  Density-functional theory has been applied to investigate systematics of
sodium clusters Na_n in the size range of n= 39-55. A clear evolutionary trend
in the growth of their ground-state geometries emerges. The clusters at the
beginning of the series (n=39-43) are symmetric and have partial icosahedral
(two-shell) structure. The growth then goes through a series of disordered
clusters (n=44-52) where the icosahedral core is lost. However, for n>52 a
three shell icosahedral structure emerges. This change in the nature of the
geometry is abrupt. In addition, density-functional molecular dynamics has been
used to calculate the specific heat curves for the representative sizes n= 43,
45, 48 and 52. These results along with already available thermodynamic
calculations for n= 40, 50, and 55 enable us to carry out a detailed comparison
of the heat capacity curves with their respective geometries for the entire
series. Our results clearly bring out strong correlation between the evolution
of the geometries and the nature of the shape of the heat capacities. The
results also firmly establish the size-sensitive nature of the heat capacities
in sodium clusters.
