We report a study of the thermodynamic properties of indium clusters on a S
iNx surface during the early stages of thin film growth using a sensitive n
anocalorimetry technique. The measurements reveal the presence of abnormal
discontinuities in the heat of melting below 100 degreesC, These discontinu
ities, for which temperature separation corresponds to a spatial periodicit
y equal to the thickness of an indium monolayer, are found to be related to
the atomic "magic numbers," i.e., the number of atoms necessary to form a
complete shell of atoms at particle surface.