Effect of Potential Energy Distribution on the Melting of Clusters

Abstract

We find that the potential energy distribution of atoms in clusters can consistently explain many important phenomena related to the phase changes of clusters, such as the nonmonotonic variation of melting temperature with size, the dependence of melting, boiling, and sublimation temperatures on the interatomic potentials, the existence of a surface-melted phase, and the absence of a premelting peak in heat capacity curves. We also find a new type of premelting mechanism in double icosahedral Pd 19 clusters, where one of the two internal atoms escapes to the surface at the premelting temperature. DOI: 10.1103/PhysRevLett.86.999 PACS numbers: 36.40.Ei, 61.46.+w, 64.70.Dv With the possibility that metal clusters could be used as building blocks for new nanomaterials [1], the understanding of the structures and the thermal stabilities of metal clusters has become important. Recent experimental measurements of the heat capacities for unsupported metal clusters by Schmidt and co-workers [2,3] have given a strong motivation for the atomistic understanding of the melting of metal clusters. It has been observed both in experiments [4] and in theoretical simulations [5] that clusters melt at temperatures lower than those of bulk melting due to the high proportion of surface atoms with lower binding energies. As the cluster size decreases, the melting temperature monotonically decreases [4,5]. However, when the cluster size is small enough (# 200 atoms), the melting temperature does not vary monotonically with the size of cluster [3,6,7].Multimodal heat capacity curves observed in small clusters indicate that thermal energy can be dissipated by a "premelting" mechanism before overall melting [7]. Premelting has been attributed to surface melting [8], partial melting [9], orientational disordering in molecular cluster [10], and isomerization [7,11]. It has been observed that clusters can dissipate thermal energy even by boiling [12] and sublimation [13]. In some clusters, the premelting peak in the heat capacity curve is not observed [9,[14][15][16].Previously published simulations of cluster melting have used either Monte Carlo (MC) methods at constant temperature (canonical ensemble) or molecular dynamics (MD) at constant energy (microcanonical ensemble). There has been some controversy concerning the dependence of the simulated thermodynamic properties on the ensemble until the work by Calvo and Labastie [17]. These authors [17] showed that if the sampling of the phase space is accurate enough (a large enough number of MC configurations and MD trajectories), the thermodynamic results are identical in both ensembles because the thermodynamics is determined by the configurational density of states [7,8,17,18].In this Letter, we show that the potential energy distribution of atoms in the clusters can consistently explain many of the important phenomena which occur during phase changes of small clusters, such as the nonmonotonic variation of melting temperature with the size of clusters [3,6,7], the dependence of meltin...

Metal clusters with hidden ground states: Melting and structural transitions in Al115+, Al116+, and Al117+

“…In simulations, there are a number of examples where two peaks have been observed in the heat capacity. [25][26][27][28][29][30][31][32][33][34] This behavior is usually called premelting when the low temperature peak is the smaller of the two and postmelting when the higher temperature peak is the smaller. However, multiple peaks have rarely been seen in the experimental studies.…”

Metal clusters that freeze into high energy geometries

“…We normally attribute heat capacity plots with two peaks to premelting phenomena ͑such as surface premelting [46][47][48][49][50][51][52] ͒. The simulations reported here show that when the freezing rate for the thermodynamically preferred solid is small, the melting of two different solid states with different melting temperatures can also lead to two peaks in the heat capacities.…”

Effect of surface morphology and temperature on the structural stability of nanoscale wavy films

“…It has been mentioned earlier that the melting point of crystalline materials, a unique physical behavior of bulk crystalline solids, becomes size-dependent when the dimensions of the material reduce to the nanoscale [9][10][11][12][13][14][15][16][17][18]. It is observed that the melting point of nanowires [12], nanoparticles [10,11,[13][14][15][16] or nanocrystalline films [17,18] may be reduced by 50-60% from the bulk. It is, however, difficult to know the exact amount of reduction for a particular material because melting is influenced by many other factors including surface energy and density of materials.…”

“…The phenomenon of MPD implies reduction of melting temperature (T m ) and is observed quite frequently in nanostructured materials [10][11][12][13][14][15][16][17][18].…”

“…It is shown both experimentally [14] and thermodynamically [9] that the MPD is also size-dependent where the T m of nanomaterials can drop to as low as 60% from the bulk. It is found that most of the experimental and theoretical observations of MPD [10][11][12][13][14][15][16][17][18] can be well predicted by a model theorized by Pawlow [8]. While the model was originally developed for spherical particle clusters, it can be easily generalized for any shape of nanostructured materials with a suitable geometric factor.…”