Looks like we got carried away, thanks.
Spock presents the last crystal to Kirk in his cabin just prior to the arrival of the miners and it looks like a crystal and not like the 'paddle'. Maybe the change in appearance is another changed premise in the series or they used lithium crystals prior to dilithium crystals / paddles (maybe the "di" prefix stands for the mounting compatible ends
?) or else. But after the last / fourth crystal burned out, do I hear Kirk saying "the lithium crystals" or "dilithium crystals"?
I have a few concerns about re-interpreting actual dialogue.
In "The Alternative Factor" Kirk orders Masters to immediately "re-amplify" the dilithium paddles and they later talk about "re-amplification" which I believe is more in line with the re-crystalisation mentioned in ST IV than simply charging these with energy like batteries. There is no evidence that the crystals are being "re-energised" only that the "energiser" providing energy for the re-amplification components is short circuited by Lazarus.
The other thing is that the cage (or structure it sits in) in the engine room is a "dilithium crystal converter
assembly". Another component specifically mentioned in TOS are "power converters". As to what these dilithium crystals convert
may be a subject of speculation if one doesn't want to follow the official line but conversion seems the major purpose of dilithium crystals.
# 1 - There are 3 active dilithium crystal circuits with a corresponding engine room
for each of the three crystals (should the crystal in one of the engine rooms fail, the "cycling station" will reroute power from the remaining two to compensate the power loss) The 4th dilithium crystal circuit is a spare circuit.
# 2 -There are 3 active dilithium crystal circuits with a 4th "hot" standby circuit
in the warp engine room (1 for each of the three reactors).
# 3 - There are 4 lithium/dilithium crystal circuits housed in a single crystal converter assembly.
Does this cover all the options?
Where I'm unable to subscribe is "In Season 1, it was in the Main Energizer room."
The Re-Amplification room or chamber seemed to be a place for the dilithium paddles to rest and relax, not to work. If we were to assume that the paddles can rest and work at the same spot, the large GNDN pods in the engine rooms would seem to be more suitable candidates, IMHO.
P.S. What could "re-amplification" mean? Here's a quote from Wikipedia concerning "stability and aging" of "crystal oscillator" to illustrate the stress crystals could be exposed to:
"The frequency stability is determined by the crystal's Q
. It is inversely dependent on the frequency, and on the constant that is dependent on the particular cut. Other factors influencing Q are the overtone used, the temperature, the level of driving of the crystal, the quality of the surface finish, the mechanical stresses imposed on the crystal by bonding and mounting, the geometry of the crystal and the attached electrodes, the material purity and defects in the crystal, type and pressure of the gas in the enclosure, interfering modes, and presence and absorbed dose of ionizing and neutron radiation."