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.     

Influence of Tb incorporation on the structural and the optical properties of ZnO nanoparticles

Structural and optical properties of the Tb doped ZnO nanoparticles are systematically studied as a function of the Tb mole-fraction. Our study suggests that the Tb incorporates mostly on the surface and affects the optical properties of the ZnO nanoparticles by influencing the attachment of certain adsorbed groups, which are found to be responsible for the appearance of a broad green luminescence (GL) band in the photoluminescence spectra recorded for these nanoparticles. It has been found that the accumulation of Tb on the surface of the nanoparticles not only enhances the band edge to green luminescence intensity ratio under the vacuum condition but also increases the band gap energy by introducing a hydrostatic compressive strain in individual nanoparticles, which provides a unique opportunity to study the pressure dependence of the optical properties of nanoparticles without applying any external pressure. The hydrostatic compressive strain is explained in terms of the increase of the surface strain energy as a result of the Tb accumulation on the surface of the nanoparticles. The average value of the surface energy density for the particles has been estimated as a function of Tb mole-fraction. The pressure coefficient of the band gap which is obtained from the variation of the band gap energy with the hydrostatic strain has been found to decrease significantly with the particle size for the ZnO nanoparticles.     

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.     

Size-dependent nanoparticle reaction enthalpy: Oxidation of aluminum nanoparticles

Here we present a model describing the particle size dependence of the oxidation enthalpy of aluminum nanoparticles. The model includes the size dependence of the cohesive energy of the reactant particles, the size dependence of the product lattice energy, extent of product agglomeration, and surface capping effects. The strongest effects on aluminum nanoparticle energy release occur for particle diameters below 10 nm, with enhanced energy release for agglomerated oxide products and decreased energy release for nanoscale oxide products. An unusual effect is observed with all nanoparticle reaction enthalpies converging to the bulk value when agglomeration of the products approaches the transition between nanoparticle→nanoparticle and nanoparticle→bulk energetics. Optimal energy output for Al NP oxidation should occur for sub-10-nm particles reacting with significant agglomeration.     

Evaporation of free PbS nanoparticles: evidence of the Kelvin effect

The size-dependent evaporation of free-spherical PbS nanoparticles has been investigated by in-flight sintering of size-classified aerosols. The temperature (T(ev)) at which the particle size decreases due to evaporation is found to be size dependent and decreases with decreasing particle size. A linear relationship between the evaporation temperature and the inverse of the particle size is obtained as is the case with size-dependent melting of nanoparticles. This gives a direct evidence of the Kelvin effect and allows one to estimate the surface energy of nanoparticles. The surface energy of PbS nanoparticles has been found to be 2.45 J m(2).     

EXAFS study of size dependence of atomic structure in palladium nanoparticles

Dependence of atomic structure of Palladium nanoparticles on supports Al₂O₃ and SiO₂ upon their size, changed from 1.3 to 10.5 nm, was studied by Pd K-edge EXAFS. To determine the structure of the interior (core) and the near surface regions of nanoparticle, the fitting technique of the Fourier-transforms F(R) of spectra was used, which enabled to overcome instabilities of the obtained structural parameters values. The processing of experimental data was performed using results of the study of features formation in │F(R)│ of Pd K-EXAFS in Pd foil. By this approach it was revealed that the local structure of Pd atoms in the core is similar to fcc structure of bulk Pd, irrespective of size. The percentage of Pd atoms, which can be attributed to the core, upon the particles size was determined and the obtained dependence was described by the “cluster size equation”. In the near surface region of nanoparticles, nearest-neighbors Pd–Pd distances show a large Debye–Waller parameters and the mean bond length slightly contracted for nanoparticles of sizes less than ~2 nm. The effect of small structural distortions in the vicinity of absorbing Pd atom in the near surface region was studied using the cluster model of nanoparticle.     

钛酸钡纳米颗粒铁电性临界尺寸的理论分析

从铁电体的Eular-Lagrange方程出发, 取贝塞尔方程级数解的形式, 得到了钛酸钡陶瓷颗粒的总极化强度表达式, 分析了各系数对总极化强度的影响. 根据总极化强度表达式, 采用MATLAB软件对尺寸在100 nm以下的钛酸钡纳米颗粒的铁电性进行了仿真分析. 结合实际数据探讨了尺寸效应对陶瓷颗粒铁电性的影响, 获得了与实验数据相符的数值解和极小值, 从而预测了钛酸钡纳米颗粒铁电性存在的临界尺寸为6 nm.     

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.     

An energy approach to the modelling of particle removal by pulsed laser irradiation

An energy model to explain particle removal mechanism has been developed. This model is based on a detailed investigation of contact deformation of a particle on a solid surface, as well as particle motion during the process of substrate surface expansion under uniform laser irradiation. Calculation results show that small particles mainly gain kinetic energy during pulsed laser irradiation, whereas large particles mainly gain elastic deforming potential energy. The particle removal condition is derived from the viewpoint of energy. The relationship of particle removal efficiency with laser fluence and particle size is discussed. Theoretical results are compared with experimental results. Received: 30 July 1998 / Accepted: 14 December 1998 / Published online: 17 March 1999     

Particle size prediction of magnesium nanoparticle produced by inert gas condensation method

Properties of nanoparticles are normally depending on particle size; therefore, developing a model to predict particle size is of vital importance. This paper established an energy analysis model to predict average particle size of magnesium nanoparticles fabricated by inert gas condensation method. Predictions of average particle size ranging from 20 to 50 nm by energy analysis model have relative errors of less than 10% compared with experimental research. Further, the model is applied to investigate operation conditions to decrease the average particle size of magnesium nanoparticles. It is found that decreasing the absolute pressure in the condensation room and increasing the temperature rise of the inert gas can both produce nanoparticles with smaller average particle sizes. Temperature rise of the inert gas plays a more important role in effect on average nanoparticle size than the absolute pressure in the condensation room. Energy transformed by collision bonding and dissipated by convection are the dominant processes for particle growth when number of atoms in one particle is greater than 2000 atoms.     

Tunable metastability of surface nanostructure arrays

A Fokker-Planck equation is used to model the coarsening of surface nanostructure arrays. Metastable states are identified which are associated with a narrow size distribution and a coverage dependent mean island size. This is a general feature linked to nanostructures which, as a function of island size, are associated with a minimum in formation energy per atom and a positive chemical potential gradient. This has important implications for the self-organization of quantum dots.     

Fluorescence quenching of 3,7-diamino-2,8-dimethyl-5-phenyl phenazinium chloride by AgCl and Ag nanoparticles

Quenching of fluorescence of the dye 3,7-diamino-2,8-dimethyl-5-phenyl Phenazinium Chloride (Safranine T) has been investigated by AgCl nanoparticles in the W/O microemulsion medium at different [H₂O]/[AOT] ratios (ω) and with Ag nanoparticles and Ag⁺ in aqueous medium. A simple straightforward method has been introduced to prepare AgCl nanoparticles in well-characterized, monodispersed biomimicking nanocavities formed by sodium bis(2-ethylhexyl)sulfosuccinate (AOT) in heptane. Experimental results reveal that the size of the AgCl nanoparticles increases with increase in hydration. The results of the quenching experiment were analysed in the light of Stern Volmer equation. Quenching of fluorescence of the dye has been found to decrease with decrease in the size of the nanoparticles of AgCl and the variation of Stern Volmer quenching constants (K_SV) with particle size is different for two different size regimes.     

Radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to circumferential magnetic field

Knowledge of the vibrational properties of nanoparticles is of fundamental interest since it is a signature of their morphology, and it can be utilized to characterize their physical properties. In addition, the vibration characteristics of the nanoparticles coupled with surrounding media and subjected to magnetic field are of recent interest. This paper develops an analytical approach to study the radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to magnetic field. Based on Maxwell's equations, the nonlocal differential equation of radial motion is derived in terms of radial displacement and Lorentz's force. Bessel functions are used to obtain a frequency equation. The model is justified by a good agreement between the results given by the present model and available experimental and atomic simulation data. Furthermore, the model is used to elucidate the effect of nanoparticle size, the magnetic field and the stiffness of the elastic medium on the radial breathing-mode frequencies of several nanoparticles. Our results reveal that the effects of the magnetic field and the elastic medium are significant for nanoparticle with small size.     

Broad band light emission from Ag-ion implanted silicon nanocrystals

Silicon nanoparticles formed using low energy (<50 keV) silver ion implantation in crystalline Si exhibit broad band light emission from ultraviolet (UV) to green. The formation of nanoparticles is confirmed using high resolution electron microscopy (HRTEM) and the resulting microscopy is used to obtain the size distribution of Si nanoparticles. Photoluminescence (PL) spectra were observed in the range of the UV to the green. The origin of emission is most likely from highly localized defects at the Si/SiO2 which is further confirmed from Photoluminescence Excitation (PLE) and effective mass theory estimation.     

Size-dependent interaction of gold nanoparticles with transport protein: A spectroscopic study

Gold nanoparticles of different sizes have been synthesized using sodium citrate as a reducing agent for tetrachloroauric (III) acid. The formed gold nanoparticles have been characterized by the UV-visible and transmission electron microscopy (TEM) measurements. The different sized gold nanoparticles have been used to study the interaction with model transport protein, bovine serum albumin (BSA). Experimental results reveal that BSA molecules adsorbed on the metallic surfaces, suffer strong quenching of their fluorescence and the rate of quenching efficiency is different for different particle size. The analysis of the quenching results has been performed in terms of the Stern-Volmer equation. The mechanism of quenching of fluorescence has been explained. The extent of adsorption of BSA on the gold nanoparticles has been estimated.     

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.     

Finite size effect on critical transition temperature of superconductive nanosolids

A simple and unified model is developed for finite size effect on the critical transition temperature of superconductive nanosolids, which is based on the size-dependent Debye temperature of crystals within the McMillan expression. In the model, two material and structure dependent parameters of D₀ and α are used, which, respectively, are the critical size at which all atoms of a low-dimensional material are located on its surface, and the ratio of the mean square vibrational amplitude between surface atoms and interior atoms, In light of this model, the critical transition temperatures of superconductive nanosolids can decrease or increase with the dropping size of nanosolids depending on the bond strength changes of interfacial atoms. The predicated results are consistent with the available experimental results for superconductors MgB₂ and Nb thin films, Bi and Pb granular thin films and nanoparticles, Al thin films and nanoparticles.     

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.     

Molecular dynamics simulation of iron nanoparticle sintering during flame synthesis

The sintering process of iron nanoparticles produced in a flame environment is investigated by molecular dynamic (MD) simulations. The thermodynamic characteristics and restructuring pathways are studied for two-body and three-body sintering processes. The melting point, energy, and structures are computed for nanoparticles before and after sintering. A simplified model is proposed to predict the equilibrium temperature of nanoparticles upon sintering. The MD results are used to explain the formation mechanisms of two size ranges of nanoparticles during the flame synthesis. The role of sintering during nanoparticle growth is analyzed.     

Nucleation and growth mechanisms of Fe on Au(111) in the sub-monolayer regime

The growth of Fe on Au(111) at 300 K in the sub-monolayer regime has been investigated using scanning tunneling microscopy, focusing on the mechanisms of nucleation, coalescence and interlayer diffusion. Below a coverage of 0.1 ML, Fe growth proceeds in a well-ordered fashion producing regular arrays of islands, while approaching the island coalescence threshold (above 0.35–0.4 ML), we observed a consistent increasing of random island nucleation. These observations have been interpreted through rate equation models for the island densities in the presence of preferred nucleation sites. The evolution of the second layer fraction has also been interpreted in a rate equation scheme. Our results show that the ordered to random growth transition can be explained by including in the model bond breaking mechanisms due to finite Fe–Fe bond energy. A moderate interlayer diffusion has been inferred from data analysis between the second and the first layer, which has been used to estimate the energy barrier of the adatoms descending process.