Melting from one to two to three dimensions

The transformation of a crystalline solid into a liquid, seeming to have no precursor and no intermediate states, has challenged scientists for over a century. The search for the fundamental mechanism stimulated the development of quantum mechanics, concepts of the roles of dimensionality and topological order in condensed matter, and experimental techniques to test the theories. We now understand that the transition begins at lower temperatures than the melting point of the bulk. It starts at the edges of crystal planes, progresses across the surface, evolves into the successive melting of atomic layers, and ends in bulk phase coexistence. The memory of the process remains within a few molecular distances at the crystal-melt interface.     

Irreversible energy flow in forced Vlasov dynamics

Molecular dynamics (MD) simulations are used to investigate the thermodynamic properties and structural changes of KCl spherical nanoparticles at various sizes (1064, 1736, 2800, 3648, 4224 and 5832 ions) upon heating. The melting temperature is dependent on both the size and shape of KCl models, and the behaviour of the first order phase transition is also found in the present work. The surface melting found here is different from the melting phenomena of KCl models or other alkali halides studied in the past. In the premelting stage, a mixed phase containing liquid and solid ions covers the surface of nanoparticles. The only peak of heat capacity spreads out a significant segment of temperature, probably exhibiting both heterogeneous melting on the surface and homogeneous melting in the core. The coexistence of two melting mechanisms, homogeneous and heterogeneous ones, in our model is unlike those considered previously. We also found that the critical Lindemann ratio of the KCl nanoparticle becomes much more stable when the size of the nanoparticle is of the order of thousands of ions. A picture of the structural evolution upon heating is studied in more detail via the radial distribution function (RDF) and coordination numbers. Our results are in a good agreement with previous MD simulations and experimental observations.     

Superheating in metal nanoparticles with non-melting surfaces

We construct microcanonical caloric curves for aluminium nanoparticles with non-melting surface facets and diameters of up to 11 nm using molecular dynamics simulations. We find that fcc aluminium particles can be superheated above the bulk melting temperature, but only for a finite range of particle sizes i.e. diameters between 5–9 nm. We also observe a critical particle size where solid-liquid phase coexistence becomes stable, and a second larger critical size where premelted (100) facets can coexist with solid (111) facets. Ultimately, it is the premelting of the (100) facets that appears to limit the superheating effect in these particles.     

Calorimetry at surfaces using high-resolution core-level photoemission

We have developed a method to measure simultaneously the internal energy of bulk and the first layer atoms of a crystal. The internal energy of bulk and the surface atoms of lithium (110) have been evaluated from 22 K up to above the melting transition, applying the Debye model to the thermal broadening of the respective 1s photoemission lines. Our measurements clearly reveal two phase changes: the known liquid to solid transition and the surface melting, occurring 50 K below the bulk melting point.     

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.     

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.     

Surface nanocrystallization of an ionic liquid

Surface crystallization at the vapor-liquid interface of the ionic liquid (1-butyl-3-methylimidazolium hexafluorophosphate) is observed in synchrotron x-ray diffraction studies. Sharp Bragg reflections emerge in grazing-angle x-ray diffraction patterns 37?°C above the bulk melting temperature, indicating the presence of a long-range ordered phase at the surface in coexistence with the bulk parent liquid. The unique structure of the vapor-liquid interface where butyl chains attached to the cations are expelled to the vapor side facilitates interionic electrostatic interactions that lead to the crystallization. Our results demonstrate the complexity of ionic-liquid structure with their tendency to spontaneously phase separate into nanodomains with finite correlation lengths in coexistence with the liquid phase. By virtue of interfacial boundary conditions, these nanodomains grow laterally to form quasi-two-dimensional crystals.     

The phase behavior of mixed lipid membranes in the presence of the rippled phase

We propose a model describing liquid-solid phase coexistence in mixed lipid membranes by including explicitly the occurrence of a rippled phase. For a single component membrane, we employ a previous model in which the membrane thickness is used as an order parameter. As function of temperature, this model properly accounts for the phase behavior of the three possible membrane phases: solid, liquid and the rippled phase. Our primary aim is to explore extensions of this model to binary lipid mixtures by considering the composition dependence of important model parameters. The obtained phase diagrams show various liquid, solid and rippled phase coexistence regions, and are in quantitative agreement with the experimental ones for some specific lipid mixtures.     

Solid clusters above the bulk melting point

The fact that the melting points of nanoparticles are always lower than those of the corresponding bulk material is a paradigm supported by extensive experimental data for a large number of systems and by numerous calculations. Here we demonstrate that tin cluster ions with 10-30 atoms remain solid at approximately 50 K above the melting point of bulk tin. This behavior is possibly related to the fact that the structure of the clusters is completely different from that of the bulk element.     

Correlation between the size-dependent melting and crystallization temperatures of metal nanoparticles

The correlation between the melting and crystallization temperatures of metal nanoparticles is investigated by means of the thermodynamic approach. Size-dependent variations in the melting temperature of aluminum, tin, and copper nanoparticles are calculated with allowance for the corresponding size dependences of surface tensions in solid and liquid phases and interfacial tension. Size-dependent variations in crystallization temperature are determined under the assumption that a certain effective surface layer (skin-layer) arises before melting.     

The melting mechanism in binary Pd0.25Ni0.75 nanoparticles: molecular dynamics simulations

The melting mechanism for Pd_0.25Ni_0.75 alloy nanoparticles (NPs) was investigated using molecular dynamics (MD) simulations with quantum Sutton-Chen many-body potentials. NPs of six different sizes ranging from 682 to 22,242 atoms were studied to observe the effect of size on the melting point. The melting temperatures of the NPs were estimated by following the changes in both the thermodynamic and structural quantities such as the total energy, heat capacity and Lindemann index. We also used a thermodynamics model to better estimate the melting point and to check the accuracy of MD simulations. We observed that the melting points of the NPs decreased as their sizes decreased. Although the MD simulations for the bulk system yielded higher melting temperatures because of the lack of a seed for the liquid phase, the melting temperatures determined for both the bulk material and the NPs are in good agreement with those predicted from the thermodynamics model. The melting mechanism proceeds in two steps: firstly, a liquid-like shell is formed in the outer regions of the NP with increasing temperature. The thickness of the liquid-like shell increases with increasing temperature until the shell reaches a critical thickness. Then, the entire Pd–Ni NP including core-related solid-like regions melts at once.     

Pt-Au核-壳结构纳米粒子热稳定性的分子动力学研究

采用分子动力学方法结合嵌入原子势, 对Pt-Au核-壳纳米粒子的热稳定性进行了研究. 计算结果表明: Pt-Au纳米粒子的熔点明显高于Au纳米粒子而低于Pt纳米粒子. 通过计算Lindemann指数发现: 壳层中的Au首先熔化, 然后逐渐向内部扩展, 最终导致核中的Pt完全熔化; 熔化所经历的温度区间明显宽于单质纳米粒子, 而且该熔化过程呈现典型的两阶段熔化特征; 在两次熔化之间, 存在着固(核)液(壳)共存的结构. 关键词： 纳米粒子 熔化 分子动力学     

Direct observation of capillary condensation of a solid

We describe the direct condensation of a solid from vapor in an annular mica wedge. Neo-pentanol initially condenses as a liquid from 8 to 57 degrees C (the melting point T(m)), followed by nucleation of a solid from vapor for T<45 degrees C. Menthol (T(m) = 42 degrees C) gives only liquid condensates down to 12 degrees C. The adsorbed films of neo-pentanol, which unlike those of menthol show layering transitions, and the disordered crystalline phase of bulk neo-pentanol appear to facilitate condensation of the solid phase. There is evidence for a change in the nature of the solid neo-pentanol condensate with T.     

Melting,freezing and other peculiarities in small systems

The theory of solid-liquid phase changes in small systems implies that such systems may—but need not—exhibit sharp but unequal freezing and melting temperatures. The origin of this conclusion is reviewed and its implications for the theory of first-order phase transitions in bulk matter are discussed. The logical separation is made of the two temperatures as limits of stable existence, each of its own ‘phase’; and the convergence, with increasing size of cluster, of the observable coexistence to a sharp transition temperature is discussed. The equilibrium ratios of concentrations for such a coexistence are discontinuous functions of temperature at the limits of stability. The possibility of observing coexisting forms in equilibrium depends on there being a time scale separability, who validity lies outside the realm of thermodynamics. It is conjectured that spinodals are the loci of the same kind of locally stable states responsible for coexisting solid and liquid forms of clusters, and that the limits of spinodals are the points of discontinuity in the equilibrium concentration ratios, the chemical ‘equilibrium constants’.     

Acoustic studies of melting and crystallization of indium-gallium alloy in porous glass

Temperature dependences of the velocity of the longitudinal ultrasonic waves in a nanocomposite on the basis of porous glass filled with gallium-indium alloy have been measured. Acoustic anomalies due to crystallization and melting of the alloy in nanopores have been revealed for the complete and partial cooling-heating cycles. A two-step temperature hysteresis loop between the curves of the velocity change upon cooling and heating has been found, the existence of which is related to the formation in pores of two types of mixtures, with α- and β-Ga. Stabilization of β-Ga in nanopores has been observed. It was shown that the conditions of confined geometry lead to a shift to low temperature of the melting regions for both mixtures in comparison with the regions of the coexistence of the liquid and solid phases in bulk alloy.     

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.

     

Non-equilibrium cation distribution and enhanced spin disorder in hollow CoFe2O4 nanoparticles

We present magnetic properties of hollow and solid CoFe(2)O(4) nanoparticles that were obtained by annealing of Co(33)Fe(67)/CoFe(2)O(4) (core/shell) nanoparticles. Hollow nanoparticles were polycrystalline whereas the solid nanoparticles were mostly single crystal. Electronic structure studies were performed by photoemission which revealed that particles with hollow morphology have a higher degree of inversion compared to solid nanoparticles and the bulk counterpart. Electronic structure and the magnetic measurements show that particles have uncompensated spins. Quantitative comparison of saturation magnetization (M(S )), assuming bulk Néel type spin structure with cationic distribution, calculated from quantitative XPS analysis, is presented. The thickness of uncompensated spins is calculated to be significantly large for particles with hollow morphology compared to solid nanoparticles. Both morphologies show a lack of saturation up to 7 T. Moreover magnetic irreversibility exists up to 7 T of cooling fields for the entire temperature range (10-300 K). These effects are due to the large bulk anisotropy constant of CoFe(2)O(4) which is the highest among the cubic spinel ferrites. The effect of the uncompensated spins for hollow nanoparticles was investigated by cooling the sample in large fields of up to 9 T. The magnitude of horizontal shift resulting from the unidirectional anisotropy was more than three times larger than that of solid nanoparticles. As an indication signature of uncompensated spin structure, 11% vertical shift for hollow nanoparticles is observed, whereas solid nanoparticles do not show a similar shift. Deconvolution of the hysteresis response recorded at 300 K reveals the presence of a significant paramagnetic component for particles with hollow morphology which further confirms enhanced spin disorder.     

Modeling the cohesive energy and melting point of nanoparticles by their average coordination number

We present a relation between the average coordination number and the cohesive energy for nanoparticles that shows that the ratio of nanoparticles cohesive energy to the bulk value is equal to the ratio of the nanoparticles average coordination number to that of the bulk. We consider the effect of lattice and surface packing factors on the average coordination numbers of the atoms in the nanoparticle. The melting temperature of nanoparticles has been calculated from the obtained relation for cohesive energy, and predictions for the cohesive energy and melting temperature of the nanoparticles have been compared with other theoretical models and available experimental data and the results of molecular dynamics simulations.     

Reflection of structural waves at a solid/liquid interface

This paper investigates the reflection characteristics of structural or guided waves in rods at a solid/liquid interface. Structural waves, whose wavelengths are much larger than the diameter of the rod, are described in a first approximation by classical one-dimensional wave theory. The reflection characteristics of such waves at a solid/liquid (melting) interface has been reported by two different ultrasonic measurement techniques: first, measuring the fast regression rate of a melting interface during the burning of metal rod samples in an oxygen-enriched environment, and second, monitoring the propagation of the solid/liquid interface during the slow melting and solidification of a rod sample in a furnace. The second work clearly shows that the major reflection occurs from the solid/liquid interface and not the liquid/gas interface as predicted by plane longitudinal wave reflectivity theory. The present work confirms this observation by reporting on the results of some specially designed experiments to identify the main interface of reflection for structural waves in rods. Hence, it helps in explaining the fundamental discrepancy between the reflection characteristics at a solid/liquid interface between low frequency structural waves and high frequency bulk waves, and confirms that the detected echo within a burning metallic rod clearly represents a reflection from the solid/liquid interface.     

Melting, freezing and nucleation in nanoclusters of potassium chloride

Molecular dynamics simulations of the melting, freezing and nucleation are presented for unconstrained nanoclusters of KCl with a number of ions between 512 and 10648. The maximum extent of the probed liquid supercooling is analysed to the light of theoretical predictions and compared with experimental data. The fraction of the solid-like ions in the supercooled liquid is used as an indicator of heterogeneities within the liquid. Induced nucleation by seeding the supercooled liquid indicates that solid-liquid coexistence is stable, and sustained during the lifetime of the clusters, relatively to the supercooled liquid. A phenomenological analysis on the relaxation times of the crystal growth process is made. Critical nuclei sizes computed from the effectiveness of the seeds in the heterogeneous nucleation of the supercooled liquid, and from the residual crystallites in clusters not totally melted, are presented as a function of the temperature. The behavior of the systems is followed through various properties such as liquid and solid molar fractions, enthalpies of melting, heat capacities, self-diffusion coefficients and relaxation times related to the freezing process. The consistency of the simulation results for the heterogeneous nucleation is assessed by means of a classical nucleation model, from which an estimate of the interfacial surface tension is also worked out and compared with experimental data.