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The finite temperature behavior of small Silicon (Si$_{10}$, Si$_{15}$, andSi$_{20}$) and Tin (Sn$_{10}$ and Sn$_{20}$) clusters is studied usingisokinetic Born-Oppenheimer molecular dynamics. The lowest equilibriumstructures of all the clusters are built upon a highly stable tricappedtrigonal prism unit which is seen to play a crucial role in the finitetemperature behavior of these clusters. Thermodynamics of small tin clusters(Sn$_{10}$ and Sn$_{20}$) is revisited in light of the recent experiments ontin clusters of sizes 18-21 [G. A. Breaux et. al. Phys. Rev. B {\bf 71} 073410(2005)]. We have calculated heat capacities using multiple histogram techniquefor Si$_{10}$, Sn$_{10}$ and Si$_{15}$ clusters. Our calculated specific heatcurves have a main peak around 2300 K and 2200 K for Si$_{10}$ and Sn$_{10}$clusters respectively. However, various other melting indicators such as rootmean square bond length fluctuations, mean square displacements show thatdiffusive motion of atoms within the cluster begins around 650 K. The finitetemperature behavior of Si$_{10}$ and Sn$_{10}$ is dominated by isomerizationand it is rather difficult to discern the temperature range for transitionregion. On the other hand, Si$_{15}$ does show a liquid like behavior over ashort temperature range followed by the fragmentation observed around 1800 K.Finite temperature behavior of Si$_{20}$ and Sn$_{20}$ show that these clustersdo not melt but fragment around 1200 K and 650 K respectively.Comment: 9 figure

Finite-temperature behavior of small silicon and tin clusters: Anab initiomolecular dynamics study