Recent observations of the disorder-order transition for colloidal har
d spheres under microgravity revealed dendritic crystallites roughly 1
-2 mm in size for samples in the coexistence region of the phase diagr
am. Order of magnitude estimates rationalize the absence of large or d
endritic crystals under normal gravity and their stability to annealin
g in microgravity. A linear stability analysis of the Ackerson and Sch
atzel model for crystallization of hard spheres establishes the domain
of instability for diffusion-limited growth at small supersaturations
. The relationship between hard sphere and molecular crystal growth is
established and exploited to relate the predicted linear instability
to the well-developed dendrites observed.