Hi Carrie, Agate, a type of chalcedony, is a member of the quartz
family (chemically, silicon dioxide). The difference is that all the
varieties of chalcedony (agate, jasper, etc.) are microcrystalline or
cryptocrystalline. In other words, they are composed of microscopic
crystals of silicon dioxide as opposed to what we call quartz, whose
well-formed, definitely non-microscopic crystals we’re all familiar
with.
Agate is distinguished by its banded appearance and usually includes
translucent material; jasper is massive, dense and opaque.
Microcrystalline quartz which is translucent but not necessarily
banded is called simply chalcedony (like the recently very popular
blue chalcedony).
Assuming the material you’ve described is actually natural quartz
(as opposed to a simulant, like glass) and if it is even slightly
translucent rather than opaque (which I suspect), I would be tempted
to call it chalcedony. It’s difficult to nail down without seeing
the rough material it came from.
On the other hand, if in the rough it formed a band between other
colors of quartz minerals, then it might properly be called agate.
Either way, you can’t really go wrong calling it quartz which is the
umbrella term for the whole family of minerals.
I’ve not seen this material, by the way, but I am not aware of the
availability of large quantities of a dark blue quartz. My guess is
that it’s dyed or otherwise color-enhanced.
Beth