Correlation between the latent heats and cohesive energies of metal clusters

Thermophysical behavior of mercury-lead liquid alloy

Thermophysical properties of compound forming binary liquid mercury-lead alloy at temperature 600 K have been reported as a function of concentration by considering HgPb2 complex using different modelling equations. The thermodynamic properties such as the Gibbs free energy, enthalpy of mixing, chemical activity of each component, and microscopic properties such as concentration fluctuation in long-wavelength limit and Warren-Cowley short range order parameter of the alloy are studied by quasi-chemical approximation. This research paper places additional emphasis on the interaction energy parameters between the atoms of the alloy. The theoretical and experimental data are compared to determine the model’s validity. Compound formation model, statistical mechanical technique, and improved derivation of the Butler equation have all been used to investigate surface tension. The alloy’s viscosity is investigated using the Kozlov-Ronanov-Petrov equation, the Kaptay equation, and the Budai-Benko-Kaptay model. The study depicts a weak interaction of the alloy, and the theoretical thermodynamic data derived at 600 K are in good agreement with the experimental results. The surface tension is slightly different in the compound formation model than in the statistical mechanical approach and the Butler equation at greater bulk concentrations of lead. The estimated viscosities in each of the three models are substantially identical.

A machine learning based deep potential for seeking the low-lying candidates of Al clusters

A Machine-Learning based Deep Potential (DP) model for Al clusters is developed through training with an extended database including ab initio data of both bulk and several clusters in only 6 CPU/h. This DP model has good performance in accurately predicting the low-lying candidates of Al clusters in a broad size range. Based on our developed DP model, the low-lying structures of 101 different sized Al clusters are extensively searched, among which the lowest-energy candidates of 69 sized clusters are updated. Our calculations demonstrate that machine-learning is indeed powerful in generating potentials to describe the interaction of atoms in complex materials.

Understanding the ML black box with simple descriptors to predict cluster–adsorbate interaction energy

Density functional theory (DFT) is currently one of the most accurate and yet practical theories used to gain insight into the properties of materials.

Excess thermal energy and latent heat in nanocluster collisional growth

Nanoclusters can form and grow by nanocluster-monomer collisions (condensation) and nanocluster-nanocluster collisions (coagulation). During growth, product nanoclusters have elevated thermal energies due to potential and thermal energy exchange following a collision. Even though nanocluster collisional heating may be significant and strongly size dependent, no prior theory describes this phenomenon for collisions of finite-size clusters. We derive a model to describe the excess thermal energy of collisional growth, defined as the kinetic energy increase in the product cluster, and latent heat of collisional growth, defined as the heat released to the background upon thermalization of the nonequilibrium cluster. Both quantities are composed of a temperature-independent term related to potential energy minimum differences and a size- and temperature-dependent term, which hinges upon heat capacity and energy partitioning. Example calculations using gold nanoclusters demonstrate that collisional heating can be important and strongly size dependent, particularly for reactive collisions involving nanoclusters composed of 14-20 atoms. Excessive latent heat release may have considerable implications in cluster formation and growth.

Oxygen adsorption onto pure and doped Al surfaces--the role of surface dopants

Using density functional theory (DFT) with the PBE0 density functional we investigated the role of surface dopants in the molecular and dissociative adsorption of O2 onto Al clusters of types Al50, Al50Alad, Al50X and Al49X, where X represents a dopant atom of the following elements Si, Mg, Cu, Sc, Zr, and Ti. Each dopant atom was placed on the Al(111) surface as an adatom or as a substitutional atom, in the last case replacing a surface Al atom. We found that for the same dopant geometry, the closer is the ionization energy of the dopant element to that of elemental Al, the more exothermic is the dissociative adsorption of O2 and the stronger are the bonds between the resulting O atoms and the surface. Additionally we show that the Mulliken concept of electronegativity can be applied in the prediction of the dissociative adsorption energy of O2 on the doped surfaces. The Mulliken modified second-stage electronegativity of the dopant atom is proportional to the exothermicity of the dissociative adsorption of O2. For the same dopant element in an adatom position the dissociation of O2 is more exothermic when compared to the case where the dopant occupies a substitutional position. These observations are discussed in view of the overlap population densities of states (OPDOS) computed as the overlap between the electronic states of the adsorbate O atoms and the clusters. It is shown that a more covalent character in the bonding between the Al surface and the dopant atom causes a more exothermic dissociation of O2 and stronger bonding with the O atoms when compared to a more ionic character in the bonding between the dopant and the Al surface. The extent of the adsorption site reconstruction is dopant atom dependent and is an important parameter for determining the mode of adsorption, adsorption energy and electronic structure of the product of O2 adsorption. The PBE0 functional could predict the existence of the O2 molecular adsorption product for many of the cases investigated here.

Nanothermodynamics of metal nanoparticles

This article presents a perspective on thermodynamic characterization of metal nanoparticles by computational chemistry. Topics emphasized include structural stability, phases, phase changes, and free energy functions of aluminum nanoparticles.

Reactions of CO2 on solid and liquid Al100+

The reactions of CO(2) on the Al(100)(+) cluster have been investigated as a function of cluster temperature (300-1100 K) and relative kinetic energy (0.2-10 eV). Two main products are observed at low cluster temperature: Al(100)O(+) (which is believed to result from a stripping reaction) and Al(100)CO(2)(+) from complex formation. As the cluster temperature is raised, both products dissociate by loss of Al(2)O. Al(100)O(+) forms Al(98)(+), while Al(100)CO(2)(+) forms Al(98)CO(+) and Al(96)C(+). In both cases, loss of Al(2)O turns-on above the melting temperature of Al(100)(+). This presumably occurs because the overall reaction leading to the loss of Al(2)O is significantly less endothermic for the liquid cluster than for the solid.

Neutral and charged gallium clusters: structures, physical properties and implications for the melting features

We report the putative Global Minimum (GM) structures and electronic properties of Ga(N)(+), Ga(N) and Ga(N)(-) clusters with N = 13-37 atoms, obtained from first-principles density functional theory structural optimizations. The calculations include spin polarization and employ an exchange-correlation functional which accounts for van der Waals dispersion interactions (vdW-DFT). We find a wide diversity of structural motifs within the located GM, including decahedral, polyicosahedral, polytetrahedral and layered structures. The GM structures are also extremely sensitive to the number of electrons in the cluster, so that the structures of neutral and charged clusters differ for most sizes. The main magic numbers (clusters with an enhanced stability) are identified and interpreted in terms of electronic and geometric shell closings. The theoretical results are consistent with experimental abundance mass spectra of Ga(N)(+) and with photoelectron spectra of Ga(N)(-). The size dependence of the latent heats of melting, the shape of the heat capacity peaks, and the temperature dependence of the collision cross-sections, all measured for Ga(N)(+) clusters, are properly interpreted in terms of the calculated cohesive energies, spectra of configurational excitations, and cluster shapes, respectively. The transition from "non-melter" to "magic-melter" behaviour, experimentally observed between Ga(30)(+) and Ga(31)(+), is traced back to a strong geometry change. Finally, the higher-than-bulk melting temperatures of gallium clusters are correlated with a more typically metallic behaviour of the clusters as compared to the bulk, contrary to previous theoretical claims.

Melting and Freezing of Metal Clusters

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.

Half-solidity of tetrahedral-like Al(55) clusters

A new dynamic melting state, which has both solid and liquid characteristics, is revealed from first-principles molecular dynamics simulations of Al(55) clusters. In thermal fluctuations near the melting point, the low-energy tetrahedral-like Al(55) survives through rapid, collective surface transformations-such as parity conversions and correlated diffusion of two distant vacancies-without losing its structural orders. The emergence of the collective motions is solely due to efficient thermal excitation of soft phonon modes at nanoscale. A series of spontaneous surface reconfigurations result in a mixture or effective flow of surface atoms as is random color shuffling of a Rubik's cube. This novel flexible solid state (termed as half-solidity) provides useful insights into understanding stability, flexibility, and functionality of nanosystems near or below melting temperatures.

Metal clusters with hidden ground states: Melting and structural transitions in Al115(+), Al116(+), and Al117(+)

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.

Premelting and postmelting in clusters

Caloric curves for sodium clusters with N=139 and 147 atoms show a fine structure near the solid-to-liquid transition. Neither of the two sizes exhibit surface melting. For N=139, diffusion of the surface vacancies is observed, which is not possible in the closed-shell N=147 cluster. A few kelvin above the peak in the heat capacity, N=139 is completely liquid. This is not the case for N=147. Here the inner 13 atoms remain nearly fixed up to several tens of kelvin above the melting temperature of the outer two layers. A simple physical reason is suggested for this unexpected behavior.