I planning some experiments for which I need
special cut quartz crystals.

Does anyone know where one can buy a machine for cutting quartz ?

Rotated and doubly rotated crystals are commercial to exquisite
accuracy for frequency control,

http://www.morion.com.ru/eng/blanks/

If you need a custom cut, 3-D orientation, or thickness, you want
experts to do it,

http://www.wafer-dicing.com/what.htm
http://www.quartz-silica.net/dicing.htm
http://www.siliconwafers.net/dicing.htm
http://www.icproto.com/cap_wafer_dicing.html
http://life.sportsdigg.com/Wafer-Dicing.htm
 list

There is quartz, quartz, quartz, and quartz.

   1) Natural quartz is crap no matter how good it looks - multiple
kinds of twinning; impurities, water, inclusions.
   2) Commercial z-plate quartz contains aluminum impurity (from the
lascas), is wet (Grade C, low Q), and variably has dislocations (etch
pits/cm^2).  It is vastly better than anything natural.
   3) Swept quartz is of higher quality - but you haven't solved the
basic problems.  Sweeping quartz makes it much more stable as an
oscillator frequency standard toward radiation,

US Pat. 3932777, 4311938
<http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&ident...>

   4) The highest quality quartz is Sawyer Research x-plate grown from
cultured quartz in plated autoclaves.  Extreme chemical purity, dry
(Grade A, very high Q), low etch pit density.

All commercial cultured quartz is optically right handed,
crystallographic space group P3(2)21 (left-handed screw axis).  The
direction of optical rotation and the direction of crystallographic
screw axis are measured in opposite directions.  The optical and
geometric axes here have the same helicity.