AlD3 was synthesized by ball milling of 3LiAlD(4) + AlCl3. Planetary ball milling at room temperature resulted in a mixture of AlD3 (alpha and alpha') and Al in addition to LiCl, whereas cryomilling at 77 K resulted in only AlD3 and LiCl. The AlD3 obtained was a mixture of about (2)/(3)alpha and (1)/(3)alpha'. alpha' was determined by powder neutron diffraction to take the beta-AlF3 structure with space group Cmcm and a = 6.470(3), b = 11.117(5), and c = 6.562(2) A. It is built up of corner-sharing AlD6 octahedra in an open structure with hexagonal holes of radius 3.9 A. alpha' slowly decomposes during storage at 40 degrees C. alpha-AlD3 is also described by a corner-sharing AlD6 network but in a more dense ReO3-type arrangement. Both AlD3 modifications have slightly shorter Al-D distances compared to Na3AlD6, Na2LiAlD6, and K2NaAlH6.