Melting behavior of Ag₁₄ cluster: An order parameter by instantaneous normal modes

This paper studies the melting behavior of Ag₁₄ cluster employing the instantaneous normal mode (INM) analysis that was previously developed for bimetallic cluster Ag₁₇Cu₂. The isothermal Brownian-type molecular dynamics simulation is used to generate atom configurations of Ag₁₄ at different temperatures up to 1500 K. At each temperature, these atomic configurations are then analyzed by the INM technique. To delve into the melting behavior of Ag₁₄ cluster which differs from Ag₁₇Cu₂ by the occurrence of an anomalous prepeak in the specific heat curve in addition to the typical principal peak, we appeal to examining the order parameter τ(T) defined in the context of the INM method. Two general approaches are proposed to calculate τ(T). In one, τ(T) is defined in terms of the INM vibrational density of states; in another, τ(T) is defined considering the cluster as a rigid body with its rotational motions described by three orthogonal eigenvectors. Our results for Ag₁₄ by these two methods indicate the mutual agreement of τ(T) calculated and also the consistent interpretation of the melting behavior with the specific heat data. The order parameter τ(T) provides in addition an insightful interpretation between the melting of clusters and the concept of broken symmetry which has been found successful in studies of the melting transition of bulk systems.