Improved Familiar says you can take "any type" of small elemental. Does that include a Lightning Elemental? A Crysmal? An Ice Elemental?
PFS takes that to mean one of the four elemental types given in the first Bestiary. I would take it to mean any creature that has the name (not just sub-type) of Elemental, which would add the four additional Elementals given in Bestiary 2. I think the Crysmal can be ruled out either way.