Hot and solid gallium clusters: too small to melt

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.     

Melting Transition of Small Aluminium Clusters Al11-20

Heat capacities of small aluminium clusters A111-20 are investigated using MD simulation with empirical many- body Gupta potential. The heat capacities of some clusters A111, A112, A113 and A119 show well-defined peaks while the heat capacities of Alls-ls indicate a gradual melting transition. The spectra of isomers obtained by quenches along the MD trajectory give good interpretation for those results.     

Melting and evaporation transitions in small Al clusters: canonical Monte-Carlo simulations

A dimer of bound atoms cannot melt, only dissociate. Bulk metals show a well defined first order transition between their solid and liquid phases. The appearance of the melting transition is explored for increasing clusters sizes via the signatures in the specific heat and the root mean square of the bond lengths B (Berry parameter) by means of Monte-Carlo simulations of Al clusters modelled by Gupta potentials. Clear signatures of a melting transition appear for N6 atoms. Closed-shell effects are shown for clusters with up to 56 atoms. The melting transition is compared in detail with the dissociation transition, which induces a second and possibly much larger local maximum in the specific heat at higher temperatures. Larger clusters are shown to fragment into dimers and trimers, which in turn dissociate at higher temperatures.     

Thermodynamic properties of noble metal clusters:molecular dynamics simulation

The thermodynamics properties of noble metal clusters Au_N, Ag_N, Cu_N, and Pt_N (N = 80, 106, 140, 180, 216, 256, 312, 360, 408, 500, 628, 736, and 864) are simulated by micro-canonical molecular dynamics simulation technique. The potential energy and heat capacities change with temperature are obtained. The results reveal that the phase transition temperature of big noble metal clusters (N ⩾ 312 for Au, 180 for Ag and Cu, and 360 for Pt) increases linearly with the atom number slowly and approaches gently to bulk crystals. This phenomenon indicates that clusters are intermediate between single atoms and molecules and bulk crystals. But for the small noble clusters, the phase transition temperature changes irregularly with the atom number due to surface effect. All noble metal clusters have negative heat capacity around the solid-liquid phase transition temperature, and hysteresis in the melting/freezing circle is derived in noble metal clusters.     

Phase transitions and kinetic properties of gold nanoparticles confined between two-layer graphene nanosheets

The thermodynamic and kinetic behaviors of gold nanoparticles confined between two-layer graphene nanosheets (two-layer-GNSs) are examined and investigated during heating and cooling processes via molecular dynamics (MD) simulation technique. An EAM potential is applied to represent the gold–gold interactions while a Lennard–Jones (L–J) potential is used to describe the gold–GNS interactions. The MD melting temperature of 1345 K for bulk gold is close to the experimental value (1337 K), confirming that the EAM potential used to describe gold–gold interactions is reliable. On the other hand, the melting temperatures of gold clusters supported on graphite bilayer are corrected to the corresponding experimental values by adjusting the ε_Au–C value. Therefore, the subsequent results from current work are reliable. The gold nanoparticles confined within two-layer GNSs exhibit face center cubic structures, which is similar to those of free gold clusters and bulk gold. The melting points, heats of fusion, and heat capacities of the confined gold nanoparticles are predicted based on the plots of total energies against temperature. The density distribution perpendicular to GNS suggests that the freezing of confined gold nanoparticles starts from outermost layers. The confined gold clusters exhibit layering phenomenon even in liquid state. The transition of order–disorder in each layer is an essential characteristic in structure for the freezing phase transition of the confined gold clusters. Additionally, some vital kinetic data are obtained in terms of classical nucleation theory.     

Na(n)(5<=n<=10)小团簇相变

采用紧密结合的分子动力学模型,对Na(n)(5<=n<=10)小团簇的键长涨落、势能、热容量等熔化性质在50K到1500K温区进行了模拟研究,结果表明：它们发生两次相变,一种在230K到300K的温度范围内,依次有块体玻璃态转变;一种在550K到870K温度段,依次经历了熔化相变.同时也得到随着团簇体系的减小,势能由下向上排列的曲线,即体系的势能由低变高.     

Melting properties of mixed Ni13-xAlx(x=0 to 13) clusters

Starting from the configuration full optimized by Genetic Algorithm (GA), the melting behaviors of Binary Ni13-xAlx(x=0 to 13) clusters have been investigated by Monte Carlo (MC) simulations with Metropolis algorithm with a n-body Gupta potential. In contrast to bulk, these clusters have smeared first order transitions occurring over a range of temperature. The melting temperature Tm calculated from Lindemanns criterion vary drastically with concentrations x. For most clusters studied, the average energy per atom E, the relative root-mean-square (rms) bond length fluchuation δ and the heat capacity C per atom related to the energy fluctuation of the system change with temperature in the transition region in manners differing from LJ and alkali metal clusters. For Ni12Al, Ni7Al6, Ni6Al7, Ni5Al8 clusters, there are behaviors characteristic of magic number in C, which do not exist in the pure TM clusters.     

金原子纳米团簇的负热容现象的分子动力学模拟研究

文中采用微正则分子动力学方法模拟研究了原子数N=60到675之间的6种金原子纳米团簇从固态到液态的熔解过程,得到了势能和热容量随温度的变化关系.其结果表明,所模拟的6种团簇在熔点附近出现负热容,通过对这些团簇熔解前后的势能以及结构变化的分析,探讨了产生负热容的微观机制.     

Structure, dynamic and energetic of mixed transition metal clusters

Classical molecular dynamics simulation (MD) with Sutton-Chen potential has been used to generate the minimum energy and to study the thermodynamic and dynamic properties of mixed transition metal cluster motifs of Ag _n Ni_(13?n) for n ?? 13. Literature results of thirteen particle clusters of neat silver and nickel atoms were first reproduced before the successive replacement of the silver atom by nickel. Calculation was repeated for both silver-centred and nickel-centred clusters. It was found that the nickel-centred clusters were more stable than the silver-centred clusters. Heat capacities and hence the melting points of silver and nickel-centred clusters were determined by using the Histogram method. Species-centric order parameters developed by Hewage and Amar were used to understand the dynamic behaviour in the transition of silver-centred clusters to more stable nickel-centred clusters. This species-centric order parameter calculation further confirmed the stability of nickel-centred clusters over those of silver-centred species.     

Influence of electronic and geometric properties on melting of sodium clusters

Systematics of the melting transition for sodium clusters with 40-355 atoms has been studied with both ab initio and semiclassical molecular dynamics simulations. The melting temperatures obtained with an ab initio method for Na₅₅ ⁺ and Na₉₃ ⁺ correlate well with the experimental results. The semiclassically determined melting temperatures show similarities with the experimentally determined ones in the size region from 55 to 93 and near size 142, and the latent heat in the size region from 55 to 139, but not elsewhere in the size region studied. This indicates that the nonmonotonical melting behavior observed experimentally cannot be fully explained by geometrical effects. The semiclassically determined melting temperature and the latent heat correlate quite well, indicating that they respond similarly to changes in cluster geometry and size. Similarly, the binding energy per atom seems to correlate with the melting temperature and the latent heat of fusion.Received: 30 October 2003, Published online: 20 January 2004PACS: 36.40.Ei Phase transitions in clusters     

Thermodynamic properties of AuyAgx bimetallic clusters through the evolutive ensemble

The caloric and specific heat curves for the bimetallic nanoclusters Au_7-xAg_x (x=0,3,4,7) are obtained through a statistical determination of the configurational density of states in the evolutive ensemble obtained with a genetic algorithm. The effect of the value of x (the relative concentrations) on the thermodynamics is studied. Three peaks are observed in the specific heat curves for all values of x. This is interpreted as being due to melting, and fragmentation of the cluster into first two, and then into 3 or more parts. A fourth pre-melting peak is observed for Au₄Ag₃ and is attributed to a new phenomena related to the breaking of the degeneracy of the permutational isomers. The melting transition for the bimetallic clusters is significantly wider than that for the pure clusters. The boiling transition displays a larger specific heat for the bimetallic clusters.     

Effect of an ionic impurity on the caloric curves of water clusters

The equilibrium heat capacities of model pure and heterogeneous water clusters have been calculated using exchange Monte Carlo simulations. For the pure water cluster (H₂O)₂₀, microcanonical and canonical caloric curves obtained from various rigid intermolecular potentials indicate the onset of melting to lie in the range 140–180 K, in reasonable agreement with previous estimates. Clusters doped with a single hydronium or ammonium impurity show a significant shift of the melting point in the 20-molecule system, but a reduced effect when 50 molecules are reached.     

Aln(n=13–32)团簇熔化行为的分子动力学模拟研究

基于半经验的Gupta原子间多体相互作用势, 采用分子动力学方法并结合模拟退火及淬火技术, 系统研究了小尺寸铝团簇Al_n (n=13–32)的熔化行为. 模拟结果表明: 除个别尺寸(Al₁₃ 和Al₁₉) 外, 团簇熔化过程比热曲线普遍呈现杂乱无规(无明显单峰)现象, 这与实验观测小Al团簇比热普遍无规的结果完全一致. 通过分析不同温度点上团簇淬火构型的势能分布图给出了小Al团簇比热呈现无规或有规现象的成因. 对于比热无规团簇, 可以利用原子等价指数判断给出团簇熔点, 所得团簇熔点随团簇尺寸的变化趋势与实验观测结果完全一致. 关键词： Gupta势 团簇 分子动力学 熔化     

Thermodynamic properties of noble metal clusters: molecular dynamics simulation

The thermodynamics properties of noble metal clusters Au_N, Ag_N, Cu_N, and Pt_N (N = 80, 106, 140, 180, 216, 256, 312, 360, 408, 500, 628, 736, and 864) are simulated by micro-canonical molecular dynamics simulation technique. The potential energy and heat capacities change with temperature are obtained. The results reveal that the phase transition temperature of big noble metal clusters (N ? 312 for Au, 180 for Ag and Cu, and 360 for Pt) increases linearly with the atom number slowly and approaches gently to bulk crystals. This phenomenon indicates that clusters are intermediate between single atoms and molecules and bulk crystals. But for the small noble clusters, the phase transition temperature changes irregularly with the atom number due to surface effect. All noble metal clusters have negative heat capacity around the solid-liquid phase transition temperature, and hysteresis in the melting/freezing circle is derived in noble metal clusters.     

Size and shape-dependent melting mechanism of Pd nanoparticles

Molecular dynamics simulation was employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2–20 number of full shells. The original embedded atom method (EAM) was compared to the more recent highly optimized version as inter-atomic potential. The thermal stability of clusters were probed using potential energy and specific heat capacity as well as structure analysis by radial distribution function (G(r)) and common neighbor analysis (CNA), simultaneously, to make a comprehensive picture of the solid-state and melting transitions. The result shows ico is the only stable shape of small clusters (Pd₅₅–Pd₃₀₉ using original EAM and Pd₅₅ using optimized version) those are melting uniformly due to their small diameter. An exception is cub Pd₃₀₉ modeled via optimized EAM that transforms to ico at elevated temperatures. A similar cub to ico transition was predicted by original EAM for Pd₉₂₃–Pd₂₀₇₅ clusters, while for the larger clusters both cub and ico are stable up to the melting point. As detected by \(G(r)\) and CNA, moderate and large cub clusters were showing surface melting by nucleation of the liquid phase at (100) planes and growth of liquid phase at the surface before inward growth. While diagonal (one corner to another) melting was dominating over ico clusters owing to their partitioned structure, which retarded the growth of the liquid phase. The large ico clusters, using optimized EAM, presented a combination of surface and diagonal melting due to the simultaneous diagonal melting started from different corners. Finally, the melting temperature as well as latent heat of fusion were calculated and compared with the available models and previous studies, which showed, unlike the present result, the models failed to predict size-dependent motif cross-over.     

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.     

A molecular dynamics study on melting point and specific heat of Ni<Subscript>3</Subscript>Al alloy

Using the Embedding Atom Method (EAM) for highly undercooled Ni₃Al alloy, the melting point and the specific heat were studied by a molecular dynamics simulation. The simulation of melting point was carried out by means of the sandwich method and the NVE ensemble method, and the results show a good agreement, whereas are larger than the experimental value of 1663 K. This difference is attributed to the influence of surface melting on experimental results, which causes the smaller measurements compared with the thermodynamic melting point. The simulated specific heat of Ni₃Al alloy weakly and linearly increases with the increase of undercooling in the temperature range from 800 K to 2000 K. Supported by the National Natural Science Foundation of China (Grant No. 50395101)     

Isotopic effect in the solid–liquid phase diagram of quantum clusters

Applying the Fourier path integral formalism to the isothermal-isobaric ensemble, the solid–liquid transition for 13-atom pure Lennard–Jones clusters was characterized. The masses of the clusters were taken as the masses of hydrogen, deuterium and tritium, hence isotopic effects of quantum clusters were considered. The parallel tempering Monte Carlo algorithm was used to solve all multidimensional integral in the FPI method. The volume of the system was defined with respect to the centroids of the quantum particles and a variable constraining potential was used to restrict undesirable thermodynamic events. The maximum value of the constant pressure heat capacity at a given temperature was used to identify the melting temperature. Pressure versus temperature phase diagrams were constructed for these systems with and without the inclusion of quantum effects. A significant difference in the melting temperature was encountered for the different isotopes due to quantum contribution.     

Ferromagnetic ordering in an organic compound: Di-(2, 2, 6, 6-tetramethyl-4 piperidinol-1 oxyl) (tanol suberate)

Specific heat measurements on a nitroxide biradical (tanol suberate), between 0.35 K and 3.2 K, are reported. A sharp peak in the specific heat due to a ferromagnetic transition is observed at 0.38 K.