The outstanding developments of computers and theoretical methods especially on first principles electronic structure calculations enable us to investigate the stability and reactivity of bulk materials and hetero interfaces in atomistic scale with high precision, although we still have limitations on the time domain and system size. If we can extensively extend the accessible regions about time domain and system size in atomistic simulations at the same time, it will be a further development in computer simulations for materials designing. In order to realize such an extended computational tool, we have been developing a full atomistic kinetic Monte Carlo code which can easily incorporate kinetic date from first principles calculations. The characteristic points in the kMC code are 1) parallelization in domain decomposition scheme, 2) easy constructions of hetero structures and reactions, 3) boundary conditions including open-boundary, 4) Poisson solver, and 5) direct counting of flowing current. Points 1, 2, and 3 (partly) were already described in our previous paper [1]. The standard cases for the developed kMC execution in a single computer are roughly μs-to-ms time domain for 1 million atoms. Although the size in the kMC might seem to be not so large, the atomistic system represented in kMC cell is defined as a function of electrochemical potential, together with thermodynamic parameters (i.e., temperature and pressure) and chemical conditions such as dopant conditions. That is, the kMC cell can be regarded as a semi-infinite system, and thus the problems on the size limitation is technically avoided. To explain this point in more detail, let’s consider a whole SOFC system composed of anode (A), solid electrolyte (SE), and cathode (C). The chemical composition in deep inside of SE can be regarded as a stoichiometric one even at a working situation with no degradation, and this is of course true at around equilibrium conditions, OCV. On the other hand, the compositions of interfaces A/SE and C/SE can be significantly deviated from the stoichiometry, depending on the thermodynamic conditions. Our kMC can handle the hetero interfaces A/SE and C/SE smoothly connected with stoichiometric SE in the kMC computational cell. That’s why the size limitation cannot be so problematic; it should be mentioned that we can also handle the whole system of A-SE-C in one kMC computational cell when the thickness of SE is too small to realize an equilibrium composition at the inside of SE. To check the reliability of the developed kMC code, we applied it to the calculations of electromotive force (EMF) of oxide concentration cells, and compared the calculated EMF with that obtained from Nernst equation. We adopted 8mol% doped YSZ as SE. In the EMF calculations, the direct counting approach of ionic current, one of the characteristic points in our kMC, was used to find OCV condition depending on gas partial pressures. As a result, we found the excellent agreements between simulated EMF and ideal EMF from Nernst equation. This means that the reliability of our kMC dynamics in the atomistic model is guaranteed in terms of thermodynamics because the equilibrium situations and steady states in the concentration cells are recognized using ionic motions (i.e., direct counting) in kMC. The details of calculated results and computational algorisms especially for direct counting and open-boundary condition will be explained in the conference.

Reference

[1] T. Tada and N. Watanabe, ECS Transactions 57(1), 2437-2447 (2013).