Hot and solid gallium clusters: too small to melt

Ambient printing of native oxides for ultrathin transparent flexible circuit boards

Metal oxide films are essential in most electronic devices, yet they are typically deposited at elevated temperatures by using slow, vacuum-based processes. We printed native oxide films over large areas at ambient conditions by moving a molten metal meniscus across a target substrate. The oxide gently separates from the metal through fluid instabilities that occur in the meniscus, leading to uniform films free of liquid residue. The printed oxide has a metallic interlayer that renders the films highly conductive. The metallic character of the printed films promotes wetting of trace amounts of evaporated gold that would otherwise form disconnected islands on conventional oxide surfaces. The resulting ultrathin (<10 nanometers) conductors can be patterned into flexible circuits that are transparent, mechanically robust, and electrically stable, even at elevated temperatures.

Core atoms escape from the shell: reverse segregation of Pb-Al core-shell nanoclusters via nanoscale melting

Melting is a phase transition that profoundly affects the fabrication and diverse applications of metal nanoclusters. Core-shell clusters offer distinctive properties and thus opportunities compared with other classes of nano-alloys. Molecular dynamics simulations have been employed to investigate the melting behaviour of Pb-Al core-shell clusters containing a fixed Pb147 core and varying shell thickness. Our results show that the core and shell melt separately. Surprisingly, core melting always drives the core Pb atoms to break out the shell and coat the nanoclusters in a reversed segregation process at the nanoscale. The melting point of the core increases with the shell thickness to exceed that of the bare core cluster, but the thinnest shell always supresses the core melting point. These results can be a reference for the future fabrication, manipulation, and exploitation of the core-shell nanoalloys chosen. The system chosen is ideally suited for experimental observations.

Mapping the Finite-Temperature Behavior of Conformations to Their Potential Energy Barriers: Case Studies on Si6B and Si5B Clusters

Dynamical simulations of molecules and materials have been the route to understand the rearrangement of atoms within them at different temperatures. Born-Oppenheimer molecular dynamical simulations have further helped to comprehend the reaction dynamics at various finite temperatures. We take a case study of Si₆B and Si₅B clusters and demonstrate that their finite-temperature behavior is rather mapped to the potential energy surface. The study further brings forth the fact that an accurate description of the dynamics is rather coupled with the accuracy of the method in defining the potential energy surface. A more precise potential energy surface generated through the coupled cluster method is finally used to identify the most accurate description of the potential energy surface and the interconnected finite-temperature behavior.

Evidencing the relationship between isomer spectra and melting: the 20- and 55-atom silver and gold cluster cases

The present work highlights the links between melting properties and structural excitation spectra of small gold and silver clusters. The heat capacity curves are computed for Ag₂₀, Au₂₀, Ag₅₅, Au₅₅ and their ions, using a parallel-tempering molecular dynamics scheme to explore the density functional based tight binding (DFTB) potential energy surfaces and the multiple histogram method. It is found that clusters having very symmetric lowest energy structures (Au₂₀, Ag₅₅ and their ions) present sharp or relatively sharp solid-to-liquid transitions and large melting temperatures, important structural excitation energies and a discrete isomer spectrum. Opposite trends are observed for less ordered clusters (Ag₂₀, Au₅₅ and their ions). Regarding the structural evolution with temperature, very symmetric clusters exhibit minor evolution up to the starting melting temperature. The present study also highlights that, in contrast with the case of Au₂₀, a single electron excess or deficiency is not determinant regarding the melting characteristics, even quantitatively, for clusters containing 55 atoms, for gold as for silver.

Mean first passage times reconstruct the slowest relaxations in potential energy landscapes of nanoclusters

Relaxation modes are the collective modes in which all probability deviations from equilibrium states decay with the same relaxation rates. In contrast, a first passage time is the required time for arriving for the first time from one state to another. In this paper, we discuss how and why the slowest relaxation rates of relaxation modes are reconstructed from the first passage times. As an illustrative model, we use a continuous-time Markov state model of vacancy diffusion in KCl nanoclusters. Using this model, we reveal that all characteristics of the relaxations in KCl nanoclusters come from the fact that they are hybrids of two kinetically different regions of the fast surface and slow bulk diffusions. The origin of the different diffusivities turns out to come from the heterogeneity of the activation energies on the potential energy landscapes. We also develop a stationary population method to compute the mean first passage times as mean times required for pair annihilations of particle-hole pairs, which enables us to obtain the symmetric results of relaxation rates under the exchange of the sinks and the sources. With this symmetric method, we finally show why the slowest relaxation times can be reconstructed from the mean first passage times.

Entropy and the Tolman Parameter in Nucleation Theory

Thermodynamic aspects of the theory of nucleation are commonly considered employing Gibbs’ theory of interfacial phenomena and its generalizations. Utilizing Gibbs’ theory, the bulk parameters of the critical clusters governing nucleation can be uniquely determined for any metastable state of the ambient phase. As a rule, they turn out in such treatment to be widely similar to the properties of the newly-evolving macroscopic phases. Consequently, the major tool to resolve problems concerning the accuracy of theoretical predictions of nucleation rates and related characteristics of the nucleation process consists of an approach with the introduction of the size or curvature dependence of the surface tension. In the description of crystallization, this quantity has been expressed frequently via changes of entropy (or enthalpy) in crystallization, i.e., via the latent heat of melting or crystallization. Such a correlation between the capillarity phenomena and entropy changes was originally advanced by Stefan considering condensation and evaporation. It is known in the application to crystal nucleation as the Skapski–Turnbull relation. This relation, by mentioned reasons more correctly denoted as the Stefan–Skapski–Turnbull rule, was expanded by some of us quite recently to the description of the surface tension not only for phase equilibrium at planar interfaces, but to the description of the surface tension of critical clusters and its size or curvature dependence. This dependence is frequently expressed by a relation derived by Tolman. As shown by us, the Tolman equation can be employed for the description of the surface tension not only for condensation and boiling in one-component systems caused by variations of pressure (analyzed by Gibbs and Tolman), but generally also for phase formation caused by variations of temperature. Beyond this particular application, it can be utilized for multi-component systems provided the composition of the ambient phase is kept constant and variations of either pressure or temperature do not result in variations of the composition of the critical clusters. The latter requirement is one of the basic assumptions of classical nucleation theory. For this reason, it is only natural to use it also for the specification of the size dependence of the surface tension. Our method, relying on the Stefan–Skapski–Turnbull rule, allows one to determine the dependence of the surface tension on pressure and temperature or, alternatively, the Tolman parameter in his equation. In the present paper, we expand this approach and compare it with alternative methods of the description of the size-dependence of the surface tension and, as far as it is possible to use the Tolman equation, of the specification of the Tolman parameter. Applying these ideas to condensation and boiling, we derive a relation for the curvature dependence of the surface tension covering the whole range of metastable initial states from the binodal curve to the spinodal curve.

Atomic-resolution imaging of surface and core melting in individual size-selected Au nanoclusters on carbon

Although the changes in melting behaviour on the nanoscale have long attracted the interest of researchers, the mechanism by which nanoparticles melt remains an open problem. We report the direct observation, at atomic resolution, of surface melting in individual size-selected Au clusters (2-5 nm diameter) supported on carbon films, using an in situ heating stage in the aberration corrected scanning transmission electron microscope. At elevated temperatures the Au nanoparticles are found to form a solid core-liquid shell structure. The cluster surface melting temperatures, show evidence of size-dependent melting point suppression. The cluster core melting temperatures are significantly greater than predicted by existing models of free clusters. To explore the effect of the interaction between the clusters and the carbon substrate, we employ a very large-scale ab initio simulation approach to investigate the influence of the support. Theoretical results for surface and core melting points are in good agreement with experiment.

Gallium selenide clusters generated via laser desorption ionisation quadrupole ion trap time-of-flight mass spectrometry

RATIONALE

Gallium selenide thin films important for electronics and phase-change materials are prepared via pulsed laser deposition (PLD); however, there are no studies concerning the analysis of gallium selenide clusters formed in the gas phase. Laser desorption ionisation (LDI) combined with time-of-flight mass spectrometry (TOF-MS) has great potential to generate charged Ga_m Se_n clusters, to analyse them and thus to develop new materials.

METHODS

LDI of Ga-Se mixtures using a pulsed laser (337 nm nitrogen) was used to generate gallium-selenide clusters. Mass spectra were recorded (in positive and negative ion mode) on a TOF mass spectrometer equipped with a quadrupole ion trap and reflectron mass analyser.

RESULTS

Ga-Se mixtures were found to be suitable for laser ablation synthesis (LAS) of gallium selenide clusters, although their composition was strongly dependent on the laser energy. The effect of laser energy on the stoichiometry of the generated clusters was established. In total, over 100 gallium selenide Ga_m Se_n clusters were generated and identified from Ga-Se mixtures. LDI of Ga₂ Se₃ crystals showed almost the same clusters up to m/z 1000 with lower intensities, whereas no clusters from Ga₂ Se₃ were observed above m/z 1000.

CONCLUSIONS

A family of over 100 gallium selenide clusters, generated and identified for the first time, shows rich and complex chemistry. Some of the clusters represent new compounds that have the potential to be used in the development of advanced materials.

Surface melting and breakup of metal nanowires: Theory and molecular dynamics simulation

We consider the surface melting of metal nanowires by solving a phenomenological two-parabola Landau model and by conducting molecular dynamics simulations of nickel and aluminum nanowires. The model suggests that surface melting will precede bulk melting when the melt completely wets the surface and the wire is sufficiently thick, as is the case for planar surfaces and sufficiently large nanoparticles. Surface melting does not occur if the melt partially wets or does not wet the surface. We test this model, which assumes that the surface energies of the wire are isotropic, using molecular dynamics simulations. For nickel, we observe the onset of anisotropic surface melting associated with each of the two surface facets present, but this gives way to uniform surface melting and the solid melts radially until the solid core eventually breaks up. For aluminum, while we observe complete surface melting of one facet, the lowest energy surface remains partially dry even up to the point where the melt completely penetrates the solid core.

Slowest kinetic modes revealed by metabasin renormalization

Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009)PLEEE81539-375510.1103/PhysRevE.80.036112] and a Jacobi method. We test the method on an illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al., Chem. Phys. Lett. 654, 52 (2016)CHPLBC0009-261410.1016/j.cplett.2016.04.088], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes.

How robust is the metallicity of two dimensional gallium?

Atomically thin gallium layers have recently been experimentally produced via solid–melt exfoliation, and show promise as robustly metallic 2D materials for electronic applications.

Theoretical investigation of the solid–liquid phase transition in protonated water clusters

Molecular dynamics simulations provide an atomistic scale description of the phase transition in protonated water clusters (H₂O)_nH⁺(n= 20–23) and an interpretation to recent nano-calorimetric experiments.

First-principles calculations of the electronic structure and bonding in metal cluster-fullerene materials considered within the superatomic framework

Inspired by recent success of synthesizing cluster assembled compounds we address the question to what extent the three new materials [Co₆Se₈(PEt₃)₆][C₆₀]₂, [Cr₆Te₈(PEt₃)₆][C₆₀]₂, and [Ni₉Te₆(PEt₃)₈]C₆₀, upon forming bulk compounds, imitate atomic analogues. Although experimental results suggest the latter, a theoretical approach is the method of choice for offering a conclusive answer and for studying the actual superatomic character. The concept of superatoms for describing atom-imitating clusters is very intriguing since it allows chemists to apply their chemical intuition - a useful tool for predicting new materials - when it comes to inter-cluster reactions. Thus, we systematically study the lattice structure, the intercluster binding, and the electronic structure by density functional theory and assess them in terms of their superatomic features. We show that collective properties arise upon bulk formation, which promotes arguments for the formation of solids in which the constituent clusters have a superatomic character that determines some form of chemical bonding. Additionally, we find evidence for the formation of superatomic states. Unfortunately, however, due to the mixing of electronic states of transition metals and chalcogen atoms, no typical electronic shell closing in the cluster cores can be identified.

A Two-Dimensional Liquid Structure Explains the Elevated Melting Temperatures of Gallium Nanoclusters

Melting in finite-sized materials differs in two ways from the solid-liquid phase transition in bulk systems. First, there is an inherent scaling of the melting temperature below that of the bulk, known as melting point depression. Second, at small sizes changes in melting temperature become nonmonotonic and show a size-dependence that is sensitive to the structure of the particle. Melting temperatures that exceed those of the bulk material have been shown to occur for a very limited range of nanoclusters, including gallium, but have still never been ascribed a convincing physical explanation. Here, we analyze the structure of the liquid phase in gallium clusters based on molecular dynamics simulations that reproduce the greater-than-bulk melting behavior observed in experiments. We observe persistent nonspherical shape distortion indicating a stabilization of the surface, which invalidates the paradigm of melting point depression. This shape distortion suggests that the surface acts as a constraint on the liquid state that lowers its entropy relative to that of the bulk liquid and thus raises the melting temperature.

Thermodynamics of confined gallium clusters

We report the results of ab initio molecular dynamics simulations of Ga13 and Ga17 clusters confined inside carbon nanotubes with different diameters. The cluster-tube interaction is simulated by the Lennard-Jones (LJ) potential. We discuss the geometries, the nature of the bonding and the thermodynamics under confinement. The geometries as well as the isomer spectra of both the clusters are significantly affected. The degree of confinement decides the dimensionality of the clusters. We observe that a number of low-energy isomers appear under moderate confinement while some isomers seen in the free space disappear. Our finite-temperature simulations bring out interesting aspects, namely that the heat capacity curve is flat, even though the ground state is symmetric. Such a flat nature indicates that the phase change is continuous. This effect is due to the restricted phase space available to the system. These observations are supported by the mean square displacement of individual atoms, which are significantly smaller than in free space. The nature of the bonding is found to be approximately jellium-like. Finally we note the relevance of the work to the problem of single file diffusion for the case of the highest confinement.

The dimeric nature of bonding in gallium: from small clusters to the α-gallium phase

We consider the structural similarity of small gallium clusters to the bulk structure of α-gallium, which has been previously described as a molecular metal, via density functional theory-based computations. Previous calculations have shown that the tetramer, the hexamer, and the octamer of gallium are all structurally similar to the α-phase. We perform an analysis of the bonding in these clusters in terms of the molecular orbitals and atoms in molecules description in order to assess whether we can see similarities at these sizes to the bonding pattern, which is ascribed to the co-existence of covalent and metallic bonding in the bulk. The singlet Ga4 and Ga8 clusters can be constructed in a singlet ground state from the Ga-dimers in the first excited triplet state of the Ga2-molecule, the (3)Σg(-) state. Molecular orbital (MO) analysis confirms that the dimer is an essential building block of these small clusters. Comparison of the AIM characteristics of the bonds within the clusters to the bonds in the bulk α-phase supports the identification of the covalent bond in the bulk as related to the (3)Σg(-) state of the dimer.

Thermodynamics of nanoalloys

This article reviews recent advances in our understanding of how temperature affects the structure and the phase of multimetallic nanoparticles. Focusing on bimetallic systems, we discuss the interplay of size, shape and chemical order on the stable configurations at thermal equilibrium. Besides some considerations about experimental evidence for thermally-induced transformations, most insight is generally gained from theory and computation. The perspectives offered by mesoscopic approaches (i.e. corrected from the bulk) and atomistic simulations complement each other and often provide detailed information about the respective roles of coordination, composition and more generally surface effects to be evaluated. Order-disorder transitions and the melting phase change are strongly altered in nanoscale systems, and we describe how they possibly impact entire phase diagrams.

Al20+ does melt, albeit above the bulk melting temperature of aluminium

Employing first principles parallel tempering molecular dynamics in the microcanonical ensemble, we report the presence of a clear solid–liquid-like melting transition in Al₂₀⁺ clusters, not found in experiments.

Nanothermodynamics of large iron clusters by means of a flat histogram Monte Carlo method

The thermodynamics of iron clusters of various sizes, from 76 to 2452 atoms, typical of the catalyst particles used for carbon nanotubes growth, has been explored by a flat histogram Monte Carlo (MC) algorithm (called the σ-mapping), developed by Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. This method provides the classical density of states, gp(Ep) in the configurational space, in terms of the potential energy of the system, with good and well controlled convergence properties, particularly in the melting phase transition zone which is of interest in this work. To describe the system, an iron potential has been implemented, called "corrected EAM" (cEAM), which approximates the MEAM potential of Lee et al. [Phys. Rev. B 64, 184102 (2001)] with an accuracy better than 3 meV/at, and a five times larger computational speed. The main simplification concerns the angular dependence of the potential, with a small impact on accuracy, while the screening coefficients S(ij) are exactly computed with a fast algorithm. With this potential, ergodic explorations of the clusters can be performed efficiently in a reasonable computing time, at least in the upper half of the solid zone and above. Problems of ergodicity exist in the lower half of the solid zone but routes to overcome them are discussed. The solid-liquid (melting) phase transition temperature T(m) is plotted in terms of the cluster atom number N(at). The standard N(at)(-1/3) linear dependence (Pawlow law) is observed for N(at) >300, allowing an extrapolation up to the bulk metal at 1940 ±50 K. For N(at) <150, a strong divergence is observed compared to the Pawlow law. The melting transition, which begins at the surface, is stated by a Lindemann-Berry index and an atomic density analysis. Several new features are obtained for the thermodynamics of cEAM clusters, compared to the Rydberg pair potential clusters studied in Paper I.

Where macro meets micro

Reconciling or somehow linking the macroscopic and microscopic approaches to chemical and physical processes has been a challenge unaddressed for many years. One approach, presented here, treats the issue by examining individual phenomena well described by a macro approach that fails when applied to small systems. The key to the approach is determining the approximate system size below which the breakdown of the macro description is observable. The most developed example is the failure of the Gibbs phase rule for sufficiently small atomic clusters. Other examples, such as the onset, at sufficient size, of the insulator-to-metal transition, are discussed, as are some still more challenging phenomena.

First principles study of gallium cleaning for hydrogen-contaminated α-Al2O3(0001) surfaces

The use of gallium for cleaning hydrogen-contaminated Al2O3 surfaces is explored by performing first principles density functional calculations of gallium adsorption on a hydrogen-contaminated Al-terminated α-Al2O3(0001) surface. Both physisorbed and chemisorbed H-contaminated α-Al2O3(0001) surfaces with one monolayer (ML) gallium coverage are investigated. The thermodynamics of gallium cleaning are considered for a variety of different asymptotic products, and are found to be favorable in all cases. Physisorbed H atoms have very weak interactions with the Al2O3 surface and can be removed easily by the Ga ML. Chemisorbed H atoms form stronger interactions with the surface Al atoms. Bonding energy analysis and departure simulations indicate, however, that chemisorbed H atoms can be effectively removed by the Ga ML.

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.

Gas-phase calorimetry of protonated water clusters

Protonated water clusters with 60 to 79 molecules have been studied by nanocalorimetry. The technique is based on multi-collision excitations of the accelerated clusters with helium. The caloric curves indicate transitions that resemble those of water clusters charged by an excess electron, but the transition temperatures of the protonated clusters are higher.

Thermodynamic properties of Ga27Si3 cluster using density functional molecular dynamics

Density functional molecular dynamical calculations have been carried out to explore the effect of silicon impurities on thermodynamic properties of Ga(30). We have obtained 500 distinct low energy equilibrium geometries of Ga(27)Si(3) in order to obtain reliable ground state geometry. The specific heat has been calculated using multiple histogram techniques and compared with that of Ga(30). We demonstrate that silicon impurities have a dramatic effect on the thermodynamic properties of the host cluster. In contrast to Ga(30), the specific heat of Ga(27)Si(3) shows a clear melting peak at ≈500 K, changing the character of Ga(30) from a nonmelter to a melter.

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.