I was talking to a founder of a battery company the other day and he said "there are two kinds of moving parts in your iphone, the buttons and the battery". The lithium literally moves from side to side as it charges and discharges.
1: Aluminum foil (about 1/10th as thick as household foil)
2: Cathode material (metal oxides, like NMC or NCA)
3. Separator film (polypropylene + polyethylene, which blocks electrical short circuits but lets li ions through- only ~20 microns thick)
4. Spheroidal graphite anode (mostly artificial, some natural)
5. Copper foil
The ions (and some amount of solvent- the solvation sheath!) travel from cathode <-> anode.
Li-ion battery comes off the production line as one continuous, miles-long tape that is rolled into shape and then sliced off. The tape is made of a few layers, and li ions move from one layer to another. All of the movement cancels out.
You could measure the state of charge by mass, though! As electrons are moved from anode to cathode, they occupy a lower energy state and therefore have less mass. You'd measure that in eV, electron-volts: convert amp-hours to coulombs and you have the number of electrons, and the average voltage change is from roughly 3.7 volts to 3.2 volts. Or you could use the much easier formula- E=MC^2 :D
For the center of mass, that’s right, but that will change the moment of rotational inertia, won’t it? Mass will either move inwards or outwards as the battery gets discharged.
The battery as a whole swells slightly due to the stress of intercalation, which is certainly a much larger effect.