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.
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¶
batteries1.ipynb will guide you through the first day of the
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
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
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
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?