Higher surface energy of free nanoparticles

We present an accurate online method for the study of size-dependent evaporation of free nanoparticles allowing us to detect a size change of 0.1 nm. This method is applied to Ag nanoparticles. The linear relation between the onset temperature of evaporation and the inverse of the particle size verifies the Kelvin effect and predicts a surface energy of 7.2 J/m(2) for free Ag nanoparticles. The surface energy of nanoparticles is significantly higher as compared to that of the bulk and is essential for processes such as melting, coalescence, evaporation, growth, etc., of nanoparticles.     

Thermodynamic model for the size-dependent melting of prism-shaped nanoparticles

We report on the size-dependent melting of prism-shaped nanoparticles based on thermodynamic model and applied to understand the melting of prism-shaped indium nanoparticles. It is shown here that the bulk melting temperature cannot be extrapolated from the nanoscale and the extrapolated value will always be lower than the bulk melting temperature as has been observed experimentally.     

Modeling cohesive energy and melting temperature of nanocrystals

A model has been developed to account for the size dependent cohesive energy and melting temperature of nanocrystals. This model can deal with the thermodynamic properties of nanoparticles (spherical and non-spherical), nanowires and nanofilms with free surface or non-free surface (embedded in a matrix). The cohesive energy depression of nanocrystals has been predicted, and the conditions of superheating are obtained. It is found that the present theoretical results are consistent with the available experimental values.     

Empirical correlation between melting temperature and cohesive energy of binary Laves phases

A list of 143 binary Laves phases with their melting temperature and melting type is collected, and used to study a correlation between melting temperature and cohesive energy. It is found that the melting temperature of Laves phases is roughly proportional to its cohesive energy calculated by Miedema's empirical model from their intrinsic atomic properties. The average predicted error of melting temperature of compounds is as low as 8.0%. This empirical rule is consistent with the result of the universal binding energy theory of solids.     

Structural and short-range order analysis of glassy system

To understand the effects of structural features and to locate their signatures in the As-Ag-Te glassy system, various properties were studied as a function of average coordination number, 〈r〉. The structure of the sample is analyzed by X-ray diffraction technique and is found to be crystalline. The d-spacing and the lattice parameters of the samples were calculated. The structural parameters were discussed on the basis of Ag (silver) effect on As-Ag-Te glassy system. Structural investigations on these compositions revealed the polycrystalline nature of compositions with the presence of hexagonal As-Ag-Te phases. Grain size increased with the Ag content and parameters of unit cell are determined. The variations in the mean atomic volume, V, and the glass transition temperature, T_g, for glass transition, with composition have been reported. The change in thermal parameters was measured using differential thermal analysis (DTA). The results of the program are in agreement with those of analytical method and realized by binding energy represented by the cohesive energy values. The generalized ‘8-n’ rule was used to estimate the average coordination number. Obtained results were treated in the frame of chemical bond approach. We estimated some of physical parameters viz. mean bond energy, glass transition temperature, cohesive energy, average single bond energy, density, compactness and molar volume of all bulk samples. Our experimental and theoretical results were discussed in light of the topological bonding structure, which involves a hierarchy of correlation ranges in short-range order.     

Effect of germanium addition on the physical properties of Se–Te glassy semiconductors

The effect of germanium addition on the physical properties, i.e. density, molar volume, compactness, number of lone-pair electrons, average coordination number, heat of atomization, mean bond energy, cohesive energy and glass-transition temperature, of (Se₈₀Te₂₀)_{100? x} Ge _x (x = 0, 2, 4, 6) bulk glassy alloys was investigated. The density of the glassy alloys is found to decrease with increasing Ge content. The molar volume and compactness of the structure of the glass were determined from the measured density. The mean bond energy is proportional to the glass-transition temperature. The cohesive energy of the samples has been calculated using a chemical bond approach and is correlated with an increase in the optical energy gap with increase in the Ge content. The heat of atomization was also calculated and correlated with the optical energy gap. The glass-transition temperature has been estimated using different methods and is found to increase with an increase of Ge content.     

Computer study of the temperature dependence of physical properties of noncrystalline silicon nanoparticles

Variations in the structure and kinetic properties of vitreous and amorphous Si₄₀₀ nanoparticles upon heating from 300 to 1700 K are studied by molecular dynamics. The nanoparticle density increases with temperature and approaches the density of bulk solid silicon. A transition from a unimodal to a bimodal distribution of bond lengths is observed upon heating. This transition is more pronounced in the case of the vitreous nanoparticle. The average bond length in the amorphous nanoparticle is, as a rule, larger than that in the vitreous one, and the average number of bonds per atom is lower than that in the vitreous nanoparticle for nearly all studied temperatures. Negative values of the excess potential energy correspond to middle concentric layers of nanoparticles. Liquid layers form in the surface region of nanoparticles in the vicinity of the melting transition. A kinetic test indicating the beginning of nanoparticle melting is formulated.     

Molecular dynamics simulations on the melting of gold nanoparticles

Molecular dynamics is employed to study the melting of bulk gold and gold nanoparticles. PCFF, Sutton-Chen and COMPASS force fields are adopted to study the melting point of bulk gold and we find out that the Sutton-Chen force field is the most accurate model in predicting the melting point of bulk gold. Consequently, the Sutton-Chen force field is applied to study the melting points of spherical gold nanoparticles with different diameters. Variations of diffusion coefficient, potential energy and translational order parameter with temperature are analyzed. The simulated melting points of gold nanoparticles are between 615～1115 K, which are much lower than that of bulk gold (1336 K). As the diameter of gold nanoparticle drops, the melting point also descends. The melting mechanism is also analyzed for gold nanoparticles.     

Modeling the thermodynamic properties of bimetallic nanosolids

A model has been developed to account for size, shape, surface segregation, composition and dimension dependent cohesive energy of bimetallic nanosolids, and further been extended to predict the size dependent thermodynamic properties, such as melting temperature, Curie temperatures, ordering temperature and phase diagram. The cohesive energy, melting temperature, Curie temperatures and ordering temperature of bimetallic nanosolids decrease with decreasing the particle size. The depression is dramatic in the lower range of size, while it becomes smoothly in large size. For nano phase diagram, the solidus and liquidus curves drop and the two-phase zones become small, as the size of the nanosolids decreases. The two-phase zones of the nano phase are always lower than the regions indicated in the bulk Ag-Pd alloy phase diagram, and they may deteriorate into a curve at a critical size. It is also found that the thermodynamic properties of nanosolids not only depend on the compositions, the atomic diameter and the cohesive energy of each component, but also depend on the size and the shape. The model predictions are consistent with the corresponding simulation, semi-empirical model and experimental data.     

Effects of particle size, shape and crystal structure on the formation energy of Schottky vacancies in free-standing metal nanoparticles: A model study

A simplified model based on cohesive energy is proposed to estimate the formation energy of Schottky vacancies (VFE) in free-standing metal nanoparticles with BCC and FCC crystal structures. To study the effect of particle size and shape, the surface energy, elastic contraction and average coordination number of particles at the surface and core was considered. It is shown that the energy of vacancy formation in FCC nanoparticles increases with decreasing the size while the effect of particle shape (sphere, cubic and icosahedral) is marginal. In spite of this behavior, BCC nanoparticles exhibit a critical particle size at around 25 Å, at which a minimum VFE is attained. Additionally, the energy of vacancy formation is notably lower for BCC nanoparticles with cubic shape than spherical ones. The application of the developed model is shown for free-standing Fe and Cu nanoparticles.     

纳米团簇熔化过程的分子动力学模拟

本文采用分子动力学结合嵌入原子多体势,模拟了不同半径的Ni纳米团簇的升温熔化过程,研究团簇尺寸对熔点和表面能的影响.模拟结果表明:团簇的熔点显著低于体材料的熔点.团簇熔化的过程首先是在团簇的表面出现预熔,然后向团簇内部扩展,直到整个团簇完全熔为液态.在模拟的纳米尺度范围内,团簇的熔点与团簇尺寸基本成线性关系.团簇的表面能随着团簇尺寸的增大而减小,而且表面能均高于体材料的表面能.     

Superheating and solid-liquid phase coexistence in nanoparticles with nonmelting surfaces

We present a phenomenological model of melting in nanoparticles with facets that are only partially wet by their liquid phase. We show that in this model, as the solid nanoparticle seeks to avoid coexistence with the liquid, the microcanonical melting temperature can exceed the bulk melting point and that the onset of coexistence is a first-order transition. We show that these results are consistent with molecular dynamics simulations of aluminum nanoparticles which remain solid above the bulk melting temperature.     

Liquid-drop model for the surface energy of nanoparticles

Based on the liquid-drop model, we have evaluated the Tolman length and surface energy of nanoparticles for different elements and compared with other theoretical models as well as the available simulated data. The predictions of the model show good agreement with the simulated results. Like the cohesive energy and melting temperature, the size-dependency of surface energy is also shape-dependent.     

Cohesive energy and physical properties of nanocrystals

Recently, a lattice-type-sensitive model, free of any adjustable parameter, for the size dependence of the cohesive energy of nanocrystals (nanodisks, -films, -wires and -particles) has been developed, taking into account the effects of the averaged structural and energetic properties of their surface and volume. These effects are related to the first- and second-nearest-neighbor atomic interactions. Now, considering the intimate relation between cohesive energy and other physical properties of materials, the recently obtained formula for the cohesive energy of nanocrystals has been applied to the cases of melting point (In, Bi, Si and Ag), evaporation temperature (Ag and Au), vacancy formation energy (Au), diffusion activation energy (Au), surface energy (Au, Al and Na), liquid–vapor interfacial energy (Al and Na), Curie temperature (Pb), Debye temperature (Au and Fe) and band gap energy (Si) of nanocrystals. In general, good agreement between the present model and the data has been obtained. Moreover, the surface-area-difference (SAD) model has been derived as a first-order approximation of the present model.     

Construction and evaluation of embedding functions

Non-self-consistent density functional theories require specification of the embedding energy for an atom in a reference system. We combine the embedding energies determined from linear muffin tin orbital (LMTO) calculations of the bulk cohesive energy curves with those determined from the experimental diatomic binding curve. These new embedding functions contain information about the variation of binding with both coordination and separation between atomic centers. These are shown to be superior to embedding functions determined solely from bulk cohesive energy curves through tests on structures and energies of small metal clusters, self-diffusion of adatoms on metal surfaces, and scattering of metal atoms from metal surfaces.     

Microstructural analysis of liquid and amorphous SiO2 nanoparticles

Microstructural properties of liquid and amorphous SiO₂ nanoparticles have been investigated via molecular dynamics (MD) simulations with the interatomic potentials that have weak Coulomb interaction and Morse-type short-range interaction under non-periodic boundary conditions. Structural properties of spherical nanoparticles with different sizes of 2, 4 and 6 nm obtained at 3500 K have been studied through partial radial distribution functions (PRDFs), coordination number and bond-angle distributions, and compared with those observed in the bulk. The core and surface structures of liquid SiO₂ nanoparticles have been studied in detail. We found significant size effects on structure of nanoparticles. Calculations also show that if the size is larger than 4 nm, liquid SiO₂ nanoparticles at the temperature of 3500 K have a lightly distorted tetrahedral network structure with the mean coordination number Z_Si-O≈4.0 and Z_O-Si≈2.0 like those observed in the bulk. Moreover, temperature dependence of structural defects and SiO_x stoichiometry in nanoparticles on cooling from the melt has been found and presented.     

Prediction of nanoparticles’ size-dependent melting temperature using mean coordination number concept

Many models have been developed to predict size-dependent melting temperature of nanoparticles. A new model based on the cluster mean coordination number (MCN) calculations is developed in this work. Results of the model for Al, Au, Pb, Ag, Cu, In, Sn, and Bi were compared with other models and experiments. The comparison indicated that the MCN model is in good agreement with available experimental values. It is also found that the melting temperature is more dependent on particle size as the atomic radius increased.     

Can Nano-Particle Melt below the Melting Temperature of Its Free Surface Partner?

The phonon thermal contribution to the melting temperature of nano-particles is inspected. The discrete summation of phonon states and its corresponding integration form as an approximation for a nano-particle or for a bulk system have been analyzed. The discrete phonon energy levels of pure size effect and the wave-vector shifts of boundary conditions are investigated in detail. Unlike in macroscopic thermodynamics, the integration volume of zero-mode of phonon for a nano-particle is not zero, and it plays an important role in pure size effect and boundary condition effect. We find that a nano-particle will have a rising melting temperature due to purely finite size effect; a lower melting temperature bound exists for a nano-particle in various environments, and the melting temperature of a nano-particle with free boundary condition reaches this lower bound. We suggest an easy procedure to estimation the melting temperature, in which the zero-mode contribution will be excluded, and only several bulk quantities will be used as input. We would like to emphasize that the quantum effect of discrete energy levels in nano-particles, which is not present in early thermodynamic studies on finite size corrections to melting temperature in small systems, should be included in future researches.     

Generalized bond-energy model for cohesive energy of small metallic particles

A generalized bond-energy model has been developed to calculate the cohesive energy of nanoparticles by considering the different contributions of face-, edge- and corner-atoms. The model is adapted for metallic particles in a large size range from several atoms to infinity, studying their morphology, phase stability and melting point, etc.     

Effect of voids and pressure on melting of nano-particulate and bulk aluminum

Molecular dynamics simulations are performed using isobaric–isoenthalpic (NPH) ensembles to study the effect of internal defects in the form of voids on the melting of bulk and nano-particulate aluminum in the size range of 2–9 nm. The main objectives are to determine the critical interfacial area required to overcome the free energy barrier for the thermodynamic phase transition, and to explore the underlying mechanisms for defect-nucleated melting. The inter-atomic interactions are captured using the Glue potential, which has been validated against the melting temperature and elastic constants for bulk aluminum. A combination of structural and thermodynamic parameters, such as the potential energy, Lindemann index, translational-order parameter, and radial-distribution functions, are employed to characterize the melting process. The study considers a variety of void shapes and sizes, and results are compared with perfect crystals. For nano aluminum particles smaller than 9 nm, the melting temperature is size dependent. The presence of voids does not impact the melting properties due to the dominancy of nucleation at the surface, unless the void size exceeds a critical value beyond which lattice collapse occurs. The critical void size depends on the particle dimension. The effect of pressure on the particulate melting is found to be insignificant in the range of 1–300 atm. The melting behavior of bulk aluminum is also examined as a benchmark. The critical interfacial area required for the solid–liquid phase transition is obtained as a function of the number of atoms considered in the simulation. Imperfections such as voids reduce the melting point. The ratio between the structural and thermodynamic melting points is 1.32. This value is comparable to the ratio of 1.23 for metals like copper.