I came to IAP because I was looking for "how tos" about turning stone pens. I've been a rockhound, flintknapper and stone carver for a lot longer than a pen turner. But I've gotten so wrapped up in pen turning that stone turning has gone on the back burner. Rock turning is still my number one interest in pen turning, but I can't seem to get around to it with all the wood and resin that I need to turn.
I have turned pens out of alabaster and various other types of gypsum, I've turned several types of soapstone, but when I get to slightly harder stone, maybe 3+ on the Mohs, I get nowhere. If you can't cut it with a wood saw without dulling the blades, you can't turn it with wood tools. I've destroyed a couple band saw blades to learn that.
There are lapidary lathes to buy (for way too much money to get just to play with).
http://www.diamondpacific.net/lathe.html They remind me of a metal lathe but have a cutoff style grinding wheel instead of a static tool holder and they have a water system for dust and cooling.
At a rock show I saw a Taig that was modified with a drip system for water (a gallon jug hanging from above with a partially clamped hose). For the powered grinder there was a angle grinder strapped to the tool rest/adjustment system.
Your pen looks good, the alt ivory solves the problem of the stone crumbling at the ends. You said you used alt ivory because of the legnth, but protecting the ends is another good reason, even very hard rocks and minerals will tend to crumble on an unprotected end beause they are so totally non-pliable. Do you know what kind of stone it is?
Thanks for sharing and good luck with stone turning.