What are the crystals you collect in the main story from primals?

[Vicious1915]

I think the ligntning crystal we got via helping the sylph out.
The water crystal was given after fighting siren the 1st time.

I find this confusing because I did get the lightning crystal as you've described, and I got the ice crystal from Stone Vigil as described, but I'm fairly certain I've had the water crystal since my first contact with Hydaelyn - and there are only two bluish-colored crystals, correct? I've only just recently beaten the story and I don't believe I got any crystal from beating Siren. I didn't really get anything out of visiting the Isles of Umbra that I can recall.

[DragonSlayer45]

Yeah, we get no crystal from Siren if I remember.

Water - First
Fire - Ifrit
Lightning - Sylphs
Earth - Titan
Ice - Stone Vigil
Wind - Garuda

[ColorOfSakura]

Maybe there are "Crystals of Darkness" // 'Dark' Primals associated with Zodiark? ^_^; that could be quite cool.

It's entirely possible given the nature of the Ascians. In FFXII they explored the whole "Dark Summons" concept. All the Espers in FFXII were "Scions of Darkness", who rose up against the Gods and were trapped in Glyphs. The two exceptions were Ultima and Zodiark (who were both Dark and Light Scions.)

Even more interesting is that Lahabrea is the name of one of the Scions of Light in FFXII (Lahabrea, Abyssal Celebrant), and existed as the opposite of Mateus, the Corrupt.

The other Ascians in the game that have been named also share names with the "Scions of Light" from FFXII:
Pashtarot (Pashtarot, Knight-Star, opposite of Zeromus, the Condemner)
Igeyorhm (Igeyorhm, the Martyr, opposite of Shemhazai, the Whisperer)
and Nabriales (Nabriales, the Majestic, opposite of Cúchulainn, the Impure)

It could be possible that the Espers from XII could be utilized as "dark primals" and used as a way to help revive Zodiark.

[Enkidoh]

There are in fact 'Crystals of Darkness' in ARR - you first see one on the ground briefly after defeating the 'Masked Mage' and his gargoyle during the level 15 story quest (it soon disintegrates), and Minfilia directly confirms their existence much later just prior to

Operation Archon being undertaken, where she shows the synthetic one the Students of Baldesion gave her to free Thancred from Lahabrea's control.

So they definitely exist.

EDIT: I just looked through my screenshots and Minfilia mentioned in that above scene that the Crystals of Darkness are the specific means the

Ascians use to take host bodies, like what Lahabrea did to Thancred

- there's no mention of them being used as part of a summoning process, but I wouldn't be surprised if that was also the case. In any event, this is the dialogue from the scene in question (spoilered for those who haven't yet reached this part):

Minfilia: "Thancred's fate weighs heavily on my mind. I cannot bear to think of him in thrall to an Ascian."
Minfilia: "Mayhap you know this already, but the Ascians are immortal beings without physical form. Since time immemorial, they have fanned the flames of chaos from the shadows."
Minfilia: "That they might work unseen, the Ascians entrap and possess mortal men by means of malign artifacts known as Crystals of Darkness."
Minfilia: "One such Crystal may yet be the key to saving Thancred." (she hands over a purple crystal)
Alphinaud: "This is a Crystal of Darkness?"
Y'shtola: "A mere replica, created using data obtained from anomalous crystals found across Eorzea."

So yeah, this showed the Crystals of Darkness pretty much do exist, but are used in ways by the Ascians different to how the player makes use of the Crystals of Light.