Creating Temperature Dependent Free Energy Functionals for Multi-scale Modelling of Electrode Materials

First-Principles Derived Free Energy Functionals for Multi-scale Modelling of Electrode Materials

S. Hammadi, J. Kullgren, D. Brandell, P. Broqvist
Department of Chemistry-Ångström Laboratory, Uppsala University, Sweden

The development of computational methods that allow for an accurate determination of the temperature distribution in a multi-particle cathode system at operating conditions is essential for designing secure batteries [1]. In this work, we aim to build a mechano-chemical coupled phase-field model to investigate intercalation in cathode materials. More specifically, we are building a framework for the generation of free energy functionals by integrating force-field and cluster expansion models based on ab initio data with efficient sampling algorithms. In this presentation, I will focus on the generation of ab initio data and the problems encountered when generating data sets for training models, in particular for cases where we expect phase transformations during intercalation, such as for LFP (LiFePO4, see figure). During the intercalation of Li in FePO4, the redox couple Fe(+III)/Fe(+II) is used to compensate for the Li+ -ion formation. At the electronic level, Li intercalation leads to the formation of a polaron through the occupation of a low-level t2g electron d-orbital in Fe(II). At the atomic level, the position of these in relation to the Li-ions adds to the degree of freedom of the system, and thereby to the configurational entropy of the system. It is thus
important to quantify the fundamental interactions between polarons and Li-ions if we want to model temperature-dependent properties of the intercalation process.
From a first-principles point of view, simulations of strongly correlated systems are complicated and computationally expensive. For example, self-interaction errors encountered in standard semi-local DFT make these methods incapable of predicting the energetics of systems with polarons. To overcome this problem, Hubbard-corrected semi-local functionals, so-called DFT+U functionals, are often used, which penalize delocalization by endorsing integer orbital occupations at a low computational cost. However, the use of these methods often results in “corrupted” potential energy surfaces with many metastable states, thereby making it difficult for the generation of training data in a high-throughput fashion. In this work, we show how occupation matrix control can be used to circumvent this problem.
The DFT+U data is used to fit an interatomic potential and through Monte-Carlo sampling, we show that while polarons initially cluster together with Li-ions, they separate at temperatures relevant to battery applications. To account for such effects, special care needs to be taken when using DFT+U calculations in conjunction with high-throughput workflows.

[1] Li, Y., et al. (2014). Current-induced transition from particle-by-particle to concurrent intercalation
in phase-separating battery electrodes. Nature materials, 13(12), 1149-1156.