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Abstract
Recent developments allow heat capacities to be measured for size-selected clusters isolated in the gas phase. For clusters with tens to hundreds of atoms, the heat capacities determined as a function of temperature usually have a single peak attributed to a melting transition. The melting temperatures and latent heats show large size-dependent fluctuations. In some cases, the melting temperatures change by hundreds of degrees with the addition of a single atom. Theory has played a critical role in understanding the origin of the size-dependent fluctuations, and in understanding the properties of the liquid-like and solid-like states. In some cases, the heat capacities have extra features (an additional peak or a dip) that reveal a more complex behavior than simple melting. In this article we provide a description of the methods used to measure the heat capacities and provide an overview of the experimental and theoretical results obtained for sodium and aluminum clusters.
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Affiliation(s)
- Andrés Aguado
- Departamento de Física Teórica, Universidad de Valladolid, Valladolid 47011, Spain
| | - Martin F. Jarrold
- Chemistry Department, Indiana University, Bloomington, Indiana 47401;,
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Abstract
ABSTRACTSurface melting on clusters is investigated by a combination of analytic modeling and computer simulation. Homogeneous, argon-like clusters bound by Lennard-Jones forces and Cu-like clusters bound by ‘embedded atom’ potentials are the systems considered. Molecular dynamics (MD) calculations have been carried out for clusters with 40–147 atoms. Well below the bulk melting temperature, the surfaces become very soft, exhibiting well-defined diffusion constants even while the cores remain nearly rigid and solid-like. The simulations, particularly animations, of atomic motion reveal that the surface melting is associated not with amorphous, random surface structures in constant, irregular motion, but rather in large-amplitude, organized, collective motion of most of the surface atoms accompanied by a few “floaters” and holes. At any time, a few of the surface atoms move out of the surface layer, leaving vacancies; these promoted particles wander diffusively, the holes also but less so, and occasionally exchange with atoms in the surface layer. This result is the basis for an analytic, statistical model. The caloric curves, particularly the latent heats, show that surface melting of clusters is a “phase change” different from the bulk melting of clusters.
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Echt O, Reyes Flotte A, Knapp M, Sattler K, Recknagel E. Magic Numbers in Mass Spectra of Xe, C2F4Cl2 and SF6 Clusters. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19820860919] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Cao B, Starace AK, Judd OH, Bhattacharyya I, Jarrold MF. Metal clusters with hidden ground states: Melting and structural transitions in Al115(+), Al116(+), and Al117(+). J Chem Phys 2009; 131:124305. [PMID: 19791879 DOI: 10.1063/1.3224124] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Heat capacities measured as a function of temperature for Al(115)(+), Al(116)(+), and Al(117)(+) show two well-resolved peaks, at around 450 and 600 K. After being annealed to 523 K (a temperature between the two peaks) or to 773 K (well above both peaks), the high temperature peak remains unchanged but the low temperature peak disappears. After considering the possible explanations, the low temperature peak is attributed to a structural transition and the high temperature peak to the melting of the higher enthalpy structure generated by the structural transition. The annealing results show that the liquid clusters freeze exclusively into the higher enthalpy structure and that the lower enthalpy structure is not accessible from the higher enthalpy one on the timescale of the experiments. We suggest that the low enthalpy structure observed before annealing results from epitaxy, where the smaller clusters act as a nucleus and follow a growth pattern that provides access to the low enthalpy structure. The solid-to-solid transition that leads to the low temperature peak in the heat capacity does not occur under equilibrium but requires a superheated solid.
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Affiliation(s)
- Baopeng Cao
- Department of Chemistry, Indiana University, 800 East Kirkwood Ave., Bloomington, Indiana 47405, USA
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Patashinski A, Ratner M. Heterophasic oscillations in nanoscale systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:041106. [PMID: 18999378 DOI: 10.1103/physreve.78.041106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2008] [Indexed: 05/27/2023]
Abstract
Both the energy differences between metastable and stable phases and the energy barriers separating these phases decrease with decreasing particle number. Then, for small enough systems, random heterophasic fluctuations of the entire system become an observable form of thermal motion. We discuss mechanisms and observation conditions for these random transitions between phases.
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Jarrold MF, Cao B, Starace AK, Neal CM, Judd OH. Metal clusters that freeze into high energy geometries. J Chem Phys 2008; 129:014503. [PMID: 18624479 DOI: 10.1063/1.2939579] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.
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Affiliation(s)
- Martin F Jarrold
- Chemistry Department, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, USA.
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Stephen Berry R, Beck TL, Davis HL, Jellinek J. Solid-Liquid Phase Behavior in Microclusters. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470122693.ch3] [Citation(s) in RCA: 115] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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Affiliation(s)
- N. Quirke
- a BP Research Centre , Chertsey Road, Sunbury on Thames , UK
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Neal CM, Starace AK, Jarrold MF. Ion calorimetry: Using mass spectrometry to measure melting points. JOURNAL OF THE AMERICAN SOCIETY FOR MASS SPECTROMETRY 2007; 18:74-81. [PMID: 17010642 DOI: 10.1016/j.jasms.2006.08.019] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2006] [Revised: 08/17/2006] [Accepted: 08/19/2006] [Indexed: 05/12/2023]
Abstract
Calorimetry measurements have been used to probe the melting of aluminum cluster cations with 63 to 83 atoms. Heat capacities were determined as a function of temperature (from 150 to 1050 K) for size-selected cluster ions using an approach based on multicollision-induced dissociation. The experimental method is described in detail and the assumptions are critically evaluated. Most of the aluminum clusters in the size range examined here show a distinct peak in their heat capacities that is attributed to a melting transition (the peak is due to the latent heat). The melting temperatures are below the bulk melting point and show enormous fluctuations as a function of cluster size. Some clusters (for example, n = 64, 68, and 69) do not show peaks in their heat capacities. This behavior is probably due to the clusters having a disordered solid-like phase, so that melting occurs without a latent heat.
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Affiliation(s)
- Colleen M Neal
- Chemistry Department, Indiana University, Bloomington, Indiana 47405, USA
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Barboy B, Schatz G, Ratner MA, Gerber R. Dynamical instabilities and structural changes in molecules. Mol Phys 2006. [DOI: 10.1080/00268978300102401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Bogdan TV, Wales DJ, Calvo F. Equilibrium thermodynamics from basin-sampling. J Chem Phys 2006; 124:044102. [PMID: 16460144 DOI: 10.1063/1.2148958] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a "basin-sampling" approach for calculation of the potential energy density of states for classical statistical models. It combines a Wang-Landau-type uniform sampling of local minima and a novel approach for approximating the relative contributions from local minima in terms of the volumes of basins of attraction. We have employed basin-sampling to study phase changes in atomic clusters modeled by the Lennard-Jones potential and for ionic clusters. The approach proves to be efficient for systems involving broken ergodicity and has allowed us to calculate converged heat capacity curves for systems that could previously only be treated using the harmonic superposition approximation. Benchmarks are also provided by comparison with parallel tempering and Wang-Landau simulations, where these proved feasible.
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Affiliation(s)
- Tetyana V Bogdan
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK
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Breaux GA, Neal CM, Cao B, Jarrold MF. Melting, premelting, and structural transitions in size-selected aluminum clusters with around 55 atoms. PHYSICAL REVIEW LETTERS 2005; 94:173401. [PMID: 15904287 DOI: 10.1103/physrevlett.94.173401] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2004] [Indexed: 05/02/2023]
Abstract
Heat capacities have been determined for unsupported aluminum clusters, Al49(+) - Al63(+), from 150 to 1050 K. Peaks in the heat capacities due to melting occur between 450 and 650 K (well below the bulk melting point of 933 K). The peaks for Al+51 and Al+52 are bimodal, suggesting the presence of a premelting transition where the surface of the clusters melts around 100 K before the core. For clusters with n > 55 the melting temperatures suddenly drop, and there is a dip in the heat capacities due to a transition between two solid forms before the clusters melt.
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Affiliation(s)
- Gary A Breaux
- Department of Chemistry, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47404, USA
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Abstract
Melting in Na(n) clusters described with an empirical embedded-atom potential has been reexamined in the size range 55</=n</=147 with a special attention at sizes close to 130. Contrary to previous findings, premelting effects are also present at such medium sizes, and they turn out to be even stronger than the melting process itself for Na(133) or Na(135). These results indicate that the empirical potential is qualitatively inadequate to model sodium clusters.
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Affiliation(s)
- F Calvo
- Laboratoire de Physique Quantique, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, F31062 Toulouse Cedex, France
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Breaux GA, Benirschke RC, Sugai T, Kinnear BS, Jarrold MF. Hot and solid gallium clusters: too small to melt. PHYSICAL REVIEW LETTERS 2003; 91:215508. [PMID: 14683319 DOI: 10.1103/physrevlett.91.215508] [Citation(s) in RCA: 88] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2003] [Indexed: 05/24/2023]
Abstract
A novel multicollision induced dissociation scheme is employed to determine the energy content for mass-selected gallium cluster ions as a function of their temperature. Measurements were performed for Ga(+)(n) (n=17 39, and 40) over a 90-720 K temperature range. For Ga+39 and Ga+40 a broad maximum in the heat capacity-a signature of a melting transition for a small cluster-occurs at around 550 K. Thus small gallium clusters melt at substantially above the 302.9 K melting point of bulk gallium, in conflict with expectations that they will remain liquid to below 150 K. No melting transition is observed for Ga+17.
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Affiliation(s)
- Gary A Breaux
- Chemistry Department, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405-7102, USA
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Zhou Y, Karplus M, Ball KD, Berry RS. The distance fluctuation criterion for melting: Comparison of square-well and Morse potential models for clusters and homopolymers. J Chem Phys 2002. [DOI: 10.1063/1.1426419] [Citation(s) in RCA: 189] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Frantz DD. Magic number behavior for heat capacities of medium-sized classical Lennard-Jones clusters. J Chem Phys 2001. [DOI: 10.1063/1.1397329] [Citation(s) in RCA: 91] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Phases and Phase Changes of Small Systems. ACTA ACUST UNITED AC 1999. [DOI: 10.1007/978-3-642-58389-6_1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Salian UA. Microcanonical temperature and “heat capacity” computation of Lennard-Jones clusters under isoergic molecular dynamics simulation. J Chem Phys 1998. [DOI: 10.1063/1.476040] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chitra R, Yashonath S. Effect of confinement in the α-cages of zeolite NaCaA on the properties of Ar13 cluster: A Monte Carlo study. J CHEM SCI 1997. [DOI: 10.1007/bf02883489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Vekhter B, Berry RS. Phase coexistence in clusters: An “experimental” isobar and an elementary model. J Chem Phys 1997. [DOI: 10.1063/1.473636] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chitra R, Yashonath S. Inverse Surface Melting in Confined Clusters: Ar13 in Zeolite L. J Phys Chem B 1997. [DOI: 10.1021/jp961872j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- R. Chitra
- Solid State and Structural Chemistry Unit and Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore 560012, India
| | - S. Yashonath
- Solid State and Structural Chemistry Unit and Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore 560012, India
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McClurg RB, Flagan RC, Goddard WA. Thermodynamic properties and homogeneous nucleation rates for surface‐melted physical clusters. J Chem Phys 1996. [DOI: 10.1063/1.473002] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Calvo F, Labastie P. Evidence for surface melting in clusters made of double icosahedron units. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(96)00608-2] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Chitra R, Yashonath S. Monte Carlo simulation of an argon cluster confined in zeolite NaCaA. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(96)00193-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Wales DJ, Doye JPK. Coexistence and phase separation in clusters: From the small to the not‐so‐small regime. J Chem Phys 1995. [DOI: 10.1063/1.470494] [Citation(s) in RCA: 77] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kunz RE, Berry RS. Statistical interpretation of topographies and dynamics of multidimensional potentials. J Chem Phys 1995. [DOI: 10.1063/1.469714] [Citation(s) in RCA: 97] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Doye JPK, Wales DJ. An order parameter approach to coexistence in atomic clusters. J Chem Phys 1995. [DOI: 10.1063/1.468786] [Citation(s) in RCA: 68] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kunz RE, Berry RS. Multiple phase coexistence in finite systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:1895-1908. [PMID: 9961430 DOI: 10.1103/physreve.49.1895] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kunz RE, Berry RS. Coexistence of multiple phases in finite systems. PHYSICAL REVIEW LETTERS 1993; 71:3987-3990. [PMID: 10055125 DOI: 10.1103/physrevlett.71.3987] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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van de Waal BW. Icosahedral, decahedral, fcc, and defect‐fcc structural models for ArNclusters,N≳500: How plausible are they? J Chem Phys 1993. [DOI: 10.1063/1.464946] [Citation(s) in RCA: 63] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Cheng HP, Li X, Whetten RL, Berry RS. Complete statistical thermodynamics of the cluster solid-liquid transition. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:791-800. [PMID: 9908180 DOI: 10.1103/physreva.46.791] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Cheng HP, Berry RS. Surface melting of clusters and implications for bulk matter. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:7969-7980. [PMID: 9906888 DOI: 10.1103/physreva.45.7969] [Citation(s) in RCA: 76] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Vlachos DG, Schmidt LD, Aris R. Structures of small metal clusters. II. Phase transitions and isomerization. J Chem Phys 1992. [DOI: 10.1063/1.462583] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cheng H, Berry RS, Whetten RL. Electronic structure and binding energies of aluminum clusters. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:10647-10653. [PMID: 9996793 DOI: 10.1103/physrevb.43.10647] [Citation(s) in RCA: 80] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Labastie P, Whetten RL. Statistical thermodynamics of the cluster solid-liquid transition. PHYSICAL REVIEW LETTERS 1990; 65:1567-1570. [PMID: 10042303 DOI: 10.1103/physrevlett.65.1567] [Citation(s) in RCA: 257] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Adams JE, Stratt RM. Instantaneous normal mode analysis as a probe of cluster dynamics. J Chem Phys 1990. [DOI: 10.1063/1.459145] [Citation(s) in RCA: 82] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Garzón IL, Blaisten-Barojas E. Phenomenological model of melting in Lennard-Jones clusters. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:4749-4759. [PMID: 9992470 DOI: 10.1103/physrevb.40.4749] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wales DJ, Kirkland AI, Jefferson DA. Structure and growth of colloidal metal particles. J Chem Phys 1989. [DOI: 10.1063/1.457446] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Diep HT, Sawada S, Sugano S. Melting and magnetic ordering in transition-metal microclusters. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:9252-9259. [PMID: 9947656 DOI: 10.1103/physrevb.39.9252] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Beck TL, Leitner DM, Berry RS. Melting and phase space transitions in small clusters: Spectral characteristics, dimensions, and K entropy. J Chem Phys 1988. [DOI: 10.1063/1.455114] [Citation(s) in RCA: 94] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Beck TL, Berry RS. The interplay of structure and dynamics in the melting of small clusters. J Chem Phys 1988. [DOI: 10.1063/1.453840] [Citation(s) in RCA: 187] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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