# Gibbs energy for Lithiation in Lithium batteries

• JulesP
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JulesP
TL;DR Summary
The calculation for lithiation in a Lithium Iron Phosphate battery
In writing up a paper on some research work on the effects of transients on Lithium Iron Phosphate batteries, I am laying out the thermodynamics and energetics for the reaction laid out below, but am having trouble finding the numbers for the reaction.

Does anyone know the correct figures to insert so I can get an overall Gibbs value for the reaction?

Thank you

for sharing your research work on Lithium Iron Phosphate batteries. I can understand the difficulty in finding the specific numbers for the reaction, as it is a complex and constantly evolving field of study. However, to calculate the Gibbs energy for lithiation in Lithium batteries, we need to consider the overall reaction:

Li + xLiFePO4 -> Li1+xFePO4

The Gibbs energy for this reaction can be calculated using the equation: ΔG = ΔH - TΔS, where ΔH is the enthalpy change and ΔS is the entropy change.

To find the enthalpy change, we need to know the standard enthalpy of formation for LiFePO4 and Li1+xFePO4. This information can be found in thermodynamic databases or literature sources. Similarly, the entropy change can also be found from these sources. Once we have these values, we can calculate the enthalpy and entropy change for the reaction and then use them to calculate the overall Gibbs energy.

I recommend consulting with experts in the field or looking for recent studies on Lithium Iron Phosphate batteries to get accurate and updated values for the enthalpy and entropy changes. Additionally, you can also try reaching out to the research team or authors of the papers you are citing for their specific values. I hope this helps you in your research and good luck with your paper.

Thank you. I have only just found your reply! I got no email notice and I have posted something similar again today.

When you write Li1 you mean monoatomic and non-ionic Lithium and with Li non-attached Lithium + ions?

No, he means Li1+xFePO4. (At least I think so; the equation doesn't balance however you interpret it.) He has not formatted it properly, and for this and other inaccuracies and curiosities of expression, I think this is a chatbot answer. The reaction he writes is wrong. LiFePO4 is the discharged form of the cathode, and Li is removed on charging:
LiFePO4 + 6C → Li1-xFePO4 + LixC6
Discharge is the reverse reaction.

There are lots of complicating factors in the energetics. Just on a quick search I found this: https://pubs.rsc.org/en/content/articlelanding/2019/nj/c9nj03041g

JulesP

As I understand it, the overall reaction is:

LiFePO4 + 6xC ⇄ Li(1-x)FePO4 + Li(x)C6

(I haven’t used the proper subscript formatting here)

but the proportion ‘x’ makes the calculations difficult.

Just looking at charging, the only relevant activity is:

6C + xLi+ + xe- to LixC6 (intercalated, lithiated Carbon) since the Iron Phosphate is common to both sides so can be ignored.

I’m inclined then to use published figures for specific energy density (90-160 Wh/kg) and work backwards to other values. Something of a cop out but, given the various unknowns, a reasonable approach

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For your calculations, I would estimate the theoretical capacity by using the approximation x = 1, though I don't think it ever goes fully to 1.
From what I remember, the theoretical potential for this reaction (from ΔG° =-nFE°) is considerably higher than the actual potential you measure for a cell (ca. 4V vs. ca. 2V, IIRC). For various reasons you don't convert all the free energy to electrical energy, so working back from the measured energy density may not give you what you're looking for.

JulesP
Thank you. If I may, I will assemble my thoughts in a 1-2 page document over the next week, laying out the workable calculations. I would like to post that here, as a pdf or a link to it, and would appreciate your comments and thoughts on it. This is for preparations for a second research study on the most likely source of energy gains observed, particularly in LiFePO4 batteries, in response to inductive pulse charging (IPC) using high voltage transients. You can see the data from the first completed study on my site at kerrowenergetics.org.uk or via the Open Science Project at: http://osf.io/ZTFUB.

On second thoughts, I don't wish to bore anyone with all the details of my proposals for showing if IPC-related energy gains are from internal enthalpy or the local environment, as part of an open system, so I will just show the calculation for the charge and energy capacity of a specific battery.

The figures look reasonable and I have used a standard cell voltage of 3.45V for LiFePO4.

Charge and Energy Capacity Calculation

Why do you add the masses on both sides of the equation? Reactants are converted to products without change of mass.
The "active material" here is LiFePO4. You can't treat "FePO4" as a spectator. The oxidation state of Fe is changing. The C will be present in excess, so the key parameter is energy per kg LiFePO4. But what are the "actual" figures you are quoting? Are they energy per kg active material, or per kg total battery weight?

JulesP
I have revised the calculations and page based on your feedback and this is here:

Revised Calculations

I was using an approach that had previously worked but translated it across incorrectly.

Thanks

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So to be clear, the three figures for charge capacity are: theoretical specific charge capacity (Ah/kg from the molar masses), theoretical charge capacity for a specific battery (Ah and based on the masses of its active ingredients), and lastly the working charge capacity derived from actual discharge measurements on the specific battery. The latter are indeed a low percentage of the first value.

There is a corresponding set of values for the energy density and capacity in Wh/kg and Wh. I assume that the energy densities often quoted for new battery developments are theoretical values and not the much lower operational ones.

I note that the first values, using the molar masses method, are about 3% higher than some official values I have found using the Gibbs/reaction energies. Not sure why that is but it might be accounted for by the uncertainties in the tabulated values of formation energies. I think that molar masses are more consistently recorded and historically confirmed.

This has been very helpful in getting my thinking clear for the research proposal. Thank you.

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