Anomalous size dependence in the melting temperatures of free sodium clusters: an explanation for the calorimetry experiments

The meltinglike transition in unsupported Na(N) clusters (N = 55, 92, 147, 181, 189, 215, 249, 271, 281 and 299) is studied by first-principles isokinetic molecular dynamics simulations. The irregular size dependence of the melting temperatures Tm observed in the calorimetry experiments of Schmidt et al. [Nature (London) 393, 238 (1998)] is quantitatively reproduced. We demonstrate that structural effects alone can explain all broad features of experimental observations. Specifically, maxima in Tm(N) correlate with high surface stability and with structural features such as a high compactness degree.     

On the size dependence of melting parameters for silicon

Using the dependences of melting point T_m and crystallization point T_c on the number of atoms (N) in a spherical silicon crystal that were calculated elsewhere [6] by the method of molecular dynamics, (i) the number of atoms at which the latent heat of the solid–liquid phase transition disappears and (ii) temperature T₀ = T_m(N₀) = _Tc(N₀) below which solidifying nanoclusters remain noncrystalline are estimated. These values are found to be N₀ = 22.8156 and T₀ = 400.851 K. The N dependences for silicon melting parameters, namely, a jump of entropy of melting, latent melting heat, slope of the melting line, and jumps in the surface energy and volume, are derived.     

On the size dependence of the melting temperature of nanoparticles

The size dependence of the melting temperature of nanocrystals has been investigated within the thermodynamic approach. A formula is obtained, which, in contrast to the classical Thomson formula, takes into account the metastable character of equilibrium between the crystal core and melt shell. Comparative investigation of the size dependence of the melting temperature, disregarding and taking into account the size dependences of the surface tension of the solid and liquid phases and the interface tension, has been performed by the example of aluminum, tin, and copper nanoparticles.     

Modeling size dependence of melting temperature of metallic nanoparticles

A model has been developed to account for the dependence of melting temperature of nanoparticles on their size, shape and lattice type. This model is consistent with reported experimental data and shows better consistency than the liquid drop and bond energy model. A general equation is proposed which correlates with the bond energy model formula and has high potential for application in research and development. The model also leads to an equation showing the limiting size for nanoparticles.     

On the size dependence of the heats of melting of metal nanoclusters

The size dependence of the heats of melting of transition metal nanoclusters (Ni, Au, Cu and Ag) is investigated using two alternative methods of computer simulation (isothermal molecular dynamics and Monte Carlo). Au and Cu nanoclusters are subjected to more detailed study over a wide range of their sizes. The heats of melting are shown to fall along with nanocluster size and to tend in some approximation to a linear dependence on inverse particle radii.     

On the size dependence of surface tension in the temperature range from melting point to critical point

The problem of size dependence of surface tension was investigated in view of a more general problem of the applicability of Gibbs’ thermodynamics to nanosized objects. For the first time, the effective surface tension (coinciding with the specific excess free energy for an equimolecular dividing surface) was calculated within a wide temperature range, from the melting temperature to the critical point, using the thermodynamic perturbation theory. Calculations were carried out for Lennard-Jones and metallic nanosized droplets. It was found that the effective surface tension decreases both, with temperature and particle size.     

Temperature dependence of spall strength and the effect of anomalous melting temperatures in shock-wave loading

The effects of temperature anomalies in materials subjected to the action of shock waves are studied. The spall failure of aluminum single crystals and polycrystals at various temperatures was experimentally studied in [1]. An analysis of the experimental data for polycrystalline aluminum shows that the breaking strength only weakly changes with temperature when it increases from room temperature to 90% of the melting temperature and, then, drops sharply to zero with a further increase in the temperature. For aluminum single crystals, the effect of anomalously high temperatures was experimentally detected; i.e., their strength remained high in the state where melting was expected during tension. The criterion of incubation time of failure is used to obtain an analytical expression for the temperature dependence of the spall strength of the materials. A new melting criterion, which relates the instant of a phase transition to the melting incubation period, is introduced. This criterion allows one to naturally explain the effect of anomalously high melting temperatures detected during the pulsed action.     

On the correlation between the temperatures of eutectic and contact melting of bilayer metallic films

The correlation between the temperatures of eutectic and contact melting of bilayer metallic films with given thicknesses is determined. This correlation is used to predict the temperatures of contact melting for bilayer films not studied earlier.     

The growth temperatures dependence of optical and electrical properties of InN films

InN films grown on sapphire at different substrate temperatures from 550°C to 700°C by metalorganic chemical vapor deposition were investigated. The low-temperature GaN nucleation layer with high-temperature annealing (1100°C) was used as a buffer for main InN layer growth. X-ray diffraction and Raman scattering measurements reveal that the quality of InN films can be improved by increasing the growth temperature to 600°C. Further high substrate temperatures may promote the thermal decomposition of InN films and result in poor crystallinity and surface morphology. The photoluminescence and Hall measurements were employed to characterize the optical and electrical properties of InN films, which also indicates strong growth temperature dependence. The InN films grown at temperature of 600°C show not only a high mobility with low carrier concentration, but also a strong infrared emission band located around 0.7 eV. For a 600 nm thick InN film grown at 600°C, the Hall mobility achieves up to 938 cm²/Vs with electron concentration of 3.9 × 10¹⁸ cm⁻³. Supported by the National Basic Research Program of China (Grant No. 2006CB6049), the National Natural Science Foundation of China (Grant Nos. 6039072, 60476030 and 60421003), the Great Fund of the Ministry of Education of China (Grant No. 10416), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050284004), and the Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK2005210 and BK2006126)     

Thermodynamic calculation of the melting point of aluminum

The free energies of aluminum in the solid and liquid phases are calculated. The free energy in the solid state is determined in the quasiharmonic approximation. The radial distribution function of liquid aluminum is found by solving the Bogolyubov-Born-Green equation. The convergence of the series for finding the electrostatic energy of the liquid metal is discussed. The value obtained for the melting point agrees well with the experimental value.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.12, pp.29–32, December, 1980.     

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.     

Volume dependence of the melting temperature for aluminium

We present a simple and straightforward relationship for evaluating the volume dependence of melting temperature based on the Lindemann’s melting equation (F.A. Lindemann, Z. Phys. 11 (1910) 609) and the Al’tshular et al. model for the volume dependence of the Gruneisen parameter (L.V. Al’tshuler, S.E. Brusnikin, E.A. Kuz’ menkov, J. Appl. Mech. Tech. Phys. 28 (1987) 129). The formula for the volume dependence of melting temperature obtained in the present study has been used to determine the results for aluminium up to a pressure range of 77 GPa. The results obtained for the melting temperature present a good agreement with the available experimental data.     

A new approach to melting under pressure

Abstract

A theory is presented that predicts the melting curve and the solid-solid-liquid triple point of a solid. It is based on the elastic properties of the crystal.     

Unified approach to Thermodynamic Bethe Ansatz and finite size corrections for lattice models and field theories

We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for magnetic chains and field theories that includes the finite size (and zero-temperature) calculations for lattice BA models. In all cases, the free energy follows by quadratures from the solution of a single nonlinear integral equation (NLIE) (a system of NLIE appears for nested BA). We derive the NLIE for: (a) the six-vertex model with twisted boundary conditions, (b) the XXZ chain in an external magnetic field h_z and (c) the massive Thirring sine-Gordon model (mT-sG) in a periodic box of size β ≡ T^-1 using the light-cone approach. This NLIE is solved by iteration in one regime (high T in the XXZ chain and low T in the sG-mT model). In the opposite (conformal) regime, the leading behaviors are obtained in closed form. Higher corrections can be derived from the Riemann-Hilbert form of the NLIE that we present.     

Non-extensive thermostatistics approach to metal melting entropy

A generalized Mott relation of metal melting entropy is derived by means of non-extensive solid and liquid quantum entropy that we calculate from grand partition functions of the localized ordered quantum solid and of the disordered quantum Boltzmann liquid. For each of the 18 elements considered, the entropic parameter _qm$q_m$, depending on particle correlations, is deduced such that a better agreement is obtained between calculated non-extensive metal melting entropy and available experimental data. The non-extensive entropic parameter makes the difference between normal and anomalous metals. Therefore, those elements not reported here should also belong to one of the two classes. Possible applications to condensed matter, Earth, and other solar planets seismology are mentioned.     

Pulsed laser deposition of metals at target temperatures close to the melting point

Tin and bismuth metals are irradiated by KrF excimer laser pulses of fluences around 5 J/cm². Supressing the formation of surface inhomogeneities on the target is achieved by increasing the target temperature to close to its melting point. The characteristics of surface structures developed on targets ablated at room temperature and heated to approximately 40 °C below the melting point of the respective metal, are presented. Optical microscopy is used to follow the changes in the surface morphology of the deposited films, and especially in the surface number density of particulates. Approaching the melting point of the tin target resulted in a threefold decrease in surface number density of particulates, while for bismuth only a slight decrease was obtained. In the latter case, the anisotropic growth properties of bismuth precluded the effective smoothing of certain domains on the target surface, even at temperatures close to its melting point.