Battery Cathodes: Intercalation Potential and Volume Change

Batteries Cathode materials Intercalation potential Volume change MLPotential

Note

This tutorial is intended for AMS2026 with access to the UMA-S-1.2-OMat machine learning potential.

This tutorial will teach you how to:

• Optimize the lithiated and delithiated crystal structures of LiFePO₄.

• Compute the intercalation potential from the two total energies.

• Compute the relative volume change upon delithiation.

• Adapt the workflow to explore doped cathodes.

If you follow this tutorial, you will be able to calculate the properties of the materials cited in Ref. [1].

Table 9 Comparison of the calculated average intercalation potential (IP, in V vs. Li/Li⁺) and the relative volume change upon delithiation (VC, in %) with the experimental data from Tables II and IV of Ref. [1].

Structure	Expt. IP	Calc. IP	Expt. VC	Calc. VC
LiCoO2	4.10	3.926	-7.958	-2.102
LiNiO2	3.90	4.014	-9.422	-8.461
LiTiS2	2.10	1.972	-10.605	-8.849
LiMn2O4	4.10	3.913	-5.051	-5.939
LiMnPO4	4.10	3.872	-9.046	-8.534
LiFePO4	3.50	3.573	-6.534	-5.764
LiCoPO4	4.80	4.412	-1.846	-4.310

Fig. 27 Calculated versus experimental benchmark values for the materials in Table II and Table IV of Ref. [1]. Blue circles show the intercalation potential (IP, in V vs. Li/Li⁺) and red crosses show the relative volume change upon delithiation (VC, in %). The dashed diagonal corresponds to y = x.

Note

Overall, UMA-S-1.2-OMat reproduces these properties very well, with noticeable deviations observed only for the Co-based materials.

Introduction

Olivine phosphate materials are widely studied as battery cathodes because they can combine good stability with high operating voltage. In this tutorial, we use LiFePO₄ as a starting point and evaluate two simple descriptors for cathode performance:

• the intercalation potential

• the volume change upon charging

This requires optimizing two crystal structures:

• the lithiated material LiFePO₄

• the delithiated material FePO₄

From these calculations, you can estimate the average lithium intercalation potential and the relative volume change.

\[IP = \frac{E(\mathrm{FePO_4}) + E(\mathrm{Li}) - E(\mathrm{LiFePO_4})}{F}\]

\[\Delta V (\%) = 100 \times \frac{V_{\mathrm{delithiated}} - V_{\mathrm{lithiated}}}{V_{\mathrm{lithiated}}}\]

The output of a lattice optimization job provides both the Energy (hartree) and the Unit cell volume (angstrom^3), which can be used to extract the relevant data for this tutorial. In addition, a consistent reference energy for the lithium metal is required when evaluating the intercalation potential. You should therefore review 10 Ways to Get the Energy and Other Properties.

Tip

We recommend creating a table to keep track of the energies and volumes for each calculation you perform below.

For comparison, the experimental values for LiFePO₄ and FePO₄ from Tables II and IV of Ref. [1] are:

Property	Experimental value
LiFePO4 volume (Å3 /f.u.)	72.85
FePO4 volume (Å3 /f.u.)	68.09
Relative volume change upon delithiation (%)	-6.534
Average intercalation potential (V vs. Li/Li+)	3.5

Determining the Lithium Reference

You will first calculate the lithium reference energy needed to compute the intercalation potential. Build and optimize bulk lithium in AMSinput:

1. Open AMSinput: SCM → New Input

2. Build the crystal: Builders → Crystal Structure → Cubic → bcc

3. Select Li from the element presets and click OK

4. Switch to the machine learning potential engine: →

5. Set Model to UMA-S-1.2-OMat

6. Set Task to Geometry Optimization

7. Go to Details → Engine Add-ons

8. Enable the D4 repulsion

9. Go to Details → GeometryOptimization

10. Set Optimize lattice to Yes

11. Save the job using File → Save

12. Run the calculation using File → Run

We find a lithium reference energy of E(Li) = -0.070836 Ha per atom.

Optimizing LiFePO₄ and FePO₄

You will now perform the lattice optimization for both the lithiated and delithiated structures.

First, set up the geometry optimization for LiFePO₄ in AMSinput:

1. Open AMSinput: SCM → New Input

2. Import the crystal structure: File → Import Coordinates (System) and select LiFePO4.cif

3. Switch to the machine learning potential engine: →

4. Set Model to UMA-S-1.2-OMat

5. Set Task to Geometry Optimization

6. Go to Details → Engine Add-ons

7. Enable the D4 repulsion

8. Go to Details → GeometryOptimization

9. Set Optimize lattice to Yes

10. Save the job using File → Save

11. Start the calculation using File → Run

Next, create the delithiated structure of FePO₄:

1. Reopen the LiFePO4 input

2. Select the lithium atoms in the structure view. To achieve this, select one Li atom and then use Select → Atoms of the Same → Type

3. Delete the selected lithium atoms with the Delete key

4. Save the input as a new job using File → Save As

5. Start the calculation using File → Run

After both jobs have finished, collect the total energies and optimized cell volumes. A summary of the results is shown below:

Calculation	Total energy (Ha)	Cell volume (Å 3)	Comment
Li metal	-0.070836 per atom	40.53114	bcc Li reference
LiFePO4	-7.21135362	293.76580	optimized lithiated structure
FePO4	-6.40276118	276.83367	optimized delithiated structure

Intercalation Potential and Volume Change

Use the total energies and volumes of LiFePO₄ and FePO₄ together with the lithium metal reference energy to compute the average intercalation potential and volume change. Note that our structure contains 4 stoichiometric units. We therefore divide our output energy values by 4 in order to compare the different phases.

For the reaction

\[\mathrm{LiFePO_4} \rightarrow \mathrm{FePO_4} + \mathrm{Li}\]

the benchmark calculation reported above gives the following LiFePO₄ values:

Property	Value
Average intercalation potential	3.573 V
Relative volume change	-5.764 %
Experimental intercalation potential	3.5 V
Experimental volume change	-6.534 %

You can repeat the workflow with other cathode materials to obtain Table 9.

Doped Cathode Materials

It is straightforward to extend the current analysis to investigate the impact of dopants in the cathode material. In this tutorial, we will replace a fraction of the Fe atoms by a different element and evaluate whether the modified material offers an improved trade-off between voltage and volume change.

Consider a composition of the form

\[\mathrm{LiFe}_{0.875}\mathrm{X}_{0.125}\mathrm{PO}_4\]

where X can be chosen from:

• Mg

• Ti

• Nb

• Si

• Co

The doped structure can be created easily in AMSinput:

1. Reopen the LiFePO4 input

2. Go to Edit → Crystal → Create Supercell. Place (2, 1, 1) on the diagonal and choose OK. This will create a cell containing 8 Fe atoms.

3. Select 1 of the Fe atoms and use Atom → Change Atom Type → Mg to add the dopant. (This matches the 0.125 fraction of our composition)

4. Save the input as a new job using File → Save As

5. Start the calculation using File → Run

We repeat these steps for the delithiated system:

1. Reopen the FePO4 input

2. Go to Edit → Crystal → Create Supercell. Place (2, 1, 1) on the diagonal and choose OK

3. Select 1 of the Fe atoms and use Atom → Change Atom Type → Mg to add the dopant

4. Save the input as a new job using File → Save As

5. Start the calculation using File → Run

The results of these calculations are summarized in the table below:

Dopant	Mg	Ti	Nb	Si	Co
Average intercalation potential (V)	3.756	3.176	2.993	3.040	3.670
Relative volume change (%)	-5.764	-5.740	-5.088	-9.902	-6.112
IP/-VC	0.738	0.574	0.725	0.307	0.601

We see that the dopant can significantly affect both IP and VC of the olivine structure. For most dopants, these shifts correlate, as higher IP coincide with increase VC. Identifying promising battery materials involves finding a host-dopant combination enhancing the intrinsic energy density. Utilising the IP per VC as a proxy metric, performance yields are noted only for Mg and Nb, likely on account of their greater electropositivity relative to Fe. Of these, Mg doping appears more appealing due to the higher intrinsic IP (in addition to material availability).

Summary

In this tutorial, you learned how to use AMSinput with a machine learning potential to:

• optimize lithiated and delithiated cathode structures

• extract total energies and cell volumes from the AMS GUI

• compute the average intercalation potential

• compute the relative volume change

• compare pristine and doped phosphate cathodes

The same approach can be extended to other battery materials and to larger screening studies.

References

[1] (1,2,3,4)

22. 12. Chevrier, S. P. Ong, R. Armiento, M. K. Y. Chan, G. Ceder. Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds. Phys. Rev. B 82, 075122 (2010).