Outstanding developments of computers and theoretical methods enable us to investigate stability and reactivity of bulk materials and hetero interfaces in atomistic scale with high precision, although we still have limitations about time domain and system size in computations. If we can extensively extend the accessible regions about both time and size domains at the same time in atomistic simulations, it will be a further development in computer simulations for materials and devise designing. In order to realize such an extended computational tool, we have been developing a full atomistic kinetic Monte Carlo (kMC) code [1,2] which can easily incorporate kinetic date from first principles atomistic calculations. The characteristic points involved in the developed kMC code are 1) parallelization in domain decomposition scheme, 2) easy constructions of hetero structures and reaction events, 3) boundary conditions for periodic/closed/open-boundary are available, 4) Poisson solver for the electrostatic field and on-the-fly update of reaction barriers, and 5) direct counting of passing ions.

A standard computation for an electrochemical cell with the developed kMC code using a single computer reaches μs-to-ms dynamics for 1 million atoms. Although the size of the computational cell seems not to be so huge, the “open” boundary condition enables us to investigate the ionic dynamics for “semi-infinite” system characterized by electrochemical potentials, and thus the concern about the size limitation is not problematic in the present approach. We applied the developed kMC method to the calculations of i) electromotive force (EMF) of an oxygen concentration cell composed of a standard oxides, zirconia, and ii) ionic current densities of a solid oxide fuel cell (SOFC) composed of Ni metal, gases, and zirconia-based oxide (see Figure for the atomistic model for SOFC anode). In the first target, we compared the calculated EMF with that obtained from Nernst’s equation and we found the excellent agreements between the simulated EMF and ideal EMF from the Nernst equation. This means, the ionic flow calculated in the atomistic scale can be seamlessly connected to the ionic flow in macroscopic scale in the Nernst-Plank phenomenological equation of flow. Our approach based on the atomistic modelling with direct counting for ionic flow thus opens a new direction for multi-scale simulations, that is, a “seamless” approach instead of a conventional “scale-bridging” approach. The first target corresponds to a demonstration of the applicability of our seamless approach in an equilibrium situation, and thus let us next move on an out-of-equilibrium situation, which is the scope of the second target (i.e., ionic current density of SOFC). We calculated current densities I of SOFC anode as a function of polarization V. By making up a corresponding continuum model for SOFC which is solved in a finite element method (FEM), the calculated current densities in our atomistic kMC approach is compared with those from the FEM calculations. We confirmed 1) the exchange current density (i.e., current density in an equilibrium situation) shows good correspondence with those with FEM, 2) the current densities with kMC at small polarization conditions also show good correspondence with those with FEM, and 3) small deviations of current densities between kMC and FEM appears when the polarization becomes large. The detailed discussion on each target will be presented in the talk.

References

1. T. Tada and N. Watanabe, ECS Transactions, 2013, 57, 2437-2447.

2. T. Tada, ECS Transactions, 2017, 78, 2815-2822.