Gallium Cluster “Magic Melters”

The Native Oxide Skin of Liquid Metal Ga Nanoparticles Prevents Their Rapid Coalescence during Electrocatalysis

Liquid metals (LMs) have been used in electrochemistry since the 19th century, but it is only recently that they have emerged as electrocatalysts with unique properties, such as inherent resistance to coke poisoning, which derives from the dynamic nature of their surface. The use of LM nanoparticles (NPs) as electrocatalysts is highly desirable to enhance any surface-related phenomena. However, LM NPs are expected to rapidly coalesce, similarly to liquid drops, which makes their implementation in electrocatalysis hard to envision. Herein, we demonstrate that liquid Ga NPs (18 nm, 26 nm, 39 nm) drive the electrochemical CO₂ reduction reaction (CO₂RR) while remaining well-separated from each other. CO is generated with a maximum faradaic efficiency of around 30% at -0.7 V_RHE, which is similar to that of bulk Ga. The combination of electrochemical, microscopic, and spectroscopic techniques, including operando X-ray absorption, indicates that the native oxide skin of the Ga NPs is still present during CO₂RR and provides a barrier to coalescence during operation. This discovery provides an avenue for future development of Ga-based LM NPs as a new class of electrocatalysts.

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.

A universal signature in the melting of metallic nanoparticles

Predicting when phase changes occur in nanoparticles is fundamental for designing the next generation of devices suitable for catalysis, biomedicine, optics, chemical sensing and electronic circuits. The estimate of the temperature at which metallic nanoparticles become liquid is, however, a challenge and a standard definition is still missing. We discover a universal feature in the distribution of the atomic-pair distances that distinguishes the melting transition of monometallic nanoparticles. We analyse the solid-liquid change of several late-transition metals nanoparticles, i.e. Ni, Cu, Pd, Ag, Au and Pt, through classical molecular dynamics. We consider various initial shapes from 146 to 976 atoms, corresponding to the 1.5-4.1 nm size range, placing the nanoparticles in either a vacuum or embedded in a homogeneous environment, simulated by an implicit force-field. Regardless of the material, its initial shape, size and environment, the second peak in the pair-distance distribution function, expected at the bulk lattice distance, disappears when the nanoparticle melts. As the pair-distance distribution is a measurable quantity, the proposed criterion holds for both numerical and experimental investigations. For a more straightforward calculus of the melting temperature, we demonstrate that the cross-entropy between a reference solid pair-distance distribution function and the one of nanoparticles at increasing temperatures present a quasi-first order transition at the phase-change temperature.

Optical Scattering of Liquid Gallium Nanoparticles Coupled to Thin Metal Films

We investigate experimentally and numerically the scattering properties of liquid gallium nanoparticles coupled to a thin gold or silver film. The gallium nanoparticles are excited either directly by using inclined white light or indirectly by surface plasmon polaritons generated on the surface of the gold/silver film. In the former case, the scattering spectrum is always dominated by a scattering peak at ∼540 nm with a long-wavelength shoulder which is redshifted with increasing diameter of the gallium nanoparticle. Under the excitation of the surface plasmon polaritons, optical resonances with much narrower linewidths, which are dependent on the incidence angle of the white light, appear in the scattering spectra. In this case, the scattering spectrum depends weakly on the diameter of the gallium nanoparticle but the radiation pattern exhibits a strong dependence. In addition, a significant enhancement of electric field is expected in the gap region between the gallium nanoparticles and the gold film based on numerical simulation. As compared with the gallium nanoparticle coupled to the gold film which exhibit mainly yellow and orange colors, vivid scattering light spanning the visible light spectrum can be achieved in the gallium nanoparticles coupled to the silver film by simply varying the incidence angle. Gallium nanoparticles coupled to thin metal films may find potential applications in light-matter interaction and color display.

Superatomic Gallium Clusters in Dendrimers: Unique Rigidity and Reactivity Depending on their Atomicity

Superatoms have been investigated due to their possible substitution for other elements. The solution-phase synthesis of superatoms has attracted attention to realize the availability of superatoms. However, the previous approach is basically limited to the formation of a single cluster. Here, superatoms are investigated and the number of valence electrons in these superatoms is changed by designing the number of gallium atoms present. Based on the dendrimer template method, clusters consisting of 3, 12, 13, and other numbers of atoms have been synthesized. The halogen-like superatomic nature of Ga₁₃ is structurally and electrochemically observed as completely different to the other clusters. The gallium clusters of 13 and 3 atoms, which can fill the 2P and 1P superatomic orbitals, respectively, exhibit different reactivities. The 3-atom gallium cluster is suggested as being reduced to Ga₃ H₂ ^- due to the lower shift of energy levels in the unoccupied orbitals. The results for these gallium clusters provide candidates for superatoms.

Ultra stable superatomic structure of doubly magic Ga13 and Ga13Li electrolyte

We report the extreme thermal stability of the superatomic electronic structure for 13-atom gallium clusters and the Ga₁₃Li electrolyte. Using previously-validated first-principles simulations, [K. G. Steenbergen and N. Gaston, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 161402-161405] we show that the superatomic shell progression of doubly-magic Ga₁₃^- remains stable up to 1000 K, making this cluster an ideal candidate for high-temperature applications requiring an exceptionally stable electronic structure. Using the neutral and cationic clusters for comparison, we quantify the extent to which cluster stability (geometric and electronic) is modified through addition or subtraction of a single electron. Finally, combining 13-atom gallium with lithium, we illustrate that superatomic closed-shell Ga₁₃Li exhibits the same exceptionally high thermal stability as naked Ga₁₃^-. For technological use as a superatomic electrolyte, we demonstrate that Ga₁₃Li has a low affinity to water as well as a low Li⁺ binding energy.

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.

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.

Thickness dependent thermal stability of 2D gallenene

Freestanding 2D metallic gallenene exhibits remarkable stability when the thickness is three atomic layers.

Liquid metals: fundamentals and applications in chemistry

Post-transition elements, together with zinc-group metals and their alloys belong to an emerging class of materials with fascinating characteristics originating from their simultaneous metallic and liquid natures. These metals and alloys are characterised by having low melting points (i.e. between room temperature and 300 °C), making their liquid state accessible to practical applications in various fields of physical chemistry and synthesis. These materials can offer extraordinary capabilities in the synthesis of new materials, catalysis and can also enable novel applications including microfluidics, flexible electronics and drug delivery. However, surprisingly liquid metals have been somewhat neglected by the wider research community. In this review, we provide a comprehensive overview of the fundamentals underlying liquid metal research, including liquid metal synthesis, surface functionalisation and liquid metal enabled chemistry. Furthermore, we discuss phenomena that warrant further investigations in relevant fields and outline how liquid metals can contribute to exciting future applications.

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.

Thermally stable coexistence of liquid and solid phases in gallium nanoparticles

Gallium (Ga), a group III metal, is of fundamental interest due to its polymorphism and unusual phase transition behaviours. New solid phases have been observed when Ga is confined at the nanoscale. Herein, we demonstrate the stable coexistence, from 180 K to 800 K, of the unexpected solid γ-phase core and a liquid shell in substrate-supported Ga nanoparticles. We show that the support plays a fundamental role in determining Ga nanoparticle phases, with the driving forces for the nucleation of the γ-phase being the Laplace pressure in the nanoparticles and the epitaxial relationship of this phase to the substrate. We exploit the change in the amplitude of the evolving surface plasmon resonance of Ga nanoparticle ensembles during synthesis to reveal in real time the solid core formation in the liquid Ga nanoparticle. Finally, we provide a general framework for understanding how nanoscale confinement, interfacial and surface energies, and crystalline relationships to the substrate enable and stabilize the coexistence of unexpected phases.

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.

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.

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.

Dehydrogenation of benzene on liquid Al100(+)

The reactions of benzene on Al100(+) have been investigated as a function of cluster temperature (300-1100 K) and relative kinetic energy (1-14 eV) by low-energy ion-beam methods and mass spectrometry. Benzene chemisorbs on both solid and liquid aluminum clusters to generate Al100C6D6(+). A series of Al(100-n)(+) (n = 1, 2, 3, ...) products was also observed. As the cluster temperature was raised above the melting temperature of Al100(+), the Al100C6D6(+) product dehydrogenates to form Al100C6D4(+), Al100C6D2(+), and Al100C6(+). The degree of dehydrogenation was measured as a function of temperature. Very little Al100C6D2(+) was observed, suggesting that the losses of the second and third D2 molecules are coordinated.

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.

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.

Density functional investigations on structural and electronic properties of anionic and neutral sodium clusters Na(N) (N = 40-147): comparison with the experimental photoelectron spectra

Density functional calculations have been carried out to obtain low energy equilibrium geometries of anionic and neutral sodium clusters over a wide range of sizes 40 ≤ N ≤ 147, where N is the number of atoms. An exhaustive search for the low energy equilibrium geometries has been carried out. The density of states of the lowest energy geometries are compared with the experimental photoelectron spectra (Huber et al 2009 Phys. Rev. B 80 235425; Kostko et al 2007 Phys. Rev. Lett.98 043401) for N > 41. The agreement between theory and experiment is good for almost all the clusters and the changes in the spectrum with size correlate very well with the changes in the shapes as observed in the evolutionary trend of the ground state geometries.

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.

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.

Metal clusters that freeze into high energy geometries

Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.

Ab Initio Molecular Dynamical Investigation of the Finite Temperature Behavior of the Tetrahedral Au19and Au20Clusters

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap, and an atomic packing similar to that of the bulk gold (Li, J.; et al. Science 2003, 299, 864). Our results show that the geometry of Au19 is exactly identical with that of Au20 with one missing corner atom (called a vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold clusters exhibit dramatic differences. Au20 undergoes a clear and distinct solid-like to liquid-like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving a series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid-like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature that has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.

Density functional analysis of the structural evolution of Gan (n=30–55) clusters and its influence on the melting characteristics

Recent experimental results have reported surprising variations in the shapes of the heat capacity curves and melting temperatures of gallium clusters in the size range of 30-55 atoms [G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004)]. In the present work, we have carried out an extensive density functional investigation on ten selected clusters in the above mentioned size range. In particular, we have analyzed the ground state geometry and the nature of bonding in these clusters using electron localization function. We demonstrate that the existence or otherwise of a large island of atoms bonded with similar strength (i.e., the local order) in the ground state geometry is responsible for the variation in the shape of the heat capacity curve. We attribute the observed higher melting temperatures of some of the clusters (viz., Ga45-Ga48) to the presence of a distinct core and strong covalent bonds between the core and surface atoms. The present work clearly demonstrates that it is possible to understand the general trends observed in the heat capacity curves across the entire series on the basis of the analysis of their ground state.