/I honestly am not qualified to parse the linguistics of this.  I will note
that the definitions I used, never talked about electrons in regard to the
electrodes; it talks about cation and anions.  Not the same thing.  THe
definitions of cathode and anode are related to cations and anions -
electrochemical terms../
I disagree. I think cations and anions get their names from the electrodes
they are attracted toward when a cell is discharging.  

/In the external circuit electrons are moving, between the electrodes it is
ions./

Agree.  That is what I said.  

/Chemically there is a charge imbalance that is created or relieved by
electrons at the terminals of the conductors.  When there is no imbalance
the lithium ions reside in the positive electrodes, intercalated
in the the lithium metal oxide (or phosphate with LFP), this is a stable
state even when the terminals are connected./

The lithium is not charged, they are neutral atoms intercalated in the
lattice.  

/If you create an imbalance, in other words a potential difference, at the
terminals the ions will be
attracted to and intercalate in the graphite negative electrode./  

Depends on the polarity of the applied potential, but I assume you meant
graphite negative relative to the electrode with the lithium compound.

I think there is nothing more to be gained here.  We both have some
understanding of how the cells work.  The confusion over anode/cathode,
positive/negative comes from whether there is an external power source
connected to the cell or not, or as you stated it, whether the cell is
consuming energy or supplying energy. That's what I thought I explained in
the previous post.



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