Multifaceted Thermodynamics of Pb n (n = 16−24) Clusters: A Case Study (original) (raw)
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Physical Review B, 2019
Ab initio molecular dynamics simulations were performed to analyze changes in the structure and dynamics of molten Pb along the melting line for pressures ranging from ambient to 70 GPa. Common neighbor analysis reveals a local structural order of the underlying crystalline phase at the corresponding pressure, which increasingly competes with the existing icosahedral local order with pressure. Obtained dispersions of longitudinal and transverse collective excitations contain two branches of transverse modes for all pressures. Analysis of the pressure dependence of observed two-peak structure of the Fourier spectra of velocity autocorrelation functions allowed us to identify their peak locations with the frequencies of nonpropagating transverse branches in the second pseudo-Brillouin zone.
Energetics and structures of small clusters: Pt< sub> N,< i> N= 2–21
Surface science, 2003
The Voter and Chen version of an embedded-atom model, derived by fitting to experimental data of both diatomic molecule and bulk platinum simultaneously, has been applied to study the locally stable structures, energies and growth patterns of small platinum clusters in the size range of N ¼ 2-21. Using molecular dynamics and thermal quenching simulations, the global minima and the other locally stable structures have been distinguished from those stationary structures that correspond to saddle points of the potential energy surface. Ten thousand independent initial configurations generated at high temperatures (about 2600 K) were used to obtain the number of isomers and the probabilities of sampling different basins of attractions, for each size of the clusters. Their energy spectra have been analyzed. Comparisons have been made with the results of previous calculations using electronic structure and empirical potential methods. Although many of the lowest energy structures correspond to icosahedral growth, a number of new structures have been identified for N ¼ 15, 16, 17, 18, 20 and 21. It has been found that the lowest energy structures are not always the most probable isomers for each size.
Physical Review B, 2005
The geometric and electronic structure of the Pb n clusters ͑n =2-15͒ has been calculated to elucidate its structural evolution and compared with other group-IV elemental clusters. The search for several low-lying isomers was carried out using the ab initio molecular dynamics simulations under the framework of the density functional theory formalism. The results suggest that unlike Si, Ge, and Sn clusters, which favor less compact prolate shape in the small size range, Pb clusters favor compact spherical structures consisting of fivefold or sixfold symmetries. The difference in the growth motif can be attributed to their bulk crystal structure, which is diamond-like for Si, Ge, and Sn but fcc for Pb. The relative stability of Pb n clusters is analyzed based on the calculated binding energies and second difference in energy. The results suggest that n = 4, 7, 10, and 13 clusters are more stable than their respective neighbors, reflecting good agreement with experimental observation. Based on the fragmentation pattern it is seen that small clusters up to n = 12 favor monomer evaporation, larger ones fragment into two stable daughter products. The experimental observation of large abundance for n = 7 and lowest abundance of n = 14 have been demonstrated from their fragmentation pattern. Finally a good agreement of our theoretical results with that of the experimental findings reported earlier implies accurate predictions of the ground state geometries of these clusters.
Energetics and structures of small clusters: Pt N , N=2–21
Surface Science, 2003
The Voter and Chen version of an embedded-atom model, derived by fitting to experimental data of both diatomic molecule and bulk platinum simultaneously, has been applied to study the locally stable structures, energies and growth patterns of small platinum clusters in the size range of N=2–21. Using molecular dynamics and thermal quenching simulations, the global minima and the other locally stable structures have been distinguished from those stationary structures that correspond to saddle points of the potential energy surface. Ten thousand independent initial configurations generated at high temperatures (about 2600 K) were used to obtain the number of isomers and the probabilities of sampling different basins of attractions, for each size of the clusters. Their energy spectra have been analyzed. Comparisons have been made with the results of previous calculations using electronic structure and empirical potential methods. Although many of the lowest energy structures correspond to icosahedral growth, a number of new structures have been identified for N=15, 16, 17, 18, 20 and 21. It has been found that the lowest energy structures are not always the most probable isomers for each size.
The European Physical Journal D, 2009
Here we report a systematic theoretical study of the structure and electronic properties of Snn−1Pb and Pbn−1Sn (n = 2−13) clusters and compare these results with pure Snn and Pbn to understand the influence of the dopant elements. The calculations were carried out using the density functional theory with generalized gradient approximation for the exchange-correlation potential. Extensive search based on large number of initial configurations has been carried out to locate the stable isomers of Snn−1Pb and Pbn−1Sn (n = 2−13) clusters. The relative stability of Snn−1Pb and Pbn−1Sn (n = 2−13) clusters is analyzed based on the calculated binding energies and second difference in energy. The stability analysis of these clusters suggests that, while the substitution of Sn by Pb lowers the stability of Snn clusters, presence of Sn enhances the stability of the Pbn clusters. The results suggest that while for Snn−1Pb, n = 4, 7, 10, 12 clusters are more stable than their respective neighbors, Pbn−1Sn clusters with n = 4, 7 and 9 are found to be more stable. Based on the fragmentation pattern it is seen that for Snn−1Pb and Pbn−1Sn clusters favor monomer evaporation of the Pb atom up to n = 11 and n = 12, respectively. Unlike this trend, the Sn11Pb undergoes fission type fragment into Sn5Pb and Sn6 clusters. A comparison between our theoretical results and surface induced dissociation experiment shows good agreement, which gives confidence on the prediction of the ground state geometries.
Electronic and atomic structure of Na, Mg, Al and Pb clusters
Zeitschrift f�r Physik D Atoms, Molecules and Clusters, 1988
Density functional theory is used to study the electronic and atomic structure of small clusters of Na, Mg, A1 and Pb. We study the quantity Eu_~-EN, which has relevance to the processes of cluster growth and evaporation (E N is the total energy of the cluster with N atoms). By comparing the results of the jellium model with those of a more realistic model (although still simple) we are able to appreciate "structural" effects beyond the "electronic-shell effects" which form the essence of the predictions of the jellium model. The calculations predict formation of atomic shells and appreciable reconstruction as the cluster grows.
Thermodynamics of small platinum clusters
Computational materials science, 2006
Using the Voter and Chen version of an embedded atom model, derived by fitting simultaneously to experimental data of both the diatomic molecule and bulk platinum, we have studied the melting behavior of free, small platinum clusters in the size range of N = 15–19 in the molecular dynamics simulation technique. We present an atom-resolved analysis method that includes physical quantities such as the root-mean-square bond-length fluctuation and coordination number for individual atoms as functions of temperature. The results show that as the Pt15–Pt18 clusters exhibit multistage melting, melting in Pt19 cluster takes place in a single but interesting stage. None of these melting stages occurs at a specific temperature, rather, melting processes take place over a finite temperature range. This range is larger for less symmetric clusters. An ensemble of clusters in the melting region is a mixture of different isomeric forms of the clusters. The multistage melting and the occurrence of a single melting stage over a temperature range are two different phenomena.
Energetic and thermodynamic size effects in molecular clusters
The Journal of Chemical Physics, 1989
In this paper we explore the interrelationship between the energetics and the thermodynamic properties of molecular clusters. We advance simple models for the energy spectrum, which are used to derive analytical results for the thermodynamic properties of these clusters. The energy spectrum is characterized by the distribution of the energies of the local minima of the nuclear potential energy hypersurface, i.e., the inherent structures. On each of these energy levels the vibrational density of states of the particular inherent structure is superimposed. The energy spectra were specified in terms of the energy gap, a, between the (single) ground state and the excited-state inherent structures, the number, R, of the inherent structures and their energetic spread W. Four classes of energy spectra were considered. (1) A large energy gap with nearly degenerate excited-state manifold, i.e., a~ W. (2) A large energy gap with a considerable spread of the excited-state manifold, i.e., a < Wand W / R < a. (3) A gapless spectrum with W / R ~ A. (4) A multiple bunched spectrum with several energy gaps. Explicit analytical relations for the temperature dependence of the internal energy were derived for energy spectra of types (1), (2), and (3) both for the canonical and for the microcanonical ensembles. For energy spectra oftypes and the caloric curve exhibits a single inflection, which marks the "transition". A unified description of multistate isomerization with large R, which corresponds to rare-gas clusters, and of molecular isomerization with R= 1, which prevails for alkali-halide clusters, was provided. For energy spectra of type (3) the transition disappears, while for energy spectra of type (4) hierarchical isomerization is exhibited. Our analytical models have established the ensemble dependence of the transition for types (1) and (2), which is manifested by a considerable broadening of the transition range for the canonical ensemble, reflecting the role of energy fluctuations in the finite system.
Structures and energetics Of Pd n ( n=2–20) clusters using an embedded-atom model potential
Surface Science, 2002
We have studied the structure and energetics of the stable isomers of Pd n (n ¼ 2-20) clusters by using molecular dynamics and slow-quenching techniques. Cohesion of the clusters is modeled by an embedded-atom potential due to Voter and Chen, which contains many-body atomic interactions. The isomers' statistics are obtained from 10 000 independent initial configurations, which have been generated along a high-energy trajectory (the chosen energy value is high enough to melt the cluster). The internal kinetic energy of these initial conditions is removed slowly. Because of this slow minimization process the locally stable isomers are separated from those meta-stable ones. Probabilities belonging to sampling the basins of attractions of each isomer are computed, and compared with each other. Furthermore, the spectrum, which is formed by isomers' energies, is analyzed. Ó
Dynamics of phase changes and melting of Pd7 clusters
Acta Physica Slovaca, 2004
We have obtained the stable geometrical structures, energetics, melting behaviors and phase changes of Pd7 clusters by using molecular dynamics and thermal quenching simulations. Cohesion of the clusters is modeled by an embedded-atom potential, which contains manybody atomic interactions. Isomers' energy-spectrum-width and their sampling probabilities are calculated. Melting phenomenon of a cluster is described in terms of relative root-meansquare bond-length fluctuations, and of behavior of the specific heats. The transition region from solid-to liquid-like phases is investigated, and the melting temperature of the cluster is estimated. Minimum energy pathways for the phase changes among the isomers of the Pd7 are determined.