Size-dependent Melting Temperature Research Articles

Single crystallization of Pb in carbon nanotubes

The formation mechanism of Pb single crystals in carbon nanotubes is considered in terms of the classical nucleation and growth theory modified by our models for size-dependent solid–liquid interface energy and size-dependent melting temperature. It is found that since the growing time of a cylindrical nucleus of Pb along carbon nanotubes is much shorter than the time to form the nucleus, a single crystallization is present. Moreover, the possible smallest diameter of crystalline nanowire is discussed.

Melting enthalpy depression of nanocrystals based on surface effect

Takagi was the first to demonstrate that ultrafine metallic particles melt below their corresponding bulk melting temperature in 1954 [1]. Now it is known that the melting temperatures of all nanocrystals, including metals [2, 3], semiconductors [4, 5] and organic nanocrystals [6, 7], depend on their size and this has been explained in terms of various models related to interface energy [8]. This size effect is experimentally also observed on the melting enthalpy [2, 6]. However, none of the above models can interpret sizedependent melting enthalpy of nanocrystals directly [8]. Knowledge of thermodynamic parameter are important for complete understanding of melting transition of nanocrystals and will deepen our insight into the size effect on melting. Therefore, a direct consideration on the size-dependence of melting enthalpy is needed. In this contribution, a simple physical model for the size-dependent melting enthalpy of nanocrystals in terms of the effect of bond number and bond energy of surface atoms of nanocrystals and that of the corresponding liquids on the internal energy of the system is developed. Combining with Mott’s expression for the vibrational entropy of melting for metallic crystals, size-dependent melting temperature of metallic nanocrystals is also predicted. The model predictions correspond well to the latest experimental results of indium nanocrystals. We consider that size-dependent melting enthalpy H (r ) is additive where r denotes radius of nanoparticles and nanowires, or half thickness of thin films,

Melting thermodynamics of nanocrystals embedded in a matrix

A simple model, free of any adjustable parameter, is established for the melting temperature and melting entropy of nanocrystals embedded in a matrix where the interface between the nanocrystals and the matrix is coherent. The model is based on Lindemann's criterion for the melting, Mott's equation for the melting entropy of bulk crystals and our model for the size-dependent melting temperature. It is shown that the melting temperature and the melting entropy of nanocrystals embedded in a matrix increase as the size of the nanocrystals decreases. The above predictions are supported by available experimental results on Pb and In nanocrystals embedded in an Al matrix. On the basis of the model, the melting mechanism of superheating is discussed.

Thermal stability of low dimensional crystals

A model, free of any adjustable parameter, has been developed for the size-dependent melting temperature and melting entropy of nanocrystals. The model can be utilized to predict the thermal stability both for metallic and organic low dimensional materials. The results show that their melting thermodynamic functions are dependent on their size, dimension, and environment. The theoretical predictions in terms of the above model are fully consistent with experimental evidences and the results of molecular dynamics simulation.

Finite size effect on melting enthalpy and melting entropy of nanocrystals

It is demonstrated that a simple model, free of any adjustable parameter, can be developed for the melting enthalpy and melting entropy of nanocrystals based on Mott's equation for the melting entropy and a model for the size-dependent melting temperature. It is shown that the enthalpy and entropy of melting for a nanocrystal decrease as its size decreases. The results are supported by available experimental results on metallic and organic nanocrystals. The model suggests that the size-dependent melting enthalpy and melting entropy for non-semiconductor nanocrystals are determined by the vibrational component of overall melting enthalpy and entropy.

Melting thermodynamics of organic nanocrystals

The size-dependent melting temperature and the size-dependent melting entropy of organic nanocrystals are predicted by use of our simple model being free of any adjustable parameter. The model predictions for the size-dependent melting temperature and the size-dependent melting entropy are supported by the experimental results on benzene, chlorobenzene, heptane, and naphthalene nanocrystals.

Free energy of crystal–liquid interface

It is demonstrated that a simple model, free of any adjustable parameter, can be developed to predict the free energy of a crystal–liquid interface σ sl based on the Gibbs–Thomson equation and a model for the size-dependent melting temperature. This model has improved Turnbull's empirical equation. In the model, σ sl depends on not only the melting enthalpy of crystals, but also the vibrational component of the overall melting entropy of the crystals. The predicted values of σ sl for different types of crystals, such as true metals, meta metals, semiconductors, ionic crystals and organic crystals, are confirmed by available experimental results in the experimental error range.

Melting of Pb nanocrystals

The size-dependent melting and surface melting of Pb nanocrystals is demonstrated by x-ray powder diffraction in ultrahigh vacuum. Whereas some prior studies have measured the size-dependent melting temperature via the diffraction intensity, it is shown here that crystallite reorientation makes the diffraction intensity an unreliable indicator of melting. Instead of the diffraction intensity, the diffraction peak shape reveals the size-dependent melting via changes in the crystallite size distribution. Measurements showed that the melting temperature varies inversely with the crystallite size and quantitatively favors the liquid-skin melting model over the homogeneous melting model. Surface melting is demonstrated via the reversible growth of a 0.5 nm liquid skin on 50 nm crystallites just below the size-dependent melting temperature.

The melting of silicon nanocrystals: Submicron thin-film structures derived from nanocrystal precursors

The size-dependent melting temperature has been shown for the group IV semiconductor silicon. A cursory comparison is made between silicon nanocrystal melting and that observed in the group II–VI material Cds and the group III–V material GaAs. Particles dispersed at a number density such that there are interactions between nanocrystals are observed to sinter before size-dependent melting occurs. Using an electron beam to selectively remove an organic mask from a substrate, this phenomenon is exploited to produce thin-film structures. This work has implications in the production of nanoelectronics, nonlinear optics and solar conversion technologies.

Size dependent thermal vibrations and melting in nanocrystals

A simple model for the size-dependent amplitude of the atomic thermal vibrations of a nanocrystal is presented which leads to the development of a model for the size dependent melting temperature in nanocrystals on the basis of Lindemann's criterion. The two models are in terms of a directly measurable parameter for the corresponding bulk crystal, i.e., the ratio between the amplitude of thermal vibrations for surface atoms and that for interior ones. It is shown that the present model for the melting temperature offers not only a qualitative but even an excellent quantitative agreement with the experimentally observed size-dependent superheating, as well as melting point suppression in both the supported and embedded metallic and semiconductor nanocrystals.

Surface effects in vibrational and melting properties of Pb clusters

We have studied the structural, dynamical and thermodynamical behaviour of Pb clusters in theN=147−2057 range, using a phenomenological many-body potential and molecular dynamics. Cuboctahedral structures, previously found to be particularly stable for this system, are used as starting configurations at lowT. Calculated size-dependent melting temperatures appear to be reasonably accounted for by Pawlow's law,Tm(N)=Tm(∞)−AN−1/3. The behaviour of the mean square displacements and direct structural observations suggest that melting initiates at the surface, in agreement with recent experimental observations. High-frequency surface peaks in the vibrational spectrum disappear asT approachesTm, in coincidence with the onset of surface diffusion.

Size-dependent melting temperature of individual nanometer-sized metallic clusters.

Gold and silver clusters with diameters in the nanometer-size range were grown in an inert-gas beam and deposited on the end of a tungsten field emitter. The field-emission current from an individual cluster is used to study a size-dependent change in shape of the cluster as a function of temperature. Three experimental signatures indicate an abrupt change in cluster shape at a temperature below the bulk melting point. This temperature is found to depend on cluster size and is in agreement with a thermodynamic model for cluster melting, provided the cluster diameter is greater than \ensuremath{\sim}2 nm.

The Lindemann hypothesis and the size dependence of melting temperatures. II

Abstract The concept that melting occurs when the root-mean-square atomic vibrational amplitude is a particular fraction of the nearest–neighbour separation, and an expression for the effect of system size and geometry on the summed phonon spectrum, provide an explicit equation for size–dependent melting temperatures. Further, it is shown that for certain classes of solids the ratio of size–dependent to bulk melting temperatures can be described by one equation. For example, this approach holds for the four noble–gas solids Kr, Ar, Xe, Ne, yielding a size–dependent ' corresponding–states principle ' for this species. The results of these formal considerations are compared to those of two other theories for size–dependent melting temperatures: the thermodynamic treatment, and the Kosterlitz–Thouless–Feynman description of melting in two–dimensional solids. The first of these comparisons yields an equation for solid–liquid interfacial energies in terms of bulk properties; the second an equation for bulk melting temperatures.

The Lindmann hypothesis and the size-dependence of melting temperature

Abstract The Lindemann hypothesis of melting is applied to systems of arbitrary size and a simple explicit relation for the effect of particle size and geometry on melting temperatures is derived. The predicted melting temperature agrees well with the result of a recent molecular dynamics simulation of melting in a thin Lennard-Jones crystal.

Thermodynamic theory of size dependence of melting temperature in metals

The way that small particles melt is a crucial clement in the construction of a thermodynamic treatment of the relation between particle size and melting temperature. There are indications that melting is initiated at the surface and that the solid–liquid interface sweeps rapidly through the solid at the melting temperature. The formal and physical elements of the indicated nucleation and growth criterion for melting are discussed and the existence of upper and lower limits on the melting temperature is outlined. Theoretical predictions show satisfactory agreement with experimental observations.

Glass, ceramics and refractory oxides

Nanoparticles were prepared with a consumable-electrode direct current arc (CDCA) technique. The results showed that the calorimetric melting onset temperature of the nanoparticles of SnAgCu solder alloy could be as low as 179 °C, equivalent to that of the traditionally used SnPb eutectic alloy (183 °C). Moreover, the homogenous melting model (HMM) and Gibbs–Thomson equation were employed to theoretically estimate the size-dependent melting temperature of the as-prepared nanoparticles. The structure and morphology of the nanoparticles were analyzed with a high-resolution transmission electron microscopy (HRTEM). The CDCA technique showed promising prospect in manufacturing large amounts of nanoparticles with controlled shape, small size, narrow particle size distribution and nearly oxide-free composition. This undoubtedly puts forward a novel feasible approach to manufacture high quality lead-free solders for electronic products.

149. High temperature laboratory vacuum furnace.: E. V. Komelsen and J. O. Weeks, Rev. Sci. Instrum., 30, 290.

Nanoparticles were prepared with a consumable-electrode direct current arc (CDCA) technique. The results showed that the calorimetric melting onset temperature of the nanoparticles of SnAgCu solder alloy could be as low as 179 °C, equivalent to that of the traditionally used SnPb eutectic alloy (183 °C). Moreover, the homogenous melting model (HMM) and Gibbs–Thomson equation were employed to theoretically estimate the size-dependent melting temperature of the as-prepared nanoparticles. The structure and morphology of the nanoparticles were analyzed with a high-resolution transmission electron microscopy (HRTEM). The CDCA technique showed promising prospect in manufacturing large amounts of nanoparticles with controlled shape, small size, narrow particle size distribution and nearly oxide-free composition. This undoubtedly puts forward a novel feasible approach to manufacture high quality lead-free solders for electronic products.

148. High-temperature pressure-vacuum furnace.: William Ladding and Laurence Hammell, Rev. Sci. Instrum., 30, 885.

Nanoparticles were prepared with a consumable-electrode direct current arc (CDCA) technique. The results showed that the calorimetric melting onset temperature of the nanoparticles of SnAgCu solder alloy could be as low as 179 °C, equivalent to that of the traditionally used SnPb eutectic alloy (183 °C). Moreover, the homogenous melting model (HMM) and Gibbs–Thomson equation were employed to theoretically estimate the size-dependent melting temperature of the as-prepared nanoparticles. The structure and morphology of the nanoparticles were analyzed with a high-resolution transmission electron microscopy (HRTEM). The CDCA technique showed promising prospect in manufacturing large amounts of nanoparticles with controlled shape, small size, narrow particle size distribution and nearly oxide-free composition. This undoubtedly puts forward a novel feasible approach to manufacture high quality lead-free solders for electronic products.