Configurational transitions in processes involving metal clusters

We define the configurational state of an atomic system, e.g. a cluster of metal atoms, in terms of the nuclear coordinates of a specific local minimum of the potential energy surface (PES). Three types of configurational transitions are reviewed: chemical reactions, phase transitions in clusters and catalytic chemical processes involving clusters as catalysts. The analysis of the first two cases shows that although vibrational degrees of freedom of nuclei and configurational degrees of freedom are separable in lowest order, thermal motion of nuclei nevertheless influences the rate of a configurational transition. Therefore the height of the barrier that separates configurational states of the transition for the PES differs from the effective activation energy for this transition. For example, ignoring the thermal motion of atoms in Lennard-Jones clusters leads to a predicted value of their melting points twice which accounts for the thermal motion of atoms. Hence, in determining parameters governing configurational transitions, evaluation of the PES parameters, say, within the framework of DFT (density functional theory) must be augmented by information from molecular dynamics or some other method that accounts for nuclear motion.     

Size dependence of freezing temperature and structure instability in simulated Lennard-Jones clusters

Liquid Lennard-Jones clusters of 14 different sizes from N=55 to 923 particles were cooled down to find their temperature of liquid-solid transition and the internal structure of the solidified clusters. The decrease of the cluster temperature was attained by a gradual change of the system temperature in Monte Carlo simulations. The liquid-to-solid transition was found by analysis of the specific heat as well as by detection of the structural units of face-centred cubic, hexagonal close-packed and decahedral type. It was observed that near the detected transition temperature the solid-like cluster structure is not always stable and fluctuates between solid and liquid states. The fluctuations of the state were observed frequently for small clusters with N ≤147, where the temporary solid structure is created by a large part of internal atoms. Manual inspection of cluster structural data and the 10%N condition for minimal number of atoms as centres of solid-like units enable detection of stable cluster solidification at freezing temperature. It was found that the freezing temperature of all clusters, with the exception of N=55, decreases linearly with N^-1/3. The extrapolated freezing temperature of the bulk LJ system is 13% lower than the experimental value of argon. After freezing, the solid phase remains but some atoms close to the cluster surface are not firmly included into the structure and oscillate mainly between solid structure and disordered one.     

Glassy-like states of bulk rare gases

Defining a glassy-like state of a system of bound atoms as a frozen, amorphous, thermodynamically unstable state, we consider a glassy-like state of a condensed rare gas as a configurationally excited state of bound atoms that tends to the thermodynamic equilibrium by diffusion of voids. The criterion for a critical cooling rate is the minimum cooling rate of the liquid state that leads to formation of a glassy-like state. Comparing this glassy-like state with that experimentally obtained by deposition of argon atoms on a cold target, we conclude that glassy-like states are characterized by short-range parameters. On the basis of cluster studies, peculiarities of the liquid aggregate states and glassy-like states are formulated. A glassy-like state of a cluster or a bulk system of bound atoms is a configurationally excited state below the freezing point; the liquid aggregate state exhibits configurational excitations but is characterized by thermal motion of atoms, consistent with the Lindemann criterion.     

Statistics of internal excitations of atomic systems

The character of internal excitations is compared for phase transitions and chemical transitions in atomic systems. Although the temperature dependences of some physical parameters of atomic systems have resonance-like structures with maxima in both cases, the dependences of the partition functions on the number of elementary excitations or the excitation energy differ because of the difference in the numbers of interactions that govern the transitions. The phase changes of condensed rare gases are considered in the case where the external pressure is small and the differences between phases are predominantly associated with differences in configurations. Important energy parameters of rare gases are determined by the attractive part of the pairwise interaction potential between atoms. The statistical analysis shows the existence of a “freezing limit” temperature for these systems, below which the liquid state becomes unstable. The kinetics of decay of such unstable states is analyzed in terms of the diffusion of voids.     

Structural phase transition in a large cluster

The effect of a phase transition between structures in a large cluster with a pair interatomic interaction on the thermodynamic parameters of the cluster is analyzed. The statistical parameters of a cluster consisting of 923 atoms are determined for an icosahedron and a face-centered cubic (fcc) structure. The specific heat and entropy of this cluster are calculated in the case when the transition between the icosahedron and fcc structures has the greatest effect on these parameters, so that at zero temperature this cluster has the structure of an icosahedron, and as the temperature increases to the melting point it assumes an fcc structure. Even with this, the contribution of the excitations of the atomic configurations to the thermodynamic parameters of a cluster is small compared with the excitation of vibrations in the cluster. The contribution of a configurational excitation in the thermodynamic parameters of a cluster becomes substantial for the liquid state of clusters.     

Heat capacity of isolated clusters

The character of interaction between thermal (vibrational) and configurational cluster excitations is considered under adiabatic conditions when a cluster is a member of a microcanonical ensemble. The hierarchy of equilibration times determines the character of atomic equilibrium in the cluster. The behavior of atoms in the cluster can be characterized by two effective (mean) temperatures, corresponding to the solid and liquid aggregate states, because the typical time for equilibration of atomic motion is less than the transition time between aggregate states. If the cluster is considered for a time much longer than the typical dwell time in either phase, then it is convenient to characterize the system by only one temperature, which is determined from the statistical-thermodynamic long-time average. These three temperatures are not far apart, nor are the cluster heat capacities evaluated on the basis of these definitions of temperature. The heat capacity of a microcanonical ensemble may be negative for two coexisting phases if the mean temperature is defined in terms of the mean kinetic energy, rather than as the derivative of energy with respect to microcanonical entropy. However, if the configurational excitation energy is smaller than the total excitation energy separating the phases, then the two-state model predicts a positive heat capacity under either definition of temperature. Moreover, if the cluster is sufficiently large, then the maximum values of the microcanonical and canonical heat capacities are equal.     

Structure and thermal properties of supported catalyst clusters for single-walled carbon nanotube growth

Structure and thermal properties of supported iron clusters were studied using molecular dynamics simulations. When supported clusters are in the liquid state, their surfaces have spherical curvature, whereas solid clusters form a layered crystalline structure. The cluster freezing (melting) point increases dramatically with increasing cluster-substrate interaction strength, and rapid diffusion of cluster surface atoms is observed below the freezing point.     

Stability conditions for an anharmonic crystal in the mixed state

Stability conditions and the existence of metastable states for anharmonic crystals are examined within the framework of the theory of self-consistent phonons. Taking account of the self-consistent formation of liquid-like and crystal-like clusters in a crystal of fluid, the temperature nature of the behavior of the rms displacements and vibrations frequencies of atoms, the specific heat and the fraction of atoms in the liquid phase are investigated at the crystal-fluid transition. Expressions are obtained for the melting point and the absolute stability of the crystalline state, and domains of existence of crystal overheating and fluid supercooling are determined. The results of the computation are compared with experimental data for inert gases and with results obtained within the framework of a single-phase theory of consistent phonons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 15–19, December, 1990.     

Structural transitions in small nickel clusters

The processes of a thermal impact on Ni nanoclusters with a radius of up to 0.8 nm have been studied by means of molecular dynamics with the use of a tight-binding potential. The simulation indicates that the structural transition from the initial fcc phase to the icosahedral modification occurs under the influence of temperature. The transition temperature is shifted towards the cluster melting temperature with an increase in the cluster size. A similar behavior has been observed for copper and gold nanoparticles. A conclusion has been drawn that 200–250 atoms is presumably the limiting size of a metallic cluster, below which the initial fcc modification cannot be kept under realistic industrial conditions. The adequacy of the results is checked in the computer experiments with Lennard-Jones nanoparticles. The results for the Lennard-Jones and metallic nanoparticles have been shown to agree with each other.     

Intrinsic Features of an Ideal Glass

In order to understand the long-standing problem of the nature of glass states, we perform intensive simulations on the thermodynamic properties and potential energy surface of an ideal glass. It is found that the atoms of an ideal glass manifest cooperative diffusion, and show clearly different behavior from the liquid state. By determining the potential energy surface, we demonstrate that the glass state has a flat potential landscape, which is the critical intrinsic feature of ideal glasses. When this potential region is accessible through any thermal or kinetic process, the glass state can be formed and a glass transition will occur, regardless of any special structural character. With this picture, the glass transition can be interpreted by the emergence of configurational entropies,as a consequence of flat potential landscapes.     

Discrete path sampling

A theoretical framework is developed for the calculation of rate constants by sampling connected pathways composed of local minima and transition states that link them together. The theory is applicable to two-state or effective two-state systems and is applied to permutational or morphological isomerization in a two-dimensional cluster of seven Lennard-Jones atoms, water clusters containing eight and nine molecules, and a cluster of 38 Lennard-Jones atoms, which exhibits a double funnel energy landscape.     

Optical switching in a Ξ system: A comparative study on DROP and EIT

Liquid Lennard-Jones clusters with magic number of atoms N = 55, 147, 309, 561 and 923 were cooled down in Monte Carlo simulations until freezing. Structural properties of the clusters, including the radial dependence of atomic concentration/density and the local regular structure in arrangement of atoms, just before freezing were analysed. Existence of spherical layers in atomic density around the centre of mass of liquid LJ clusters was confirmed. Formation of layers is explained by central net forces acting on every cluster atom and leading to positioning an atom close to the cluster centre of mass. The strong layering in small clusters of N = 55 and 147 affects atomic diffusion in radial and tangential directions inside the cluster, leading to easier movement of atoms on the layer surface. Analysis of radial profiles of four types of structural units detected in liquid clusters reveals that icosahedral units are the most numerous and are located mainly near cluster surface of all clusters and also in the centre of small clusters.     

Melting,freezing and other peculiarities in small systems

The theory of solid-liquid phase changes in small systems implies that such systems may—but need not—exhibit sharp but unequal freezing and melting temperatures. The origin of this conclusion is reviewed and its implications for the theory of first-order phase transitions in bulk matter are discussed. The logical separation is made of the two temperatures as limits of stable existence, each of its own ‘phase’; and the convergence, with increasing size of cluster, of the observable coexistence to a sharp transition temperature is discussed. The equilibrium ratios of concentrations for such a coexistence are discontinuous functions of temperature at the limits of stability. The possibility of observing coexisting forms in equilibrium depends on there being a time scale separability, who validity lies outside the realm of thermodynamics. It is conjectured that spinodals are the loci of the same kind of locally stable states responsible for coexisting solid and liquid forms of clusters, and that the limits of spinodals are the points of discontinuity in the equilibrium concentration ratios, the chemical ‘equilibrium constants’.     

Simulating the thermal stability and phase changes of small carbon clusters and fullerenes

The thermal stability, phases and phase changes of small carbon clusters and fullerenes are investigated by constant energy Molecular Dynamics simulations performed over a wide range of temperatures, i.e., from to above the melting point of graphitic carbon. The covalent bonds between the carbon atoms in the clusters are represented by the many-body Tersoff potential. The zero temperature structural characteristics of the clusters, i.e., the minimum energy structures as well as the isomer hierarchy can be rationalized in terms of the interplay between the strain energy (due to the surface curvature) and the number of dangling bonds in the cluster. Minimization of the strain energy opposes the formation of cage structures whereas minimization of the number of dangling bonds favors it. To obtain a reliable picture of the processes experienced by carbon clusters as a function of temperature, both thermal and dynamical characteristics of the clusters are carefully analyzed. We find that higher excitation temperatures are required for producing structural transformations in the minimum energy structures than in higher lying isomers. We have also been able to unambiguously identify some structural changes of the clusters occurring at temperatures well below the melting-like transition. On the other hand, the melting-like transition is interrupted before completion, i.e., the thermal decomposition of the clusters (evaporation or ejection of or units) occurs, from highly excited configurations, before the clusters have fully developed a liquid-like phase. Comparison with experiments on the thermal decomposition of and a discussion of the possible implications of our results on the growth mechanisms leading to the formation of different carbon structures are included. Received: 25 March 1998 / Received in final form: 30 October 1998     

Physical cluster mechanics: Statics and energy surfaces for monatomic systems

The potential energy surfaces for clusters of some three to sixty atoms under Lennard-Jones forces have been systematically explored using numerical optimization techniques. In searching for minimum-energy configurations three particularly compact non-lattice growth schemes emerge showing tetrahedral, pentagonal (D_{5 ^h} ) and icosahedral symmetry respectively. All these systems were found to be appreciably more stable than microcrystallites based on the face-centred cubic structure while certain lattice elements were shown to be metastable for small numbers of atoms.

Some qualitative conclusions are then drawn concerning the occurrence of saddle-points for delocalized motion and the contribution of these to the generation of configurational entropy in small clusters. A crucial feature of the energy surfaces examined is the breakdown of strict local symmetry in compact clusters of more than two ‘shells’ of atoms and the possibility of delocalized motion of surface atoms around a solid-like core. These and other qualitative thresholds are pointed out as possible manifestations of entropy which could contribute to the existence of a ‘critical nucleus’ for discrete clusters with a role similar to that played in liquid-drop theories.     

Peculiar thermodynamic properties of LJ<Subscript> N</Subscript> (N = 39–55) clusters

The solid-liquid phase transitions of Lennard-Jones clusters LJ_N (N=39–55) were simulated by a microcanonical molecular dynamics method using Lennard-Jones potential, and their thermodynamic quantities were calculated. The caloric curves of clusters (except N=42) have S-bend. To understand this behaviour, configurational and total entropies were evaluated, and dents on the entropy curves were taken as a sign of negative heat capacity. The heat capacities were evaluated for N=39–55 clusters using configurational entropy data. The potential energy distributions have bimodal behaviour for all clusters in the given range at the melting temperature. The distinct melting behaviour of LJ₄₂ was explained by the topology of the potential energy surface by examining the isomer distributions at phase transitions for LJ₃₉-LJ₅₅. The isomer distributions were found to be a useful way to interpret this behaviour and melting dynamics in general. Melting temperature, latent heat and entropy change upon melting values were reported and are consistent with literature values and values calculated from bulk thermodynamic properties. The dependence of these quantities on the size of the clusters was examined and it is found that latent heat is the key quantity to determine the magic numbers.     

Entangling Two Multi-atomic Clusters Through a Cavity Field

Two atomic clusters, which have NA and Ns two-level atoms, respectively, are placed in a cavity but separated spatially. There is no direct interaction between the atoms. All the atoms interact with a single-mode of the cavity field. Quantum entanglement between the two atomic clusters is investigated for various initial states of the two atomic clusters and the field. When the cavity field is initially in a Fock state, we find that the time evolution of entanglement quasi-periodically oscillates regardless of the initial states of atoms. The oscillation period increases as the initial photon number increases. When all the atoms in both of the atomic clusters are initially in the excited state, we show that there is no entanglement between the atomic clusters with NA = NB = 1 regardless the initial state of the cavity field. However, when either NA or NB is larger than one, we find that the entanglement always exists even for a strong thermal field. In cases with different initial states of the atomic clusters, we notice that the entanglement becomes stronger as number of the atoms increases. When all the atoms in both of the clusters in the ground state, we also find that the entanglement can be enhanced even by a thermal field. We also notice that a single qubit can be entangled with multi-atoms which are initially in the ground state by the cavity field initially being in vacuum, thermal, coherent, and squeezed states.     

Thermodynamic Stability of Transition States in Nanosystems

We present a theory which shows that, in a closed system of fixed volume capable of undergoing a phase transition, the transition state can be thermodynamically stable against the bulk phases if a certain material parameters criterion is fulfilled. In a small system below the critical size the transition state turns into a globally stable phase that can be observed experimentally. This effect is analogous to stabilization of icosahedral structures in clusters of certain sizes and energies. Stabilization of the transition state in small systems of limited resources allows us to conjecture that, in the case of a melting/freezing transition in pure substances, this state corresponds to an amorphous phase. Although unstable in open systems, this phase may be observed experimentally due to slow kinetics of its decomposition at low temperatures. The material-parameters criterion should help experimenters select the materials for the experimental verification of the phenomenon. In the present paper we consider thin films where the phase separation is permitted only parallel to the plane of the film. The calculations, however, hold true for 3D small systems: e.g., nanoparticles.     

Rb原子激发态碰撞能量转移

报道了用连续单模激光激发Rb原子至特定的激发态，从而观察激发态间的碰撞形成更高Rb原子激发态的实验结果.实验观察到Rb原子激发态的自发辐射与高激发态的碰撞形成通道之间的明显竞争，测得了高激发态的形成概率与激发光功率、原子蒸气温度及激光失谐的关系，所提出的碰撞能量转移机理较好地解释了实验结果. 关键词：     

On the problem of the existence of a supercooled liquid phase of cryovacuum ethanol condensates

Our previous IR-spectrometry and thermodesorption studies of thin films of cryovacuum ethanol condensates and comparison of these data with the results obtained in works of some groups have allowed us to make several conclusions relative to temperature ranges of existence of low-temperature states of ethanol. Newly acquired experimental data indicate that the cryovacuum condensates of ethanol formed at temperatures considerably below the glass transition temperature T _g ≈ 98 K pass through the state that can be characterized as a supercooled liquid phase in the course of subsequent thermally stimulated transformations. The temperature range of the solid-liquid transformation (97–100 K) agrees well with the data of researchers who studied the ethanol samples obtained by the vitrification from the liquid phase.