  Growing crystals form a cavity when placed against a wall. The birth of the
cavity is observed both by optical microscopy of sodium chlorate crystals
(NaClO$_3$) growing in the vicinity of a glass surface, and in simulations with
a thin film model. The cavity appears when growth cannot be maintained in the
center of the contact region due to an insufficient supply of growth units
through the liquid film between the crystal and the wall. We obtain a
non-equilibrium morphology diagram characterizing the conditions under which a
cavity appears. Cavity formation is a generic phenomenon at the origin of the
formation of growth rims observed in many experiments, and is a source of
complexity for the morphology of growing crystals in natural environments. Our
results also provide restrictions for the conditions under which compact
crystals can grow in confinement.
