BotB 1: Introduction & Capacity
Building a "back of the battery" calculator, starting with theoretical capacities
🧮 Back of the Battery (BotB) Calculator
Welcome to our new series on making a basic battery energy density calculator! In each instalment, we'll build up our intuition on what design parameters affect the performance and cost of a battery.
The goal is to provide a tool to perform "back of the envelope" calculations to quickly understand questions like:
Why is LFP considered a lower energy material?
Why does Quantumscape's solid electrolyte have to be 20 um thick?
How much packaging efficiency is gained in Tesla's new 4680 cell?
Why are researchers encouraged to report the volume of electrolyte used?
As an overview, we'll go from small to large, with why different chemistries store different amounts of lithium, how active material thicknesses play a role, and how different casing formats also change energy densities. Later on, we can also try to tack on material-level costs to add another dimension to the tool.
We're not the first to do this sort of bottom-up modelling for batteries. The Viswanathan group at CMU have published a great article on EV battery cost breakdowns which uses their open-source battery cost model based on component and manufacturing expenses. Argonne National Lab also has BatPac, an industry staple for battery performance and cost modelling based in Excel. Matt Lacey also hosts a handy calculator for estimating cylindrical battery energy densities.
These are already excellent tools, and we're starting this series to provide a step-by-step walkthrough of the core principles so that anyone with a "can-do" attitude and enthusiasm for batteries can get some technical insights.
Prereq 1: read about Li-ion batteries
Before we get quantitative it's probably a good idea to get a grasp on what's going on inside a lithium-ion battery. Some of our favourite resources to check out:
"The Li(ttle) ion that could" by Adrian Yao is the perfect primer for key terminology, definitions, and battery components that we'll reference
The Hidden Science Making Batteries Better, Cheaper and Everywhere by Akshath Rathi talks through tweaks in cell design over the years
For today, it’s a good idea to understand what “capacity” means in a battery context!
Prereq 2: get familiar with Python
Assembling our BotB calculator "model" will require some familiarity with Python notebooks, while we originally wanted to build it in Google Colab, an interactive UI will also be made towards the end of BotB!
Part 1: Theoretical Capacities
We've reproduced screenshots from the python notebook here too.
The capacity of a battery material is the amount of charge (lithium ions) that can be stored by the material. The theoretical capacity for a particular compound is related to its molecular mass and chemical formulation, relative to the amount of lithium that moves in and out during charge and discharge.
Michael Faraday discovered in the 1800s that the amount of a substance deposited electrochemically by passing charge is directly related to the molecular mass of that substance. This remains the case for batteries where Li-ions (or other metal-ions) are shuttled between the cathode and anode materials.
By using this equation for some common electrode materials, we can compare their theoretical specific capacities:
In real life materials, not all of the lithium is extracted and so the true reversible capacity achievable is considerably lower. This is because cycling 100% of theoretical capacity causes severe degradation. For example, LCO (LiCoO2) practical capacities are around 165 mAh/g, or around 60% of the theoretical limit. We shall take this into consideration in future analyses.
We can also see why LFP is considered a lower capacity material than NMC. It also shows that the automotive trends of increasing the nickel content actually reduces the specific capacity (a little bit) but is done to improve rate capability and cycle stability.
Next time, we'll look at the voltages that each material provides, which will allow us to compare the energy densities.
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Regular instalments of BotB as we add to it. We welcome questions and comments, as we’re making this portion of BotB open to all readers as an educational tool.
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🌞 Thanks for reading!
📧 For tips, feedback, or inquiries, please reach out!
About the writers: Andrew is a PhD researcher at the University of Oxford (@ndrewwang). Nicholas is a Business Manager at UCL Business and Venture Fellow with Berkeley SkyDeck (@nicholasyiu). Ethan is a battery scientist who’s set to join the Jeff Dahn Research Group in September (@ethandalter).