Size dependence of freezing temperature and structure instability in simulated Lennard-Jones clusters

Liquid Lennard-Jones clusters of 14 different sizes from N=55 to 923 particles were cooled down to find their temperature of liquid-solid transition and the internal structure of the solidified clusters. The decrease of the cluster temperature was attained by a gradual change of the system temperature in Monte Carlo simulations. The liquid-to-solid transition was found by analysis of the specific heat as well as by detection of the structural units of face-centred cubic, hexagonal close-packed and decahedral type. It was observed that near the detected transition temperature the solid-like cluster structure is not always stable and fluctuates between solid and liquid states. The fluctuations of the state were observed frequently for small clusters with N ≤147, where the temporary solid structure is created by a large part of internal atoms. Manual inspection of cluster structural data and the 10%N condition for minimal number of atoms as centres of solid-like units enable detection of stable cluster solidification at freezing temperature. It was found that the freezing temperature of all clusters, with the exception of N=55, decreases linearly with N^-1/3. The extrapolated freezing temperature of the bulk LJ system is 13% lower than the experimental value of argon. After freezing, the solid phase remains but some atoms close to the cluster surface are not firmly included into the structure and oscillate mainly between solid structure and disordered one.