Phase field modeling for atoms

The application of phase-field modeling has been expanded into smaller and smaller-scale phenomena. However, phase-field models are typically based on the phase transition theory of continuum mechanics and their application to atomic systems has been limited. Here, we have developed phase-field modeling for atoms, in which atom fluctuations are represented by Gaussian distributions, and their motions are calculated by the conservative type phase-field equation. We found that our modeling successfully reproduced the stabilization of ${\mathrm{SrTiO}}_3$ lattices under $NVT$ and $NPT$ conditions. Moreover, we found that our modeling may enable us to obtain nonequilibrium thermodynamics properties such as the time evolution of entropy and local free energy distributions for atomic systems, which are difficult for the conventional molecular dynamics simulation. This research will expand the application of the phase-field concept into the single atom length scale, suggesting that this methodology can be applied to more diverse systems and purposes.