Research into the rationality and the application scopes of different melting models of nanoparticles

A rational melting model is indispensable to address the fundamental issue regarding the melting of nanoparticles. To ascertain the rationality and the application scopes of the three classical thermodynamic models, namely Pawlow, Rie, and Reiss melting models, corresponding accurate equations for size-dependent melting temperature of nanoparticles were derived. Comparison of the melting temperatures of Au, Al, and Sn nanoparticles calculated by the accurate equations with available experimental results demonstrates that both Reiss and Rie melting models are rational and capable of accurately describing the melting behaviors of nanoparticles at different melting stages. The former (surface pre-melting) is applicable to the stage from initial melting to critical thickness of liquid shell, while the latter (solid particles surrounded by a great deal of liquid) from the critical thickness to complete melting. The melting temperatures calculated by the accurate equation based on Reiss melting model are in good agreement with experimental results within the whole size range of calculation compared with those by other theoretical models. In addition, the critical thickness of liquid shell is found to decrease with particle size decreasing and presents a linear variation with particle size. The accurate thermodynamic equations based on Reiss and Rie melting models enable us to quantitatively and conveniently predict and explain the melting behaviors of nanoparticles at all size range in the whole melting process.

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Graphical abstract Both Reiss and Rie melting models are rational and capable of accurately describing the melting behaviors of nanoparticles at different melting stages. The former is applicable to the stage from initial melting to critical thickness of liquid shell, while the latter from the critical thickness to complete melting. The critical thickness of liquid shell decreases with decreasing particle size and a linear relationship between them is observed. This paper provides us an effective and convenient method to address the fundamental issue regarding the melting temperature of nanoparticles.

     

Lindemann's criterion and the melting of solids at high pressures

The generalized Lindemann's criterion is utilized to derive the variation of the melting temperature T_m with compression. The result incorporates the basic features of the lattice potential as well as the volume dependence of the frequency distribution through the first two moments of the mode Grüneisen parameter. This melting relation predicts that when T_m is plotted against the volume of the melting solid, the fusion curves of solids bonded by Van der Waals forces are concave to the temperature axis and in accordance with the predictions of the Simon equation. On the other hand, the predicted melting curves of ionic compounds, as the alkali-halides, are concave to the volume axis and exhibit a maxima at higher pressures. Since silicates generally possess an ionic contribution to the lattice energy, this melting relation should give a more accurate estimate of the high pressure melting temperature for these compounds than Simon's and theoretically similar equations.     

Second law optimization of a latent heat storage system with PCMS having different melting points

The exergy efficiency, as well as the charging and discharging rates, in a latent heat storage system can be improved by use of the PCMs having different melting points. The melting point distribution of the PCMs has substantial effects on the exergy efficiency. The optimum melting point distribution of the PCMs has been estimated from numerical simulations and also from simple equations. The fast charging or discharging rate leads to high exergy efficiency.     

A phase diagram of ammonia close to the melting point

We calculate here the phase line equations using the mean field theory for the liquid-solid I - solid II phases in the ammonia close to the melting point. Our calculated phase line equations have been fitted to the experimental data. Our calculated phase diagram agrees very well with the experimentally obtained P-T phase diagram from the literature.     

溶解与热对流对固体颗粒运动影响的直接数值模拟

对牛顿流体内溶解与热对流对单颗粒在垂直管道中的沉降运动进行了直接数值模拟.流体运动由守恒方程计算,密度和黏性的变化考虑流场温度变化的影响,通过积分黏性应力和压力获得颗粒的受力跟踪颗粒运动,溶解引起的相变及其形状的变化由溶解潜热、溶解质量与分散相边界处的温度梯度的关系建立的方程决定.通过颗粒和流体间相互的作用力和力矩及边界条件的施加实现相间耦合.分别模拟了颗粒在等温流体、热流体、冷流体及颗粒溶解四种情况下的沉降过程.结果表明,在一定雷诺数内,热对流产生的颗粒尾迹处涡的脱落以及溶解引起的颗粒表面形态的变化引起了颗粒的横向摆动,并使颗粒沉降速度发生了变化. 关键词： 溶解 热对流 颗粒两相流 直接数值模拟     

Simulation of the melting and crystallization processes in monocrystalline silicon exposed to nanosecond laser radiation

Numerical simulation of the melting and crystallization processes of monocrystalline silicon exposed to the nanosecond radiation of a ruby laser was carried out with the kinetics of the phase transformations accounted for on the basis of Kolmogorov equations. A two-dimensional mechanism of nucleation and growth of the new phase was invoked to describe the phase transitions. It was shown that the temporal dependences of monocrystal overheating and liquid phase supercooling in the melting and crystallization stages, respectively, are nonmonotonic and determined by the kinetics of the phase transitions. The maximum values of the overheating and supercooling were ∼100 K.     

Solid-solid phase transformation via virtual melting significantly below the melting temperature

A new phenomenon is theoretically predicted, namely, that solid-solid transformation with a relatively large transformation strain can occur through virtual melting along the interface at temperatures significantly (more than 100 K) below the melting temperature. The energy of elastic stresses, induced by transformation strain, increases the driving force for melting and reduces the melting temperature. Immediately after melting, the stresses relax and the unstable melt solidifies. Fast solidification in a thin layer leads to nanoscale cracking, which does not affect the thermodynamics and kinetics of solid-solid transformation. Seven theoretical predictions are in quantitative agreement with experiments conducted on the beta-->delta transformation in the HMX energetic crystal.     

High-pressure melting of molybdenum

The melting curve of the body-centered cubic (bcc) phase of Mo has been determined for a wide pressure range using both direct ab initio molecular dynamics simulations of melting as well as a phenomenological theory of melting. These two methods show very good agreement. The simulations are based on density functional theory within the generalized gradient approximation. Our calculated equation of state of bcc Mo is in excellent agreement with experimental data. However, our melting curve is substantially higher than the one determined in diamond anvil cell experiments up to a pressure of 100 GPa. An explanation is suggested for this discrepancy.     

Theoretical curves in thermal analysis for the melting of binaries showing solid solution

The theoretical shape of the D.S.C. or D.T.A. thermograms for the melting of binary solutions has been determined from the basic equations of the corresponding calorimeters. The case of binary solutions with immiscible solid phases or with solid solutions is examined.     

Structure and melting of dipole clusters

Two-dimensional clusters of particles, repelling due to dipole-dipole interactions and confined by an external parabolic potential, are considered. The model describes different physical systems, particularly electrons in semiconductor structures, or electrons above a drop of He near a metal electrode, a drop of colloid liquid etc. Two kinds of ordering are in competition in the clusters: a triangular lattice and a shell structure. The ground-state configurations corresponding to the local and global minima of the potential energy for clusters with N = 1 – 40 “particles” are calculated. The structure, the potential energy and the radial and angular r.m.s. displacements as functions of temperature are also calculated. Analysing these quantities the melting of clusters is studied. One- or two-stage melting occurs depending on the number of particles in the cluster. In the case of clusters consisting of two shells melting has two stages: at lower temperature reorientation of neighbouring shells (“orientational melting”) arises; at much higher temperatures the radial shell order disappears. In clusters consisting of more than two shells total melting occurs as a first-order one-stage transition (analogously to a dipole crystal). This is connected with the barrier of rotation being less than the barrier of interchange of particles between shells for small microclusters while the barriers are of equal order for clusters with a greater number of particles.     

Coulomb clusters: melting and potential barriers

The melting of two-dimensional and three-dimensional Coulomb micro- and macroclusters is studied. Temperature dependences of radial and angular square deviations of particles are investigated. The melting of microclusters has two stages: at lower temperature there is a transition from a frozen phase to a state with a rotatory reorientation of “crystalline” shells relative to each other, different pairs of shells melting at different temperatures. In the case of large N and high triangular symmetry inside the cluster, orientational melting takes place only for external pairs of shells. In this case external shells lose their order. At higher temperature a transition with a loss of radial shell order occurs. The origin of two-stage melting is in the smallness of the barrier energy relative to the rotation of shells in comparison with the barrier corresponding to the radial disordering of shells. It is shown also that the temperatures of orientational and total melting are at 5–15 times lower than the temperatures of disappearance of corresponding potential barriers. The influence of confinement anisotropy on the character of cluster melting is considered. It is found that at some degree of anisotropy the melting becomes one stage. The last is connected with an increase of the ratios of barriers of intershell rotation to barriers of jumps of a particle between the shells.     

The melting and solidification of nanowires

A mathematical model is developed to describe the melting of nanowires. The first section of the paper deals with a standard theoretical situation, where the wire melts due to a fixed boundary temperature. This analysis allows us to compare with existing results for the phase change of nanospheres. The equivalent solidification problem is also examined. This shows that solidification is a faster process than melting; this is because the energy transfer occurs primarily through the solid rather than the liquid which is a poorer conductor of heat. This effect competes with the energy required to create new solid surface which acts to slow down the process, but overall conduction dominates. In the second section, we consider a more physically realistic boundary condition, where the phase change occurs due to a heat flux from surrounding material. This removes the singularity in initial melt velocity predicted in previous models of nanoparticle melting. It is shown that even with the highest possible flux the melting time is significantly slower than with a fixed boundary temperature condition.     

Vacancy formation and squashing during surface melting and the size effect on surface-induced melting of metals

On the basis of a vacancy-squashing model for melting that we developed recently, a vacancy formed in the premelting liquid-like-layer is proposed to be squashed at the instance of its formation, which will significantly facilitate vacancy formation. Accordingly, the temperature for surface-induced melting and its size dependence are quantitatively calculated. By comparing the calculated data with the reported experimental results for metals, we show that the present approach may potentially predict the size-dependent melting point of other metals.     

Surface theory of melting

We demonstrate that melting is a surface initiated process. The surface becomes unstable before the bulk and the process of melting consists in the unstable surface that proceeds into the otherwise stable bulk.     

Acoustic studies of melting and crystallization of nanostructured decane

Acoustic studies of melting and crystallization of decane loaded in porous glasses (Vycor and laboratory-produced glass) have been performed. Measurements of the temperature dependences of the ultrasound velocity have revealed a decrease in the melting and crystallization temperatures of decane as compared to the melting point of bulk decane and a diffuseness of these phase transitions. The results obtained are compared with the predictions of the models describing melting of individual small particles. The specific features revealed in the acoustic properties of nanocomposites based on decane-loaded porous glasses are discussed.     

High-pressure melting of MgSiO3

The melting curve of MgSiO(3) perovskite has been determined by means of ab initio molecular dynamics complemented by effective pair potentials, and a new phenomenological model of melting. Using first principles ground state calculations, we find that the MgSiO(3) perovskite phase transforms into post perovskite at pressures above 100 GPa, in agreement with recent theoretical and experimental studies. We find that the melting curve of MgSiO(3), being very steep at pressures below 60 GPa, rapidly flattens on increasing pressure. The experimental controversy on the melting of the MgSiO(3) perovskite at high pressures is resolved, confirming the data by Zerr and Boehler.     

Surface and bulk melting of small metal clusters

We present an analytical solution to the two-parabola Landau model, applied to melting of metal particles with sizes in the nanoscale range. The results provide an analytical understanding of the recently observed pseudo-crystalline phase of nanoscale Sn particles. Liquid skin formation as a precursor of melting is found to occur only for particles with radii greater than an explicitly given critical radius. The size dependences of the melting temperature, and of the latent heat, have been calculated, and a quantitative agreement is found with the experiment on tin particles.     

The high-pressure melting curve of CaO

Shell-model molecular dynamics simulation has been performed to investigate the melting of the major Earth-forming mineral CaO at elevated temperatures and high pressures, based on thermal instability analysis. The interatomic potential is taken to be the sum of effective pair-wise additive Coulomb, van der Waals attraction, and repulsive interactions. It is shown that the simulated molar volume of CaO is successful in reproducing recent experimental data and our DFT-GGA calculations up to the core–mantle boundary pressure of 135 GPa. The pressure dependence of the simulated high pressure melting temperature of CaO is in good agreement with the results obtained from the Lindemann melting equation at a pressure of below 7 GPa. The extrapolated melting temperatures are in good agreement with the results obtained from Wang’s empirical model up to 60 GPa. The predicted high pressure melting curve, being very steep at lower pressures, rapidly flattens on increasing pressure. The thermodynamic properties of the rocksalt phase of CaO are summarized in the 0–135 GPa pressure range and for temperatures up to 9300 K.