Magic numbers for classical Lennard-Jones cluster heat capacities

Abstract

Heat capacity curves as functions of temperature for classical atomic clusters bound by pairwise Lennard-Jones potentials were calculated for aggregate sizes 4 ≤ N ≤ 24 using Monte Carlo methods. J-walking (or jump-walking) was used to overcome convergence difficulties due to quasi-ergodicity in the solid-liquid transition region. The heat capacity curves were found to differ markedly and nonmonotonically as functions of cluster size. Curves for N = 4, 5 and 8 consisted of a smooth, featureless, monotonic increase throughout the transition region, while curves for N = 7 and 15-17 showed a distinct shoulder in this region; the remaining clusters had distinguishable transition heat capacity peaks. The size and location of these peaks exhibited "magic number" behavior, with the most pronounced peaks occurring for magic number sizes of N = 13, 19 and 23. This is consistent with the magic numbers found for many other cluster properties, but there are interesting differences for some of the other cluster sizes. Further insight into the transition region was obtained by comparing rms bond length fluctuation behavior with the heat capacity trends. A comparison of the heat capacities with other cluster 1 properties in the solid-liquid transition region that have been reported in the literature indicates partial support for the view that, for some clusters, the solid-liquid transition region is a coexistence region demarcated by relatively sharp, but separate, melting and freezing temperatures; some discrepancies, however, remain unresolved.

Magic number behavior for heat capacities of medium-sized classical Lennard-Jones clusters

“…Caution must also be exercised when interpreting δ(T ) curves, since they are dependent on simulation parameters such as the walk length, as well as the ensemble that is used. 3,11,39 A. J-walking J-walking runs were done for cluster sizes 25 ≤ N ≤ 38, using sampling from externally stored distributions as described in the preceding study. 11 Distributions for each temperature consisted of several files, totaling 2.5 × 10 6 configurations, sampled every 100, 50, 25, or 10 passes, depending on the temperature (100 passes for higher temperatures having broad distributions, 10 passes for very low temperatures having very narrow distributions).…”

“…3,11,39 A. J-walking J-walking runs were done for cluster sizes 25 ≤ N ≤ 38, using sampling from externally stored distributions as described in the preceding study. 11 Distributions for each temperature consisted of several files, totaling 2.5 × 10 6 configurations, sampled every 100, 50, 25, or 10 passes, depending on the temperature (100 passes for higher temperatures having broad distributions, 10 passes for very low temperatures having very narrow distributions). The distributions were generated in stages from higher temperatures to lower, beginning with temperatures well within the cluster liquid region (50 to 60 K).…”

“…In a previous study, I examined these generalized magic number effects in LJ clusters ranging in size from 4 to 24 atoms. 11 In this study, I extend the sequence to 60 atoms, which completes the filling of the second Mackay icosahedral shell (to N = 55) and just begins the filling of the third shell (to N = 147).…”

“…5 Although clusters having magic number sizes such as 13 and 55 have pronounced heat capacity peaks that correspond closely to the solid-liquid phase-change region determined from other cluster properties, other cluster sizes such as N = 15, 16 and 17 do not have heat capacity peaks in their phase-change regions. 11 Since heat capcity peaks have often been used to identify phasechange regions, 20,25,32,33,35,39 characterizing their temperature dependencies for sequences of LJ clusters can help elucidate the underlying reasons for such varied behavior.…”

“…Because of their high proportion of surface atoms, many clusters have physical properties that typically exhibit a very irregular dependence on their aggregate size, with certain sizes standing out in particular. For example, the mass spectra of clusters typically exhibit especially abundant sizes that often reflect particularly stable structures, specially reactive clusters, or closed electronic shells, [12][13][14]17 These "magic number" sizes have been of great theoretical interest, [11][12][13] and much work has been done in relating magic number sequences to cluster structure in terms of "soft" sphere packings, since many magic number sizes in LJ clusters such as N = 13, 19, 55, and 147 correspond to compact structures that are especially stable. 1, 7 Many cluster properties obtained from simulation studies such as binding energies, root mean square (rms) bond length fluctuations and heat capacities also show very irregular dependencies on the cluster size that mostly correspond to their usual magic number sequences.…”