Hello Linda,

"Lime" deposits on shells and other hard surfaces exposed to the marine
environment are generally not deposited by simple chemical
precipitation.  Such material, while largely inorganic in composition,
is typically biological in origin, deposited by a variety of organisms,
both macroscopic and microscopic.  The larger organisms include those
you mentioned - corals, barnacles, tubeworms, and others, including
molluscs.  The
predominant microscopic forms are bryozoans and coralline algae, but
various other types of organisms may contribute, such as encrusting
foraminiferans, and even the spat of sessile bivalves like Ostreidae,
Spondylidae, and Chamidae.  If the calcific material is freshly
deposited, structural detail can often be seen with a low power
microscope.  Bryozoans often create interesting, intricate patterns, superficially
resembling microscopic corals.  However, such material, once deposited,
is subject to ongoing erosion, and old deposits are often worn smooth,
just as old dead coral
often is.

Regards,
Paul M.