Lindemann’s criterion

Between temperatures of 28 and 29 K the rms bond length fluctuations of the 13-particle system increase dramatically. Similar results have been obtained for all the other clusters N = 5, 6, and 7) for which S(T) is cal-culated. - The curves of S T) for these systems are similar to those occurring with first-order phase transitions of macroscopic systems.Lindemann s criterion states that melting occurs for such systems when rms fluctuations reach 10%.For the small clusters studied, the rise in this function occurs at values of S slightly below 10%—an effect that can be attributed to the large ratio of surface to core atoms. 

The root mean square fluctuation of the particle distance 5, which is referred to as Lindemann s criterion, has been successfully used to monitor the phase transition of a micro-cluster ... 

Figure 21. Lindemann s criterion against the temperature using the original potential energy surface.

The accuracy of Lindemann s criterion depends also on the steepness of its variation with temperature at phase transition and on the specification of its percentage increase which should be adequate to discriminate surface (partial) from all-cluster melting. In the present case, we assign to the temperature at which Lindemann s index starts increasing. This allows us... 

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