A Theoretical Study Of Thermodynamic Phase Transitions Of Sodium Clusters Na_n (n=4, 6 And 8)

Based on the distance dependent tight-binding molecular dynamics simulations, the phase transitions properties for sodium clusters Na4, Nq6 and Na8 have been studied .The relationship of the averaged nearest-neighbor distance, the heat capacity,the temperature ,the potential energy and the kinetic energy for these clusters with the total energy is investigated.The solid-glass transition and melting transition for sodium clusters Na4, Nq6 and Na8 have been simulated. One finds that the atoms of these clusters are oscillating with small amplitudes around their equilibrium positions at low temperatures; Continuing adding the total energy , these clusters seem to undergo phase transitions ,one is a solid-glass transition : at a temperature of about 99K for sodium cluster na4,the bond-length fluctuation jumps from 0 to 0.3.At the temperatures the atoms are oscillating most of the time with small amplitudes around the equilibrium position and once in a while some of them jump to other equilibria. This phase was characterized as a "glassy" of the cluster. The temperature of glassy for Nq and Na8 is 100K and 92K respectively. The other is a melting transition : At temperatures corresponding to the second "phase transition", there is another dramatic increase in the bond-length fluctuation to a value of about 0.5.The cluster becomes fluid-like and all the atoms move across the entire cluster .At the same time there is a significant evaporation probability .This phase is named as liquid-like phase. The temperature of liquid-like phase for Na6, Nq and Na8 is 440K,515K and 613K respectively. During the transition from glassy to liquid-like phase, it is found that na4,Nq6 and Na8 clusters have negative heat capacity around melting temperature, which perfects Juan A .Reyes-Nava and his Colleague's results that clusters for Nan (n = 135,142,147) exist negative heat capacity. To understand the micro-mechanism of the negative heat capacities, the curves of the temperature, the potential energy and the kinetic energy varying with the total energy are analyzed.By studying the negative heat capacity of sodium clusters, it is not only beneficial to the study of sodium clusters but also helpful to that of the negative heat capacity of macroscopic matter, which is important to study the evolution of the universe and to get lower temperature.