利用分子動力學的方法研究溫度對原子叢集的影響，和利用理論上的Gupta-type potential來表示原子之間的作用力，可以了解隨著不同的原子數，顯示出不同的熱力學特性，可以藉此來瞭解為何叢集原子系統不同於大體系統的原因。

The Brownian-type molecular dynamics simulation is re-visited and applied to study the thermal and geometric properties of four mono- and two polyvanent metallic clusters. For the thermal property, we report the specific heat at constant volume and study the solidlike-liquidlike transition by scrutinizing the characteristic of Cv For the geometric property, we calculate the relative root mean square bond-length fluctuation delta as a function of increasing temperature. The thermal change in delta reflects the movement of atoms and hence is a relevant parameter in understanding the phase transition in clusters. The simulated results for the Cv of alkali and aluminium clusters whose ground state structures exhibit icosahedral generally show one phase transition. In contrast, the tetravalent lead, even if predicted to be icosahedral at T=0 K, displays two phase transitions, a pre-melting process before undergoing the pregressive melting. In connection with the latter scenario, it is found here that those clusters identified to be lesser stable according to the second energy difference can qualitatively be classified to be the clusetrs with the possibility of undergoing pre-melting process. To delve further into the thermal behavior of clusters, we have analyzed also the thermal variation of delta(T) and attempted to correlate it with Cv(T). It turns out that the pre-melting or/and melting temperature of a cluster extracted from Cv do not always agree quantitatively with that drawing from delta . This implies that a quantitative understanding of the phase transformation in microstructures will need further effort to search for more useful cluster parameters.

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