Reaction rates for the conversion of ice nanocrystals within 3-D arrays, to the hemi- and monohydrates land deuterates) of ammonia, have been determined for temperatures in the range 100 to 128 K. The loss of ice and the growth of the hydrate product, as a function of time, temperature, and the activity of ammonia at the surface of the particles, has been monitored using transmission FT-IR spectroscopy. Though this study has focused on the ammonia-ice system, the results may provide general insights to the low-temperature formation of hydrates from ice particles. The ammonia hydrate formation follows a nucleation stage that occurs only after saturation of the ice surface with ammonia molecules; the propagation of the reaction depends on ammonia diffusion, not within the ice but through a hydrate crust that quickly envelops the particles. Apparently, adsorbed ammonia molecules do not achieve a free energy consistent with the nucleation of a new (hydrate) phase until saturation of the low free energy ice surface sites is complete. After nucleation occurs, diffusion of ammonia through the hydrate crust may be rate controlling, the determining parameters being the chemical activity of the ammonia adsorbed on the particle (hydrate) surface and the thickness of the hydrate crust. A diffusion coefficient for ammonia in the amorphous "hemihydrate" has been determined as 2.8 x 10(-19) cm(2)/s at 102 K with E-a = 15 kcal/mol, while the coefficient found for the crystalline hemihydrate was 1.1 x 10(-17) at 107 K with E-a estimated as 12 kcal/mol.