  A systematic and detailed investigation of the finite-temperature behavior of
small sodium clusters, Na_n, in the size range of n= 8 to 50 are carried out.
The simulations are performed using density-functional molecular-dynamics with
ultrasoft pseudopotentials. A number of thermodynamic indicators such as
specific heat, caloric curve, root-mean-square bond length fluctuation,
deviation energy, etc. are calculated for each of the clusters. Size dependence
of these indicators reveals several interesting features. The smallest clusters
with n= 8 and 10, do not show any signature of melting transition. With the
increase in size, broad peak in the specific heat is developed, which
alternately for larger clusters evolves into a sharper one, indicating a
solidlike to liquidlike transition. The melting temperatures show irregular
pattern similar to experimentally observed one for larger clusters [ M. Schmidt
et al., Nature (London) 393, 238 (1998) ]. The present calculations also reveal
a remarkable size-sensitive effect in the size range of n= 40 to 55. While
Na_40 and Na_55 show well developed peaks in the specific heat curve, Na_50
cluster exhibits a rather broad peak, indicating a poorly-defined melting
transition. Such a feature has been experimentally observed for gallium and
aluminum clusters [ G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); G.
A.Breaux et al., Phys. Rev. Lett. 94, 173401 (2005) ].
