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It is commonly believed that melting occurs when mean square displacement(MSD) of a particle of crystalline solid exceeds a threshold value. This isknown as the Lindemann criterion, first introduced in the year of 1910 byLindemann. However, Chakravarty et al. demonstrated that this common wisdom isinadequate because the MSD at melting can be temperature dependent whenpressure is also allowed to vary along the coexistence line of the phasediagram [Chakravarty C, Debenedetti P G and Stillinger F H 2007 J. Chem.Phys.126 204508]. We show here by extensive molecular dynamics simulation ofboth two and three dimensional polydisperse Lennard-Jones solids that particleson the small and large limits of size distribution exhibit substantiallydifferent Lindemann ratio at melting. Despite all the dispersion in MSD,melting is found to be first order in both the dimensions at 5-10% dispersityin size.

How universal is the Lindemann criteria in melting of Lennard-Jones polydisperse solids?