a client and computes the electronic energy and forces.
See README.rst
Ceriotti, More, Manolopoulos, Comp. Phys. Comm. 185, 1019-1026 (2014)
This project, as i-Pi software, is under the MIT/GPLv3 License.