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.
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