Understanding melting behavior of aluminum clusters using machine learned deep neural network potential energy surfaces

Abstract

Deep neural network-based deep potentials (DP), developed by Tuo et al., have been used to compute the thermodynamic properties of free aluminum clusters with accuracy close to that of density functional theory. Although Jarrold and collaborators have reported extensive experimental measurements on the melting temperatures and heat capacities of free aluminum clusters, no reports exist for finite-temperature ab initio simulations on larger clusters (N > 55 atoms). We report the heat capacities and melting temperatures for 32 clusters in the size range of 48–342 atoms, computed using the multiple histogram technique. Extensive molecular dynamics (MD) simulations at twenty four temperatures have been performed for all the clusters. Our results are in very good agreement with the experimental melting temperatures for 19 clusters. Except for a few sizes, the interesting features in the heat capacities have been reproduced. To gain insight into the striking features reported in the experiments, we used structural and dynamical descriptors such as temperature-dependent mean squared displacements and the Lindemann index. Bimodal features observed in Al116 and the weak shoulder seen in Al52 are attributed to solid–solid structural transitions. In confirmation of the earlier reports, we observe that the behavior of the heat capacities is significantly influenced by the nature of the ground state geometries. Our findings show that the sharp drop in the melting temperature of the 56-atom cluster is a consequence of the change in the geometry of Al55. Mulliken population analysis of Al55 reveals that the charge-induced local electric field is responsible for the strong bonding between core and surface atoms, leading to the higher melting temperature. Our calculations do not support the lower melting temperature observed in experimental studies of Al69. Our results indicate that Al48 is in a liquid state above 600 K and does not support the high melting temperature reported in the experiment. It turns out that the accuracy of the DP model by Tuo et al. is not reliable for MD simulations beyond 750 K. We also report low-lying equilibrium geometries and thermodynamics of 11 larger clusters (N = 147–342) that have not been previously reported, and the melting temperatures of these clusters are in good agreement with the experimental ones.