Solid‐Liquid Phase Behavior in Microclusters

Berry, R. Stephen; Beck, Thomas L.; Davis, Heidi L.; Jellinek, Julius

doi:10.1002/9780470122693.ch3

Cited by 142 publications

(17 citation statements)

References 82 publications

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“…For finite systems in the microcanonical ensemble T K differs by O(N −1 ) from the thermodynamic definition of temperature (Allen and Tildesley 1987). An average of T K over a short time interval has been found to serve as a useful order parameter to distinguish between phase-like forms of clusters (Berry et al 1988) and is used in section 5 to elucidate the melting behaviour of M 55 .…”

Section: Methodsmentioning

confidence: 99%

“…In this section we shall illustrate the effects of the range of the potential on cluster thermodynamics in more detail, by presenting results of simulations of M 55 at different values of the range parameter, ρ 0 . Much work has been done on the simulation of clusters, particularly Lennard-Jones clusters (Berry et al 1988). One focus of these studies has been the character of the melting transition.…”

Section: Thermodynamics Of M 55mentioning

confidence: 99%

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The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to

Doye

Wales

1996

J. Phys. B: At. Mol. Opt. Phys.

145

126

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For systems with sufficiently short-ranged interparticle forces, such as some colloidal systems and perhaps C 60 , the liquid phase can be thermodynamically unstable. By analysing the effect of the range of the interatomic forces on the multidimensional potential energy surfaces of bulk material and clusters, a microscopic view of this phenomenon is provided. Structural analysis of the minima on the potential energy surface provides evidence for the polytetrahedral character of the liquid phase, and allows us to examine the evolution of the phase-like forms of clusters to the bulk limit. We find that essentially bulk-like liquid structure can develop in clusters with as few as 55 atoms. The effect of the range of the potential on the thermodynamics is illustrated by a series of simulations of 55-atom clusters. For small clusters bound by longranged potentials the lowest energy minimum has an amorphous structure typical of the liquidlike state. This suggests an explanation for the transition from electronic to geometric magic numbers observed in the mass spectra of sodium clusters.

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Section: Methodsmentioning

confidence: 99%

Section: Thermodynamics Of M 55mentioning

confidence: 99%

The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to

Doye

Wales

1996

J. Phys. B: At. Mol. Opt. Phys.

145

126

View full text Add to dashboard Cite

show abstract

“…Because of their low coordination number and the greater degree of freedom in their motions, surface atoms have higher mobility than atoms in the bulk. The latter fact makes the melting temperature of the surface atoms even lower than that of the core atoms of a nanoparticle, causing the phenomenon of surface melting, or “surface premelting”, as designated by Bachels, or “dynamic coexistence melting”, by Alavi et al From extensive studies of phase transitions in small clusters, Berry et al concluded that there exists a finite range of temperatures over which solidlike and liquidlike clusters can coexist in equilibrium. A very interesting case of phase coexistence in nanoparticles is that of gallium, with coexistence of melted surfaces and solid core over a broad range of temperature from 180 to 800 K. The materials were reported as “neither solid nor liquid” .…”

Section: Introductionmentioning

confidence: 97%

“…Theoretical modeling has also contributed a great deal to the understanding of the structural evolution of nanoparticles, including the solid–liquid phase behavior in microclusters, the existence of a quasi-melting regime in small particles, the liquid skin nucleation model of melting, the role of bond order deficiency on the size-dependent melting of nanoparticles, the amorphization of nanoparticles, , their melting and freezing, − and their morphological transitions. − For more information on these aspects, the reader may refer to the review articles of Baletto, Barnard, and Marks …”

Section: Introductionmentioning

confidence: 99%

Surface Activation of Transition Metal Nanoparticles for Heterogeneous Catalysis: What We Can Learn from Molecular Dynamics

2018

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Many heterogeneous reactions catalyzed by nanoparticles occur at relatively high temperatures, which may modulate the surface morphology of nanoparticles during reaction. Inspired by the discovery of dynamic formation of active sites on gold nanoparticles, we explore theoretically the nature of the highly mobile atoms on the surface of nanoparticles of various sizes for 11 transition metals. Using molecular dynamics simulations, on a 3 nm Fe nanoparticle as an example, the effect of surface premelting and overall melting on the structure and physical properties of the nanoparticles is analyzed. When the nanoparticle is heated up, the atoms in the outer shell appear amorphous already at 900 K. Surface premelting is reached at 1050 K, with more than three liquid atoms, based on the Lindemann criterion. The activated atoms may transfer their extra kinetic energy to the rest of the nanoparticle and activate other atoms. The dynamic studies indicate that the number of highly mobile atoms on the surface increases with temperature. Those atoms with a high Lindemann index, usually located on the edges or vertices, attain much higher kinetic energy than other atoms and potentially form different active sites in situ. When the temperature passes the surface premelting temperature, a drastic change in the coordination number (SCN) of the surface atoms occurs, with attendant dramatic broadening of the distribution of the SCN, suppling active sites with more diverse atomic coordination numbers. The electronic density of states of a nanoparticle tends to “equalize”, due to the breaking of the translational symmetry of the atoms in the nanoparticle, and the d-band center of the nanoparticle moves further away from the Fermi level as the temperature increases. Besides Au, other nanoparticles of the transition metals, such as Pt, Pd, and Ag, may also have active sites easily formed in situ.

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“…The onset of melting in the cluster is therefore related to the occurrence of frequent passages through the potential minima wells associated to the possible stable isomers. 1,[19][20][21] The notion of phase transitions in very small clusters, however, contradicts the seemingly well accepted dogma which requires systems to possess a large number of particles to show a true sharp phase change. 22 This issue has been discussed, for three-atom systems, with analogs between phases and energy localization modes in a molecule.…”

Section: Introductionmentioning

confidence: 99%

A path-integral Monte Carlo study of a small cluster: The Ar trimer

Tudela

Márquez-Mijares

González‐Lezana

et al. 2010

The Journal of Chemical Physics

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The Ar(3) system has been studied between T=0 K and T=40 K by means of a path-integral Monte Carlo (PIMC) method. The behavior of the average energy in terms of the temperature has been explained by comparison with results obtained with the thermal averaged rovibrational spectra estimated via: (i) a quantum mechanical method based on distributed Gaussian functions for the interparticle distances and (ii) an analytical model which precisely accounts for the participation of the dissociative continua Ar(2)+Ar and Ar+Ar+Ar. Beyond T approximately 20 K, the system explores floppier configurations than the rigid equilateral geometry, as linear and Ar-Ar(2)-like arrangements, and fragmentates around T approximately 40 K. A careful investigation of the specific heat in terms of a confining radius in the PIMC calculation seems to discard a proper phase transition as in larger clusters, in apparent contradiction with previous reports of precise values for a liquid-gas transition. The onset of this noticeable change in the dynamics of the trimer occurs, however, at a remarkably low value of the temperature in comparison with Ar(n) systems formed with more Ar atoms. Quantum mechanical effects are found of relevance at T

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Solid‐Liquid Phase Behavior in Microclusters

Cited by 142 publications

References 82 publications

The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to

The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to

Surface Activation of Transition Metal Nanoparticles for Heterogeneous Catalysis: What We Can Learn from Molecular Dynamics

A path-integral Monte Carlo study of a small cluster: The Ar trimer

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