Direct coupling of first-principles calculations with replica exchange Monte Carlo sampling of ion disorder in solids

Facilitating ab initio configurational sampling of multicomponent solids using an on-lattice neural network model and active learning

We propose a scheme for ab initio configurational sampling in multicomponent crystalline solids using Behler-Parinello type neural network potentials (NNPs) in an unconventional way: the NNPs are trained to predict the energies of relaxed structures from the perfect lattice with configurational disorder instead of the usual way of training to predict energies as functions of continuous atom coordinates. An active learning scheme is employed to obtain a training set containing configurations of thermodynamic relevance. This enables bypassing of the structural relaxation procedure which is necessary when applying conventional NNP approaches to the lattice configuration problem. The idea is demonstrated on the calculation of the temperature dependence of the degree of A/B site inversion in three spinel oxides, MgAl2O4, ZnAl2O4, and MgGa2O4. The present scheme may serve as an alternative to cluster expansion for `difficult' systems, e.g., complex bulk or interface systems with many components and sublattices that are relevant to many technological applications today.

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/t algorithm, in particular the short iteration performance. A proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li_{0.5}La_{0.5}TiO_{3}. This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li_{0.5}La_{0.5}TiO_{3} are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li_{0.5}La_{0.5}TiO_{3} system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.