New physics occurs in semiconductors when one or more dimensions of the crystal are reduced to a size comparable to bulk electron delocalization lengths (tens to hundreds of angstroms). The properties of "quantum dots" or semiconductor nanocrystals are now being studied, as techniques to fabricate the crystallites are developed. Temperature-dependent electron diffraction studies on nanocrystals of CdS show a large depression in the melting temperature with decreasing size, as a larger fraction of the total number of atoms is on the surface. Thermal stability may play a role in determining the uses of semiconductor nanocrystals.