Size-dependent Cohesive Energy Research Articles

First-Principles Investigation of Size Effects on Cohesive Energies of Transition-Metal Nanoclusters.

The cohesive energy of transition-metal nanoparticles is crucial to understanding their stability and fundamental properties, which are essential for developing new technologies and applications in fields such as catalysis, electronics, energy storage, and biomedical engineering. In this study, we systematically investigate the size-dependent cohesive energies of all the 3d, 4d, and 5d transition-metal nanoclusters (small nanoparticles) based on a plane-wave-based method within general gradient approximation using first-principles density functional theory calculations. Our results show that the cohesive energies of nanoclusters decrease with decreasing size due to the increased surface-to-volume ratio and quantum confinement effects. A comparison of nanoclusters with different geometries reveals that the cohesive energy decreases as the number of nanocluster layers decreases. Notably, monolayer nanoclusters exhibit the lowest cohesive energies. We also find that the size-dependent cohesive energy trends are different for different transition metals, with some metals exhibiting stronger size effects than others. Our findings provide insights into the fundamental properties of transition-metal nanoclusters and have potential implications for their applications in various fields, such as catalysis, electronics, and biomedical engineering.

Electron irradiation effects on Ag nanoparticles

In situ electron irradiation effects on shape and size of plate-like Ag nanoparticles (NPs) embedded in silicon nitride self-standing $$\approx$$ 70-nm-thick membranes are investigated as a function of the beam energy (120, 160 and 200 keV) and fluence using a conventional transmission electron microscope. The irradiations are performed at room temperature and cause a rapid spheroidization of the initially observed plate-like structures. Preferential sputtering of N and Si atoms exposes the resulting Ag NPs to the vacuum. At this point the sputtering of the Ag atoms causes a size decrease at distinct rates depending on the NP size and on the beam energy. This is modeled considering the influence of a size-dependent surface binding of the Ag atoms on the sputtering process. The results are compared with literature models for size-dependent cohesive energy. Our experiments discloses a new way to modify sizes and shapes and test for the size-dependent properties of thermally unstable nanoscopic objects.

Modeling the interfacial energy of embedded metallic nanoparticles

The surface/interface energy is a key parameter for determining the properties of nanomaterials. Many studies have investigated the surface energy for free standing nanoparticles but the interface energy of embedded nanoparticles requires further analysis. In this study, we developed a model of the size-dependent interfacial energy for embedded metallic nanoparticles in terms of the size-dependent cohesive energy. The model was applied to Pb–Cu, Pb–Al, and Ag–Ni systems as three examples, and the results were compared with those obtained using previously developed models and the available experimental data. Depending on the system considered, the interface energy could increase or decrease as the particle size decreased. Similarly, the dependence of the interface energy on the temperature was also related to the system considered, where the interface energy could decrease or increase as the temperature increased. The results also showed that there was a critical value for interface coherency where the effect of size on the interface energy was reversed.

A combined study of thermodynamic and first-principle calculation for single bond energy of Cu clusters

In the past, single bond energy of nanomaterials did not attract much attention, since many of their properties show a direct relation to cohesive energy. However, it is the single bond energy that determines the interaction between two atoms and even their bond lengths. Through introducing the bond number and the size-dependent cohesive energy model, the size-related single bond energy ɛ(N) of Cu clusters is resolved in this work, with the support of a thermodynamic method combined with first-principle calculation. It is found that the single bond is gradually strengthened as the size drops when compared with the bulk. Moreover, this enhanced bond strength is greatly important, especially in analyzing the Raman shift of semiconductor nanoparticles.

Size Effects on Cohesive Energy, Debye Temperature and Lattice Heat Capacity from First-Principles Calculations of Sn Nanoparticles

The size-dependent cohesive energy, melting temperature, Debye temperature and lattice heat capacity are investigated using density functional theory within generalized gradient approximation of Sn nanoparticles. The analyses of the obtained total energies are presented by considering effect of mean bond length and the ratio number of surface atoms to that of its internal with size. The cohesive energy is calculated for Sn nanoparticles and the obtained data are used to determine melting temperature, Debye temperature and lattice heat capacity. The cohesive energy, melting point and Debye temperature drop while the lattice specific heat rise when the size is decreased due to the effects of the elevated bond length stretch. The results obtained are in excellent agreement with the available experimental results for melting point and Debye temperature of Sn nanoparticles. Also, the same trend variations of the lattice heat capacity obtained for Sn nanoparticles to that calculated theoretically in Se and Cu.

Size-dependent cohesive energy of fcc nanomaterials

ABSTRACTA theoretical model for the study of size dependent cohesive energy of face-centered cubic (fcc) nanomaterials has been developed by considering the cluster order and particle size of these materials. Using the newly developed theoretical model, cohesive energy of Au, Ag and Al nanomaterials have been calculated and compared with other theoretical models and existing experimental data. The comparison of theoretical findings of the present work indicates that present developed theoretical model is in good agreement with available experimental results which show the validity of our work.

Size-dependent cohesive energy, melting temperature, and Debye temperature of spherical metallic nanoparticles

It is necessary to theoretically evaluate the thermodynamic properties of metallic nanoparticles due to the lack of experimental data. Considering the surface effects and crystal structures, a simple theoretical model is developed to study the size dependence of thermodynamic properties of spherical metallic nanoparticles. Based on the model, we have considered Co and Cu nanoparticles for the study of size dependence of cohesive energy, Au and Cu nanoparticles for size dependence of melting temperature, and Cu, Co and Au nanoparticles for size dependence of Debye temperature, respectively. The results show that the size effects on melting temperature, cohesive energy and Debye temperature of the spherical metallic nanoparticles are predominant in the sizes ranging from about 3 nm to 20 nm. The present theoretical predictions are in agreement with available corresponding experimental and computer simulation results for the spherical metallic nanoparticles. The model could be used to determine the thermodynamic properties of other metallic nanoparticles to some extent.

Surface Energy in Nanocrystalline Carbon Thin Films: Effect of Size Dependence and Atmospheric Exposure.

Surface energy (SE) is the most sensitive and fundamental parameter for governing the interfacial interactions in nanoscale carbon materials. However, on account of the complexities involved of hybridization states and surface bonds, achieved SE values are often less in comparison with their theoretical counterparts and strongly influenced by stability aspects. Here, an advanced facing-target pulsed dc unbalanced magnetron-sputtering process is presented for the synthesis of undoped and H/N-doped nanocrystalline carbon thin films. The time-dependent surface properties of the undoped and H/N-doped nanocrystalline carbon thin films are systematically studied. The advanced plasma process induced the dominant deposition of high-energy neutral carbon species, consequently controlling the intercolumnar spacing of nanodomain morphology and surface anisotropy of electron density. As a result, significantly higher SE values (maximum = 79.24 mJ/m2) are achieved, with a possible window of 79.24-66.5 mJ/m2 by controlling the experimental conditions. The intrinsic (size effects and functionality) and extrinsic factors (atmospheric exposure) are resolved and explained on the basis of size-dependent cohesive energy model and long-range van der Waals interactions between hydrocarbon molecules and the carbon surface. The findings anticipate the enhanced functionality of nanocrystalline carbon thin films in terms of selectivity, sensitivity, and stability.

Phase Diagram of Continuous Binary Nanoalloys: Size, Shape, and Segregation Effects

The phase diagrams of continuous binary nanoalloys are important in providing guidance for material designs and industrial applications. However, experimental determination of the nano-phase diagram is scarce since calorimetric measurements remain quite challenging at the nanoscale. Based on the size-dependent cohesive energy model, we developed a unified nano-thermodynamic model to investigate the effects of the size, shape, and segregation on the phase diagrams of continuous binary nanoalloys. The liquidus/solidus dropped in temperature, two-phase zone was narrowed, and the degree of surface segregation decreased with decrease in the size or increase in the shape factor. The congruent melting point of Cu-Au nanoalloys with and without segregation is linearly shifted to higher Au component and lower temperature with decreasing size or increasing shape factor. By reviewing surface segregated element of different binary nanoalloys, two segregation rules based on the solid surface energy and atomic size have been identified. Moreover, the established model can be employed to describe other physicochemical properties of nanoalloys, e.g. the cohesive energy, catalytic activation energy, and order-disorder transition temperature, and the validity is supported by available other theoretical prediction, experimental data and molecular dynamic simulations results. This will help the experimentalists by guiding them in their attempts to design bimetallic nanocrystals with the desired properties.

Size, Shape and Structure Dependent Cohesive Energy of Gold Nanoparticles: Empirical Many-Body Potential Energy Function Calculations

A thermodynamic model based on an empirical many-body potential energy function is used, to investigate the stability and energetic features of gold nanoparticles as a function of both size and shape. The concept of a localized atomic bond for surface atoms, and a non-relaxed atomic bond for the interior atoms is used. Among the five different investigated shapes, the qualitative behaviour for the cohesive energy per atom of gold nanoparticles with size range 200 1000 atoms, the general behaviour prefers; sphere < cubic <cuboctahedron < truncated octahedron < octahedron. On the other hand, the surface energy for gold nanoparticles is observed to be prominent in the nano-scale and it differs from shape to another, and falls down fast in the size range 200 < n < 1000 atoms having general trend; sphere < cubic <octahedron < truncated octahedron < cuboctahedron.

Nanophase diagram of binary eutectic Au-Ge nanoalloys for vapor-liquid-solid semiconductor nanowires growth

Although the vapor-liquid-solid growth of semiconductor nanowire is a non-equilibrium process, the equilibrium phase diagram of binary alloy provides important guidance on the growth conditions, such as the temperature and the equilibrium composition of the alloy. Given the small dimensions of the alloy seeds and the nanowires, the known phase diagram of bulk binary alloy cannot be expected to accurately predict the behavior of the nanowire growth. Here, we developed a unified model to describe the size- and dimensionality-dependent equilibrium phase diagram of Au-Ge binary eutectic nanoalloys based on the size-dependent cohesive energy model. It is found that the liquidus curves reduce and shift leftward with decreasing size and dimensionality. Moreover, the effects of size and dimensionality on the eutectic composition are small and negligible when both components in binary eutectic alloys have the same dimensionality. However, when two components have different dimensionality (e.g. Au nanoparticle-Ge nanowire usually used in the semiconductor nanowires growth), the eutectic composition reduces with decreasing size.

Grain-size effects on the thermal conductivity of nanosolids

A theoretical model has been developed for the calculation of the thermal conductivity of nanomaterials with different shapes, such as spherical nanosolids, nanowires and nanofilms, based on size-dependent atomic cohesive energy. Thermal conductivity of nanosolids with different shapes decreased as the grain size decreased. The obtained results are compared with the available experimental data. A close agreement between theory and experiment confirmed the validity of the discussed method.

Cohesive-energy-resolved bandgap of nanoscale graphene derivatives.

With a size-dependent cohesive energy formula for two-dimensional coordinated materials, the bandgap variation in quantum dots and nanoribbons of graphene derivatives, such as graphane, fluorographene and graphene oxides, is investigated. The bandgap is found to increase substantially as the diameter or width of the nano-sized material decreases. The bandgap variation is attributed to the change in cohesive energy of edge carbon atoms, and is associated with the physicochemical nature and degree of edge saturation. These predictions agree with previously reported computer simulation results, and have potential application in wide-band optics and optoelectronics.

Role of Edge Geometry and Magnetic Interaction in Opening Bandgap of Low-Dimensional Graphene

By using a size-dependent cohesive energy formula for two-dimensional coordination materials, the bandgap openings of ideal graphene quantum dots (GQDs) and nanoribbons (GNRs) have been investigated systematically regarding dimension, edge geometry, and magnetic interaction. Results demonstrate that the bandgap openings in GQDs can be dominated by the change of atomic cohesive energy. Relative to zigzag GQDs, the openings in the armchair ones are more substantial, attributed to its edge instability. The change of cohesive energy can also lead to bandgap openings in zigzag and armchair GNRs. The contribution from the interedge magnetic interaction in zigzag GNRs is negligible, while the cohesive-energy induced openings in armchair GNRs can oscillate according to the so-called full-wavelength effect, depending on the width. The model prediction provides physicochemical insight into the bandgap openings in graphene.

Morse function for nanoscaled cubic metals

Relying on our size-dependent cohesive energy and lattice constant functions, we established the Morse function in a unified form for nanoscaled cubic metals, involving metallic nanoparticles (NPs) and nanostructured materials (NSs). At the equilibrium position at 0 K, the depth of the potential well becomes shallow with smaller D especially for NPs, where D denotes the diameter of NPs or the grain size of NSs. This gives rise to the contraction or expansion of the interatomic spacing for NPs or NSs, respectively. The asymmetry of the binding energy curve in NPs is stronger than in NSs. The difference between NPs and NSs is largely associated with the distinction in the coordination imperfection between the surface and the grain boundary. The established function was supported by available experimental and computer simulation results for NPs and NSs.

Gap openings in graphene regarding interfacial interaction from substrates

Based on the size-dependent cohesive energy formula for two-dimensional materials, we investigate the gap openings in graphene layers regarding distinct interfacial interaction from substrates. Depending on the interfacial physicochemical nature, the gap is opened weakly induced by the van der Waals interaction but readily by the chemical bonding. Relative to the former, in essence, the distinct opening behavior for the latter comes from the substantial change in atomic cohesive energy of graphene associated with the coordination imperfection. Our predictions agree with the available experimental or computer simulation results for graphene layers on layered BN or bulk truncated SiC. The present work is of benefit for the application of graphene in electronics.

Physicochemical insight into gap openings in graphene

Based on a newly developed size-dependent cohesive energy formula for two-dimensional materials, a unified theoretical model was established to illustrate the gap openings in disordered graphene flakes, involving quantum dots, nanoribbons and nanoporous sheets. It tells us that the openings are essentially dominated by the variation in cohesive energy of C atoms, associated to the edge physicochemical nature regarding the coordination imperfection or the chemical bonding. In contrast to those ideal flakes, consequently, the gaps can be opened monotonously for disordered flakes on changing their sizes, affected by the dimension, geometric shape and the edge saturation. Using the density functional theory, accordingly, the electronic structures of disordered flakes differ to the ideal case because of the edge disorder. Our theoretical predictions have been validated by available experimental results, and provide us a distinct way for the quantitative modulation of bandgap in graphene for nanoelectronics.

Size-Dependent Eutectic Temperature of Ag–Pb Alloy Nanoparticles

In terms of size-dependent cohesive energy model, we have deduced an analytic model to describe the size dependence of the eutectic temperature for Ag-Pb alloy nanoparticles. The eutectic temperature is found to drop with decreasing of the particle diameter. Moreover, a linear relationship exists between the eutectic temperature and the reciprocal of the particle diameter when the diameter is large enough (e.g., 5 nm). The model predictions correspond to the experimental observations.

Size-dependent absorption properties of CdX (X = S, Se, Te) quantum dots

A unified nanothermodynamic model was developed to study the size effects on first absorption peak energy and molar extinction coefficient of semiconductor quantum dots (QDs) based on size-dependent cohesive energy and quantum confinement effect. It is found that: (1) the first absorption peak energy increases as QD size decreases; (2) the molar extinction coefficient decreases with decreasing QD size in strong confinement regime and (3) tunable absorption properties of semiconductor QDs are caused by size-induced cohesive energy variation owing to severe bond dangling. The accuracy of the developed model was verified with experimental data of CdS, CdSe and CdTe QDs.

A comprehensive understanding of melting temperature of nanowire, nanotube and bulk counterpart

Surface energies of nanostructures are of considerable interest, and thermodynamic methods have provided valuable insight into the physics and chemistry of these systems. Although the effect of surface energy on melting behaviors of nanostructures has been widely investigated in theoretical calculations and simulations, from the thermodynamics at the nanometer scale point of view, the comprehensive understanding of the fundamental physical and chemical issues involved in nanostructures' melting is still lacking. For instance, nanostructures with negative curvature, such as nanotubes, show different melting behaviors compared with the nanostructures with positive curvature such as nanowires, and both nanotubes and nanowires exhibit abnormal melting temperature compared with that of the bulk counterparts. Herein, we put forward a general model to elucidate the melting temperature of the nanostructures with positive and negative curvatures based on the surface energy at the nanometer. Further, the surface mean square relative atomic displacement (MSRD) of these nanostructures has been studied from the perspective of the size-dependent cohesive energy consideration, which can provide the atomic understanding of the nanostructures' melting. Theoretical analyses indicate that both melting temperatures of the nanostructures with the positive and negative curvatures decrease with decreasing dimensionality, and the surface MSRDs show different size effects in the systems with the positive and negative curvatures, respectively. The melting temperature of the surface with the negative curvature is higher than that of the surface with the positive curvature, and both melting temperatures are smaller than that of the bulk counterpart when the size of nanostructures is less than a threshold value. The unique melting behaviors of nanostructures are attributed to the size- and curvature-dependent surface energy of nanostructures. These results provide new insight into the fundamental understanding of the melting temperature of nanostructures.