The main compound in Li-ion rechargeable batteries can be found in the electrolyte composed by lithium salts though the battery cathode is made of different materials, each one with advantages and disadvantages. Ions of lithium constantly appear at the electrolyte between the cathode and anode for recharging the battery.
With another anode composition, perhaps those ions might move differently giving better specifications in energy storage per unit of volume, recharging and discharging rate, cycles of recharging and self discharge. Any of these specifications are now still needing upgrades to compete with liquid fuel, as hydrocarbons as a ready-for-use natural product outperforms any sort of contemporary technology, while these chemical bonds after combustion endanger the quality of air and atmospheric health and increase environmental toxicity, affecting present and future generations due to their massive, uncontrolled use. They are going to be exhausted, and the price will be reaching records as the last decades, plundering and destroying natural areas in extraction locations with so much connivance and pages of unsustainable history.
It's true that there are constant efforts for finding substitutes, but there's technology ready by the way! We should hope the jump it's near in time.
A LiFePo4 battery, with that component in the cathode, lasts more recharging cycles with an increased level of security with a bit less capacity per unit of volume. The name is lithium iron phosphate versus lithium cobalt oxide for the usual Li-ion cathodes.
Some confusion could arise with LiPo as this do not reference the cathode or electrolyte but the case of the battery. Yes, the case! Lithium polymer using a plastic enclosure, a polymer like any other plastic.