# Batteries¶

In this exercise we will study the anode and cathode material of a Li-ion battery. The cathode material will be LiFePO4 a typical cathode material in rechargeable Li-ion batteries. The anode will be graphite.

The first day we start out soft by calculating the intercalation energy of Li in graphite while we learn the methods and workflow using ASE and GPAW. The second day will be about determining the equilibrium potential of a LiFePO4/C battery, we will also use a Bayesian approach to estimate the DFT error we expect on this important value. On the final day we will determine important battery characteristics such Li transport barriers and the voltage profile.

Tools used:

• Structure creation and modification with ASE

• Unit cell relaxation

• Bayesian error estimation

• Nudged Elastic Band (NEB) calculations for estimating Li migration barriers

## Part 1: Li intercalation energy in graphite¶

The notebook batteries1.ipynb will guide you through the first day of the battery exercise.

• Setup a graphite structure

• Calculate C-C and interlayer distances

• Use an empirical potential and DFT with a couple of exchange correlation functionals and compare with experimental values

• Setup and calculate the energy of Li metal

• Using DFT only from now on

• Setup and calculate the combined structure of Li between graphene layers

• Use all values to determine the Li intercalation energy

• Compare the results of different functionals with experimental values.

## Part 2: Equilibrium potential of a LiFePO4/C battery¶

You will calculate the equilibrium potential and use Bayesian error estimation to quantify how sensitive the calculated equilibrium potential is towards choice of functional. The notebook is batteries2.ipynb.

• Setup and calculate FePO4 and LiFePO4 structures

• Use these and the previous Li metal calculation to determine the equilibrium potential of a FePO4/Li battery

• Get an uncertainty estimation on the potential by using an ensemble of functionals called a BEEFEnsemble

• Using values from the previous day calculate the equilibrium potential of the full Li FePO4/C battery

## Part 3: Transport barriers and voltage profile¶

You will calculate the energy barriers for transport of Li intercalated in the graphite anode. You will examine how sensitive this barrier is to the interlayer distance in graphite. You will also examine the energy of intermediate states during the charge/discharge process. This will allow some basic discussion of the voltage profile of the battery. The notebook is batteries3.ipynb.

• Create intial and final structures for a NEB calculation, that will determine the transition state

• If time permits you can study the influence of changing the interlayer graphite distance on the energy barrier.

• Create structures for a Li vacancy in LiFePO4 and a single Li in FePO4

• Calculate the Li vacancy/insertion energies and compare them to the equilibrium potential

• What can they tell you about the charge/discharge potential curves?